diff --git a/.ipynb_checkpoints/Untitled-checkpoint.ipynb b/.ipynb_checkpoints/Untitled-checkpoint.ipynb new file mode 100644 index 0000000..8bba4ae --- /dev/null +++ b/.ipynb_checkpoints/Untitled-checkpoint.ipynb @@ -0,0 +1,204 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 8, + "id": "3e3ae5f0-9a0b-48bf-94a4-01d645f5c49d", + "metadata": {}, + "outputs": [], + "source": [ + "using Revise" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "62143b80-f5eb-4f31-b537-51eed82a5291", + "metadata": {}, + "outputs": [], + "source": [ + "using NonlinearNormalForm, TPSAInterface, GTPSA\n", + "import TPSAInterface as TI\n", + "import NonlinearNormalForm as NNF" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "8f4f2601-c371-411e-83af-1e4bf4a87a57", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0e-9" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "GTPSA.show_eps=1e-9" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "bed44cca-3ff1-4752-915d-4681ed7de6ea", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "read_fpp_map (generic function with 1 method)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"test/readfpp.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "6be3dd50-4409-4ce3-8ee0-08ca50542cf0", + "metadata": {}, + "outputs": [], + "source": [ + "#m = read_fpp_map(\"test/radiation/test.map\", spin=false);\n", + "#r_fpp = read_fpp_map(\"test/radiation/R.map\", spin=false);\n", + "#m = read_fpp_map(\"test/order6var4/test.map\",spin=false)\n", + "#r_fpp = read_fpp_map(\"test/order6var4/R.map\",spin=false)\n", + "m = real(read_fpp_map(\"test/canonize_rad/test.map\", spin=false));\n", + "a_fpp = real(read_fpp_map(\"test/canonize_rad/ac.map\", spin=false));" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "acc00a9e-7db8-485b-b13f-52a3b2e4127e", + "metadata": {}, + "outputs": [], + "source": [ + "a = normal(m);" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "9ccd9c90-8fda-4cd7-9045-7b0732a99d8b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.028272880922649e-15\n", + "damp = [-1.0488645846794094e-7, -1.5779694936159807e-6, -5.449690493512178e-6]\n" + ] + }, + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " -1.0488645846794094e-7\n", + " -1.5779694936159807e-6\n", + " -5.449690493512178e-6" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "damp = [0.,0.,0.]\n", + "r_c = canonize(a, damping=true, damp=damp);\n", + "NNF.checksymp(NNF.jacobian(r_c))\n", + "NNF.jacobian(a∘r_c)\n", + "println(norm(NNF.jacobian(a_fpp) - NNF.jacobian(a∘r_c)))\n", + "damp" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "id": "8f5949e1-10f0-4568-a307-9c8592e7e776", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "9.028272880922649e-15" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "r_c = canonize(a, damping=true);\n", + "NNF.checksymp(NNF.jacobian(r_c))\n", + "NNF.jacobian(a∘r_c) #-real(a_fpp)\n", + "norm(NNF.jacobian(a_fpp) - NNF.jacobian(a∘r_c))" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "435466b9-215c-481d-8dc5-b583be488d8c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6×6 StaticArraysCore.SMatrix{6, 6, Float64, 36} with indices SOneTo(6)×SOneTo(6):\n", + " -5.25831e-7 1.00089 -0.010719 0.00214115 0.00406777 0.00440329\n", + " -0.998985 0.00553445 -0.00489753 -0.00968604 0.00395478 0.00595919\n", + " 0.00191131 -0.00986871 -0.995125 0.00208363 0.0339313 0.00609627\n", + " 0.01084 0.00484174 -8.58974e-5 -1.00376 0.0105029 0.0318269\n", + " -0.00424473 -0.00556934 0.0313766 -0.00293569 0.999196 0.0200211\n", + " 0.00369695 0.00374198 -0.0131774 0.0337981 9.62622e-5 0.99979" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "NNF.jacobian(a)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "600cb76f-e92e-42ed-817b-5f13488ce6fb", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/.ipynb_checkpoints/canonize_rad-Copy1-checkpoint.ipynb b/.ipynb_checkpoints/canonize_rad-Copy1-checkpoint.ipynb new file mode 100644 index 0000000..0ad65e4 --- /dev/null +++ b/.ipynb_checkpoints/canonize_rad-Copy1-checkpoint.ipynb @@ -0,0 +1,309 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "0d376b20-40c6-4722-8a9a-61975bad5c9d", + "metadata": {}, + "outputs": [], + "source": [ + "using Revise\n", + "using NonlinearNormalForm, BeamTracking, Beamlines, GTPSA\n", + "import NonlinearNormalForm as NNF\n", + "using SciBmad" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "7e0afcee-4bb6-46c8-b36f-8c17fa436a3a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6-element Vector{Float64}:\n", + " -2.6000686032132613e-7\n", + " 1.5303928131191435e-5\n", + " -3.556902826710349e-9\n", + " 3.9231617960303014e-8\n", + " -0.02704383542507716\n", + " -0.0003522717640595932" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"../SciBmad/lattices/esr-v6.3.1.jl\");\n", + "# Set RF for 0.05 synch tune (from previous optimization)\n", + "cavities = ring.line[findall(x->x.kind==\"RFCavity\", ring.line)];\n", + "foreach(x->x.voltage=3.355606790694894e6, cavities);\n", + "\n", + "# Set all elements radiation damping, second order Yoshida\n", + "foreach(x->x.tracking_method=Yoshida(order=2, radiation_damping_on=true), ring.line);\n", + "\n", + "t = twiss(ring)\n", + "co = [t.orbit_x[1], t.orbit_px[1], t.orbit_y[1], t.orbit_py[1], t.orbit_z[1], t.orbit_pz[1]]\n", + "# Closed orbit from previous check:\n", + "#co = [-2.6000686032132613e-7, 1.5303928131191435e-5, -3.556902826710349e-9, 3.9231617960303014e-8, -0.02704383542507716, -0.0003522717640595932];" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "66edee15-0027-4c2d-9e40-88540b921c64", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Setting bunch.species = Species(electron, charge=-1.0e, mass=510998.95069 eV/c², spin=0.5ħ) (reference species from the Beamline)\n", + "Setting bunch.R_ref = -59.5287244902766 (reference R_ref from the Beamline)\n" + ] + }, + { + "data": { + "text/plain": [ + "true" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d4 = Descriptor(6, 4);\n", + "b0 = Bunch(co+vars(d4));\n", + "track!(b0, ring);\n", + "m = DAMap(v=b0.coords.v)\n", + "norm(scalar.(m.v) .- co) < 1e-12 || println(\"not on closed orbit\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "eda0dab2-567f-49c4-bd76-7d55895cf07e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "TPS64{GTPSA.Dynamic}:\n", + "Descriptor(NV=6, MO=4)\n", + " Coefficient Order Exponent\n", + " 5.9066016888039496e-01 0 0 0 0 0 0 0\n" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Check symplectic error:\n", + "a = normal(m)\n", + "damp = [0.,0.,0.]\n", + "a0, a1, a2 = factorize(a)\n", + "ac = a ∘ canonize(a1, damping=true, damp=damp);\n", + "a0, a1, a2 = factorize(ac)\n", + "compute_sagan_rubin(a1, Val{true}()).beta[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "id": "ca132cbd-7f45-4ce4-9b42-b54681051494", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.590660168880395" + ] + }, + "execution_count": 89, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "scalar(compute_sagan_rubin(factorize(a).a1∘canonize(factorize(a).a1,damping=true)).beta[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "id": "50b10794-6ccc-4db6-ad0f-d5848ee59048", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.590660168880395" + ] + }, + "execution_count": 86, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "scalar(compute_sagan_rubin(a1∘r_c).beta[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "id": "55544a66-17f8-48de-ac45-cd456a265010", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5866968053123066" + ] + }, + "execution_count": 91, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b0.coords.v .= view((a∘r_c).v, 1:6)'\n", + "#b0 = Bunch((co+a.v)');\n", + "track!(b0, ring);\n", + "aend = DAMap(v=b0.coords.v)\n", + "dampend = zeros(3)\n", + "rend = canonize(aend, damping=true, damp=dampend);\n", + "a0e, a1e, a2e = factorize(aend∘rend)\n", + "scalar(compute_sagan_rubin(factorize(aend).a1∘canonize(factorize(aend).a1,damping=true)).beta[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "e691ef6c-f3df-4af2-9d65-da31a19ac943", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 0.0008124780226362984\n", + " 0.0010549097317526213\n", + " 0.002351194915378987" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phase = [0.,0.,0.]\n", + "rend = canonize(aend, phase=phase, damping=true, damp=dampend);\n", + "dampend" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "3b399ded-000f-47fa-9a95-d10e4ad816c8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 0.0700700373959855\n", + " 0.15344937330719371\n", + " -0.04382444058656845" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phase" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "32439acd-a59e-4cc4-961d-1eb3f7694150", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6×6 StaticArraysCore.SMatrix{6, 6, ComplexF64, 36} with indices SOneTo(6)×SOneTo(6):\n", + " 0.899224-0.435093im … 5.04549e-18+1.43746e-18im\n", + " 9.99201e-16+1.94289e-16im -1.38955e-19+2.81743e-18im\n", + " 1.06005e-16-1.30363e-17im 1.94005e-18-4.95366e-17im\n", + " -6.81705e-17-7.37268e-17im 6.83323e-17+5.58629e-17im\n", + " -2.37277e-17+5.2132e-18im -1.66533e-16-3.05311e-16im\n", + " -2.93242e-17+6.59316e-18im … 0.959645-0.273604im" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "NNF.jacobian(ci_map(a)*inv(a)*m*a*c_map(a))" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "id": "696a6540-7dcb-482e-a4b3-d3aa334e2bc5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.0 + 0.0717227709692705im" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + " imag(log(0.899224-0.435093im ))/(2*pi*im)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5e6b05eb-9507-4460-b767-c2029c8f2c50", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/.ipynb_checkpoints/canonize_rad-checkpoint.ipynb b/.ipynb_checkpoints/canonize_rad-checkpoint.ipynb new file mode 100644 index 0000000..996961b --- /dev/null +++ b/.ipynb_checkpoints/canonize_rad-checkpoint.ipynb @@ -0,0 +1,364 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 191, + "id": "0d376b20-40c6-4722-8a9a-61975bad5c9d", + "metadata": {}, + "outputs": [], + "source": [ + "using Revise\n", + "using NonlinearNormalForm, TPSAInterface, GTPSA, JET, BenchmarkTools\n", + "import TPSAInterface as TI\n", + "import NonlinearNormalForm as NNF\n", + "using LinearAlgebra" + ] + }, + { + "cell_type": "code", + "execution_count": 192, + "id": "7e0afcee-4bb6-46c8-b36f-8c17fa436a3a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0e-9" + ] + }, + "execution_count": 192, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "GTPSA.show_eps=1e-9" + ] + }, + { + "cell_type": "code", + "execution_count": 193, + "id": "8912351a-4bf9-49f6-83f4-502a7ef2a7a7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "read_fpp_map (generic function with 1 method)" + ] + }, + "execution_count": 193, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"test/readfpp.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 194, + "id": "5e6b05eb-9507-4460-b767-c2029c8f2c50", + "metadata": {}, + "outputs": [], + "source": [ + "m = real(read_fpp_map(\"test/canonize_rad2/test.map\", spin=false, stochastic=false));\n", + "a_fpp = real(read_fpp_map(\"test/canonize_rad2/a.map\", spin=false, stochastic=false));\n", + "ac_norad_fpp = real(read_fpp_map(\"test/canonize_rad2/ac_norad.map\", spin=false, stochastic=false));\n", + "ac_fpp = real(read_fpp_map(\"test/canonize_rad2/ac.map\", spin=false, stochastic=false));" + ] + }, + { + "cell_type": "code", + "execution_count": 195, + "id": "86db2524-8cb2-461e-aaa6-278eb5569a5a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.0270205354294195e-14" + ] + }, + "execution_count": 195, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = normal(m);\n", + "ac_norad = a ∘ canonize(a)\n", + "norm(NNF.jacobian(ac_norad - ac_norad_fpp)) # Identical" + ] + }, + { + "cell_type": "code", + "execution_count": 196, + "id": "c91339b0-d327-4e2b-96f7-7fec0c0a1efc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "diagonal: [1.000000007079415 0.0 0.0 0.0 0.0 0.0; 0.0 1.000000007079415 0.0 0.0 0.0 0.0; 0.0 0.0 1.0000003292721718 0.0 0.0 0.0; 0.0 0.0 0.0 1.0000003292721718 0.0 0.0; 0.0 0.0 0.0 0.0 1.0000005598543975 0.0; 0.0 0.0 0.0 0.0 0.0 1.0000005598543975]\n", + "a before:\n", + "[1.0 0.0 0.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0 0.0 0.0; 0.0 0.0 1.0 0.0 0.0 0.0; 0.0 0.0 0.0 1.0 0.0 0.0; 0.0 0.0 0.0 0.0 1.0 0.0; 0.0 0.0 0.0 0.0 0.0 1.0]\n", + "4.965067803394708e-16\n" + ] + }, + { + "data": { + "text/plain": [ + "6×6 StaticArraysCore.SMatrix{6, 6, Float64, 36} with indices SOneTo(6)×SOneTo(6):\n", + " -1.75415e-14 0.0 6.50521e-19 … 9.6494e-18 8.5652e-18\n", + " 2.17604e-14 8.88178e-15 6.05629e-19 -1.12757e-17 -1.89735e-17\n", + " -8.94467e-19 1.20617e-18 8.88178e-16 -1.72984e-16 5.02636e-16\n", + " -7.91468e-18 -2.1684e-18 1.27676e-15 8.25119e-16 4.74013e-16\n", + " 6.23416e-19 -4.55365e-18 -1.37233e-16 -1.11022e-16 1.92593e-34\n", + " -1.0842e-19 -5.47522e-18 1.22271e-16 … -2.22045e-15 -2.22045e-16" + ] + }, + "execution_count": 196, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "damp = zeros(3)\n", + "ac = ac_norad ∘ canonize(ac_norad; damping=true, damp=damp)\n", + "println(norm(damp - [ 7.0794145850303742E-009 , 3.2927211731860217E-007 , 5.5985424078986008E-007]))\n", + "NNF.jacobian(ac-ac_fpp)" + ] + }, + { + "cell_type": "code", + "execution_count": 197, + "id": "b7225fd1-16c7-4802-805b-1904ba72ac51", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7.021666937153402e-16" + ] + }, + "execution_count": 197, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lambdafpp = reshape([ 1.0000000070794146 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000070794146 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000003292721715 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000003292721715 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000005598543975 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000005598543975], (6,6))\n", + "norm(lambdafpp - [1.000000007079415 0.0 0.0 0.0 0.0 0.0; 0.0 1.000000007079415 0.0 0.0 0.0 0.0; 0.0 0.0 1.0000003292721718 0.0 0.0 0.0; 0.0 0.0 0.0 1.0000003292721718 0.0 0.0; 0.0 0.0 0.0 0.0 1.0000005598543975 0.0; 0.0 0.0 0.0 0.0 0.0 1.0000005598543975])" + ] + }, + { + "cell_type": "code", + "execution_count": 198, + "id": "a408590f-4955-401a-884f-c9bbeeda3168", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.0088927366606835e-14\n", + "5.169391260095872e-16\n" + ] + } + ], + "source": [ + "a_before = [ 1.4338964279515740 -1.0429846794179958 -2.3570745104877473E-004 2.6262433147074087E-004 -1.1622855493497868E-004 -2.4830774444213496E-004;\n", + " 0.0000000000000000 0.69740039709121038 -5.6963396668069055E-005 -2.5344223264124729E-004 -2.6963112129992518E-004 -4.4781540226155144E-004;\n", + " 3.2095498585761557E-004 -6.5644456769718596E-006 0.90954598906121942 0.31682388106900750 1.0873929838182747E-004 1.8075859732463265E-004;\n", + " -9.1093681800944834E-005 2.6038105865456624E-004 0.0000000000000000 1.0994483139658224 -2.6186501157691305E-004 1.5773820802234262E-003;\n", + " 9.2386297069853697E-004 -8.9967415302002584E-004 -2.5891049089962905E-004 3.3946102928534663E-005 0.78995961443071061 -0.51904306741849293 ;\n", + " -9.5435643284262238E-004 8.9108155914763970E-004 -1.1516106612173820E-003 -1.6357668265082929E-003 -1.9259299443872359E-034 1.2658858226033121 ]'\n", + "println(norm(NNF.jacobian(ac_norad) - a_before))\n", + "println(norm(a_before-NNF.jacobian(ac_norad_fpp)))" + ] + }, + { + "cell_type": "code", + "execution_count": 199, + "id": "3823b7e7-ce95-4cb2-b6de-decec9326dfc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6×6 Matrix{Float64}:\n", + " 2.22045e-16 0.0 5.42101e-20 … 0.0 0.0\n", + " 2.22045e-16 0.0 0.0 0.0 0.0\n", + " 0.0 6.77626e-21 0.0 -5.42101e-20 2.1684e-19\n", + " 0.0 -5.42101e-20 0.0 0.0 0.0\n", + " 0.0 0.0 -1.35525e-20 0.0 4.27642e-50\n", + " -5.42101e-20 -5.42101e-20 2.71051e-20 … 0.0 -2.22045e-16" + ] + }, + "execution_count": 199, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a_before*Diagonal(lambdafpp)-a_after" + ] + }, + { + "cell_type": "code", + "execution_count": 201, + "id": "1f076567-c58d-4544-9738-3f356b5dd70e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.9482741224155094e-14\n" + ] + } + ], + "source": [ + "a_after = [ 1.433896438102721 0.000000000000000 0.3209550915391607E-03 -0.9109371179555925E-04 0.9238634879272838E-03 -0.9543569671432681E-03;\n", + " -1.042984686801717 0.6974004020283969 -0.6564447838461143E-05 0.2603811443908029E-03 -0.8996746567065567E-03 0.8910820580235691E-03;\n", + " -0.2357074527174455E-03 -0.5696339707133656E-04 0.9095462885494023 0.000000000000000 -0.2589106358518059E-03 -0.1151611305951675E-02;\n", + " 0.2626243333299674E-03 -0.2534422344354699E-03 0.3168239853902948 1.099448675983556 0.3394612193340967E-04 -0.1635767742299544E-02;\n", + " -0.1162285557578088E-03 -0.2696311232087557E-03 0.1087393341866524E-03 -0.2618650978017741E-03 0.7899600566930746 -0.1925931022627585E-33;\n", + " -0.2483077462000084E-03 -0.4478154054318223E-03 0.1807586568434085E-03 0.1577382599611449E-02 -0.5190433580070367 1.265886531315057 ]\n", + "println(norm(a_after-NNF.jacobian(ac)))" + ] + }, + { + "cell_type": "markdown", + "id": "38b55bf8-5f17-4e88-8e55-77bfde004e1c", + "metadata": {}, + "source": [ + "# EOD NOTE FOR 1/13/26\n", + "THEY BOTH AGREE\n", + "REMEMBER THAT CANONIZE IN SCIBMAD RETURNS ROTATION UNLIKE IN FPP WHERE IT RETURNS A\n", + "REMEMBER THAT WE WILL NEED TO INCLUDE PARAMETERS SO CANNOT JUST DO CANONIZER * \\Lambda i\n", + "IT SEEMS FINE NOW? IDK WHY IT ISN'T PERIODIC...\n", + "IT DOES AGREE WITH FPP SO WE WILL HAVE TO SIMULATE AN EXAMPLE OR ASK ETIENNE :(" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "52c61536-2deb-4d01-9ddd-bc096fae6801", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 185, + "id": "5b7e55b6-1ec5-4c75-ba94-4dc0e5e7aec5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "diagonal: [1.0000000070794148 0.0 0.0 0.0 0.0 0.0; 0.0 1.0000000070794148 0.0 0.0 0.0 0.0; 0.0 0.0 1.0000003292721718 0.0 0.0 0.0; 0.0 0.0 0.0 1.0000003292721718 0.0 0.0; 0.0 0.0 0.0 0.0 1.0000005598543975 0.0; 0.0 0.0 0.0 0.0 0.0 1.0000005598543975]\n", + "a before:\n", + "[1.0782589624650461e-7 0.9999999999999941 0.0 0.0 0.0 0.0; -0.9999999999999941 1.0782589624650461e-7 0.0 0.0 0.0 0.0; 0.0 0.0 -0.9608991686520796 0.27689851513459274 0.0 0.0; 0.0 0.0 -0.27689851513459274 -0.9608991686520796 0.0 0.0; 0.0 0.0 0.0 0.0 0.9252444168617395 0.379371544882032; 0.0 0.0 0.0 0.0 -0.379371544882032 0.9252444168617395]\n" + ] + }, + { + "data": { + "text/plain": [ + "3.400479869349483e-15" + ] + }, + "execution_count": 185, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = normal(m)\n", + "dampdec = zeros(3)\n", + "r_c = canonize(a; damp=dampdec, damping=true)\n", + "ac = a∘r_c\n", + "norm(NNF.jacobian(inv(ac)*m*ac) - NNF.jacobian(inv(ac_fpp)*m*ac_fpp))" + ] + }, + { + "cell_type": "code", + "execution_count": 128, + "id": "83afc05a-e743-445b-8382-d53d17cd10ba", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " -18.766074587024786\n", + " -14.92638132305711\n", + " -14.395589371400876" + ] + }, + "execution_count": 128, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "log.(dampdec)" + ] + }, + { + "cell_type": "code", + "execution_count": 124, + "id": "ad6d6465-fe3f-43f7-a86f-7bbcdd67d8be", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6×6 StaticArraysCore.SMatrix{6, 6, Float64, 36} with indices SOneTo(6)×SOneTo(6):\n", + " -1.21431 0.762561 0.000330239 … -0.0003392 0.00128424\n", + " 0.512381 -1.14527 -0.000112 0.000349042 -0.00121721\n", + " 0.000229906 -7.71115e-5 0.830759 0.000788974 0.00087793\n", + " -8.76237e-5 0.000354297 -0.15822 0.000770268 0.00144346\n", + " 0.000241822 0.000166529 0.000205929 -0.689072 0.386285\n", + " 0.000448436 0.000247186 -0.000477073 … -0.166255 -1.35803" + ] + }, + "execution_count": 124, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "NNF.jacobian(a_fpp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bf6a2aad-1a95-400b-9ca3-10ff96b23f7d", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/.ipynb_checkpoints/canonize_rad3-checkpoint.ipynb b/.ipynb_checkpoints/canonize_rad3-checkpoint.ipynb new file mode 100644 index 0000000..0e6fd4e --- /dev/null +++ b/.ipynb_checkpoints/canonize_rad3-checkpoint.ipynb @@ -0,0 +1,197 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 7, + "id": "d7186c9a-6d16-4e6d-8d5b-0431822f3323", + "metadata": {}, + "outputs": [], + "source": [ + "using Revise\n", + "using NonlinearNormalForm, TPSAInterface, GTPSA, JET, BenchmarkTools\n", + "import TPSAInterface as TI\n", + "import NonlinearNormalForm as NNF\n", + "using LinearAlgebra" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "5826f509-423e-4f25-89d6-65f2405a24a6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0e-9" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "GTPSA.show_eps=1e-9" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "8019c020-2efb-4aae-82c7-02c486d43cb9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "read_fpp_map (generic function with 1 method)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"test/readfpp.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ccfff21d-4873-430b-974e-24bc23a35089", + "metadata": {}, + "outputs": [], + "source": [ + "m = real(read_fpp_map(\"test/canonize_rad3/test.map\", spin=false, stochastic=false));\n", + "ac_norad_fpp = real(read_fpp_map(\"test/canonize_rad3/ac_norad.map\", spin=false, stochastic=false));\n", + "#ac_fpp = real(read_fpp_map(\"test/canonize_rad3/ac.map\", spin=false, stochastic=false));" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "8e958ba8-d3b5-4f79-be50-e21cb242160b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4.2092546059575386e-15" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = normal(m)\n", + "ac_norad = a∘canonize(a)\n", + "norm(NNF.jacobian(ac_norad-ac_norad_fpp))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "8e7c9272-7d37-455d-a61f-4520044f229c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 1.5315832874937697e-6\n", + " 2.817861217013314e-6\n", + " 2.1421678332848425e-6" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ac = ac_norad∘canonize(ac_norad; damping=true)\n", + "a_end = m∘ac\n", + "damp=zeros(3)\n", + "ac_end = a_end∘canonize(a_end; damping=true, damp=damp)\n", + "norm(damp-[0.1531583287271725E-05, 0.2817861217457402E-05, 0.2142167833506887E-05])\n", + "damp" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "92af3f73-7715-4749-b3dc-b276486fb610", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-1.5315832873166573e-6 - 2.366801815732135im" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = c_map(a)\n", + "reallog((inv(c)∘inv(ac_norad)∘m∘ac_norad∘c).v[1][1])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "effb66e9-f812-4f78-a8bf-bf1a61821ca7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 5.6974835447389954e-8\n", + " -2.1736512048935732e-8\n", + " -3.55658602232123e-8" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "\n", + "damp" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0e7858db-c6dc-4df9-9606-cd3a81561c41", + "metadata": {}, + "outputs": [], + "source": [ + "0.1531583287271725E-05 0.2817861217457402E-05 0.2142167833506887E-05" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Project.toml b/Project.toml index 0caa39f..6cb638a 100644 --- a/Project.toml +++ b/Project.toml @@ -1,7 +1,7 @@ name = "NonlinearNormalForm" uuid = "05e19671-dec8-4f15-984f-54eaa6ca64be" authors = ["Matt Signorelli"] -version = "0.4.1" +version = "0.4.2" [deps] DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" diff --git a/Untitled.ipynb b/Untitled.ipynb new file mode 100644 index 0000000..b85970d --- /dev/null +++ b/Untitled.ipynb @@ -0,0 +1,272 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "3e3ae5f0-9a0b-48bf-94a4-01d645f5c49d", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m packages...\n", + " 602.2 ms\u001b[32m ✓ \u001b[39mIJulia → IJuliaReviseExt\n", + " 1 dependency successfully precompiled in 1 seconds. 18 already precompiled.\n" + ] + } + ], + "source": [ + "using Revise" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "62143b80-f5eb-4f31-b537-51eed82a5291", + "metadata": {}, + "outputs": [], + "source": [ + "using NonlinearNormalForm, TPSAInterface, GTPSA, JET, BenchmarkTools\n", + "import TPSAInterface as TI\n", + "import NonlinearNormalForm as NNF" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8f4f2601-c371-411e-83af-1e4bf4a87a57", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0e-9" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "GTPSA.show_eps=1e-9" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "bed44cca-3ff1-4752-915d-4681ed7de6ea", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "read_fpp_map (generic function with 1 method)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"test/readfpp.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "6be3dd50-4409-4ce3-8ee0-08ca50542cf0", + "metadata": {}, + "outputs": [], + "source": [ + "#m = read_fpp_map(\"test/radiation/test.map\", spin=false);\n", + "#r_fpp = read_fpp_map(\"test/radiation/R.map\", spin=false);\n", + "#m = read_fpp_map(\"test/order6var4/test.map\",spin=false)\n", + "#r_fpp = read_fpp_map(\"test/order6var4/R.map\",spin=false)\n", + "m = real(read_fpp_map(\"test/canonize_rad/test.map\", spin=false));\n", + "a_fpp = real(read_fpp_map(\"test/canonize_rad/ac.map\", spin=false));" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "acc00a9e-7db8-485b-b13f-52a3b2e4127e", + "metadata": {}, + "outputs": [], + "source": [ + "a = normal(m);" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "id": "9ccd9c90-8fda-4cd7-9045-7b0732a99d8b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.028272880922649e-15\n" + ] + }, + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " -1.0488645846794094e-7\n", + " -1.5779694936159807e-6\n", + " -5.449690493512178e-6" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "damp = [0.,0.,0.]\n", + "r_c = canonize(a, damping=true, damp=damp);\n", + "NNF.checksymp(NNF.jacobian(r_c))\n", + "NNF.jacobian(a∘r_c)\n", + "println(norm(NNF.jacobian(a_fpp) - NNF.jacobian(a∘r_c)))\n", + "damp" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "3a11a0b5-f5dd-4666-a477-6931c5a95946", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 534.169 ns (14 allocations: 4.44 KiB)\n" + ] + }, + { + "data": { + "text/plain": [ + "DAMap{StaticArraysCore.MVector{6, Float64}, StaticArraysCore.MVector{6, TPS64{Descriptor(NV=6, MO=3)}}, Nothing, Nothing}([0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 6-element StaticArraysCore.MVector{6, TPS64{Descriptor(NV=6, MO=3)}}:\n", + " Index Coefficient Order Exponent\n", + "--------------------------------------------------------------------\n", + " 1: -5.2536081308078367e-07 1 1 0 0 0 0 0\n", + " 1: -9.9999989511340903e-01 1 0 1 0 0 0 0\n", + "--------------------------------------------------------------------\n", + " 2: 9.9999989511340903e-01 1 1 0 0 0 0 0\n", + " 2: -5.2536081308078367e-07 1 0 1 0 0 0 0\n", + "--------------------------------------------------------------------\n", + " 3: -9.9999622995586834e-01 1 0 0 1 0 0 0\n", + " 3: -2.0938338145159224e-03 1 0 0 0 1 0 0\n", + "--------------------------------------------------------------------\n", + " 4: 2.0938338145159224e-03 1 0 0 1 0 0 0\n", + " 4: -9.9999622995586834e-01 1 0 0 0 1 0 0\n", + "--------------------------------------------------------------------\n", + " 5: 9.9979386638524081e-01 1 0 0 0 0 1 0\n", + " 5: -2.0033108018037715e-02 1 0 0 0 0 0 1\n", + "--------------------------------------------------------------------\n", + " 6: 2.0033108018037715e-02 1 0 0 0 0 1 0\n", + " 6: 9.9979386638524081e-01 1 0 0 0 0 0 1\n", + ", nothing, nothing)" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "@btime canonize($a, damping=$true)" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "id": "8f5949e1-10f0-4568-a307-9c8592e7e776", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.018323538264002e-15\n" + ] + }, + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " -1.0488645846794094e-7\n", + " -1.5779694936159807e-6\n", + " -5.449690493512178e-6" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "r_c = canonize(a, damping=true);\n", + "NNF.checksymp(NNF.jacobian(r_c))\n", + "NNF.jacobian(a∘r_c) #-real(a_fpp)\n", + "println(norm(NNF.jacobian(a_fpp) - NNF.jacobian(a∘r_c)))\n", + "damp" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "435466b9-215c-481d-8dc5-b583be488d8c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6×6 StaticArraysCore.SMatrix{6, 6, Float64, 36} with indices SOneTo(6)×SOneTo(6):\n", + " -5.25831e-7 1.00089 -0.010719 0.00214115 0.00406777 0.00440329\n", + " -0.998985 0.00553445 -0.00489753 -0.00968604 0.00395478 0.00595919\n", + " 0.00191131 -0.00986871 -0.995125 0.00208363 0.0339313 0.00609627\n", + " 0.01084 0.00484174 -8.58974e-5 -1.00376 0.0105029 0.0318269\n", + " -0.00424473 -0.00556934 0.0313766 -0.00293569 0.999196 0.0200211\n", + " 0.00369695 0.00374198 -0.0131774 0.0337981 9.62622e-5 0.99979" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "NNF.jacobian(a)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "600cb76f-e92e-42ed-817b-5f13488ce6fb", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/fpp-ptc-sandbox/code/.ipynb_checkpoints/z_canonize_matt_fake_maps-checkpoint.f90 b/fpp-ptc-sandbox/code/.ipynb_checkpoints/z_canonize_matt_fake_maps-checkpoint.f90 new file mode 100644 index 0000000..8f23284 --- /dev/null +++ b/fpp-ptc-sandbox/code/.ipynb_checkpoints/z_canonize_matt_fake_maps-checkpoint.f90 @@ -0,0 +1,1470 @@ +program example + use c_tpsa + use gauss_dis + implicit none + integer no,nd,i,nv,k,j(lnv),n,np,j1,ndpt,i1,i2,is1(3),is2(3),is3(3),is2n(3),is3n(3) + type(c_taylor) f,F_FLOQUET,F_FLOQUET_cs,courant_snyder,nu_spin + type(c_damap), target :: m,m1,rot,as,a0,a1,a2,a_cs,R_TE,CS_TE + type(c_damap), pointer :: o + type(c_vector_field) vf1,vf2,vf3 !,h_rot,K_r,K_r_real + real(dp) r1,r2,sca,decrement(6),radfluc,radx,emi(3),eigen_emi(3) !,emi_chao(3) + complex(dp) c1 + type(c_normal_form) normal + type(c_vector_field) vf + type(c_ray) ray,ray2 + type(c_lattice_function) Lat_function + logical :: damp = .false.,fastcanonize=.true.,COSLIKE,t_e + type(c_taylor), allocatable :: phase(:) + type(c_damap), allocatable :: mt(:) + real(dp) ph(3),spintune(2),dampdec(3) + type(c_lattice_function) cl + !type(c_damap) one_turn_map, id_s,m01,m12,m23,m3f,a0,a1,a2,as + logical putspin + + radfluc=0.0001d0 + remove_tune_shift=.false. + putspin=.true. + n_cai=-i_ + !write(6,*) " If deltap/p0 is a canonical variable enter 3" + !write(6,*) " else enter 2" + !read(5,*) nd + nd=3 ! coasting + !if(nd/=2.and.nd/=3) stop 44 + if(nd==1) ndpt = 0 + if(nd==2) ndpt = 0 + if(nd==3) ndpt = 6 ! BMAD choice + !if(nd==3) ndpt = 0 ! BMAD choice + no=3; ! no: the order of the polynomial nv: the number of variables + np=4 + c_lda_used=1500 + call gaussian_seed(2463) + use_quaternion=.true. + write(*,*) "ndpt = ", ndpt + call c_init(no,nd,np1=np,ndpt1=ndpt) ! initializes taylor series with maps + allocate(phase(nd)) + + do_damping =.true. + + call alloc(f,F_FLOQUET,F_FLOQUET_cs,courant_snyder,nu_spin) ! must be constructed after init + call alloc(vf1,vf2,vf3) + call alloc(m,m1,as,a0,a1,a2,a_cs,rot,R_TE,CS_TE) ! + call alloc(phase) + call alloc(nu_spin) + call alloc(vf) + + n=1 + allocate(mt(n)) + do i=1,n + call alloc(mt(i)) + enddo + !default_fractional_tune_positive=.false. + negative_synchrotron_tune=.false. + + + call alloc(normal) + + r1=1.0_dp + r2=0.5d0 + + + do k=1,n + vf1=0 + + call c_TAYLOR_ran(f,r1,r2) + f=f-i_*aimag(f) ! remove the imaginary part + f=f-(f.cut.2) + f=-f*0.002d0 + do i=1,nd + sca=.1342d0 + !do while(sca==0.d0) + ! call GRNF(sca,5.d0) + !enddo + !sca=sign(sca,1.d0)+sca + sca=abs(sca)/i + f=f+sca*(dz_c(2*i-1)**2+dz_c(2*i)**2) + enddo + + ! Removing time terms for coasting + if(c_%ndpt==6) then + m1=1 + m1%v(2*nd-1)=0.0_dp + f=f*m1 + endif + if(c_%ndpt==5) then + m1=1 + m1%v(2*nd)=0.0_dp + f=f*m1 + endif + + + vf1=getvectorfield(f) ! + + ! putting spin + if(putspin) then + do i=1,3 + call c_TAYLOR_ran(vf1%q%x(i),r1,r2) ! putting spin + vf1%q%x(i)=vf1%q%x(i)-i_*aimag(vf1%q%x(i)) + vf1%q%x(i)=0.3d0*vf1%q%x(i)*m1 ! + + enddo + endif + + mt(k)=exp(vf1) + + goto 999 + do i1=1,c_%nd2 + do i2=i1,c_%nd2 + call GRNF(radx,4.d0) + radx=radx*radfluc + if(i1==i2) then + mt(k)%e_ij(i1,i2)=abs(radx) + else + mt(k)%e_ij(i1,i2)=abs(radx)/10 + mt(k)%e_ij(i2,i1)=abs(radx)/10 + + endif + enddo + enddo + 999 continue + + + enddo + + m=1 + do i=1,n + m=mt(i)*m + enddo + + + + + decrement(1)=0.99999993d0 + decrement(2)=0.9999997d0 + decrement(3)=0.9999996d0 + decrement(4)=0.99999995d0 + decrement(5)=0.99999993d0 + decrement(6)=0.99999999d0 + + decrement(1)=0.89d0 + decrement(2)=0.87d0 + decrement(3)=0.86d0 + decrement(4)=0.895d0 + decrement(5)=0.83d0 + decrement(6)=0.89d0 + + decrement(1)=0.9993d0 + decrement(2)=0.997d0 + decrement(3)=0.996d0 + decrement(4)=0.9995d0 + decrement(5)=0.9993d0 + decrement(6)=0.9999d0 + + !remove_tune_shift=.true. + do i=1,c_%nd2 + !m%v(i)=m%v(i)*decrement(i) + enddo + !call print(m) + !stop + + lielib_print(4)=0 + call c_normal(m,normal,dospin=putspin,phase=phase,nu_spin=nu_spin) + call c_full_factorise(normal%atot,as,a0,a1,a2,dir=1) + call print(as) + stop + !call print(m) + ! call print(normal%atot) + ! stop + !stop + !call c_fast_canonise(normal%atot, normal%atot) + !write(*,*) "before" + + !write(*,*) "after" + stop + !call print(a2) + !write(*,*) "hi" + stop + call print(normal%atot) + stop +write(*,*) "hi" + call c_full_factorise(normal%atot,as,a0,a1,a2,dir=1) + !call print(a0) + call print(a1) + !call print(a2) + stop + + m=ci_phasor()*normal%atot**(-1)*m*normal%atot*c_phasor() + call print(m) + !stop + !call print(normal%atot) + !stop + !call c_fast_canonise(normal%atot,a1,dospin=putspin) + call c_fast_canonise_clean_julia(normal%atot,a1,dospin=putspin) + + call print(a1) + stop + + normal%atot=a1 + write(6,*) normal%damping(1:3) + m=normal%atot**(-1)*m*normal%atot + m=ci_phasor()*m*c_phasor() + + call clean(m,m,prec=1.d-10) + m=m.cut.2 + call print(m) + stop + + m1= mt(1)*m*mt(1)**(-1) + !m1=m1.cut.2 + + normal%atot= mt(1)*normal%atot + a2=normal%atot + !a2=a2.cut.(2) + a_cs=a2.cut.(2) + call print(a_cs) + + call c_fast_canonise(a2,a0,dospin=putspin) + + call print(a0) + + m1=a2**(-1)*m*a2 + m1=a0**(-1)*m*a0 + m1=ci_phasor()*m1*c_phasor() + call clean(m1,m1,prec=1.d-10) + m1=m1.cut.2 + call print(m1) + + stop + !a0=a0.cut.(-2) + !normal%atot=normal%atot.cut.(-2) + + call c_fast_canonise_clean_julia(normal%atot,a1,dospin=putspin) + + do i=1,c_%nd2 + a0%v(i)= a0%v(i)+i_*a1%v(i) + enddo + do i=0,3 + a0%q%x(i)= a0%q%x(i)+i_*a1%q%x(i) + enddo + call print(a0) + do i=1,c_%nd2 + a1%v(i)= a1%v(i)+i_*a2%v(i) + enddo + do i=0,3 + a1%q%x(i)= a1%q%x(i)+i_*a2%q%x(i) + enddo + !call print(a1) + + stop + !call print(phase(1)) + + !call clean(phase,phase,prec=1.d-5) + !call clean(nu_spin,nu_spin,prec=1.d-5) + + write(6,'(A,3(1x,g23.16),/)') "The tune is ",normal%tune(1:nd) + write(6,'(A,3(1x,g23.16),/)') "The damping is ",normal%damping(1:nd) + write(6,'(A,1x,g23.16,/)') "The spin tune is ",normal%spin_tune + + + m=ci_phasor()*m*c_phasor() + + + call clean(normal%h_l,normal%h_l,prec=1.d-13) + + !call print(normal%h_l) + + do i1=1,c_%nd2,-1 + do i2=i1,c_%nd2,-1 + write(6,*) normal%s_ij0(i1,i2) + enddo + enddo + + call compute_lattice_functions(normal%atot,cl) + + call eigen_emit(normal%s_ij0,nd,eigen_emi) + + call emit(normal%s_ij0,nd,emi) + write(6,*) " Chao emittances " + write(6,*)normal%emittance + write(6,*) "Radar eigen emittances " + write(6,*)eigen_emi(1:nd) + write(6,*) "Radar eigen emittances analytic " + write(6,*)emi(1:nd) + write(6,*) " correct and via emittances" + write(6,*) normal%s_ij0(1,1) + write(6,*) cl%e(1,1,1)*normal%emittance(1)+cl%e(2,1,1)*normal%emittance(2)+cl%e(3,1,1)*normal%emittance(3) + + call sort(normal%emittance,nd,is1) + + + call sort(eigen_emi,nd,is2,is2n) + + call sort(emi,nd,is3,is3n) + + write(6,*) " Chao emittances " + write(6,*)normal%emittance + write(6,*) is1 + write(6,*) "Radar eigen emittances " + write(6,*)eigen_emi(1:nd) + write(6,*) is2 + + write(6,*) "Radar eigen emittances analytic " + write(6,*)emi(1:nd) + write(6,*) is3 + + write(6,*) "emittances from stochastic normal form" + write(6,*) normal%emittance(1:nd) + write(6,*) "Radar eigen emittances " + write(6,*)eigen_emi(1:nd) + write(6,*) "Radar eigen emittances analytic " + write(6,*)emi(1:nd) + + + + write(6,*) " correct and via emittances" + write(6,*) normal%s_ij0(1,1) + write(6,*) cl%e(is1(1),1,1)*normal%emittance(1)+cl%e(is1(2),1,1)*normal%emittance(2)+cl%e(is1(3),1,1)*normal%emittance(3) + write(6,*) cl%e(is1(1),1,1)*eigen_emi(1)+cl%e(is1(2),1,1)*eigen_emi(2)+cl%e(is1(3),1,1)*eigen_emi(3) + write(6,*) cl%e(is1(1),1,1)*emi(1)+cl%e(is1(2),1,1)*emi(2)+cl%e(is1(3),1,1)*emi(3) + + write(6,*) is1 + write(6,*) is2 + write(6,*) is3 + write(6,*) is3n + + contains + + subroutine sort(emi,nd,is,isi) + implicit none + real(dp) emi(3), emic(3) + integer nd,i, k,is(3),isc(3) + integer,optional:: isi(3) + + is=[1,2,3] + isc=[1,2,3] + + emic=emi + do k=1,nd**2 + do i=1,nd-1 + if(emic(i)>emi(i+1)) then + isc(i)=is(i+1) + isc(i+1)=is(i) + emic(i)=emi(i+1) + emic(i+1)=emi(i) + else + emic(i)=emi(i) + emic(i+1)=emi(i+1) + endif + emi=emic + is=isc + enddo + enddo + + if(present(isi)) then + do i=1,3 + write(6,*) is(i),i + isi(is(i))=i + enddo + endif + + end subroutine sort + + subroutine emit(sig,nd,emi) + implicit none + complex(dp) sig(6,6) + real(dp) emi(3),i2,i4,i6,sig0(6,6),sig2(6,6),dis,xj(6,6),p,q + integer nd,i,j,k + + if(nd==1) then + emi(1)=sqrt(abs(sig(1,1)*sig(2,2)-sig(1,2)**2)) + return + endif + + if(nd==2) then + do i=1,6 + do j=1,6 + sig0(i,j)=sig(i,j) + enddo + enddo + + xj=0 + + do i=1,nd + xj(2*i-1,2*i)=1 + xj(2*i,2*i-1)=-1 + enddo + + sig0=matmul(sig0,xj) + + sig0=matmul(sig0,sig0) + i2=sig0(1,1)+sig0(2,2)+sig0(3,3)+sig0(4,4) + + sig0=matmul(sig0,sig0) + i4=sig0(1,1)+sig0(2,2)+sig0(3,3)+sig0(4,4) + i6=0 + !write(6,*) " i2,i4,i6 analytical " + !write(6,*) i2,i4,i6 + + dis=sqrt(abs(i4- i2**2/4)) + + emi(1)=sqrt(abs((i2/2+dis)))/sqrt(2.d0) + emi(2)=sqrt(abs((i2/2-dis)))/sqrt(2.d0) + + endif + + if(nd==3) then + do i=1,6 + do j=1,6 + sig0(i,j)=sig(i,j) + enddo + enddo + + xj=0 + + do i=1,nd + xj(2*i-1,2*i)=1 + xj(2*i,2*i-1)=-1 + enddo + + sig0=matmul(sig0,xj) + + sig2=matmul(sig0,sig0) + sig0=sig2 + i2=sig0(1,1)+sig0(2,2)+sig0(3,3)+sig0(4,4)+sig0(5,5)+sig0(6,6) + + sig0=matmul(sig0,sig0) + i4=sig0(1,1)+sig0(2,2)+sig0(3,3)+sig0(4,4)+sig0(5,5)+sig0(6,6) + + sig0=matmul(sig0,sig2) + i6=sig0(1,1)+sig0(2,2)+sig0(3,3)+sig0(4,4)+sig0(5,5)+sig0(6,6) + + + !write(6,*) " i2,i4,i6 analytical " + !write(6,*) i2,i4,i6 + + + p=-i4/4+i2**2/24 + + q= -i2**3/108 +i2*i4/12 -i6/6; + + dis=(3.0_dp*q/2.0_dp/p) + + dis=acos(dis*sqrt(3.0_dp/-p)) + + do k=1,3 + + emi(k)=2.0_dp*sqrt(-p/3)*cos((dis-k*twopi)/3.0_dp)+I2/6 + emi(k)=sqrt(abs(emi(k))) + enddo + + + endif + end subroutine emit + + subroutine eigen_emit(sig,nd,emi) + implicit none + complex(dp) sig(:,:) + real(dp) emi(3),sig0(ndim2t,ndim2t),xj(ndim2t,ndim2t),i2,i4,i6 + integer nd,i,j + real(dp) reval(ndim2t),imval(ndim2t),vr(ndim2t,ndim2t),vi(ndim2t,ndim2t),vrt(ndim2t,ndim2t),vit(ndim2t,ndim2t) + complex(dp) emic(6) + sig0=0 + sig0(1:6,1:6)=sig(1:6,1:6) + + + xj=0 + + do i=1,nd + xj(2*i-1,2*i)=1 + xj(2*i,2*i-1)=-1 + enddo + sig0=matmul(sig0,xj) + + + + call c_eig6(sig0,reval,imval,vr,vi) + + + + do i=1,c_%nd2 + emic(i)=reval(i)+i_*imval(i) + enddo + do i=1,c_%nd + emi(i)=abs(imval(2*i)) + enddo + i2=0 + i4=0 + i6=0 + do i=1,c_%nd2 + i2=i2+emic(i)**2 + i4=i4+emic(i)**4 + i6=i6+emic(i)**6 + enddo + + !write(6,*) " i2,i4,i6 numerical " + + ! write(6,*) i2,i4,i6 + !pause 667 + !write(6,*)"sum ",2*(imval(2)**2+imval(4)**2) + + end subroutine eigen_emit + + subroutine invert_with_log(M,MI) + implicit none + type(c_damap) m,mi,m1,nl + type(c_vector_field) f + call alloc(m1,nl) + + call alloc(f) + + m1=m.cut.2 + m1=m1**(-1) + + nl=m1*m + + f=ln(nl) + f=-f + + nl=exp(f) + + mi=nl*m1 + + call kill(f) + + call kill(m1,nl) + + end subroutine invert_with_log + + subroutine invert_with_1minusx(M,MI,minimum_step) + implicit none + type(c_damap) m,mi,m1,nl,dl,id + integer i,nt + logical minimum_step + call alloc(m1,nl,dl,id) + + nt=c_%no + if(minimum_step) nt=(c_%no +mod(c_%no,2))/2 + + write(6,*) nt,c_%no + pause 100 + m1=m.cut.2 + m1=m1**(-1) + + nl=m1*m + dl=nl + call print(nl) + + pause 1 + + mi=1 + id=1 + do i=1,nt + dl=nl-id + dl=id-dl + call clean(nl,nl,prec=1.d-10) + call print(nl%v(1)) + call print(nl%q%x(1)) + write(6,*) i,nt + pause 2 + + nl=dl*nl + + mi=dl*mi + + enddo + + mi=mi*m1 + call kill(m1,nl,dl,id) + + end subroutine invert_with_1minusx + + + + subroutine c_normal1(xyso3,n,dospin,no_used,rot,phase,nu_spin,canonize) + !#general: normal + !# This routine normalises the map xy + !# xy = n%a_t**(-1)*r*n%a_t + !# The linear part of r is described in Chap.4 for the orbital part + !# and in Chap.6 for the spin. The nonlinear parts are in Chap.5 and 6. + !# Dospin must be set to .true. if spin is to be normalised. + !# Resonances can be left in the map. Their number is in n%nres. + !# They are nres resonances The kth resonance is n%m(i,k).Q_i+n%ms(k)=integer + !# canonize=.true. Then it is put into courant-snyder form or anti- courant-snyder form + !# depending on the logical courant_snyder_teng_edwards=true or false. (See blue or yellow book) + !# The map in phasors is exp(n%H_l.grad) exp(n%H_nl.grad) + !# if fully normalized into a rotation then the map is exp(n%h.grad) + + implicit none + type(c_damap) , intent(inout) :: xyso3 + type(c_damap) m1,ri,nonl,a1,a2,mt,AS,xy,Nf,N_cut_2,N_nl + type(c_normal_form), intent(inout) :: n + type(c_damap), optional :: rot + type(c_taylor), optional :: phase(:),nu_spin + type(taylor) c1,s1 + integer,optional :: no_used + integer i,j,k,l,kr,not,ncoast + integer, allocatable :: je(:) + logical(lp) removeit,rad_in + complex(dp) v,lam,egspin(3) + complex(dp), allocatable :: eg(:) + real(dp) norm,alpha,prec !,cx,sx + logical(lp), optional :: dospin,canonize + logical dospinr,change + type(c_spinor) n0,nr + type(c_quaternion) qnr + integer mker, mkers,mdiss,mdis,ndptbmad + real(dp), allocatable :: da(:) + integer nd2t,ndc2t,nd2,ndptb,nv,no + + nd2t=c_%nd2t + ndc2t=c_%ndc2t + nd2=c_%nd2 + ndptb=c_%ndptb + nv=c_%nv + no=c_%no + + call kill(n%ker) + call kill(n%g) + call alloc(n%ker) + call alloc(n%g) + n%g%dir=-1 + n%ker%dir=1 + + if(lielib_print(13)/=0) then + call kanalnummer(mker,"kernel.txt") + call kanalnummer(mdis,"distortion.txt") + call kanalnummer(mkers,"kernel_spin.txt") + call kanalnummer(mdiss,"distortion_spin.txt") + endif + + dospinr=.false. + if(present(dospin)) then + dospinr=dospin + else + if(force_spin_input_normal) then + write(6,*) " your default forces you to include dospin in the input of c_normal" + stop + endif + endif + + + if(bmad_automatic) then + if(nd2t+ndc2t/=6) then + write(6,*) " nd2t , ndc2t ",nd2t,ndc2t + write(6,*) " not BMAD on entrance, suspicious" + endif + ndptbmad=0 + alpha=abs(xyso3%v(6).sub.'000001') + norm=full_abs(xyso3%v(6)) + alpha=abs(alpha-1.0_dp)+abs(norm-1.0_dp) + if(alpha<1.d-12) then + ndptbmad=6 + call in_bmad_units + endif + alpha=abs(xyso3%v(5).sub.'000010') + norm=full_abs(xyso3%v(5)) + alpha=abs(alpha-1.0_dp)+abs(norm-1.0_dp) + if(alpha<1.d-12) then + ndptbmad=5 + call in_ptc_units + endif + call c_bmad_reinit(ndptbmad) + + + if(use_quaternion) then + call c_full_norm_quaternion(xyso3%q,k,norm) + if(k==-1) dospinr=.true. + else + call c_full_norm_spin(xyso3%s,k,norm) + if(k==-1) dospinr=.true. + endif + endif + + if(spin_automatic) then + dospinr=.false. + if(use_quaternion) then + call c_full_norm_quaternion(xyso3%q,k,norm) + if(k==-1) dospinr=.true. + else + call c_full_norm_spin(xyso3%s,k,norm) + if(k==-1) dospinr=.true. + endif + write(6,*)"dospin ", dospinr + endif + + inside_normal=.true. + !call c_count_da(i_alloc) + !write(6,*)" entering c_normal ", i_alloc + change=.false. + not=no + if(present(no_used)) then + not=no_used ! sometimes only linear stuff is needed + else + if(complex_extra_order==1.and.special_extra_order_1) not=not-1 + endif + + call alloc(xy); + xy=xyso3 + if(use_quaternion_in_so3.and.(.not.use_quaternion.and.dospinr)) then + call makequaternion(xy) + use_quaternion=.true. + change=.true. + endif + call alloc(m1);call alloc(nonl);call alloc(a1);call alloc(a2);call alloc(ri); + + allocate(je(nv)) + allocate(eg(xyso3%n)) + allocate(da(c_%nd)) + da=0.0_dp + + m1=xy + + ! Brings the map to the parameter dependent fixed point + ! including the coasting beam gymnastic: time-energy is canonical + ! but energy is constant. (Momentum compaction, phase slip etc.. falls from there) + ! etienne + + if(c_skip_gofix) then + a1=1 + else + call c_gofix(m1,a1) + + endif + + + m1=c_simil(a1,m1,-1) + + + + ! Does the the diagonalisation into a rotation + call c_linear_a(m1,a2) + + + + + !!! Now the linear map is normalised + m1=c_simil(a2,m1,-1) + + + !!! We go into the phasors' basis + ri=from_phasor(-1) + + m1=c_simil(ri,m1,1) + + + !stop 999 + ri=(m1.sub.-1)**(-1) + + ri%s=1 ! make spin identity + ri%q=1.0_dp ! make spin identity + + + + !!! The tunes are stored for the nonlinear normal form recursive algorithm + do k=1,xy%n + if(coast(k)) then + eg(k)=1 + else + je=0 + je(k)=1 + eg(k)=ri%v(k).sub.je + if(mod(k,2)==0) then + da(k/2)=log(abs(eg(k))) + endif + endif + enddo + + n%ker=0 ! In case reusing normal form + + do i=2,not + if(lielib_print(13)/=0) then + write(mdis,*) " **************************************** " + write(mdis,*) "Order ",i + write(mker,*) " **************************************** " + write(mker,*) "Order ",i + endif + + nonl=(m1*ri) + nonl= exp_inv(n%ker,nonl) + nonl=nonl.sub.i + + + + do k=1,xy%n + if(lielib_print(13)/=0) then + write(mdis,*) " **************************************** " + write(mdis,*) "field component ",k + write(mker,*) " **************************************** " + write(mker,*) "field component ",k + endif + + n%g%f(i)%v(k)=0.0_dp + n%ker%f(i)%v(k)=0.0_dp + + + j=1 + + do while(.true.) + + call c_cycle(nonl%v(k),j,v ,je); if(j==0) exit; + call check_kernel(k,xy%n,je,removeit) + + if(n%nres>0.and.removeit) then + do kr=1,n%nres + if(n%ms(kr)/=0) cycle ! a spin resonance + call check_resonance(k,xy%n,je,kr,n%m,removeit) + if(.not.removeit) then + exit + endif + enddo + endif + + if(removeit) then + + lam=1.0_dp + je(k)=je(k)-1 + do l=1,xy%n + if(coast(l)) cycle + lam=lam*eg(l)**je(l) + enddo + + if(lielib_print(13)/=0) then + write(mdis,*) k + write(mdis,'(6(1x,i4))') je(1:nd2) + write(mdis,*) v + write(mdis,*) abs(v/(1-lam)) + endif + + je(k)=je(k)+1 + + n%g%f(i)%v(k)=n%g%f(i)%v(k)+(v.cmono.je)/(1.0_dp-lam) + + else ! Put in the kernel + + if(lielib_print(13)/=0) then + je(k)=je(k)-1 + write(mker,*) k + write(mker,'(6(1x,i4))') je(1:nd2) + write(mker,*) v + write(mker,*) abs(v/(1-lam)) + je(k)=je(k)+1 + endif + n%ker%f(i)%v(k)=n%ker%f(i)%v(k)+(v.cmono.je) + endif + + enddo ! over monomial + enddo ! over vector index + + m1=c_simil(n%g%f(i),m1,-1) + !call c_full_norm_vector_field(n%g%f(i),norm) + !write(6,*) " old ",i,norm + enddo + + ! if(dospinr)then + do i=1,size(n%g%f) + n%g%f(i)%q=0.0_dp ! makes identity 2024.1.2 + enddo + do i=1,size(n%ker%f) + n%ker%f(i)%q=0.0_dp + enddo + ! endif + + + n%a_t=a1*a2*from_phasor()*texp(n%g)*from_phasor(-1) + ! + n%a1=a1 + n%a2=a2 + + + !!!!! here we put the normalised linear part into the factored vector field + !!!!! not necessary but useful + do k=1,xy%n + if(.not.coast(k)) then + je=0 + je(k)=1 + n%ker%f(1)%v(k)=n%ker%f(1)%v(k)-(log(eg(k)).cmono.je) + + if(mod(k,2)==1) then + n%tune((k+1)/2)=aimag(log(eg(k)))/twopi + n%damping((k+1)/2)=real(log(eg(k))) + if(n%tune((k+1)/2)<0.and.n%positive) n%tune((k+1)/2)=n%tune((k+1)/2)+1.0_dp + if(n%tune((k+1)/2)<-0.5_dp.and.(.not.n%positive)) n%tune((k+1)/2)=n%tune((k+1)/2)+1.0_dp + if(n%tune((k+1)/2)> 0.5_dp.and.(.not.n%positive)) n%tune((k+1)/2)=n%tune((k+1)/2)-1.0_dp + + endif + endif + enddo + + if(c_skip_gofix) then + do k=1,xy%n + if(mod(k,2)==1) then + if(n%tune((k+1)/2)>0.50_dp) n%tune((k+1)/2)=n%tune((k+1)/2)-1.0_dp + endif + enddo + endif + if(nd2t==6) then + if(n%tune(3)>0.50_dp.and.negative_synchrotron_tune) n%tune(3)=n%tune(3)-1.0_dp + endif + + if(ndpt/=0) then + je=0 + je(ndpt)=1 + lam=(ri%v(ndptb).sub.je) + n%ker%f(1)%v(ndptb)=n%ker%f(1)%v(ndptb)-(lam.cmono.je) + if(mod(ndpt,2)==0) then + n%tune(ndpt/2)=-lam + else + n%tune(ndptb/2)=-lam + endif + endif + + + if(dospinr) then + + if(use_quaternion)then + call c_full_norm_quaternion(m1%q,k,norm) + else + call c_full_norm_spin(m1%s,k,norm) + endif + if(k>=0) then + dospinr=.false. + if(use_quaternion) then + write(6,*) " no quaternion spin in map: dospin command ignored " + else + write(6,*) " no spin matrix in map: dospin command ignored " + endif + endif + endif + + + if(dospinr) then + call alloc(n0) + call alloc(nr) + call alloc(mt) + call alloc(AS) + call alloc(qnr) + n%AS=1 + + + if(use_quaternion)then + + call c_normal_spin_linear_quaternion(m1,m1,n%AS,alpha) + + n%quaternion_angle=alpha/2.0_dp + ri=1 ; ri%q=m1%q.sub.0 ; ! exp(theta_0 L_y) (2) + ! sx=sqrt(ri%q%x(1)**2+ri%q%x(2)**2+ri%q%x(3)**2) + ! cx=ri%q%x(0) + !write(6,*) alpha + ! alpha=-(-2*atan2(sx,cx)) + !write(6,*) alpha + !pause 723 + egspin(3)=cos(alpha)-i_*sin(alpha) + egspin(2)=1.0_dp + egspin(1)=cos(alpha)+i_*sin(alpha) + else + call c_normal_spin_linear(m1,m1,n%AS,n0) ! (1) + ri=1 ; ri%s=m1%s.sub.0 ; ! exp(theta_0 L_y) (2) + egspin(3)=ri%s%s(1,1)-i_*ri%s%s(1,3) + egspin(2)=1.0_dp + egspin(1)=ri%s%s(1,1)+i_*ri%s%s(1,3) + endif + + + + + + + if(lielib_print(13)/=0) then + write(mdiss,*) " eg(1:4),spin_def_tune" ,spin_def_tune + write(mdiss,*)eg(1) + write(mdiss,*)eg(2) + write(mdiss,*)eg(3) + write(mdiss,*)eg(4) + write(mdiss,*) " egspin(1:3)" + write(mdiss,*)egspin(1) + write(mdiss,*)egspin(2) + write(mdiss,*)egspin(3) + endif + if(lielib_print(13)/=0) then + write(mkers,*) " eg(1:4),spin_def_tune" ,spin_def_tune + write(mkers,*)eg(1) + write(mkers,*)eg(2) + write(mkers,*)eg(3) + write(mkers,*)eg(4) + write(mkers,*) " egspin(1:3)" + write(mkers,*)egspin(1) + write(mkers,*)egspin(2) + write(mkers,*)egspin(3) + endif + + !!! tune is taken from egspin(1) or egspin(3) spin_def_tune= +/- 1 + n%spin_tune=aimag(log(egspin(2+spin_def_tune))/twopi) + + + + ! because exp(a L_y) x = x- a z + O(a**2) + ri=ri**(-1) ! exp(-alpha_0 L_y) (3) + + + if(use_quaternion)then + nonl=m1.sub.1 ; nonl%q=1.0_dp ;nonl=nonl**(-1) ! R_0^-1 (4) + else + nonl=m1.sub.1 ; nonl%s=1 ;nonl=nonl**(-1) ! R_0^-1 (4) + endif + ! nonl=m1.sub.1 ; nonl%s=1 ;nonl=nonl**(-1) ! R_0^-1 (4) + + + do i=1,no !+2 + if(lielib_print(13)/=0) then + write(mdiss,*) " **************************************** " + write(mdiss,*) "Order ",i + write(mkers,*) " **************************************** " + write(mkers,*) "Order ",i + endif + + + + mt=m1*ri ! S*exp(-theta_0 L_y) (5) + + + if(use_quaternion)then + n0=mt%q + else + call c_find_om_da(mt%s,n0) ! (4) + endif + + call c_n0_to_nr(n0,n0) ! n0 = > eigen-operator of spin (7) + + + + n0=n0*nonl ! no * R^-1 (8) + + + nr=0 + + do k=1,3 + if(lielib_print(13)/=0) then + write(mdiss,*) " $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ " + write(mdiss,*) "Spin component ",k + write(mdiss,*) " " + write(mkers,*) " $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ " + write(mkers,*) "Spin component ",k + write(mkers,*) " " + endif + + j=1 + do while(.true.) + call c_cycle(n0%v(k),j,v ,je); if(j==0) exit; + call check_kernel_spin1(k,xy%n,je,da,removeit) + if(n%nres>0.and.removeit) then + do kr=1,n%nres + call check_resonance_spin(k,xy%n,je,kr,n%ms,n%m,removeit) + if(.not.removeit) then + exit + endif + enddo + endif + + if(removeit) then + lam=egspin(k) + do l=1,xy%n + if(coast(l)) cycle + lam=lam*eg(l)**je(l) + enddo + + if(lielib_print(13)/=0) then + !do kr=1,nd2 + !je(kr)=-(-1)**kr*je(kr) + !enddo + write(mdiss,'(6(1x,i4))') je(1:nd2) + write(mdiss,*)lam + write(mdiss,*) v + write(mdiss,*) abs(v/(1-lam)) + !do kr=1,nd2 + !je(kr)=-(-1)**kr*je(kr) + !enddo + endif + nr%v(k)=nr%v(k) +(v.cmono.je)/(1.0_dp-lam) ! (9) + else + if(lielib_print(13)/=0) then + do kr=1,nd2 + je(kr)=-(-1)**kr*je(kr) + enddo + write(mkers,'(6(1x,i4))') je(1:nd2) + write(mkers,*) v + do kr=1,nd2 + je(kr)=-(-1)**kr*je(kr) + enddo + endif + endif + enddo ! cycle + enddo ! k + + + call c_nr_to_n0(nr,nr) ! (10) + + + + + + if(use_quaternion)then + qnr=nr + AS=1 ; + AS%q=exp(qnr) + else + AS=1 ; AS%s=exp(nr)*AS%s + endif + + + + + n%AS=n%AS*AS ! (12) + + + + m1=c_simil(AS,m1,-1) + + + enddo + + n%AS=from_phasor()*n%AS*from_phasor(-1) + + n%AS=n%A_t*n%AS*n%a_t**(-1) + + call kill(AS) + call kill(mt) + call kill(n0) + call kill(nr) + call kill(qnr) + endif + + call c_check_rad(m1%e_ij,rad_in) + if(rad_in) call c_normal_radiation(m1,n) + + ri=from_phasor() + n%n=c_simil(ri,m1,1) + n%Atot=n%as*n%a_t + + if(present(canonize)) then + if(canonize) call c_full_canonise(n%atot,n%atot) + endif + + + + if(present(rot)) then + rot=n%Atot**(-1)*xy*n%Atot + endif + + if(present(nu_spin)) nu_spin=0.0_dp + if(present(phase)) then + do i=1,size(phase) + phase(i)=0.0_dp + enddo + endif + if((present(phase).or.present(nu_spin)).and.old_phase_calculation) then + + + + if(present(rot)) then + m1=rot + else + m1=n%Atot**(-1)*xy*n%Atot + endif + + + + + qphase=.false. + call c_full_canonise(m1,a1,phase=phase,nu_spin=nu_spin) + ! if(dospinr.and.present(nu_spin)) then + ! if(real(nu_spin.sub.'0')<0) nu_spin=-nu_spin ! 2018.11.01 to match phase advance + ! endif + qphase=qphasedef + endif + + ! error because m1 was reutilized in present(rot) + ! call c_check_rad(m1%e_ij,rad_in) + !! if(rad_in) call c_normal_radiation(m1,n) + ! call c_check_rad(m1%e_ij,rad_in) + !! if(rad_in) call c_normal_radiation(m1,n) + + call kill(m1);call kill(nonl);call kill(a1);call kill(a2);call kill(ri); + + deallocate(eg) + deallocate(da) + deallocate(je) + + if(lielib_print(13)/=0) then + close(mker) + close(mdis) + close(mdiss) + close(mkers) + endif + + if(change) then + call makeso3(n%a1) + call makeso3(n%a2) + call makeso3(n%a_t) + call makeso3(n%atot) + call makeso3(n%as) + call makeso3(n%n) + n%a1%q=0.0_dp + n%a2%q=0.0_dp + n%a_t%q=0.0_dp + n%atot%q=0.0_dp + n%as%q=0.0_dp + n%n%q=0.0_dp + use_quaternion=.false. + endif + call kill(xy) + !call c_count_da(i_alloc) + !write(6,*) " exiting c_normal ",i_alloc + inside_normal=.false. + !!!! finding a Lie exponent + + ! if(use_quaternion.and.rf==0) then + call alloc(Nf,N_cut_2,N_nl ) + Nf=n%atot**(-1)*xyso3*n%atot + N_cut_2=Nf.cut.(-2) + + ! creating the linear vector field in phasors variables + ncoast=0 + if(c_%ndpt/=0) ncoast=1 + !!!! create a full vector field for N_cut_2 + do i=1,(c_%nd-ncoast) + n%H_l%v(2*i-1)=-(i_*twopi*n%tune(i))*dz_c(2*i-1)-n%damping(i)*dz_c(2*i-1) + n%H_l%v(2*i)=(i_*twopi*n%tune(i))*dz_c(2*i)-n%damping(i)*dz_c(2*i) + enddo + if(ncoast/=0) then + n%H_l%v(c_%ndptb)=n%tune(c_%nd)*dz_c(c_%ndpt) + endif + if(dospinr) then + n%H_l%q=0.0_dp + n%H_l%q%x(2)=n%quaternion_angle + endif + !!!! Going into variables moving on a circle + n%H_l=ci_phasor()*n%H_l + + !!! Reverse-Dragt-Finn order for Lie map + N_nl=N_cut_2**(-1)*nf + + n%H_nl=ln(N_nl) + + n%H_l=c_phasor()*n%H_l + n%H_nl=c_phasor()*n%H_nl + + n%H=n%H_l+n%H_nl + call kill(Nf,N_cut_2,N_nl ) + ! endif + + if(.not.old_phase_calculation) then + if(present(phase)) then + ! ncoast=0 + !if(c_%ndpt/=0) ncoast=1 + do i=1,c_%nd !-ncoast + phase(i)=aimag(n%h%v(2*i).k.(2*i))/twopi + enddo + + if(c_%ndptb/=0) then + phase(c_%nd)=n%h%v(c_%ndptb) ! overwrites if necessary + endif + endif + + if(present(nu_spin)) nu_spin=-spin_def_tune*n%h%q%x(2)/pi + + endif + + + end subroutine c_normal1 !_with_quaternion + + + subroutine c_fast_canonise_clean_julia(u,u_c,phase,damping,q_cs,q_as,q_orb,q_rot,spin_tune ,dospin) + implicit none + type(c_damap), intent(inout) :: u,u_c + real(dp), optional, intent(inout) :: phase(:),damping(:) + real(dp), optional, intent(inout) :: spin_tune(2) + type(c_linear_map), optional :: q_cs,q_as,q_rot,q_orb ! q_c is properly factorised + real(dp) b(6,6),b0(6,6),ri(6,6),id(6,6),st(6,6),ang,damp(3),t,cphi,sphi,s(6,6),aq,daq + type(c_linear_map) q ,qr,qc,qrot + complex(dp) cri(6,6) + integer i + logical dos,rota + logical, optional :: dospin + type(c_damap) uct + integer ndt,ndptb,ndpt,ndct + + ! nd = number dimensions + ! ndt = number harmonic oscillators = 4 if coastings + + ndt=c_%nd2t/2 + ndptb=c_%ndptb + ndpt=c_%ndpt + ndct=c_%ndc2t/2 + write(6,*) "ndt,ndptb,ndpt,ndct" + write(6,*) ndt,ndptb,ndpt,ndct + pause + ! ndc2t=2*ndct ! 2 if coasting, otherwise 0 + + call alloc(uct) + + dos=.false. + if(present(dospin)) then + dos=dospin + else + if(force_spin_input_normal) then + write(6,*) " your default forces you to include dospin in the input of c_fast_canonise" + stop + endif + endif + s=0 + b0=0 + id=0 + do i=1,nd + b0(2*i-1,2*i-1)=1 ! I + b0(2*i,2*i)=1 ! + s(2*i-1,2*i)=1 + s(2*i,2*i-1)=-1 + enddo + if(present(q_rot) ) then + qrot=0 ! actually makes identity + endif + b=0 + id=b0 + ri=0 + b=u + + if(ndpt/=0) call extract_a0_mat(b,b0) + + + + damp=1 + + + + do i=1,ndt + ! if((i<=ndt)) then !.or.(i>nd-rf)) then + t=sqrt(b(2*i-1,2*i-1)**2+b(2*i-1,2*i)**2) + cphi=b(2*i-1,2*i-1)/t + sphi=b(2*i-1,2*i)/t + if(sphi*b(2*i-1,2*i)+cphi*b(2*i-1,2*i-1)< 0) then !2023.12.10 bug in China? + cphi=-cphi + sphi=-sphi + endif + + + ri(2*i-1,2*i-1)=cphi + ri(2*i,2*i)=cphi + ri(2*i-1,2*i)=-sphi + ri(2*i,2*i-1)=sphi + ! endif + + if(present(phase)) then + ang=-atan2(sphi,cphi) + phase(i)=phase(i)-ang/twopi + endif + + + enddo + + + + if(ndpt/=0) then + ri(5,5)=1 + ri(6,6)=1 + ri(ndptb,ndpt)=- b(ndptb,ndpt) + if(mod(ndpt,2)==0) then + i=ndpt/2 + else + i=ndptb/2 + endif + if(present(phase)) phase(i)=phase(i)+b(ndptb,ndpt) + if(present(q_rot) ) then + qrot%mat(ndptb,ndpt)=-ri(ndptb,ndpt) + qrot%mat(5,5)=ri(5,5) + qrot%mat(6,6)=ri(6,6) + endif + endif + + + st=matmul(b,ri) + st=matmul(b0,st) + if(do_damping) then + + + call canonize_damping(st,id,damp) + + st=matmul(st,id) + + if(present(damping)) then + do i=1,ndt + damping(i)=damping(i)+log(damp(i)) + enddo + endif + + endif + + if(present(q_rot) ) then + if(ndpt/=0) then !2023.12.10 + do i=1,2 + qrot%mat(2*i-1,2*i-1)=ri(2*i-1,2*i-1)/damp(i) + qrot%mat(2*i,2*i)=ri(2*i,2*i)/damp(i) + qrot%mat(2*i-1,2*i)=-ri(2*i-1,2*i)/damp(i) + qrot%mat(2*i,2*i-1)=-ri(2*i,2*i-1)/damp(i) + enddo + else + do i=1,3 + qrot%mat(2*i-1,2*i-1)=ri(2*i-1,2*i-1)/damp(i) + qrot%mat(2*i,2*i)=ri(2*i,2*i)/damp(i) + qrot%mat(2*i-1,2*i)=-ri(2*i-1,2*i)/damp(i) + qrot%mat(2*i,2*i-1)=-ri(2*i,2*i-1)/damp(i) + enddo + endif + endif + + uct=st + if(use_quaternion.and.dos) then + q=1 + q=u%q + + + qr=1 + qr=0.0_dp + + + aq=-atan2(real(q%q(2,0)),real(q%q(0,0))) + + qr%q(0,0)= cos(aq) + qr%q(2,0)= sin(aq) + + daq=0 + if(ndpt/=0) then + + daq=(q%q(0,ndpt)*qr%q(2,0)+q%q(2,ndpt)*qr%q(0,0))/(q%q(2,0)*qr%q(2,0)-q%q(0,0)*qr%q(0,0)) + qr%q(0,ndpt)= -daq*qr%q(2,0) + qr%q(2,ndpt)= daq*qr%q(0,0) + endif + qc=q*qr + + if(present(spin_tune).and.dos) then + spin_tune(1)=spin_tune(1)+aq/pi ! changed 2018.11.01 + endif + cri=ri + qc=qc*cri + uct%q=qc + + + + endif + + if(present(spin_tune).and.dos) then + spin_tune(2)=spin_tune(2)+daq/pi ! changed 2018.11.01 + endif + + + + + + u_c=uct + call kill(uct) + end subroutine c_fast_canonise_clean_julia + + end program example \ No newline at end of file diff --git a/fpp-ptc-sandbox/code/CMakeCache.txt b/fpp-ptc-sandbox/code/CMakeCache.txt new file mode 100644 index 0000000..60717f2 --- /dev/null +++ b/fpp-ptc-sandbox/code/CMakeCache.txt @@ -0,0 +1,1142 @@ +# This is the CMakeCache file. +# For build in directory: /Users/matthewsignorelli/.julia/dev/NonlinearNormalForm/fpp-ptc-sandbox/code +# It was generated by CMake: /opt/homebrew/bin/cmake +# You can edit this file to change values found 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defined(__GNUC_PATCHLEVEL__) +# define SIMULATE_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__) +#endif + +#elif defined(__PATHCC__) +# define COMPILER_ID "PathScale" +# define COMPILER_VERSION_MAJOR DEC(__PATHCC__) +# define COMPILER_VERSION_MINOR DEC(__PATHCC_MINOR__) +# if defined(__PATHCC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__PATHCC_PATCHLEVEL__) +# endif + +#elif defined(__BORLANDC__) && defined(__CODEGEARC_VERSION__) +# define COMPILER_ID "Embarcadero" +# define COMPILER_VERSION_MAJOR HEX(__CODEGEARC_VERSION__>>24 & 0x00FF) +# define COMPILER_VERSION_MINOR HEX(__CODEGEARC_VERSION__>>16 & 0x00FF) +# define COMPILER_VERSION_PATCH DEC(__CODEGEARC_VERSION__ & 0xFFFF) + +#elif defined(__BORLANDC__) +# define COMPILER_ID "Borland" + /* __BORLANDC__ = 0xVRR */ +# define COMPILER_VERSION_MAJOR HEX(__BORLANDC__>>8) +# define COMPILER_VERSION_MINOR HEX(__BORLANDC__ & 0xFF) + +#elif defined(__WATCOMC__) && __WATCOMC__ < 1200 +# define COMPILER_ID "Watcom" + /* __WATCOMC__ = VVRR */ +# define COMPILER_VERSION_MAJOR DEC(__WATCOMC__ / 100) +# define COMPILER_VERSION_MINOR DEC((__WATCOMC__ / 10) % 10) +# if (__WATCOMC__ % 10) > 0 +# define COMPILER_VERSION_PATCH DEC(__WATCOMC__ % 10) +# endif + +#elif defined(__WATCOMC__) +# define COMPILER_ID "OpenWatcom" + /* __WATCOMC__ = VVRP + 1100 */ +# define COMPILER_VERSION_MAJOR DEC((__WATCOMC__ - 1100) / 100) +# define COMPILER_VERSION_MINOR DEC((__WATCOMC__ / 10) % 10) +# if (__WATCOMC__ % 10) > 0 +# define COMPILER_VERSION_PATCH DEC(__WATCOMC__ % 10) +# endif + +#elif defined(__SUNPRO_C) +# define COMPILER_ID "SunPro" +# if __SUNPRO_C >= 0x5100 + /* __SUNPRO_C = 0xVRRP */ +# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_C>>12) +# define COMPILER_VERSION_MINOR HEX(__SUNPRO_C>>4 & 0xFF) +# define COMPILER_VERSION_PATCH HEX(__SUNPRO_C & 0xF) +# else + /* __SUNPRO_CC = 0xVRP */ +# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_C>>8) +# define COMPILER_VERSION_MINOR HEX(__SUNPRO_C>>4 & 0xF) +# define COMPILER_VERSION_PATCH HEX(__SUNPRO_C & 0xF) +# endif + +#elif defined(__HP_cc) +# define COMPILER_ID "HP" + /* __HP_cc = VVRRPP */ +# define COMPILER_VERSION_MAJOR DEC(__HP_cc/10000) +# define COMPILER_VERSION_MINOR DEC(__HP_cc/100 % 100) +# define COMPILER_VERSION_PATCH DEC(__HP_cc % 100) + +#elif defined(__DECC) +# define COMPILER_ID "Compaq" + /* __DECC_VER = VVRRTPPPP */ +# define COMPILER_VERSION_MAJOR DEC(__DECC_VER/10000000) +# define COMPILER_VERSION_MINOR DEC(__DECC_VER/100000 % 100) +# define COMPILER_VERSION_PATCH DEC(__DECC_VER % 10000) + +#elif defined(__IBMC__) && defined(__COMPILER_VER__) +# define COMPILER_ID "zOS" + /* __IBMC__ = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__IBMC__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMC__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMC__ % 10) + +#elif defined(__open_xl__) && defined(__clang__) +# define COMPILER_ID "IBMClang" +# define COMPILER_VERSION_MAJOR DEC(__open_xl_version__) +# define COMPILER_VERSION_MINOR DEC(__open_xl_release__) +# define COMPILER_VERSION_PATCH DEC(__open_xl_modification__) +# define COMPILER_VERSION_TWEAK DEC(__open_xl_ptf_fix_level__) +# define COMPILER_VERSION_INTERNAL_STR __clang_version__ + + +#elif defined(__ibmxl__) && defined(__clang__) +# define COMPILER_ID "XLClang" +# define COMPILER_VERSION_MAJOR DEC(__ibmxl_version__) +# define COMPILER_VERSION_MINOR DEC(__ibmxl_release__) +# define COMPILER_VERSION_PATCH DEC(__ibmxl_modification__) +# define COMPILER_VERSION_TWEAK DEC(__ibmxl_ptf_fix_level__) + + +#elif defined(__IBMC__) && !defined(__COMPILER_VER__) && __IBMC__ >= 800 +# define COMPILER_ID "XL" + /* __IBMC__ = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__IBMC__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMC__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMC__ % 10) + +#elif defined(__IBMC__) && !defined(__COMPILER_VER__) && __IBMC__ < 800 +# define COMPILER_ID "VisualAge" + /* __IBMC__ = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__IBMC__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMC__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMC__ % 10) + +#elif defined(__NVCOMPILER) +# define COMPILER_ID "NVHPC" +# define COMPILER_VERSION_MAJOR DEC(__NVCOMPILER_MAJOR__) +# define COMPILER_VERSION_MINOR DEC(__NVCOMPILER_MINOR__) +# if defined(__NVCOMPILER_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__NVCOMPILER_PATCHLEVEL__) +# endif + +#elif defined(__PGI) +# define COMPILER_ID "PGI" +# define COMPILER_VERSION_MAJOR DEC(__PGIC__) +# define COMPILER_VERSION_MINOR DEC(__PGIC_MINOR__) +# if defined(__PGIC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__PGIC_PATCHLEVEL__) +# endif + +#elif defined(__clang__) && defined(__cray__) +# define COMPILER_ID "CrayClang" +# define COMPILER_VERSION_MAJOR DEC(__cray_major__) +# define COMPILER_VERSION_MINOR DEC(__cray_minor__) +# define COMPILER_VERSION_PATCH DEC(__cray_patchlevel__) +# define COMPILER_VERSION_INTERNAL_STR __clang_version__ + + +#elif defined(_CRAYC) +# define COMPILER_ID "Cray" +# define COMPILER_VERSION_MAJOR DEC(_RELEASE_MAJOR) +# define COMPILER_VERSION_MINOR DEC(_RELEASE_MINOR) + +#elif defined(__TI_COMPILER_VERSION__) +# define COMPILER_ID "TI" + /* __TI_COMPILER_VERSION__ = VVVRRRPPP */ +# define COMPILER_VERSION_MAJOR DEC(__TI_COMPILER_VERSION__/1000000) +# define COMPILER_VERSION_MINOR DEC(__TI_COMPILER_VERSION__/1000 % 1000) +# define COMPILER_VERSION_PATCH DEC(__TI_COMPILER_VERSION__ % 1000) + +#elif defined(__CLANG_FUJITSU) +# define COMPILER_ID "FujitsuClang" +# define COMPILER_VERSION_MAJOR DEC(__FCC_major__) +# define COMPILER_VERSION_MINOR DEC(__FCC_minor__) +# define COMPILER_VERSION_PATCH DEC(__FCC_patchlevel__) +# define COMPILER_VERSION_INTERNAL_STR __clang_version__ + + +#elif defined(__FUJITSU) +# define COMPILER_ID "Fujitsu" +# if defined(__FCC_version__) +# define COMPILER_VERSION __FCC_version__ +# elif defined(__FCC_major__) +# define COMPILER_VERSION_MAJOR DEC(__FCC_major__) +# define COMPILER_VERSION_MINOR DEC(__FCC_minor__) +# define COMPILER_VERSION_PATCH DEC(__FCC_patchlevel__) +# endif +# if defined(__fcc_version) +# define COMPILER_VERSION_INTERNAL DEC(__fcc_version) +# elif defined(__FCC_VERSION) +# define COMPILER_VERSION_INTERNAL DEC(__FCC_VERSION) +# endif + + +#elif defined(__ghs__) +# define COMPILER_ID "GHS" +/* __GHS_VERSION_NUMBER = VVVVRP */ +# ifdef __GHS_VERSION_NUMBER +# define COMPILER_VERSION_MAJOR DEC(__GHS_VERSION_NUMBER / 100) +# define COMPILER_VERSION_MINOR DEC(__GHS_VERSION_NUMBER / 10 % 10) +# define COMPILER_VERSION_PATCH DEC(__GHS_VERSION_NUMBER % 10) +# endif + +#elif defined(__TASKING__) +# define COMPILER_ID "Tasking" + # define COMPILER_VERSION_MAJOR DEC(__VERSION__/1000) + # define COMPILER_VERSION_MINOR DEC(__VERSION__ % 100) +# define COMPILER_VERSION_INTERNAL DEC(__VERSION__) + +#elif defined(__ORANGEC__) +# define COMPILER_ID "OrangeC" +# define COMPILER_VERSION_MAJOR DEC(__ORANGEC_MAJOR__) +# define COMPILER_VERSION_MINOR DEC(__ORANGEC_MINOR__) +# define COMPILER_VERSION_PATCH DEC(__ORANGEC_PATCHLEVEL__) + +#elif defined(__RENESAS__) +# define COMPILER_ID "Renesas" +/* __RENESAS_VERSION__ = 0xVVRRPP00 */ +# define COMPILER_VERSION_MAJOR HEX(__RENESAS_VERSION__ >> 24 & 0xFF) +# define COMPILER_VERSION_MINOR HEX(__RENESAS_VERSION__ >> 16 & 0xFF) +# define COMPILER_VERSION_PATCH HEX(__RENESAS_VERSION__ >> 8 & 0xFF) + +#elif defined(__TINYC__) +# define COMPILER_ID "TinyCC" + +#elif defined(__BCC__) +# define COMPILER_ID "Bruce" + +#elif defined(__SCO_VERSION__) +# define COMPILER_ID "SCO" + +#elif defined(__ARMCC_VERSION) && !defined(__clang__) +# define COMPILER_ID "ARMCC" +#if __ARMCC_VERSION >= 1000000 + /* __ARMCC_VERSION = VRRPPPP */ + # define COMPILER_VERSION_MAJOR DEC(__ARMCC_VERSION/1000000) + # define COMPILER_VERSION_MINOR DEC(__ARMCC_VERSION/10000 % 100) + # define COMPILER_VERSION_PATCH DEC(__ARMCC_VERSION % 10000) +#else + /* __ARMCC_VERSION = VRPPPP */ + # define COMPILER_VERSION_MAJOR DEC(__ARMCC_VERSION/100000) + # define COMPILER_VERSION_MINOR DEC(__ARMCC_VERSION/10000 % 10) + # define COMPILER_VERSION_PATCH DEC(__ARMCC_VERSION % 10000) +#endif + + +#elif defined(__clang__) && defined(__apple_build_version__) +# define COMPILER_ID "AppleClang" +# if defined(_MSC_VER) +# define SIMULATE_ID "MSVC" +# endif +# define COMPILER_VERSION_MAJOR DEC(__clang_major__) +# define COMPILER_VERSION_MINOR DEC(__clang_minor__) +# define COMPILER_VERSION_PATCH DEC(__clang_patchlevel__) +# if defined(_MSC_VER) + /* _MSC_VER = VVRR */ +# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100) +# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100) +# endif +# define COMPILER_VERSION_TWEAK DEC(__apple_build_version__) + +#elif defined(__clang__) && defined(__ARMCOMPILER_VERSION) +# define COMPILER_ID "ARMClang" + # define COMPILER_VERSION_MAJOR DEC(__ARMCOMPILER_VERSION/1000000) + # define COMPILER_VERSION_MINOR DEC(__ARMCOMPILER_VERSION/10000 % 100) + # define COMPILER_VERSION_PATCH DEC(__ARMCOMPILER_VERSION/100 % 100) +# define COMPILER_VERSION_INTERNAL DEC(__ARMCOMPILER_VERSION) + +#elif defined(__clang__) && defined(__ti__) +# define COMPILER_ID "TIClang" + # define COMPILER_VERSION_MAJOR DEC(__ti_major__) + # define COMPILER_VERSION_MINOR DEC(__ti_minor__) + # define COMPILER_VERSION_PATCH DEC(__ti_patchlevel__) +# define COMPILER_VERSION_INTERNAL DEC(__ti_version__) + +#elif defined(__clang__) +# define COMPILER_ID "Clang" +# if defined(_MSC_VER) +# define SIMULATE_ID "MSVC" +# endif +# define COMPILER_VERSION_MAJOR DEC(__clang_major__) +# define COMPILER_VERSION_MINOR DEC(__clang_minor__) +# define COMPILER_VERSION_PATCH DEC(__clang_patchlevel__) +# if defined(_MSC_VER) + /* _MSC_VER = VVRR */ +# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100) +# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100) +# endif + +#elif defined(__LCC__) && (defined(__GNUC__) || defined(__GNUG__) || defined(__MCST__)) +# define COMPILER_ID "LCC" +# define COMPILER_VERSION_MAJOR DEC(__LCC__ / 100) +# define COMPILER_VERSION_MINOR DEC(__LCC__ % 100) +# if defined(__LCC_MINOR__) +# define COMPILER_VERSION_PATCH DEC(__LCC_MINOR__) +# endif +# if defined(__GNUC__) && defined(__GNUC_MINOR__) +# define SIMULATE_ID "GNU" +# define SIMULATE_VERSION_MAJOR DEC(__GNUC__) +# define SIMULATE_VERSION_MINOR DEC(__GNUC_MINOR__) +# if defined(__GNUC_PATCHLEVEL__) +# define SIMULATE_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__) +# endif +# endif + +#elif defined(__GNUC__) +# define COMPILER_ID "GNU" +# define COMPILER_VERSION_MAJOR DEC(__GNUC__) +# if defined(__GNUC_MINOR__) +# define COMPILER_VERSION_MINOR DEC(__GNUC_MINOR__) +# endif +# if defined(__GNUC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__) +# endif + +#elif defined(_MSC_VER) +# define COMPILER_ID "MSVC" + /* _MSC_VER = VVRR */ +# define COMPILER_VERSION_MAJOR DEC(_MSC_VER / 100) +# define COMPILER_VERSION_MINOR DEC(_MSC_VER % 100) +# if defined(_MSC_FULL_VER) +# if _MSC_VER >= 1400 + /* _MSC_FULL_VER = VVRRPPPPP */ +# define COMPILER_VERSION_PATCH DEC(_MSC_FULL_VER % 100000) +# else + /* _MSC_FULL_VER = VVRRPPPP */ +# define COMPILER_VERSION_PATCH DEC(_MSC_FULL_VER % 10000) +# endif +# endif +# if defined(_MSC_BUILD) +# define COMPILER_VERSION_TWEAK DEC(_MSC_BUILD) +# endif + +#elif defined(_ADI_COMPILER) +# define COMPILER_ID "ADSP" +#if defined(__VERSIONNUM__) + /* __VERSIONNUM__ = 0xVVRRPPTT */ +# define COMPILER_VERSION_MAJOR DEC(__VERSIONNUM__ >> 24 & 0xFF) +# define COMPILER_VERSION_MINOR DEC(__VERSIONNUM__ >> 16 & 0xFF) +# define COMPILER_VERSION_PATCH DEC(__VERSIONNUM__ >> 8 & 0xFF) +# define COMPILER_VERSION_TWEAK DEC(__VERSIONNUM__ & 0xFF) +#endif + +#elif defined(__IAR_SYSTEMS_ICC__) || defined(__IAR_SYSTEMS_ICC) +# define COMPILER_ID "IAR" +# if defined(__VER__) && defined(__ICCARM__) +# define COMPILER_VERSION_MAJOR DEC((__VER__) / 1000000) +# define COMPILER_VERSION_MINOR DEC(((__VER__) / 1000) % 1000) +# define COMPILER_VERSION_PATCH DEC((__VER__) % 1000) +# define COMPILER_VERSION_INTERNAL DEC(__IAR_SYSTEMS_ICC__) +# elif defined(__VER__) && (defined(__ICCAVR__) || defined(__ICCRX__) || defined(__ICCRH850__) || defined(__ICCRL78__) || defined(__ICC430__) || defined(__ICCRISCV__) || defined(__ICCV850__) || defined(__ICC8051__) || defined(__ICCSTM8__)) +# define COMPILER_VERSION_MAJOR DEC((__VER__) / 100) +# define COMPILER_VERSION_MINOR DEC((__VER__) - (((__VER__) / 100)*100)) +# define COMPILER_VERSION_PATCH DEC(__SUBVERSION__) +# define COMPILER_VERSION_INTERNAL DEC(__IAR_SYSTEMS_ICC__) +# endif + +#elif defined(__DCC__) && defined(_DIAB_TOOL) +# define COMPILER_ID "Diab" + # define COMPILER_VERSION_MAJOR DEC(__VERSION_MAJOR_NUMBER__) + # define COMPILER_VERSION_MINOR DEC(__VERSION_MINOR_NUMBER__) + # define COMPILER_VERSION_PATCH DEC(__VERSION_ARCH_FEATURE_NUMBER__) + # define COMPILER_VERSION_TWEAK DEC(__VERSION_BUG_FIX_NUMBER__) + + +#elif defined(__SDCC_VERSION_MAJOR) || defined(SDCC) +# define COMPILER_ID "SDCC" +# if defined(__SDCC_VERSION_MAJOR) +# define COMPILER_VERSION_MAJOR DEC(__SDCC_VERSION_MAJOR) +# define COMPILER_VERSION_MINOR DEC(__SDCC_VERSION_MINOR) +# define COMPILER_VERSION_PATCH DEC(__SDCC_VERSION_PATCH) +# else + /* SDCC = VRP */ +# define COMPILER_VERSION_MAJOR DEC(SDCC/100) +# define COMPILER_VERSION_MINOR DEC(SDCC/10 % 10) +# define COMPILER_VERSION_PATCH DEC(SDCC % 10) +# endif + + +/* These compilers are either not known or too old to define an + identification macro. Try to identify the platform and guess that + it is the native compiler. */ +#elif defined(__hpux) || defined(__hpua) +# define COMPILER_ID "HP" + +#else /* unknown compiler */ +# define COMPILER_ID "" +#endif + +/* Construct the string literal in pieces to prevent the source from + getting matched. Store it in a pointer rather than an array + because some compilers will just produce instructions to fill the + array rather than assigning a pointer to a static array. */ +char const* info_compiler = "INFO" ":" "compiler[" COMPILER_ID "]"; +#ifdef SIMULATE_ID +char const* info_simulate = "INFO" ":" "simulate[" SIMULATE_ID "]"; +#endif + +#ifdef __QNXNTO__ +char const* qnxnto = "INFO" ":" "qnxnto[]"; +#endif + +#if defined(__CRAYXT_COMPUTE_LINUX_TARGET) +char const *info_cray = "INFO" ":" "compiler_wrapper[CrayPrgEnv]"; +#endif + +#define STRINGIFY_HELPER(X) #X +#define STRINGIFY(X) STRINGIFY_HELPER(X) + +/* Identify known platforms by name. */ +#if defined(__linux) || defined(__linux__) || defined(linux) +# define PLATFORM_ID "Linux" + +#elif defined(__MSYS__) +# define PLATFORM_ID "MSYS" + +#elif defined(__CYGWIN__) +# define PLATFORM_ID "Cygwin" + +#elif defined(__MINGW32__) +# define PLATFORM_ID "MinGW" + +#elif defined(__APPLE__) +# define PLATFORM_ID "Darwin" + +#elif defined(_WIN32) || defined(__WIN32__) || defined(WIN32) +# define PLATFORM_ID "Windows" + +#elif defined(__FreeBSD__) || defined(__FreeBSD) +# define PLATFORM_ID "FreeBSD" + +#elif defined(__NetBSD__) || defined(__NetBSD) +# define PLATFORM_ID "NetBSD" + +#elif defined(__OpenBSD__) || defined(__OPENBSD) +# define PLATFORM_ID "OpenBSD" + +#elif defined(__sun) || defined(sun) +# define PLATFORM_ID "SunOS" + +#elif defined(_AIX) || defined(__AIX) || defined(__AIX__) || defined(__aix) || defined(__aix__) +# define PLATFORM_ID "AIX" + +#elif defined(__hpux) || defined(__hpux__) +# define PLATFORM_ID "HP-UX" + +#elif defined(__HAIKU__) +# define PLATFORM_ID "Haiku" + +#elif defined(__BeOS) || defined(__BEOS__) || defined(_BEOS) +# define PLATFORM_ID "BeOS" + +#elif defined(__QNX__) || defined(__QNXNTO__) +# define PLATFORM_ID "QNX" + +#elif defined(__tru64) || defined(_tru64) || defined(__TRU64__) +# define PLATFORM_ID "Tru64" + +#elif defined(__riscos) || defined(__riscos__) +# define PLATFORM_ID "RISCos" + +#elif defined(__sinix) || defined(__sinix__) || defined(__SINIX__) +# define PLATFORM_ID "SINIX" + +#elif defined(__UNIX_SV__) +# define PLATFORM_ID "UNIX_SV" + +#elif defined(__bsdos__) +# define PLATFORM_ID "BSDOS" + +#elif defined(_MPRAS) || defined(MPRAS) +# define PLATFORM_ID "MP-RAS" + +#elif defined(__osf) || defined(__osf__) +# define PLATFORM_ID "OSF1" + +#elif defined(_SCO_SV) || defined(SCO_SV) || defined(sco_sv) +# define PLATFORM_ID "SCO_SV" + +#elif defined(__ultrix) || defined(__ultrix__) || defined(_ULTRIX) +# define PLATFORM_ID "ULTRIX" + +#elif defined(__XENIX__) || defined(_XENIX) || defined(XENIX) +# define PLATFORM_ID "Xenix" + +#elif defined(__WATCOMC__) +# if defined(__LINUX__) +# define PLATFORM_ID "Linux" + +# elif defined(__DOS__) +# define PLATFORM_ID "DOS" + +# elif defined(__OS2__) +# define PLATFORM_ID "OS2" + +# elif defined(__WINDOWS__) +# define PLATFORM_ID "Windows3x" + +# elif defined(__VXWORKS__) +# define PLATFORM_ID "VxWorks" + +# else /* unknown platform */ +# define PLATFORM_ID +# endif + +#elif defined(__INTEGRITY) +# if defined(INT_178B) +# define PLATFORM_ID "Integrity178" + +# else /* regular Integrity */ +# define PLATFORM_ID "Integrity" +# endif + +# elif defined(_ADI_COMPILER) +# define PLATFORM_ID "ADSP" + +#else /* unknown platform */ +# define PLATFORM_ID + +#endif + +/* For windows compilers MSVC and Intel we can determine + the architecture of the compiler being used. This is because + the compilers do not have flags that can change the architecture, + but rather depend on which compiler is being used +*/ +#if defined(_WIN32) && defined(_MSC_VER) +# if defined(_M_IA64) +# define ARCHITECTURE_ID "IA64" + +# elif defined(_M_ARM64EC) +# define ARCHITECTURE_ID "ARM64EC" + +# elif defined(_M_X64) || defined(_M_AMD64) +# define ARCHITECTURE_ID "x64" + +# elif defined(_M_IX86) +# define ARCHITECTURE_ID "X86" + +# elif defined(_M_ARM64) +# define ARCHITECTURE_ID "ARM64" + +# elif defined(_M_ARM) +# if _M_ARM == 4 +# define ARCHITECTURE_ID "ARMV4I" +# elif _M_ARM == 5 +# define ARCHITECTURE_ID "ARMV5I" +# else +# define ARCHITECTURE_ID "ARMV" STRINGIFY(_M_ARM) +# endif + +# elif defined(_M_MIPS) +# define ARCHITECTURE_ID "MIPS" + +# elif defined(_M_SH) +# define ARCHITECTURE_ID "SHx" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__WATCOMC__) +# if defined(_M_I86) +# define ARCHITECTURE_ID "I86" + +# elif defined(_M_IX86) +# define ARCHITECTURE_ID "X86" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__IAR_SYSTEMS_ICC__) || defined(__IAR_SYSTEMS_ICC) +# if defined(__ICCARM__) +# define ARCHITECTURE_ID "ARM" + +# elif defined(__ICCRX__) +# define ARCHITECTURE_ID "RX" + +# elif defined(__ICCRH850__) +# define ARCHITECTURE_ID "RH850" + +# elif defined(__ICCRL78__) +# define ARCHITECTURE_ID "RL78" + +# elif defined(__ICCRISCV__) +# define ARCHITECTURE_ID "RISCV" + +# elif defined(__ICCAVR__) +# define ARCHITECTURE_ID "AVR" + +# elif defined(__ICC430__) +# define ARCHITECTURE_ID "MSP430" + +# elif defined(__ICCV850__) +# define ARCHITECTURE_ID "V850" + +# elif defined(__ICC8051__) +# define ARCHITECTURE_ID "8051" + +# elif defined(__ICCSTM8__) +# define ARCHITECTURE_ID "STM8" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__ghs__) +# if defined(__PPC64__) +# define ARCHITECTURE_ID "PPC64" + +# elif defined(__ppc__) +# define ARCHITECTURE_ID "PPC" + +# elif defined(__ARM__) +# define ARCHITECTURE_ID "ARM" + +# elif defined(__x86_64__) +# define ARCHITECTURE_ID "x64" + +# elif defined(__i386__) +# define ARCHITECTURE_ID "X86" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__clang__) && defined(__ti__) +# if defined(__ARM_ARCH) +# define ARCHITECTURE_ID "ARM" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__TI_COMPILER_VERSION__) +# if defined(__TI_ARM__) +# define ARCHITECTURE_ID "ARM" + +# elif defined(__MSP430__) +# define ARCHITECTURE_ID "MSP430" + +# elif defined(__TMS320C28XX__) +# define ARCHITECTURE_ID "TMS320C28x" + +# elif defined(__TMS320C6X__) || defined(_TMS320C6X) +# define ARCHITECTURE_ID "TMS320C6x" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +# elif defined(__ADSPSHARC__) +# define ARCHITECTURE_ID "SHARC" + +# elif defined(__ADSPBLACKFIN__) +# define ARCHITECTURE_ID "Blackfin" + +#elif defined(__TASKING__) + +# if defined(__CTC__) || defined(__CPTC__) +# define ARCHITECTURE_ID "TriCore" + +# elif defined(__CMCS__) +# define ARCHITECTURE_ID "MCS" + +# elif defined(__CARM__) || defined(__CPARM__) +# define ARCHITECTURE_ID "ARM" + +# elif defined(__CARC__) +# define ARCHITECTURE_ID "ARC" + +# elif defined(__C51__) +# define ARCHITECTURE_ID "8051" + +# elif defined(__CPCP__) +# define ARCHITECTURE_ID "PCP" + +# else +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__RENESAS__) +# if defined(__CCRX__) +# define ARCHITECTURE_ID "RX" + +# elif defined(__CCRL__) +# define ARCHITECTURE_ID "RL78" + +# elif defined(__CCRH__) +# define ARCHITECTURE_ID "RH850" + +# else +# define ARCHITECTURE_ID "" +# endif + +#else +# define ARCHITECTURE_ID +#endif + +/* Convert integer to decimal digit literals. */ +#define DEC(n) \ + ('0' + (((n) / 10000000)%10)), \ + ('0' + (((n) / 1000000)%10)), \ + ('0' + (((n) / 100000)%10)), \ + ('0' + (((n) / 10000)%10)), \ + ('0' + (((n) / 1000)%10)), \ + ('0' + (((n) / 100)%10)), \ + ('0' + (((n) / 10)%10)), \ + ('0' + ((n) % 10)) + +/* Convert integer to hex digit literals. */ +#define HEX(n) \ + ('0' + ((n)>>28 & 0xF)), \ + ('0' + ((n)>>24 & 0xF)), \ + ('0' + ((n)>>20 & 0xF)), \ + ('0' + ((n)>>16 & 0xF)), \ + ('0' + ((n)>>12 & 0xF)), \ + ('0' + ((n)>>8 & 0xF)), \ + ('0' + ((n)>>4 & 0xF)), \ + ('0' + ((n) & 0xF)) + +/* Construct a string literal encoding the version number. */ +#ifdef COMPILER_VERSION +char const* info_version = "INFO" ":" "compiler_version[" COMPILER_VERSION "]"; + +/* Construct a string literal encoding the version number components. */ +#elif defined(COMPILER_VERSION_MAJOR) +char const info_version[] = { + 'I', 'N', 'F', 'O', ':', + 'c','o','m','p','i','l','e','r','_','v','e','r','s','i','o','n','[', + COMPILER_VERSION_MAJOR, +# ifdef COMPILER_VERSION_MINOR + '.', COMPILER_VERSION_MINOR, +# ifdef COMPILER_VERSION_PATCH + '.', COMPILER_VERSION_PATCH, +# ifdef COMPILER_VERSION_TWEAK + '.', COMPILER_VERSION_TWEAK, +# endif +# endif +# endif + ']','\0'}; +#endif + +/* Construct a string literal encoding the internal version number. */ +#ifdef COMPILER_VERSION_INTERNAL +char const info_version_internal[] = { + 'I', 'N', 'F', 'O', ':', + 'c','o','m','p','i','l','e','r','_','v','e','r','s','i','o','n','_', + 'i','n','t','e','r','n','a','l','[', + COMPILER_VERSION_INTERNAL,']','\0'}; +#elif defined(COMPILER_VERSION_INTERNAL_STR) +char const* info_version_internal = "INFO" ":" "compiler_version_internal[" COMPILER_VERSION_INTERNAL_STR "]"; +#endif + +/* Construct a string literal encoding the version number components. */ +#ifdef SIMULATE_VERSION_MAJOR +char const info_simulate_version[] = { + 'I', 'N', 'F', 'O', ':', + 's','i','m','u','l','a','t','e','_','v','e','r','s','i','o','n','[', + SIMULATE_VERSION_MAJOR, +# ifdef SIMULATE_VERSION_MINOR + '.', SIMULATE_VERSION_MINOR, +# ifdef SIMULATE_VERSION_PATCH + '.', SIMULATE_VERSION_PATCH, +# ifdef SIMULATE_VERSION_TWEAK + '.', SIMULATE_VERSION_TWEAK, +# endif +# endif +# endif + ']','\0'}; +#endif + +/* Construct the string literal in pieces to prevent the source from + getting matched. Store it in a pointer rather than an array + because some compilers will just produce instructions to fill the + array rather than assigning a pointer to a static array. */ +char const* info_platform = "INFO" ":" "platform[" PLATFORM_ID "]"; +char const* info_arch = "INFO" ":" "arch[" ARCHITECTURE_ID "]"; + + + +#define C_STD_99 199901L +#define C_STD_11 201112L +#define C_STD_17 201710L +#define C_STD_23 202311L + +#ifdef __STDC_VERSION__ +# define C_STD __STDC_VERSION__ +#endif + +#if !defined(__STDC__) && !defined(__clang__) && !defined(__RENESAS__) +# if defined(_MSC_VER) || defined(__ibmxl__) || defined(__IBMC__) +# define C_VERSION "90" +# else +# define C_VERSION +# endif +#elif C_STD > C_STD_17 +# define C_VERSION "23" +#elif C_STD > C_STD_11 +# define C_VERSION "17" +#elif C_STD > C_STD_99 +# define C_VERSION "11" +#elif C_STD >= C_STD_99 +# define C_VERSION "99" +#else +# define C_VERSION "90" +#endif +const char* info_language_standard_default = + "INFO" ":" "standard_default[" C_VERSION "]"; + +const char* info_language_extensions_default = "INFO" ":" "extensions_default[" +#if (defined(__clang__) || defined(__GNUC__) || defined(__xlC__) || \ + defined(__TI_COMPILER_VERSION__) || defined(__RENESAS__)) && \ + !defined(__STRICT_ANSI__) + "ON" +#else + "OFF" +#endif +"]"; + +/*--------------------------------------------------------------------------*/ + +#ifdef ID_VOID_MAIN +void main() {} +#else +# if defined(__CLASSIC_C__) +int main(argc, argv) int argc; char *argv[]; +# else +int main(int argc, char* argv[]) +# endif +{ + int require = 0; + require += info_compiler[argc]; + require += info_platform[argc]; + require += info_arch[argc]; +#ifdef COMPILER_VERSION_MAJOR + require += info_version[argc]; +#endif +#if defined(COMPILER_VERSION_INTERNAL) || defined(COMPILER_VERSION_INTERNAL_STR) + require += info_version_internal[argc]; +#endif +#ifdef SIMULATE_ID + require += info_simulate[argc]; +#endif +#ifdef SIMULATE_VERSION_MAJOR + require += info_simulate_version[argc]; +#endif +#if defined(__CRAYXT_COMPUTE_LINUX_TARGET) + require += info_cray[argc]; +#endif + require += info_language_standard_default[argc]; + require += info_language_extensions_default[argc]; + (void)argv; + return require; +} +#endif diff --git a/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdC/a.out b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdC/a.out new file mode 100755 index 0000000..04ad807 Binary files /dev/null and b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdC/a.out differ diff --git a/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdC/apple-sdk.c b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdC/apple-sdk.c new file mode 100644 index 0000000..db846b4 --- /dev/null +++ b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdC/apple-sdk.c @@ -0,0 +1 @@ +#include diff --git a/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdCXX/CMakeCXXCompilerId.cpp b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdCXX/CMakeCXXCompilerId.cpp new file mode 100644 index 0000000..b35f567 --- /dev/null +++ b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdCXX/CMakeCXXCompilerId.cpp @@ -0,0 +1,949 @@ +/* This source file must have a .cpp extension so that all C++ compilers + recognize the extension without flags. Borland does not know .cxx for + example. */ +#ifndef __cplusplus +# error "A C compiler has been selected for C++." +#endif + +#if !defined(__has_include) +/* If the compiler does not have __has_include, pretend the answer is + always no. */ +# define __has_include(x) 0 +#endif + + +/* Version number components: V=Version, R=Revision, P=Patch + Version date components: YYYY=Year, MM=Month, DD=Day */ + +#if defined(__INTEL_COMPILER) || defined(__ICC) +# define COMPILER_ID "Intel" +# if defined(_MSC_VER) +# define SIMULATE_ID "MSVC" +# endif +# if defined(__GNUC__) +# define SIMULATE_ID "GNU" +# endif + /* __INTEL_COMPILER = VRP prior to 2021, and then VVVV for 2021 and later, + except that a few beta releases use the old format with V=2021. */ +# if __INTEL_COMPILER < 2021 || __INTEL_COMPILER == 202110 || __INTEL_COMPILER == 202111 +# define COMPILER_VERSION_MAJOR DEC(__INTEL_COMPILER/100) +# define COMPILER_VERSION_MINOR DEC(__INTEL_COMPILER/10 % 10) +# if defined(__INTEL_COMPILER_UPDATE) +# define COMPILER_VERSION_PATCH DEC(__INTEL_COMPILER_UPDATE) +# else +# define COMPILER_VERSION_PATCH DEC(__INTEL_COMPILER % 10) +# endif +# else +# define COMPILER_VERSION_MAJOR DEC(__INTEL_COMPILER) +# define COMPILER_VERSION_MINOR DEC(__INTEL_COMPILER_UPDATE) + /* The third version component from --version is an update index, + but no macro is provided for it. */ +# define COMPILER_VERSION_PATCH DEC(0) +# endif +# if defined(__INTEL_COMPILER_BUILD_DATE) + /* __INTEL_COMPILER_BUILD_DATE = YYYYMMDD */ +# define COMPILER_VERSION_TWEAK DEC(__INTEL_COMPILER_BUILD_DATE) +# endif +# if defined(_MSC_VER) + /* _MSC_VER = VVRR */ +# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100) +# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100) +# endif +# if defined(__GNUC__) +# define SIMULATE_VERSION_MAJOR DEC(__GNUC__) +# elif defined(__GNUG__) +# define SIMULATE_VERSION_MAJOR DEC(__GNUG__) +# endif +# if defined(__GNUC_MINOR__) +# define SIMULATE_VERSION_MINOR DEC(__GNUC_MINOR__) +# endif +# if defined(__GNUC_PATCHLEVEL__) +# define SIMULATE_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__) +# endif + +#elif (defined(__clang__) && defined(__INTEL_CLANG_COMPILER)) || defined(__INTEL_LLVM_COMPILER) +# define COMPILER_ID "IntelLLVM" +#if defined(_MSC_VER) +# define SIMULATE_ID "MSVC" +#endif +#if defined(__GNUC__) +# define SIMULATE_ID "GNU" +#endif +/* __INTEL_LLVM_COMPILER = VVVVRP prior to 2021.2.0, VVVVRRPP for 2021.2.0 and + * later. Look for 6 digit vs. 8 digit version number to decide encoding. + * VVVV is no smaller than the current year when a version is released. + */ +#if __INTEL_LLVM_COMPILER < 1000000L +# define COMPILER_VERSION_MAJOR DEC(__INTEL_LLVM_COMPILER/100) +# define COMPILER_VERSION_MINOR DEC(__INTEL_LLVM_COMPILER/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__INTEL_LLVM_COMPILER % 10) +#else +# define COMPILER_VERSION_MAJOR DEC(__INTEL_LLVM_COMPILER/10000) +# define COMPILER_VERSION_MINOR DEC(__INTEL_LLVM_COMPILER/100 % 100) +# define COMPILER_VERSION_PATCH DEC(__INTEL_LLVM_COMPILER % 100) +#endif +#if defined(_MSC_VER) + /* _MSC_VER = VVRR */ +# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100) +# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100) +#endif +#if defined(__GNUC__) +# define SIMULATE_VERSION_MAJOR DEC(__GNUC__) +#elif defined(__GNUG__) +# define SIMULATE_VERSION_MAJOR DEC(__GNUG__) +#endif +#if defined(__GNUC_MINOR__) +# define SIMULATE_VERSION_MINOR DEC(__GNUC_MINOR__) +#endif +#if defined(__GNUC_PATCHLEVEL__) +# define SIMULATE_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__) +#endif + +#elif defined(__PATHCC__) +# define COMPILER_ID "PathScale" +# define COMPILER_VERSION_MAJOR DEC(__PATHCC__) +# define COMPILER_VERSION_MINOR DEC(__PATHCC_MINOR__) +# if defined(__PATHCC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__PATHCC_PATCHLEVEL__) +# endif + +#elif defined(__BORLANDC__) && defined(__CODEGEARC_VERSION__) +# define COMPILER_ID "Embarcadero" +# define COMPILER_VERSION_MAJOR HEX(__CODEGEARC_VERSION__>>24 & 0x00FF) +# define COMPILER_VERSION_MINOR HEX(__CODEGEARC_VERSION__>>16 & 0x00FF) +# define COMPILER_VERSION_PATCH DEC(__CODEGEARC_VERSION__ & 0xFFFF) + +#elif defined(__BORLANDC__) +# define COMPILER_ID "Borland" + /* __BORLANDC__ = 0xVRR */ +# define COMPILER_VERSION_MAJOR HEX(__BORLANDC__>>8) +# define COMPILER_VERSION_MINOR HEX(__BORLANDC__ & 0xFF) + +#elif defined(__WATCOMC__) && __WATCOMC__ < 1200 +# define COMPILER_ID "Watcom" + /* __WATCOMC__ = VVRR */ +# define COMPILER_VERSION_MAJOR DEC(__WATCOMC__ / 100) +# define COMPILER_VERSION_MINOR DEC((__WATCOMC__ / 10) % 10) +# if (__WATCOMC__ % 10) > 0 +# define COMPILER_VERSION_PATCH DEC(__WATCOMC__ % 10) +# endif + +#elif defined(__WATCOMC__) +# define COMPILER_ID "OpenWatcom" + /* __WATCOMC__ = VVRP + 1100 */ +# define COMPILER_VERSION_MAJOR DEC((__WATCOMC__ - 1100) / 100) +# define COMPILER_VERSION_MINOR DEC((__WATCOMC__ / 10) % 10) +# if (__WATCOMC__ % 10) > 0 +# define COMPILER_VERSION_PATCH DEC(__WATCOMC__ % 10) +# endif + +#elif defined(__SUNPRO_CC) +# define COMPILER_ID "SunPro" +# if __SUNPRO_CC >= 0x5100 + /* __SUNPRO_CC = 0xVRRP */ +# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_CC>>12) +# define COMPILER_VERSION_MINOR HEX(__SUNPRO_CC>>4 & 0xFF) +# define COMPILER_VERSION_PATCH HEX(__SUNPRO_CC & 0xF) +# else + /* __SUNPRO_CC = 0xVRP */ +# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_CC>>8) +# define COMPILER_VERSION_MINOR HEX(__SUNPRO_CC>>4 & 0xF) +# define COMPILER_VERSION_PATCH HEX(__SUNPRO_CC & 0xF) +# endif + +#elif defined(__HP_aCC) +# define COMPILER_ID "HP" + /* __HP_aCC = VVRRPP */ +# define COMPILER_VERSION_MAJOR DEC(__HP_aCC/10000) +# define COMPILER_VERSION_MINOR DEC(__HP_aCC/100 % 100) +# define COMPILER_VERSION_PATCH DEC(__HP_aCC % 100) + +#elif defined(__DECCXX) +# define COMPILER_ID "Compaq" + /* __DECCXX_VER = VVRRTPPPP */ +# define COMPILER_VERSION_MAJOR DEC(__DECCXX_VER/10000000) +# define COMPILER_VERSION_MINOR DEC(__DECCXX_VER/100000 % 100) +# define COMPILER_VERSION_PATCH DEC(__DECCXX_VER % 10000) + +#elif defined(__IBMCPP__) && defined(__COMPILER_VER__) +# define COMPILER_ID "zOS" + /* __IBMCPP__ = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__IBMCPP__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMCPP__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMCPP__ % 10) + +#elif defined(__open_xl__) && defined(__clang__) +# define COMPILER_ID "IBMClang" +# define COMPILER_VERSION_MAJOR DEC(__open_xl_version__) +# define COMPILER_VERSION_MINOR DEC(__open_xl_release__) +# define COMPILER_VERSION_PATCH DEC(__open_xl_modification__) +# define COMPILER_VERSION_TWEAK DEC(__open_xl_ptf_fix_level__) +# define COMPILER_VERSION_INTERNAL_STR __clang_version__ + + +#elif defined(__ibmxl__) && defined(__clang__) +# define COMPILER_ID "XLClang" +# define COMPILER_VERSION_MAJOR DEC(__ibmxl_version__) +# define COMPILER_VERSION_MINOR DEC(__ibmxl_release__) +# define COMPILER_VERSION_PATCH DEC(__ibmxl_modification__) +# define COMPILER_VERSION_TWEAK DEC(__ibmxl_ptf_fix_level__) + + +#elif defined(__IBMCPP__) && !defined(__COMPILER_VER__) && __IBMCPP__ >= 800 +# define COMPILER_ID "XL" + /* __IBMCPP__ = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__IBMCPP__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMCPP__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMCPP__ % 10) + +#elif defined(__IBMCPP__) && !defined(__COMPILER_VER__) && __IBMCPP__ < 800 +# define COMPILER_ID "VisualAge" + /* __IBMCPP__ = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__IBMCPP__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMCPP__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMCPP__ % 10) + +#elif defined(__NVCOMPILER) +# define COMPILER_ID "NVHPC" +# define COMPILER_VERSION_MAJOR DEC(__NVCOMPILER_MAJOR__) +# define COMPILER_VERSION_MINOR DEC(__NVCOMPILER_MINOR__) +# if defined(__NVCOMPILER_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__NVCOMPILER_PATCHLEVEL__) +# endif + +#elif defined(__PGI) +# define COMPILER_ID "PGI" +# define COMPILER_VERSION_MAJOR DEC(__PGIC__) +# define COMPILER_VERSION_MINOR DEC(__PGIC_MINOR__) +# if defined(__PGIC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__PGIC_PATCHLEVEL__) +# endif + +#elif defined(__clang__) && defined(__cray__) +# define COMPILER_ID "CrayClang" +# define COMPILER_VERSION_MAJOR DEC(__cray_major__) +# define COMPILER_VERSION_MINOR DEC(__cray_minor__) +# define COMPILER_VERSION_PATCH DEC(__cray_patchlevel__) +# define COMPILER_VERSION_INTERNAL_STR __clang_version__ + + +#elif defined(_CRAYC) +# define COMPILER_ID "Cray" +# define COMPILER_VERSION_MAJOR DEC(_RELEASE_MAJOR) +# define COMPILER_VERSION_MINOR DEC(_RELEASE_MINOR) + +#elif defined(__TI_COMPILER_VERSION__) +# define COMPILER_ID "TI" + /* __TI_COMPILER_VERSION__ = VVVRRRPPP */ +# define COMPILER_VERSION_MAJOR DEC(__TI_COMPILER_VERSION__/1000000) +# define COMPILER_VERSION_MINOR DEC(__TI_COMPILER_VERSION__/1000 % 1000) +# define COMPILER_VERSION_PATCH DEC(__TI_COMPILER_VERSION__ % 1000) + +#elif defined(__CLANG_FUJITSU) +# define COMPILER_ID "FujitsuClang" +# define COMPILER_VERSION_MAJOR DEC(__FCC_major__) +# define COMPILER_VERSION_MINOR DEC(__FCC_minor__) +# define COMPILER_VERSION_PATCH DEC(__FCC_patchlevel__) +# define COMPILER_VERSION_INTERNAL_STR __clang_version__ + + +#elif defined(__FUJITSU) +# define COMPILER_ID "Fujitsu" +# if defined(__FCC_version__) +# define COMPILER_VERSION __FCC_version__ +# elif defined(__FCC_major__) +# define COMPILER_VERSION_MAJOR DEC(__FCC_major__) +# define COMPILER_VERSION_MINOR DEC(__FCC_minor__) +# define COMPILER_VERSION_PATCH DEC(__FCC_patchlevel__) +# endif +# if defined(__fcc_version) +# define COMPILER_VERSION_INTERNAL DEC(__fcc_version) +# elif defined(__FCC_VERSION) +# define COMPILER_VERSION_INTERNAL DEC(__FCC_VERSION) +# endif + + +#elif defined(__ghs__) +# define COMPILER_ID "GHS" +/* __GHS_VERSION_NUMBER = VVVVRP */ +# ifdef __GHS_VERSION_NUMBER +# define COMPILER_VERSION_MAJOR DEC(__GHS_VERSION_NUMBER / 100) +# define COMPILER_VERSION_MINOR DEC(__GHS_VERSION_NUMBER / 10 % 10) +# define COMPILER_VERSION_PATCH DEC(__GHS_VERSION_NUMBER % 10) +# endif + +#elif defined(__TASKING__) +# define COMPILER_ID "Tasking" + # define COMPILER_VERSION_MAJOR DEC(__VERSION__/1000) + # define COMPILER_VERSION_MINOR DEC(__VERSION__ % 100) +# define COMPILER_VERSION_INTERNAL DEC(__VERSION__) + +#elif defined(__ORANGEC__) +# define COMPILER_ID "OrangeC" +# define COMPILER_VERSION_MAJOR DEC(__ORANGEC_MAJOR__) +# define COMPILER_VERSION_MINOR DEC(__ORANGEC_MINOR__) +# define COMPILER_VERSION_PATCH DEC(__ORANGEC_PATCHLEVEL__) + +#elif defined(__RENESAS__) +# define COMPILER_ID "Renesas" +/* __RENESAS_VERSION__ = 0xVVRRPP00 */ +# define COMPILER_VERSION_MAJOR HEX(__RENESAS_VERSION__ >> 24 & 0xFF) +# define COMPILER_VERSION_MINOR HEX(__RENESAS_VERSION__ >> 16 & 0xFF) +# define COMPILER_VERSION_PATCH HEX(__RENESAS_VERSION__ >> 8 & 0xFF) + +#elif defined(__SCO_VERSION__) +# define COMPILER_ID "SCO" + +#elif defined(__ARMCC_VERSION) && !defined(__clang__) +# define COMPILER_ID "ARMCC" +#if __ARMCC_VERSION >= 1000000 + /* __ARMCC_VERSION = VRRPPPP */ + # define COMPILER_VERSION_MAJOR DEC(__ARMCC_VERSION/1000000) + # define COMPILER_VERSION_MINOR DEC(__ARMCC_VERSION/10000 % 100) + # define COMPILER_VERSION_PATCH DEC(__ARMCC_VERSION % 10000) +#else + /* __ARMCC_VERSION = VRPPPP */ + # define COMPILER_VERSION_MAJOR DEC(__ARMCC_VERSION/100000) + # define COMPILER_VERSION_MINOR DEC(__ARMCC_VERSION/10000 % 10) + # define COMPILER_VERSION_PATCH DEC(__ARMCC_VERSION % 10000) +#endif + + +#elif defined(__clang__) && defined(__apple_build_version__) +# define COMPILER_ID "AppleClang" +# if defined(_MSC_VER) +# define SIMULATE_ID "MSVC" +# endif +# define COMPILER_VERSION_MAJOR DEC(__clang_major__) +# define COMPILER_VERSION_MINOR DEC(__clang_minor__) +# define COMPILER_VERSION_PATCH DEC(__clang_patchlevel__) +# if defined(_MSC_VER) + /* _MSC_VER = VVRR */ +# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100) +# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100) +# endif +# define COMPILER_VERSION_TWEAK DEC(__apple_build_version__) + +#elif defined(__clang__) && defined(__ARMCOMPILER_VERSION) +# define COMPILER_ID "ARMClang" + # define COMPILER_VERSION_MAJOR DEC(__ARMCOMPILER_VERSION/1000000) + # define COMPILER_VERSION_MINOR DEC(__ARMCOMPILER_VERSION/10000 % 100) + # define COMPILER_VERSION_PATCH DEC(__ARMCOMPILER_VERSION/100 % 100) +# define COMPILER_VERSION_INTERNAL DEC(__ARMCOMPILER_VERSION) + +#elif defined(__clang__) && defined(__ti__) +# define COMPILER_ID "TIClang" + # define COMPILER_VERSION_MAJOR DEC(__ti_major__) + # define COMPILER_VERSION_MINOR DEC(__ti_minor__) + # define COMPILER_VERSION_PATCH DEC(__ti_patchlevel__) +# define COMPILER_VERSION_INTERNAL DEC(__ti_version__) + +#elif defined(__clang__) +# define COMPILER_ID "Clang" +# if defined(_MSC_VER) +# define SIMULATE_ID "MSVC" +# endif +# define COMPILER_VERSION_MAJOR DEC(__clang_major__) +# define COMPILER_VERSION_MINOR DEC(__clang_minor__) +# define COMPILER_VERSION_PATCH DEC(__clang_patchlevel__) +# if defined(_MSC_VER) + /* _MSC_VER = VVRR */ +# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100) +# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100) +# endif + +#elif defined(__LCC__) && (defined(__GNUC__) || defined(__GNUG__) || defined(__MCST__)) +# define COMPILER_ID "LCC" +# define COMPILER_VERSION_MAJOR DEC(__LCC__ / 100) +# define COMPILER_VERSION_MINOR DEC(__LCC__ % 100) +# if defined(__LCC_MINOR__) +# define COMPILER_VERSION_PATCH DEC(__LCC_MINOR__) +# endif +# if defined(__GNUC__) && defined(__GNUC_MINOR__) +# define SIMULATE_ID "GNU" +# define SIMULATE_VERSION_MAJOR DEC(__GNUC__) +# define SIMULATE_VERSION_MINOR DEC(__GNUC_MINOR__) +# if defined(__GNUC_PATCHLEVEL__) +# define SIMULATE_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__) +# endif +# endif + +#elif defined(__GNUC__) || defined(__GNUG__) +# define COMPILER_ID "GNU" +# if defined(__GNUC__) +# define COMPILER_VERSION_MAJOR DEC(__GNUC__) +# else +# define COMPILER_VERSION_MAJOR DEC(__GNUG__) +# endif +# if defined(__GNUC_MINOR__) +# define COMPILER_VERSION_MINOR DEC(__GNUC_MINOR__) +# endif +# if defined(__GNUC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__) +# endif + +#elif defined(_MSC_VER) +# define COMPILER_ID "MSVC" + /* _MSC_VER = VVRR */ +# define COMPILER_VERSION_MAJOR DEC(_MSC_VER / 100) +# define COMPILER_VERSION_MINOR DEC(_MSC_VER % 100) +# if defined(_MSC_FULL_VER) +# if _MSC_VER >= 1400 + /* _MSC_FULL_VER = VVRRPPPPP */ +# define COMPILER_VERSION_PATCH DEC(_MSC_FULL_VER % 100000) +# else + /* _MSC_FULL_VER = VVRRPPPP */ +# define COMPILER_VERSION_PATCH DEC(_MSC_FULL_VER % 10000) +# endif +# endif +# if defined(_MSC_BUILD) +# define COMPILER_VERSION_TWEAK DEC(_MSC_BUILD) +# endif + +#elif defined(_ADI_COMPILER) +# define COMPILER_ID "ADSP" +#if defined(__VERSIONNUM__) + /* __VERSIONNUM__ = 0xVVRRPPTT */ +# define COMPILER_VERSION_MAJOR DEC(__VERSIONNUM__ >> 24 & 0xFF) +# define COMPILER_VERSION_MINOR DEC(__VERSIONNUM__ >> 16 & 0xFF) +# define COMPILER_VERSION_PATCH DEC(__VERSIONNUM__ >> 8 & 0xFF) +# define COMPILER_VERSION_TWEAK DEC(__VERSIONNUM__ & 0xFF) +#endif + +#elif defined(__IAR_SYSTEMS_ICC__) || defined(__IAR_SYSTEMS_ICC) +# define COMPILER_ID "IAR" +# if defined(__VER__) && defined(__ICCARM__) +# define COMPILER_VERSION_MAJOR DEC((__VER__) / 1000000) +# define COMPILER_VERSION_MINOR DEC(((__VER__) / 1000) % 1000) +# define COMPILER_VERSION_PATCH DEC((__VER__) % 1000) +# define COMPILER_VERSION_INTERNAL DEC(__IAR_SYSTEMS_ICC__) +# elif defined(__VER__) && (defined(__ICCAVR__) || defined(__ICCRX__) || defined(__ICCRH850__) || defined(__ICCRL78__) || defined(__ICC430__) || defined(__ICCRISCV__) || defined(__ICCV850__) || defined(__ICC8051__) || defined(__ICCSTM8__)) +# define COMPILER_VERSION_MAJOR DEC((__VER__) / 100) +# define COMPILER_VERSION_MINOR DEC((__VER__) - (((__VER__) / 100)*100)) +# define COMPILER_VERSION_PATCH DEC(__SUBVERSION__) +# define COMPILER_VERSION_INTERNAL DEC(__IAR_SYSTEMS_ICC__) +# endif + +#elif defined(__DCC__) && defined(_DIAB_TOOL) +# define COMPILER_ID "Diab" + # define COMPILER_VERSION_MAJOR DEC(__VERSION_MAJOR_NUMBER__) + # define COMPILER_VERSION_MINOR DEC(__VERSION_MINOR_NUMBER__) + # define COMPILER_VERSION_PATCH DEC(__VERSION_ARCH_FEATURE_NUMBER__) + # define COMPILER_VERSION_TWEAK DEC(__VERSION_BUG_FIX_NUMBER__) + + + +/* These compilers are either not known or too old to define an + identification macro. Try to identify the platform and guess that + it is the native compiler. */ +#elif defined(__hpux) || defined(__hpua) +# define COMPILER_ID "HP" + +#else /* unknown compiler */ +# define COMPILER_ID "" +#endif + +/* Construct the string literal in pieces to prevent the source from + getting matched. Store it in a pointer rather than an array + because some compilers will just produce instructions to fill the + array rather than assigning a pointer to a static array. */ +char const* info_compiler = "INFO" ":" "compiler[" COMPILER_ID "]"; +#ifdef SIMULATE_ID +char const* info_simulate = "INFO" ":" "simulate[" SIMULATE_ID "]"; +#endif + +#ifdef __QNXNTO__ +char const* qnxnto = "INFO" ":" "qnxnto[]"; +#endif + +#if defined(__CRAYXT_COMPUTE_LINUX_TARGET) +char const *info_cray = "INFO" ":" "compiler_wrapper[CrayPrgEnv]"; +#endif + +#define STRINGIFY_HELPER(X) #X +#define STRINGIFY(X) STRINGIFY_HELPER(X) + +/* Identify known platforms by name. */ +#if defined(__linux) || defined(__linux__) || defined(linux) +# define PLATFORM_ID "Linux" + +#elif defined(__MSYS__) +# define PLATFORM_ID "MSYS" + +#elif defined(__CYGWIN__) +# define PLATFORM_ID "Cygwin" + +#elif defined(__MINGW32__) +# define PLATFORM_ID "MinGW" + +#elif defined(__APPLE__) +# define PLATFORM_ID "Darwin" + +#elif defined(_WIN32) || defined(__WIN32__) || defined(WIN32) +# define PLATFORM_ID "Windows" + +#elif defined(__FreeBSD__) || defined(__FreeBSD) +# define PLATFORM_ID "FreeBSD" + +#elif defined(__NetBSD__) || defined(__NetBSD) +# define PLATFORM_ID "NetBSD" + +#elif defined(__OpenBSD__) || defined(__OPENBSD) +# define PLATFORM_ID "OpenBSD" + +#elif defined(__sun) || defined(sun) +# define PLATFORM_ID "SunOS" + +#elif defined(_AIX) || defined(__AIX) || defined(__AIX__) || defined(__aix) || defined(__aix__) +# define PLATFORM_ID "AIX" + +#elif defined(__hpux) || defined(__hpux__) +# define PLATFORM_ID "HP-UX" + +#elif defined(__HAIKU__) +# define PLATFORM_ID "Haiku" + +#elif defined(__BeOS) || defined(__BEOS__) || defined(_BEOS) +# define PLATFORM_ID "BeOS" + +#elif defined(__QNX__) || defined(__QNXNTO__) +# define PLATFORM_ID "QNX" + +#elif defined(__tru64) || defined(_tru64) || defined(__TRU64__) +# define PLATFORM_ID "Tru64" + +#elif defined(__riscos) || defined(__riscos__) +# define PLATFORM_ID "RISCos" + +#elif defined(__sinix) || defined(__sinix__) || defined(__SINIX__) +# define PLATFORM_ID "SINIX" + +#elif defined(__UNIX_SV__) +# define PLATFORM_ID "UNIX_SV" + +#elif defined(__bsdos__) +# define PLATFORM_ID "BSDOS" + +#elif defined(_MPRAS) || defined(MPRAS) +# define PLATFORM_ID "MP-RAS" + +#elif defined(__osf) || defined(__osf__) +# define PLATFORM_ID "OSF1" + +#elif defined(_SCO_SV) || defined(SCO_SV) || defined(sco_sv) +# define PLATFORM_ID "SCO_SV" + +#elif defined(__ultrix) || defined(__ultrix__) || defined(_ULTRIX) +# define PLATFORM_ID "ULTRIX" + +#elif defined(__XENIX__) || defined(_XENIX) || defined(XENIX) +# define PLATFORM_ID "Xenix" + +#elif defined(__WATCOMC__) +# if defined(__LINUX__) +# define PLATFORM_ID "Linux" + +# elif defined(__DOS__) +# define PLATFORM_ID "DOS" + +# elif defined(__OS2__) +# define PLATFORM_ID "OS2" + +# elif defined(__WINDOWS__) +# define PLATFORM_ID "Windows3x" + +# elif defined(__VXWORKS__) +# define PLATFORM_ID "VxWorks" + +# else /* unknown platform */ +# define PLATFORM_ID +# endif + +#elif defined(__INTEGRITY) +# if defined(INT_178B) +# define PLATFORM_ID "Integrity178" + +# else /* regular Integrity */ +# define PLATFORM_ID "Integrity" +# endif + +# elif defined(_ADI_COMPILER) +# define PLATFORM_ID "ADSP" + +#else /* unknown platform */ +# define PLATFORM_ID + +#endif + +/* For windows compilers MSVC and Intel we can determine + the architecture of the compiler being used. This is because + the compilers do not have flags that can change the architecture, + but rather depend on which compiler is being used +*/ +#if defined(_WIN32) && defined(_MSC_VER) +# if defined(_M_IA64) +# define ARCHITECTURE_ID "IA64" + +# elif defined(_M_ARM64EC) +# define ARCHITECTURE_ID "ARM64EC" + +# elif defined(_M_X64) || defined(_M_AMD64) +# define ARCHITECTURE_ID "x64" + +# elif defined(_M_IX86) +# define ARCHITECTURE_ID "X86" + +# elif defined(_M_ARM64) +# define ARCHITECTURE_ID "ARM64" + +# elif defined(_M_ARM) +# if _M_ARM == 4 +# define ARCHITECTURE_ID "ARMV4I" +# elif _M_ARM == 5 +# define ARCHITECTURE_ID "ARMV5I" +# else +# define ARCHITECTURE_ID "ARMV" STRINGIFY(_M_ARM) +# endif + +# elif defined(_M_MIPS) +# define ARCHITECTURE_ID "MIPS" + +# elif defined(_M_SH) +# define ARCHITECTURE_ID "SHx" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__WATCOMC__) +# if defined(_M_I86) +# define ARCHITECTURE_ID "I86" + +# elif defined(_M_IX86) +# define ARCHITECTURE_ID "X86" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__IAR_SYSTEMS_ICC__) || defined(__IAR_SYSTEMS_ICC) +# if defined(__ICCARM__) +# define ARCHITECTURE_ID "ARM" + +# elif defined(__ICCRX__) +# define ARCHITECTURE_ID "RX" + +# elif defined(__ICCRH850__) +# define ARCHITECTURE_ID "RH850" + +# elif defined(__ICCRL78__) +# define ARCHITECTURE_ID "RL78" + +# elif defined(__ICCRISCV__) +# define ARCHITECTURE_ID "RISCV" + +# elif defined(__ICCAVR__) +# define ARCHITECTURE_ID "AVR" + +# elif defined(__ICC430__) +# define ARCHITECTURE_ID "MSP430" + +# elif defined(__ICCV850__) +# define ARCHITECTURE_ID "V850" + +# elif defined(__ICC8051__) +# define ARCHITECTURE_ID "8051" + +# elif defined(__ICCSTM8__) +# define ARCHITECTURE_ID "STM8" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__ghs__) +# if defined(__PPC64__) +# define ARCHITECTURE_ID "PPC64" + +# elif defined(__ppc__) +# define ARCHITECTURE_ID "PPC" + +# elif defined(__ARM__) +# define ARCHITECTURE_ID "ARM" + +# elif defined(__x86_64__) +# define ARCHITECTURE_ID "x64" + +# elif defined(__i386__) +# define ARCHITECTURE_ID "X86" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__clang__) && defined(__ti__) +# if defined(__ARM_ARCH) +# define ARCHITECTURE_ID "ARM" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__TI_COMPILER_VERSION__) +# if defined(__TI_ARM__) +# define ARCHITECTURE_ID "ARM" + +# elif defined(__MSP430__) +# define ARCHITECTURE_ID "MSP430" + +# elif defined(__TMS320C28XX__) +# define ARCHITECTURE_ID "TMS320C28x" + +# elif defined(__TMS320C6X__) || defined(_TMS320C6X) +# define ARCHITECTURE_ID "TMS320C6x" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +# elif defined(__ADSPSHARC__) +# define ARCHITECTURE_ID "SHARC" + +# elif defined(__ADSPBLACKFIN__) +# define ARCHITECTURE_ID "Blackfin" + +#elif defined(__TASKING__) + +# if defined(__CTC__) || defined(__CPTC__) +# define ARCHITECTURE_ID "TriCore" + +# elif defined(__CMCS__) +# define ARCHITECTURE_ID "MCS" + +# elif defined(__CARM__) || defined(__CPARM__) +# define ARCHITECTURE_ID "ARM" + +# elif defined(__CARC__) +# define ARCHITECTURE_ID "ARC" + +# elif defined(__C51__) +# define ARCHITECTURE_ID "8051" + +# elif defined(__CPCP__) +# define ARCHITECTURE_ID "PCP" + +# else +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__RENESAS__) +# if defined(__CCRX__) +# define ARCHITECTURE_ID "RX" + +# elif defined(__CCRL__) +# define ARCHITECTURE_ID "RL78" + +# elif defined(__CCRH__) +# define ARCHITECTURE_ID "RH850" + +# else +# define ARCHITECTURE_ID "" +# endif + +#else +# define ARCHITECTURE_ID +#endif + +/* Convert integer to decimal digit literals. */ +#define DEC(n) \ + ('0' + (((n) / 10000000)%10)), \ + ('0' + (((n) / 1000000)%10)), \ + ('0' + (((n) / 100000)%10)), \ + ('0' + (((n) / 10000)%10)), \ + ('0' + (((n) / 1000)%10)), \ + ('0' + (((n) / 100)%10)), \ + ('0' + (((n) / 10)%10)), \ + ('0' + ((n) % 10)) + +/* Convert integer to hex digit literals. */ +#define HEX(n) \ + ('0' + ((n)>>28 & 0xF)), \ + ('0' + ((n)>>24 & 0xF)), \ + ('0' + ((n)>>20 & 0xF)), \ + ('0' + ((n)>>16 & 0xF)), \ + ('0' + ((n)>>12 & 0xF)), \ + ('0' + ((n)>>8 & 0xF)), \ + ('0' + ((n)>>4 & 0xF)), \ + ('0' + ((n) & 0xF)) + +/* Construct a string literal encoding the version number. */ +#ifdef COMPILER_VERSION +char const* info_version = "INFO" ":" "compiler_version[" COMPILER_VERSION "]"; + +/* Construct a string literal encoding the version number components. */ +#elif defined(COMPILER_VERSION_MAJOR) +char const info_version[] = { + 'I', 'N', 'F', 'O', ':', + 'c','o','m','p','i','l','e','r','_','v','e','r','s','i','o','n','[', + COMPILER_VERSION_MAJOR, +# ifdef COMPILER_VERSION_MINOR + '.', COMPILER_VERSION_MINOR, +# ifdef COMPILER_VERSION_PATCH + '.', COMPILER_VERSION_PATCH, +# ifdef COMPILER_VERSION_TWEAK + '.', COMPILER_VERSION_TWEAK, +# endif +# endif +# endif + ']','\0'}; +#endif + +/* Construct a string literal encoding the internal version number. */ +#ifdef COMPILER_VERSION_INTERNAL +char const info_version_internal[] = { + 'I', 'N', 'F', 'O', ':', + 'c','o','m','p','i','l','e','r','_','v','e','r','s','i','o','n','_', + 'i','n','t','e','r','n','a','l','[', + COMPILER_VERSION_INTERNAL,']','\0'}; +#elif defined(COMPILER_VERSION_INTERNAL_STR) +char const* info_version_internal = "INFO" ":" "compiler_version_internal[" COMPILER_VERSION_INTERNAL_STR "]"; +#endif + +/* Construct a string literal encoding the version number components. */ +#ifdef SIMULATE_VERSION_MAJOR +char const info_simulate_version[] = { + 'I', 'N', 'F', 'O', ':', + 's','i','m','u','l','a','t','e','_','v','e','r','s','i','o','n','[', + SIMULATE_VERSION_MAJOR, +# ifdef SIMULATE_VERSION_MINOR + '.', SIMULATE_VERSION_MINOR, +# ifdef SIMULATE_VERSION_PATCH + '.', SIMULATE_VERSION_PATCH, +# ifdef SIMULATE_VERSION_TWEAK + '.', SIMULATE_VERSION_TWEAK, +# endif +# endif +# endif + ']','\0'}; +#endif + +/* Construct the string literal in pieces to prevent the source from + getting matched. Store it in a pointer rather than an array + because some compilers will just produce instructions to fill the + array rather than assigning a pointer to a static array. */ +char const* info_platform = "INFO" ":" "platform[" PLATFORM_ID "]"; +char const* info_arch = "INFO" ":" "arch[" ARCHITECTURE_ID "]"; + + + +#define CXX_STD_98 199711L +#define CXX_STD_11 201103L +#define CXX_STD_14 201402L +#define CXX_STD_17 201703L +#define CXX_STD_20 202002L +#define CXX_STD_23 202302L + +#if defined(__INTEL_COMPILER) && defined(_MSVC_LANG) +# if _MSVC_LANG > CXX_STD_17 +# define CXX_STD _MSVC_LANG +# elif _MSVC_LANG == CXX_STD_17 && defined(__cpp_aggregate_paren_init) +# define CXX_STD CXX_STD_20 +# elif _MSVC_LANG > CXX_STD_14 && __cplusplus > CXX_STD_17 +# define CXX_STD CXX_STD_20 +# elif _MSVC_LANG > CXX_STD_14 +# define CXX_STD CXX_STD_17 +# elif defined(__INTEL_CXX11_MODE__) && defined(__cpp_aggregate_nsdmi) +# define CXX_STD CXX_STD_14 +# elif defined(__INTEL_CXX11_MODE__) +# define CXX_STD CXX_STD_11 +# else +# define CXX_STD CXX_STD_98 +# endif +#elif defined(_MSC_VER) && defined(_MSVC_LANG) +# if _MSVC_LANG > __cplusplus +# define CXX_STD _MSVC_LANG +# else +# define CXX_STD __cplusplus +# endif +#elif defined(__NVCOMPILER) +# if __cplusplus == CXX_STD_17 && defined(__cpp_aggregate_paren_init) +# define CXX_STD CXX_STD_20 +# else +# define CXX_STD __cplusplus +# endif +#elif defined(__INTEL_COMPILER) || defined(__PGI) +# if __cplusplus == CXX_STD_11 && defined(__cpp_namespace_attributes) +# define CXX_STD CXX_STD_17 +# elif __cplusplus == CXX_STD_11 && defined(__cpp_aggregate_nsdmi) +# define CXX_STD CXX_STD_14 +# else +# define CXX_STD __cplusplus +# endif +#elif (defined(__IBMCPP__) || defined(__ibmxl__)) && defined(__linux__) +# if __cplusplus == CXX_STD_11 && defined(__cpp_aggregate_nsdmi) +# define CXX_STD CXX_STD_14 +# else +# define CXX_STD __cplusplus +# endif +#elif __cplusplus == 1 && defined(__GXX_EXPERIMENTAL_CXX0X__) +# define CXX_STD CXX_STD_11 +#else +# define CXX_STD __cplusplus +#endif + +const char* info_language_standard_default = "INFO" ":" "standard_default[" +#if CXX_STD > CXX_STD_23 + "26" +#elif CXX_STD > CXX_STD_20 + "23" +#elif CXX_STD > CXX_STD_17 + "20" +#elif CXX_STD > CXX_STD_14 + "17" +#elif CXX_STD > CXX_STD_11 + "14" +#elif CXX_STD >= CXX_STD_11 + "11" +#else + "98" +#endif +"]"; + +const char* info_language_extensions_default = "INFO" ":" "extensions_default[" +#if (defined(__clang__) || defined(__GNUC__) || defined(__xlC__) || \ + defined(__TI_COMPILER_VERSION__) || defined(__RENESAS__)) && \ + !defined(__STRICT_ANSI__) + "ON" +#else + "OFF" +#endif +"]"; + +/*--------------------------------------------------------------------------*/ + +int main(int argc, char* argv[]) +{ + int require = 0; + require += info_compiler[argc]; + require += info_platform[argc]; + require += info_arch[argc]; +#ifdef COMPILER_VERSION_MAJOR + require += info_version[argc]; +#endif +#if defined(COMPILER_VERSION_INTERNAL) || defined(COMPILER_VERSION_INTERNAL_STR) + require += info_version_internal[argc]; +#endif +#ifdef SIMULATE_ID + require += info_simulate[argc]; +#endif +#ifdef SIMULATE_VERSION_MAJOR + require += info_simulate_version[argc]; +#endif +#if defined(__CRAYXT_COMPUTE_LINUX_TARGET) + require += info_cray[argc]; +#endif + require += info_language_standard_default[argc]; + require += info_language_extensions_default[argc]; + (void)argv; + return require; +} diff --git a/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdCXX/a.out b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdCXX/a.out new file mode 100755 index 0000000..c64f787 Binary files /dev/null and b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdCXX/a.out differ diff --git a/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdCXX/apple-sdk.cpp b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdCXX/apple-sdk.cpp new file mode 100644 index 0000000..db846b4 --- /dev/null +++ b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdCXX/apple-sdk.cpp @@ -0,0 +1 @@ +#include diff --git a/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdFortran/CMakeFortranCompilerId.F b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdFortran/CMakeFortranCompilerId.F new file mode 100644 index 0000000..1c9275d --- /dev/null +++ b/fpp-ptc-sandbox/code/CMakeFiles/4.2.1/CompilerIdFortran/CMakeFortranCompilerId.F @@ -0,0 +1,1119 @@ + PROGRAM CMakeFortranCompilerId +#if 0 +! Identify the compiler +#endif +#if defined(_MSC_VER) + PRINT *, 'INFO:simulate[MSVC]' +# if _MSC_VER >= 1900 + PRINT *, 'INFO:simulate_version[019.00]' +# elif _MSC_VER >= 1800 + PRINT *, 'INFO:simulate_version[018.00]' +# elif _MSC_VER >= 1700 + PRINT *, 'INFO:simulate_version[017.00]' +# elif _MSC_VER >= 1600 + PRINT *, 'INFO:simulate_version[016.00]' +# elif _MSC_VER >= 1500 + PRINT *, 'INFO:simulate_version[015.00]' +# elif _MSC_VER >= 1400 + PRINT *, 'INFO:simulate_version[014.00]' +# elif _MSC_VER >= 1310 + PRINT *, 'INFO:simulate_version[013.01]' +# else + PRINT *, 'INFO:simulate_version[013.00]' +# endif +#endif +#if defined(__INTEL_LLVM_COMPILER) + PRINT *, 'INFO:compiler[IntelLLVM]' +! __INTEL_LLVM_COMPILER = VVVVRP prior to 2021.2.0, VVVVRRPP for 2021.2.0 and +! later. Look for 6 digit vs. 8 digit version number to decide encoding. +! VVVV is no smaller than the current year when a version is released. +# if __INTEL_LLVM_COMPILER < 1000000 +# define COMPILER_VERSION_MAJOR DEC(__INTEL_LLVM_COMPILER/100) +# define COMPILER_VERSION_MINOR DEC(__INTEL_LLVM_COMPILER/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__INTEL_LLVM_COMPILER % 10) +# else +# define COMPILER_VERSION_MAJOR DEC(__INTEL_LLVM_COMPILER/10000) +# define COMPILER_VERSION_MINOR DEC(__INTEL_LLVM_COMPILER/100 % 100) +# define COMPILER_VERSION_PATCH DEC(__INTEL_LLVM_COMPILER % 100) +# endif +#elif defined(__INTEL_COMPILER) && __INTEL_COMPILER == 201900 + PRINT *, 'INFO:compiler[IntelLLVM]' +! ifx 2021.1 forgot to define __INTEL_LLVM_COMPILER. +! Instead it defines __INTEL_COMPILER == 201900. +# define COMPILER_VERSION_MAJOR DEC(2021) +# define COMPILER_VERSION_MINOR DEC(1) +# define COMPILER_VERSION_PATCH DEC(__INTEL_COMPILER_UPDATE) +# define COMPILER_VERSION_TWEAK DEC(__INTEL_COMPILER_BUILD_DATE) +#elif defined(__INTEL_COMPILER) || defined(__ICC) + PRINT *, 'INFO:compiler[Intel]' +! __INTEL_COMPILER = VRP prior to 2021, and then VVVV for 2021 and later. +# if __INTEL_COMPILER < 2021 +# define COMPILER_VERSION_MAJOR DEC(__INTEL_COMPILER/100) +# define COMPILER_VERSION_MINOR DEC(__INTEL_COMPILER/10 % 10) +# if defined(__INTEL_COMPILER_UPDATE) +# define COMPILER_VERSION_PATCH DEC(__INTEL_COMPILER_UPDATE) +# else +# define COMPILER_VERSION_PATCH DEC(__INTEL_COMPILER % 10) +# endif +# else +# define COMPILER_VERSION_MAJOR DEC(__INTEL_COMPILER) +# define COMPILER_VERSION_MINOR DEC(__INTEL_COMPILER_UPDATE) +! The third version component from --version is an update index, +! but no macro is provided for it. +# define COMPILER_VERSION_PATCH DEC(0) +# endif +# if defined(__INTEL_COMPILER_BUILD_DATE) +# define COMPILER_VERSION_TWEAK DEC(__INTEL_COMPILER_BUILD_DATE) +# endif +#elif defined(__SUNPRO_F95) + PRINT *, 'INFO:compiler[SunPro]' +# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_F95>>8) +# define COMPILER_VERSION_MINOR HEX(__SUNPRO_F95>>4 & 0xF) +# define COMPILER_VERSION_PATCH HEX(__SUNPRO_F95 & 0xF) +#elif defined(__SUNPRO_F90) + PRINT *, 'INFO:compiler[SunPro]' +# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_F90>>8) +# define COMPILER_VERSION_MINOR HEX(__SUNPRO_F90>>4 & 0xF) +# define COMPILER_VERSION_PATCH HEX(__SUNPRO_F90 & 0xF) +#elif defined(_CRAYFTN) + PRINT *, 'INFO:compiler[Cray]' +# define COMPILER_VERSION_MAJOR DEC(_RELEASE_MAJOR) +# define COMPILER_VERSION_MINOR DEC(_RELEASE_MINOR) +# if defined(_RELEASE_PATCHLEVEL) +# define COMPILER_VERSION_PATCH DEC(_RELEASE_PATCHLEVEL) +# endif +#elif defined(__G95__) + PRINT *, 'INFO:compiler[G95]' +# define COMPILER_VERSION_MAJOR DEC(__G95__) +# define COMPILER_VERSION_MINOR DEC(__G95_MINOR__) +#elif defined(__PATHSCALE__) + PRINT *, 'INFO:compiler[PathScale]' +# define COMPILER_VERSION_MAJOR DEC(__PATHCC__) +# define COMPILER_VERSION_MINOR DEC(__PATHCC_MINOR__) +# if defined(__PATHCC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__PATHCC_PATCHLEVEL__) +# endif +#elif defined(__ABSOFT__) + PRINT *, 'INFO:compiler[Absoft]' +#elif defined(__LCC__) && (defined(__GNUC__) || defined(__GNUG__) || defined(__MCST__)) + PRINT *, 'INFO:compiler[LCC]' +# define COMPILER_VERSION_MAJOR DEC(1) +# define COMPILER_VERSION_MINOR DEC(__LCC__ - 100) +# if defined(__LCC_MINOR__) +# define COMPILER_VERSION_PATCH DEC(__LCC_MINOR__) +# endif +#elif defined(__GNUC__) + PRINT *, 'INFO:compiler[GNU]' +# define COMPILER_VERSION_MAJOR DEC(__GNUC__) +# define COMPILER_VERSION_MINOR DEC(__GNUC_MINOR__) +# if defined(__GNUC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__) +# endif +#elif defined(__IBMC__) +# if defined(__COMPILER_VER__) + PRINT *, 'INFO:compiler[zOS]' +# elif __IBMC__ >= 800 + PRINT *, 'INFO:compiler[XL]' +# define COMPILER_VERSION_MAJOR DEC(__IBMC__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMC__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMC__ % 10) +# else + PRINT *, 'INFO:compiler[VisualAge]' +# define COMPILER_VERSION_MAJOR DEC(__IBMC__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMC__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMC__ % 10) +# endif +#elif defined(__NVCOMPILER) || defined(__NVCOMPILER_LLVM__) + PRINT *, 'INFO:compiler[NVHPC]' +# if defined(__NVCOMPILER_MAJOR__) +# define COMPILER_VERSION_MAJOR DEC(__NVCOMPILER_MAJOR__) +# else +# define COMPILER_VERSION_MAJOR DEC(__PGIC__) +# endif +# if defined(__NVCOMPILER_MINOR__) +# define COMPILER_VERSION_MINOR DEC(__NVCOMPILER_MINOR__) +# else +# define COMPILER_VERSION_MINOR DEC(__PGIC_MINOR__) +# endif +# if defined(__NVCOMPILER_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__NVCOMPILER_PATCHLEVEL__) +# elif defined(__PGIC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__PGIC_PATCHLEVEL__) +# endif +#elif defined(__PGI) + PRINT *, 'INFO:compiler[PGI]' +# define COMPILER_VERSION_MAJOR DEC(__PGIC__) +# define COMPILER_VERSION_MINOR DEC(__PGIC_MINOR__) +# if defined(__PGIC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__PGIC_PATCHLEVEL__) +# endif +#elif defined(__FLANG) + PRINT *, 'INFO:compiler[Flang]' +# define COMPILER_VERSION_MAJOR DEC(__FLANG_MAJOR__) +# define COMPILER_VERSION_MINOR DEC(__FLANG_MINOR__) +# if defined(__FLANG_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__FLANG_PATCHLEVEL__) +# endif +#elif defined(__flang__) + PRINT *, 'INFO:compiler[LLVMFlang]' +# define COMPILER_VERSION_MAJOR DEC(__flang_major__) +# define COMPILER_VERSION_MINOR DEC(__flang_minor__) +# if defined(__flang_patchlevel__) +# define COMPILER_VERSION_PATCH DEC(__flang_patchlevel__) +# endif +#elif defined(_AIX) || defined(__AIX) || defined(__AIX__) || defined(__aix) || defined(__aix__) + PRINT *, 'INFO:compiler[VisualAge]' +#elif defined(__hpux) || defined(__hpux__) + PRINT *, 'INFO:compiler[HP]' +#elif defined(NAGFOR) + PRINT *, 'INFO:compiler[NAG]' +#define COMPILER_VERSION_MAJOR DEC(__NAG_COMPILER_RELEASE/10) +#define COMPILER_VERSION_MINOR DEC(__NAG_COMPILER_RELEASE % 10) +#define COMPILER_VERSION_PATCH DEC(__NAG_COMPILER_BUILD) +#elif defined(__FUJITSU) + PRINT *, 'INFO:compiler[Fujitsu]' +# if defined(__FRT_major__) +# define COMPILER_VERSION_MAJOR DEC(__FRT_major__) +# define COMPILER_VERSION_MINOR DEC(__FRT_minor__) +# define COMPILER_VERSION_PATCH DEC(__FRT_patchlevel__) +# elif defined(__FRT_version__) + PRINT *, 'INFO:compiler_version['//__FRT_version__//']' +# endif +#elif defined(__LFORTRAN__) + PRINT *, 'INFO:compiler[LFortran]' +#define COMPILER_VERSION_MAJOR DEC(__LFORTRAN_MAJOR__) +#define COMPILER_VERSION_MINOR DEC(__LFORTRAN_MINOR__) +#define COMPILER_VERSION_PATCH DEC(__LFORTRAN_PATCHLEVEL__) +#else + PRINT *, 'INFO:compiler[]' +#endif +#if defined(__CRAYXT_COMPUTE_LINUX_TARGET) + PRINT *, 'INFO:compiler_wrapper[CrayPrgEnv]' +#endif + +#if 0 +! Identify the platform +#endif +#if defined(__linux) || defined(__linux__) || defined(linux) + PRINT *, 'INFO:platform[Linux]' +#elif defined(__CYGWIN__) + PRINT *, 'INFO:platform[Cygwin]' +#elif defined(__MINGW32__) + PRINT *, 'INFO:platform[MinGW]' +#elif defined(__APPLE__) + PRINT *, 'INFO:platform[Darwin]' +#elif defined(_WIN32) || defined(__WIN32__) || defined(WIN32) + PRINT *, 'INFO:platform[Windows]' +#elif defined(__FreeBSD__) || defined(__FreeBSD) + PRINT *, 'INFO:platform[FreeBSD]' +#elif defined(__NetBSD__) || defined(__NetBSD) + PRINT *, 'INFO:platform[NetBSD]' +#elif defined(__OpenBSD__) || defined(__OPENBSD) + PRINT *, 'INFO:platform[OpenBSD]' +#elif defined(__sun) || defined(sun) + PRINT *, 'INFO:platform[SunOS]' +#elif defined(_AIX) || defined(__AIX) || defined(__AIX__) || defined(__aix) || defined(__aix__) + PRINT *, 'INFO:platform[AIX]' +#elif defined(__hpux) || defined(__hpux__) + PRINT *, 'INFO:platform[HP-UX]' +#elif defined(__HAIKU__) + PRINT *, 'INFO:platform[Haiku]' +#elif defined(__BeOS) || defined(__BEOS__) || defined(_BEOS) + PRINT *, 'INFO:platform[BeOS]' +#elif defined(__QNX__) || defined(__QNXNTO__) + PRINT *, 'INFO:platform[QNX]' +#elif defined(__tru64) || defined(_tru64) || defined(__TRU64__) + PRINT *, 'INFO:platform[Tru64]' +#elif defined(__riscos) || defined(__riscos__) + PRINT *, 'INFO:platform[RISCos]' +#elif defined(__sinix) || defined(__sinix__) || defined(__SINIX__) + PRINT *, 'INFO:platform[SINIX]' +#elif defined(__UNIX_SV__) + PRINT *, 'INFO:platform[UNIX_SV]' +#elif defined(__bsdos__) + PRINT *, 'INFO:platform[BSDOS]' +#elif defined(_MPRAS) || defined(MPRAS) + PRINT *, 'INFO:platform[MP-RAS]' +#elif defined(__osf) || defined(__osf__) + PRINT *, 'INFO:platform[OSF1]' +#elif defined(_SCO_SV) || defined(SCO_SV) || defined(sco_sv) + PRINT *, 'INFO:platform[SCO_SV]' +#elif defined(__ultrix) || defined(__ultrix__) || defined(_ULTRIX) + PRINT *, 'INFO:platform[ULTRIX]' +#elif defined(__XENIX__) || defined(_XENIX) || defined(XENIX) + PRINT *, 'INFO:platform[Xenix]' +#else + PRINT *, 'INFO:platform[]' +#endif +#if defined(_MSC_VER) +# if defined(_M_IA64) + PRINT *, 'INFO:arch[IA64]' +# elif defined(_M_X64) || defined(_M_AMD64) + PRINT *, 'INFO:arch[x64]' +# elif defined(_M_IX86) + PRINT *, 'INFO:arch[X86]' +# endif +#endif + +#if 0 +! Encode compiler version digits +#endif +#define DEC_8(n) (((n) / 10000000) % 10) +#define DEC_7(n) (((n) / 1000000) % 10) +#define DEC_6(n) (((n) / 100000) % 10) +#define DEC_5(n) (((n) / 10000) % 10) +#define DEC_4(n) (((n) / 1000) % 10) +#define DEC_3(n) (((n) / 100) % 10) +#define DEC_2(n) (((n) / 10) % 10) +#define DEC_1(n) (((n) ) % 10) +#define HEX_8(n) ((n)>>28 & 0xF) +#define HEX_7(n) ((n)>>24 & 0xF) +#define HEX_6(n) ((n)>>20 & 0xF) +#define HEX_5(n) ((n)>>16 & 0xF) +#define HEX_4(n) ((n)>>12 & 0xF) +#define HEX_3(n) ((n)>>8 & 0xF) +#define HEX_2(n) ((n)>>4 & 0xF) +#define HEX_1(n) ((n) & 0xF) + +#if defined(COMPILER_VERSION_MAJOR) +# undef DEC +# undef HEX +# define DEC(n) DEC_1(n) +# define HEX(n) HEX_1(n) +# if COMPILER_VERSION_MAJOR == 0 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[0]' +# elif COMPILER_VERSION_MAJOR == 1 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[1]' +# elif COMPILER_VERSION_MAJOR == 2 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[2]' +# elif COMPILER_VERSION_MAJOR == 3 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[3]' +# elif COMPILER_VERSION_MAJOR == 4 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[4]' +# elif COMPILER_VERSION_MAJOR == 5 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[5]' +# elif COMPILER_VERSION_MAJOR == 6 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[6]' +# elif COMPILER_VERSION_MAJOR == 7 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[7]' +# elif COMPILER_VERSION_MAJOR == 8 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[8]' +# elif COMPILER_VERSION_MAJOR == 9 + PRINT *, 'INFO:compiler_version_MAJOR_digit_1[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_2(n) +# define HEX(n) HEX_2(n) +# if COMPILER_VERSION_MAJOR == 0 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[0]' +# elif COMPILER_VERSION_MAJOR == 1 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[1]' +# elif COMPILER_VERSION_MAJOR == 2 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[2]' +# elif COMPILER_VERSION_MAJOR == 3 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[3]' +# elif COMPILER_VERSION_MAJOR == 4 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[4]' +# elif COMPILER_VERSION_MAJOR == 5 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[5]' +# elif COMPILER_VERSION_MAJOR == 6 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[6]' +# elif COMPILER_VERSION_MAJOR == 7 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[7]' +# elif COMPILER_VERSION_MAJOR == 8 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[8]' +# elif COMPILER_VERSION_MAJOR == 9 + PRINT *, 'INFO:compiler_version_MAJOR_digit_2[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_3(n) +# define HEX(n) HEX_3(n) +# if COMPILER_VERSION_MAJOR == 0 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[0]' +# elif COMPILER_VERSION_MAJOR == 1 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[1]' +# elif COMPILER_VERSION_MAJOR == 2 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[2]' +# elif COMPILER_VERSION_MAJOR == 3 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[3]' +# elif COMPILER_VERSION_MAJOR == 4 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[4]' +# elif COMPILER_VERSION_MAJOR == 5 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[5]' +# elif COMPILER_VERSION_MAJOR == 6 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[6]' +# elif COMPILER_VERSION_MAJOR == 7 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[7]' +# elif COMPILER_VERSION_MAJOR == 8 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[8]' +# elif COMPILER_VERSION_MAJOR == 9 + PRINT *, 'INFO:compiler_version_MAJOR_digit_3[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_4(n) +# define HEX(n) HEX_4(n) +# if COMPILER_VERSION_MAJOR == 0 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[0]' +# elif COMPILER_VERSION_MAJOR == 1 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[1]' +# elif COMPILER_VERSION_MAJOR == 2 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[2]' +# elif COMPILER_VERSION_MAJOR == 3 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[3]' +# elif COMPILER_VERSION_MAJOR == 4 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[4]' +# elif COMPILER_VERSION_MAJOR == 5 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[5]' +# elif COMPILER_VERSION_MAJOR == 6 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[6]' +# elif COMPILER_VERSION_MAJOR == 7 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[7]' +# elif COMPILER_VERSION_MAJOR == 8 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[8]' +# elif COMPILER_VERSION_MAJOR == 9 + PRINT *, 'INFO:compiler_version_MAJOR_digit_4[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_5(n) +# define HEX(n) HEX_5(n) +# if COMPILER_VERSION_MAJOR == 0 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[0]' +# elif COMPILER_VERSION_MAJOR == 1 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[1]' +# elif COMPILER_VERSION_MAJOR == 2 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[2]' +# elif COMPILER_VERSION_MAJOR == 3 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[3]' +# elif COMPILER_VERSION_MAJOR == 4 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[4]' +# elif COMPILER_VERSION_MAJOR == 5 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[5]' +# elif COMPILER_VERSION_MAJOR == 6 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[6]' +# elif COMPILER_VERSION_MAJOR == 7 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[7]' +# elif COMPILER_VERSION_MAJOR == 8 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[8]' +# elif COMPILER_VERSION_MAJOR == 9 + PRINT *, 'INFO:compiler_version_MAJOR_digit_5[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_6(n) +# define HEX(n) HEX_6(n) +# if COMPILER_VERSION_MAJOR == 0 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[0]' +# elif COMPILER_VERSION_MAJOR == 1 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[1]' +# elif COMPILER_VERSION_MAJOR == 2 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[2]' +# elif COMPILER_VERSION_MAJOR == 3 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[3]' +# elif COMPILER_VERSION_MAJOR == 4 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[4]' +# elif COMPILER_VERSION_MAJOR == 5 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[5]' +# elif COMPILER_VERSION_MAJOR == 6 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[6]' +# elif COMPILER_VERSION_MAJOR == 7 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[7]' +# elif COMPILER_VERSION_MAJOR == 8 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[8]' +# elif COMPILER_VERSION_MAJOR == 9 + PRINT *, 'INFO:compiler_version_MAJOR_digit_6[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_7(n) +# define HEX(n) HEX_7(n) +# if COMPILER_VERSION_MAJOR == 0 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[0]' +# elif COMPILER_VERSION_MAJOR == 1 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[1]' +# elif COMPILER_VERSION_MAJOR == 2 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[2]' +# elif COMPILER_VERSION_MAJOR == 3 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[3]' +# elif COMPILER_VERSION_MAJOR == 4 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[4]' +# elif COMPILER_VERSION_MAJOR == 5 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[5]' +# elif COMPILER_VERSION_MAJOR == 6 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[6]' +# elif COMPILER_VERSION_MAJOR == 7 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[7]' +# elif COMPILER_VERSION_MAJOR == 8 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[8]' +# elif COMPILER_VERSION_MAJOR == 9 + PRINT *, 'INFO:compiler_version_MAJOR_digit_7[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_8(n) +# define HEX(n) HEX_8(n) +# if COMPILER_VERSION_MAJOR == 0 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[0]' +# elif COMPILER_VERSION_MAJOR == 1 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[1]' +# elif COMPILER_VERSION_MAJOR == 2 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[2]' +# elif COMPILER_VERSION_MAJOR == 3 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[3]' +# elif COMPILER_VERSION_MAJOR == 4 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[4]' +# elif COMPILER_VERSION_MAJOR == 5 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[5]' +# elif COMPILER_VERSION_MAJOR == 6 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[6]' +# elif COMPILER_VERSION_MAJOR == 7 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[7]' +# elif COMPILER_VERSION_MAJOR == 8 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[8]' +# elif COMPILER_VERSION_MAJOR == 9 + PRINT *, 'INFO:compiler_version_MAJOR_digit_8[9]' +# endif + +#endif +#if defined(COMPILER_VERSION_MINOR) +# undef DEC +# undef HEX +# define DEC(n) DEC_1(n) +# define HEX(n) HEX_1(n) +# if COMPILER_VERSION_MINOR == 0 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[0]' +# elif COMPILER_VERSION_MINOR == 1 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[1]' +# elif COMPILER_VERSION_MINOR == 2 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[2]' +# elif COMPILER_VERSION_MINOR == 3 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[3]' +# elif COMPILER_VERSION_MINOR == 4 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[4]' +# elif COMPILER_VERSION_MINOR == 5 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[5]' +# elif COMPILER_VERSION_MINOR == 6 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[6]' +# elif COMPILER_VERSION_MINOR == 7 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[7]' +# elif COMPILER_VERSION_MINOR == 8 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[8]' +# elif COMPILER_VERSION_MINOR == 9 + PRINT *, 'INFO:compiler_version_MINOR_digit_1[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_2(n) +# define HEX(n) HEX_2(n) +# if COMPILER_VERSION_MINOR == 0 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[0]' +# elif COMPILER_VERSION_MINOR == 1 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[1]' +# elif COMPILER_VERSION_MINOR == 2 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[2]' +# elif COMPILER_VERSION_MINOR == 3 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[3]' +# elif COMPILER_VERSION_MINOR == 4 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[4]' +# elif COMPILER_VERSION_MINOR == 5 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[5]' +# elif COMPILER_VERSION_MINOR == 6 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[6]' +# elif COMPILER_VERSION_MINOR == 7 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[7]' +# elif COMPILER_VERSION_MINOR == 8 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[8]' +# elif COMPILER_VERSION_MINOR == 9 + PRINT *, 'INFO:compiler_version_MINOR_digit_2[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_3(n) +# define HEX(n) HEX_3(n) +# if COMPILER_VERSION_MINOR == 0 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[0]' +# elif COMPILER_VERSION_MINOR == 1 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[1]' +# elif COMPILER_VERSION_MINOR == 2 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[2]' +# elif COMPILER_VERSION_MINOR == 3 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[3]' +# elif COMPILER_VERSION_MINOR == 4 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[4]' +# elif COMPILER_VERSION_MINOR == 5 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[5]' +# elif COMPILER_VERSION_MINOR == 6 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[6]' +# elif COMPILER_VERSION_MINOR == 7 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[7]' +# elif COMPILER_VERSION_MINOR == 8 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[8]' +# elif COMPILER_VERSION_MINOR == 9 + PRINT *, 'INFO:compiler_version_MINOR_digit_3[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_4(n) +# define HEX(n) HEX_4(n) +# if COMPILER_VERSION_MINOR == 0 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[0]' +# elif COMPILER_VERSION_MINOR == 1 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[1]' +# elif COMPILER_VERSION_MINOR == 2 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[2]' +# elif COMPILER_VERSION_MINOR == 3 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[3]' +# elif COMPILER_VERSION_MINOR == 4 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[4]' +# elif COMPILER_VERSION_MINOR == 5 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[5]' +# elif COMPILER_VERSION_MINOR == 6 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[6]' +# elif COMPILER_VERSION_MINOR == 7 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[7]' +# elif COMPILER_VERSION_MINOR == 8 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[8]' +# elif COMPILER_VERSION_MINOR == 9 + PRINT *, 'INFO:compiler_version_MINOR_digit_4[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_5(n) +# define HEX(n) HEX_5(n) +# if COMPILER_VERSION_MINOR == 0 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[0]' +# elif COMPILER_VERSION_MINOR == 1 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[1]' +# elif COMPILER_VERSION_MINOR == 2 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[2]' +# elif COMPILER_VERSION_MINOR == 3 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[3]' +# elif COMPILER_VERSION_MINOR == 4 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[4]' +# elif COMPILER_VERSION_MINOR == 5 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[5]' +# elif COMPILER_VERSION_MINOR == 6 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[6]' +# elif COMPILER_VERSION_MINOR == 7 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[7]' +# elif COMPILER_VERSION_MINOR == 8 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[8]' +# elif COMPILER_VERSION_MINOR == 9 + PRINT *, 'INFO:compiler_version_MINOR_digit_5[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_6(n) +# define HEX(n) HEX_6(n) +# if COMPILER_VERSION_MINOR == 0 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[0]' +# elif COMPILER_VERSION_MINOR == 1 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[1]' +# elif COMPILER_VERSION_MINOR == 2 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[2]' +# elif COMPILER_VERSION_MINOR == 3 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[3]' +# elif COMPILER_VERSION_MINOR == 4 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[4]' +# elif COMPILER_VERSION_MINOR == 5 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[5]' +# elif COMPILER_VERSION_MINOR == 6 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[6]' +# elif COMPILER_VERSION_MINOR == 7 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[7]' +# elif COMPILER_VERSION_MINOR == 8 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[8]' +# elif COMPILER_VERSION_MINOR == 9 + PRINT *, 'INFO:compiler_version_MINOR_digit_6[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_7(n) +# define HEX(n) HEX_7(n) +# if COMPILER_VERSION_MINOR == 0 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[0]' +# elif COMPILER_VERSION_MINOR == 1 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[1]' +# elif COMPILER_VERSION_MINOR == 2 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[2]' +# elif COMPILER_VERSION_MINOR == 3 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[3]' +# elif COMPILER_VERSION_MINOR == 4 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[4]' +# elif COMPILER_VERSION_MINOR == 5 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[5]' +# elif COMPILER_VERSION_MINOR == 6 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[6]' +# elif COMPILER_VERSION_MINOR == 7 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[7]' +# elif COMPILER_VERSION_MINOR == 8 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[8]' +# elif COMPILER_VERSION_MINOR == 9 + PRINT *, 'INFO:compiler_version_MINOR_digit_7[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_8(n) +# define HEX(n) HEX_8(n) +# if COMPILER_VERSION_MINOR == 0 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[0]' +# elif COMPILER_VERSION_MINOR == 1 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[1]' +# elif COMPILER_VERSION_MINOR == 2 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[2]' +# elif COMPILER_VERSION_MINOR == 3 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[3]' +# elif COMPILER_VERSION_MINOR == 4 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[4]' +# elif COMPILER_VERSION_MINOR == 5 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[5]' +# elif COMPILER_VERSION_MINOR == 6 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[6]' +# elif COMPILER_VERSION_MINOR == 7 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[7]' +# elif COMPILER_VERSION_MINOR == 8 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[8]' +# elif COMPILER_VERSION_MINOR == 9 + PRINT *, 'INFO:compiler_version_MINOR_digit_8[9]' +# endif + +#endif +#if defined(COMPILER_VERSION_PATCH) +# undef DEC +# undef HEX +# define DEC(n) DEC_1(n) +# define HEX(n) HEX_1(n) +# if COMPILER_VERSION_PATCH == 0 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[0]' +# elif COMPILER_VERSION_PATCH == 1 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[1]' +# elif COMPILER_VERSION_PATCH == 2 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[2]' +# elif COMPILER_VERSION_PATCH == 3 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[3]' +# elif COMPILER_VERSION_PATCH == 4 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[4]' +# elif COMPILER_VERSION_PATCH == 5 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[5]' +# elif COMPILER_VERSION_PATCH == 6 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[6]' +# elif COMPILER_VERSION_PATCH == 7 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[7]' +# elif COMPILER_VERSION_PATCH == 8 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[8]' +# elif COMPILER_VERSION_PATCH == 9 + PRINT *, 'INFO:compiler_version_PATCH_digit_1[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_2(n) +# define HEX(n) HEX_2(n) +# if COMPILER_VERSION_PATCH == 0 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[0]' +# elif COMPILER_VERSION_PATCH == 1 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[1]' +# elif COMPILER_VERSION_PATCH == 2 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[2]' +# elif COMPILER_VERSION_PATCH == 3 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[3]' +# elif COMPILER_VERSION_PATCH == 4 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[4]' +# elif COMPILER_VERSION_PATCH == 5 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[5]' +# elif COMPILER_VERSION_PATCH == 6 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[6]' +# elif COMPILER_VERSION_PATCH == 7 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[7]' +# elif COMPILER_VERSION_PATCH == 8 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[8]' +# elif COMPILER_VERSION_PATCH == 9 + PRINT *, 'INFO:compiler_version_PATCH_digit_2[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_3(n) +# define HEX(n) HEX_3(n) +# if COMPILER_VERSION_PATCH == 0 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[0]' +# elif COMPILER_VERSION_PATCH == 1 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[1]' +# elif COMPILER_VERSION_PATCH == 2 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[2]' +# elif COMPILER_VERSION_PATCH == 3 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[3]' +# elif COMPILER_VERSION_PATCH == 4 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[4]' +# elif COMPILER_VERSION_PATCH == 5 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[5]' +# elif COMPILER_VERSION_PATCH == 6 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[6]' +# elif COMPILER_VERSION_PATCH == 7 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[7]' +# elif COMPILER_VERSION_PATCH == 8 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[8]' +# elif COMPILER_VERSION_PATCH == 9 + PRINT *, 'INFO:compiler_version_PATCH_digit_3[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_4(n) +# define HEX(n) HEX_4(n) +# if COMPILER_VERSION_PATCH == 0 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[0]' +# elif COMPILER_VERSION_PATCH == 1 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[1]' +# elif COMPILER_VERSION_PATCH == 2 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[2]' +# elif COMPILER_VERSION_PATCH == 3 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[3]' +# elif COMPILER_VERSION_PATCH == 4 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[4]' +# elif COMPILER_VERSION_PATCH == 5 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[5]' +# elif COMPILER_VERSION_PATCH == 6 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[6]' +# elif COMPILER_VERSION_PATCH == 7 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[7]' +# elif COMPILER_VERSION_PATCH == 8 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[8]' +# elif COMPILER_VERSION_PATCH == 9 + PRINT *, 'INFO:compiler_version_PATCH_digit_4[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_5(n) +# define HEX(n) HEX_5(n) +# if COMPILER_VERSION_PATCH == 0 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[0]' +# elif COMPILER_VERSION_PATCH == 1 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[1]' +# elif COMPILER_VERSION_PATCH == 2 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[2]' +# elif COMPILER_VERSION_PATCH == 3 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[3]' +# elif COMPILER_VERSION_PATCH == 4 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[4]' +# elif COMPILER_VERSION_PATCH == 5 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[5]' +# elif COMPILER_VERSION_PATCH == 6 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[6]' +# elif COMPILER_VERSION_PATCH == 7 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[7]' +# elif COMPILER_VERSION_PATCH == 8 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[8]' +# elif COMPILER_VERSION_PATCH == 9 + PRINT *, 'INFO:compiler_version_PATCH_digit_5[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_6(n) +# define HEX(n) HEX_6(n) +# if COMPILER_VERSION_PATCH == 0 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[0]' +# elif COMPILER_VERSION_PATCH == 1 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[1]' +# elif COMPILER_VERSION_PATCH == 2 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[2]' +# elif COMPILER_VERSION_PATCH == 3 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[3]' +# elif COMPILER_VERSION_PATCH == 4 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[4]' +# elif COMPILER_VERSION_PATCH == 5 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[5]' +# elif COMPILER_VERSION_PATCH == 6 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[6]' +# elif COMPILER_VERSION_PATCH == 7 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[7]' +# elif COMPILER_VERSION_PATCH == 8 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[8]' +# elif COMPILER_VERSION_PATCH == 9 + PRINT *, 'INFO:compiler_version_PATCH_digit_6[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_7(n) +# define HEX(n) HEX_7(n) +# if COMPILER_VERSION_PATCH == 0 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[0]' +# elif COMPILER_VERSION_PATCH == 1 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[1]' +# elif COMPILER_VERSION_PATCH == 2 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[2]' +# elif COMPILER_VERSION_PATCH == 3 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[3]' +# elif COMPILER_VERSION_PATCH == 4 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[4]' +# elif COMPILER_VERSION_PATCH == 5 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[5]' +# elif COMPILER_VERSION_PATCH == 6 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[6]' +# elif COMPILER_VERSION_PATCH == 7 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[7]' +# elif COMPILER_VERSION_PATCH == 8 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[8]' +# elif COMPILER_VERSION_PATCH == 9 + PRINT *, 'INFO:compiler_version_PATCH_digit_7[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_8(n) +# define HEX(n) HEX_8(n) +# if COMPILER_VERSION_PATCH == 0 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[0]' +# elif COMPILER_VERSION_PATCH == 1 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[1]' +# elif COMPILER_VERSION_PATCH == 2 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[2]' +# elif COMPILER_VERSION_PATCH == 3 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[3]' +# elif COMPILER_VERSION_PATCH == 4 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[4]' +# elif COMPILER_VERSION_PATCH == 5 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[5]' +# elif COMPILER_VERSION_PATCH == 6 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[6]' +# elif COMPILER_VERSION_PATCH == 7 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[7]' +# elif COMPILER_VERSION_PATCH == 8 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[8]' +# elif COMPILER_VERSION_PATCH == 9 + PRINT *, 'INFO:compiler_version_PATCH_digit_8[9]' +# endif + +#endif +#if defined(COMPILER_VERSION_TWEAK) +# undef DEC +# undef HEX +# define DEC(n) DEC_1(n) +# define HEX(n) HEX_1(n) +# if COMPILER_VERSION_TWEAK == 0 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[0]' +# elif COMPILER_VERSION_TWEAK == 1 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[1]' +# elif COMPILER_VERSION_TWEAK == 2 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[2]' +# elif COMPILER_VERSION_TWEAK == 3 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[3]' +# elif COMPILER_VERSION_TWEAK == 4 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[4]' +# elif COMPILER_VERSION_TWEAK == 5 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[5]' +# elif COMPILER_VERSION_TWEAK == 6 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[6]' +# elif COMPILER_VERSION_TWEAK == 7 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[7]' +# elif COMPILER_VERSION_TWEAK == 8 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[8]' +# elif COMPILER_VERSION_TWEAK == 9 + PRINT *, 'INFO:compiler_version_TWEAK_digit_1[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_2(n) +# define HEX(n) HEX_2(n) +# if COMPILER_VERSION_TWEAK == 0 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[0]' +# elif COMPILER_VERSION_TWEAK == 1 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[1]' +# elif COMPILER_VERSION_TWEAK == 2 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[2]' +# elif COMPILER_VERSION_TWEAK == 3 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[3]' +# elif COMPILER_VERSION_TWEAK == 4 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[4]' +# elif COMPILER_VERSION_TWEAK == 5 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[5]' +# elif COMPILER_VERSION_TWEAK == 6 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[6]' +# elif COMPILER_VERSION_TWEAK == 7 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[7]' +# elif COMPILER_VERSION_TWEAK == 8 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[8]' +# elif COMPILER_VERSION_TWEAK == 9 + PRINT *, 'INFO:compiler_version_TWEAK_digit_2[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_3(n) +# define HEX(n) HEX_3(n) +# if COMPILER_VERSION_TWEAK == 0 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[0]' +# elif COMPILER_VERSION_TWEAK == 1 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[1]' +# elif COMPILER_VERSION_TWEAK == 2 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[2]' +# elif COMPILER_VERSION_TWEAK == 3 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[3]' +# elif COMPILER_VERSION_TWEAK == 4 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[4]' +# elif COMPILER_VERSION_TWEAK == 5 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[5]' +# elif COMPILER_VERSION_TWEAK == 6 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[6]' +# elif COMPILER_VERSION_TWEAK == 7 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[7]' +# elif COMPILER_VERSION_TWEAK == 8 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[8]' +# elif COMPILER_VERSION_TWEAK == 9 + PRINT *, 'INFO:compiler_version_TWEAK_digit_3[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_4(n) +# define HEX(n) HEX_4(n) +# if COMPILER_VERSION_TWEAK == 0 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[0]' +# elif COMPILER_VERSION_TWEAK == 1 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[1]' +# elif COMPILER_VERSION_TWEAK == 2 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[2]' +# elif COMPILER_VERSION_TWEAK == 3 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[3]' +# elif COMPILER_VERSION_TWEAK == 4 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[4]' +# elif COMPILER_VERSION_TWEAK == 5 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[5]' +# elif COMPILER_VERSION_TWEAK == 6 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[6]' +# elif COMPILER_VERSION_TWEAK == 7 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[7]' +# elif COMPILER_VERSION_TWEAK == 8 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[8]' +# elif COMPILER_VERSION_TWEAK == 9 + PRINT *, 'INFO:compiler_version_TWEAK_digit_4[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_5(n) +# define HEX(n) HEX_5(n) +# if COMPILER_VERSION_TWEAK == 0 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[0]' +# elif COMPILER_VERSION_TWEAK == 1 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[1]' +# elif COMPILER_VERSION_TWEAK == 2 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[2]' +# elif COMPILER_VERSION_TWEAK == 3 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[3]' +# elif COMPILER_VERSION_TWEAK == 4 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[4]' +# elif COMPILER_VERSION_TWEAK == 5 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[5]' +# elif COMPILER_VERSION_TWEAK == 6 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[6]' +# elif COMPILER_VERSION_TWEAK == 7 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[7]' +# elif COMPILER_VERSION_TWEAK == 8 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[8]' +# elif COMPILER_VERSION_TWEAK == 9 + PRINT *, 'INFO:compiler_version_TWEAK_digit_5[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_6(n) +# define HEX(n) HEX_6(n) +# if COMPILER_VERSION_TWEAK == 0 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[0]' +# elif COMPILER_VERSION_TWEAK == 1 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[1]' +# elif COMPILER_VERSION_TWEAK == 2 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[2]' +# elif COMPILER_VERSION_TWEAK == 3 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[3]' +# elif COMPILER_VERSION_TWEAK == 4 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[4]' +# elif COMPILER_VERSION_TWEAK == 5 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[5]' +# elif COMPILER_VERSION_TWEAK == 6 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[6]' +# elif COMPILER_VERSION_TWEAK == 7 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[7]' +# elif COMPILER_VERSION_TWEAK == 8 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[8]' +# elif COMPILER_VERSION_TWEAK == 9 + PRINT *, 'INFO:compiler_version_TWEAK_digit_6[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_7(n) +# define HEX(n) HEX_7(n) +# if COMPILER_VERSION_TWEAK == 0 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[0]' +# elif COMPILER_VERSION_TWEAK == 1 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[1]' +# elif COMPILER_VERSION_TWEAK == 2 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[2]' +# elif COMPILER_VERSION_TWEAK == 3 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[3]' +# elif COMPILER_VERSION_TWEAK == 4 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[4]' +# elif COMPILER_VERSION_TWEAK == 5 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[5]' +# elif COMPILER_VERSION_TWEAK == 6 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[6]' +# elif COMPILER_VERSION_TWEAK == 7 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[7]' +# elif COMPILER_VERSION_TWEAK == 8 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[8]' +# elif COMPILER_VERSION_TWEAK == 9 + PRINT *, 'INFO:compiler_version_TWEAK_digit_7[9]' +# endif + +# undef DEC +# undef HEX +# define DEC(n) DEC_8(n) +# define HEX(n) HEX_8(n) +# if COMPILER_VERSION_TWEAK == 0 + PRINT *, 'INFO:compiler_version_TWEAK_digit_8[0]' +# elif COMPILER_VERSION_TWEAK == 1 + PRINT *, 'INFO:compiler_version_TWEAK_digit_8[1]' +# elif COMPILER_VERSION_TWEAK == 2 + PRINT *, 'INFO:compiler_version_TWEAK_digit_8[2]' +# elif COMPILER_VERSION_TWEAK == 3 + PRINT *, 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search_context: + ENV{PATH}: + - "/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/20260112-0/production/bin" + - "/Users/matthewsignorelli/miniconda3/condabin" + - "/Users/matthewsignorelli/.juliaup/bin" + - "/opt/homebrew/bin" + - "/opt/homebrew/sbin" + - "/usr/local/bin" + - "/System/Cryptexes/App/usr/bin" + - "/usr/bin" + - "/bin" + - "/usr/sbin" + - "/sbin" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/local/bin" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/bin" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/appleinternal/bin" + - "/opt/pmk/env/global/bin" + CMAKE_INSTALL_PREFIX: "/usr/local" + CMAKE_SYSTEM_PREFIX_PATH: + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr" + - "/opt/homebrew" + - "/usr/local" + - "/usr" + - "/" + - "/opt/homebrew" + - "/usr/local" + - "/usr/X11R6" + - "/usr/pkg" + - "/opt" + - "/sw" + - "/opt/local" + CMAKE_SYSTEM_INCLUDE_PATH: + - "/usr/include/X11" + 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"/opt/pmk/env/global/bin/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/" + - "/opt/homebrew/include/" + - "/opt/homebrew/" + - "/usr/local/include/" + - "/usr/local/" + - "/usr/include/" + - "/usr/" + - "/include/" + - "/usr/X11R6/include/" + - "/usr/X11R6/" + - "/usr/pkg/include/" + - "/usr/pkg/" + - "/opt/include/" + - "/opt/" + - "/sw/include/" + - "/sw/" + - "/opt/local/include/" + - "/opt/local/" + - "/usr/include/X11/" + - "/Users/matthewsignorelli/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/Network/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/System/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/Library/Frameworks/" + - "/Library/Frameworks/" + - "/Network/Library/Frameworks/" + - "/System/Library/Frameworks/" + - "/usr/pkg/xorg/include/" + - "/usr/X11R6/include/" + - "/usr/X11R7/include/" + - "/usr/openwin/include/" + - "/usr/openwin/share/include/" + - "/opt/graphics/OpenGL/include/" + - "/opt/X11/include/" + searched_directories: + - "/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/20260112-0/production/bin/X11/extensions/Xrender.h" + - "/Users/matthewsignorelli/miniconda3/condabin/X11/extensions/Xrender.h" + - "/Users/matthewsignorelli/.juliaup/bin/X11/extensions/Xrender.h" + - "/opt/homebrew/bin/X11/extensions/Xrender.h" + - "/opt/homebrew/sbin/X11/extensions/Xrender.h" + - "/usr/local/bin/X11/extensions/Xrender.h" + - "/System/Cryptexes/App/usr/bin/X11/extensions/Xrender.h" + - "/usr/bin/X11/extensions/Xrender.h" + - "/bin/X11/extensions/Xrender.h" + - "/usr/sbin/X11/extensions/Xrender.h" + - "/sbin/X11/extensions/Xrender.h" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/local/bin/X11/extensions/Xrender.h" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/bin/X11/extensions/Xrender.h" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/appleinternal/bin/X11/extensions/Xrender.h" + - "/opt/pmk/env/global/bin/X11/extensions/Xrender.h" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/X11/extensions/Xrender.h" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/X11/extensions/Xrender.h" + found: "/opt/homebrew/include/" + search_context: + ENV{PATH}: + - "/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/20260112-0/production/bin" + - "/Users/matthewsignorelli/miniconda3/condabin" + - "/Users/matthewsignorelli/.juliaup/bin" + - "/opt/homebrew/bin" + - "/opt/homebrew/sbin" + - "/usr/local/bin" + - "/System/Cryptexes/App/usr/bin" + - "/usr/bin" + - "/bin" + - "/usr/sbin" + - "/sbin" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/local/bin" + - 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"/Network/Library/Frameworks" + - "/System/Library/Frameworks" + - + kind: "find-v1" + backtrace: + - "/opt/homebrew/share/cmake/Modules/FindX11.cmake:244 (find_path)" + - "/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/util/Master.cmake:211 (find_package)" + - "CMakeLists.txt:49 (include)" + mode: "path" + variable: "X11_XRes_INCLUDE_PATH" + description: "Path to a file." + settings: + SearchFramework: "NEVER" + SearchAppBundle: "FIRST" + CMAKE_FIND_USE_CMAKE_PATH: true + CMAKE_FIND_USE_CMAKE_ENVIRONMENT_PATH: true + CMAKE_FIND_USE_SYSTEM_ENVIRONMENT_PATH: true + CMAKE_FIND_USE_CMAKE_SYSTEM_PATH: true + CMAKE_FIND_USE_INSTALL_PREFIX: true + names: + - "X11/extensions/XRes.h" + candidate_directories: + - "/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/20260112-0/production/bin/" + - "/Users/matthewsignorelli/miniconda3/condabin/" + - "/Users/matthewsignorelli/.juliaup/bin/" + - "/opt/homebrew/bin/" + - "/opt/homebrew/sbin/" + - "/usr/local/bin/" + - "/System/Cryptexes/App/usr/bin/" + - "/usr/bin/" + - "/bin/" + - "/usr/sbin/" + - "/sbin/" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/local/bin/" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/bin/" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/appleinternal/bin/" + - "/opt/pmk/env/global/bin/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/" + - "/opt/homebrew/include/" + - "/opt/homebrew/" + - "/usr/local/include/" + - "/usr/local/" + - "/usr/include/" + - "/usr/" + - "/include/" + - "/usr/X11R6/include/" + - "/usr/X11R6/" + - "/usr/pkg/include/" + - "/usr/pkg/" + - "/opt/include/" + - "/opt/" + - "/sw/include/" + - "/sw/" + - "/opt/local/include/" + - "/opt/local/" + - "/usr/include/X11/" + - "/Users/matthewsignorelli/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/Network/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/System/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/Library/Frameworks/" + - "/Library/Frameworks/" + - "/Network/Library/Frameworks/" + - "/System/Library/Frameworks/" + - "/usr/pkg/xorg/include/" + - "/usr/X11R6/include/" + - "/usr/X11R7/include/" + - "/usr/openwin/include/" + - "/usr/openwin/share/include/" + - "/opt/graphics/OpenGL/include/" + - "/opt/X11/include/" + searched_directories: + - "/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/20260112-0/production/bin/X11/extensions/XRes.h" + - "/Users/matthewsignorelli/miniconda3/condabin/X11/extensions/XRes.h" + - "/Users/matthewsignorelli/.juliaup/bin/X11/extensions/XRes.h" + - "/opt/homebrew/bin/X11/extensions/XRes.h" + - "/opt/homebrew/sbin/X11/extensions/XRes.h" + - "/usr/local/bin/X11/extensions/XRes.h" + - "/System/Cryptexes/App/usr/bin/X11/extensions/XRes.h" + - 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"/Network/Library/Frameworks/X11/extensions/XRes.h" + - "/System/Library/Frameworks/X11/extensions/XRes.h" + - "/usr/pkg/xorg/include/X11/extensions/XRes.h" + - "/usr/X11R6/include/X11/extensions/XRes.h" + - "/usr/X11R7/include/X11/extensions/XRes.h" + - "/usr/openwin/include/X11/extensions/XRes.h" + - "/usr/openwin/share/include/X11/extensions/XRes.h" + - "/opt/graphics/OpenGL/include/X11/extensions/XRes.h" + - "/opt/X11/include/X11/extensions/XRes.h" + found: false + search_context: + ENV{PATH}: + - "/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/20260112-0/production/bin" + - "/Users/matthewsignorelli/miniconda3/condabin" + - "/Users/matthewsignorelli/.juliaup/bin" + - "/opt/homebrew/bin" + - "/opt/homebrew/sbin" + - "/usr/local/bin" + - "/System/Cryptexes/App/usr/bin" + - "/usr/bin" + - "/bin" + - "/usr/sbin" + - "/sbin" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/local/bin" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/bin" + 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backtrace: + - "/opt/homebrew/share/cmake/Modules/FindX11.cmake:245 (find_path)" + - "/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/util/Master.cmake:211 (find_package)" + - "CMakeLists.txt:49 (include)" + mode: "path" + variable: "X11_Xss_INCLUDE_PATH" + description: "Path to a file." + settings: + SearchFramework: "NEVER" + SearchAppBundle: "FIRST" + CMAKE_FIND_USE_CMAKE_PATH: true + CMAKE_FIND_USE_CMAKE_ENVIRONMENT_PATH: true + CMAKE_FIND_USE_SYSTEM_ENVIRONMENT_PATH: true + CMAKE_FIND_USE_CMAKE_SYSTEM_PATH: true + CMAKE_FIND_USE_INSTALL_PREFIX: true + names: + - "X11/extensions/scrnsaver.h" + candidate_directories: + - "/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/20260112-0/production/bin/" + - "/Users/matthewsignorelli/miniconda3/condabin/" + - "/Users/matthewsignorelli/.juliaup/bin/" + - "/opt/homebrew/bin/" + - "/opt/homebrew/sbin/" + - "/usr/local/bin/" + - "/System/Cryptexes/App/usr/bin/" + - "/usr/bin/" + - "/bin/" + - "/usr/sbin/" + - "/sbin/" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/local/bin/" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/bin/" + - "/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/appleinternal/bin/" + - "/opt/pmk/env/global/bin/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/" + - "/opt/homebrew/include/" + - "/opt/homebrew/" + - "/usr/local/include/" + - "/usr/local/" + - "/usr/include/" + - "/usr/" + - "/include/" + - "/usr/X11R6/include/" + - "/usr/X11R6/" + - "/usr/pkg/include/" + - "/usr/pkg/" + - "/opt/include/" + - "/opt/" + - "/sw/include/" + - "/sw/" + - "/opt/local/include/" + - "/opt/local/" + - "/usr/include/X11/" + - "/Users/matthewsignorelli/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/Library/Frameworks/" + - "/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/Network/Library/Frameworks/" + - 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cmake_files/cmake.main_matt_3nux cmake_files/cmake.main_matt_nux_2nuy + cmake_files/cmake.z_canonize ) -include($ENV{ACC_BUILD_SYSTEM}/Master.cmake) \ No newline at end of file +include(/Users/matthewsignorelli/Documents/Bmad/bmad-ecosystem/${bmad_version}/util/Master.cmake) \ No newline at end of file diff --git a/fpp-ptc-sandbox/code/Ci_tpsa.f90 b/fpp-ptc-sandbox/code/Ci_tpsa.f90 new file mode 100644 index 0000000..6799a2d --- /dev/null +++ b/fpp-ptc-sandbox/code/Ci_tpsa.f90 @@ -0,0 +1,24967 @@ +!The Full Polymorphic Packageg + +!Copyright (C) Etienne Forest +! ndct=iabs(ndpt-ndptb) ! 1 if coasting, otherwise 0 +! ndc2t=2*ndct ! 2 if coasting, otherwise 0 +! nd2t=nd2-2*rf-ndc2t ! size of harmonic oscillators minus modulated clocks +! ndt=nd2t/2 ! ndt number of harmonic oscillators minus modulated clocks +! nd2harm=nd2t+2*rf !!!! total dimension of harmonic phase space +! ndharm=ndt+rf !!!! total number of harmonic planes +! +MODULE c_TPSA + !use newda + use definition + use file_handler + use tree_element_MODULE +use duan_zhe_map, probe_zhe=>probe,tree_element_zhe=>tree_element,dp_zhe=>dp, & +DEFAULT0_zhe=>DEFAULT0,TOTALPATH0_zhe=>TOTALPATH0,TIME0_zhe=>TIME0,ONLY_4d0_zhe=>ONLY_4d0,RADIATION0_zhe=>RADIATION0, & +NOCAVITY0_zhe=>NOCAVITY0,FRINGE0_zhe=>FRINGE0,STOCHASTIC0_zhe=>STOCHASTIC0,ENVELOPE0_zhe=>ENVELOPE0, & +DELTA0_zhe=>DELTA0,SPIN0_zhe=>SPIN0,MODULATION0_zhe=>MODULATION0,only_2d0_zhe=>only_2d0 , & +INTERNAL_STATE_zhe=>INTERNAL_STATE,ALLOC_TREE_zhe=>ALLOC_TREE + + IMPLICIT NONE + + public + private ety2,etdiv,ety,etyt,checksympn +!integer,private,parameter::nmaxn=1000 + integer,private::nd2par,nd2part,nd2partt + integer,private,target ::pos_of_delta + + integer,private,dimension(lnv)::jfil,jfilt + + private equal,DAABSEQUAL,Dequaldacon ,equaldacon ,Iequaldacon,derive,DEQUALDACONS !,AABSEQUAL 2002.10.17 + private pow, GETORDER,CUTORDER,getchar,GETint,GETORDERMAP,GETORDERVEC !, c_bra_v_spinmatrix + private getdiff,getdATRA ,mul,dmulsc,dscmul,GETintmat,GETintnd2_universal !,c_spinor_spinmatrix + private mulsc,scmul,imulsc,iscmul,DAREADTAYLORS,c_pri_c_ray,EQUALql_c_spin,exp_mat_,c_exp_mat_ + private div,ddivsc,dscdiv,divsc,scdiv,idivsc,iscdiv,equalc_ray_r6r,complex_mul_map + private unaryADD,add,daddsca,dscadd,addsc,scadd,iaddsc,iscadd,print_ql,matrixvecfr,r_matrixvecfr + private unarySUB,subs,dsubsc,dscsub,subsc,scsub,isubsc,iscsub,c_clean_taylors + private c_allocda,c_killda,c_a_opt,K_opt,c_,c_allocdas,filter_part,c_clean_c_factored_lie + private dexpt,dcost,dsint,dtant,DAPRINTTAYLORS,c_clean_yu_w,mul_ql_m,mul_ql_cm + PRIVATE GETCHARnd2,GETintnd2,dputchar,dputint, filter,check_j,c_dputint0,c_dputint0r + private GETintnd2t,equalc_cspinor_cspinor,c_AIMAG,c_real,equalc_ray_ray,EQUALql_q,EQUALq_ql,EQUALql_i,EQUALql_ql + PRIVATE DEQUAL,REQUAL,varf,varf001,equalc_spinor_cspinor,EQUALql_r !,CHARINT,pbbrav,cpbbrav + ! PUBLIC VAR,ASS + private pbbra,liebra,full_absT,c_asstaylor,getcharnd2s,GETintnd2s,GETintk,c_get_coeff,pri_matrix,c_pri_matrix + private shiftda,shift000,cDEQUAL,pri,rea,cfu000,alloc_DA,alloc_c_spinmatrix,cpbbra,alloc_c_damaps + private alloc_c_damap,c_DPEKMAP,c_DPOKMAP,kill_c_damap,kill_c_spinmatrix,c_etcct,c_spinmatrix_mul_cray + private EQUALspinmatrix,c_trxtaylor,powmap,POWMAPs,alloc_c_vector_field,kill_c_vector_field,kill_c_damaps + private alloc_c_normal_form,kill_c_normal_form,c_EQUALVEC,c_spinmatrix_spinmatrix,c_IdentityEQUALVEC,qua_ql + private liebraquaternion,liebraso3,pow_tpsaMAP,c_concat_quaternion_ray,matrix_to_quaternion_in_c_damap,iexp_ad + private EQUALql_cmap,EQUALcmap_ql,EQUAL_complex_quaternion_c_quaternion,EQUAL_c_quaternion_complex_quaternion + private NO,ND,ND2,NP,NDPT,NV,ndptb,rf,c_real_spinmatrix,c_taylor_spinmatrix + private c_concat_c_uni_ray,c_concat_c_uni_rays,c_EQUALVECqua + integer, target :: NP,NO,ND,ND2,NV,NDPT,ndptb,rf + private nd_used + integer nd_used + logical(lp):: do_linear_ac_longitudinal=.true. + private old +!private map_mul_vec + logical(lp) :: old + logical(lp),target :: c_real_warning =.true. + logical(lp) :: c_mess_up_vector=.false. + real(dp) :: a_mess=0.0_dp , b_mess=1.0_dp + integer :: i_piotr(3)= (/0,0,0/) + logical :: c_skip_gofix=.false. + PRIVATE null_it,Set_Up,de_Set_Up,LINE_L,RING_L,kill_DALEVEL,dealloc_DASCRATCH,set_up_level + private insert_da,append_da,GETINTegrate,c_pek000,c_pok000,cDEQUALDACON + private cdaddsc,cdscadd,cdsubsc,cdscsub,cdmulsc,cdscmul,cddivsc,cdscdiv + private equalc_t_ct,equalc_ct_c,matrixMAPr,MAPmatrixr,r_MAPmatrixr,c_EQUALMAP,c_IdentityEQUALMAP + private c_IdentityEQUALSPIN,c_pri_spinmatrix,c_pri_map,r_matrixMAPr + private equalc_cmap_map,c_bra_v_ct,c_bra_v_dm,equalc_cvec_vec,c_expflo,c_expflo_map + private alloc_c_factored_lie,kill_c_factored_lie,c_expflo_fac + private c_trxspinmatrix,c_inv_as,sqrtt,alloc_c_spinor,kill_c_spinor,c_complex_spinmatrix,c_trxspinmatrixda + private c_spinmatrix_add_spinmatrix,c_exp_spinmatrix,unarySUB_spinor,c_spinor_add_spinor,c_taylor_spinor + private c_IdentityEQUALSPINOR,c_spinmatrix_spinor,c_logt,c_pri_factored_lie,equalc_map_cmap + private c_expflo_fac_inv,c_logc,c_complex_spinor,c_real_spinor,GETORDERSPINMATRIX,c_pri_spinor + private c_spinor_cmap,c_adjoint_vec,c_adjoint,c_trxtaylor_da,c_spinmatrix_sub_spinmatrix,c_spinor_cmap_tpsa + PRIVATE CUTORDERMAP,CUTORDERspin,CUTORDERspinor,c_concat_tpsa,c_concat_spinor_ray,GETORDERquaternion + private unarySUB_spinmatrix,spinmatrix_spinmatrix + type(C_dalevel) c_scratchda(ndumt) !scratch levels of DA using linked list +integer, private,target :: nd2t=6,ndt=3,ndc2t=2,ndct=1,nd2harm,ndharm +!integer, private, parameter :: ndim2t=10 +logical(lp), private :: c_similarity=my_false +logical(lp) :: symp =my_false +logical(lp) :: c_normal_auto=my_true,c_verbose=my_true +integer :: spin_def_tune=1 !, private +integer :: order_gofix=1 +logical(lp) :: time_lie_choice=my_false,courant_snyder_teng_edwards=my_true,dosymp=.true. +integer :: K_phase_choice=1 +character(20):: phase_choice(1:3)=["Courant-Snyder ", "Anti-Courant-Snyder ","Mengyu "] + private copy_damap_matrix,copy_matrix_matrix,invert_22,dALLOC_33t,dkill_33t,matmul_33,prin_33t + private A_OPT_C_damap,K_OPT_c_damap,equalc_t,equalt_c,matmulr_33 +private c_add_vf,real_mul_vec +private c_sub_vf,c_spinor_sub_spinor,matmult_33,EQUALq_i +private c_IdentityEQUALfactored,c_log_spinmatrix,c_concat_c_ray,equalc_ray_r6,equalc_r6_ray +private equalc_r6r_ray +private dotc_spinor,c_spinor_spinor,c_read_spinmatrix,c_read_map,c_concat_spinmatrix_ray +private GETdiff_universal + +!integer,private,parameter::ndd=6 +private c_concat_vector_field_ray,CUTORDERVEC,kill_c_vector_field_fourier,alloc_c_vector_field_fourier +private complex_mul_vec,equal_c_vector_field_fourier,c_IdentityEQUALVECfourier,c_taylor_mul_vec +private c_add_map,c_sub_map,c_read_spinor,flatten_c_factored_lie_r,c_EQUALcray,c_read_quaternion +integer :: n_fourier=12,n_extra=0 +logical :: remove_tune_shift=.false. +complex(dp) :: n_cai=-2*i_ +integer :: complex_extra_order=0 +logical :: special_extra_order_1=.true. +real(dp) :: epso_factor =1000.0_dp ! for log +logical(lp):: extra_terms_log=.false. +logical :: add_constant_part_concat=.true.,assume_c_quaternion_normalised=.true. +private EQUAL_c_spinmatrix_probe,EQUAL_c_spinmatrix_3_by_3,EQUAL_3_by_3_probe,EQUAL_probe_c_spinmatrix +private EQUAL_probe_3_by_3,equalc_cspinor_spinor,EQUAL_3_by_3_c_spinmatrix +private EQUALq_r,EQUALq_8_c,EQUALq_c_8,EQUALq,POWq,c_invq,subq,mulq,addq,alloc_c_quaternion,kill_c_quaternion +private c_pri_quaternion,CUTORDERquaternion,c_trxquaternion,EQUALq_c_r,EQUALq_r_c,mulcq,c_exp_quaternion +private equalc_quaternion_c_spinor,equalc_spinor_c_quaternion,unarySUB_q,c_trxquaternion_tpsa +private c_exp_vectorfield_on_quaternion,c_vector_field_quaternion,c_vector_field_so3,addql,subql,mulqdiv,powql +private copy_tree_into_tree_zhe,absq2,absq,c_MAP_VEC,c_VEC_MAP,printcomplex,printpoly,print6 +!private equal_map_real8,equal_map_complex8,equal_real8_map,equal_complex8_map +real(dp) dts +real(dp), private :: sj(6,6) +logical :: use_new_stochastic_normal_form=.true. +logical :: qphase=.false.,qphasedef=.false. + integer :: size_tree=15 + integer :: ind_spin0(3,3),ind_spin(3,3),k1_spin(9),k2_spin(9) +logical :: hypercube_integration = .true. +!private ip_mat,jp_mat,jt_mat +real(dp) ip_mat(3,6,6),jp_mat(3,6,6),jt_mat(6,6) +character(24) formatlf(6) +!----------------------------------- +logical :: inside_normal=.false.,bmad_automatic=.false.,spin_automatic=.false. +real(dp) :: Eigenvalues_off_unit_circle = 1.0_dp +real(dp) :: eps_Eigenvalues_off_unit_circle =1.d-10 +!private in1,in2,in3,in4,in5,in6,posin,sigdis,sigdis0,dfac ,pascal,mono_order +integer, pointer :: in1(:)=>null(),in2(:)=>null(),in3(:)=>null(),in4(:)=>null(),in5(:)=>null(),in6(:)=>null() +integer, pointer :: posin(:) => null() +integer(2), pointer :: hash(:,:,:,:,:,:) => null(),pascal(:,:) => null(),mono_order(:)=>null() +real(dpn), pointer :: sigdis(:)=> null(),sigdis0(:)=> null(),dfac(:)=> null(),vsol(:)=> null() +integer i_alloc +integer, private :: nmono +integer nmono_from_moment +real(dp), private :: tiny =1e-20_dp + logical :: sagan_gen =.false.,symplectify_map=.false. +integer mf_,n1_,n2_ +logical :: do_damping=.false.,do_spin=.false.,use_radiation_inverse = .true. +logical :: force_spin_input_normal=.false. +private c_clean_linear_map +private c_fill_uni_r,c_null_uni,c_fill_uni,c_refill_uni,c_equal_UNI +integer :: no_uni = 10000 +type(c_linear_map) q_phasor,qi_phasor +private compute_lattice_functions_1,compute_lattice_functions_2 +!private c_clean_vector,c_clean_matrix,c_clean_vector_complex,c_clean_matrix_complex +private A_opt_c_vector,K_OPT_c_vector,r_field_for_demin,clean_c_universal_taylor +logical :: old_phase_calculation=.false. +logical :: new_cycle=.true. +private EQUAL_arrayreal_arraytaylor,EQUAL_arraycomplex_arraytaylor +private EQUAL_arraytaylor_arrayreal,EQUAL_arraytaylor_arraycomplex +private quaternion_to_spinmatrix,makeso3_equal +logical :: correct_quaternion_field=.true. + logical,private :: unstable(NDIM2t/2) !,hyperbolic + +! These routines computes lattice functions a la Ripken-Forest-Wolski +!type c_lattice_function +! real(dp) :: E(3,6,6) =0 ,K(3,6,6) =0 ! E : moments, K : Invariants +! real(dp) :: H(3,6,6) = 0,B(3,6,6) =0 ! ML=exp( -alpha_i H(i,:,:) + mu_i B(i,:,:)) +! real(dp) :: S(1:3,1:3,0:6) =0 ! l,m,n as function of z_i=1,6; 0 is the constant part +! real(dp) ::phase(3) =0 ,damping(3) =0 , spin(2) =0 ! Phase advances, spin can have a delta +! part if no cavity +! real(dp) fix(6) =0 ! closed orbit +! type(fibre), pointer :: f => null() ! Pointer to the fibre is relevant +! type(integration_node), pointer :: t => null() ! Pointer to the integration node is relevant +! logical :: symplectic = .true. ! if true, then map assumed symplectic (faster inverse computation) +!!!! radiation quantity +! real(dp) :: sigmas(6,6) ! Beam sizes can be put there if computed +!end type c_lattice_function + + INTERFACE compute_lattice_functions + MODULE PROCEDURE compute_lattice_functions_1 ! call compute_lattice_functions(ML,Lat) + MODULE PROCEDURE compute_lattice_functions_2 ! call compute_lattice_functions(M,Lat) + END INTERFACE + + INTERFACE abs_square + MODULE PROCEDURE absq2 + END INTERFACE + INTERFACE abs + MODULE PROCEDURE absq + END INTERFACE + + + INTERFACE assignment (=) + MODULE PROCEDURE EQUAL + MODULE PROCEDURE EQUALq_r + MODULE PROCEDURE EQUALq_8_c + MODULE PROCEDURE EQUALq_c_8 + MODULE PROCEDURE EQUALql_q + MODULE PROCEDURE EQUALql_c_spin + MODULE PROCEDURE EQUALq_ql + MODULE PROCEDURE EQUALql_i + MODULE PROCEDURE EQUALq_i + MODULE PROCEDURE EQUALql_r + MODULE PROCEDURE EQUALq + MODULE PROCEDURE EQUALq_c_r + MODULE PROCEDURE EQUALq_r_c + MODULE PROCEDURE EQUALql_ql + MODULE PROCEDURE EQUAL_c_l_f ! c_lattice_function = true or false (symplectic) + MODULE PROCEDURE EQUAL_complex_quaternion_c_quaternion + MODULE PROCEDURE EQUAL_c_quaternion_complex_quaternion + MODULE PROCEDURE EQUALql_cmap + MODULE PROCEDURE EQUALcmap_ql + MODULE PROCEDURE cDEQUAL + MODULE PROCEDURE DEQUAL ! added 2002.10.17 ! check2002.10.17 + MODULE PROCEDURE REQUAL ! added 2002.10.17 ! check2002.10.17 + MODULE PROCEDURE cDEQUALDACON + MODULE PROCEDURE Dequaldacon + MODULE PROCEDURE DEQUALDACONS ! C_taylor(:) = real(dp)) + MODULE PROCEDURE Iequaldacon + MODULE PROCEDURE equalc_t_ct !# complex Taylor + MODULE PROCEDURE equalc_ct_c + MODULE PROCEDURE equalc_t !# Taylor + MODULE PROCEDURE equalt_c + MODULE PROCEDURE c_EQUALMAP !# c_damap=c_damap + MODULE PROCEDURE c_MAP_VEC + MODULE PROCEDURE c_VEC_MAP + MODULE PROCEDURE c_IdentityEQUALMAP + MODULE PROCEDURE c_IdentityEQUALSPIN + MODULE PROCEDURE c_IdentityEQUALSPINOR !# c_spinor = 0,1,2, or 3 + MODULE PROCEDURE c_IdentityEQUALVEC + MODULE PROCEDURE c_IdentityEQUALfactored + MODULE PROCEDURE c_IdentityEQUALVECfourier + MODULE PROCEDURE EQUAL_c_spinmatrix_probe + MODULE PROCEDURE EQUAL_c_spinmatrix_3_by_3 + module procedure EQUAL_3_by_3_c_spinmatrix + MODULE PROCEDURE EQUAL_3_by_3_probe + MODULE PROCEDURE EQUAL_probe_3_by_3 + MODULE PROCEDURE EQUAL_probe_c_spinmatrix + + MODULE PROCEDURE matrixMAPr + MODULE PROCEDURE r_matrixMAPr + MODULE PROCEDURE MAPmatrixr + MODULE PROCEDURE r_MAPmatrixr + MODULE PROCEDURE r_matrixvecfr + MODULE PROCEDURE matrixvecfr + ! MODULE PROCEDURE c_DPEKMAP + ! MODULE PROCEDURE c_DPOKMAP + MODULE PROCEDURE EQUALspinmatrix + + MODULE PROCEDURE c_EQUALcray !# c_ray=integer + MODULE PROCEDURE equalc_cmap_map + MODULE PROCEDURE equalc_map_cmap + + MODULE PROCEDURE equalc_cvec_vec + + MODULE PROCEDURE c_EQUALVEC !# c_vector_field=c_vector_field + MODULE PROCEDURE c_EQUALVECqua ! quaternion vector field into SO(3) vector field + MODULE PROCEDURE equalc_cspinor_cspinor + MODULE PROCEDURE equalc_ray_r6 + MODULE PROCEDURE equalc_ray_r6r + MODULE PROCEDURE equalc_r6_ray + MODULE PROCEDURE equalc_r6r_ray + MODULE PROCEDURE equalc_ray_ray + MODULE PROCEDURE equal_c_vector_field_fourier + MODULE PROCEDURE equalc_spinor_cspinor + MODULE PROCEDURE equalc_cspinor_spinor + MODULE PROCEDURE flatten_c_factored_lie_r !# same as flatten_c_factored_lie + MODULE PROCEDURE equalc_quaternion_c_spinor + MODULE PROCEDURE equalc_spinor_c_quaternion + + MODULE PROCEDURE equal_map_real8 + MODULE PROCEDURE equal_map_complex8 ! replaces c_dpokmap + MODULE PROCEDURE equal_real8_map + MODULE PROCEDURE equal_complex8_map ! replaces c_dpekmap + MODULE PROCEDURE copy_tree_into_tree_zhe + MODULE PROCEDURE EQUAL_arrayreal_arraytaylor + MODULE PROCEDURE EQUAL_arraycomplex_arraytaylor + MODULE PROCEDURE EQUAL_arraytaylor_arrayreal + MODULE PROCEDURE EQUAL_arraytaylor_arraycomplex + end INTERFACE + + ! UNIVERSAL_TAYLOR + + INTERFACE assignment (=) + MODULE PROCEDURE c_fill_uni_r + MODULE PROCEDURE c_null_uni + MODULE PROCEDURE c_fill_uni ! new sagan + MODULE PROCEDURE c_refill_uni + MODULE PROCEDURE c_equal_UNI ! s1=s2 + end INTERFACE + + INTERFACE OPERATOR (+) + MODULE PROCEDURE unaryADD !@2 This is a unary operation + MODULE PROCEDURE add + MODULE PROCEDURE addq + MODULE PROCEDURE addql + + MODULE PROCEDURE cdaddsc + MODULE PROCEDURE daddsca + MODULE PROCEDURE cdscadd + MODULE PROCEDURE iscadd + + MODULE PROCEDURE dscadd + MODULE PROCEDURE addsc + MODULE PROCEDURE scadd + MODULE PROCEDURE iaddsc + MODULE PROCEDURE c_spinmatrix_add_spinmatrix + MODULE PROCEDURE c_spinor_add_spinor ! adding c_spinor + MODULE PROCEDURE c_add_vf !# adding vector field for exp(ad VF) + MODULE PROCEDURE c_add_map + + END INTERFACE + + + + INTERFACE OPERATOR (-) + MODULE PROCEDURE unarySUB + + MODULE PROCEDURE subq + MODULE PROCEDURE subql + MODULE PROCEDURE subs + MODULE PROCEDURE dsubsc + MODULE PROCEDURE dscsub + MODULE PROCEDURE cdsubsc + MODULE PROCEDURE cdscsub + MODULE PROCEDURE subsc + MODULE PROCEDURE scsub + MODULE PROCEDURE isubsc + MODULE PROCEDURE iscsub + + MODULE PROCEDURE unarySUB_vec + MODULE PROCEDURE unarySUB_q + MODULE PROCEDURE unarySUB_spinor + MODULE PROCEDURE unarySUB_spinmatrix + MODULE PROCEDURE c_spinor_sub_spinor + MODULE PROCEDURE c_spinmatrix_sub_spinmatrix + MODULE PROCEDURE c_sub_vf + MODULE PROCEDURE c_sub_map + END INTERFACE + + INTERFACE OPERATOR (*) + ! MODULE PROCEDURE transform_vector_field_by_map + MODULE PROCEDURE mul + MODULE PROCEDURE mulq + MODULE PROCEDURE mulql + MODULE PROCEDURE mulcq + MODULE PROCEDURE mul_ql_m + MODULE PROCEDURE mul_ql_cm + + MODULE PROCEDURE dmulsc + MODULE PROCEDURE cdmulsc + MODULE PROCEDURE dscmul + MODULE PROCEDURE cdscmul + MODULE PROCEDURE mulsc + MODULE PROCEDURE scmul + MODULE PROCEDURE imulsc + MODULE PROCEDURE iscmul + + END INTERFACE + + INTERFACE OPERATOR (*) + MODULE PROCEDURE c_concat !# c_damap o c_damap M= A*B (DA concact) + MODULE PROCEDURE c_trxtaylor ! c_taylor o c_damap t=a*A (DA substitution) + MODULE PROCEDURE c_trxquaternion !# c_quaternion= c_quaternion * c_damap + MODULE PROCEDURE real_mul_vec ! real(dp)*vf G=rF → F.grad + MODULE PROCEDURE complex_mul_vec !# complex(dp)*vf G=cF + MODULE PROCEDURE c_taylor_mul_vec !# c_taylor*vf G=cF + MODULE PROCEDURE real_mul_map !# real(dp)*c_damap B=rA + MODULE PROCEDURE complex_mul_map !# real(dp)*c_damap B=rA +! Vector fields + MODULE PROCEDURE c_bra_v_ct !# F.grad taylor t = F*a (no quaternion effect) + MODULE PROCEDURE c_bra_v_dm !# c_damap=(F.grad +q ) c_damap !T = F* A + MODULE PROCEDURE c_vector_field_quaternion !# (f.grad + q)quaternion q'=F*q + ! bra_v_q(f,quaternion) = f.grad quaternion + MODULE PROCEDURE c_vector_field_so3 + MODULE PROCEDURE map_mul_vec_q ! c_damap * c_vector_field means "transform field by map" +! G=AF is the same as G=AFA^(-1) +! SO(3) stuff : used only these days on the ISF once computed via quaternions + MODULE PROCEDURE c_spinmatrix_spinmatrix !# Spinmatrix*Spinmatrix S3=S2*S1 + MODULE PROCEDURE c_complex_spinmatrix !# c*Spinmatrix scalar multiplication + MODULE PROCEDURE c_taylor_spinor !# taylor * c_spinor + MODULE PROCEDURE c_complex_spinor !# c_spinor= complex * c_spinor + MODULE PROCEDURE c_real_spinor !# spinor = real(dp) * spinor + MODULE PROCEDURE c_spinor_spinor !# c_spinor = c_spinor x c_spinor !cross product + MODULE PROCEDURE c_spinmatrix_spinor !# c_spinor = matrix * c_spinor s' =S2 s + MODULE PROCEDURE c_spinor_cmap !# c_spinor =c_spinor * c_damap substitution + MODULE PROCEDURE c_trxspinmatrix !# c_spinmatrix= c_spinmatrix * c_damap + MODULE PROCEDURE c_real_spinmatrix + MODULE PROCEDURE c_taylor_spinmatrix + END INTERFACE + + INTERFACE OPERATOR (.o.) + ! + + + module procedure c_concat_tpsa !# c_damap o c_damap M= A*B (TPSA concact) + module procedure c_trxtaylor_da !c_taylor o c_damap t=a*A (TPSA substitution) + module procedure c_trxquaternion_tpsa !# c_quaternion= c_quaternion .o. c_damap + + + module procedure c_concat_spinor_ray !# c_spinor= c_spinor .o. c_ray +! c_ray is a general ray contain c_ray%x(lnv) and quaternion + MODULE PROCEDURE c_quaternion_mul_cray !# c_ray%q = c_quaternion.o.c_ray%x + module procedure c_concat_c_uni_ray !# c__universal_taylor .o. c_ray + module procedure c_concat_c_uni_rays !# c__universal_taylor(:) .o. c_ray + module procedure c_concat_c_ray !# c_taylor .o. c_ray + module procedure c_concat_map_ray !# c_ray= c_damap .o. c_ray +!!! almost obsolete + module procedure c_trxspinmatrixda !# c_spinmatrix=c_spinmatrix .o. c_damap + MODULE PROCEDURE c_spinmatrix_mul_cray !# c_ray%s = spin_matrix.o.c_ray%x c_ray%S(1:3) +! used with ISF perhaps + MODULE PROCEDURE c_spinor_cmap_tpsa !# spinor=spinor .o. c_damap + + + END INTERFACE + + INTERFACE OPERATOR (.oo.) + module procedure pow_tpsaMAP ! Power of a TPSA map + END INTERFACE + + INTERFACE OPERATOR (/) + MODULE PROCEDURE div + MODULE PROCEDURE cddivsc + MODULE PROCEDURE ddivsc + MODULE PROCEDURE cdscdiv + MODULE PROCEDURE dscdiv + MODULE PROCEDURE divsc + MODULE PROCEDURE scdiv + MODULE PROCEDURE idivsc + MODULE PROCEDURE iscdiv + MODULE PROCEDURE mulqdiv + END INTERFACE + + + INTERFACE OPERATOR (**) + MODULE PROCEDURE POW ! t=a**(n) negative n OK if TPSA permitted (t0/=0) + MODULE PROCEDURE POWQ ! q'=q**(n) negative n OK if TPSA permitted (q%x(0)/=0) + END INTERFACE + + INTERFACE OPERATOR (**) + MODULE PROCEDURE POWql ! TL=AL**(n) negative n OK if map has inverse + MODULE PROCEDURE powmap ! T=A**(n) negative n OK if map has inverse + MODULE PROCEDURE powmaps ! S2=S1**(n) negative n OK if map has inverse (c_spinmatrix) + END INTERFACE + + + ! New Operators + + INTERFACE OPERATOR (.cmono.) + MODULE PROCEDURE c_dputint0 !@1   single integer -> complex(dp).cmono.i = c dz_i + MODULE PROCEDURE c_dputint0r !@1   single integer -> real(dp).cmono.i = r dz_i + MODULE PROCEDURE dputint !@1   Accepts J(nv) > complex(dp).cmono.j(:) = c dz_1^j(1)...dz_n^j(n) + MODULE PROCEDURE dputchar !@1   Accepts String such as '13' -> c.cmono.'13'=c dz_1^1 dz_2^3 + MODULE PROCEDURE dputintr !@1   Accepts J(nv) -> real(dp).cmono.j(:) = r dz_1^j(1)...dz_n^j(n) + MODULE PROCEDURE dputcharr !@1   Accepts String such as '13' -> r.cmono.'13'=r dz_1^1 dz_2^3 + END INTERFACE + + INTERFACE OPERATOR (.var.) ! not very useful + MODULE PROCEDURE varf !@1   varf=S1 + ((1.0_dp,0.0_dp).cmono.S2) + MODULE PROCEDURE varf001 !@1 varf001=S1(1) + (s1(2).cmono.S2) + END INTERFACE + + INTERFACE OPERATOR (.d.) + MODULE PROCEDURE getdiff !@1 takes derivatives of c_taylor dt/dz_i = t.d.i + MODULE PROCEDURE GETdiff_universal !@1 takes derivatives of c_universal_taylor dt_uni/dz_i=t_uni.d.i + END INTERFACE + + INTERFACE OPERATOR (.i.) + MODULE PROCEDURE GETINTegrate !@1 takes anti-derivatives of c_taylor (lose one order!), t = dt/dz_i.d.i + END INTERFACE + + + INTERFACE OPERATOR (.SUB.) + MODULE PROCEDURE GETORDER ! t2=t.sub.i extracts second order part only + MODULE PROCEDURE getchar ! complex(dp)= t.sub.'12' coefficient of z_1 z_2^2 extracted + MODULE PROCEDURE GETint ! complex(dp)= t.sub.j(:) same as above using array + MODULE PROCEDURE GETORDERMAP ! extract order i of map N=M.sub.i +!with negative integer map.sub.i the spin is handled with iabs(i)-1 + MODULE PROCEDURE GETORDERVEC + MODULE PROCEDURE GETORDERquaternion! same as above for quaternion (negative not accepted) + MODULE PROCEDURE GETORDERSPINMATRIX ! same FOR SPIN MATRICES (negative not accepted) + MODULE PROCEDURE c_get_coeff + END INTERFACE + + + INTERFACE OPERATOR (.index.) +! extract linear dependence on ith variables. Useful to get matrices. + MODULE PROCEDURE GETintmat ! complex(dp)=t.index.i for example t.index.2= t.sub[0,1,0,...] + END INTERFACE + + INTERFACE OPERATOR (.PAR.) +! same as .sub. put returns a c_taylor as a function of parameters + MODULE PROCEDURE getcharnd2 ! w=t.par.'13' returns w=a(z_1^1 z2^3) +! where is a polynomial in variables 3,4,...nv +! notice that w=t.par.'13 0' returns w=a(z_1^1 z2^3 z3^0) where a contains variables 4,5,... + MODULE PROCEDURE GETintnd2 !same using array t.par.[1,3] + MODULE PROCEDURE GETintnd2t + MODULE PROCEDURE GETintnd2_universal ! .par. on unversal into a c_taylor + END INTERFACE + + +! not used much +!TYPE sub_taylor +! INTEGER j(lnv) + +! INTEGER min,max +! END TYPE sub_taylor +! extract coefficient of x^j(st%min:t%max) as a polynomial (so far useless routine) + INTERFACE OPERATOR (.part.) + MODULE PROCEDURE GETintnd2t + END INTERFACE + + + + +! same as .par. But the variables are moved to position 4,5 are moved to 1,2 in .par. example +! For example, dbeta/ddelta the variable 6 of BMAD become variable 1. + INTERFACE OPERATOR (<=) + MODULE PROCEDURE getcharnd2s ! w=t<='11' + MODULE PROCEDURE GETintnd2s ! w=t<=[1,1] +!!! Just moves index by integer input + MODULE PROCEDURE GETintk ! for example,w=t<=[1,1] same as w=(t.par.[1,1])<=2 + END INTERFACE + +!!!! To cut high order terms + INTERFACE OPERATOR (.CUT.) + MODULE PROCEDURE CUTORDER ! w=t.cut.n Order n and above are gone + MODULE PROCEDURE CUTORDERMAP ! N=M.cut.|n| if n<0 quaternion part cut |n|-1 + MODULE PROCEDURE CUTORDERvec ! G=F.cut.|n| if n<0 quaternion part cut |n|-1 + MODULE PROCEDURE CUTORDERspin ! cut spin matrix S2=s1.cut.n + MODULE PROCEDURE CUTORDERspinor ! Spinor2=spinor1.cut.n + MODULE PROCEDURE CUTORDERquaternion ! Q2=q1.cut.|n| if n<0 quaternion part cut |n|-1 + END INTERFACE + + INTERFACE OPERATOR (.dot.) ! Used internally primarily + MODULE PROCEDURE dotc_spinor ! c_taylor=c_spin1.dot.c_spin2 (regular real dot product) + END INTERFACE + + INTERFACE OPERATOR (.K.) ! Used internally primarily + MODULE PROCEDURE getdATRA ! lowers the power of the nth variable w=t.k.n (fake derivative) + END INTERFACE + + INTERFACE OPERATOR (.pb.) + MODULE PROCEDURE pbbra ! Poisson bracket w=t1.pb.t2 = [t1,t2] + END INTERFACE + + INTERFACE OPERATOR (.cpb.) + MODULE PROCEDURE cpbbra ! Poisson bracket in phasors w=t1.pb.t2 = -n_cai*[t1,t2] + END INTERFACE + + INTERFACE OPERATOR (.lb.) + ! The Lie bracket of two vector field. + MODULE PROCEDURE liebra !# F= includes spin now + MODULE PROCEDURE liebraquaternion !# used by liebra mostly private (not to be used alone) + MODULE PROCEDURE liebraso3 !# used by liebra mostly private (not to be used alone) + + END INTERFACE + + ! INTERFACE getvf + ! MODULE PROCEDURE pbbrav + !end INTERFACE getvf + + !INTERFACE cgetvf + ! MODULE PROCEDURE cpbbrav + !end INTERFACE cgetvf + + ! intrisic functions overloaded + INTERFACE checksymp + MODULE PROCEDURE checksympn + end INTERFACE checksymp + + INTERFACE q_part + MODULE PROCEDURE qua_ql + end INTERFACE q_part + + +!!! produce C such that C**(-1)*R*C=diagonal! c_phasor(n)= c_phasor()**(n) +! if n_cai=-2i (default) +! C(1) = 1/2 x_1 + 1/2 x_2 C(2) = -i/2 x_1 + i/2 x_2 +! if n_cai=-2i (default) +! C(2) = 1/sqrt(2) x_1 + 1/sqrt(2) x_2 C(2) = -i/sqrt(2) x_1 + i/sqrt(2) x_2 + INTERFACE c_phasor + MODULE PROCEDURE from_phasor + end INTERFACE c_phasor + +! Ci_phasor() is the inverse of C_phasor() + INTERFACE ci_phasor + MODULE PROCEDURE to_phasor + end INTERFACE ci_phasor + + + ! Exponential of Lie Operators + + INTERFACE clean +! MODULE PROCEDURE c_clean + MODULE PROCEDURE c_clean_c_factored_lie + MODULE PROCEDURE c_clean_linear_map + MODULE PROCEDURE c_clean_spinor + MODULE PROCEDURE c_clean_taylor + MODULE PROCEDURE c_clean_spinmatrix + MODULE PROCEDURE c_clean_damap + MODULE PROCEDURE c_clean_vector_field + MODULE PROCEDURE c_clean_yu_w + MODULE PROCEDURE c_clean_quaternion + MODULE PROCEDURE c_clean_taylors + MODULE PROCEDURE c_clean_vector_field_fourier + MODULE PROCEDURE clean_c_universal_taylor + end INTERFACE clean + ! Exponential of Lie Operators + + + INTERFACE c_simil + MODULE PROCEDURE c_adjoint + MODULE PROCEDURE c_adjoint_vec + end INTERFACE c_simil + + INTERFACE texp_inv + MODULE PROCEDURE c_expflo_fac_inv + END INTERFACE + + INTERFACE exp_inv + MODULE PROCEDURE c_expflo_fac_inv ! v9 + END INTERFACE + + INTERFACE real + MODULE PROCEDURE c_real + END INTERFACE + + INTERFACE aimag + MODULE PROCEDURE c_AIMAG + END INTERFACE + + INTERFACE cget_field_c_universal_taylor + MODULE PROCEDURE d_field_for_demin + END INTERFACE + + INTERFACE get_field_c_universal_taylor + MODULE PROCEDURE r_field_for_demin + END INTERFACE + + INTERFACE exp_mat + MODULE PROCEDURE exp_mat_ ! flow on c_taylor w=exp(F,t) w=exp(F.grad)t + MODULE PROCEDURE c_exp_mat_ !T=exp(F,M) T=exp(F.grad)M M=1 of omitted + END INTERFACE + +!exp_mat(f,m) is a subroutine to exponentiate matrices + INTERFACE exp + MODULE PROCEDURE c_expflo ! flow on c_taylor w=exp(F,t) w=exp(F.grad)t + MODULE PROCEDURE c_expflo_map !T=exp(F,M) T=exp(F.grad)M M=1 of omitted + + +! TYPE c_factored_lie Internally useful (Dragt-Finn factorization) +! integer :: n = 0 +! integer :: dir= 0 ! 1=dragt-Finn -1=reverse-dragt-Finn +! type (c_vector_field), pointer :: f(:)=>null() +! END TYPE c_factored_lie +! F is of type c_factor_lie + MODULE PROCEDURE c_expflo_fac ! T=exp(F,M) => T=exp(F_1.grad)...exp(F_no.grad)M or T=exp(F_no.grad)...exp(F_1.grad)M + MODULE PROCEDURE c_exp_spinmatrix ! obsolescent + ! MODULE PROCEDURE c_exp_vectorfield_on_quaternion ! internal use etienne_remove + MODULE PROCEDURE c_exp_quaternion ! internal use + +! same as map_mul_vec_q in (*) If G=exp(G.grad)I same as G*F=exp()F + MODULE PROCEDURE exp_ad ! exp()F F and G are vector fields + + END INTERFACE + +! call MAKEquaternion(M) ! M%q is created from the c_spinmatrix m%s +! Not so useful + INTERFACE MAKEquaternion + MODULE PROCEDURE matrix_to_quaternion_in_c_damap + END INTERFACE + + + INTERFACE MAKESO3 +!!! opposite of MAKEquaternion (Very useful) + MODULE PROCEDURE quaternion_to_matrix_in_c_damap +!! call MAKESO3(Ml,m) uses the quaternion in the linear map + MODULE PROCEDURE c_linear_map_to_matrix + MODULE PROCEDURE quaternion_to_spinmatrix + END INTERFACE + + INTERFACE assignment (=) + MODULE PROCEDURE makeso3_equal + END INTERFACE + + + INTERFACE AVERAGE + MODULE PROCEDURE c_AVERAGE !2000.12.25 + END INTERFACE + ! management routines + + INTERFACE iexp + MODULE PROCEDURE iexp_ad + END INTERFACE iexp + + INTERFACE texp + MODULE PROCEDURE c_expflo + MODULE PROCEDURE c_expflo_map + MODULE PROCEDURE c_expflo_fac + MODULE PROCEDURE c_exp_spinmatrix + MODULE PROCEDURE c_exp_vectorfield_on_quaternion + MODULE PROCEDURE c_exp_quaternion + MODULE PROCEDURE exp_ad ! exp()F F is a vector field + END INTERFACE + + INTERFACE abs + MODULE PROCEDURE DAABSEQUAL ! remove 2002.10.17 + END INTERFACE + + INTERFACE dabs + MODULE PROCEDURE DAABSEQUAL ! remove 2002.10.17 + END INTERFACE + + INTERFACE exp + MODULE PROCEDURE dexpt + END INTERFACE + INTERFACE dexp + MODULE PROCEDURE dexpt + END INTERFACE + INTERFACE cexp + MODULE PROCEDURE dexpt + END INTERFACE + INTERFACE cdexp + MODULE PROCEDURE dexpt + END INTERFACE + + INTERFACE log + MODULE PROCEDURE c_logt + MODULE PROCEDURE c_logc + MODULE PROCEDURE c_logf !# log of a map see subroutine c_flofacg + MODULE PROCEDURE c_log_spinmatrix !# spinor=log(s) +! c_logf_spin is overloaded as ln +! F=ln(M,H,epso,n,tpsa) then M=exp(F)I +! H is a guess for F is known +! epso = is a small number (optional) for convergence +! n = maximal number of iteration (optional, defaulted to 1000) +! tpsa is true by default, otherwise it is a DA calculation + END INTERFACE + + INTERFACE ln + MODULE PROCEDURE c_logf_spin + END INTERFACE + + INTERFACE cos + MODULE PROCEDURE dcost + END INTERFACE + INTERFACE cdcos + MODULE PROCEDURE dcost + END INTERFACE + INTERFACE dcos + MODULE PROCEDURE dcost + END INTERFACE + INTERFACE ccos + MODULE PROCEDURE dcost + END INTERFACE + + + + + INTERFACE sin + MODULE PROCEDURE dsint + END INTERFACE + INTERFACE cdsin + MODULE PROCEDURE dsint + END INTERFACE + INTERFACE ccsin + MODULE PROCEDURE dsint + END INTERFACE + INTERFACE dsin + MODULE PROCEDURE dsint + END INTERFACE + + INTERFACE sqrt + MODULE PROCEDURE sqrtt + END INTERFACE + + + INTERFACE tan + MODULE PROCEDURE dtant + END INTERFACE + + INTERFACE dtan + MODULE PROCEDURE dtant + END INTERFACE + + ! Non-intrisic Functions + + INTERFACE c_pek + MODULE PROCEDURE c_pek000 ! + END INTERFACE + + INTERFACE c_pok + MODULE PROCEDURE c_pok000 ! + END INTERFACE + + INTERFACE shiftda + MODULE PROCEDURE shift000 ! not private + END INTERFACE + + ! INTERFACE var + ! MODULE PROCEDURE var000 ! not private + ! MODULE PROCEDURE var001 ! not private + ! END INTERFACE + + INTERFACE cfu + MODULE PROCEDURE c_cfu000 ! not private + END INTERFACE + + INTERFACE full_abs + MODULE PROCEDURE full_absT + END INTERFACE + + INTERFACE daread + MODULE PROCEDURE c_rea + module procedure c_read_spinmatrix + module procedure c_read_map + MODULE PROCEDURE c_read_spinor + MODULE PROCEDURE DAREADTAYLORS + MODULE PROCEDURE c_read_quaternion + END INTERFACE + + INTERFACE read + MODULE PROCEDURE c_rea + module procedure c_read_spinmatrix + module procedure c_read_map + MODULE PROCEDURE c_read_spinor + MODULE PROCEDURE DAREADTAYLORS + MODULE PROCEDURE c_read_quaternion + END INTERFACE + + INTERFACE daprint + MODULE PROCEDURE c_pri + MODULE PROCEDURE c_pri_spinmatrix + MODULE PROCEDURE c_pri_map + MODULE PROCEDURE c_pri_vec + MODULE PROCEDURE c_pri_factored_lie + MODULE PROCEDURE c_pri_spinor + MODULE PROCEDURE prin_33t + MODULE PROCEDURE c_pri_quaternion + MODULE PROCEDURE DAPRINTTAYLORS + MODULE PROCEDURE c_pri_c_ray + MODULE PROCEDURE print_vector_field_fourier + END INTERFACE + + INTERFACE print + MODULE PROCEDURE c_pri + MODULE PROCEDURE c_pri_spinmatrix + MODULE PROCEDURE c_pri_map + MODULE PROCEDURE c_pri_vec + MODULE PROCEDURE c_pri_factored_lie + MODULE PROCEDURE c_pri_spinor + MODULE PROCEDURE prin_33t + MODULE PROCEDURE DAPRINTTAYLORS + MODULE PROCEDURE c_pri_quaternion + MODULE PROCEDURE print_ql + MODULE PROCEDURE c_pri_c_ray + ! MODULE PROCEDURE c_printunitaylor + MODULE PROCEDURE c_printunitaylors + MODULE PROCEDURE c_printunitaylor_old + MODULE PROCEDURE print_vector_field_fourier + END INTERFACE + + + INTERFACE daprint + MODULE PROCEDURE printcomplex + MODULE PROCEDURE printpoly + MODULE PROCEDURE print6 + END INTERFACE + + INTERFACE print + MODULE PROCEDURE printcomplex + MODULE PROCEDURE printpoly + MODULE PROCEDURE print6 + MODULE PROCEDURE c_pri_matrix + MODULE PROCEDURE pri_matrix + END INTERFACE + + + + ! Constructors and Destructors + + INTERFACE alloc + MODULE PROCEDURE c_allocda + MODULE PROCEDURE c_a_opt + MODULE PROCEDURE A_OPT_c_damap + MODULE PROCEDURE A_opt_c_vector + MODULE PROCEDURE c_allocdas + MODULE PROCEDURE alloc_c_spinmatrix + MODULE PROCEDURE alloc_c_vector_field_fourier + MODULE PROCEDURE alloc_c_damap + MODULE PROCEDURE alloc_c_damaps + MODULE PROCEDURE alloc_c_vector_field + MODULE PROCEDURE alloc_c_factored_lie + MODULE PROCEDURE alloc_c_normal_form + MODULE PROCEDURE alloc_c_spinor + MODULE PROCEDURE alloc_c_yu_w + MODULE PROCEDURE alloc_c_quaternion + END INTERFACE + + INTERFACE ALLOC_nn + MODULE PROCEDURE dALLOC_33t + END INTERFACE + + INTERFACE kill_nn + MODULE PROCEDURE dkill_33t + END INTERFACE + + + INTERFACE matmul_nn + MODULE PROCEDURE matmul_33 + END INTERFACE + + INTERFACE matmulr_nn + MODULE PROCEDURE matmulr_33 + MODULE PROCEDURE matmult_33 + END INTERFACE + + INTERFACE KILL + MODULE PROCEDURE c_killda + MODULE PROCEDURE c_killdas + MODULE PROCEDURE K_opt + MODULE PROCEDURE K_OPT_c_damap + MODULE PROCEDURE K_OPT_c_vector + MODULE PROCEDURE kill_c_damap + MODULE PROCEDURE kill_c_damaps + MODULE PROCEDURE kill_c_spinmatrix + MODULE PROCEDURE kill_c_vector_field + MODULE PROCEDURE kill_c_factored_lie + MODULE PROCEDURE kill_c_vector_field_fourier + MODULE PROCEDURE kill_c_normal_form + MODULE PROCEDURE kill_c_spinor + MODULE PROCEDURE kill_c_yu_w + MODULE PROCEDURE kill_c_quaternion + END INTERFACE + + INTERFACE alloctpsa + MODULE PROCEDURE c_allocda + END INTERFACE + + INTERFACE KILLtpsa + MODULE PROCEDURE c_killda + END INTERFACE + + + + INTERFACE ass + MODULE PROCEDURE c_asstaylor !2000.12.25 + END INTERFACE + + + + INTERFACE alloc + MODULE PROCEDURE c_alloc_u + MODULE PROCEDURE c_alloc_us + END INTERFACE + + INTERFACE KILL + MODULE PROCEDURE c_kill_uni + MODULE PROCEDURE c_kill_unis + END INTERFACE + + +CONTAINS + + + +subroutine get_rf(rfo,nd2to,nd2o) +implicit none +integer rfo,nd2to,nd2o +rfo=rf +nd2to=nd2t +nd2o=nd2 + +end subroutine get_rf + + + + +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + subroutine c_get_indices(n,mf) +!#general: informationc_% +!# In the arrary n(>11), important parameters of the normal +!# form can be retrieved. +!# If mf/=0, they are printed on file mf. +!# n(1)=NO +!# n(2)=ND +!# n(3)=ND2 +!# n(4)=NV +!# n(5)=Ndpt +!# n(6)=ndptb +!# n(7)=np +!# n(8)=rf*2 +!# n(9)=ndc2t +!# n(10)=nd2t +!# n(11)=nd2harm + implicit none + integer n(:),mf + + if(size(n)<11) then + write(6,*) " index array to small in c_get_indices " + stop + endif + n(1)=NO + n(2)=ND + n(3)=ND2 + n(4)=NV + n(5)=Ndpt + n(6)=ndptb + n(7)=np + n(8)=rf*2 + n(9)=ndc2t + n(10)=nd2t + n(11)=nd2harm + +if(mf/=0) then + write(mf,"(11(a7))") " NO "," ND "," ND2"," NV "," NDPT "," NDPTB "," NP "," RF "," NDC2T ", & + " ND2T "," HARM " + write(mf,"(11(3x,i2,2x))") n(1:11) +endif + +end subroutine c_get_indices + + subroutine locally_set_da_pointers() + use da_arrays,only : c_ + implicit none + c_%no => no + c_%nv => nv + c_%nd => nd + c_%nd2 => nd2 + c_%np => np + c_%ndpt => ndpt + end subroutine locally_set_da_pointers + + subroutine c_count_taylor(n,ns,ne) +!#restricted : information +!# Counts number of c_taylor allocated; +!# it is used for debugging purposes. + implicit none + integer n,ns,ne,i + call c_count_da(n) + ns=0 + do i=1,ndumt + ns=c_scratchda(i)%n+ns + enddo + ne=n-ns + end subroutine c_count_taylor + + FUNCTION unaryADD( S1 ) + implicit none + TYPE (c_taylor) unaryADD + TYPE (c_taylor), INTENT (IN) :: S1 + integer localmaster + + IF(.NOT.C_STABLE_DA) then + unaryADD%i=0 + RETURN + endif + + localmaster=c_master + + ! call check(s1) + call ass(unaryADD) + + unaryADD=s1 + + c_master=localmaster + + END FUNCTION unaryADD + + FUNCTION unarySUB( S1 ) + implicit none + TYPE (c_taylor) unarySUB + TYPE (c_taylor), INTENT (IN) :: S1 + integer localmaster + + IF(.NOT.C_STABLE_DA) then + unarySUB%i=0 + RETURN + endif + + localmaster=c_master + + ! call check(s1) + call ass(unarySUB) + + ! unarySUB=(-one)*s1 + ! if(old) then + call c_dacmu(s1%i,(-1.0_dp,0.0_dp),c_temp%i) + call c_dacop(c_temp%i,unarySUB%i) + ! else + ! call newc_dacmu(s1%j,-one,unarySUB%j) + ! ! call newc_dacmu(s1%j,-one,c_temp%i%il) + ! ! call newc_dacop(c_temp%i%il,unarySUB%j) + ! endif + c_master=localmaster + + END FUNCTION unarySUB + + + FUNCTION unarySUB_vec( S1 ) + implicit none + TYPE (c_vector_field) unarySUB_vec + TYPE (c_vector_field), INTENT (IN) :: S1 + integer localmaster,i + + IF(.NOT.C_STABLE_DA) then + unarySUB_vec%v%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + unarySUB_vec%n=s1%n + call c_ass_vector_field(unarySUB_vec) + + do i=1,s1%n + unarySUB_vec%v(i)=-s1%v(i) + enddo + + if(use_quaternion) THEN + unarySUB_vec%q=-s1%q + else +! unarySUB_vec%h=-s1%h + unarySUB_vec%L=-s1%L + endif + unarySUB_vec%nrmax=s1%nrmax + unarySUB_vec%eps=s1%eps + + c_master=localmaster + + END FUNCTION unarySUB_vec + + + + FUNCTION unarySUB_q( S1 ) + implicit none + TYPE (c_quaternion) unarySUB_q + TYPE (c_quaternion), INTENT (IN) :: S1 + integer localmaster,i + + IF(.NOT.C_STABLE_DA) then + unarySUB_q%x(0)%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_quaternion(unarySUB_q) + + do i=0,3 + unarySUB_q%x(i)=-s1%x(i) + enddo + + + c_master=localmaster + + END FUNCTION unarySUB_q + + FUNCTION unarySUB_spinor( S1 ) + implicit none + TYPE (c_spinor) unarySUB_spinor + TYPE (c_spinor), INTENT (IN) :: S1 + integer localmaster,i + + IF(.NOT.C_STABLE_DA) then + unarySUB_spinor%v%i=0 + RETURN + endif + localmaster=c_master + + + call c_ass_spinor(unarySUB_spinor) + + do i=1,3 + unarySUB_spinor%v(i)=-s1%v(i) + enddo + + + c_master=localmaster + + END FUNCTION unarySUB_spinor + + FUNCTION unarySUB_spinmatrix( S1 ) + implicit none + TYPE (c_spinmatrix) unarySUB_spinmatrix + TYPE (c_spinmatrix), INTENT (IN) :: S1 + integer localmaster,i,j + + IF(.NOT.C_STABLE_DA) then + unarySUB_spinmatrix%s(1,1)%i=0 + endif + localmaster=c_master + + + call c_ass_spinmatrix(unarySUB_spinmatrix) + + do i=1,3 + do j=1,3 + unarySUB_spinmatrix%s(i,j)=-s1%s(i,j) + enddo + enddo + + + c_master=localmaster + + END FUNCTION unarySUB_spinmatrix + + subroutine normalise_spinor(n1) +!#general: manipulation +!# The c_spinor n1 is normalised. + implicit none + type(c_spinor), intent(inout) :: n1 + type(c_taylor) norm + + call alloc(norm); + + norm=n1.dot.n1 + norm=1.0_dp/sqrt(norm) + n1=norm*n1 + + call kill(norm); + + end subroutine normalise_spinor + + subroutine orthogonalise_spin_matrix(s) +!#general: manipulation +!# The c_spinmatrix s is normalised, that is to say +!# forced into O(3). + + implicit none + TYPE (c_spinmatrix) s + type(c_spinor) n1,n2,n3 + type(c_taylor) norm + integer i + call alloc(norm); + call alloc(n1); call alloc(n2); call alloc(n3); + do i=1,3 + n1%v(i)=s%s(1,i) + n2%v(i)=s%s(2,i) + enddo + + call normalise_spinor(n1) + + norm=-(n1.dot.n2) + + n2=n2+norm*n1 + + call normalise_spinor(n2) + + n3=n1*n2 + + + call normalise_spinor(n3) + + do i=1,3 + s%s(1,i)=n1%v(i) + s%s(2,i)=n2%v(i) + s%s(3,i)=n3%v(i) + enddo + + + call kill(norm); + call kill(n1); call kill(n2); call kill(n3); + + end subroutine orthogonalise_spin_matrix + + FUNCTION dotc_spinor( S1, S2 ) ! spin routine + implicit none + TYPE (c_taylor) dotc_spinor + TYPE (c_spinor), INTENT (IN) :: S1,S2 + + INTEGER I + integer localmaster + IF(.NOT.C_STABLE_DA) RETURN + localmaster=c_master + + + ! call checkdamap(s1) + call c_asstaylor(dotc_spinor) + + dotc_spinor=0.0_dp + + DO I=1,3 + dotc_spinor=dotc_spinor+s1%v(i)*s2%v(i) + ENDDO + + + c_master=localmaster + + END FUNCTION dotc_spinor + + SUBROUTINE c_maketree(S1,s2) + implicit none + type (c_taylor),INTENT(IN)::S1 + type (c_taylor),INTENT(inOUT):: s2 + IF(.NOT.C_STABLE_DA) RETURN + + ! if(old) then + call c_mtree((/s1%i/),1,(/s2%i/),1) + ! else + ! call newc_dacop(s1%j,s2%j) + ! endif + END SUBROUTINE c_maketree + + SUBROUTINE c_allocda(S1) +!* + implicit none + type (c_taylor),INTENT(INOUT)::S1 + + ! IF(first_time) THEN + IF(c_last_tpsa==0) THEN + + write(6,*) " No TPSA package ever initialized c_allocda " + + ! call !write_e(111) + ENDIF + ! if(old) then + s1%i=0 +!call c_count_da(i_alloc) +!write(6,*) 1,i_alloc + call c_etall1(s1%i) + + + ! else + ! call nullnewda(s1%j) + ! call allocnewda(s1%j) + ! endif + END SUBROUTINE c_allocda + + SUBROUTINE alloc_c_quaternion(S2) + implicit none + type (c_quaternion),INTENT(INOUT)::S2 + integer i + do i=0,3 + call alloc(s2%x(i)) + enddo + + END SUBROUTINE alloc_c_quaternion + + SUBROUTINE kill_c_quaternion(S2) + implicit none + type (c_quaternion),INTENT(INOUT)::S2 + integer i + do i=0,3 + call kill(s2%x(i)) + enddo + + END SUBROUTINE kill_c_quaternion + + SUBROUTINE c_a_opt(S1,S2,s3,s4,s5,s6,s7,s8,s9,s10) +!* + implicit none + type (c_taylor),INTENT(INout)::S1,S2 + type (c_taylor),optional, INTENT(INout):: s3,s4,s5,s6,s7,s8,s9,s10 + call c_allocda(s1) + call c_allocda(s2) + if(present(s3)) call c_allocda(s3) + if(present(s4)) call c_allocda(s4) + if(present(s5)) call c_allocda(s5) + if(present(s6)) call c_allocda(s6) + if(present(s7)) call c_allocda(s7) + if(present(s8)) call c_allocda(s8) + if(present(s9)) call c_allocda(s9) + if(present(s10))call c_allocda(s10) + END SUBROUTINE c_a_opt + + SUBROUTINE K_OPT(S1,S2,s3,s4,s5,s6,s7,s8,s9,s10) +!* + implicit none + type (c_taylor),INTENT(INout)::S1,S2 + type (c_taylor),optional, INTENT(INout):: s3,s4,s5,s6,s7,s8,s9,s10 + call c_killda(s1) + call c_killda(s2) + if(present(s3)) call c_killda(s3) + if(present(s4)) call c_killda(s4) + if(present(s5)) call c_killda(s5) + if(present(s6)) call c_killda(s6) + if(present(s7)) call c_killda(s7) + if(present(s8)) call c_killda(s8) + if(present(s9)) call c_killda(s9) + if(present(s10))call c_killda(s10) + END SUBROUTINE K_opt + + + SUBROUTINE A_opt_c_damap(S1,S2,s3,s4,s5,s6,s7,s8,s9,s10) +!* + implicit none + type (c_damap),INTENT(INout)::S1,S2 + type (c_damap),optional, INTENT(INout):: s3,s4,s5,s6,s7,s8,s9,s10 + call alloc(s1) + call alloc(s2) + if(present(s3)) call alloc(s3) + if(present(s4)) call alloc(s4) + if(present(s5)) call alloc(s5) + if(present(s6)) call alloc(s6) + if(present(s7)) call alloc(s7) + if(present(s8)) call alloc(s8) + if(present(s9)) call alloc(s9) + if(present(s10))call alloc(s10) + END SUBROUTINE A_opt_c_damap + + + SUBROUTINE K_OPT_c_damap(S1,S2,s3,s4,s5,s6,s7,s8,s9,s10) +!* + implicit none + type (c_damap),INTENT(INout)::S1,S2 + type (c_damap),optional, INTENT(INout):: s3,s4,s5,s6,s7,s8,s9,s10 + call KILL(s1) + call KILL(s2) + if(present(s3)) call KILL(s3) + if(present(s4)) call KILL(s4) + if(present(s5)) call KILL(s5) + if(present(s6)) call KILL(s6) + if(present(s7)) call KILL(s7) + if(present(s8)) call KILL(s8) + if(present(s9)) call KILL(s9) + if(present(s10))call KILL(s10) + END SUBROUTINE K_OPT_c_damap + + SUBROUTINE A_opt_c_vector(S1,S2,s3,s4,s5,s6,s7,s8,s9,s10) +!* + implicit none + type (c_vector_field),INTENT(INout)::S1,S2 + type (c_vector_field),optional, INTENT(INout):: s3,s4,s5,s6,s7,s8,s9,s10 + call alloc(s1) + call alloc(s2) + if(present(s3)) call alloc(s3) + if(present(s4)) call alloc(s4) + if(present(s5)) call alloc(s5) + if(present(s6)) call alloc(s6) + if(present(s7)) call alloc(s7) + if(present(s8)) call alloc(s8) + if(present(s9)) call alloc(s9) + if(present(s10))call alloc(s10) + END SUBROUTINE A_opt_c_vector + + + SUBROUTINE K_OPT_c_vector(S1,S2,s3,s4,s5,s6,s7,s8,s9,s10) +!* + implicit none + type (c_vector_field),INTENT(INout)::S1,S2 + type (c_vector_field),optional, INTENT(INout):: s3,s4,s5,s6,s7,s8,s9,s10 + call KILL(s1) + call KILL(s2) + if(present(s3)) call KILL(s3) + if(present(s4)) call KILL(s4) + if(present(s5)) call KILL(s5) + if(present(s6)) call KILL(s6) + if(present(s7)) call KILL(s7) + if(present(s8)) call KILL(s8) + if(present(s9)) call KILL(s9) + if(present(s10))call KILL(s10) + END SUBROUTINE K_OPT_c_vector + + SUBROUTINE c_allocdas(S1,k) +!* + implicit none + type (c_taylor),INTENT(INOUT),dimension(:)::S1 + INTEGER,optional,INTENT(IN)::k + INTEGER J,i,N + + if(present(k)) then + I=LBOUND(S1,DIM=1) + N=LBOUND(S1,DIM=1)+K-1 + else + I=LBOUND(S1,DIM=1) + N=UBOUND(S1,DIM=1) + endif + + DO J=I,N + CALL c_allocda(S1(j)) + ENDDO + + END SUBROUTINE c_allocdas + + SUBROUTINE c_killda(S1) +!* + implicit none + type (c_taylor),INTENT(INOUT)::S1 + ! if(old) then + + call c_DADAL1(s1%i) +!call c_count_da(i_alloc) +!write(6,*) 2,i_alloc + + ! else + ! call KILLNEWDAs(s1%j) + ! endif + + END SUBROUTINE c_killda + + SUBROUTINE c_killdaS(S1,k) +!* + implicit none + type (c_taylor),INTENT(INOUT),dimension(:)::S1 + INTEGER,optional,INTENT(IN)::k + INTEGER J,i,N + + if(present(k)) then + I=LBOUND(S1,DIM=1) + N=LBOUND(S1,DIM=1)+K-1 + else + I=LBOUND(S1,DIM=1) + N=UBOUND(S1,DIM=1) + endif + + DO J=I,N + CALL c_killda(S1(j)) + ENDDO + + END SUBROUTINE c_killdaS + + SUBROUTINE alloc_c_damap(S1) +!* + implicit none + type (c_damap),INTENT(INOUT) :: S1 + INTEGER i,N + + + + if(s1%n==0) then + s1%n=nd2 + endif + + n=s1%n + + call alloc(s1%v,n) + + CALL alloc(s1%s) + CALL alloc(s1%q) + s1%q=0.0_dp + ! s1%q=1.0_dp + + + do i=n+1,size(s1%v) + s1%v(i)%i=0 + enddo + s1%e_ij=0.0_dp +! s1%damps=0.0_dp +! s1%sm=0.0_dp +! s1%b_kin=0.0_dp +! s1%d_spin=0.0_dp +! do i=1,3 +! s1%sm(i,i)=1.0_dp +! enddo + s1%x0=0.0_dp +! s1%tpsa=use_tpsa +! if(associated(s1%m)) deallocate(s1%M) +! if(associated(s1%db)) deallocate(s1%db) + if(associated(s1%cm)) deallocate(s1%cM) + END SUBROUTINE alloc_c_damap + + SUBROUTINE alloc_c_damaps(S1) +!* + implicit none + type (c_damap),INTENT(INOUT) :: S1(:) + INTEGER i + + do i=1,size(s1) + call alloc(s1(i)) + enddo + END SUBROUTINE alloc_c_damaps + + SUBROUTINE alloc_c_yu_w(S1) +!* + implicit none + type (c_yu_w),INTENT(INOUT) :: S1 + INTEGER i,j + + if(s1%n==0) then + s1%n=(no-1)/2 + endif + + allocate(s1%w(nd2t,0:s1%n)) + + do i=1,nd2t + do j=0,s1%n + call alloc(s1%w(i,j)) + enddo + enddo + + + END SUBROUTINE alloc_c_yu_w + + SUBROUTINE kill_c_yu_w(S1) +!* + implicit none + type (c_yu_w),INTENT(INOUT) :: S1 + INTEGER i,j + + + + do i=1,nd2t + do j=0,s1%n + call kill(s1%w(i,j)) + enddo + enddo + s1%n=0 + deallocate(s1%w) + + END SUBROUTINE kill_c_yu_w + + SUBROUTINE alloc_c_vector_field(S1) +!* + implicit none + type (c_vector_field),INTENT(INOUT) :: S1 + INTEGER i,n + + + s1%eps = eps_tpsalie + s1%nrmax = nrmax + if(s1%n==0) then + s1%n=nd2 + endif + + n=s1%n + + call alloc(s1%v,n) + + call alloc(s1%q) +! call alloc(s1%h) + call alloc(s1%L) + + do i=n+1,size(s1%v) + s1%v(i)%i=0 + enddo + + END SUBROUTINE alloc_c_vector_field + + + SUBROUTINE alloc_c_factored_lie(S1,N) +!* + implicit none + type (c_factored_lie),INTENT(INOUT) :: S1 + integer,optional :: n + INTEGER i + ! logical existed + + ! existed=.false. + ! if(s1%n/=0) existed=.true. + + if(present(n)) then + s1%n=n + else + s1%n=no + endif + + if(associated(s1%f) ) then + deallocate(s1%f) + nullify(s1%f) + endif + + allocate(s1%f(s1%n)) + do i=1,s1%n + call alloc(s1%f(i)) + enddo + + + END SUBROUTINE alloc_c_factored_lie + + SUBROUTINE alloc_c_normal_form(S1) +!* + implicit none + type (c_normal_form),INTENT(INOUT) :: S1 + + call alloc(s1%g) + call alloc(s1%ker) + call alloc(s1%n) + call alloc(s1%a2) + call alloc(s1%a1) + call alloc(s1%a_t) + call alloc(s1%AS) + call alloc(s1%Atot) + call alloc(s1%H,s1%H_l,s1%H_nl) + s1%as=1 + s1%nres=0 + s1%positive=default_fractional_tune_positive + s1%m=0 ! orbital resonance + s1%ms=0 ! spin resonance + s1%g%dir=-1 + s1%ker%dir=1 + s1%s_ij0=0 + s1%s_ijr=0 + s1%b_ijr=0 + s1%tune=0 + s1%damping=0 + s1%spin_tune=0 + s1%quaternion_angle=0 + s1%unstable=.false. + ! s1%hyperbolic=.false. + END SUBROUTINE alloc_c_normal_form + + SUBROUTINE kill_c_normal_form(S1) +!* + implicit none + type (c_normal_form),INTENT(INOUT) :: S1 + + call kill(s1%g) + call kill(s1%ker) + call kill(s1%n) + call kill(s1%a_t) + call kill(s1%a2) + call kill(s1%a1) + call kill(s1%AS) + call kill(s1%Atot) + call kill(s1%H,s1%H_l,s1%H_nl) + + s1%positive=.true. + s1%nres=0 + s1%m=0 ! orbital resonance + s1%ms=0 ! spin resonance + s1%g%dir=-1 + s1%ker%dir=1 + s1%s_ij0=0 + s1%s_ijr=0 + s1%b_ijr=0 + s1%tune=0 + s1%damping=0 + s1%spin_tune=0 + s1%quaternion_angle=0 + END SUBROUTINE kill_c_normal_form + + SUBROUTINE kill_c_factored_lie(S1) +!* + implicit none + type (c_factored_lie),INTENT(INOUT) :: S1 + INTEGER i + + + do i=1,s1%n + call kill(s1%f(i)) + enddo + s1%n=0 + deallocate(s1%f) + + END SUBROUTINE kill_c_factored_lie + + SUBROUTINE kill_c_damap(S1) +!* + implicit none + type (c_damap),INTENT(INOUT) :: S1 + integer i + call kill(s1%v,s1%n) + CALL kill(s1%s) + CALL kill(s1%q) + s1%n=0 + s1%e_ij=0.0_dp +! s1%damps=0.0_dp +! s1%sm=0.0_dp +! s1%d_spin=0.0_dp +! s1%b_kin=0.0_dp + s1%e_ij=0.0_dp +! do i=1,3 +! s1%sm(i,i)=1.0_dp +! enddo +! if(associated(s1%db)) deallocate(s1%db) + if(associated(s1%m)) deallocate(s1%m) + if(associated(s1%cm)) deallocate(s1%cm) + END SUBROUTINE kill_c_damap + + SUBROUTINE kill_c_damaps(S1) +!* + implicit none + type (c_damap),INTENT(INOUT) :: S1(:) + integer i + do i=1,size(s1) + call kill(s1(i)) + enddo + END SUBROUTINE kill_c_damaps + + SUBROUTINE kill_c_vector_field(S1) +!* + implicit none + type (c_vector_field),INTENT(INOUT) :: S1 + + + + call kill(s1%v,s1%n) + + call kill(s1%q) + call kill(s1%L) + ! call kill(s1%h) + + s1%n=0 + + END SUBROUTINE kill_c_vector_field + + SUBROUTINE alloc_c_spinmatrix(S1) ! spin routine +!* + implicit none + type (c_spinmatrix),INTENT(INOUT) :: S1 + INTEGER i,J + + do i=1,3 + do j=1,3 + call alloc(s1%s(i,j)) + enddo + enddo + + END SUBROUTINE alloc_c_spinmatrix + + + SUBROUTINE alloc_c_spinor(S1) ! spin routine +!* + implicit none + type (c_spinor),INTENT(INOUT) :: S1 + INTEGER i + + do i=1,3 + call alloc(s1%v(i)) + enddo + + END SUBROUTINE alloc_c_spinor + + SUBROUTINE kill_c_spinor(S1) ! spin routine +!* + implicit none + type (c_spinor),INTENT(INOUT) :: S1 + INTEGER i + + do i=1,3 + call kill(s1%v(i)) + enddo + + END SUBROUTINE kill_c_spinor + + + SUBROUTINE kill_c_spinmatrix(S1) ! spin routine +!* + implicit none + type (c_spinmatrix),INTENT(INOUT) :: S1 + INTEGER i,J + + do i=1,3 + do j=1,3 + call kill(s1%s(i,j)) + enddo + enddo + + END SUBROUTINE kill_c_spinmatrix + + + + + function c_real(S1) + implicit none + type (c_taylor) c_real + type (c_taylor),INTENT(IN)::S1 + integer i,n,localmaster + complex(dp) x + complex(dp) value + integer, allocatable :: j(:) + + + IF(.NOT.C_STABLE_DA) then + c_real%i=0 + RETURN + endif + + localmaster=c_master + + ! call check(s1) + call ass(c_real) + + ! if(old) then + + if(s1%i==0) call c_crap1("EQUAL 2") ! call allocw(s1) + + if(new_cycle) then + + call c_real_imag(s1%i,c_real%i,1) + + else + allocate(j(c_%nv)) + c_real=0.0_dp + + call c_taylor_cycle(s1,size=n) + + do i=1,n + call c_taylor_cycle(s1,ii=i,value=value,j=j) + x=real(value) + c_real=c_real+(x.cmono.j) +!write(6,*) i,n + enddo + deallocate(j) + endif + c_master=localmaster + + + END function c_real + + function c_aimag(S1) + implicit none + type (c_taylor) c_aimag + type (c_taylor),INTENT(IN)::S1 + integer i,n,localmaster + complex(dp) x + complex(dp) value + integer, allocatable :: j(:) + + IF(.NOT.C_STABLE_DA) then + c_aimag%i=0 + RETURN + endif + + localmaster=c_master + + ! call check(s1) + call ass(c_aimag) + + ! if(old) then + + if(s1%i==0) call c_crap1("EQUAL 2") ! call allocw(s1) + + if(new_cycle) then + + call c_real_imag(s1%i,c_aimag%i,2) + + else + allocate(j(c_%nv)) + c_aimag=0.0_dp + + call c_taylor_cycle(s1,size=n) + + do i=1,n + call c_taylor_cycle(s1,ii=i,value=value,j=j) + x=aimag(value) + c_aimag=c_aimag+(x.cmono.j) + enddo + deallocate(j) + + endif + c_master=localmaster + + + END function c_aimag + + + SUBROUTINE equalc_t(S2,S1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2 + type (taylor),INTENT(IN)::S1 + integer i,n + real(dp) x + integer, allocatable :: j(:) + IF(.NOT.C_STABLE_DA) RETURN + +! call c_check_snake + call check_snake + ! if(old) then + if(s2%i==0) then + call c_crap1("EQUAL 1 in tpsa") !call allocw(s2) + endif + if(s1%i==0) call crap1("EQUAL 2") ! call allocw(s1) + + allocate(j(c_%nv)) + s2=0.0_dp + + call taylor_cycle(s1,size=n) + + do i=1,n + call taylor_cycle(s1,ii=i,value=x,j=j) + s2=s2+(x.cmono.j) + enddo + + + deallocate(j) + END SUBROUTINE equalc_t + + SUBROUTINE equalt_c(S2,S1) +!* + implicit none + type (taylor),INTENT(inOUT)::S2 + type (c_taylor),INTENT(IN)::S1 + integer i,n + complex(dp) value + integer, allocatable :: j(:) + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + ! call check_snake + ! if(old) then + if(s2%i==0) then + call crap1("EQUAL 1 in tpsa") !call allocw(s2) + endif + if(s1%i==0) call c_crap1("EQUAL 2") ! call allocw(s1) + + allocate(j(nv)) + s2=0.0_dp + + call c_taylor_cycle(s1,size=n) + + do i=1,n + call c_taylor_cycle(s1,ii=i,value=value,j=j) + s2=s2+(value.mono.j) + enddo + + deallocate(j) + END SUBROUTINE equalt_c + + SUBROUTINE equalc_ray_ray(S2,S1) +!* + implicit none + type (c_ray),INTENT(inOUT)::S2 + type (c_ray),INTENT(IN)::S1 + + s2%x = s1%x + s2%s1 = s1%s1 + s2%s2 = s1%s2 + s2%s3 = s1%s3 + s2%q = s1%q + s2%n = s1%n +! s2%x0 = s1%x0 + END SUBROUTINE equalc_ray_ray + + SUBROUTINE equalc_ray_r6(S2,S1) +!* + implicit none + type (c_ray),INTENT(inOUT)::S2 + complex(dp),INTENT(IN)::S1(:) + integer i + + +! + s2%x=0.0_dp +! s2%x0=0.0_dp + do i=1,size(s1) + s2%x(i)=s1(i) + enddo + ! s2%q=1.0_dp + s2%n=size(s1) + s2%s1=0 + s2%s2=0 + s2%s3=0 + + s2%s1(1)=1 + s2%s2(2)=1 + s2%s3(3)=1 + + END SUBROUTINE equalc_ray_r6 + + SUBROUTINE equalc_ray_r6r(S2,S1) +!* + implicit none + type (c_ray),INTENT(inOUT)::S2 + real(dp),INTENT(IN)::S1(:) + integer i + + + + + s2%x=0.0_dp + do i=1,size(s1) + s2%x(i)=s1(i) + enddo + ! s2%q=1.0_dp + s2%s1=0 + s2%s2=0 + s2%s3=0 + s2%n=size(s1) + + s2%s1(1)=1 + s2%s2(2)=1 + s2%s3(3)=1 + + END SUBROUTINE equalc_ray_r6r + + SUBROUTINE equalc_r6_ray(S1,S2) +!* + implicit none + type (c_ray),INTENT(in)::S2 + complex(dp),INTENT(inOUT)::S1(:) + integer i + + + + + do i=1,size(s1) + s1(i)=s2%x(i) + enddo + + + END SUBROUTINE equalc_r6_ray + + SUBROUTINE equalc_r6r_ray(S1,S2) +!* + implicit none + type (c_ray),INTENT(in)::S2 + real(dp),INTENT(inOUT)::S1(:) + integer i + + do i=1,size(s1) + s1(i)=s2%x(i) + enddo + + END SUBROUTINE equalc_r6r_ray + + + SUBROUTINE equalc_t_ct(S2,S1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2 + type (complextaylor),INTENT(IN)::S1 + integer i,n + complex(dp) x + real(dp) value + integer, allocatable :: j(:) + IF(.NOT.C_STABLE_DA) RETURN + +! call c_check_snake + call check_snake + ! if(old) then + if(s2%i==0) then + call c_crap1("EQUAL 1 in tpsa") !call allocw(s2) + endif + if(s1%r%i==0) call crap1("EQUAL 2") ! call allocw(s1) + + allocate(j(c_%nv)) + s2=0.0_dp + + call taylor_cycle(s1%r,size=n) + + do i=1,n + call taylor_cycle(s1%r,ii=i,value=value,j=j) + x=value + s2=s2+(x.cmono.j) + enddo + + call taylor_cycle(s1%i,size=n) + + do i=1,n + call taylor_cycle(s1%i,ii=i,value=value,j=j) + x=value*i_ + s2=s2+(x.cmono.j) + enddo + + + deallocate(j) + END SUBROUTINE equalc_t_ct + + SUBROUTINE equalc_ct_c(S2,S1) +!* + implicit none + type (complextaylor),INTENT(inOUT)::S2 + type (c_taylor),INTENT(IN)::S1 + integer i,n + complex(dp) value + integer, allocatable :: j(:) + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + ! call check_snake + ! if(old) then + if(s2%r%i==0) then + call c_crap1("EQUAL 1 in tpsa") !call allocw(s2) + endif + if(s1%i==0) call crap1("EQUAL 2") ! call allocw(s1) + + allocate(j(nv)) + s2=0.0_dp + + call c_taylor_cycle(s1,size=n) + + do i=1,n + call c_taylor_cycle(s1,ii=i,value=value,j=j) + s2=s2+(value.mono.j) + enddo + + deallocate(j) + END SUBROUTINE equalc_ct_c + + SUBROUTINE equalc_cmap_map(S2,S1) +!* + implicit none + type (c_damap),INTENT(inOUT)::S2 + type (damap),INTENT(IN)::S1 + type(complextaylor) ct + integer i,i1(4),i2(4) + + + + call check_snake + call alloc(ct) + call liepeek(i1,i2) + if(i1(4)/=s2%n) then + write(6,*) "Error in equalc_cmap_map",i1(4),s2%n + endif + do i=1,i1(4) + ct=s1%v(i) +! ct=ct-(ct.sub.'0') + s2%v(i)=ct + enddo + + call kill(ct) + + end SUBROUTINE equalc_cmap_map + + SUBROUTINE equalc_map_cmap(S2,S1) +!* + implicit none + type (damap),INTENT(inOUT)::S2 + type (c_damap),INTENT(IN)::S1 + type(complextaylor) ct + integer i,i1(4),i2(4) + + + + call c_check_snake + + call alloc(ct) + call liepeek(i1,i2) + if(i1(4)/=s1%n) then + write(6,*) "Error in equalc_map_cmap",i1(4),s1%n + endif + do i=1,i1(4) + ct=s1%v(i) +! ct=ct-(ct.sub.'0') + s2%v(i)=ct%r + enddo + + call kill(ct) + + end SUBROUTINE equalc_map_cmap + + + subroutine EQUAL_c_spinmatrix_probe(S,R) +!* + implicit none + TYPE(probe), INTENT(IN) :: R + TYPE(c_spinmatrix), INTENT(INOUT) :: S + + s%s(1,1)=r%s(1)%x(1); s%s(2,1)=r%s(1)%x(2); s%s(3,1)=r%s(1)%x(3); + s%s(1,2)=r%s(2)%x(1); s%s(2,2)=r%s(2)%x(2); s%s(3,2)=r%s(2)%x(3); + s%s(1,3)=r%s(3)%x(1); s%s(2,3)=r%s(3)%x(2); s%s(3,3)=r%s(3)%x(3); + + END subroutine EQUAL_c_spinmatrix_probe + + subroutine EQUAL_probe_c_spinmatrix(R,S) +!* + implicit none + TYPE(probe), INTENT(INout) :: R + TYPE(c_spinmatrix), INTENT(IN) :: S + + r%s(1)%x(1)=s%s(1,1); r%s(1)%x(2)=s%s(2,1); r%s(1)%x(3)=s%s(3,1); + r%s(2)%x(1)=s%s(1,2); r%s(2)%x(2)=s%s(2,2); r%s(2)%x(3)=s%s(3,2); + r%s(3)%x(1)=s%s(1,3); r%s(3)%x(2)=s%s(2,3); r%s(3)%x(3)=s%s(3,3); + + END subroutine EQUAL_probe_c_spinmatrix + + subroutine EQUAL_c_spinmatrix_3_by_3(S,R) +!* + implicit none + real(dp), INTENT(IN) :: R(3,3) + TYPE(c_spinmatrix), INTENT(INOUT) :: S + integer i,j + do i=1,3 + do j=1,3 + s%s(i,j)=r(i,j) + enddo + enddo + + END subroutine EQUAL_c_spinmatrix_3_by_3 + + + subroutine EQUAL_3_by_3_c_spinmatrix(R,S) +!* + implicit none + real(dp), INTENT(INOUT) :: R(3,3) + TYPE(c_spinmatrix), INTENT(IN) :: S + integer i,j + do i=1,3 + do j=1,3 + r(i,j)=s%s(i,j) + enddo + enddo + + END subroutine EQUAL_3_by_3_c_spinmatrix + + + subroutine EQUAL_3_by_3_probe(R,S) +!* + implicit none + real(dp), INTENT(INout) :: R(3,3) + TYPE(probe), INTENT(IN) :: S + integer i,j + + r(1,1)=s%s(1)%x(1); r(2,1)=s%s(1)%x(2); r(3,1)=s%s(1)%x(3); + r(1,2)=s%s(2)%x(1); r(2,2)=s%s(2)%x(2); r(3,2)=s%s(2)%x(3); + r(1,3)=s%s(3)%x(1); r(2,3)=s%s(3)%x(2); r(3,3)=s%s(3)%x(3); + + END subroutine EQUAL_3_by_3_probe + + subroutine EQUAL_probe_3_by_3(S,R) +!* + implicit none + real(dp), INTENT(IN) :: R(3,3) + TYPE(probe), INTENT(INout) :: S + integer i,j + + s%s(1)%x(1)=r(1,1); s%s(1)%x(2)=r(2,1); s%s(1)%x(3)=r(3,1); + s%s(2)%x(1)=r(1,2); s%s(2)%x(2)=r(2,2); s%s(2)%x(3)=r(3,2); + s%s(3)%x(1)=r(1,3); s%s(3)%x(2)=r(2,3); s%s(3)%x(3)=r(3,3); + + END subroutine EQUAL_probe_3_by_3 + + + SUBROUTINE equalc_cvec_vec(S2,S1) +!* + implicit none + type (c_vector_field),INTENT(inOUT)::S2 + type (vecfield),INTENT(IN)::S1 + type(complextaylor) ct + integer i,i1(4),i2(4) + + + + call check_snake + + call alloc(ct) + + call liepeek(i1,i2) + if(i1(4)/=s2%n) then + write(6,*) "Error in equalc_cmap_map",i1(4),s2%n + endif + + do i=1,i1(4) + ct=s1%v(i) + s2%v(i)=ct + enddo + + call kill(ct) + + end SUBROUTINE equalc_cvec_vec + + SUBROUTINE equalc_cspinor_cspinor(S2,S1) ! spin routine +!* + implicit none + type (c_spinor),INTENT(inOUT)::S2 + type (c_spinor),INTENT(IN)::S1 + + integer i + + call c_check_snake + + do i=1,3 + s2%v(i)=s1%v(i) + enddo + + + end SUBROUTINE equalc_cspinor_cspinor + + SUBROUTINE equalc_spinor_c_quaternion(S2,S1) ! spin routine +!* + implicit none + type (c_spinor),INTENT(inOUT)::S2 + type (c_quaternion),INTENT(IN)::S1 + + integer i + + call c_check_snake + + do i=1,3 + s2%v(i)=s1%x(i) + enddo + + + end SUBROUTINE equalc_spinor_c_quaternion + + SUBROUTINE equalc_quaternion_c_spinor(S2,S1) ! spin routine +!* + implicit none + type (c_quaternion),INTENT(inOUT)::S2 + type (c_spinor),INTENT(IN)::S1 + + integer i + + call c_check_snake + s2%x(1)=0.0_dp + do i=1,3 + s2%x(i)=s1%v(i) + enddo + + + end SUBROUTINE equalc_quaternion_c_spinor + + SUBROUTINE equalc_spinor_cspinor(S2,S1) ! spin routine +!* + implicit none + type (spinor),INTENT(inOUT)::S2 + type (c_spinor),INTENT(IN)::S1 + + integer i + + call check_snake + + do i=1,3 + s2%x(i)=s1%v(i) + enddo + + + end SUBROUTINE equalc_spinor_cspinor + + SUBROUTINE equalc_cspinor_spinor(S1,S2) ! spin routine +!* + implicit none + type (spinor),INTENT(in)::S2 + type (c_spinor),INTENT(inOUT)::S1 + + integer i + + call check_snake + + do i=1,3 + s1%v(i)=s2%x(i) + enddo + + + end SUBROUTINE equalc_cspinor_spinor + + SUBROUTINE c_DPEKMAP(S2,S1) + implicit none + complex(dp),INTENT(inOUT),dimension(:)::S2 + type (c_damap),INTENT(IN)::S1 + IF(.NOT.C_STABLE_DA) RETURN + call c_check_snake + ! if(old) then + CALL c_DAPEK0(S1%V%I,S2,s1%n) + ! else + ! CALL newDAPEK0(S1%V%J,S2,nd2) + ! endif + END SUBROUTINE c_DPEKMAP + + SUBROUTINE c_DPOKMAP(S1,S2) + implicit none + complex(dp),INTENT(IN),dimension(:)::S2 + type (c_damap),INTENT(inOUT)::S1 + IF(.NOT.C_STABLE_DA) RETURN + + ! if(old) then + if(s1%V(1)%i==0) call crap1("DPOKMAP 1") !call allocw_old(s1%V(1)) !call etall(s1%V%i,ND2) + CALL c_DAPOK0(S1%V%I,S2,s1%n) + ! else + ! if(.NOT. ASSOCIATED(s1%V(1)%j%r)) call crap1("DPOKMAP 2") ! !call allocw_old(s1%V(1)) !call newetall(s1%V%j,ND2) + ! CALL NEWDAPOK0(S1%V%J,S2,nd2) + ! endif + END SUBROUTINE c_DPOKMAP + + SUBROUTINE EQUAL(S2,S1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2 + type (c_taylor),INTENT(IN)::S1 + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + ! if(old) then + if(s2%i==0) then + call c_crap1("EQUAL 1 in tpsa") !call allocw(s2) + endif + if(s1%i==0) call c_crap1("EQUAL 2") ! call allocw(s1) + CALL c_dacop(S1%I,S2%I) + + END SUBROUTINE EQUAL + + + SUBROUTINE EQUAL_arraytaylor_arrayreal(S2,S1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2(:) + real(dp),INTENT(IN)::S1(:) + integer i + IF(.NOT.C_STABLE_DA) RETURN + + do i=1,size(s1) + s2(i)=s1(i) + enddo + + end SUBROUTINE EQUAL_arraytaylor_arrayreal + + SUBROUTINE EQUAL_arrayreal_arraytaylor(S2,S1) +!* + implicit none + real(dp),INTENT(inOUT)::S2(:) + type (c_taylor),INTENT(IN)::S1(:) + integer i + IF(.NOT.C_STABLE_DA) RETURN + + do i=1,size(s1) + s2(i)=s1(i) + enddo + + end SUBROUTINE EQUAL_arrayreal_arraytaylor + + SUBROUTINE EQUAL_arraytaylor_arraycomplex(S2,S1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2(:) + complex(dp),INTENT(IN)::S1(:) + integer i + IF(.NOT.C_STABLE_DA) RETURN + + do i=1,size(s1) + s2(i)=s1(i) + enddo + + end SUBROUTINE EQUAL_arraytaylor_arraycomplex + + SUBROUTINE EQUAL_arraycomplex_arraytaylor(S2,S1) +!* + implicit none + complex(dp),INTENT(inOUT)::S2(:) + type (c_taylor),INTENT(IN)::S1(:) + integer i + IF(.NOT.C_STABLE_DA) RETURN + + do i=1,size(s1) + s2(i)=s1(i) + enddo + + end SUBROUTINE EQUAL_arraycomplex_arraytaylor + + SUBROUTINE equal_map_real8(S2,S1) +!* + implicit none + type (c_damap),INTENT(inOUT)::S2 + real(dp),INTENT(IN),dimension(:)::S1 + + integer i + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + ! if(old) then + if(s2%v(1)%i==0) then + call c_crap1("EQUAL 1 in tpsa") !call allocw(s2) + endif + + do i=1, min(s2%n,size(s1,1)) + S2%v(i)=s1(i) + enddo + + END SUBROUTINE equal_map_real8 + + SUBROUTINE equal_map_complex8(S2,S1) +!* + implicit none + type (c_damap),INTENT(inOUT)::S2 + complex(dp),INTENT(IN),dimension(:)::S1 + + integer i + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + ! if(old) then + if(s2%v(1)%i==0) then + call c_crap1("EQUAL 1 in tpsa") !call allocw(s2) + endif + + do i=1, min(s2%n,size(s1,1)) + S2%v(i)=s1(i) + enddo + + END SUBROUTINE equal_map_complex8 + + SUBROUTINE equal_real8_map(S2,S1) +!* + implicit none + real(dp),INTENT(inOUT),dimension(:)::S2 + type (c_damap),INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + ! if(old) then + if(s1%v(1)%i==0) then + call c_crap1("EQUAL 1 in tpsa") !call allocw(s2) + endif + + do i=1, min((s1%n),size(s2,1)) + s2(i)=S1%v(i) + enddo + + END SUBROUTINE equal_real8_map + + SUBROUTINE equal_complex8_map(S2,S1) +!* + implicit none + complex(dp),INTENT(inOUT),dimension(:)::S2 + type (c_damap),INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + ! if(old) then + if(s1%v(1)%i==0) then + call c_crap1("EQUAL 1 in tpsa") !call allocw(s2) + endif + + do i=1, min(s1%n,size(s2,1)) + s2(i)=S1%v(i) + enddo + + END SUBROUTINE equal_complex8_map + +!skowron to bypass strange gfortran error when using s2=s1 + SUBROUTINE equal_c_tayls(S2,S1) + implicit none + type (c_taylor),INTENT(inOUT)::S2 + type (c_taylor),INTENT(IN)::S1 + + call equal(s2,s1) + + end SUBROUTINE equal_c_tayls + + SUBROUTINE EQUALspinmatrix(S2,S1) ! spin routine +!* + implicit none + type (c_spinmatrix),INTENT(inOUT)::S2 + type (c_spinmatrix),INTENT(IN)::S1 + integer i,j + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + + + do i=1,3 + do j=1,3 + s2%s(i,j)=s1%s(i,j) + enddo + enddo + + END SUBROUTINE EQUALspinmatrix + + SUBROUTINE cDEQUAL(R1,S2) +!* + implicit none + type (c_taylor),INTENT(IN)::S2 + complex(dp), INTENT(inOUT)::R1 + IF(.NOT.C_STABLE_DA) RETURN + call c_check_snake + + R1=S2.SUB.'0' + END SUBROUTINE cDEQUAL + + SUBROUTINE DEQUAL(R1,S2) +!* + implicit none + type (c_taylor),INTENT(IN)::S2 + real(dp), INTENT(inOUT)::R1 + IF(.NOT.C_STABLE_DA) RETURN + call c_check_snake + + R1=S2.SUB.'0' + END SUBROUTINE DEQUAL + + SUBROUTINE REQUAL(R1,S2) +!* + implicit none + type (c_taylor),INTENT(IN)::S2 + REAL(SP), INTENT(inOUT)::R1 + IF(.NOT.C_STABLE_DA) RETURN + + if(c_real_warning) call c_real_stop + call c_check_snake + + R1=S2.SUB.'0' + + END SUBROUTINE REQUAL + + function DAABSEQUAL(S2) + implicit none + type (c_taylor),INTENT(IN)::S2 + real(dp) DAABSEQUAL + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + DAABSEQUAL=abs(S2.sub.'0') + + END function DAABSEQUAL + + + SUBROUTINE cDEQUALDACON(S2,R1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2 + complex(dp), INTENT(IN)::R1 + IF(.NOT.C_STABLE_DA) RETURN + + ! if(old) then + if(s2%i==0) call c_crap1("DEQUALDACON 1") !call allocw(s2) + CALL c_dacon(S2%I,R1) + ! else + ! IF (.NOT. ASSOCIATED(s2%j%r)) call c_crap1("DEQUALDACON 2") !call allocw(s2) + ! CALL newDACON(S2%j,R1) + ! endif + END SUBROUTINE cDEQUALDACON + + SUBROUTINE DEQUALDACON(S2,R1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2 + real(dp), INTENT(IN)::R1 + complex(dp) rt + IF(.NOT.C_STABLE_DA) RETURN + + ! if(old) then + if(s2%i==0) call c_crap1("DEQUALDACON 1") !call allocw(s2) + rt=r1 + CALL c_dacon(S2%I,rt) + ! else + ! IF (.NOT. ASSOCIATED(s2%j%r)) call c_crap1("DEQUALDACON 2") !call allocw(s2) + ! CALL newDACON(S2%j,R1) + ! endif + END SUBROUTINE DEQUALDACON + + SUBROUTINE DEQUALDACONS(S2,R1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2(:) + real(dp), INTENT(IN)::R1 + complex(dp) rt + integer k + IF(.NOT.C_STABLE_DA) RETURN + + ! if(old) then + if(s2(1)%i==0) call c_crap1("DEQUALDACON 1") !call allocw(s2) + do k=lbound(s2,1),ubound(s2,1) + rt=r1 + CALL c_dacon(S2(k)%I,rt) + enddo + ! else + ! IF (.NOT. ASSOCIATED(s2%j%r)) call c_crap1("DEQUALDACON 2") !call allocw(s2) + ! CALL newDACON(S2%j,R1) + ! endif + END SUBROUTINE DEQUALDACONS + + + SUBROUTINE EQUALDACON(S2,R1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2 + REAL(SP), INTENT(IN)::R1 + real(dp) R2 + IF(.NOT.C_STABLE_DA) RETURN + if(c_real_warning) call c_real_stop + ! call c_check_snake + + if(c_real_warning) call c_real_stop + ! if(old) then + if(s2%i==0) call c_crap1("EQUALDACON 1") !call allocw(s2) + ! else + ! IF (.NOT. ASSOCIATED(s2%j%r)) call c_crap1("EQUALDACON 2") !call allocw(s2) + ! endif + r2=REAL(r1,kind=DP) + s2=r2 + END SUBROUTINE EQUALDACON + + SUBROUTINE IEQUALDACON(S2,R1) +!* + implicit none + type (c_taylor),INTENT(inOUT)::S2 + INTEGER, INTENT(IN)::R1 + real(dp) r2 + IF(.NOT.C_STABLE_DA) RETURN + ! call c_check_snake + + + ! if(old) then + if(s2%i==0) call c_crap1("IEQUALDACON 1") !call allocw(s2) + ! else + ! IF (.NOT. ASSOCIATED(s2%j%r)) call c_crap1("IEQUALDACON 2") !call allocw(s2) + ! endif + r2=REAL(r1,kind=DP) + s2=r2 + END SUBROUTINE IEQUALDACON + + FUNCTION dexpt( S1 ) + implicit none + TYPE (c_taylor) dexpt + TYPE (c_taylor), INTENT (IN) :: S1 + integer localmaster + + IF(.NOT.C_STABLE_DA) then + dexpt%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + call ass(dexpt) + + ! if(old) then + call c_dafun('EXP ',s1%i,c_temp%i) + call c_dacop(c_temp%i,dexpt%i) + ! else + ! call newdafun('EXP ',s1%j,dexpt%j) + ! endif + + c_master=localmaster + + END FUNCTION dexpt + + + + FUNCTION c_logt( S1 ) + implicit none + TYPE (c_taylor) c_logt + TYPE (c_taylor), INTENT (IN) :: S1 + integer localmaster + + IF(.NOT.C_STABLE_DA) then + c_logt%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + call ass(c_logt) + + ! if(old) then + call c_dafun('LOG ',s1%i,c_temp%i) + call c_dacop(c_temp%i,c_logt%i) + ! else + ! call newdafun('EXP ',s1%j,dexpt%j) + ! endif + + c_master=localmaster + + END FUNCTION c_logt + + SUBROUTINE flatten_c_factored_lie_r(St,S1) + implicit none + type (c_factored_lie),INTENT(IN) :: S1 + type (c_vector_field),INTENT(inOUT) :: ST + call flatten_c_factored_lie(S1,ST) +end SUBROUTINE flatten_c_factored_lie_r + + SUBROUTINE flatten_c_factored_lie(S1,ST) +!#general: manipulation +!# Type c_factored_lie is a product of Lie exponents. +!# Lie map=exp(s1%f(1).grad)...exp(s1%f(s1%n).grad) if s1%dir=1. +!# or Lie map=exp(s1%f(s1%n).grad)...exp(s1%f(1).grad) if s1%dir=-1. +!# In some cases, these exponents commute and can be added; for example +!# if the map is a rotation. +!# s2 = s1%f(1)+...+s1%f(s1%n) + implicit none + type (c_factored_lie),INTENT(IN) :: S1 + type (c_vector_field),INTENT(inOUT) :: ST + integer i,j + type (c_vector_field) S2 +! This routine assumes commutation of all the factored Lie exponents + + s2%n = s1%f(1)%n + call alloc(s2) + + s2%eps = s1%f(1)%eps + s2%nrmax = s1%f(1)%nrmax + + + s2=0 + do j=1,s1%n +if(use_quaternion) THEN + s2%q=s2%q+s1%f(j)%q + else +! s2%h=s2%h+s1%f(j)%h + s2%L=s2%L+s1%f(j)%L + +endif + + + do i=1,s2%n + s2%v(i)=s2%v(i)+s1%f(j)%v(i) + enddo + enddo + st=s2 + if(complex_extra_order==1.and.special_extra_order_1) s2=s2.cut.no + call kill(s2) + END SUBROUTINE flatten_c_factored_lie + + + +! etienne2 + FUNCTION c_logf( s1,h,epso,n,tpsa ) +!#internal: manipulation +!# Accessable with the interface log if desired. +!# Takes the logarithm of a nonlinear map s1 +!# s1=exp(log(s1).grad) I +!# The map must be near the identity. +!# H, epso and n are optional. +!# epso is a small positive number estimated automatically. +!# The algorithm goes nonlinear when the norm of the correction +!# is smaller than epso. See Chap.11. +!# H is a guess for the logarithm: optional. + + implicit none + TYPE (c_vector_field) c_logf + TYPE (c_vector_field) , optional :: h + TYPE (c_damap), INTENT (INOUT) :: S1 + real(dp), optional :: epso + integer, optional :: n + logical, optional :: tpsa + type(c_damap) s1t + logical da + integer localmaster,i + IF(.NOT.C_STABLE_DA) then + c_logf%v%i=0 + RETURN + endif + localmaster=c_master + s1t%n=s1%n + call alloc(s1t) + s1t=s1 + da=.true. + if(present(tpsa)) da=.not.tpsa + if(da) then + do i=1,s1t%n + s1t%v(i)=s1t%v(i)-(s1t%v(i).sub.'0') + enddo + endif + + c_logf%n=s1%n + call c_ass_vector_field(c_logf) + c_logf=0 + if(present(h)) c_logf=h + call c_flofacg(s1t,c_logf,epso,n) + call kill(s1t) + c_master=localmaster + if(complex_extra_order==1.and.special_extra_order_1) c_logf=c_logf.cut.no + END FUNCTION c_logf + + FUNCTION c_logc( S1 ) + implicit none + complex(dp) c_logc + complex(dp), INTENT (IN) :: S1 + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_logc=0 + RETURN + endif + localmaster=c_master + + c_logc = LOG(abs(S1)) + (0.0_dp,1.0_dp)*atan2(aimag(S1),real(S1)) + + + END FUNCTION c_logc + + + +! inspired by Mr. LU Yao +subroutine get_log(one_turn_map,vflog,n) +implicit none +type(c_damap),intent(in):: one_turn_map +type(c_vector_field),intent(inout):: vflog +integer i,j,n,m +integer, parameter :: nt=5 +real(dp) k1,k0 +type(c_damap) id,rot +type(c_vector_field) vtt ,vt +logical descent +real(dp), allocatable :: b(:) + +allocate(b(n)) +b=0 + +call alloc(vt) +call alloc(vtt) +call alloc(id,rot) + +vflog=0 +vt=0 + +id=one_turn_map +rot=one_turn_map + + +id=1 +do i=1,n + + do j=1,id%n + vt%v(j)=rot%v(j) - ID%v(j) + vtt%v(j)=-0.5_dp*(vt*vt%v(j)) + enddo + vt=vt+vtt +vtt=0.5_dp*(vflog.lb.vt) +vtt=vtt+vt +!vflog=vflog+vt +vflog=vflog+vtt + + +rot=exp(-vflog,one_turn_map) + +call c_full_norm_vector_field(vtt,k1) + +if(i==1) then + k0=k1/100 +endif + +!call c_full_norm_damap(rot,k1) + b(i)=k1 + + if(i>=nt+1) then + descent=.true. + do m=i-nt,i-1 + descent=descent.and.(b(m)>b(m+1)) + enddo + if(k1<=k0.and.(.not.descent)) goto 1 + endif + +enddo + +write(6,*) " did not converged in", n, "steps",k1 +n=-n +1 continue + +deallocate(b) + +call kill(vt) +call kill(vtt) +call kill(id,rot) + +end subroutine get_log + + FUNCTION FULL_ABST( S1 ) +!#general: manipulation +!# This routine computes the norm of the c_taylor s1. +!# This routine is called with the interface +!# full_abs(s1) where s1 is a c_taylor. + implicit none + real(dp) FULL_ABST + TYPE (c_taylor), INTENT (IN) :: S1 + + IF(.NOT.C_STABLE_DA) then + full_abst=0 + RETURN + endif + ! call check(s1) + + ! if(old) then + CALL c_DAABS(S1%I,FULL_ABST) + ! else + ! CALL newDAABS(S1%j,FULL_ABST) + ! endif + + END FUNCTION FULL_ABST + + + + + FUNCTION dtant( S1 ) + implicit none + TYPE (c_taylor) dtant + TYPE (c_taylor), INTENT (IN) :: S1 + integer localmaster + IF(.NOT.C_STABLE_DA) then + dtant%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + call ass(dtant) + + ! if(old) then + call c_dafun('SIN ',s1%i,c_temp%i) + call c_dacop(c_temp%i,dtant%i) + call c_dafun('COS ',s1%i,c_temp%i) + call c_dadiv(dtant%i,c_temp%i,dtant%i) + ! else + ! call newdafun('SIN ',s1%j,c_temp%il) + ! call newc_dacop(c_temp%il,dtant%j) + ! call newdafun('COS ',s1%j,c_temp%il) + ! call newdadiv(dtant%j,c_temp%il,dtant%j) + ! endif + + c_master=localmaster + + END FUNCTION dtant + + + FUNCTION dcost( S1 ) + implicit none + TYPE (c_taylor) dcost + TYPE (c_taylor), INTENT (IN) :: S1 + integer localmaster + IF(.NOT.C_STABLE_DA) then + dcost%i=0 + RETURN + endif + localmaster=c_master + + + + ! call check(s1) + call ass(dcost) + + ! if(old) then + call c_dafun('COS ',s1%i,c_temp%i) + call c_dacop(c_temp%i,dcost%i) + ! else + ! call newdafun('COS ',s1%j,dcost%j) + ! endif + + c_master=localmaster + + END FUNCTION dcost + + FUNCTION dsint( S1 ) + implicit none + TYPE (c_taylor) dsint + TYPE (c_taylor), INTENT (IN) :: S1 + integer localmaster + IF(.NOT.C_STABLE_DA) then + dsint%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(dsint) + ! if(old) then + call c_dafun('SIN ',s1%i,c_temp%i) + call c_dacop(c_temp%i,dsint%i) + + + c_master=localmaster + + END FUNCTION dsint + + FUNCTION sqrtt( S1 ) + implicit none + TYPE (c_taylor) sqrtt + TYPE (c_taylor), INTENT (IN) :: S1 + integer localmaster + IF(.NOT.C_STABLE_DA) then + sqrtt%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(sqrtt) + ! if(old) then + call c_dafun('SQRT',s1%i,c_temp%i) + call c_dacop(c_temp%i,sqrtt%i) + + + c_master=localmaster + + END FUNCTION sqrtt + + + FUNCTION mul( S1, S2 ) + implicit none + TYPE (c_taylor) mul + TYPE (c_taylor), INTENT (IN) :: S1, S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + mul%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + ! call check(s2) + call ass(mul) + + ! if(old) then + call c_damul(s1%i,s2%i,c_temp%i) + call c_dacop(c_temp%i,mul%i) + ! else + ! call newdamul(s1%j,s2%j,mul%j) + ! endif + + c_master=localmaster + + END FUNCTION mul + + FUNCTION pbbra( S1, S2 ) + implicit none + TYPE (c_taylor) pbbra + TYPE (c_taylor), INTENT (IN) :: S1, S2 + integer localmaster + integer i + IF(.NOT.C_STABLE_DA) then + pbbra%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + ! call check(s2) + call ass(pbbra) + + ! if(old) then + pbbra=0.0_dp + do i=1,nd-rf + pbbra=(s1.d.(2*i-1))*(s2.d.(2*i))-(s2.d.(2*i-1))*(s1.d.(2*i))+pbbra + enddo + ! call DAPOI(s1%i,s2%i,c_temp%i,nd) + ! call c_dacop(c_temp%i,pbbra%i) + ! else + ! call newDAPOI(s1%j,s2%j,c_temp%il,nd) + ! call newc_dacop(c_temp%il,pbbra%j) + ! endif + + c_master=localmaster + + END FUNCTION pbbra + + +! FUNCTION pbbrav( S1 ) +! implicit none +! TYPE (c_vector_field) pbbrav +! TYPE (c_taylor), INTENT (IN) :: S1 +! type(c_damap) s2 +! integer localmaster +! integer i! +! +! IF(.NOT.C_STABLE_DA) then +! pbbrav%v%i=0 +! RETURN +! endif +! localmaster=c_master +! call alloc(s2) +! pbbrav%n=nd2 +! call c_ass_vector_field(pbbrav) +! pbbrav=0 +!s2=1 +! do i=1,nd2 +! pbbrav%v(i)=s1.pb.s2%v(i) +! enddo +! c_master=localmaster +! call kill(s2) +! END FUNCTION pbbrav + +! FUNCTION cpbbrav( S1, S2 ) +! implicit none +! TYPE (c_vector_field) cpbbrav +! TYPE (c_taylor), INTENT (IN) :: S1 +! type(c_damap) s2 +! integer localmaster +! integer i +! +! IF(.NOT.C_STABLE_DA) then +! cpbbrav%v%i=0 +! RETURN +! endif +! localmaster=c_master +! call alloc(s2) +! s2=1 +! cpbbrav%n=nd2 +! call c_ass_vector_field(cpbbrav) +! cpbbrav=0 +! +! do i=1,nd2 +! cpbbrav%v(i)=s1.cpb.s2%v(i) +! enddo +! c_master=localmaster +! call kill(s2) +! END FUNCTION cpbbrav + + +FUNCTION cpbbra( S1, S2 ) + implicit none + TYPE (c_taylor) cpbbra + TYPE (c_taylor), INTENT (IN) :: S1, S2 + integer localmaster + + IF(.NOT.C_STABLE_DA) then + cpbbra%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + ! call check(s2) + call ass(cpbbra) + + ! if(old) then + cpbbra=n_cai*(s1.pb.s2) + + c_master=localmaster + + END FUNCTION cpbbra + + + + FUNCTION liebraquaternion( S1, S2 ) + implicit none + TYPE (c_quaternion) liebraquaternion + TYPE (c_quaternion), INTENT (IN) :: S1, S2 + integer localmaster + + IF(.NOT.C_STABLE_DA) then + liebraquaternion%x(1)%i=0 + RETURN + endif + + localmaster=c_master + + + + call c_ass_quaternion(liebraquaternion) + + if(correct_quaternion_field) then + + liebraquaternion=s2*s1-s1*s2 + + else + liebraquaternion=s1*s2-s2*s1 + + endif + c_master=localmaster + + END FUNCTION liebraquaternion + + FUNCTION liebraso3( S1, S2 ) + implicit none + TYPE (c_spinmatrix) liebraso3 + TYPE (c_spinmatrix), INTENT (IN) :: S1, S2 + integer localmaster + + IF(.NOT.C_STABLE_DA) then + liebraso3%s(1,1)%i=0 + RETURN + endif + + localmaster=c_master + + + + call c_ass_spinmatrix(liebraso3) + + + if(correct_quaternion_field) then + + + + liebraso3=s2*s1-s1*s2 + + else + liebraso3=s1*s2-s2*s1 + + endif + c_master=localmaster + + END FUNCTION liebraso3 + + FUNCTION liebra( S1, S2 ) + implicit none + TYPE (c_vector_field) liebra + TYPE (c_vector_field), INTENT (IN) :: S1, S2 + integer localmaster,i + + IF(.NOT.C_STABLE_DA) then + liebra%v%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + ! call check(s2) + liebra%n=s1%n + call c_ass_vector_field(liebra) + liebra=0 + call c_etcom(s1%v%i,s2%v%i,liebra%v%i,s1%n) + + + + + if(use_quaternion) THEN + + liebra%q=s1%q.lb.s2%q + + liebra%q=liebra%q+c_bra_v_q(s1,s2%q)-c_bra_v_q(s2,s1%q) + ! c_bra_v_q + else + +! liebra%h=s1%h.lb.s2%h + liebra%L=s1%L.lb.s2%L + +! liebra%h=liebra%h+c_bra_v_so3(s1,s2%h)-c_bra_v_so3(s2,s1%h) + liebra%L=liebra%L+c_bra_v_so3(s1,s2%L)-c_bra_v_so3(s2,s1%L) + endif + if(complex_extra_order==1.and.special_extra_order_1) liebra=liebra.cut.no + c_master=localmaster + + END FUNCTION liebra + + + + + FUNCTION GETORDER( S1, S2 ) + implicit none + TYPE (c_taylor) GETORDER + TYPE (c_taylor), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETORDER%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(GETORDER) + + ! if(old) then + CALL c_TAKE(S1%I,S2,c_temp%i) + call c_dacop(c_temp%i,GETORDER%i) + ! else + ! CALL NEWTAKE(S1%J,S2,c_temp%iL) + ! call NEWc_dacop(c_temp%iL,GETORDER%J) + ! endif + c_master=localmaster + + END FUNCTION GETORDER + + + FUNCTION GETORDERMAP( S1, S2 ) + implicit none + TYPE (c_damap) GETORDERMAP + TYPE (c_damap), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + INTEGER I,s22 + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETORDERMAP%v%i=0 + RETURN + endif + localmaster=c_master + + s22=iabs(s2) + GETORDERMAP%n=s1%n + call c_assmap(GETORDERMAP) + GETORDERMAP=s1 + DO I=1,s1%n + GETORDERMAP%V(I)=(GETORDERMAP%V(I)).SUB.S22 + ENDDO + + if(s2<0) s22=s22-1 + +if(use_quaternion) THEN + GETORDERMAP%q=GETORDERMAP%q.SUB.S22 +else + GETORDERMAP%s=GETORDERMAP%s.SUB.S22 +endif + + +! DO I=1,3 +! DO j=1,3 +! GETORDERMAP%s%s(I,j)=(GETORDERMAP%s%s(I,j)).SUB.S22 +! ENDDO +! ENDDO + + c_master=localmaster + + END FUNCTION GETORDERMAP + + + + FUNCTION GETORDERquaternion( S1, S2 ) ! spin routine function + implicit none + TYPE (c_quaternion) GETORDERquaternion + TYPE (c_quaternion), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + INTEGER I,J + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETORDERquaternion%x(1)%i=0 + RETURN + endif + localmaster=c_master + call c_ass_quaternion(GETORDERquaternion) + + DO I=0,3 + GETORDERquaternion%x(I)=(S1%x(I)).SUB.S2 + ENDDO + + + c_master=localmaster + + END FUNCTION GETORDERquaternion + + + FUNCTION GETORDERSPINMATRIX( S1, S2 ) ! spin routine function + implicit none + TYPE (c_spinmatrix) GETORDERSPINMATRIX + TYPE (c_spinmatrix), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + INTEGER I,J + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETORDERSPINMATRIX%s%i=0 + RETURN + endif + localmaster=c_master + call c_ass_spinmatrix(GETORDERSPINMATRIX) + + + + + + DO I=1,3 + DO j=1,3 + GETORDERSPINMATRIX%s(I,j)=(S1%s(I,j)).SUB.S2 + ENDDO + ENDDO + + c_master=localmaster + + END FUNCTION GETORDERSPINMATRIX + + FUNCTION GETORDERVEC( S1, S2 ) + implicit none + TYPE (c_vector_field) GETORDERVEC + TYPE (c_vector_field), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + INTEGER I,j,s22,k + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETORDERVEC%v%i=0 + RETURN + endif + localmaster=c_master + + s22=iabs(s2) + GETORDERVEC%n=s1%n + call C_ass_vector_field(GETORDERVEC) + GETORDERVEC=s1 + DO I=1,s1%n + GETORDERVEC%V(I)=(GETORDERVEC%V(I)).SUB.S22 + ENDDO + + if(s2<0) s22=s22-1 + if(use_quaternion) then + GETORDERVEC%q=GETORDERVEC%q.SUB.S22 + else + do i=1,3 + do j=1,3 + GETORDERVEC%L%S(i,j)=GETORDERVEC%L%S(i,j).SUB.S22 +! GETORDERVEC%h%v(i)=GETORDERVEC%h%v(i).SUB.S22 + enddo + enddo + endif + + + + c_master=localmaster + + END FUNCTION GETORDERVEC + + + FUNCTION from_phasor(k) + implicit none + TYPE (c_damap) from_phasor + integer, optional :: k + INTEGER I,k1 + integer localmaster + TYPE (c_damap) from_phasori + complex(dp) N + real(dp) xn + IF(.NOT.C_STABLE_DA) then + from_phasor%v%i=0 + RETURN + endif + localmaster=c_master + + + call alloc(from_phasori) + + + k1=1 + from_phasor%n=nd2 + call c_assmap(from_phasor) + from_phasor=1 + + if( present(k) ) k1=k + + if(symp) then + n=sqrt(2.e0_dp) + n_cai=1 + do i=1,ndt + from_phasori%v(2*i-1)=((1.0_dp.cmono.(2*i-1))+i_*(1.0_dp.cmono.(2*i)))/N + from_phasori%v(2*i)=((1.0_dp.cmono.(2*i-1))-i_*(1.0_dp.cmono.(2*i)))/N/(-i_) + enddo + do i=nd,nd-rf+1,-1 + from_phasori%v(2*i-1)=((1.0_dp.cmono.(2*i-1))+i_*(1.0_dp.cmono.(2*i)))/N + from_phasori%v(2*i)=((1.0_dp.cmono.(2*i-1))-i_*(1.0_dp.cmono.(2*i)))/N/(-i_) + enddo + from_phasor=from_phasori**(-1) + else + xn=abs(n_cai) + if(xn>1.5_dp) then + n=1.e0_dp + else + if(aimag(n_cai)/=-1) then + Write(6,*) "n_cai can only be -2i or -i " + stop + endif + n=sqrt(2.e0_dp) + endif + do i=1,ndt + if(.not.unstable(i)) then !.and.(.not.hyperbolic)) then + from_phasor%v(2*i-1)=n*((0.5_dp.cmono.(2*i-1))+(0.5_dp.cmono.(2*i))) + from_phasor%v(2*i)=n*((0.5_dp.cmono.(2*i-1))-(0.5_dp.cmono.(2*i)))/i_ + endif + enddo + + do i=nd,nd-rf+1,-1 + from_phasor%v(2*i-1)=n*((0.5_dp.cmono.(2*i-1))+(0.5_dp.cmono.(2*i))) + from_phasor%v(2*i)=n*((0.5_dp.cmono.(2*i-1))-(0.5_dp.cmono.(2*i)))/i_ + enddo + endif + + + from_phasor=from_phasor**(k1) + + call kill(from_phasori) + !!! spin later + + c_master=localmaster + + END FUNCTION from_phasor + + FUNCTION to_phasor(k) + implicit none + TYPE (c_damap) to_phasor + integer, optional :: k + integer localmaster,k1 + + IF(.NOT.C_STABLE_DA) then + to_phasor%v%i=0 + RETURN + endif + localmaster=c_master + + k1=-1 + if(Present(k)) k1=-k + + + to_phasor%n=nd2 + call c_assmap(to_phasor) + + to_phasor=from_phasor(k1) + + + c_master=localmaster + + END FUNCTION to_phasor + + FUNCTION CUTORDER( S1, S2 ) + implicit none + TYPE (c_taylor) CUTORDER + TYPE (c_taylor), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + CUTORDER%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + call ass(CUTORDER) + + ! if(old) then + call c_datrunc(S1%I,s2,CUTORDER%i) + ! call c_dacop(S1%I,CUTORDER%i) + + ! DO I=S2,NO + ! CALL TAKE(CUTORDER%I,I,c_temp%i) + ! CALL DASUB(CUTORDER%I,c_temp%i,CUTORDER%I) + ! ENDDO + ! else + ! call NEWc_dacop(S1%J,CUTORDER%J) + ! DO I=S2,NO + ! CALL NEWTAKE(CUTORDER%J,I,c_temp%iL) + ! CALL NEWDASUB(CUTORDER%J,TEMPL,CUTORDER%J) + ! ENDDO + ! endif + c_master=localmaster + + END FUNCTION CUTORDER + + FUNCTION CUTORDERMAP( S1, S2 ) + implicit none + TYPE (c_DAMAP) CUTORDERMAP + TYPE (c_DAMAP), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster,I,s22 + IF(.NOT.C_STABLE_DA) then + CUTORDERMAP%v%i=0 + RETURN + endif + localmaster=c_master + s22=iabs(s2) + CUTORDERMAP%N=S1%N + call C_assMAP(CUTORDERMAP) + CUTORDERMAP=S1 + + DO I=1,CUTORDERMAP%N + CUTORDERMAP%V(I)=CUTORDERMAP%V(I).CUT.S22 + ENDDO + if(s2<0) s22=s22-1 +if(use_quaternion) THEN + CUTORDERMAP%q=CUTORDERMAP%q.cut.s22 +else + CUTORDERMAP%s=CUTORDERMAP%s.cut.s22 +endif + + + c_master=localmaster + + END FUNCTION CUTORDERMAP + + + + FUNCTION CUTORDERVEC( S1, S2 ) + implicit none + TYPE (c_vector_field) CUTORDERVEC + TYPE (c_vector_field), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster,I,s22,J + IF(.NOT.C_STABLE_DA) then + CUTORDERVEC%v%i=0 + RETURN + endif + localmaster=c_master + s22=iabs(s2) + CUTORDERVEC%N=S1%N + CUTORDERVEC%nrmax=S1%nrmax + + call C_ass_vector_field(CUTORDERVEC) + + CUTORDERVEC=S1 + + DO I=1,CUTORDERVEC%N + CUTORDERVEC%V(I)=CUTORDERVEC%V(I).CUT.S22 + ENDDO + if(s2<0) s22=s22-1 + if(use_quaternion) then + DO I=0,3 + CUTORDERVEC%q%x(I)= CUTORDERVEC%q%x(I).CUT.s22 + ENDDO + else + DO I=1,3 + DO j=1,3 +! CUTORDERVEC%h%v(I)= CUTORDERVEC%h%v(I).CUT.s22 + CUTORDERVEC%L%S(I,J)= CUTORDERVEC%L%S(I,J).CUT.s22 + ENDDO + ENDDO + ENDIF + c_master=localmaster + + END FUNCTION CUTORDERVEC + + FUNCTION CUTORDERspin( S1, S2 ) ! spin routine function + implicit none + TYPE (c_spinmatrix) CUTORDERspin + TYPE (c_spinmatrix), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster,I,j + IF(.NOT.C_STABLE_DA) then + CUTORDERspin%s%i=0 + RETURN + endif + localmaster=c_master + + + call c_ass_spinmatrix(CUTORDERspin) + CUTORDERspin=S1 + + DO I=1,3 + do j=1,3 + CUTORDERspin%s(i,j)=CUTORDERspin%s(i,j).CUT.S2 + ENDDO + enddo + + c_master=localmaster + + END FUNCTION CUTORDERspin + + FUNCTION CUTORDERquaternion( S1, S2 ) ! spin routine function + implicit none + TYPE (c_quaternion) CUTORDERquaternion + TYPE (c_quaternion), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster,I,j,s22 + IF(.NOT.C_STABLE_DA) then + CUTORDERquaternion%x(1)=0 + RETURN + endif +!!!! changed 2023.4.10 + localmaster=c_master + s22=iabs(s2) + call c_ass_quaternion(CUTORDERquaternion) + ! CUTORDERquaternion=S1 + if(s2<0) s22=s22-1 + DO I=0,3 + CUTORDERquaternion%x(i)=S1%x(i).cut.s22 + enddo + + c_master=localmaster + + END FUNCTION CUTORDERquaternion + + FUNCTION CUTORDERspinor( S1, S2 ) ! spin routine function + implicit none + TYPE (c_spinor) CUTORDERspinor + TYPE (c_spinor), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster,I + IF(.NOT.C_STABLE_DA) then + CUTORDERspinor%v(1)%i=0 + RETURN + endif + localmaster=c_master + + + call c_ass_spinor(CUTORDERspinor) + CUTORDERspinor=S1 + + DO I=1,3 + CUTORDERspinor%v(i)=CUTORDERspinor%v(i).CUT.S2 + ENDDO + + c_master=localmaster + + END FUNCTION CUTORDERspinor + + FUNCTION dputchar( S1, S2 ) + implicit none + TYPE (c_taylor) dputchar + complex(dp), INTENT (IN) :: S1 + CHARACTER(*) , INTENT (IN) :: S2 + CHARACTER (LEN = LNV) resul + integer j(lnv),i,io + integer localmaster + IF(.NOT.C_STABLE_DA) then + dputchar%i=0 + RETURN + endif + localmaster=c_master + + + call ass(dputchar) + + + resul = trim(ADJUSTL (s2)) + + do i=1,lnv + j(i)=0 + enddo + + !frs get around compiler problem + nd2par= len(trim(ADJUSTL (s2))) + !frs do i=1,len(trim(ADJUSTL (s2))) +io=0 + do i=1,nd2par + CALL CHARINT(RESUL(I:I),J(I)) + io=io+j(i) + if(i>nv) then + if(j(i)>0) then + dputchar=0.0_dp + ! call var(dputchar,zero,0) + c_master=localmaster + return + endif + endif + enddo + + if(io>no) then + dputchar=0.0_dp + ! call var(dputchar,zero,0) + c_master=localmaster + return + endif + + dputchar=0.0_dp + ! call var(dputchar,zero,0) + + CALL c_pok(dputchar,j,s1) + c_master=localmaster + + END FUNCTION dputchar + + FUNCTION dputcharr( S1r, S2 ) + implicit none + TYPE (c_taylor) dputcharr + real(dp), INTENT (IN) :: S1r + CHARACTER(*) , INTENT (IN) :: S2 + CHARACTER (LEN = LNV) resul + integer j(lnv),i,io + integer localmaster + complex(dp) s1 + IF(.NOT.C_STABLE_DA) then + dputcharr%i=0 + RETURN + endif + localmaster=c_master + + s1=s1r + call ass(dputcharr) + + + resul = trim(ADJUSTL (s2)) + + do i=1,lnv + j(i)=0 + enddo + + !frs get around compiler problem + nd2par= len(trim(ADJUSTL (s2))) + !frs do i=1,len(trim(ADJUSTL (s2))) +io=0 + do i=1,nd2par + CALL CHARINT(RESUL(I:I),J(I)) + io=io+j(i) + if(i>nv) then + if(j(i)>0) then + dputcharr=0.0_dp + ! call var(dputchar,zero,0) + c_master=localmaster + return + endif + endif + enddo + + + if(io>no) then + dputcharr=0.0_dp + ! call var(dputchar,zero,0) + c_master=localmaster + return + endif + dputcharr=0.0_dp + ! call var(dputchar,zero,0) + CALL c_pok(dputcharr,j,s1) + c_master=localmaster + + END FUNCTION dputcharr + + FUNCTION dputint( S1, S2 ) + implicit none + TYPE (c_taylor) dputint + complex(dp), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2(:) + integer j(lnv),i,io + integer localmaster + IF(.NOT.C_STABLE_DA) then + dputint%i=0 + RETURN + endif + localmaster=c_master + + + call ass(dputint) + + + + do i=1,lnv + j(i)=0 + enddo + + !frs get around compiler problem + nd2par= size(s2) + !frs do i=1,len(trim(ADJUSTL (s2))) + do i=1,nd2par + j(i)=s2(i) + enddo +io=0 + do i=1,nd2par + io=io+j(i) + if(i>nv) then + if(j(i)>0) then + ! call var(dputint,zero,0) + dputint=0.0_dp + c_master=localmaster + return + endif + endif + enddo + + + if(io>no) then + dputint=0.0_dp + ! call var(dputchar,zero,0) + c_master=localmaster + return + endif + + + dputint=0.0_dp + ! call var(dputint,zero,0) + CALL c_pok(dputint,j,s1) + c_master=localmaster + + END FUNCTION dputint + + FUNCTION dputintr( S1r, S2 ) + implicit none + TYPE (c_taylor) dputintr + real(dp), INTENT (IN) :: S1r + integer , INTENT (IN) :: S2(:) + integer j(lnv),i,io + integer localmaster + complex(dp) s1 + IF(.NOT.C_STABLE_DA) then + dputintr%i=0 + RETURN + endif + localmaster=c_master + + s1=s1r + call ass(dputintr) + + + + do i=1,lnv + j(i)=0 + enddo + + !frs get around compiler problem + nd2par= size(s2) + !frs do i=1,len(trim(ADJUSTL (s2))) + do i=1,nd2par + j(i)=s2(i) + enddo +io=0 + do i=1,nd2par + io=io+j(i) + if(i>nv) then + if(j(i)>0) then + ! call var(dputint,zero,0) + dputintr=0.0_dp + c_master=localmaster + return + endif + endif + enddo + + if(io>no) then + dputintr=0.0_dp + ! call var(dputchar,zero,0) + c_master=localmaster + return + endif + + dputintr=0.0_dp + ! call var(dputint,zero,0) + CALL c_pok(dputintr,j,s1) + c_master=localmaster + + END FUNCTION dputintr + + FUNCTION c_dputint0( S1, S2 ) + implicit none + TYPE (c_taylor) c_dputint0 + complex(dp), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2 + integer j(lnv) + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_dputint0%i=0 + RETURN + endif + localmaster=c_master + + + call ass(c_dputint0) + j=0 + if(s2>nv) then + c_dputint0=0.0e0_dp + c_master=localmaster + return + endif + if(s2==0) then + c_dputint0=s1 + c_master=localmaster + return + endif + + c_dputint0=0.0_dp + ! call var(c_dputint0,zero,s2) + + j(s2)=1 + CALL c_pok(c_dputint0,j,s1) + + c_master=localmaster + + END FUNCTION c_dputint0 + + FUNCTION c_dputint0r( S1, S2 ) + implicit none + TYPE (c_taylor) c_dputint0r + real(dp), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2 + integer j(lnv) + integer localmaster + complex(dp) ss + IF(.NOT.C_STABLE_DA) then + c_dputint0r%i=0 + RETURN + endif + localmaster=c_master + + ss=s1 + + call ass(c_dputint0r) + j=0 + if(s2>nv) then + c_dputint0r=0.0_dp + c_master=localmaster + return + endif + if(s2==0) then + c_dputint0r=ss + c_master=localmaster + return + endif + + c_dputint0r=0.0_dp + ! call var(c_dputint0,zero,s2) + + j(s2)=1 + CALL c_pok(c_dputint0r,j,ss) + + c_master=localmaster + + END FUNCTION c_dputint0r + + + FUNCTION GETCHARnd2s( S1, S2 ) + implicit none + TYPE (c_taylor) GETCHARnd2s + TYPE (c_taylor), INTENT (IN) :: S1 + CHARACTER(*) , INTENT (IN) :: S2 + + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETCHARnd2s%i=0 + RETURN + endif + localmaster=c_master + + + call ass(GETCHARnd2s) + + + GETCHARnd2s=s1.par.s2 + call shiftda(GETCHARnd2s,GETCHARnd2s, len(trim(ADJUSTR (s2) ))) + + c_master=localmaster + + + END FUNCTION GETCHARnd2s + + FUNCTION GETintnd2s( S1, S2 ) + implicit none + TYPE (c_taylor) GETintnd2s + TYPE (c_taylor), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2(:) + + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETintnd2s%i=0 + RETURN + endif + localmaster=c_master + + + call ass(GETintnd2s) + + + GETintnd2s=s1.par.s2 + + call shiftda(GETintnd2s,GETintnd2s, size(s2) ) + + c_master=localmaster + + + END FUNCTION GETintnd2s + + FUNCTION GETintk( S1, S2 ) + implicit none + TYPE (c_taylor) GETintk + TYPE (c_taylor), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2 + + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETintk%i=0 + RETURN + endif + localmaster=c_master + + + call ass(GETintk) + + + + call shiftda(s1,GETintk, s2 ) + + c_master=localmaster + + + END FUNCTION GETintk + + + + FUNCTION GETchar( S1, S2 ) + + implicit none + complex(dp) GETchar,r1 + TYPE (c_taylor), INTENT (IN) :: S1 + CHARACTER(*) , INTENT (IN) :: S2 + CHARACTER (LEN = LNV) resul + integer j(lnv),i,c,cm + IF(.NOT.C_STABLE_DA) then + GETchar=0 + RETURN + endif + + + + resul = s2 + call context(resul) + + do i=1,lnv + j(i)=0 + enddo + + + nd2par= len_trim(resul) + + + + + + do i=1,nd2par + CALL CHARINT(RESUL(I:I),J(I)) + enddo + +c=0 + do i=nv+1,lnv + c=j(i)+c + enddo +cm=0 + do i=1,nv + cm=j(i)+cm + enddo + +!if(c>0.or.cm>nv) then ! 2017.1.16 +if(c>0.or.cm>no) then +r1=0.0_dp +else + CALL c_dapek(S1%I,j,r1) +endif + + + GETchar=r1 + + END FUNCTION GETchar + + + + + FUNCTION GETint( S1, S2 ) + implicit none + complex(dp) GETint,r1 + TYPE (c_taylor), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2(:) + integer j(lnv),i,c,cm + IF(.NOT.C_STABLE_DA) then + GETint=0 + RETURN + endif + + + + do i=1,lnv + j(i)=0 + enddo + + + nd2par= size(s2) + + do i=1,nd2par + J(I)=s2(i) + enddo + + c=0 + do i=nv+1,lnv + c=j(i)+c + enddo +cm=0 + do i=1,nv + cm=j(i)+cm + enddo + + +!if(c>0.or.cm>nv) then ! 2017.1.16 +if(c>0.or.cm>no) then + +r1=0.0_dp +else + CALL c_dapek(S1%I,j,r1) +endif + + GETint=r1 + + END FUNCTION GETint + + FUNCTION GETintmat( S1, S2 ) + implicit none + complex(dp) GETintmat,r1 + TYPE (c_taylor), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2 + integer j(lnv),i,c,cm + IF(.NOT.C_STABLE_DA) then + GETintmat=0 + endif + + + if(s2==0) then + GETintmat=S1 + return + endif + do i=1,lnv + j(i)=0 + enddo + j(s2)=1 + + c=0 + do i=nv+1,lnv + c=j(i)+c + enddo +cm=0 + do i=1,nv + cm=j(i)+cm + enddo + + +!if(c>0.or.cm>nv) then ! 2017.1.16 +if(c>0.or.cm>no) then + +r1=0.0_dp +else + CALL c_dapek(S1%I,j,r1) +endif + + GETintmat=r1 + + END FUNCTION GETintmat + + + + FUNCTION GETdiff( S1, S2 ) + implicit none + TYPE (c_taylor) GETdiff + TYPE (c_taylor), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETdiff%i=0 + RETURN + endif + + + localmaster=c_master + + + ! call check(s1) + call ass(GETdiff) + + ! if(old) then + CALL c_dader(S2,S1%I,c_temp%i) +! call c_dacop(c_temp%i,GETdiff%i) + + getdiff=c_temp + ! else + ! CALL NEWdader(S2,S1%J,TEMPL) + ! call NEWc_dacop(tempL,GETdiff%J) + ! endif + + + c_master=localmaster + + END FUNCTION GETdiff + + FUNCTION GETdiff_universal( S1, S2 ) + implicit none + TYPE (c_taylor) GETdiff_universal,d_temp + TYPE (c_universal_taylor), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster,i + integer, allocatable :: J(:) + + IF(.NOT.C_STABLE_DA) then + GETdiff_universal%i=0 + RETURN + endif + + allocate(J(s1%nv)) + + localmaster=c_master + + call alloc(d_temp) + ! call check(s1) + call ass(GETdiff_universal) + d_temp=0.0_dp + + do i=1,s1%n + if(s2<=s1%nv) then + if(s1%j(i,s2)>0) then + j=s1%j(i,1:s1%nv) + j(s2)=j(s2)-1 + d_temp=d_temp+((s1%j(i,s2)*s1%c(i)).cmono.j) + endif + endif + enddo + + GETdiff_universal=d_temp + + call kill(d_temp) + + c_master=localmaster + deallocate(J) + END FUNCTION GETdiff_universal + + + + FUNCTION GETINTegrate( S1, S2 ) + implicit none + TYPE (c_taylor) GETINTegrate + TYPE (c_taylor), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster,n,i + type(c_taylor) t,x + complex(dp) value + integer, allocatable :: jc(:) + IF(.NOT.C_STABLE_DA) then + GETINTegrate%i=0 + RETURN + endif + + localmaster=c_master + + allocate(jc(nv)) + jc=0 + ! call check(s1) + call ass(GETINTegrate) + call alloc(t,x) + t=s1 + x=0 + call c_taylor_cycle(t,size=n) + + do i=1,n + call c_taylor_cycle(t,ii=i,value=value,j=jc) + + x=((value/(jc(s2)+1)).cmono.jc)*((1.0_dp,0.0_dp).cmono.s2)+x + + enddo + + GETINTegrate=x + + call kill(t,x) + deallocate(jc) + c_master=localmaster + + END FUNCTION GETINTegrate + +! computes Lie polynomial in relevant planes : s2=1 generating function, ss=0 potential +! Does not included the nonsymplectic modulated planes + FUNCTION getpb( S1,S1p, S2 ) + implicit none + TYPE (c_taylor) getpb + TYPE (c_vector_field),optional, INTENT (IN) :: S1 + TYPE (c_damap),optional, INTENT (IN) :: S1p + INTEGER,optional, INTENT (IN) :: S2 + integer localmaster,n,i,j,l,fac,nd2here,ss + type(c_taylor) t,x + complex(dp) value + integer, allocatable :: jc(:) + IF(.NOT.C_STABLE_DA) then + getpb%i=0 + RETURN + endif + + localmaster=c_master + + nd2here=nd2-2*rf + ss=-1 + if(present(s2)) ss=s2 + allocate(jc(c_%nv)) + jc=0 + ! call check(s1) + call ass(getpb) + getpb=0.0_dp + call alloc(t,x) + + do j=1,nd2here + if(present(s1)) then + t=s1%v(j) + elseif(present(s1p)) then + t=s1p%v(j) + if(.not.present(s2))ss=1 + else + write(6,*) " error in getpb " + stop + endif + x=0 + call c_taylor_cycle(t,size=n) + + do i=1,n + call c_taylor_cycle(t,ii=i,value=value,j=jc) + fac=0 + do l=1,nd2here + fac=jc(l)+fac + enddo + fac=fac+1 + if(ss<0) then ! fixed bug 2017 jan 9 + if(mod(j,2)==0) then + x=((value/fac).cmono.jc)*(1.0_dp.cmono.(j-1))+x + else + x=ss*((value/fac).cmono.jc)*(1.0_dp.cmono.(j+1))+x + endif + else + x=((value/fac).cmono.jc)*(1.0_dp.cmono.(j))+x + endif + enddo + + getpb=x+getpb + + + enddo ! j + + call kill(t,x) + deallocate(jc) + c_master=localmaster + + END FUNCTION getpb + + + FUNCTION cgetpb( S1,S1p, S2 ) + implicit none + TYPE (c_taylor) cgetpb + TYPE (c_vector_field),optional, INTENT (IN) :: S1 + TYPE (c_damap),optional, INTENT (IN) :: S1p + INTEGER,optional, INTENT (IN) :: S2 + integer localmaster,n,i,j,l,fac,nd2here,ss + type(c_taylor) t,x + complex(dp) value + complex(dp), allocatable :: ncai(:) + integer, allocatable :: jc(:) + IF(.NOT.C_STABLE_DA) then + cgetpb%i=0 + RETURN + endif + + localmaster=c_master + + nd2here=nd2-2*rf + ss=-1 + if(present(s2)) ss=s2 + allocate(jc(c_%nv)) + jc=0 + ! call check(s1) + call ass(cgetpb) + cgetpb=0.0_dp + call alloc(t,x) + + + allocate(ncai(nd2here)) + ncai=n_cai + + + if(c_%ndpt/=0) then + ncai(c_%ndpt)=1 + ncai(c_%ndptb)=1 + endif + + + + + + do j=1,nd2here + if(present(s1)) then + t=s1%v(j) + elseif(present(s1p)) then + t=s1p%v(j) + if(.not.present(s2))ss=1 + else + write(6,*) " error in cgetpb " + stop + endif + x=0 + call c_taylor_cycle(t,size=n) + + do i=1,n + call c_taylor_cycle(t,ii=i,value=value,j=jc) + value=value/ncai(j) + fac=0 + do l=1,nd2here + fac=jc(l)+fac + enddo + fac=fac+1 + if(ss<0) then ! fixed bug 2017 jan 9 + if(mod(j,2)==0) then + x=((value/fac).cmono.jc)*(1.0_dp.cmono.(j-1))+x + else + x=ss*((value/fac).cmono.jc)*(1.0_dp.cmono.(j+1))+x + endif + else + x=((value/fac).cmono.jc)*(1.0_dp.cmono.(j))+x + endif + enddo + + cgetpb=x+cgetpb + + + enddo ! j + + call kill(t,x) + deallocate(jc) + deallocate(ncai) + + c_master=localmaster + + END FUNCTION cgetpb + + FUNCTION getpb_from_transverse( S1,f,S1p, S2 ) + implicit none + TYPE (c_taylor) getpb_from_transverse + TYPE (c_vector_field),optional, INTENT (IN) :: S1 + TYPE (c_damap),optional, INTENT (IN) :: S1p + INTEGER,optional, INTENT (IN) :: S2 + integer localmaster,n,i,j,l,fac,nd2here,ss,k + type(c_taylor) t,x + complex(dp) value + real(dp) c + integer, allocatable :: jc(:) + type(c_vector_field), INTENT (INout) :: f + IF(.NOT.C_STABLE_DA) then + getpb_from_transverse%i=0 + RETURN + endif + + localmaster=c_master + + nd2here=4 !nd2-2*rf + ss=-1 + if(present(s2)) ss=s2 + allocate(jc(c_%nv)) + jc=0 + ! call check(s1) + call ass(getpb_from_transverse) + getpb_from_transverse=0.0_dp + call alloc(t,x) + f=0 + + do j=1,nd2here + if(present(s1)) then + t=s1%v(j) + elseif(present(s1p)) then + t=s1p%v(j) + if(.not.present(s2))ss=1 + else + write(6,*) " error in getpb " + stop + endif + x=0 + call c_taylor_cycle(t,size=n) + + do i=1,n + call c_taylor_cycle(t,ii=i,value=value,j=jc) + fac=0 + do l=1,nd2here + fac=jc(l)+fac + enddo + fac=fac+1 + if(ss<0) then ! fixed bug 2017 jan 9 + if(mod(j,2)==0) then + x=((value/fac).cmono.jc)*(1.0_dp.cmono.(j-1))+x + jc(j-1)=jc(j-1)+1 + value=value/fac + else + x=ss*((value/fac).cmono.jc)*(1.0_dp.cmono.(j+1))+x + jc(j+1)=jc(j+1)+1 + value=ss*value/fac + endif + do k=1,nd + l=2*k + call derive(jc,l,c) + if(jc(l)>=0) f%v(2*k-1)=f%v(2*k-1)-((value*c).cmono.jc) + jc(2*k)=jc(2*k)+1 + l=2*k-1 + call derive(jc,l,c) + if(jc(l)>=0) f%v(2*k)=f%v(2*k)+((value*c).cmono.jc) + jc(2*k-1)=jc(2*k-1)+1 + enddo + else + x=((value/fac).cmono.jc)*(1.0_dp.cmono.(j))+x + endif + enddo + getpb_from_transverse=x+getpb_from_transverse + + + enddo ! j + + call kill(t,x) + deallocate(jc) + c_master=localmaster + + END FUNCTION getpb_from_transverse + + subroutine derive(j,k,c) + implicit none + integer, intent(inout):: J(:) + integer, intent(in):: k + real(dp), intent(out) :: c + + if(j(k)==0) then + c=0 + j(k)=j(k)-1 + else + c=j(k) + j(k)=j(k)-1 + endif + end subroutine derive + + + + FUNCTION getvectorfield( S1,s2 ) +!#internal: getvectorfield +!# produce vector field S1.grad= :s2: +! + implicit none + TYPE (c_vector_field) getvectorfield + TYPE (c_taylor), INTENT (IN) :: S1 + integer, optional, INTENT (IN) :: S2 + integer localmaster ,i, ss + localmaster=c_master + + getvectorfield%n=nd2 + call c_ass_vector_field(getvectorfield) + getvectorfield=0 + ss=-1 + if(present(s2)) ss=s2 + if(ss==-1) then + do i=1,nd2-2*rf + getvectorfield%v(i)= s1.pb.(1.0_dp.cmono.i) + enddo + else + do i=1,nd2-2*rf + getvectorfield%v(i)= s1.d.i + enddo + endif + c_master=localmaster + if(complex_extra_order==1.and.special_extra_order_1) getvectorfield=getvectorfield.cut.no + + END FUNCTION getvectorfield + + + FUNCTION getvectorfield_universal( S1 ) + implicit none + TYPE (c_vector_field) getvectorfield_universal + TYPE (c_universal_taylor), INTENT (IN) :: S1 + + integer localmaster ,i + localmaster=master + + getvectorfield_universal%n=nd2 + call c_ass_vector_field(getvectorfield_universal) + + getvectorfield_universal=0 + + do i=1,nd-rf + getvectorfield_universal%v(2*i-1) = -(s1.d.(2*i)) + getvectorfield_universal%v(2*i) = s1.d.(2*i-1) + enddo + + c_master=localmaster + if(complex_extra_order==1.and.special_extra_order_1) getvectorfield_universal=getvectorfield_universal.cut.no + END FUNCTION getvectorfield_universal + + FUNCTION cgetvectorfield_universal( S1 ) + implicit none + TYPE (c_vector_field) cgetvectorfield_universal + TYPE (c_universal_taylor), INTENT (IN) :: S1 + + integer localmaster ,i + localmaster=master + + cgetvectorfield_universal%n=nd2 + call c_ass_vector_field(cgetvectorfield_universal) + + cgetvectorfield_universal=0 + + do i=1,nd-rf + cgetvectorfield_universal%v(2*i-1)= -n_cai*(s1.d.(2*i)) + cgetvectorfield_universal%v(2*i)= n_cai*(s1.d.(2*i-1)) + enddo + + c_master=localmaster + if(complex_extra_order==1.and.special_extra_order_1) cgetvectorfield_universal=cgetvectorfield_universal.cut.no + END FUNCTION cgetvectorfield_universal + + + FUNCTION cgetvectorfield( S1 ) + implicit none + TYPE (c_vector_field) cgetvectorfield + TYPE (c_taylor), INTENT (IN) :: S1 + + integer localmaster ,i + localmaster=master + + cgetvectorfield%n=nd2 + call c_ass_vector_field(cgetvectorfield) + +cgetvectorfield=0 + + do i=1,nd2-2*rf + cgetvectorfield%v(i)= s1.cpb.(1.0_dp.cmono.i) + enddo + + c_master=localmaster + if(complex_extra_order==1.and.special_extra_order_1) cgetvectorfield=cgetvectorfield.cut.no + END FUNCTION cgetvectorfield + + + FUNCTION GETdatra( S1, S2 ) + implicit none + TYPE (c_taylor) GETdatra + TYPE (c_taylor), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETdatra%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(GETdatra) + + ! if(old) then + CALL c_datra(S2,S1%I,c_temp%i) + call c_dacop(c_temp%i,GETdatra%i) + ! else + ! CALL NEWdatra(S2,S1%J,TEMPL) + ! call NEWc_dacop(tempL,GETdatra%J) + ! endif + c_master=localmaster + + END FUNCTION GETdatra + + FUNCTION POW( S1, R2 ) + implicit none + TYPE (c_taylor) POW + TYPE (c_taylor), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: R2 + INTEGER I,R22 + integer localmaster + IF(.NOT.C_STABLE_DA) then + POW%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(POW) + + ! if(old) then + CALL c_dacon(c_temp%i,(1.0_dp,0.0_dp)) + + R22=IABS(R2) + DO I=1,R22 + CALL c_damul(c_temp%i,S1%I,c_temp%i) + ENDDO + IF(R2.LT.0) THEN + CALL c_dadic(c_temp%i,(1.0_dp,0.0_dp),c_temp%i) + ENDIF + call c_dacop(c_temp%i,POW%i) + + c_master=localmaster + END FUNCTION POW + + + FUNCTION cdmulsc( S1, sc ) + implicit none + TYPE (c_taylor) cdmulsc + TYPE (c_taylor), INTENT (IN) :: S1 + complex(dp), INTENT (IN) :: sc + integer localmaster + IF(.NOT.C_STABLE_DA) then + cdmulsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(cdmulsc) + + ! if(old) then + call c_dacmu(s1%i,sc,c_temp%i) + call c_dacop(c_temp%i,cdmulsc%i) + ! else + ! call newc_dacmu(s1%j,sc,dmulsc%j) + ! endif + + c_master=localmaster + END FUNCTION cdmulsc + + FUNCTION dmulsc( S1, sc ) + implicit none + TYPE (c_taylor) dmulsc + TYPE (c_taylor), INTENT (IN) :: S1 + real(dp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + dmulsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(dmulsc) + sct=sc + ! if(old) then + call c_dacmu(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,dmulsc%i) + ! else + ! call newc_dacmu(s1%j,sc,dmulsc%j) + ! endif + + c_master=localmaster + END FUNCTION dmulsc + + FUNCTION mulsc( S1, sc ) + implicit none + TYPE (c_taylor) mulsc + TYPE (c_taylor), INTENT (IN) :: S1 + real(sp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + mulsc%i=0 + RETURN + endif + localmaster=c_master + + + if(c_real_warning) call c_real_stop + ! call check(s1) + call ass(mulsc) + sct=sc + ! if(old) then + call c_dacmu(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,mulsc%i) + ! else + ! call newc_dacmu(s1%j,REAL(sc,kind=DP),mulsc%j) + ! endif + c_master=localmaster + END FUNCTION mulsc + + FUNCTION imulsc( S1, sc ) + implicit none + TYPE (c_taylor) imulsc + TYPE (c_taylor), INTENT (IN) :: S1 + integer, INTENT (IN) :: sc + integer localmaster + complex(dp) sct + IF(.NOT.C_STABLE_DA) then + imulsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(imulsc) + sct=sc + + ! if(old) then + call c_dacmu(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,imulsc%i) + ! else + ! call newc_dacmu(s1%j,REAL(sc,kind=DP),imulsc%j) + ! endif + + c_master=localmaster + END FUNCTION imulsc + + FUNCTION cdscmul( sc,S1 ) + implicit none + TYPE (c_taylor) cdscmul + TYPE (c_taylor), INTENT (IN) :: S1 + complex(dp), INTENT (IN) :: sc + integer localmaster + IF(.NOT.C_STABLE_DA) then + cdscmul%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(cdscmul) + + ! if(old) then + call c_dacmu(s1%i,sc,c_temp%i) + call c_dacop(c_temp%i,cdscmul%i) + ! else + ! call newc_dacmu(s1%j,sc,dscmul%j) + ! endif + + c_master=localmaster + + END FUNCTION cdscmul + + FUNCTION dscmul( sc,S1 ) + implicit none + TYPE (c_taylor) dscmul + TYPE (c_taylor), INTENT (IN) :: S1 + real(dp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + dscmul%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(dscmul) + sct=sc + ! if(old) then + call c_dacmu(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,dscmul%i) + ! else + ! call newc_dacmu(s1%j,sc,dscmul%j) + ! endif + + c_master=localmaster + + END FUNCTION dscmul + + FUNCTION scmul( sc,S1 ) + implicit none + TYPE (c_taylor) scmul + TYPE (c_taylor), INTENT (IN) :: S1 + real(sp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + scmul%i=0 + RETURN + endif + localmaster=c_master + + + if(c_real_warning) call c_real_stop + ! call check(s1) + call ass(scmul) + + sct=sc + + ! if(old) then + call c_dacmu(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,scmul%i) + ! else + ! call newc_dacmu(s1%j,REAL(sc,kind=DP),scmul%j) + ! endif + + c_master=localmaster + + END FUNCTION scmul + + FUNCTION iscmul( sc,S1 ) + implicit none + TYPE (c_taylor) iscmul + TYPE (c_taylor), INTENT (IN) :: S1 + integer, INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + iscmul%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(iscmul) + sct=sc + ! if(old) then + call c_dacmu(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,iscmul%i) + ! else + ! call newc_dacmu(s1%j,REAL(sc,kind=DP),iscmul%j) + ! endif + + c_master=localmaster + + END FUNCTION iscmul + + FUNCTION div( S1, S2 ) + implicit none + TYPE (c_taylor) div + TYPE (c_taylor), INTENT (IN) :: S1, S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + div%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + ! call check(s2) + call ass(div) + + ! if(old) then + call c_dadiv(s1%i,s2%i,c_temp%i) + call c_dacop(c_temp%i,div%i) + ! else + ! call newdadiv(s1%j,s2%j,templ) + ! call newc_dacop(templ,div%j) + ! endif + + c_master=localmaster + END FUNCTION div + + FUNCTION cdscdiv( sc,S1 ) + implicit none + TYPE (c_taylor) cdscdiv + TYPE (c_taylor), INTENT (IN) :: S1 + complex(dp), INTENT (IN) :: sc + integer localmaster + IF(.NOT.C_STABLE_DA) then + cdscdiv%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(cdscdiv) + + ! if(old) then + call c_dadic(s1%i,sc,c_temp%i) + call c_dacop(c_temp%i,cdscdiv%i) + ! else + ! call newc_dadic(s1%j,sc,dscdiv%j) + ! endif + + c_master=localmaster + + END FUNCTION cdscdiv + + FUNCTION dscdiv( sc,S1 ) + implicit none + TYPE (c_taylor) dscdiv + TYPE (c_taylor), INTENT (IN) :: S1 + real(dp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + dscdiv%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(dscdiv) + sct=sc + + ! if(old) then + call c_dadic(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,dscdiv%i) + ! else + ! call newc_dadic(s1%j,sc,dscdiv%j) + ! endif + + c_master=localmaster + + END FUNCTION dscdiv + + FUNCTION scdiv( sc,S1 ) + implicit none + TYPE (c_taylor) scdiv + TYPE (c_taylor), INTENT (IN) :: S1 + real(sp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + scdiv%i=0 + RETURN + endif + localmaster=c_master + + + if(c_real_warning) call c_real_stop + ! call check(s1) + call ass(scdiv) + + sct=sc + + ! if(old) then + call c_dadic(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,scdiv%i) + ! else + ! call newc_dadic(s1%j,REAL(sc,kind=DP),scdiv%j) + ! endif + + c_master=localmaster + END FUNCTION scdiv + + FUNCTION iscdiv( sc,S1 ) + implicit none + TYPE (c_taylor) iscdiv + TYPE (c_taylor), INTENT (IN) :: S1 + integer, INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + iscdiv%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(iscdiv) + sct=sc + ! if(old) then + call c_dadic(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,iscdiv%i) + ! else + ! call newc_dadic(s1%j,REAL(sc,kind=DP),iscdiv%j) + ! endif + + + c_master=localmaster + END FUNCTION iscdiv + + FUNCTION cddivsc( S1, sc ) + implicit none + TYPE (c_taylor) cddivsc + TYPE (c_taylor), INTENT (IN) :: S1 + complex(dp), INTENT (IN) :: sc + integer localmaster + IF(.NOT.C_STABLE_DA) then + cddivsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(cddivsc) + + + ! if(old) then + call c_dacdi(s1%i,sc,c_temp%i) + call c_dacop(c_temp%i,cddivsc%i) + ! else + ! call newc_dacdi(s1%j,sc,ddivsc%j) + ! endif + c_master=localmaster + + END FUNCTION cddivsc + + + FUNCTION ddivsc( S1, sc ) + implicit none + TYPE (c_taylor) ddivsc + TYPE (c_taylor), INTENT (IN) :: S1 + real(dp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + ddivsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(ddivsc) + + sct=sc + ! if(old) then + call c_dacdi(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,ddivsc%i) + ! else + ! call newc_dacdi(s1%j,sc,ddivsc%j) + ! endif + c_master=localmaster + + END FUNCTION ddivsc + + FUNCTION divsc( S1, sc ) + implicit none + TYPE (c_taylor) divsc + TYPE (c_taylor), INTENT (IN) :: S1 + real(sp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + divsc%i=0 + RETURN + endif + localmaster=c_master + + + if(c_real_warning) call c_real_stop + ! call check(s1) + call ass(divsc) + sct=sc + ! if(old) then + call c_dacdi(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,divsc%i) + ! else + ! call newc_dacdi(s1%j,REAL(sc,kind=DP),divsc%j) + ! endif + c_master=localmaster + + END FUNCTION divsc + + + FUNCTION idivsc( S1, sc ) + implicit none + TYPE (c_taylor) idivsc + TYPE (c_taylor), INTENT (IN) :: S1 + integer, INTENT (IN) :: sc + integer localmaster + complex(dp) sct + IF(.NOT.C_STABLE_DA) then + idivsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(idivsc) + + sct=sc + + ! if(old) then + call c_dacdi(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,idivsc%i) + ! else + ! call newc_dacdi(s1%j,REAL(sc,kind=DP),idivsc%j) + ! endif + c_master=localmaster + + END FUNCTION idivsc + + + FUNCTION add( S1, S2 ) + implicit none + TYPE (c_taylor) add + TYPE (c_taylor), INTENT (IN) :: S1, S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + add%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + ! call check(s2) + call ass(add) + + + ! if(old) then + call c_daadd(s1%i,s2%i,add%i) + ! call c_dacop(c_temp%i,add%i) + ! call daadd(s1%i,s2%i,c_temp%i) + ! call c_dacop(c_temp%i,add%i) + ! else + ! call newdaadd(s1%j,s2%j,add%j) + ! endif + + c_master=localmaster + + END FUNCTION add + + FUNCTION addq( S1, S2 ) + implicit none + TYPE (c_quaternion) addq + TYPE (c_quaternion), INTENT (IN) :: S1, S2 + integer i,localmaster + localmaster=c_master + call c_ass_quaternion(addq) + do i=0,3 + addq%x(i)=s1%x(i)+s2%x(i) + enddo + c_master=localmaster + + END FUNCTION addq + + + FUNCTION absq2( S1 ) + implicit none + type(c_taylor) absq2 + TYPE (c_quaternion), INTENT (IN) :: S1 + integer i,localmaster + + IF(.NOT.C_STABLE_DA) then + absq2=0 + RETURN + endif + localmaster=c_master + call ass(absq2) + absq2=0 + do i=0,3 + absq2 = s1%x(i)**2+absq2 + enddo + c_master=localmaster + END FUNCTION absq2 + + FUNCTION absq( S1 ) + implicit none + type(c_taylor) absq + TYPE (c_quaternion), INTENT (IN) :: S1 + integer i,localmaster + + IF(.NOT.C_STABLE_DA) then + absq=0 + RETURN + endif + localmaster=c_master + call ass(absq) + absq=sqrt(abs_square(s1)) + c_master=localmaster + END FUNCTION absq + + FUNCTION mulq( S1, S2 ) + implicit none + TYPE (c_quaternion) mulq + TYPE (c_quaternion), INTENT (IN) :: S1, S2 + type(c_taylor) temp(0:3) + integer i,localmaster + + localmaster=c_master + call c_ass_quaternion(mulq) + + call alloc(temp) + + + temp(0)=s1%x(0)*s2%x(0)-s1%x(1)*s2%x(1)-s1%x(2)*s2%x(2)-s1%x(3)*s2%x(3) + + temp(1)= s1%x(2)*s2%x(3)-s1%x(3)*s2%x(2) + temp(2)= s1%x(3)*s2%x(1)-s1%x(1)*s2%x(3) + temp(3)= s1%x(1)*s2%x(2)-s1%x(2)*s2%x(1) + + do i=1,3 + temp(i)= temp(i) + s1%x(0)*s2%x(i)+ s1%x(i)*s2%x(0) + enddo + + do i=0,3 + mulq%x(i)=temp(i) + enddo + c_master=localmaster + call kill(temp) + END FUNCTION mulq + + FUNCTION mulcq( S1, S2 ) + implicit none + TYPE (c_quaternion) mulcq + complex(dp), INTENT (IN) :: S1 + TYPE (c_quaternion), INTENT (IN) :: S2 + integer i,localmaster + localmaster=c_master + call c_ass_quaternion(mulcq) + + do i=0,3 + mulcq%x(i)=s1*s2%x(i) + enddo + c_master=localmaster + END FUNCTION mulcq + + + + FUNCTION subq( S1, S2 ) + implicit none + TYPE (c_quaternion) subq + TYPE (c_quaternion), INTENT (IN) :: S1, S2 + integer i,localmaster + localmaster=c_master + call c_ass_quaternion(subq) + do i=0,3 + subq%x(i)=s1%x(i)-s2%x(i) + enddo + c_master=localmaster + + END FUNCTION subq + + FUNCTION c_invq( S1 ) + implicit none + TYPE (c_quaternion) c_invq + TYPE (c_quaternion), INTENT (IN) :: S1 + type(c_taylor) norm + type(c_taylor) temp(0:3) + integer i,localmaster + + IF(.NOT.C_STABLE_DA) then + c_invq%x(1)=0 + RETURN + endif + localmaster=c_master + call c_ass_quaternion(c_invq) + call alloc(temp) + call alloc(norm) + if(assume_c_quaternion_normalised) then + norm=1.0_dp +else + norm=s1%x(0)**2+s1%x(1)**2+s1%x(2)**2+s1%x(3)**2 +endif + temp(0)=s1%x(0) + do i=1,3 + temp(i)=-s1%x(i) + enddo + do i=0,3 + temp(i)=temp(i)/norm + enddo + + do i=0,3 + c_invq%x(i)=temp(i) + enddo + + c_master=localmaster + call kill(norm) + call kill(temp) + + + END FUNCTION c_invq + + + + FUNCTION POWq( S1, R2 ) + implicit none + TYPE (c_quaternion) POWq,qtemp + TYPE (c_quaternion), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: R2 + INTEGER I,R22 + integer localmaster + IF(.NOT.C_STABLE_DA) then + POWq=0.0_dp + + RETURN + endif + localmaster=c_master + call c_ass_quaternion(powq) + + do i=0,3 + call alloc(qtemp%x(i)) + enddo + qtemp=1.0_dp + + R22=IABS(R2) + DO I=1,R22 + qtemp=qtemp*s1 + ENDDO + IF(R2.LT.0) THEN + qtemp=c_invq(qtemp) + ENDIF + + do i=0,3 + powq%x(i)=qtemp%x(i) + enddo + do i=0,3 + call kill(qtemp%x(i)) + enddo + c_master=localmaster + END FUNCTION POWq + + FUNCTION POWql( S1, R2 ) + implicit none + TYPE (c_linear_map) POWql,qtemp + TYPE (c_linear_map), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: R2 + INTEGER I,R22 + integer localmaster + + + + qtemp=0 +! qtemp%q=0 +! qtemp%q(0,0)=1.0_dp + + R22=IABS(R2) + DO I=1,R22 + qtemp=qtemp*s1 + ENDDO + IF(R2.LT.0) THEN + qtemp=inv_c_linear_map(qtemp) + ENDIF + powql=qtemp + + + + END FUNCTION POWql + + SUBROUTINE EQUALq(S2,S1) + implicit none + integer ipause, mypauses + type (c_quaternion),INTENT(inOUT)::S2 + type (c_quaternion),INTENT(IN)::S1 + integer i + + do i=0,3 + s2%x(i)=s1%x(i) + enddo + + end SUBROUTINE EQUALq + + SUBROUTINE EQUALq_c_r(S2,S1) + implicit none + integer ipause, mypauses + type (c_quaternion),INTENT(inOUT)::S2 + type (quaternion),INTENT(IN)::S1 + integer i + + + do i=0,3 + s2%x(i)=s1%x(i) + enddo + + + end SUBROUTINE EQUALq_c_r + + SUBROUTINE EQUALq_r_c(S2,S1) + implicit none + integer ipause, mypauses + type (quaternion),INTENT(inOUT)::S2 + type (c_quaternion),INTENT(IN)::S1 + integer i + + + do i=0,3 + + s2%x(i)=s1%x(i) + enddo + + end SUBROUTINE EQUALq_r_c + + SUBROUTINE EQUALql_i(S2,S1) + implicit none + integer ipause, mypauses + type (c_linear_map),INTENT(inOUT)::S2 + integer,INTENT(IN)::S1 + integer i + + S2%q(0:3,0:6)=0 + s2%mat=0.0_dp + do i=1,6 + s2%mat(i,i)=1.0_dp + enddo + S2%q(s1,0)= 1.0_dp + + end SUBROUTINE EQUALql_i + + SUBROUTINE EQUALql_r(S2,S1) + implicit none + integer ipause, mypauses + type (c_linear_map),INTENT(inOUT)::S2 + real(dp) ,INTENT(IN)::S1 + integer i,j + + S2%q(0:3,0:6)=0 + + S2%q(0,0)= s1 + + end SUBROUTINE EQUALql_r + + function qua_ql(S2) + implicit none + integer ipause, mypauses + type (c_linear_map) qua_ql + type (c_linear_map),INTENT(inOUT)::S2 + + qua_ql=0 + qua_ql%q = s2%q + + + end function qua_ql + + + SUBROUTINE EQUAL_c_l_f(S2,S1) + implicit none + type(c_lattice_function), intent(out) :: s2 + logical, intent(in) :: s1 + s2%e=0 + s2%k=0 + s2%h=0 + s2%b=0 + s2%s=0 + s2%spin=0 + s2%phase=0 + s2%damping=0 + s2%f=>null() + s2%t=>null() + s2%symplectic=s1 + S2%FIX=0 + s2%sigmas=0 + end SUBROUTINE EQUAL_c_l_f + + + +!1BMAD$linear_lattice_functions.tex + SUBROUTINE compute_lattice_functions_2(m,f) + implicit none + type(c_lattice_function) f + type(c_linear_map) ml + type(c_damap) m + ml=m + + call compute_lattice_functions_1(ml,f) + + end SUBROUTINE compute_lattice_functions_2 + + SUBROUTINE compute_lattice_functions_1(m,f) + implicit none + type(c_lattice_function) f + type(c_linear_map) m + type(c_linear_map) mi + type(c_linear_map) q + integer i,j +! This routines specializes in linear maps for speed +! It produces bona fide lattice functions with radiation +! as well as with a coasting beam (no cavity) + if(f%symplectic) then + mi=inv_c_linear_map_symplectic(m) + else + mi=m**(-1) + endif + + + f%h=0;f%b=0;f%k=0;f%e=0;f%s=0; + + !!!! Computing the de Moivre Lattice Functions !!!! + !!!! equivalent to Ripken ones + +!!!! Coefficients of vector field matrices B**2=-H + do i = 1,3 + f%B(i,:,:)=matmul(matmul(m%mat,jp_mat(i,:,:)),mi%mat) + enddo + +!!!! Coefficients of invariants + do i = 1,3 + f%K(i,:,:)= -matmul(jt_mat,f%B(i,:,:)) + enddo +!!!! Coefficient of moments as functions of emittances + do i = 1,3 + f%E(i,:,:)= -matmul(f%B(i,:,:),jt_mat) + enddo +!!!! Dispersive quantities containing zeta and eta for example +!!!! as well as \gamma C of Teng-Edwards + do i = 1,3 + f%H(i,:,:)=matmul(matmul(m%mat,ip_mat(i,:,:)),mi%mat) + enddo + +!!!! Computing the n vector using quaternions + do i = 1,3 + q=i +!!!! Formula is identical to orbital! + q=m*q*mi + do j=1,3 + f%S(i,j,0:6)=q%q(j,0:6) + enddo + enddo + + end SUBROUTINE compute_lattice_functions_1 +!2BMAD + +! SUBROUTINE d_compute_lattice_functions(a,f,a_l,a_li) +! implicit none +! type(d_lattice_function) f +! type(c_linear_map) m +! type(c_linear_map) mi +!! type(c_linear_map) q +! type(c_damap),intent(in) :: a +! type(c_linear_map),optional, intent(inout):: a_l,a_li +! integer i,j +! +! m=a + + ! if(do_damping.and.use_radiation_inverse) then + ! mi=m**(-1) + ! else + ! mi=inv_c_linear_map_symplectic(m) + ! endif + ! + + ! if(present(a_l)) a_l =m + ! if(present(a_li)) a_li=mi + ! + ! f%e=0 + ! f%h=0 + ! f%spin_lat=0 + + !!!! computing the de Moivre Lattice Functions !!!! + !!!! equivalent to Ripken ones + +!!!! Coefficient of vector field matrices B**2=-H + ! do i = 1,3 + ! f%B(i,:,:)=matmul(matmul(m%mat,jp_mat(i,:,:)),mi%mat) + ! enddo + +!!!! coefficient of invariants + ! do i = 1,3 + ! f%K(i,:,:)= -matmul(jt_mat,f%B(i,:,:)) + ! enddo +!!!! coefficient of moments + + ! do i = 1,3 + ! f%E(i,:,:)=matmul(matmul(m%mat,jp_mat(i,:,:)),mi%mat) + !! enddo + ! do i = 1,3 + ! f%E(i,:,:)= -matmul(f%E(i,:,:),jt_mat) + ! enddo + ! +!!!!! Dispersive quantities containing zeta and eta for example + ! do i = 1,3 + ! f%H(i,:,:)=matmul(matmul(m%mat,ip_mat(i,:,:)),mi%mat) + ! enddo + +!!!! computing the n vector using quaternion + ! if(do_spin) then + ! do i = 1,3 + ! q=i + ! q=m*q*mi + ! do j=1,3 + ! f%Spin_lat(i,j,0:6)=q%q(j,0:6) + ! enddo + ! enddo + ! else + ! f%Spin_lat=0 + ! f%spin=0 + ! endif + + + ! end SUBROUTINE d_compute_lattice_functions + + + SUBROUTINE EQUALql_c_spin(S2,S1) + implicit none + integer ipause, mypauses + type (c_linear_map),INTENT(inOUT)::S2 + type (c_spinor),INTENT(IN)::S1 + type (c_quaternion) q + call alloc(q) + q=s1 + s2=q + call kill(q) + end SUBROUTINE EQUALql_c_spin + + SUBROUTINE EQUALql_q(S2,S1) + implicit none + integer ipause, mypauses + type (c_linear_map),INTENT(inOUT)::S2 + type (c_quaternion),INTENT(IN)::S1 + integer i,j + + S2%q=0 + do i=0,3 + do j=0,min(6,nd2) + s2%q(i,j)=s1%x(i).index.j + enddo + enddo + + end SUBROUTINE EQUALql_q + + SUBROUTINE EQUALql_cmap(S2,S1) + implicit none + integer ipause, mypauses + type (c_linear_map),INTENT(inOUT)::S2 + type (c_damap),INTENT(IN)::S1 + + s2%mat=s1 + s2=s1%q + + end SUBROUTINE EQUALql_cmap + + SUBROUTINE EQUALcmap_ql(S1,S2) + implicit none + integer ipause, mypauses + type (c_linear_map),INTENT(in)::S2 + type (c_damap),INTENT(INOUT)::S1 + + s1=s2%mat + s1%q=s2 + + end SUBROUTINE EQUALcmap_ql + + + SUBROUTINE EQUALq_ql(S1,S2) + implicit none + integer ipause, mypauses + type (c_linear_map),INTENT(in)::S2 + type (c_quaternion),INTENT(INout)::S1 + integer i,j + + s1=0.0_dp + + do i=0,3 + s1%x(i) = s2%q(i,0) +s1%x(i) + do j=1,min(6,nd2) + s1%x(i)= s2%q(i,j)*dz_c(j)+s1%x(i) + enddo + enddo + + end SUBROUTINE EQUALq_ql + + + SUBROUTINE EQUAL_c_quaternion_complex_quaternion(S1,S2) + implicit none + type (complex_quaternion),INTENT(in)::S2 + type (c_quaternion),INTENT(INout)::S1 + integer i + + + + do i=0,3 + s1%x(i) = s2%x(i) + enddo + + end SUBROUTINE EQUAL_c_quaternion_complex_quaternion + + SUBROUTINE EQUAL_complex_quaternion_c_quaternion(S1,S2) + implicit none + type (c_quaternion),INTENT(in)::S2 + type (complex_quaternion),INTENT(INout)::S1 + integer i + + + + do i=0,3 + s1%x(i) = s2%x(i) + enddo + + + end SUBROUTINE EQUAL_complex_quaternion_c_quaternion + + + + SUBROUTINE EQUALql_ql(S1,S2) + implicit none + type (c_linear_map),INTENT(in)::S2 + type (c_linear_map),INTENT(INout)::S1 + + + s1%mat=s2%mat + S1%q(0:3,0:6)=S2%q(0:3,0:6) + + + end SUBROUTINE EQUALql_ql + + SUBROUTINE print_ql(S2,imaginary,quaternion_only,mf) + implicit none + type (c_linear_map),INTENT(inOUT)::S2 + integer, optional :: mf + logical, optional :: imaginary,quaternion_only + integer i,mff + logical q_only + + q_only=.false. + if(present(quaternion_only)) q_only=quaternion_only + + mff=6 + if(present(mf)) mff=mf + +if(.not.q_only) then + +write(mff,*) " Orbital Matrix " +if(present(imaginary) ) then + + if(imaginary) then + write(mff,*) "Real part " + do i=1,6 + + write(mff,'(6(1x,G21.14))') real(s2%mat(i,1:min(6,nd2))) + + enddo +endif + +if(imaginary) then +write(mff,*) "Imaginary part " + do i=1,6 + + write(mff,'(6(1x,G21.14))') aimag(s2%mat(i,1:min(6,nd2))) + + enddo +endif + +else + do i=1,6 + + write(mff,'(12(1x,G21.14))') (s2%mat(i,1:min(6,nd2))) + + enddo +endif +endif + +write(mff,*) " Quaternion Matrix " +if(present(imaginary) )write(mff,*) "Real part " + + do i=0,3 + + write(mff,'(7(1x,G21.14))') real(s2%q(i,0:min(6,nd2))) + + enddo + +if(present(imaginary) ) then +if(imaginary) then +write(mff,*) "Imaginary part " + + do i=0,3 + + write(mff,'(7(1x,G21.14))') aimag(s2%q(i,0:min(6,nd2))) + + enddo +endif +endif + + end SUBROUTINE print_ql + + function inv_symplectic66(S1) + implicit none + integer ipause, mypauses + real(dp) inv_symplectic66(6,6) + real(dp),intent(in) :: s1(6,6) + + inv_symplectic66=-matmul(matmul(sj,transpose(s1)),sj) + + end function inv_symplectic66 + + function inv_c_linear_map(S1) + implicit none + integer ipause, mypauses + type(c_linear_map) inv_c_linear_map + type(c_linear_map),intent (IN) :: s1 + integer i + call c_matinv(s1%mat,inv_c_linear_map%mat,6,6,i) + inv_c_linear_map%q(0,0:6)=s1%q(0,0:6) + inv_c_linear_map%q(1:3,0:6)=-s1%q(1:3,0:6) + + inv_c_linear_map=inv_c_linear_map*inv_c_linear_map%mat + + end function inv_c_linear_map + + function inv_c_linear_map_symplectic(S1) + implicit none + integer ipause, mypauses + type(c_linear_map) inv_c_linear_map_symplectic + type(c_linear_map),intent (IN) :: s1 + real(dp) matr(6,6) + integer i + matr=s1%mat + inv_c_linear_map_symplectic%mat= inv_symplectic66(matr) + inv_c_linear_map_symplectic%q(0,0:6)=s1%q(0,0:6) + inv_c_linear_map_symplectic%q(1:3,0:6)=-s1%q(1:3,0:6) + + inv_c_linear_map_symplectic=inv_c_linear_map_symplectic*inv_c_linear_map_symplectic%mat + + end function inv_c_linear_map_symplectic + + function mulqdiv(S1,s2) + implicit none + integer ipause, mypauses + type(c_linear_map) mulqdiv + type(c_linear_map),intent (IN) :: s1 ,s2 + + mulqdiv=s1*inv_c_linear_map(s2) + + end function mulqdiv + + + function mul_ql_m(S1,S2) + implicit none + integer ipause, mypauses + type (c_linear_map) mul_ql_m + type (c_linear_map),INTENT(IN)::S1 + real(dp), INTENT(IN)::S2(6,6) + integer i,j + + mul_ql_m=s1 + + ! mul_ql_m%q(0:3,0)=S1%q(0:3,0) + + do i=0,3 + mul_ql_m%q(i,1:6)= matmul(s1%q(i,1:6),s2) + enddo + + end function mul_ql_m + + + function mul_ql_cm(S1,S2) + implicit none + integer ipause, mypauses + type (c_linear_map) mul_ql_cm + type (c_linear_map),INTENT(IN)::S1 + complex(dp), INTENT(IN)::S2(6,6) + integer i,j + + mul_ql_cm=s1 + + ! mul_ql_m%q(0:3,0)=S1%q(0:3,0) + + do i=0,3 + mul_ql_cm%q(i,1:6)= matmul(s1%q(i,1:6),s2) + enddo + + end function mul_ql_cm + + function addql(S1,S2) + implicit none + integer ipause, mypauses + type (c_linear_map) addql + type (c_linear_map),INTENT(IN)::S1 + type (c_linear_map),INTENT(IN)::S2 + integer i,j + + addql%q=s1%q+s2%q + addql%mat=s1%mat+s2%mat + + + end function addql + + + function mulql(S1,S2) + implicit none + integer ipause, mypauses + type (c_linear_map) mulql + type (c_linear_map),INTENT(IN)::S1 + type (c_linear_map),INTENT(IN)::S2 + complex(dp) temp(0:3),q0(0:3),p0(0:3),p1(0:3,6),q1(0:3,6) + integer i,j + type(c_linear_map) qt + + + qt=s1 + qt=qt*s2%mat + + mulql%q=0 + mulql%mat=matmul(s1%mat,s2%mat) + + q0(0:3)=qt%q(0:3,0) + p0(0:3)=s2%q(0:3,0) + q1(0:3,1:6)=qt%q(0:3,1:6) + p1(0:3,1:6)=s2%q(0:3,1:6) + + temp(0)= q0(0)*p0(0)-q0(1)*p0(1)-q0(2)*p0(2)-q0(3)*p0(3) + temp(1)= q0(2)*p0(3)-q0(3)*p0(2) + temp(2)= q0(3)*p0(1)-q0(1)*p0(3) + temp(3)= q0(1)*p0(2)-q0(2)*p0(1) + + do i=1,3 + temp(i)= temp(i) + q0(0)*p0(i)+ q0(i)*p0(0) + enddo + mulql%q(0:3,0)=temp(0:3) + +do j=1,6 + mulql%q(0,j)= q0(0)*p1(0,j)-q0(1)*p1(1,j)-q0(2)*p1(2,j)-q0(3)*p1(3,j)+mulql%q(0,j) + mulql%q(1,j)= q0(2)*p1(3,j)-q0(3)*p1(2,j)+mulql%q(1,j) + mulql%q(2,j)= q0(3)*p1(1,j)-q0(1)*p1(3,j)+mulql%q(2,j) + mulql%q(3,j)= q0(1)*p1(2,j)-q0(2)*p1(1,j)+mulql%q(3,j) + + do i=1,3 + mulql%q(i,j)= mulql%q(i,j) + q0(0)*p1(i,j)+ q0(i)*p1(0,j) + enddo + + mulql%q(0,j)= p0(0)*q1(0,j)-p0(1)*q1(1,j)-p0(2)*q1(2,j)-p0(3)*q1(3,j)+mulql%q(0,j) + mulql%q(1,j)= -p0(2)*q1(3,j)+p0(3)*q1(2,j)+mulql%q(1,j) + mulql%q(2,j)= -p0(3)*q1(1,j)+p0(1)*q1(3,j)+mulql%q(2,j) + mulql%q(3,j)= -p0(1)*q1(2,j)+p0(2)*q1(1,j)+mulql%q(3,j) + + do i=1,3 + mulql%q(i,j)= mulql%q(i,j) + p0(0)*q1(i,j)+ p0(i)*q1(0,j) + enddo + +enddo + + end function mulql + + + + function subql(S1,S2) + implicit none + integer ipause, mypauses + type (c_linear_map) subql + type (c_linear_map),INTENT(IN)::S1 + type (c_linear_map),INTENT(IN)::S2 + integer i,j + + subql%q=s1%q-s2%q + subql%mat=s1%mat-s2%mat + + + end function subql + + + + SUBROUTINE EQUALq_c_8(S2,S1) + implicit none + integer ipause, mypauses + type (c_quaternion),INTENT(inOUT)::S2 + type (quaternion_8),INTENT(IN)::S1 + integer i + type(complextaylor) ct + call alloc(ct) + do i=0,3 + ct=s1%x(i)%t + s2%x(i)=ct + enddo + call kill(ct) + + end SUBROUTINE EQUALq_c_8 + + SUBROUTINE EQUALq_8_c(S2,S1) + implicit none + integer ipause, mypauses + type (quaternion_8),INTENT(inOUT)::S2 + type (c_quaternion),INTENT(IN)::S1 + integer i + type(complextaylor) ct + call alloc(ct) + do i=0,3 + ct=s1%x(i) + s2%x(i)=morph(ct) !morph(s1%x(i)) + enddo + call kill(ct) + end SUBROUTINE EQUALq_8_c + + SUBROUTINE EQUALq_r(S2,S1) + implicit none + integer ipause, mypauses + type (c_quaternion),INTENT(inOUT)::S2 + real(dp),INTENT(IN)::S1 + integer i + + do i=0,3 + s2%x(i)=0.0_dp + enddo + s2%x(0)=s1 + + end SUBROUTINE EQUALq_r + + + SUBROUTINE EQUALq_i(S2,S1) + implicit none + integer ipause, mypauses + type (c_quaternion),INTENT(inOUT)::S2 + integer,INTENT(IN)::S1 + integer i + + do i=0,3 + s2%x(i)=0.0_dp + enddo + s2%x(s1)=1 + + end SUBROUTINE EQUALq_i + + subroutine matrix_to_quaternion_in_c_damap(p) +! makequaternion + implicit none + TYPE(c_damap), INTENT(INOUT) :: p + TYPE(c_damap) as,m + type(c_spinor) n0 + type(c_taylor) tune,c,s,egspin(3) + + real(dp) alpha,alpha0,nr(3) + integer i,j,is + + + call alloc(n0) + call alloc(egspin) + call alloc(as,m) + call alloc(tune) + call alloc(c,s) + + + as=1 + call c_find_n0(p%s,n0,linear=my_false) +do i=1,3 +nr(i)=abs(n0%v(i)) +enddo +is=1 +if(nr(2)>nr(1))is=2 +if(nr(3)>nr(is)) is=3 + if(real(n0%v(is).sub.'0')<0) then + n0=-n0 + endif + call c_find_as(n0,AS%s) + + as%s=as%s**(-1)*p%s*as%s + + + egspin(3)=as%s%s(1,1)-i_*as%s%s(1,3) + egspin(2)=1.0_dp + egspin(1)=as%s%s(1,1)+i_*as%s%s(1,3) + + tune=aimag(log(egspin(2+spin_def_tune))/2.0_dp) + alpha=tune + if(alpha<0) tune=tune+twopi + alpha0=2.0_dp*(tune.sub.'0')/twopi + c=cos(tune) + s=sin(tune) + alpha=tune + +!write(6,*) alpha + + p%q%x(0)=c + p%q%x(1)= 0.0_dp + p%q%x(2)= s + p%q%x(3)= 0.0_dp + ! + m=1 +m%q=p%q + + call c_normal_spin_linear_quaternion(m,m,AS,alpha) + egspin(3)=cos(alpha)-i_*sin(alpha) + egspin(2)=1.0_dp + egspin(1)=cos(alpha)+i_*sin(alpha) +!write(6,*) alpha/twopi + alpha=aimag(log(egspin(2+spin_def_tune)))/twopi + +!write(6,*)alpha0,alpha + alpha=alpha/alpha0 + p%q%x(0)=c + p%q%x(1)= s*n0%v(1) + p%q%x(2)= s*n0%v(2) + p%q%x(3)= s*n0%v(3) + + + if(alpha<0) p%q=-p%q + + + call kill(c,s) + call kill(tune) + call kill(n0) + call kill(as,m) + call kill(egspin) + + end subroutine matrix_to_quaternion_in_c_damap + + + + subroutine quaternion_to_matrix_in_c_damap(p) + implicit none + TYPE(c_damap), INTENT(INOUT) :: p + type(c_quaternion) s,sf + integer i,j + + call alloc(s) + call alloc(sf) + + do i=1,3 + s=0.0_dp + s%x(i)=1.0_dp + sf=p%q*s*p%q**(-1) + do j=1,3 + p%s%s(j,i)=sf%x(j) + enddo + enddo + call kill(s) + call kill(sf) + + end subroutine quaternion_to_matrix_in_c_damap + + + subroutine quaternion_to_spinmatrix(q,p) + implicit none + TYPE(c_quaternion), INTENT(IN) :: q + TYPE(c_spinmatrix), INTENT(INOUT) :: p + type(c_quaternion) s,sf + integer i,j + + call alloc(s) + call alloc(sf) + + do i=1,3 + s=0.0_dp + s%x(i)=1.0_dp + sf=q*s*q**(-1) + do j=1,3 + p%s(j,i)=sf%x(j) + enddo + enddo + call kill(s) + call kill(sf) + + end subroutine quaternion_to_spinmatrix + + + subroutine makeso3_equal(p,q) + implicit none + TYPE(c_quaternion), INTENT(IN) :: q + TYPE(c_spinmatrix), INTENT(INOUT) :: p + call quaternion_to_spinmatrix(q,p) + end subroutine makeso3_equal + + + subroutine c_linear_map_to_matrix (q_lin,m) + implicit none + TYPE(c_spinmatrix), INTENT(INOUT) :: m + TYPE(c_linear_map), INTENT(IN) :: q_lin + type(c_quaternion) s,sf + type(c_damap) p + integer i,j + + call alloc(s) + call alloc(sf) + call alloc(p) + p%q=q_lin + do i=1,3 + s=0.0_dp + s%x(i)=1.0_dp + sf=p%q*s*p%q**(-1) + do j=1,3 + m%s(j,i)=sf%x(j) + enddo + enddo + call kill(s) + call kill(sf) + call kill(p) + + end subroutine c_linear_map_to_matrix + +! subroutine quaternion_to_matrix(q_lin,m) +! implicit none +! real(dp) m(3,3) +! TYPE(c_quaternion), INTENT(IN) :: q_lin +! type(c_quaternion) s,sf +! integer i,j + +! call alloc(s) +! call alloc(sf) +! +! do i=1,3 +! s=0.0_dp +! s%x(i)=1.0_dp +! sf=q_lin*s*q_lin**(-1) +! do j=1,3 +! m(j,i)=sf%x(j) +! enddo +! enddo +! +! call kill(s) +! call kill(sf) + +! end subroutine quaternion_to_matrix + + + FUNCTION cdaddsc( S1, sc ) + implicit none + TYPE (c_taylor) cdaddsc + TYPE (c_taylor), INTENT (IN) :: S1 + complex(dp), INTENT (IN) :: sc + integer localmaster + IF(.NOT.C_STABLE_DA) then + cdaddsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(cdaddsc) + + ! if(old) then + call c_dacad(s1%i,sc,c_temp%i) + call c_dacop(c_temp%i,cdaddsc%i) + ! else + ! call newc_dacad(s1%j,sc,daddsc%j) + ! endif + c_master=localmaster + + END FUNCTION cdaddsc + + FUNCTION daddsca( S1, sc ) + implicit none + TYPE (c_taylor) daddsca + TYPE (c_taylor), INTENT (IN) :: S1 + real(dp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + daddsca%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(daddsca) + sct=sc + ! if(old) then + call c_dacad(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,daddsca%i) + ! else + ! call newc_dacad(s1%j,sc,daddsc%j) + ! endif + c_master=localmaster + + END FUNCTION daddsca + + + FUNCTION addsc( S1, sc ) + implicit none + TYPE (c_taylor) addsc + TYPE (c_taylor), INTENT (IN) :: S1 + real(sp), INTENT (IN) :: sc + integer localmaster + complex(dp) sct + IF(.NOT.C_STABLE_DA) then + addsc%i=0 + RETURN + endif + localmaster=c_master + + sct=sc + if(c_real_warning) call c_real_stop + ! call check(s1) + call ass(addsc) + + + ! if(old) then + call c_dacad(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,addsc%i) + ! else + ! call newc_dacad(s1%j,REAL(sc,kind=DP),addsc%j) + ! endif + c_master=localmaster + + END FUNCTION addsc + + FUNCTION iaddsc( S1, sc ) + implicit none + TYPE (c_taylor) iaddsc + TYPE (c_taylor), INTENT (IN) :: S1 + integer, INTENT (IN) :: sc + integer localmaster + + complex(dp) sct + IF(.NOT.C_STABLE_DA) then + iaddsc%i=0 + RETURN + endif + localmaster=c_master + + sct=sc + ! call check(s1) + call ass(iaddsc) + + ! if(old) then + call c_dacad(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,iaddsc%i) + ! else + ! call newc_dacad(s1%j,REAL(sc,kind=DP),iaddsc%j) + ! endif + c_master=localmaster + + END FUNCTION iaddsc + + FUNCTION cdscadd( sc,S1) + implicit none + TYPE (c_taylor) cdscadd + TYPE (c_taylor), INTENT (IN) :: S1 + complex(dp), INTENT (IN) :: sc + + integer localmaster + IF(.NOT.C_STABLE_DA) then + cdscadd%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(cdscadd) + + ! if(old) then + + call c_dacad(s1%i,sc,c_temp%i) + call c_dacop(c_temp%i,cdscadd%i) + ! else + ! call newc_dacad(s1%j,sc,dscadd%j) + ! endif + c_master=localmaster + + END FUNCTION cdscadd + + FUNCTION dscadd( sc,S1) + implicit none + TYPE (c_taylor) dscadd + TYPE (c_taylor), INTENT (IN) :: S1 + real(dp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + dscadd%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(dscadd) + + ! if(old) then + sct=sc + call c_dacad(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,dscadd%i) + ! else + ! call newc_dacad(s1%j,sc,dscadd%j) + ! endif + c_master=localmaster + + END FUNCTION dscadd + + FUNCTION scadd( sc,S1) + implicit none + TYPE (c_taylor) scadd + TYPE (c_taylor), INTENT (IN) :: S1 + real(sp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + scadd%i=0 + RETURN + endif + localmaster=c_master + + sct=sc + if(c_real_warning) call c_real_stop + ! call check(s1) + call ass(scadd) + + ! if(old) then + call c_dacad(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,scadd%i) + ! else + ! call newc_dacad(s1%j,REAL(sc,kind=DP),scadd%j) + ! endif + + c_master=localmaster + + END FUNCTION scadd + + FUNCTION iscadd( sc,S1) + implicit none + TYPE (c_taylor) iscadd + TYPE (c_taylor), INTENT (IN) :: S1 + integer, INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + iscadd%i=0 + RETURN + endif + localmaster=c_master + + sct=sc + ! call check(s1) + call ass(iscadd) + + + ! if(old) then + call c_dacad(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,iscadd%i) + ! else + ! call newc_dacad(s1%j,REAL(sc,kind=DP),iscadd%j) + ! endif + c_master=localmaster + + END FUNCTION iscadd + + FUNCTION subs( S1, S2 ) + implicit none + TYPE (c_taylor) subs + TYPE (c_taylor), INTENT (IN) :: S1, S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + subs%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + ! call check(s2) + call ass(subs) + + + + ! if(old) then + call c_dasub(s1%i,s2%i,c_temp%i) + call c_dacop(c_temp%i,subs%i) + ! else + ! call newdasub(s1%j,s2%j,subs%j) + ! endif + c_master=localmaster + + END FUNCTION subs + + FUNCTION cdsubsc( S1, sc ) + implicit none + TYPE (c_taylor) cdsubsc + TYPE (c_taylor), INTENT (IN) :: S1 + complex(dp), INTENT (IN) :: sc + integer localmaster + IF(.NOT.C_STABLE_DA) then + cdsubsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(cdsubsc) + ! if(old) then + call c_dacsu(s1%i,sc,c_temp%i) + call c_dacop(c_temp%i,cdsubsc%i) + ! else + ! call newdacsu(s1%j,sc,dsubsc%j) + ! endif + + c_master=localmaster + + + END FUNCTION cdsubsc + + FUNCTION dsubsc( S1, sc ) + implicit none + TYPE (c_taylor) dsubsc + TYPE (c_taylor), INTENT (IN) :: S1 + real(dp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + dsubsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(dsubsc) + sct=sc + ! if(old) then + call c_dacsu(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,dsubsc%i) + ! else + ! call newdacsu(s1%j,sc,dsubsc%j) + ! endif + + c_master=localmaster + + + END FUNCTION dsubsc + + + FUNCTION subsc( S1, sc ) + implicit none + TYPE (c_taylor) subsc + TYPE (c_taylor), INTENT (IN) :: S1 + real(sp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + subsc%i=0 + RETURN + endif + localmaster=c_master + + + if(c_real_warning) call c_real_stop + ! call check(s1) + call ass(subsc) + sct=sc + ! if(old) then + call c_dacsu(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,subsc%i) + ! else + ! call newdacsu(s1%j,REAL(sc,kind=DP),subsc%j) + ! endif + c_master=localmaster + + END FUNCTION subsc + + FUNCTION isubsc( S1, sc ) + implicit none + TYPE (c_taylor) isubsc + TYPE (c_taylor), INTENT (IN) :: S1 + integer, INTENT (IN) :: sc + integer localmaster + complex(dp) x + IF(.NOT.C_STABLE_DA) then + isubsc%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(isubsc) + x=sc + ! if(old) then + call c_dacsu(s1%i,x,c_temp%i) + call c_dacop(c_temp%i,isubsc%i) + ! else + ! call newdacsu(s1%j,REAL(sc,kind=DP),isubsc%j) + ! endif + c_master=localmaster + + END FUNCTION isubsc + + FUNCTION cdscsub( sc,S1) + implicit none + TYPE (c_taylor) cdscsub + TYPE (c_taylor), INTENT (IN) :: S1 + complex(dp), INTENT (IN) :: sc + integer localmaster + IF(.NOT.C_STABLE_DA) then + cdscsub%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(cdscsub) + + ! if(old) then + call c_dasuc(s1%i,sc,c_temp%i) + call c_dacop(c_temp%i,cdscsub%i) + ! else + ! call newdasuc(s1%j,sc,dscsub%j) + ! endif + c_master=localmaster + + END FUNCTION cdscsub + + FUNCTION dscsub( sc,S1) + implicit none + TYPE (c_taylor) dscsub + TYPE (c_taylor), INTENT (IN) :: S1 + real(dp), INTENT (IN) :: sc + complex(dp) sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + dscsub%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(dscsub) + sct=sc + ! if(old) then + call c_dasuc(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,dscsub%i) + ! else + ! call newdasuc(s1%j,sc,dscsub%j) + ! endif + c_master=localmaster + + END FUNCTION dscsub + + FUNCTION scsub( sc,S1) + implicit none + TYPE (c_taylor) scsub + TYPE (c_taylor), INTENT (IN) :: S1 + real(sp), INTENT (IN) :: sc + complex(dp)sct + integer localmaster + IF(.NOT.C_STABLE_DA) then + scsub%i=0 + RETURN + endif + + localmaster=c_master + + + if(c_real_warning) call c_real_stop + ! call check(s1) + call ass(scsub) + sct=sc + ! if(old) then + call c_dasuc(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,scsub%i) + ! else + ! call newdasuc(s1%j,REAL(sc,kind=DP),scsub%j) + ! endif + c_master=localmaster + + END FUNCTION scsub + + FUNCTION iscsub( sc,S1) + implicit none + TYPE (c_taylor) iscsub + TYPE (c_taylor), INTENT (IN) :: S1 + integer, INTENT (IN) :: sc + integer localmaster + complex(dp) sct + IF(.NOT.C_STABLE_DA) then + iscsub%i=0 + RETURN + endif + localmaster=c_master + + + ! call check(s1) + call ass(iscsub) + sct=sc + ! if(old) then + call c_dasuc(s1%i,sct,c_temp%i) + call c_dacop(c_temp%i,iscsub%i) + + c_master=localmaster + + END FUNCTION iscsub + + ! These are new general TPSA-Routines + + FUNCTION varf( S1, S2 ) + implicit none + TYPE (c_taylor) varf + complex(dp), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + varf%i=0 + RETURN + endif + localmaster=c_master + + + call ass(varf) + + varf=S1 + ((1.0_dp,0.0_dp).cmono.S2) + + c_master=localmaster + + END FUNCTION varf + + FUNCTION varf001( S1, S2 ) + implicit none + TYPE (c_taylor) varf001 + complex(dp), INTENT (IN) :: S1(2) + integer , INTENT (IN) :: S2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + varf001%i=0 + RETURN + endif + localmaster=c_master + + + call ass(varf001) + + varf001=S1(1) + (s1(2).cmono.S2) + + c_master=localmaster + + END FUNCTION varf001 + + + + SUBROUTINE shift000(S1,S2,s) + implicit none + INTEGER,INTENT(IN)::s + type (c_taylor),INTENT(IN)::S1 + type (c_taylor),INTENT(inout)::S2 + IF(.NOT.C_STABLE_DA) RETURN + + ! if(old) then + if(s2%i==0) call c_crap1("shift000 1" ) !call etall1(s2%i) + CALL c_DAshift(s1%i,s2%i,s) + ! else + ! if(.NOT. ASSOCIATED(s2%j%r))call c_crap1("shift000 2" ) ! call newetall(s2%j,1) + ! + ! CALL NEWDAshift(s1%j,s2%j,s) + ! endif + ! + END SUBROUTINE shift000 + + + SUBROUTINE c_pek000(S1,J,R1) + implicit none + INTEGER,INTENT(IN),dimension(:)::j + complex(dp),INTENT(inOUT)::R1 + type (c_taylor),INTENT(IN)::S1 + ! integer k + IF(.NOT.C_STABLE_DA) RETURN + ! if(old) then + if(s1%i==0) call c_crap1("c_pek000 1" ) !call etall1(s1%i) + ! k=s1%i +! write(6,*) r1,k + + CALL c_DApek(s1%i,j,r1) + ! else + ! if(.NOT. ASSOCIATED(s1%j%r)) call c_crap1("c_pek000 2" ) ! newetall(s1%j,1) + ! + ! CALL newDApek(s1%j,j,r1) + ! endif + ! + END SUBROUTINE c_pek000 + + SUBROUTINE c_pok000(S1,J,R1) + implicit none + INTEGER,INTENT(in),dimension(:)::j + complex(dp),INTENT(in)::R1 + type (c_taylor),INTENT(inout)::S1 + IF(.NOT.C_STABLE_DA) RETURN + + if(check_j(j)/=0) return + ! if(old) then + if(s1%i==0) call c_crap1("c_pok000 1" ) ! call etall1(s1%i) + CALL c_DApok(s1%i,j,r1) + ! else + ! if(.NOT. ASSOCIATED(s1%j%r)) call c_crap1("c_pok000 2" ) ! call newetall(s1%j,1) + ! + ! CALL newDApok(s1%j,j,r1) + ! endif + ! + END SUBROUTINE c_pok000 + + SUBROUTINE c_TAYLOR_ran(S1,r1,R2,f) + implicit none + real(dp),INTENT(in)::R1 + real(dp),INTENT(inout)::R2 + type (c_taylor),INTENT(inout)::S1 + logical,optional :: f(:) + integer j,i + integer, allocatable:: je(:) + complex(dp) v + type (c_taylor) t + IF(.NOT.C_STABLE_DA) RETURN + + ! + ! THIS SUBROUTINE FILLS THE DA VECTOR A WITH RANDOM ENTRIES. + ! FOR R1 > 0, THE VECTOR IS FILLED WITH REALS, + ! FOR R1 < 0, THE VECTOR IS FILLED WITH SINGLE DIGIT INTEGERS + ! ABS(R1) IS THE FILLING FACTOR + ! if(old) then + if(s1%i==0) call c_crap1("c_TAYLOR_ran 1" ) ! call etall1(s1%i) + call c_daran(s1%i,r1,R2) + + if(present(f)) then + call alloc(t) + allocate(je(nv)) + j=1 + do while(.true.) + call c_cycle(s1,j,v ,je); if(j==0) exit; + do i=1,nv + if(je(i)/=0.and.(.not.f(i))) then + v=0.0_dp + exit + endif + enddo + t=t+(v.cmono.je) + enddo + s1=t + deallocate(je) + call kill(t) + endif + ! else + ! if(.NOT. ASSOCIATED(s1%j%r))call c_crap1("c_TAYLOR_ran 2" ) ! call newetall(s1%j,1) + ! + ! call newdaran(s1%j,r1,R2) + ! endif + ! + END SUBROUTINE c_TAYLOR_ran + + + SUBROUTINE c_cfu000(S2,FUN,S1) + implicit none + type (c_taylor),INTENT(INOUT)::S1 + type (c_taylor),INTENT(IN)::S2 + complex(dp) FUN + EXTERNAL FUN + IF(.NOT.C_STABLE_DA) RETURN + ! if(old) then + if(s1%i==0) call c_crap1("c_cfu000 1" ) ! call etall1(s1%i) + CALL c_DACFU(s2%i,FUN,s1%i) + ! else + ! if(.NOT. ASSOCIATED(s1%j%r))call c_crap1("c_cfu000 2" ) ! call newetall(s1%j,1) + ! CALL NEWDACFU(s2%J,FUN,s1%J) + ! endif + + END SUBROUTINE c_cfu000 + + + SUBROUTINE c_taylor_eps(r1) + implicit none + real(dp),INTENT(INOUT)::r1 + IF(.NOT.C_STABLE_DA) RETURN + ! if(old) then + CALL c_DAeps(r1) + ! else + ! CALL newDAeps(r1) + ! endif + + END SUBROUTINE c_taylor_eps + + + + FUNCTION GETCHARnd2( S1, S2 ) + implicit none + TYPE (c_taylor) GETCHARnd2,junk + TYPE (c_taylor), INTENT (IN) :: S1 + CHARACTER(*) , INTENT (IN) :: S2 + CHARACTER (LEN = LNV) resul + integer i,k + integer localmaster + + IF(.NOT.C_STABLE_DA) then + GETCHARnd2%i=0 + RETURN + endif + localmaster=c_master + + ! ndel=0 + ! call check(s1) + call ass(GETCHARnd2) + + call alloc(junk) + resul = trim(ADJUSTR (s2)) + + do i=1,lnv + jfil(i)=0 + enddo + + nd2par= len(trim(ADJUSTR (s2))) + + !frs get around compiler problem + !frs do i=1,len(trim(ADJUSTR (s2))) + do i=1,nd2par + CALL CHARINT(RESUL(I:I),Jfil(I)) + if(i>nv) then + if(Jfil(i)>0) then + GETCHARnd2=0.0_dp + return + endif + endif + + enddo + + !do i=nd2+ndel+1,nv + do i=nd2par+1,nv + if(jfil(i)/=0) then + + write(6,*)" error in getchar for .para. " + ! call !write_e(0) + stop + endif + enddo + + call cfu(s1,filter,junk) + + !DO I=1,ND2+ndel + DO I=1,ND2par + DO K=1,JFIL(I) + JUNK=JUNK.K.I + ENDDO + ENDDO + + GETCHARnd2=junk + + call kill(junk) + c_master=localmaster + + END FUNCTION GETCHARnd2 + + FUNCTION GETintnd2_universal( S1, S2 ) + implicit none + TYPE (c_taylor) GETintnd2_universal,junk + TYPE (c_universal_taylor), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2(:) + integer i,k,jj(1:lnv) + integer localmaster,nd2p + + IF(.NOT.C_STABLE_DA) then + GETintnd2_universal%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + call ass(GETintnd2_universal) + + call alloc(junk) + + do i=1,lnv + jfil(i)=0 + enddo + nd2p=size(s2) + ! ndel=0 + +!lfilter + !frs get around compiler problem + !frs do i=1,len(trim(ADJUSTR (s2))) + do i=1,nd2p + Jfil(I)=s2(i) + if(i>nv) then + if(Jfil(i)>0) then + GETintnd2_universal=0.0_dp + return + endif + endif + + enddo + + !do i=nd2+ndel+1,nv + do i=nd2p+1,nv + if(jfil(i)/=0) then + + write(6,*)" error in GETintnd2 for .para. " + ! call !write_e(0) + stop + endif + enddo + + ! TYPE c_UNIVERSAL_TAYLOR + ! INTEGER, POINTER:: N,NV,nd2 => null() ! Number of coeeficients and number of variables + ! complex(DP), POINTER,dimension(:)::C => null() ! Coefficients C(N) + ! INTEGER, POINTER,dimension(:,:)::J=> null() ! Exponents of each coefficients J(N,NV) + ! END TYPE c_UNIVERSAL_TAYLOR + + +junk=0.0_dp +do i=1,s1%n + if(lfilter(s1%j(i,1:nv),nd2p)) then + jj=0 + jj(nd2p+1:nv)=s1%j(i,nd2p+1:nv) + + junk=junk+ (s1%c(i).cmono.jj) + + endif +enddo + + + + GETintnd2_universal=junk + + call kill(junk) + c_master=localmaster + + END FUNCTION GETintnd2_universal + + + function lfilter(j,nd2p) + implicit none + logical lfilter + integer i,nd2p + integer,dimension(:)::j + + lfilter=.true. + + do i=1,nd2p + if(jfil(i)/=j(i)) lfilter=.false. + enddo + + end function lfilter + + FUNCTION GETintnd2( S1, S2 ) + implicit none + TYPE (c_taylor) GETintnd2,junk + TYPE (c_taylor), INTENT (IN) :: S1 + integer , INTENT (IN) :: S2(:) + integer i,k + integer localmaster + + IF(.NOT.C_STABLE_DA) then + GETintnd2%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + call ass(GETintnd2) + + call alloc(junk) + + do i=1,lnv + jfil(i)=0 + enddo + nd2par=size(s2) + ! ndel=0 + + !frs get around compiler problem + !frs do i=1,len(trim(ADJUSTR (s2))) + do i=1,nd2par + Jfil(I)=s2(i) + if(i>nv) then + if(Jfil(i)>0) then + GETintnd2=0.0_dp + return + endif + endif + + enddo + + !do i=nd2+ndel+1,nv + do i=nd2par+1,nv + if(jfil(i)/=0) then + + write(6,*)" error in GETintnd2 for .para. " + ! call !write_e(0) + stop + endif + enddo + + call cfu(s1,filter,junk) + + !DO I=1,ND2+ndel + DO I=1,ND2par + DO K=1,JFIL(I) + JUNK=JUNK.K.I + ENDDO + ENDDO + + GETintnd2=junk + + call kill(junk) + c_master=localmaster + + END FUNCTION GETintnd2 + + FUNCTION GETintnd2t( S1, S22 ) + implicit none + TYPE (c_taylor) GETintnd2t,junk + TYPE (c_taylor), INTENT (IN) :: S1 + type(sub_taylor), INTENT (IN) :: S22 + integer s2(lnv) + integer i + integer localmaster + IF(.NOT.C_STABLE_DA) then + GETintnd2t%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + call ass(GETintnd2t) + + call alloc(junk) + + do i=1,lnv + jfilt(i)=0 + enddo + s2=s22%j + nd2part=s22%min + nd2partt=s22%max + ! ndel=0 + !frs get around compiler problem + !frs do i=1,len(trim(ADJUSTR (s2))) + do i=nd2part,nd2partt + jfilt(I)=s2(i) + if(i>nv) then + if(jfilt(i)>0) then + GETintnd2t=0.0_dp + return + endif + endif + + enddo + + !do i=nd2+ndel+1,nv + do i=nd2partt+1,nv + if(jfilt(i)/=0) then + + write(6,*)" error in GETintnd2t for .part_taylor. " + ! call !write_e(0) + stop + endif + enddo + + call cfu(s1,c_filter_part,junk) + + !DO I=1,ND2+ndel + ! DO I=1,ND2par + ! DO K=1,jfilt(I) + ! JUNK=JUNK.K.I + ! ENDDO + ! ENDDO + + GETintnd2t=junk + + call kill(junk) + c_master=localmaster + + END FUNCTION GETintnd2t + + + SUBROUTINE c_taylor_cycle(S1,size,ii,VALUE,J) + implicit none + type (c_taylor),INTENT(IN)::S1 + integer,optional, intent(inout):: size + integer,optional, intent(in):: ii + integer,optional, intent(inout)::J(:) + complex(dp), OPTIONAL, intent(inout):: value + INTEGER ipresent,ILLA + complex(dp) VALUE0 + IF(.NOT.C_STABLE_DA) RETURN + ! if(old) THEN + IF(PRESENT(J).AND.PRESENT(VALUE).and.present(ii)) THEN + call c_dacycle(S1%i,ii,value,illa,J) + ELSEif(present(size)) then + call c_dacycle(S1%i,ipresent,value0,size) + else + write(6,*) "error in taylor_cycle" + stop 888 + ENDIF + + END SUBROUTINE c_taylor_cycle + + SUBROUTINE c_cycle(S1,i,value,j) + implicit none + type (c_taylor),INTENT(in)::S1 + integer i,n + complex(dp) value + integer j(:) +!!! always initialize i=1 +!!! check for i=0 and then exit your loop + + IF(.NOT.C_STABLE_DA) RETURN + + call c_taylor_cycle(s1,size=n) + + if(i>n) then + i=0 + return + endif + + + call c_taylor_cycle(s1,ii=i,value=value,j=j) + + i=i+1 + + END SUBROUTINE c_cycle + + subroutine c_check_snake() +!* + implicit none + c_master=c_master+1 + select case (c_master) + case(1:c_ndumt) + if(c_iass0user(c_master)>c_scratchda(c_master)%n.or.c_scratchda(c_master)%n>newscheme_max) then + + write(6,*) "c_iass0user(c_master),c_scratchda(c_master)%n,newscheme_max" + write(6,*) c_iass0user(c_master),c_scratchda(c_master)%n,newscheme_max + ! call !write_e + call c_ndum_warning_user + endif + c_iass0user(c_master)=0 + case(c_ndumt+1:) + + write(6,*) "Should not be here" + + ! call !write_e(101) + end select + C_master=C_master-1 + end subroutine c_check_snake + + ! functions used inside other routines + + + + + function check_j(j) + implicit none + integer check_j + INTEGER,INTENT(in),dimension(:)::j + integer i,no + check_j=0 + IF(.NOT.C_STABLE_DA) RETURN + + + + no=0 + do i=1,size(j) + no=j(i)+no + enddo + + if(no>no) then + check_j=no + return + endif + + do i=nv+1,size(j) + if(j(i)/=0) then + check_j=-i + endif + enddo + end function check_j + + function check_harmonic_order(j) + implicit none + integer check_harmonic_order + integer i + integer,dimension(:)::j + + check_harmonic_order=0 + !do i=1,nd2+ndel + do i=1,nd2t + check_harmonic_order=check_harmonic_order+j(i) + enddo + + end function check_harmonic_order + + function filter(j) + implicit none + complex(dp) filter + integer i + integer,dimension(:)::j + + filter=1.0_dp + !do i=1,nd2+ndel + do i=1,nd2par + if(jfil(i)/=j(i)) filter=0.0_dp + enddo + + end function filter + + + function c_filter_part(j) + implicit none + complex(dp) c_filter_part + integer i + integer,dimension(:)::j + ! WRITE(6,*) jfilt(1:4) + ! WRITE(6,*)nd2part,nd2partt + c_filter_part=1.0_dp + !do i=1,nd2+ndel + do i=nd2part,nd2partt + if(jfilt(i)/=j(i)) c_filter_part=0.0_dp + enddo + + end function c_filter_part + + ! i/o routines + + SUBROUTINE c_pri_c_ray(S1,MFILE,prec,dospin) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + REAL(DP),OPTIONAL,INTENT(INOUT)::prec + type (c_ray),INTENT(INout)::S1 + logical, optional :: dospin + integer i,j,k,mfi + logical(lp) dos + real(dp) norm + + dos=.true. + mfi=6 + if(present(mfile)) mfi=mfile + + if(present(dospin)) dos=dospin + + write(mfi,*) " " + write(mfi,*) s1%n, " Dimensional ray " + do i=1,s1%n + write(mfi,*) s1%x(i) + enddo + +if(dos) then + if(use_quaternion) then + write(mfi,*) " Quaternion " + do i=0,3 + write(mfi,*) s1%q%x(i) + enddo + write(mfi,*) " Three spin directions from quaternion " + write(mfi,*) "S1" + do i=1,3 + write(mfi,*) s1%S1(i) + enddo + write(mfi,*) "S2" + do i=1,3 + write(mfi,*) s1%S2(i) + enddo + write(mfi,*) "S3" + do i=1,3 + write(mfi,*) s1%S3(i) + enddo + else + write(mfi,*) " Three spin directions " +write(mfi,*) "S1" + do i=1,3 + write(mfi,*) s1%S1(i) + enddo + write(mfi,*) "S2" + do i=1,3 + write(mfi,*) s1%S2(i) + enddo + write(mfi,*) "S3" + do i=1,3 + write(mfi,*) s1%S3(i) + enddo + endif +else + write(mfi,*) " Spin results not printed per user's request " +endif + + END SUBROUTINE c_pri_c_ray + + + SUBROUTINE pri_matrix(S1,MFILE,for) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + real(dp),INTENT(INout)::S1(:,:) + character(*), optional :: for + integer i ,mfi + + mfi=6 + if(present(mfile)) mfi=mfile + + + do i=1,size(s1,1) + if(present(for)) then + write(mfi,for ) s1(i,:) + else + write(mfi,'(200(1X,G23.16))' ) s1(i,:) + endif + enddo + + END SUBROUTINE pri_matrix + + SUBROUTINE c_pri_matrix(S1,MFILE) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + complex(dp),INTENT(INout)::S1(:,:) + integer i ,mfi + + mfi=6 + if(present(mfile)) mfi=mfile + + + do i=1,size(s1,1) + write(mfi,'(400(1X,G23.16))' ) s1(i,:) + enddo + + END SUBROUTINE c_pri_matrix + + SUBROUTINE c_pri_map(S1,MFILE,prec,dospin) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + REAL(DP),OPTIONAL,INTENT(INOUT)::prec + type (c_damap),INTENT(INout)::S1 + logical, optional :: dospin + integer i,j,k,mfi + logical(lp) rad_in,dos,imp + real(dp) norm + dos=.true. + mfi=6 + if(present(mfile)) mfi=mfile + + if(present(dospin)) dos=dospin + + ! write(mfi,*) " tpsa status for tracking type(c_ray) ",s1%tpsa + ! if(s1%tpsa) then + write(mfi,*) s1%n, " Dimensional TPSA/DA map " + ! else + ! write(mfi,*) s1%n, " Dimensional DA map (around chosen orbit in map%x0) " + ! endif + imp=.false. + do i=1,s1%n + if(abs(s1%x0(i))/=0) then + imp=.true. + exit + endif + enddo + do i=1,s1%n + ! if(s1%tpsa.or.imp) write(6,*) "Initial orbit for TPSA calculations" + if(imp) write(6,*) "Initial orbit for TPSA calculations" + + ! if(s1%tpsa.or.imp) write(6,*) s1%x0(i) + if(imp) write(6,*) s1%x0(i) + call c_pri(s1%v(i),mfile,prec) + enddo + +if(dos) then + call c_full_norm_spin(s1%s,k,norm) + if(k==-1) then + write(mfi,*) " Spin Matrix " + call c_pri_spinmatrix(S1%s,MFILE,prec) + endif + if(k==0) then + write(mfi,*) " No Spin Matrix " + endif + if(k==1) then + write(mfi,*) " Spin Matrix is identity " + endif +else + write(mfi,*) " Spin Matrix is not printed per user's request " +endif +if(dos) then + call c_full_norm_quaternion(s1%q,k,norm) + if(k==-1) then + write(mfi,*) " Quaternion " + call c_pri_quaternion(S1%q,MFILE,prec) + endif + if(k==0) then + write(mfi,*) " No c_quaternion " + endif + if(k==1) then + write(mfi,*) " c_quaternion is identity " + endif +else + write(mfi,*) " c_quaternion is not printed per user's request " +endif + call c_check_rad(s1%e_ij,rad_in) + if(rad_in) then + call print_e_ij(S1,mfi) + else + write(mfi,*) "No Stochastic Radiation " + endif + + END SUBROUTINE c_pri_map + + + SUBROUTINE print_e_ij(S1,MFILE) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + type (c_damap),INTENT(INout)::S1 + integer i,j,mfi + + + mfi=6 + if(present(mfile)) mfi=mfile + + write(mfi,*) "Stochastic Radiation " + do i=1,6 + do j=1,6 + write(mfi,*) i,j,s1%e_ij(i,j) + enddo + enddo + + end SUBROUTINE print_e_ij + + + SUBROUTINE c_pri_quaternion(S2,mf,prec) + implicit none + integer ipause, mypauses,i,k + type (c_quaternion),INTENT(INOUT)::S2 + integer,optional :: mf + real(dp), optional :: prec + i=6 + if(present(mf)) i=mf + write(i,*) " c_quaternion " + do k=0,3 + call print(s2%x(k),i,prec) + enddo + + END SUBROUTINE c_pri_quaternion + + SUBROUTINE c_read_quaternion(S2,mfile) + implicit none + integer mfile,i + type (c_quaternion),INTENT(INOUT)::S2 + character(255) line + + read(mfile,'(a255)') line + do i=0,3 + call c_rea(s2%x(i),mfile) + enddo + + END SUBROUTINE c_read_quaternion + + + SUBROUTINE c_read_map(S1,MFILE) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + type (c_damap),INTENT(inout)::S1 + integer i,j,i1,j2 + character(255) line + + read(mfile,'(a255)') line + read(mfile,*) s1%n + do i=1,s1%n + call c_rea(s1%v(i),mfile) + enddo + read(mfile,'(a255)') line + + if(index(line,"No")/=0) then + s1%s=0 + elseif(index(line,"id")/=0) then + s1%s=1 + else + call c_read_spinmatrix(S1%s,MFILE) + endif + + read(mfile,'(a255)') line + + if(index(line,"No")/=0) then + s1%q=0.0_dp + elseif(index(line,"id")/=0) then + s1%q=1.0_dp + else + call c_read_quaternion(S1%q,MFILE) + endif + + read(mfile,'(a255)') line + if(index(line,"No")/=0) then + s1%e_ij=0.0_dp + else + do i=1,6 + do j=1,6 + read(mfile,*) i1,j2,s1%e_ij(i1,j2) + enddo + enddo + endif + + END SUBROUTINE c_read_map + + + SUBROUTINE c_pri_vec(S1,MFILE,DEPS,dospin) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + REAL(DP),OPTIONAL,INTENT(INOUT)::DEPS + type (c_vector_field),INTENT(INout)::S1 + integer i,mfi,k + real(dp) norm + logical, optional :: dospin + logical(lp) dos + + dos=.true. + if(present(dospin)) dos=dospin + + mfi=6 + if(present(mfile)) mfi=mfile + + write(mfi,*) " " + write(mfi,*) s1%n, " Dimensional Vector Field " + do i=1,s1%n + call c_pri(s1%v(i),mfile,deps) + enddo + + + + if(dos) then + if(use_quaternion) then + call c_full_norm_quaternion(s1%q,k,norm) + if(k==-1) then + write(mfi,*) " Quaternion " + call c_pri_quaternion(S1%q,MFILE,prec=deps) + endif + if(k==0) then + write(mfi,*) " No c_quaternion " + endif + if(k==1) then + write(mfi,*) " c_quaternion is identity " + endif + else + ! call c_full_norm_spinor(S1%h,norm) + ! write(mfi,*) " Spinor " + ! call c_pri_spinor(S1%h,MFILE,prec=deps) + ! call c_full_norm_spinor(S1%h,norm) + ! write(mfi,*) " Spinor " + ! call c_pri_spinor(S1%h,MFILE,prec=deps) + write(mfi,*) " Spinor in matrix form " + call c_full_norm_spinMATRIX(S1%L,norm) + call c_pri_spinmatrix(S1%L,MFILE,prec=deps) + endif + else + write(mfi,*) " Spin is not printed per user's request " + endif + + + + + + END SUBROUTINE c_pri_vec + + SUBROUTINE c_pri_factored_lie(S1,MFILE,DEPS) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + REAL(DP),OPTIONAL,INTENT(INOUT)::DEPS + type (c_factored_lie),INTENT(INout)::S1 + integer i,mfi + mfi=6 + if(present(mfile)) mfi=mfile + + write(mfi,*) " " + if(s1%dir==1) then + write(mfi,*) " Dragt-Finn Representation ", s1%dir + else + write(mfi,*) " Inverse Dragt-Finn Representation ", s1%dir + endif + write(mfi,*) s1%n, " Vector Fields " + do i=1,s1%n + write(mfi,*) " Vector field number ",i + call c_pri_vec(s1%f(i),mfile,deps) + enddo + + END SUBROUTINE c_pri_factored_lie + + + SUBROUTINE c_pri_spinmatrix(S1,MFILE,prec) ! spin routine + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + REAL(DP),OPTIONAL,INTENT(INOUT)::prec + type (c_spinmatrix),INTENT(IN)::S1 + integer i,j,mfi + mfi=6 + if(present(mfile)) mfi=mfile + + do i=1,3 + do j=1,3 + write(mfi,*) " " + write(mfi,*) i,j + write(mfi,*) " " + call c_pri(s1%s(i,j),mfile,prec) + enddo + enddo + + + END SUBROUTINE c_pri_spinmatrix + + + SUBROUTINE c_read_spinmatrix(S1,MFILE) ! spin routine + implicit none + INTEGER,INTENT(IN)::MFILE + + type (c_spinmatrix),INTENT(INout)::S1 + integer i,j,i1,j1 + character(255) line + + do i=1,3 + do j=1,3 + read(mfile,'(a255)') line + read(mfile,*) i1,j1 + read(mfile,'(a255)') line + call c_rea(s1%s(i1,j1),mfile) + enddo + enddo + + + END SUBROUTINE c_read_spinmatrix + + + SUBROUTINE c_full_norm_spin(S1,k,EPS) ! spin routine + implicit none + REAL(DP),OPTIONAL,INTENT(INOUT)::EPS + real(dp) deps + type (c_spinmatrix),INTENT(IN)::S1 + integer i,k + + deps=0.0_dp + k=-1 + call c_full_norm_spinmatrix(s1,deps) + + if(DEPS==0.0_dp) k=0 + if(DEPS==3.0_dp) then + DEPS=0.0_dp + do i=1,3 +! DEPS=DEPS+full_abs(s1%s(i,i)) + DEPS=DEPS+(s1%s(i,i)) ! in case of minus 1 + enddo + if(DEPS==3.0_dp) k=1 + endif + if(present(eps)) eps=deps + END SUBROUTINE c_full_norm_spin + + SUBROUTINE c_norm_spin(S1,k,EPS) ! spin routine + implicit none + REAL(DP),OPTIONAL,INTENT(INOUT)::EPS + real(dp) deps + type (c_spinmatrix),INTENT(IN)::S1 + integer i,k + + deps=0.0_dp + k=-1 + call c_norm_spinmatrix(s1,deps) + + if(DEPS==0.0_dp) k=0 + + if(abs(deps-3.0_dp)<=1.d-7) then + DEPS=0.0_dp + do i=1,3 + DEPS=DEPS+abs(s1%s(i,i)) + enddo + if(abs(deps-3.0_dp)<=1.d-7) then + k=1 + deps=abs(deps-3.0_dp) + endif + endif + if(present(eps)) eps=deps + END SUBROUTINE c_norm_spin + + + SUBROUTINE c_pri_spinor(S1,MFILE,prec) ! spin routine + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + REAL(DP),OPTIONAL,INTENT(INOUT)::prec + type (c_spinor),INTENT(IN)::S1 + integer i,mfi + mfi=6 + if(present(mfile)) mfi=mfile + + write(mfi,*) " Complex Spinor " + do i=1,3 + + write(mfi,*) " " + write(mfi,*) i + write(mfi,*) " " + call c_pri(s1%v(i),mfile,prec) + + enddo + + + END SUBROUTINE c_pri_spinor + + + SUBROUTINE c_read_spinor(S1,MFILE) ! spin routine + implicit none + INTEGER,INTENT(IN)::MFILE + type (c_spinor),INTENT(IN)::S1 + integer i + character(120) line + + ! write(mfile,*) " Complex Spinor " + read(mfile,'(a120)') line + do i=1,3 + + read(mfile,'(a120)') line + read(mfile,'(a120)') line + read(mfile,'(a120)') line + + call c_rea(s1%v(i),mfile) + + enddo + + + END SUBROUTINE c_read_spinor + + SUBROUTINE c_pri(S1,MFILE,prec) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + REAL(DP),OPTIONAL,INTENT(INOUT)::prec + type (c_taylor),INTENT(IN)::S1 + REAL(DP) deps + integer mfi +mfi=6 +if(present(mfile)) mfi=mfile + IF(PRESENT(prec)) THEN + deps=-1.0_dp + CALL c_taylor_eps(DEPS) + CALL c_taylor_eps(PREC) + ENDIF + + ! if(old) then + if(print77) then + CALL c_DAPRI77(s1%i,mfi) + else + CALL c_DAPRI(s1%i,mfi) + endif + + IF(PRESENT(prec)) CALL c_taylor_eps(deps) + + END SUBROUTINE c_pri + + +!!!! moved here per David so23.3.30 + + SUBROUTINE printcomplex(S2,i,PREC,ind) + implicit none + type (complextaylor),INTENT(INOUT)::S2 + integer,optional :: i,ind + REAL(DP),OPTIONAL,INTENT(INOUT)::PREC + ! type(c_taylor) t + type (c_UNIVERSAL_TAYLOR) ut + if(nice_taylor_print) then + ! call alloc(t) + ! t=s2 + ! call print(t,i,PREC) + ! call kill(t) + call c_FILL_UNI_complextaylor(ut,S2) + call print(ut,iunit=i,prec=prec,ind=ind) + call kill(ut) + else + write(i,*) " Real Part " + call daprint(s2%r,i,PREC) + write(i,*) " Imaginary Part " + call daprint(s2%i,i,PREC) + endif + END SUBROUTINE printcomplex + + + SUBROUTINE printpoly(S2,mf,ind) + implicit none + type (complex_8),INTENT(INOUT)::S2 + integer ipause,mypauses + integer,optional :: mf, ind + integer i + integer,parameter ::m1=1,m2=2,m3=3,ms=4 + integer,parameter:: m11=m1+ms*m1,m12=m1+ms*m2,m13=m1+ms*m3, & + m21=m2+ms*m1,m22=m2+ms*m2,m23=m2+ms*m3, & + m31=m3+ms*m1,m32=m3+ms*m2,m33=m3+ms*m3 + character(255) line + i=6 + if(present(mf)) i=mf + if(s2%kind/=0) then + + select case (s2%kind) + case(m1) + write(i,*) s2%r + case(m2) + call printcomplex(S2%t,i,ind=ind) + case(m3) + if (.not. nice_taylor_print) write(i,*) " printing a complex polymorph (complex_8)" + + if(s2%i>0.and.s2%j>0) then + write(line,*) s2%r," +",s2%s," (x_",s2%i,"+ i","*x_",s2%j,")" + elseif(s2%i>0)then + write(line,*) s2%r," +",s2%s," (x_",s2%i,")" + + elseif(s2%j>0)then + write(line,*) s2%r," +",s2%s," ( ","i*x_",s2%j,")" + + else + write(line,*) s2%r + endif + call context(line,maj=.false.) + write(i,'(a)') adjustr(line(1:len_trim(line))) + + end select + else + + line=" Warning not defined " + ipause=mypauses(0,line) + + endif + + END SUBROUTINE printpoly + + SUBROUTINE print6(S1,mf) + implicit none + type (complex_8),INTENT(INout)::S1(:) + integer,optional :: mf + integer i + + do i=lbound(s1,1),ubound(s1,1) + call print(s1(i),mf, ind=i) + enddo + + END SUBROUTINE print6 +!!!!!! end moved by David + + SUBROUTINE DAPRINTTAYLORS(S1,MFILE,PREC) + implicit none + INTEGER,OPTIONAL,INTENT(IN)::MFILE + type (C_TAYLOR),INTENT(IN)::S1(:) + REAL(DP),OPTIONAL,INTENT(INOUT)::PREC + INTEGER I,mfi +mfi=6 +if(present(mfile)) mfi=mfile + + DO I=1,size(S1) + if(s1(i)%i>0) then + if(size(S1)>1) write(mfi,*) "Taylor #",i + CALL C_PRI(s1(i),MFILE,PREC) + endif + ENDDO + END SUBROUTINE DAPRINTTAYLORS + + SUBROUTINE c_REA(S1,MFILE) + implicit none + INTEGER,INTENT(in)::MFILE + type (c_taylor),INTENT(IN)::S1 + + if(s1%i==0)call c_crap1("REA 1" ) ! call etall1(s1%i) + + if(read77) then + CALL c_darea77(s1%i,MFILE) + else + CALL c_DAREA(s1%i,MFILE) + endif + + + END SUBROUTINE c_REA + + SUBROUTINE DAREADTAYLORS(S1,MFILE) + implicit none + INTEGER,INTENT(in)::MFILE + type (C_TAYLOR),INTENT(INOUT)::S1(NDIM2) + INTEGER I + + DO I=1,ND2 + CALL C_REA(s1(I),MFILE) + ENDDO + + END SUBROUTINE DAREADTAYLORS + + ! Universal Taylor Routines (Sagan's Stuff) + + + + + + ! End of Universal Taylor Routines + + + + + ! Warning Routines + + subroutine c_crap1(STRING) +!* + implicit none + CHARACTER(*) STRING + + + write(6,*) "ERROR IN :" + write(6,*) STRING + ! call !write_e(3478) + + end subroutine c_crap1 + + SUBROUTINE c_real_stop() +!* + implicit none + integer i(1),j + + + write(6,*) " You are using a kind(1.0_dp) " + write(6,*)" set c_real_warning to false to permit this " + stop + i(j)=0 + c_real_warning=.false. + + END SUBROUTINE c_real_stop + + + SUBROUTINE c_ndum_warning_user() +!* + implicit none + integer ipause,II(0:1) + + + + write(6,*) " * Should never be here in New Linked List Scheme *" + + write(6,*) " do you want a crash? " + ! call !write_e + stop + ii(2000*ipause)=0 + + end SUBROUTINE c_ndum_warning_user + + ! End of Warning Routines + + ! linked list of da for scratch levels + + SUBROUTINE Set_Up( L ) ! Sets up a layout: gives a unique negative index +!* + implicit none + TYPE (c_dalevel) L + call null_it(L) + ALLOCATE(L%n); + ALLOCATE(L%CLOSED); + L%closed=.FALSE. + L%N=0 + END SUBROUTINE Set_Up + + SUBROUTINE de_Set_Up( L ) ! deallocates layout content +!* + implicit none + TYPE (c_dalevel) L + deallocate(L%closed); + deallocate(L%n); + END SUBROUTINE de_Set_Up + + + + SUBROUTINE null_it( L ) ! Nullifies layout content +!* + implicit none + TYPE (c_dalevel), intent(inout) :: L + nullify(L%N ) + nullify(L%CLOSED ) + nullify(L%PRESENT ) + ! + nullify(L%END ) + nullify(L%START ) + nullify(L%START_GROUND )! STORE THE GROUNDED VALUE OF START DURING CIRCULAR SCANNING + nullify(L%END_GROUND )! STORE THE GROUNDED VALUE OF END DURING CIRCULAR SCANNING + END SUBROUTINE null_it + + SUBROUTINE LINE_L(L,doneit) ! makes into line temporarily +!* + implicit none + TYPE (c_DALEVEL) L + logical(lp) doneit + doneit=.false. + if(L%closed) then + if(associated(L%end%next)) then + L%end%next=>L%start_ground + doneit=.true. + endif + if(associated(L%start%previous)) then + L%start%previous=>L%end_ground + endif + endif + END SUBROUTINE LINE_L + + SUBROUTINE RING_L(L,doit) ! Brings back to ring if needed +!* + implicit none + TYPE (c_DALEVEL) L + logical(lp) doit + if(L%closed.and.doit) then + if(.NOT.(associated(L%end%next))) then + L%start_ground=>L%end%next ! saving grounded pointer + L%end%next=>L%start + endif + if(.NOT.(associated(L%start%previous))) then + L%end_ground=>L%start%previous ! saving grounded pointer + L%start%previous=>L%end + endif + endif + END SUBROUTINE RING_L + + SUBROUTINE APPEND_DA( L ) ! Standard append that clones everything +!* + implicit none + TYPE (c_dascratch), POINTER :: Current + TYPE (c_DALEVEL), TARGET,intent(inout):: L + logical(lp) doneit + CALL LINE_L(L,doneit) + L%N=L%N+1 + nullify(current);ALLOCATE(current); + + call c_alloc_DA(current) + + if(L%N==1) current%next=> L%start + Current % previous => L % end ! point it to next fibre + if(L%N>1) THEN + L % end % next => current ! + ENDIF + + L % end => Current + if(L%N==1) L%start=> Current + L%PRESENT=>CURRENT ! ALWAYS IF APPENDING + CALL RING_L(L,doneit) + END SUBROUTINE APPEND_DA + + SUBROUTINE INSERT_DA( L ) ! Standard append that clones everything +!* + implicit none + logical(lp) :: doneitt=.true. + TYPE (c_dascratch), POINTER :: Current + TYPE (c_DALEVEL), TARGET,intent(inout):: L + IF(L%N>1.AND.(.NOT.ASSOCIATED(L%PRESENT,L%END))) THEN + + L%N=L%N+1 + nullify(current);ALLOCATE(current); + + call c_alloc_DA(current) + + Current % previous => L % PRESENT ! 2P -> 2 + Current % NEXT => L % PRESENT%NEXT ! 2P -> 3 + L%PRESENT%NEXT=> CURRENT ! 2 -> 2P + Current % NEXT%PREVIOUS => CURRENT ! 3 -> 2P + L%PRESENT=>CURRENT ! 2P BECOMES 3 + + ELSE + + CALL APPEND_DA( L ) + if(L%N==1) THEN + L%CLOSED=.TRUE. + CALL RING_L(L,doneitt) + ENDIF + + ENDIF + END SUBROUTINE INSERT_DA + + SUBROUTINE c_alloc_DA( c ) ! Does the full allocation of fibre and initialization of internal variables +!* + implicit none + type(c_dascratch),pointer:: c + ALLOCATE(C%T) + CALL ALLOC(C%T) + NULLIFY(C%NEXT) + NULLIFY(C%PREVIOUS) + + end SUBROUTINE c_alloc_DA + + SUBROUTINE kill_DALEVEL( L ) ! Destroys a layout +!* + implicit none + TYPE (c_DASCRATCH), POINTER :: Current + TYPE (c_DALEVEL) L + logical(lp) doneit + CALL LINE_L(L,doneit) + nullify(current) + Current => L % end ! end at the end + DO WHILE (ASSOCIATED(L % end)) + L % end => Current % previous ! update the end before disposing + call dealloc_DASCRATCH(Current) + Current => L % end ! alias of last fibre again + L%N=L%N-1 + END DO + call de_set_up(L) + END SUBROUTINE kill_DALEVEL + + SUBROUTINE dealloc_DASCRATCH( c ) ! destroys internal data if it is not pointing (i.e. not a parent) +!* + implicit none + type(c_DASCRATCH),pointer :: c + IF(ASSOCIATED(C)) THEN + CALL KILL(C%T) + IF(ASSOCIATED(C%T)) DEALLOCATE(C%T) + ! IF(ASSOCIATED(C%NEXT)) DEALLOCATE(C%NEXT) + ! IF(ASSOCIATED(C%PREVIOUS)) DEALLOCATE(C%PREVIOUS) + deallocate(c); + ENDIF + end SUBROUTINE dealloc_DASCRATCH + + SUBROUTINE set_up_level() +!* + implicit none + integer i + do i=1,c_ndumt + call set_up(c_scratchda(i)) + ! do j=1,n + ! call INSERT_da(scratchda(i)) + ! enddo + ! scratchda(i)%CLOSED=.TRUE. + ! CALL RING_L(scratchda(i),.TRUE.) + enddo + + end SUBROUTINE set_up_level + + SUBROUTINE c_report_level() +!* + implicit none + integer i + if(associated(c_scratchda(1)%n)) then + do i=1,c_ndumt + + write(6,'(a6,1x,i4,a5,1x,i4,1x,a7)') "Level ",i, " has ",c_scratchda(i)%n, "Taylors" + ! write(w_p%c(1),'(a6,1x,i4,a5,1x,i4,1x,a7)') "Level ",i, " has ",scratchda(i)%n, "Taylors" + ! ! call !write_e + enddo + endif + END SUBROUTINE c_report_level + + ! end linked list of da for scratch levels + + ! Assignments Routines + + subroutine c_ASSIGN() +!* + implicit none + integer i + do i=1,c_ndumt + c_iassdoluser(i)=0 + c_iass0user(i)=0 + enddo + ! if(old) then + CALL c_etall1(c_dummy) + call alloc(c_temp) + ! else + ! CALL allocnewda(c_dummyl) + ! call allocnewda(templ) + ! endif + CALL set_up_level + end subroutine c_ASSIGN + + subroutine c_deassign() +!* + implicit none + integer i + do i=1,c_ndumt + c_iassdoluser(i)=0 + c_iass0user(i)=0 + enddo + ! if(old) then + CALL c_dADAL1(c_dummy) + call kill(c_temp) + ! else + ! CALL KILLnewdaS(c_dummyl) + ! call KILLnewdaS(templ) + ! endif + do i=1,c_ndumt + CALL kill_DALEVEL(c_scratchda(I)) + ENDDO + end subroutine c_deassign + + subroutine c_asstaylor(s1) +!* + implicit none + TYPE (c_taylor) s1 + ! lastmaster=master ! 2002.12.13 + + select case(c_master) + case(0:c_ndumt-1) + c_master=c_master+1 + case(c_ndumt) + write(6,*) " cannot indent anymore in c_asstaylor ",ndumt + read(5,*) c_master + stop 444 + end select + ! write(26,*) " taylor ",master + call c_ass0(s1) + s1=0.0_dp + + end subroutine c_asstaylor + + subroutine c_ass0(s1) +!* + implicit none + integer ipause, mypause + TYPE (c_taylor) s1 + + IF(c_MASTER>c_NDUMT.or.c_master==0) THEN + WRITE(6,*) "more scratch level needed ",master,NDUMT + ipause=mypause(123) + write(6,*) 1/sqrt(-dble(1000+c_master)) + stop 123 + ENDIF + + if(.not.no_ndum_check) c_iass0user(c_master)=c_iass0user(c_master)+1 + if(c_iass0user(c_master)>c_scratchda(c_master)%n) then + call INSERT_DA( c_scratchda(c_master) ) + ELSE + c_scratchda(c_master)%PRESENT=>c_scratchda(c_master)%PRESENT%NEXT + ENDIF + ! if(old) then + s1%i=c_scratchda(c_master)%PRESENT%T%i + ! else + ! s1%j=scratchda(c_master)%PRESENT%T%j + ! endif + + + end subroutine c_ASS0 + +!!!!! assign routines !!! + subroutine c_assmap(s1) +!* + implicit none + TYPE (c_damap) s1 + integer i,j + + select case(c_master) + case(0:c_ndumt-1) + c_master=c_master+1 + case(c_ndumt) + write(6,*) " cannot indent anymore in c_assmap ",ndumt + read(5,*) c_master + stop 444 + end select + + do i=1,s1%n + call c_ass0(s1%v(i)) + s1%v(i)=0.0_dp + enddo + + do i=1,3 + do j=1,3 + call c_ass0(s1%s%s(i,j)) + s1%s%s(i,j)=0.0_dp + enddo + enddo + + do i=0,3 + call c_ass0(s1%q%x(i)) + s1%q%x(i)=0.0_dp + enddo + s1%x0=0.0_dp +! s1%tpsa=use_tpsa + end subroutine c_assmap + + subroutine c_ass_quaternion(s1) ! spin routine +!* + implicit none + TYPE (c_quaternion) s1 + integer i + + select case(c_master) + case(0:c_ndumt-1) + c_master=c_master+1 + case(c_ndumt) + write(6,*) " cannot indent anymore in c_ass_spinmatrix ",c_ndumt + read(5,*) c_master + stop 444 + end select + + + + do i=0,3 + + call c_ass0(s1%x(i)) + s1%x(i)=0.0_dp + enddo + s1%x(0)=1.0_dp + + end subroutine c_ass_quaternion + + subroutine c_ass_spinmatrix(s1) ! spin routine +!* + implicit none + TYPE (c_spinmatrix) s1 + integer i,j + + select case(c_master) + case(0:c_ndumt-1) + c_master=c_master+1 + case(c_ndumt) + write(6,*) " cannot indent anymore in c_ass_spinmatrix ",c_ndumt + read(5,*) c_master + stop 444 + end select + + + + do i=1,3 + do j=1,3 + call c_ass0(s1%s(i,j)) + s1%s(i,j)=0.0_dp + enddo + enddo + + end subroutine c_ass_spinmatrix + + + subroutine c_ass_spinor(s1) ! spin routine +!* + implicit none + TYPE (c_spinor) s1 + integer i + + select case(c_master) + case(0:c_ndumt-1) + c_master=c_master+1 + case(c_ndumt) + write(6,*) " cannot indent anymore in c_ass_spinmatrix ",c_ndumt + read(5,*) c_master + stop 444 + end select + + + + do i=1,3 + call c_ass0(s1%v(i)) + s1%v(i)=0.0_dp + enddo + + end subroutine c_ass_spinor + + subroutine c_ass_vector_field(s1) +!* + implicit none + TYPE (c_vector_field) s1 + integer i,J + + select case(c_master) + case(0:c_ndumt-1) + c_master=c_master+1 + case(c_ndumt) + write(6,*) " cannot indent anymore in c_ass_vector_field ",ndumt + read(5,*) c_master + stop 444 + end select + + do i=1,s1%n + call c_ass0(s1%v(i)) + s1%v(i)=0.0_dp + enddo + + do i=0,3 + call c_ass0(s1%q%x(i)) + s1%q%x(i)=0.0_dp + enddo + + ! do i=1,3 + ! call c_ass0(s1%h%v(i)) + ! s1%h%v(i)=0.0_dp + ! enddo + + do i=1,3 + do J=1,3 + call c_ass0(s1%L%s(i,j)) + s1%L%s(i,j)=0.0_dp + enddo + enddo + + + s1%eps = eps_tpsalie + s1%nrmax = nrmax + + end subroutine c_ass_vector_field + + SUBROUTINE c_norm(S1,S2,prec) + implicit none + type (c_taylor),INTENT(INOUT)::S2 + type (c_taylor), intent(INOUT):: s1 + real(dp) prec + INTEGER ipresent,n,I,illa + complex(dp) value,v + INTEGER, allocatable :: j(:) + type (c_taylor) t + + call alloc(t) + t=0.0_dp + ipresent=1 + call c_dacycle(S1%I,ipresent,value,n) + + allocate(j(nv)) + + do i=1,N + call c_dacycle(S1%I,i,value,illa,j) + v=0.0_dp + if(abs(value)>prec) v=abs(value) + t=t+(v.cmono.j) +! endif + ENDDO + s2=t + deallocate(j) + call kill(t) + + END SUBROUTINE c_norm + + ! remove small numbers + + complex(dp) function c_clean(s1,prec) + implicit none + complex(dp) v,s1 + real(dp) x,prec + + x=s1 + v=0 + if(abs(x)>prec) v=x + x=aimag(s1) + if(abs(x)>prec) v=v+i_*x + c_clean=v + + end function c_clean + + + SUBROUTINE c_clean_yu_w(S1,S2,prec) + implicit none + type (c_yu_w),INTENT(INOUT)::S2 + type (c_yu_w), intent(INOUT):: s1 + real(dp) prec + integer i,j + + do i=1,size(s1%w,1) + do j=0,s1%n + call c_clean_taylor(s1%w(i,j),s2%w(i,j),prec) + enddo + enddo + +end SUBROUTINE c_clean_yu_w + + SUBROUTINE clean_matrix_complex(S1,S2,prec) + implicit none + complex(dp) s1(:,:),s2(:,:) + real(dp) prec + + integer i,j + + do i=1,size(s1,1) + do j=1,size(s1,2) + s2(i,j)=c_clean(s1(i,j),prec) + enddo + enddo + end SUBROUTINE clean_matrix_complex + + SUBROUTINE clean_vector_complex(S1,S2,prec) + implicit none + complex(dp) s1(:),s2(:) + real(dp) prec + + integer i + + do i=1,size(s1,1) + s2(i)=c_clean(s1(i),prec) + enddo + end SUBROUTINE clean_vector_complex + + SUBROUTINE clean_matrix(S1,S2,prec) + implicit none + complex(dp) s1(:,:),s2(:,:) + integer i,j + real(dp) prec + + complex(dp) v + do i=1,size(s1,1) + do j=1,size(s1,2) + v=s1(i,j) + s2(i,j)=c_clean(v,prec) + enddo + enddo + end SUBROUTINE clean_matrix + + SUBROUTINE clean_vector(S1,S2,prec) + implicit none + complex(dp) s1(:),s2(:) + complex(dp) v + real(dp) prec + integer i + + do i=1,size(s1,1) + v=s1(i) + s2(i)=c_clean(v,prec) + enddo + end SUBROUTINE clean_vector + + + SUBROUTINE clean_c_universal_taylor(S1,S2,prec,relative) + implicit none + type (c_UNIVERSAL_TAYLOR),INTENT(INOUT)::S2 + type (c_UNIVERSAL_TAYLOR), intent(INOUT):: s1 + type (c_UNIVERSAL_TAYLOR) u,w + real(dp) prec,siz + complex(dp) c + integer i,count,j,cnv + logical,optional :: relative + logical rel + real(dp), allocatable :: norm(:) + + rel=.false. + if(present(relative)) rel=relative + if(rel) then + allocate(norm(0:c_%no+1)) + norm=0 + do i=1,s1%n + siz=abs(s1%c(i)) + cnv=0 + do j=1,s1%nv + cnv=cnv+s1%J(i,j) + enddo + norm(cnv)=siz+norm(cnv) + enddo + endif + call alloc(u,S1%n,S1%NV,S1%nd2) + + U%J=s1%J + + + + if(rel) then + count=0 + do i=1,s1%n + siz=abs(s1%c(i)) + cnv=0 + do j=1,s1%nv + cnv=cnv+s1%J(i,j) + enddo + if(norm(cnv)==0) then + U%c(i)=c_clean(s1%c(i),prec) + else + U%c(i)=c_clean(s1%c(i),prec=prec*norm(cnv)) + ! if( siz/norm(cnv) 0) count=count+1 + enddo + + + else + count=0 + do i=1,s1%n + U%c(i)=c_clean(s1%c(i),prec) + if(abs(U%c(i))>0) count=count+1 + enddo + endif + + call alloc(w,count,u%NV,u%nd2) + count=0 + do i=1,s1%n + if(abs(U%c(i))>0) then + count=count+1 + w%c(count)=U%c(i) + w%j(count,1:u%nv)=U%J(i,1:u%nv) + endif + enddo + + call kill(s2) + call alloc(s2,u%N,u%NV,u%nd2) + + s2=w + + if(rel) deallocate(norm ) + + call kill(u) + call kill(w) + + END SUBROUTINE clean_c_universal_taylor + + SUBROUTINE c_clean_taylor(S1,S2,prec,relative) + implicit none + type (c_taylor),INTENT(INOUT)::S2 + type (c_taylor), intent(INOUT):: s1 + real(dp) prec,siz + INTEGER ipresent,n,I,illa,k,cnv,j1 + complex(dp) value,v,y +! real(dp) x ,xx + INTEGER, allocatable :: j(:) + + type (c_taylor) t + + logical, optional :: relative + logical rel + real(dp), allocatable :: norm(:) + +integer nv + nv=c_%nv + allocate(j(nv)) + rel=.false. + if(present(relative)) rel=relative + if(rel) then + allocate(norm(0:c_%no)) + norm=0 + ipresent=1 + + + call c_dacycle(S1%I,ipresent,value,n) + + + do i=1,N + call c_dacycle(S1%I,i,value,illa,j) + v=0.0_dp + + + siz=abs(value) + cnv=0 + do j1=1,c_%nv + cnv=cnv+j(j1) + enddo + norm(cnv)=siz+norm(cnv) + enddo + endif + + + + call alloc(t) + t=0.0_dp + ipresent=1 + call c_dacycle(S1%I,ipresent,value,n) + + + do i=1,N + call c_dacycle(S1%I,i,value,illa,j) + v=0.0_dp + + y=value + if(rel) then + cnv=0 + do j1=1,c_%nv + cnv=cnv+j(j1) + enddo + v=c_clean(y,prec=prec*norm(cnv)) + else + v=c_clean(y,prec) + endif + ! xx=y + ! x=value + ! if(abs(xx)>prec) v=x + ! xx=aimag(y) + ! x=aimag(value) + ! if(abs(xx)>prec) v=v+i_*x + t=t+(v.cmono.j) + ENDDO +if(rel) deallocate(norm) + s2=t + deallocate(j) + call kill(t) + + END SUBROUTINE c_clean_taylor + +! SUBROUTINE c_clean_taylor(S1,S2,prec,r) +! implicit none +! type (c_taylor),INTENT(INOUT)::S2 +! type (c_taylor), intent(INOUT):: s1 +! real(dp) prec +! INTEGER ipresent,n,I,illa,k +! complex(dp) value,v,y +! +! INTEGER, allocatable :: j(:) +! type(c_ray),optional :: r +! type (c_taylor) t +! type(c_ray) s + + ! s%x=0 + ! s%s1=0 + ! s%s2=0 + ! s%s3=0 + ! s%x=1.0_dp + ! if(present(r)) s=r + ! call alloc(t) + ! t=0.0_dp + ! ipresent=1 + ! call c_dacycle(S1%I,ipresent,value,n) + ! + ! allocate(j(nv)) + +! do i=1,N +! call c_dacycle(S1%I,i,value,illa,j) +! v=0.0_dp +! if(present(r)) then +! y=value +! do k=1,nv +! y=y*r%x(k)**j(k) +! enddo +! else +! y=value +! endif +! v=c_clean(y,prec) + + + ! t=t+(v.cmono.j) + ! ENDDO + ! s2=t + ! deallocate(j) + ! call kill(t) + ! + ! END SUBROUTINE c_clean_taylor + + SUBROUTINE c_clean_linear_map(S1,S2,prec) + implicit none + type (c_linear_map),INTENT(INOUT)::S2 + type (c_linear_map), intent(INOUT):: s1 + real(dp) prec + INTEGER i,j + + s2=s1 + + do i=1,6 + do j=1,6 + s2%mat(i,j)=c_clean(s2%mat(i,j),prec) + enddo + enddo + + + do i=0,3 + do j=0,6 + s2%q(i,j)=c_clean(s2%q(i,j),prec) + enddo + enddo + + END SUBROUTINE c_clean_linear_map + + SUBROUTINE c_clean_spinmatrix(S1,S2,prec,relative) ! spin routine + implicit none + type (c_spinmatrix),INTENT(INOUT)::S2 + type (c_spinmatrix), intent(INOUT):: s1 + real(dp) prec + integer i,j + logical, optional :: relative + + do i=1,3 + do j=1,3 + call clean(s1%s(i,j),s2%s(i,j),prec,relative) + enddo + enddo + + + END SUBROUTINE c_clean_spinmatrix + + SUBROUTINE c_clean_quaternion(S1,S2,prec,relative) ! spin routine + implicit none + type (c_quaternion),INTENT(INOUT)::S2 + type (c_quaternion), intent(INOUT):: s1 + real(dp) prec + integer i,j + logical, optional :: relative + + + do i=0,3 + + call clean(s1%x(i),s2%x(i),prec,relative) + + enddo + + + END SUBROUTINE c_clean_quaternion + + SUBROUTINE c_clean_spinor(S1,S2,prec,relative) ! spin routine + implicit none + type (c_spinor),INTENT(INOUT)::S2 + type (c_spinor), intent(INOUT):: s1 + real(dp) prec + logical, optional :: relative + integer i + + do i=1,3 + call c_clean_taylor(s1%v(i),s2%v(i),prec,relative) + enddo + + END SUBROUTINE c_clean_spinor + + SUBROUTINE c_clean_damap(S1,S2,prec,relative) + implicit none + type (c_damap),INTENT(INOUT)::S2 + type (c_damap), intent(INOUT):: s1 + real(dp) prec + integer i + logical, optional :: relative + + do i=1,nd2 + call c_clean_taylor(s1%v(i),s2%v(i),prec,relative) + enddo + + call c_clean_spinmatrix(s1%s,s2%s,prec,relative) + call c_clean_quaternion(s1%q,s2%q,prec,relative) + + END SUBROUTINE c_clean_damap + + SUBROUTINE c_clean_cm(S1,S2,prec) + implicit none + type (c_damap),INTENT(INOUT)::S2 + type (c_damap), intent(INOUT):: s1 + real(dp) prec,a,b + integer i,j,n + + n=size(s1%cm,1) + + do i=1,n + do j=1,n + a=real(s1%cm(i,j)) + if(abs(a)0) count=count+1 + ! enddo + ! + ! call alloc(w,count,u%NV,u%nd2) + ! count=0 + ! do i=1,s1%n + ! if(abs(U%c(i))>0) then + ! count=count+1 + ! w%c(count)=U%c(i) + ! w%j(count,1:u%nv)=U%J(i,1:u%nv) + ! endif + ! enddo + ! + ! call kill(s2) + ! call alloc(s2,u%N,u%NV,u%nd2) + ! + ! s2=w + + + ! call kill(u) + ! call kill(w) + + ! END SUBROUTINE clean_c_universal_taylor + + + +!!!! to change between coasting and focusing + subroutine c_bmad_reinit(ndpt_bmad) !,spin + implicit none + integer, intent(in) :: ndpt_bmad + ndptb=0 + ndpt=ndpt_bmad + if(ndpt==0) then + ndct=0 ! 1 if coasting, otherwise 0 + ndc2t=0 ! 2 if coasting, otherwise 0 + else + ndct=1 ! 1 if coasting, otherwise 0 + ndc2t=2 ! 2 if coasting, otherwise 0 + ndptb=ndpt_bmad+1 + if(mod(ndpt_bmad,2)==0) ndptb=ndpt_bmad-1 + endif + nd2t=nd2-2*rf-ndc2t ! size of harmonic oscillators minus modulated clocks + ndt=nd2t/2 ! ndt number of harmonic oscillators minus modulated clocks + nd2harm=nd2t+2*rf !!!! total dimension of harmonic phase space + ndharm=ndt+rf !!!! total number of harmonic planes +call set_1(NO,ND2,ND,NDPT,NV, np) +call set_2(NO,ND2,ND,NDPT,NV, np) +call set_3(NO,ND2,ND,NDPT,NV, np) +call set_4(NO,ND2,ND,NDPT,NV, np) +call set_5(NO,ND2,ND,NDPT,NV, np) +call set_6(NO,ND2,ND,NDPT,NV, np) +!call locally_set_da_pointers() + +q_phasor=c_phasor() +qi_phasor=ci_phasor() + +end subroutine c_bmad_reinit + +! typical input if code PTC is calling c_init +!call c_init(c_%NO,c_%nd,c_%np,c_%ndpt,number_of_ac_plane,ptc=my_true) + + subroutine c_init(NO1,NV1,np1,ndpt1,AC_rf,ptc) !,spin + implicit none + integer, intent(in) :: NO1,NV1 + integer, optional :: np1,ndpt1,AC_RF + logical(lp), optional :: ptc !spin, + integer ndpt_ptc,i,i1,i2,i3,i4,i5,i6,noo,j + real tim(0:10) + logical present_newtpsa + ! if(use_quaternion) spin_def_tune=1 + !NP=np1 + !NO=no1 + !ND=nv1 ! nv1 is just nd if map used + !ND2=2*nd !!!! total dimension of phase space + !nv=nd2+np !!!! total number of Taylor variables + +! present(np1) always true if called for PTC bona fide maps + nphere=0 +if(use_np.and.present(np1)) nphere=np1 + + ip_mat=0; jp_mat=0; jt_mat=0; + + do i=1,3 + ip_mat(i,2*i-1,2*i-1)=1 + ip_mat(i,2*i,2*i)=1 + jp_mat(i,2*i-1,2*i)=1 + jp_mat(i,2*i,2*i-1)=-1 + jt_mat(2*i-1,2*i)=1 + jt_mat(2*i,2*i-1)=-1 + enddo + +formatlf(1)="(6(1x,g23.16,1x)) " +formatlf(2)="(1(25x),5(1x,g23.16,1x))" +formatlf(3)="(2(25x),4(1x,g23.16,1x))" +formatlf(4)="(3(25x),4(1x,g23.16,1x))" +formatlf(5)="(4(25x),2(1x,g23.16,1x))" +formatlf(6)="(5(25x),1(1x,g23.16,1x))" + + ! order_gofix=no1 + + if(associated(dz_c)) then + present_newtpsa=newtpsa + newtpsa=previous_newtpsa + call kill(dz_c) + deallocate(dz_c) + nullify(dz_c) + newtpsa=present_newtpsa + endif + + call set_da_pointers() + + + C_STABLE_DA=.true. + C_watch_user=.true. + read77=.true. + print77=.true. + if(c_last_tpsa/=0) then + present_newtpsa=newtpsa + newtpsa=previous_newtpsa + call c_DEASSIGN + newtpsa=present_newtpsa + c_last_tpsa=1 + endif + + ndpt_ptc=0 + + RF=0 +IF(PRESENT(AC_RF)) RF=AC_RF + +!!!! some junk for PTC's bad handling !!!! +if(present(ptc)) then + if(ptc) then + + if(ndpt1/=0) then + ndpt_ptc=2*rf + endif + endif +endif +!!!! end of some junk for PTC's bad handling !!!! + + NDPT=0 + ndptb=0 +!spin_on=MY_FALSE +if(present(np1)) then ! This true for any map calculation + if(present(ndpt1) ) then + if(ndpt1/=0) then +!REAL FPP moves ndpt to 7 when there is one modulation plane +! now put back to 5 if ndpt_ptc=2 +! This is due to horrible gymnastic in the real FPP used by PTC + NDPT= NDPT1-ndpt_ptc +! location of time, ndptb is computed here ndptb=6 + ndptb=ndpt+1 + if(mod(ndpt,2)==0) ndptb=ndpt-1 + endif + endif + NP=np1 + NO=no1 + ND=nv1 ! nv1 is just nd if map used + ND2=2*nd !!!! total dimension of phase space + nv=nd2+np !!!! total number of Taylor variables + + ndct=iabs(ndpt-ndptb) ! 1 if coasting, otherwise 0 + ndc2t=2*ndct ! 2 if coasting, otherwise 0 + nd2t=nd2-2*rf-ndc2t ! size of harmonic oscillators minus modulated clocks + ndt=nd2t/2 ! ndt number of harmonic oscillators minus modulated clocks + nd2harm=nd2t+2*rf !!!! total dimension of harmonic phase space + ndharm=ndt+rf !!!! total number of harmonic planes + +else + if(present(ndpt1).or.present(AC_RF).or.present(ptc)) then + write(6,*) " error : nonsensical input in c_init" + read(5,*) + stop + endif + NP=0 + NO=no1 + ND=0 + ND2=0 + NDPT=0 + NV=nv1 + + ndct=0 ! 1 if coasting, otherwise 0 + ndc2t=0 ! 2 if coasting, otherwise 0 + nd2t=0 ! size of harmonic oscillators minus modulated clocks + ndt=0 ! ndt number of harmonic oscillators minus modulated clocks + nd2harm=0 !!!! total dimension of harmonic phase space + ndharm=0 !!!! total number of harmonic planes + +endif +!if(present(spin)) spin_on=spin +!write(6,*) "ndc2t,nd2t,nd2harm,nd2" +!write(6,*) ndc2t,nd2t,nd2harm,nd2 + +!if(no==2.and.newtpsa) call dacctt2datest + call c_daini(no,nv,0) +if(no==2.and.newtpsa) call c_dacctt2datest(ND2) + + + c_master=0 ! master=1 2002.12.2 + + CALL c_ASSIGN + + allocate(dz_c(nv)) + call alloc(dz_c) + + do i=1,nv + dz_c(i)=1.0_dp.cmono.i + enddo + +! for fast inversion in + sj=0 + do i=1,3 + sj(2*i-1,2*i)=1 + sj(2*i,2*i-1)=-1 + enddo +if(present(np1)) then + q_phasor=c_phasor() + + qi_phasor=ci_phasor() + + + + endif +c_%rf=>rf +c_%nd2t=>nd2t +c_%nd2harm=>nd2harm +c_%ndc2t=>ndc2t +c_%no=>NO +c_%NDPT=>NDPT +c_%ND=>ND +c_%ND2=>ND2 +c_%ndptb=>ndptb +c_%nv=>nv ! 2022.11.11 +!c_%ndpt=>ndpt + +c_%pos_of_delta=>pos_of_delta +c_%pos_of_delta=0 +if(ndpt/=0) then + c_%pos_of_delta=ndpt +else +! i=nv1-nd2t-2*rf-np + if(nd==0) then + c_%pos_of_delta=0 + else + c_%pos_of_delta=nd2t-1 +ndpt_bmad + endif + + ! if(i/=0) c_%pos_of_delta=nd2t-1 +ndpt_bmad +endif + + + +c_%np=c_%nv-c_%nd2harm-c_%ndc2t + +! ndct=iabs(ndpt-ndptb) ! 1 if coasting, otherwise 0 +! ndc2t=2*ndct ! 2 if coasting, otherwise 0 +! nd2t=nd2-2*rf-ndc2t ! size of harmonic oscillators minus modulated clocks +! ndt=nd2t/2 ! ndt number of harmonic oscillators minus modulated clocks +! nd2harm=nd2t+2*rf !!!! total dimension of harmonic phase space +! ndharm=ndt+rf !!!! total number of harmonic planes +! + ind_spin(1,1)=1+6;ind_spin(1,2)=2+6;ind_spin(1,3)=3+6; + ind_spin(2,1)=4+6;ind_spin(2,2)=5+6;ind_spin(2,3)=6+6; + ind_spin(3,1)=7+6;ind_spin(3,2)=8+6;ind_spin(3,3)=9+6; + ind_spin0(1,1)=1;ind_spin0(1,2)=2;ind_spin0(1,3)=3; + ind_spin0(2,1)=4;ind_spin0(2,2)=5;ind_spin0(2,3)=6; + ind_spin0(3,1)=7;ind_spin0(3,2)=8;ind_spin0(3,3)=9; + k1_spin(1)=1;k2_spin(1)=1; + k1_spin(2)=1;k2_spin(2)=2; + k1_spin(3)=1;k2_spin(3)=3; + k1_spin(4)=2;k2_spin(4)=1; + k1_spin(5)=2;k2_spin(5)=2; + k1_spin(6)=2;k2_spin(6)=3; + k1_spin(7)=3;k2_spin(7)=1; + k1_spin(8)=3;k2_spin(8)=2; + k1_spin(9)=3;k2_spin(9)=3; + + if(ndpt==6) then + jp_mat(3,6,5)=0 + jp_mat(3,5,6)=1 + endif + if(ndpt==5) then + jp_mat(3,6,5)=-1 + jp_mat(3,5,6)=0 + endif + +if(.not.(use_np.and.present(np1))) npara_fpp=0 + + + end subroutine c_init + + + +! FPP alone +! Avoid using in PTC. Use init with an internal_state +! c_init_all(NO1,nd_or_nv,np1,ndpt1,AC_rf,ptc) +! Initiatializes both the real and complex package +! c_init_all(NO1,nd_or_nv) powers the TPSA packages with no maps: almost useless +! c_init_all(NO1,nd_or_nv,np1) with np1=0,1,2,.... present, powers also maps +! for example, c_init_all(1,2,0) allows maps with no parameters of 2-degrees of freedom +! AC_rf,ptc are reserved by the code PTC: avoid using in a non-ptc application +! init_map_all(NO1,ND1,NP1,NDPT1) call also be used, NP1,NDPT1 are optional then. + + + + subroutine init_map_all(NO1,ND1,NP1,NDPT1) + implicit none + integer NO1,ND1 + integer,optional :: NDPT1,NP1 + logical(lp) PACKAGE1 + integer ndptt,i,np11 + np11=0 + if(present(np1)) np11=np1 + call init(NO1,ND1,NP11,NDPT1) + call c_init(NO1,nd1,np11,ndpt1,0,ptc=my_false) + end subroutine init_map_all + +!!! init for ci_tpsa alone no PTC + subroutine c_init_all(NO1,nd_or_nv,np1,ndpt1,AC_rf,ptc) !,spin + implicit none + integer, intent(in) :: NO1,nd_or_nv + integer, optional :: np1,ndpt1,AC_RF + logical(lp), optional :: ptc + call c_init(NO1,nd_or_nv,np1,ndpt1,AC_rf,ptc) + if(present(np1)) then + call init(NO,nd,np,ndpt) + else + call init(NO,nd_or_nv) + endif + c_%nd2t=>nd2t +c_%nd2harm=>nd2harm +c_%ndc2t=>ndc2t +c_%no=>NO +c_%NDPT=>NDPT +c_%ND=>ND +c_%ND2=>ND2 +c_%ndptb=>ndptb +c_%nv=>nv +!c_%ndpt=>ndpt + + ind_spin(1,1)=1+6;ind_spin(1,2)=2+6;ind_spin(1,3)=3+6; + ind_spin(2,1)=4+6;ind_spin(2,2)=5+6;ind_spin(2,3)=6+6; + ind_spin(3,1)=7+6;ind_spin(3,2)=8+6;ind_spin(3,3)=9+6; + k1_spin(1)=1;k2_spin(1)=1; + k1_spin(2)=1;k2_spin(2)=2; + k1_spin(3)=1;k2_spin(3)=3; + k1_spin(4)=2;k2_spin(4)=1; + k1_spin(5)=2;k2_spin(5)=2; + k1_spin(6)=2;k2_spin(6)=3; + k1_spin(7)=3;k2_spin(7)=1; + k1_spin(8)=3;k2_spin(8)=2; + k1_spin(9)=3;k2_spin(9)=3; + end subroutine c_init_all + + subroutine c_etcct(x,n1,y,n2,z) +!* + implicit none + ! Z=XoY + integer i,nt,n1,k,n2 + integer,dimension(lnv)::ie,iv + integer,dimension(:)::x,y,z + if(.not.c_stable_da) return + + nt=nv-n2 + if(nt.gt.0) then + do k=1,nt + call c_etall1(ie(k)) + enddo + do i=n2+1,nv + call c_davar(ie(i-n2),(0.0_dp,0.0_dp),i) + enddo + do i=n2+1,nv + iv(i)=ie(i-n2) + enddo + endif + do i=1,n2 + iv(i)=y(i) + enddo + + call c_dacct(x,n1,iv,nv,z,n1) + + + + + if(nt.gt.0) then + do k=1,nt + call c_DADAL1(ie(k)) + enddo + endif + return + end subroutine c_etcct + + subroutine c_etinv(x,y) +!* + implicit none + ! Y=X^-1 + integer i + type(c_damap) ie1,ie2 + type(c_damap), intent(inout):: x,y + logical rad1 + + if(.not.c_stable_da) return + ie1%n=nv;ie2%n=nv; + call alloc(ie1) + call alloc(ie2) + do i=1,x%n + ie1%v(i)=x%v(i) + enddo + do i=x%n+1,nv + ie1%v(i)=1.0_dp.cmono.i + enddo + + + call c_dainv(ie1%v(1:nv)%i,nv,ie2%v(1:nv)%i,nv) + do i=1,x%n + y%v(i)=ie2%v(i) + enddo + +if(use_quaternion) THEN + rad1=assume_da_map + ! assume_da_map=.false. + + y%q=x%q*y + + y%q=y%q**(-1) + assume_da_map=rad1 + +else + y%s=x%s*y + call c_inv_as(y%s,y%s) +endif + + call kill(ie1) + + call kill(ie2) + + end subroutine c_etinv + + subroutine c_etpin(x,y,jind) +!* + implicit none + ! Y=X^-1 + integer i,jind(:) + type(c_damap) ie1,ie2 + type(c_damap), intent(inout):: x,y + if(.not.c_stable_da) return + + ie1%n=nv;ie2%n=nv; + call alloc(ie1) + call alloc(ie2) + do i=1,x%n + ie1%v(i)=x%v(i) + enddo + do i=x%n+1,nv + ie1%v(i)=1.0_dp.cmono.i + enddo + + call c_dapint(ie1%v(1:nv)%i,nv,ie2%v(1:nv)%i,nv,jind) + do i=1,x%n + y%v(i)=ie2%v(i) + enddo + + call kill(ie1) + + call kill(ie2) + + end subroutine c_etpin + + + + FUNCTION transform_vector_field_by_map(S1,S2) + implicit none + TYPE (c_vector_field) transform_vector_field_by_map + TYPE (c_vector_field), INTENT (IN) :: S1 + TYPE (c_damap), INTENT (IN) :: S2 + TYPE (c_damap) s2i + integer localmaster + integer i,k + IF(.NOT.C_STABLE_DA) then + transform_vector_field_by_map%v%i=0 + RETURN + endif + + localmaster=c_master + + + transform_vector_field_by_map%n=S1%n + + call c_ass_vector_field(transform_vector_field_by_map) + + call alloc(s2i) + + + s2i=s2**(-1) + + do k=1,s2%n + transform_vector_field_by_map%v(k)=0.0e0_dp + c_master=localmaster + do i=1,s2%n + transform_vector_field_by_map%v(k)=s1%v(i)*(s2i%v(k).d.i)+transform_vector_field_by_map%v(k) + enddo + enddo + + do k=1,s2%n + transform_vector_field_by_map%v(k)=transform_vector_field_by_map%v(k)*s2 + enddo + + transform_vector_field_by_map%nrmax=s1%nrmax + transform_vector_field_by_map%eps=s1%eps + + call kill(s2i) + c_master=localmaster + if(complex_extra_order==1.and.special_extra_order_1) transform_vector_field_by_map=transform_vector_field_by_map.cut.no + + END FUNCTION transform_vector_field_by_map + + FUNCTION c_concat(S1,S2) + implicit none + TYPE (c_damap) c_concat + TYPE (c_damap), INTENT (IN) :: S1, S2 + TYPE (c_damap) t1,t2,tempnew + + complex(dp) M2t(6,6),M2(6,6) + integer i + logical(lp) rad1,rad2 + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_concat%v%i=0 + RETURN + endif + localmaster=c_master + c_concat%n=s1%n + call c_assmap(c_concat) + t1%n=s1%n + t2%n=s2%n + tempnew%n=t1%n + call alloc(t1);call alloc(t2);call alloc(tempnew); + + + + t1=s1;t2=s2; + +! Code for S1 o S2 +! removes the constant part since these are da maps + do i=1,t1%n + t1%v(i)=t1%v(i)-(t1%v(i).sub.'0') + enddo + do i=1,t2%n + t2%v(i)=t2%v(i)-(t2%v(i).sub.'0') + enddo + +! calls to the concatanator in C_dabnew.f90 + call c_etcct(t1%v%i,t1%n,t2%v%i,t2%n,tempnew%v%i) +! The constant part at the end of the orbit (not necessary) + if(add_constant_part_concat) then + do i=1,t1%n + tempnew%v(i)=tempnew%v(i)+(s1%v(i).sub.'0') + enddo + endif + + if(use_quaternion) then + rad1=assume_da_map + + t1%q = t1%q*t2 + + tempnew%q=t1%q*t2%q + + assume_da_map=rad1 + else + t1%s = t1%s*t2 + tempnew%s=t1%s*t2%s + endif + + ! t1%q = t1%q*t2 + ! t1%s = t1%s*t2 + ! tempnew%s=t1%s*t2%s + ! tempnew%q=t1%q*t2%q + if(.not.c_similarity) then + call c_check_rad(t1%e_ij,rad1) + call c_check_rad(t2%e_ij,rad2) + + ! if((rad1.or.rad2).and.nd2==6) then + if(rad1.or.rad2) then + ! write(6,*) " stochastic " + t1=t1.sub.1 + m2=t1 + m2t=transpose(m2) + tempnew%e_ij=t1%e_ij + matmul(matmul(m2,t2%e_ij),m2t) + endif +endif + ! if(use_quaternion) then +! tempnew%sm=matmul(t1%sm,t2%sm) + ! tempnew%d_spin=matmul(t1%sm,t2%d_spin) + t1%d_spin + ! tempnew%damps=matmul(matmul(t1%sm,t2%damps),transpose(t1%sm)) + t1%damps + ! tempnew%b_kin=matmul(matmul(t1%sm,t2%b_kin),transpose(t1%sm)) + t1%b_kin + ! endif + c_concat=tempnew + c_concat%x0=s2%x0 +! c_concat%tpsa=s2%tpsa + if(complex_extra_order==1.and.special_extra_order_1) c_concat=c_concat.cut.no + + + call kill(t1);call kill(t2);call kill(tempnew); + c_master=localmaster + + END FUNCTION c_concat + + + + FUNCTION c_concat_tpsa(s2,s1) + implicit none + TYPE (c_damap) c_concat_tpsa,t2,t1,tempnew,t0 + TYPE (c_damap), INTENT (IN) :: s2, s1 + complex(dp) f2it(6,6),f2i(6,6),ct,c0 + + logical(lp) rad1,rad2 + integer localmaster,i + IF(.NOT.C_STABLE_DA) then + c_concat_tpsa%v%i=0 + RETURN + endif + localmaster=c_master + c_concat_tpsa%n=s2%n + call c_assmap(c_concat_tpsa) + t0%n=s2%n + t2%n=s2%n + t1%n=s1%n + tempnew%n=t2%n + call alloc(t2,t1,tempnew,t0); + + + + t2=s2;t1=s1; + + t1%x0=0 + t2%x0=0 + do i=1,s1%n + t1%v(i)=t1%v(i)-s2%x0(i) + enddo + do i=1,s1%n + tempnew%v(i)=t2%v(i).o.t1 + enddo + + + + !call c_etcct(t2%v%i,t2%n,t1%v%i,t1%n,tempnew%v%i) + + + tempnew%s = t2%s.o.t1 + tempnew%q = t2%q.o.t1 + + + tempnew%s=tempnew%s*t1%s + tempnew%q=tempnew%q*t1%q + + + if(.not.c_similarity) then + call c_check_rad(t2%e_ij,rad1) + call c_check_rad(t1%e_ij,rad2) + + if((rad1.or.rad2).and.nd2==6) then + ! write(6,*) " stochastic " + t2=t2.sub.1 + f2i=t2 + f2it=transpose(f2i) + tempnew%e_ij=t2%e_ij + matmul(matmul(f2i,t1%e_ij),f2it) + endif +endif + c_concat_tpsa=tempnew + c_concat_tpsa%x0=s1%x0 +! c_concat_tpsa%tpsa=s1%tpsa + + if(complex_extra_order==1.and.special_extra_order_1) c_concat_tpsa=c_concat_tpsa.cut.no + + + call kill(t2,t1,tempnew,t0); + c_master=localmaster + + END FUNCTION c_concat_tpsa + + +! FUNCTION MAKETPSA(s1) +! implicit none +! TYPE (c_damap) MAKETPSA,t0,t1 +! TYPE (c_damap), INTENT (IN) :: s1 +! +! integer localmaster,i +! IF(.NOT.C_STABLE_DA) then +! MAKETPSA%v%i=0 +! RETURN +! endif +! localmaster=c_master +! MAKETPSA%n=s1%n +! call c_assmap(MAKETPSA) + +! t0%n=s1%n +! t1%n=s1%n +! call alloc(t0,t1); +! t1=s1 +! t0=1 +! do i=1,s1%n +! t0%v(i)=t0%v(i)-s1%x0(i) +! enddo +! call c_etcct(t1%v%i,t1%n,t0%v%i,t0%n,t1%v%i) +! +! +! t1%s = t1%s.o.t0 +! t1%q = t1%q.o.t0 +! +! +! + +! MAKETPSA=t1 +! MAKETPSA%tpsa=.true. +! MAKETPSA%x0=s1%x0 +! +! call kill(t0,t1); +! c_master=localmaster +! end FUNCTION MAKETPSA +! +! FUNCTION MAKEDA(s1) +! implicit none +! TYPE (c_damap) MAKEDA,t0,t1 +! TYPE (c_damap), INTENT (IN) :: s1 + +! integer localmaster,i +! IF(.NOT.C_STABLE_DA) then +! MAKEDA%v%i=0 +! RETURN +! endif +! localmaster=c_master +! MAKEDA%n=s1%n +! call c_assmap(MAKEDA) + +! t0%n=s1%n +! t1%n=s1%n +! call alloc(t0,t1); +! t1=s1 +! t0=1 +! do i=1,s1%n +! t0%v(i)=t0%v(i)+s1%x0(i) +! enddo +! call c_etcct(t1%v%i,t1%n,t0%v%i,t0%n,t1%v%i) +! +! t1%s = t1%s.o.t0 +! t1%q = t1%q.o.t0 + +! MAKEDA=t1 +! MAKEDA%tpsa=.false. +! MAKEDA%x0=s1%x0 +! +! call kill(t0,t1); +! c_master=localmaster +! end FUNCTION MAKEDA +! + + FUNCTION c_adjoint(S1,S2,i) + implicit none + TYPE (c_damap) c_adjoint + TYPE (c_damap), INTENT (IN) :: S1, S2 + integer , INTENT (IN) :: i + logical(lp) rad1 + integer localmaster + complex(dp) f2it(6,6),f2i(6,6) + IF(.NOT.C_STABLE_DA) then + c_adjoint%v%i=0 + RETURN + endif + + localmaster=c_master + + c_similarity=my_true + c_adjoint%n=s1%n + call c_assmap(c_adjoint) + + if(i==1) then +!1BMAD$c_adjoint.tex + c_adjoint=s1*s2*s1**(-1) +!2BMAD + else + c_adjoint=s1**(-1)*s2*s1 + endif + + if(c_similarity) then + call c_check_rad(s2%e_ij,rad1) + + f2i=0 + f2it=0 ! 2022.11.13 + + ! if(rad1.and.nd2==6) then + if(rad1) then + ! write(6,*) " stochastic " + if(i==1) then + f2i=s1 + else + f2i=s1**(-1) + endif + f2it=transpose(f2i) + c_adjoint%e_ij= matmul(matmul(f2i,s2%e_ij),f2it) + endif + + endif + + if(complex_extra_order==1.and.special_extra_order_1) c_adjoint=c_adjoint.cut.no + c_similarity=my_false + + c_master=localmaster + + END FUNCTION c_adjoint + + FUNCTION c_adjoint_vec(S1,S2,i) + implicit none + TYPE (c_damap) c_adjoint_vec + TYPE (c_vector_field), INTENT (IN) :: S1 + TYPE (c_damap), INTENT (IN) :: S2 + integer , INTENT (IN) :: i + logical(lp) rad1 + integer localmaster + complex(dp) f2it(6,6),f2i(6,6) + IF(.NOT.C_STABLE_DA) then + c_adjoint_vec%v%i=0 + RETURN + endif + + localmaster=c_master + + c_similarity=my_true + + c_adjoint_vec%n=s1%n + call c_assmap(c_adjoint_vec) + + if(i==1) then + c_adjoint_vec=exp(s1)*s2 + c_adjoint_vec=exp(-s1,c_adjoint_vec) + else + c_adjoint_vec=exp(-s1)*s2 + c_adjoint_vec=exp(s1,c_adjoint_vec) + endif + + if(c_similarity) then + call c_check_rad(s2%e_ij,rad1) + + f2i=0 + f2it=0 + + ! if(rad1.and.nd2==6) then + if(rad1) then + ! write(6,*) " stochastic " + if(i==1) then + f2i=exp(s1) + else + f2i=exp(-s1) + endif + f2it=transpose(f2i) + c_adjoint_vec%e_ij= matmul(matmul(f2i,s2%e_ij),f2it) + endif + + endif + + if(complex_extra_order==1.and.special_extra_order_1) c_adjoint_vec=c_adjoint_vec.cut.no + + c_similarity=my_false + + c_master=localmaster + + END FUNCTION c_adjoint_vec + + + + + FUNCTION c_spinmatrix_spinmatrix(S1,S2) ! spin routine function + implicit none + TYPE (c_spinmatrix) c_spinmatrix_spinmatrix + TYPE (c_spinmatrix), INTENT (IN) :: S1, S2 + integer i,j,k + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_spinmatrix_spinmatrix%s%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinmatrix(c_spinmatrix_spinmatrix) + + + c_spinmatrix_spinmatrix=0 + + do i=1,3 + do j=1,3 + do k=1,3 + c_spinmatrix_spinmatrix%s(i,k)=s1%s(i,j)*s2%s(j,k)+c_spinmatrix_spinmatrix%s(i,k) + enddo + enddo + enddo + + + c_master=localmaster + + END FUNCTION c_spinmatrix_spinmatrix + + FUNCTION c_spinmatrix_mul_cray(S1,S2) ! spin routine function + implicit none + TYPE (c_ray) c_spinmatrix_mul_cray + TYPE (c_spinmatrix), INTENT (IN) :: S1 + TYPE (c_ray), INTENT (IN) :: S2 + TYPE (c_spinmatrix) temp + integer i,j + + call alloc(temp) + temp=s1 + c_spinmatrix_mul_cray=s2 + temp=c_concat_spinmatrix_ray(temp,s2) !.o.s2 + c_spinmatrix_mul_cray%s1=0.0_dp + c_spinmatrix_mul_cray%s2=0.0_dp + c_spinmatrix_mul_cray%s3=0.0_dp + + do i=1,3 + do j=1,3 + + c_spinmatrix_mul_cray%s1(i)=temp%s(i,j)*s2%s1(j)+c_spinmatrix_mul_cray%s1(i) + c_spinmatrix_mul_cray%s2(i)=temp%s(i,j)*s2%s2(j)+c_spinmatrix_mul_cray%s2(i) + c_spinmatrix_mul_cray%s3(i)=temp%s(i,j)*s2%s3(j)+c_spinmatrix_mul_cray%s3(i) + + enddo + enddo +! c_spinmatrix_mul_cray%x=s2%x + + call kill(temp) + END FUNCTION c_spinmatrix_mul_cray + + FUNCTION c_quaternion_mul_cray(S1,S2) ! spin routine function + implicit none + TYPE (c_ray) c_quaternion_mul_cray + TYPE (c_quaternion), INTENT (IN) :: S1 + TYPE (c_ray), INTENT (IN) :: S2 + TYPE (c_quaternion) temp + TYPE (complex_quaternion) tempc,mc + integer i,j + + + + call alloc(temp) + mc%x=0.0_dp + temp=s1 + c_quaternion_mul_cray=s2 + tempc=c_concat_quaternion_ray(temp,s2) !.o.s2 + c_quaternion_mul_cray%q=tempc + mc%x=0.0_dp + mc%x(1:3)=s2%s1 + mc=tempc*mc*tempc**(-1) + c_quaternion_mul_cray%s1=mc%x(1:3) + mc%x=0.0_dp + mc%x(1:3)=s2%s2 + mc=tempc*mc*tempc**(-1) + c_quaternion_mul_cray%s2=mc%x(1:3) + mc%x=0.0_dp + mc%x(1:3)=s2%s3 + mc=tempc*mc*tempc**(-1) + c_quaternion_mul_cray%s3=mc%x(1:3) + ! c_quaternion_mul_cray%q=tempc*s2%q*tempc**(-1) +! c_quaternion_mul_cray%x=s2%x + + call kill(temp) + END FUNCTION c_quaternion_mul_cray + + FUNCTION c_spinmatrix_spinor(S1,S2) ! spin routine function + implicit none + TYPE (c_spinor) c_spinmatrix_spinor + TYPE (c_spinmatrix), INTENT (IN) :: S1 + TYPE (c_spinor), INTENT (IN) :: S2 + integer localmaster + integer i,j + IF(.NOT.C_STABLE_DA) then + c_spinmatrix_spinor%v%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinor(c_spinmatrix_spinor) + + + c_spinmatrix_spinor=0 + + do i=1,3 + do j=1,3 + c_spinmatrix_spinor%v(i)=s1%s(i,j)*s2%v(j)+c_spinmatrix_spinor%v(i) + enddo + enddo + + c_master=localmaster + + END FUNCTION c_spinmatrix_spinor + + FUNCTION spinmatrix_spinmatrix(S1,S2) ! spin routine function + implicit none + TYPE (c_spinmatrix) spinmatrix_spinmatrix + TYPE (c_spinmatrix), INTENT (IN) :: S1 + TYPE (c_spinmatrix), INTENT (IN) :: S2 + integer localmaster + integer i,j,k + + IF(.NOT.C_STABLE_DA) then + spinmatrix_spinmatrix%s(1,1)%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinmatrix(spinmatrix_spinmatrix) + + + spinmatrix_spinmatrix=0 + + do i=1,3 + do j=1,3 + do k=1,3 + spinmatrix_spinmatrix%s(i,k)=spinmatrix_spinmatrix%s(i,k)+ s1%s(i,j)*s1%s(j,k) + enddo + enddo + enddo + + + c_master=localmaster + + END FUNCTION spinmatrix_spinmatrix + + + FUNCTION c_transpose(S1) + implicit none + TYPE (c_damap) c_transpose,t1 + TYPE (c_damap), INTENT (IN) :: S1 + complex(dp) f2t(ndim2t,ndim2t) + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_transpose%v%i=0 + RETURN + endif + + localmaster=c_master + + c_transpose%n=s1%n + call c_assmap(c_transpose) + + t1%n=s1%n + + call alloc(t1); + + t1=s1.sub.1 + + f2t=t1 + f2t=transpose(f2t) + + c_transpose=f2t + + + call kill(t1); + + c_master=localmaster + + END FUNCTION c_transpose + + + + + FUNCTION c_spinor_cmap(S1,S2) ! spin routine function + implicit none + TYPE (c_spinor) c_spinor_cmap + TYPE (c_damap), INTENT (IN) :: S2 + TYPE (c_spinor), INTENT (IN) :: S1 + integer localmaster + integer i + IF(.NOT.C_STABLE_DA) then + c_spinor_cmap%v%i=0 + RETURN + endif + + localmaster=c_master + + call c_ass_spinor(c_spinor_cmap) + + + c_spinor_cmap=0 + + do i=1,3 + c_spinor_cmap%v(i)=s1%v(i)*s2 + enddo + + if(complex_extra_order==1.and.special_extra_order_1) c_spinor_cmap=c_spinor_cmap.cut.no + c_master=localmaster + + END FUNCTION c_spinor_cmap + + FUNCTION c_spinor_cmap_tpsa(S1,S2) ! spin routine function + implicit none + TYPE (c_spinor) c_spinor_cmap_tpsa + TYPE (c_damap), INTENT (IN) :: S2 + TYPE (c_spinor), INTENT (IN) :: S1 + integer localmaster + integer i + IF(.NOT.C_STABLE_DA) then + c_spinor_cmap_tpsa%v%i=0 + RETURN + endif + + localmaster=c_master + + call c_ass_spinor(c_spinor_cmap_tpsa) + + + c_spinor_cmap_tpsa=0 + + do i=1,3 + c_spinor_cmap_tpsa%v(i)=s1%v(i).o.s2 + enddo + + if(complex_extra_order==1.and.special_extra_order_1) c_spinor_cmap_tpsa=c_spinor_cmap_tpsa.cut.no + c_master=localmaster + + END FUNCTION c_spinor_cmap_tpsa + + FUNCTION c_complex_spinmatrix(S1,S2) ! spin routine function + implicit none + TYPE (c_spinmatrix) c_complex_spinmatrix + TYPE (c_spinmatrix), INTENT (IN) :: S2 + complex (dp), INTENT (IN) :: S1 + integer i,j + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_complex_spinmatrix%s%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinmatrix(c_complex_spinmatrix) + + + c_complex_spinmatrix=0 + + do i=1,3 + do j=1,3 + c_complex_spinmatrix%s(i,j)=s1*s2%s(i,j) + enddo + enddo + + + c_master=localmaster + + END FUNCTION c_complex_spinmatrix + + FUNCTION c_spinmatrix_add_spinmatrix(S1,S2) ! spin routine function + implicit none + TYPE (c_spinmatrix) c_spinmatrix_add_spinmatrix + TYPE (c_spinmatrix), INTENT (IN) :: S1, S2 + integer i,j + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_spinmatrix_add_spinmatrix%s%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinmatrix(c_spinmatrix_add_spinmatrix) + + + c_spinmatrix_add_spinmatrix=0 + + do i=1,3 + do j=1,3 + + c_spinmatrix_add_spinmatrix%s(i,j)=s1%s(i,j)+s2%s(i,j) + + enddo + enddo + + + c_master=localmaster + + END FUNCTION c_spinmatrix_add_spinmatrix + + FUNCTION c_spinmatrix_sub_spinmatrix(S1,S2) ! spin routine function + implicit none + TYPE (c_spinmatrix) c_spinmatrix_sub_spinmatrix + TYPE (c_spinmatrix), INTENT (IN) :: S1, S2 + integer i,j + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_spinmatrix_sub_spinmatrix%s%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinmatrix(c_spinmatrix_sub_spinmatrix) + + + c_spinmatrix_sub_spinmatrix=0 + + do i=1,3 + do j=1,3 + + c_spinmatrix_sub_spinmatrix%s(i,j)=s1%s(i,j)-s2%s(i,j) + + enddo + enddo + + + c_master=localmaster + + END FUNCTION c_spinmatrix_sub_spinmatrix + + + + FUNCTION c_spinor_add_spinor(S1,S2) ! spin routine function + implicit none + TYPE (c_spinor) c_spinor_add_spinor + TYPE (c_spinor), INTENT (IN) :: S1, S2 + integer i + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_spinor_add_spinor%v%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinor(c_spinor_add_spinor) + + do i=1,3 + c_spinor_add_spinor%v(i)=s1%v(i)+s2%v(i) + enddo + + c_master=localmaster + + END FUNCTION c_spinor_add_spinor + + + FUNCTION c_spinor_sub_spinor(S1,S2) ! spin routine function + implicit none + TYPE (c_spinor) c_spinor_sub_spinor + TYPE (c_spinor), INTENT (IN) :: S1, S2 + integer i + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_spinor_sub_spinor%v%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinor(c_spinor_sub_spinor) + + do i=1,3 + c_spinor_sub_spinor%v(i)=s1%v(i)-s2%v(i) + enddo + + c_master=localmaster + + END FUNCTION c_spinor_sub_spinor + + FUNCTION c_taylor_spinmatrix(S1,S2) ! spin routine function + implicit none + TYPE (c_spinmatrix) c_taylor_spinmatrix + TYPE (c_spinmatrix), INTENT (IN) :: S2 + TYPE (c_taylor), INTENT (IN) :: S1 + integer i,j + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_taylor_spinmatrix%s(i,j)%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinmatrix(c_taylor_spinmatrix) + + do i=1,3 + do j=1,3 + c_taylor_spinmatrix%s(i,j) =s1*s2%s(i,j) + enddo + enddo + + c_master=localmaster + + END FUNCTION c_taylor_spinmatrix + + FUNCTION c_taylor_spinor(S1,S2) ! spin routine function + implicit none + TYPE (c_spinor) c_taylor_spinor + TYPE (c_spinor), INTENT (IN) :: S2 + TYPE (c_taylor), INTENT (IN) :: S1 + integer i + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_taylor_spinor%v%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinor(c_taylor_spinor) + + do i=1,3 + c_taylor_spinor%v(i)=s1*s2%v(i) + enddo + + + c_master=localmaster + + END FUNCTION c_taylor_spinor + + FUNCTION c_complex_spinor(S1,S2) ! spin routine function + implicit none + TYPE (c_spinor) c_complex_spinor + TYPE (c_spinor), INTENT (IN) :: S2 + complex(dp), INTENT (IN) :: S1 + integer i + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_complex_spinor%v%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinor(c_complex_spinor) + + do i=1,3 + c_complex_spinor%v(i)=s1*s2%v(i) + enddo + + + c_master=localmaster + + END FUNCTION c_complex_spinor + + FUNCTION c_real_spinor(S1,S2) ! spin routine function + implicit none + TYPE (c_spinor) c_real_spinor + TYPE (c_spinor), INTENT (IN) :: S2 + real(dp), INTENT (IN) :: S1 + integer i + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_real_spinor%v%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinor(c_real_spinor) + + do i=1,3 + c_real_spinor%v(i)=s1*s2%v(i) + enddo + + c_master=localmaster + + END FUNCTION c_real_spinor + +FUNCTION c_real_spinmatrix(S1,S2) ! spin routine function + implicit none + TYPE (c_spinmatrix) c_real_spinmatrix + TYPE (c_spinmatrix), INTENT (IN) :: S2 + real(dp), INTENT (IN) :: S1 + integer i,j + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_real_spinmatrix%S(I,J)%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinMATRIX(c_real_spinmatrix) + + do i=1,3 + do j=1,3 + c_real_spinmatrix%S(I,J)=s1*s2%S(I,J) + enddo + enddo + + c_master=localmaster + + END FUNCTION c_real_spinmatrix + + FUNCTION c_spinor_spinor(S1,S2) ! spin routine function + implicit none + TYPE (c_spinor) c_spinor_spinor + TYPE (c_spinor), INTENT (IN) :: S2 + TYPE (c_spinor), INTENT (IN) :: S1 + + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_spinor_spinor%v%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinor(c_spinor_spinor) + + c_spinor_spinor%v(1)=s1%v(2)*s2%v(3)-s1%v(3)*s2%v(2) + c_spinor_spinor%v(2)=s1%v(3)*s2%v(1)-s1%v(1)*s2%v(3) + c_spinor_spinor%v(3)=s1%v(1)*s2%v(2)-s1%v(2)*s2%v(1) + if(complex_extra_order==1.and.special_extra_order_1) c_spinor_spinor=c_spinor_spinor.cut.no + + c_master=localmaster + + END FUNCTION c_spinor_spinor + + FUNCTION c_trxspinmatrix( S1, S2 ) ! spin routine function + implicit none + TYPE (c_spinmatrix) c_trxspinmatrix + TYPE (c_spinmatrix), INTENT (IN) :: S1 + TYPE (c_damap), INTENT (IN) :: S2 + integer i,j + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_trxspinmatrix%s%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinmatrix(c_trxspinmatrix) + + do i=1,3 + do j=1,3 + c_trxspinmatrix%s(i,j)=s1%s(i,j)*s2 + enddo + enddo + if(complex_extra_order==1.and.special_extra_order_1) c_trxspinmatrix=c_trxspinmatrix.cut.no + c_master=localmaster + + END FUNCTION c_trxspinmatrix + + FUNCTION c_trxquaternion( S1, S2 ) ! spin routine function + implicit none + TYPE (c_quaternion) c_trxquaternion + TYPE (c_quaternion), INTENT (IN) :: S1 + TYPE (c_damap), INTENT (IN) :: S2 + integer i + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_trxquaternion%x(1)%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_quaternion(c_trxquaternion) + + do i=0,3 + + c_trxquaternion%x(i)=s1%x(i)*s2 + enddo + + if(complex_extra_order==1.and.special_extra_order_1) c_trxquaternion=c_trxquaternion.cut.no + c_master=localmaster + + END FUNCTION c_trxquaternion + + FUNCTION c_trxquaternion_tpsa( S1, S2 ) ! spin routine function + implicit none + TYPE (c_quaternion) c_trxquaternion_tpsa + TYPE (c_quaternion), INTENT (IN) :: S1 + TYPE (c_damap), INTENT (IN) :: S2 + integer i + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_trxquaternion_tpsa%x(1)%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_quaternion(c_trxquaternion_tpsa) + + do i=0,3 + + c_trxquaternion_tpsa%x(i)=s1%x(i).o.s2 + enddo + + if(complex_extra_order==1.and.special_extra_order_1) c_trxquaternion_tpsa=c_trxquaternion_tpsa.cut.no + c_master=localmaster + + END FUNCTION c_trxquaternion_tpsa + + + FUNCTION c_trxspinmatrixda( S1, S2 ) ! spin routine function + implicit none + TYPE (c_spinmatrix) c_trxspinmatrixda + TYPE (c_spinmatrix), INTENT (IN) :: S1 + TYPE (c_damap), INTENT (IN) :: S2 + integer i,j + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_trxspinmatrixda%s%i=0 + RETURN + endif + localmaster=c_master + + call c_ass_spinmatrix(c_trxspinmatrixda) + + do i=1,3 + do j=1,3 + c_trxspinmatrixda%s(i,j)=s1%s(i,j).o.s2 + enddo + enddo + if(complex_extra_order==1.and.special_extra_order_1) c_trxspinmatrixda=c_trxspinmatrixda.cut.no + c_master=localmaster + + END FUNCTION c_trxspinmatrixda + + + + FUNCTION c_trxtaylor( S1, S2 ) + implicit none + TYPE (c_taylor) c_trxtaylor + TYPE (c_taylor), INTENT (IN) :: S1 + TYPE (c_damap), INTENT (IN) :: S2 + TYPE (c_damap) S22,temp + integer i + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_trxtaylor%i=0 + RETURN + endif + localmaster=c_master + + + + + call c_ASStaylor(c_trxtaylor) + + s22%n=s2%n + call alloc(s22) + temp%n=s2%n + call alloc(temp) + + s22=s2 + do i=1,s22%n + s22%v(i)=s22%v(i)-(s22%v(i).sub.'0') + enddo + + temp%v(1)=s1 + call c_etcct(temp%v%i,temp%n,s22%v%i,s22%n,temp%v%i) + ! temp=temp*s22 !(to prevent a recursive call in c_concat) + + c_trxtaylor=temp%v(1) + + call kill(temp) + call kill(s22) + c_master=localmaster + + END FUNCTION c_trxtaylor + + + FUNCTION c_trxtaylor_da( S1, S2 ) + implicit none + TYPE (c_taylor) c_trxtaylor_da + TYPE (c_taylor), INTENT (IN) :: S1 + TYPE (c_damap), INTENT (IN) :: S2 + TYPE (c_damap) S22,temp + + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_trxtaylor_da%i=0 + RETURN + endif + localmaster=c_master + + + + + call c_ASStaylor(c_trxtaylor_da) + + s22%n=s2%n + call alloc(s22) + temp%n=s2%n + call alloc(temp) + + s22=s2 + ! do i=1,s22%n + ! s22%v(i)=s22%v(i)-(s22%v(i).sub.'0') + ! enddo + + temp%v(1)=s1 + call c_etcct(temp%v%i,temp%n,s22%v%i,s22%n,temp%v%i) + ! temp=temp*s22 !(to prevent a recursive call in c_concat) + + c_trxtaylor_da=temp%v(1) + + call kill(temp) + call kill(s22) + c_master=localmaster + + END FUNCTION c_trxtaylor_da + + + FUNCTION c_concat_spinor_ray( S1, S2 ) + implicit none + TYPE (c_spinor) c_concat_spinor_ray + TYPE (c_spinor), INTENT (IN) :: S1 + TYPE (c_ray), INTENT (IN) :: S2 + integer i + integer localmaster + + IF(.NOT.C_STABLE_DA) then + c_concat_spinor_ray=0 + RETURN + endif + + localmaster=c_master + + call c_ass_spinor(c_concat_spinor_ray) + + do i=1,3 + c_concat_spinor_ray%v(i)=s1%v(i).o.s2 + enddo + + c_master=localmaster + + END FUNCTION c_concat_spinor_ray + + + FUNCTION c_concat_spinmatrix_ray( S1, S2 ) + implicit none + TYPE (c_spinmatrix) c_concat_spinmatrix_ray + TYPE (c_spinmatrix), INTENT (IN) :: S1 + TYPE (c_ray), INTENT (IN) :: S2 + integer i,j + integer localmaster + + IF(.NOT.C_STABLE_DA) then + c_concat_spinmatrix_ray=1 + RETURN + endif + + localmaster=c_master + + call c_ass_spinmatrix(c_concat_spinmatrix_ray) + + do i=1,3 + do j=1,3 + c_concat_spinmatrix_ray%s(i,j)=s1%s(i,j).o.s2 + enddo + enddo + + c_master=localmaster + + END FUNCTION c_concat_spinmatrix_ray + + FUNCTION c_concat_quaternion_ray( S1, S2 ) + implicit none + TYPE (c_quaternion) c_concat_quaternion_ray + TYPE (c_quaternion), INTENT (IN) :: S1 + TYPE (c_ray), INTENT (IN) :: S2 + integer i,j + integer localmaster + + IF(.NOT.C_STABLE_DA) then + c_concat_quaternion_ray=1.0_dp + RETURN + endif + + localmaster=c_master + + call c_ass_quaternion(c_concat_quaternion_ray) + + do i=0,3 + c_concat_quaternion_ray%x(i)=s1%x(i).o.s2 + enddo + c_master=localmaster + + END FUNCTION c_concat_quaternion_ray + + + + FUNCTION c_concat_c_ray( S1, S2 ) + implicit none + complex(dp) c_concat_c_ray + TYPE (c_taylor), INTENT (IN) :: S1 + TYPE (c_ray), INTENT (IN) :: S2 + TYPE (c_damap) temp + integer i + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_concat_c_ray=0 + RETURN + endif + localmaster=c_master + + c_concat_c_ray=0.0_dp + + + temp%n=nv + call alloc(temp) + + do i=1,nv + temp%v(i)=s2%x(i) !-s2%x0(i) + enddo + + + c_concat_c_ray=s1.o.temp + + + call kill(temp) + c_master=localmaster + + END FUNCTION c_concat_c_ray + + + FUNCTION c_concat_map_ray( S1, S2 ) + implicit none + TYPE (c_ray) c_concat_map_ray + TYPE (c_damap), INTENT (IN) :: S1 + TYPE (c_ray), INTENT (IN) :: S2 + TYPE (c_quaternion) q + TYPE (c_damap) tempmap,tempmap1 + + real(dp) norm + integer i + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_concat_map_ray%x=0 + RETURN + endif + localmaster=c_master + c_concat_map_ray=s2 + ! c_concat_map_ray%x=0.0_dp + ! c_concat_map_ray%n=s2%n + + tempmap%n=nv !s1%n + tempmap1%n=nv !s1%n + call alloc(tempmap,tempmap1) + + ! norm=0 + ! do i=1,s1%n + ! norm=norm+abs(s2%x0(i)) + ! enddo + + ! if(norm>eps_tpsalie.and.S1%tpsa) then + ! write(6,*) "Both c_ray and c_damap are tpsa: not allowed " + ! stop 997 + ! endif + + ! if(S1%tpsa) then + do i=1,s1%n + tempmap%v(i)=s2%x(i) + tempmap%x0(i)=s1%x0(i) + tempmap1%v(i)=s1%v(i) + enddo + do i=s1%n+1,nv + tempmap%v(i)=s2%x(i) + tempmap1%v(i)=1.0_dp.cmono.i + enddo + ! else + ! do i=1,s1%n + ! tempmap%v(i)=s2%x(i) + ! tempmap%x0(i)=0.d0 !s1%x(i) + ! enddo + ! endif + if(use_quaternion) then + tempmap%q=s2%q + tempmap1%q=s1%q + + endif + + tempmap=tempmap1.o.tempmap + + if(use_quaternion) then + c_concat_map_ray%q=tempmap%q !s2 + ! else + + ! c_concat_map_ray%s=tempmap%s !s2 + endif + ! order important because the first one puts s2%x into c_concat_map_ray%x + + do i=1,s1%n + c_concat_map_ray%x(i)=tempmap%v(i) + enddo + call kill(tempmap,tempmap1) + c_master=localmaster + + END FUNCTION c_concat_map_ray + + FUNCTION c_concat_vector_field_ray( S1, S2 ) + implicit none + TYPE (c_ray) c_concat_vector_field_ray + TYPE (c_vector_field), INTENT (IN) :: S1 + TYPE (c_ray), INTENT (IN) :: S2 + + + integer i + + IF(.NOT.C_STABLE_DA) then + c_concat_vector_field_ray%x=0 + RETURN + endif + + + c_concat_vector_field_ray%x=0.0_dp + + do i=1,s1%n + c_concat_vector_field_ray%x(i)=s1%v(i).o.s2 + enddo + + + END FUNCTION c_concat_vector_field_ray + + FUNCTION c_bra_v_ct( S1, S2 ) + implicit none + TYPE (c_taylor) c_bra_v_ct + TYPE (c_vector_field), INTENT (IN) :: S1 + TYPE (c_taylor), INTENT (IN) :: S2 + TYPE (c_taylor) S22 + + integer i + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_bra_v_ct%i=0 + RETURN + endif + localmaster=c_master + + + call c_ASStaylor(c_bra_v_ct) + + call alloc(s22 ) + + + s22=(0.0_dp,0.0_dp) + + do i=1,s1%n + + s22=s22 + s1%v(i)*(s2.d.i) + + enddo + + c_bra_v_ct=s22 + + call kill(s22 ) + c_master=localmaster + + END FUNCTION c_bra_v_ct + + + FUNCTION c_bra_v_q( S1, S2 ) + implicit none + TYPE (c_quaternion) c_bra_v_q + TYPE (c_vector_field), INTENT (IN) :: S1 + TYPE (c_quaternion), INTENT (IN) :: S2 + TYPE (c_quaternion) S22 + integer i,j + integer localmaster + + IF(.NOT.C_STABLE_DA) then + c_bra_v_q%x(0)%i=0 + RETURN + endif + localmaster=c_master + + localmaster=c_master + call c_ass_quaternion(c_bra_v_q) + + + call alloc(s22 ) + + + s22=0.0_dp + + do i=1,s1%n + do j=0,3 + s22%x(j)=s22%x(j) + s1%v(i)*(s2%x(j).d.i) + enddo + enddo + + c_bra_v_q=s22 + + call kill(s22 ) + c_master=localmaster + + END FUNCTION c_bra_v_q + + + FUNCTION c_bra_v_so3( S1, S2 ) + implicit none + TYPE (c_spinmatrix) c_bra_v_so3 + TYPE (c_vector_field), INTENT (IN) :: S1 + TYPE (c_spinmatrix), INTENT (IN) :: S2 + integer i,j,k + integer localmaster + + IF(.NOT.C_STABLE_DA) then + c_bra_v_so3%s(1,1)%i=0 + RETURN + endif + localmaster=c_master + + localmaster=c_master + call c_ass_spinmatrix(c_bra_v_so3) + + + c_bra_v_so3=0 + + do i=1,s1%n + do j=1,3 + do k=1,3 + c_bra_v_so3%s(j,k)=c_bra_v_so3%s(j,k) + s1%v(i)*(s2%s(j,k).d.i) + enddo + enddo + enddo + + + c_master=localmaster + + END FUNCTION c_bra_v_so3 + + FUNCTION c_bra_v_dm( S1, S2 ) + implicit none + TYPE (c_damap) c_bra_v_dm + TYPE (c_vector_field), INTENT (IN) :: S1 + TYPE (c_damap), INTENT (IN) :: S2 + TYPE (c_damap) S22 + + integer i,j,k + integer localmaster + IF(.NOT.C_STABLE_DA) then + c_bra_v_dm%v%i=0 + RETURN + endif + localmaster=c_master + + c_bra_v_dm%n=s2%n + call c_ASSmap(c_bra_v_dm) + + s22%n=s2%n + call alloc(s22) + + + s22=0 + + do i=1,s1%n + do j=1,s2%n + s22%v(j)=s22%v(j)+ s1%v(i)*(s2%v(j).d.i) + enddo + +! do j=1,3 +! do k=1,3 +! s22%s%s(j,k)=s22%s%s(j,k)+ s1%v(i)*(s2%s%s(j,k).d.i) +! enddo +! enddo + enddo +!! from the spin itself in the vector field replacing the above and adding s1%om +!etienne + if(use_quaternion) then + s22%q=s1*s2%q + else + s22%s=s1*s2%s + endif + + if(complex_extra_order==1.and.special_extra_order_1) c_bra_v_dm=c_bra_v_dm.cut.no + c_bra_v_dm=s22 + + call kill(s22) + c_master=localmaster + + END FUNCTION c_bra_v_dm + + + + FUNCTION POWMAP( S1, R2 ) + implicit none + TYPE (c_damap) POWMAP + TYPE (c_damap), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: R2 + TYPE (c_damap) S11 + INTEGER I,R22 + integer localmaster + IF(.NOT.C_STABLE_DA) then + POWMAP%v%i=0 + RETURN + endif + localmaster=c_master + + POWMAP%N=s1%n + call c_assmap(POWMAP) + + s11%n=s1%n + call alloc(s11) + + + + s11=1 + + R22=IABS(R2) + DO I=1,R22 + s11=s1*s11 + ENDDO + + + + IF(R2.LT.0) THEN + + ! CALL c_etinv1(S11%v%i,S11%v%i,s11%n) + CALL c_etinv(S11,S11) + + ENDIF + + + + powmap=s11 + if(complex_extra_order==1.and.special_extra_order_1) powmap=powmap.cut.no + + call kill(s11) + + c_master=localmaster + + END FUNCTION POWMAP + + FUNCTION POWMAP_INV( S1, R2 ) + implicit none + TYPE (c_damap) POWMAP_INV + TYPE (c_damap), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: R2(:) + TYPE (c_damap) S11 + INTEGER I,jn(lnv) + integer localmaster + IF(.NOT.C_STABLE_DA) RETURN + localmaster=c_master + + +stop 2353 + + do i=1,lnv + jn(i)=0 + enddo + do i=1,nd2 + jn(i)=R2(I) + enddo + + call c_assmap(POWMAP_INV) + + call alloc(s11) + + + call etpin(S1%V%i,S11%v%i,jn) + + + POWMAP_INV=s11 + + + ! powmap=junk + call kill(s11) + + c_master=localmaster + + END FUNCTION POWMAP_INV + + FUNCTION pow_tpsaMAP( S1, R2 ) + implicit none + TYPE (c_damap) pow_tpsaMAP + TYPE (c_damap), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: R2 + TYPE (c_damap) S11 + INTEGER I,R22 + integer localmaster + complex(dp) v(lnv),x0(lnv) + v=0 + IF(.NOT.C_STABLE_DA) then + pow_tpsaMAP%v%i=0 + RETURN + endif + localmaster=c_master + + pow_tpsaMAP%N=s1%n + call c_assmap(pow_tpsaMAP) + + s11%n=s1%n + + call alloc(s11) + + + do i=1,s1%n + s11%v(i)=(1.0_dp.cmono.i) + s1%x0(i) + enddo + s11%x0=s1%x0 + +! etienne bug 2024.03.07 + s11%q=1.0_dp + + + R22=IABS(R2) + DO I=1,R22 + + s11=s1.o.s11 + + ENDDO + IF(R2.LT.0) THEN + + + + + v=0 +x0=s11%x0 +s11%x0=0 + + do i=1,s11%n + v(i)=s11%v(i).sub.'0' + s11%v(i)=s11%v(i)-v(i) ! making it DA + enddo + + ! CALL c_etinv1(S11%v%i,S11%v%i,s11%n) + CALL c_etinv(S11,S11) +!!!! exchange roles of x0 and constant part of TPSA + do i=1,s11%n + s11%v(i)=s11%v(i)+x0(i) + enddo + s11%x0=v + + + ENDIF + + + + pow_tpsaMAP=s11 + if(complex_extra_order==1.and.special_extra_order_1) pow_tpsaMAP=pow_tpsaMAP.cut.no + + call kill(s11) + + c_master=localmaster + + END FUNCTION pow_tpsaMAP + + FUNCTION pow_tpsaMAPnew( S1, R2 ) + implicit none + TYPE (c_damap) pow_tpsaMAPnew + TYPE (c_damap), INTENT (IN) :: S1 + INTEGER, INTENT (IN) :: R2 + TYPE (c_damap) S11 + INTEGER I,R22 + integer localmaster + complex(dp) v(lnv),x0(lnv) + v=0 + IF(.NOT.C_STABLE_DA) then + pow_tpsaMAPnew%v%i=0 + RETURN + endif + localmaster=c_master + + pow_tpsaMAPnew%N=s1%n + call c_assmap(pow_tpsaMAPnew) + + s11%n=s1%n + + call alloc(s11) + + + do i=1,s1%n + s11%v(i)=1.0_dp.cmono.i + enddo + s11%x0=s1%x0 + do i=1,s11%n + s11%v(i)=s11%v(i)+(s1%v(i).sub.'0') + enddo + + ! R22=IABS(R2) + ! DO I=1,R22 + + ! s11=s1.o.s11 + + ! ENDDO +s11=s1 + IF(R2.LT.0) THEN + + + + + v=0 +x0=s11%x0 +s11%x0=0 + + do i=1,s11%n + v(i)=s11%v(i).sub.'0' + s11%v(i)=s11%v(i)-v(i) ! making it DA + enddo + + ! CALL c_etinv1(S11%v%i,S11%v%i,s11%n) + CALL c_etinv(S11,S11) +!!!! exchange roles of x0 and constant part of TPSA + do i=1,s11%n + s11%v(i)=s11%v(i)+x0(i) + enddo + s11%x0=v + + + ENDIF + + + + pow_tpsaMAPnew=s11 + if(complex_extra_order==1.and.special_extra_order_1) pow_tpsaMAPnew=pow_tpsaMAPnew.cut.no + + call kill(s11) + + c_master=localmaster + + END FUNCTION pow_tpsaMAPnew + + + + FUNCTION POWMAPs( SS1, R2 ) + implicit none + TYPE (c_spinmatrix) POWMAPs + TYPE (c_spinmatrix), INTENT (IN) :: SS1 + INTEGER, INTENT (IN) :: R2 + TYPE (c_damap) s1,S11 + INTEGER I,R22 + integer localmaster + IF(.NOT.C_STABLE_DA) then + POWMAPs%s%i=0 + RETURN + endif + localmaster=c_master + + + call c_ass_spinmatrix(POWMAPs) + + s11%n=nv + call alloc(s11) + s1%n=nv + call alloc(s1) + + s11=1 + s1=1 + s1%s=ss1 + + R22=IABS(R2) + DO I=1,R22 + s11=s1*s11 + ENDDO + + IF(R2.LT.0) THEN + + ! CALL c_etinv1(S11%v%i,S11%v%i,s11%n) + CALL c_etinv(S11,S11) + + ENDIF + + + + powmaps=s11%s + if(complex_extra_order==1.and.special_extra_order_1) powmaps=powmaps.cut.no + + call kill(s11) + call kill(s1) + + c_master=localmaster + + END FUNCTION POWMAPs + + SUBROUTINE c_EQUALMAP(S2,S1) +!* + implicit none + type (c_damap),INTENT(inOUT)::S2 + type (c_damap),INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + + + do i=1,min(s1%n,s2%n) + s2%v(i)=s1%v(i) + enddo + if(use_quaternion) then + s2%q=s1%q + else + s2%s=s1%s + endif + s2%e_ij=s1%e_ij + s2%x0=s1%x0 +! s2%tpsa=s1%tpsa + ! if(use_quaternion) then +! s2%sm=s1%sm + ! s2%damps=s1%damps + ! s2%d_spin=s1%d_spin + ! s2%b_kin=s1%b_kin + ! endif + END SUBROUTINE c_EQUALMAP + + SUBROUTINE c_MAP_VEC(S2,S1) +!* + implicit none + type (c_damap),INTENT(inOUT)::S2 + type (c_vector_field),INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + + S2=1 + do i=1,min(s1%n,s2%n) + s2%v(i)=s1%v(i) + enddo + if(use_quaternion) then + s2%q=s1%q + else + write(6,*) " Cannot store spinor in map " + stop 777 + endif + END SUBROUTINE c_MAP_VEC + + SUBROUTINE c_VEC_MAP(S2,S1) +!* + implicit none + type (c_damap),INTENT(in)::S1 + type (c_vector_field),INTENT(INOUT)::S2 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + + S2=0 + do i=1,min(s1%n,s2%n) + s2%v(i)=s1%v(i) + enddo + if(use_quaternion) then + s2%q=s1%q + else + write(6,*) " Cannot store map in spinor " + stop 777 + endif + END SUBROUTINE c_VEC_MAP + + SUBROUTINE c_EQUALVEC(S2,S1) +!* + implicit none + type (c_vector_field),INTENT(inOUT)::S2 + type (c_vector_field),INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + + do i=1,s1%n + s2%v(i)=s1%v(i) + enddo + + + if(use_quaternion) then + do i=0,3 + s2%q%x(i)=s1%q%x(i) + enddo + else +! s2%h=s1%h + s2%L=s1%L + endif + + + s2%n=s1%n + s2%nrmax=s1%nrmax + s2%eps=s1%eps + + END SUBROUTINE c_EQUALVEC + + SUBROUTINE c_EQUALVECqua(S2,S1) +!* +! fills the quaternion into SO(3) %L equivalent + implicit none + type (c_vector_field),INTENT(inOUT)::S2 + type (c_quaternion),INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + call c_check_snake + + s2%L%s(3,2)= 2.0_dp*s1%x(1) + s2%L%s(2,3)=-2.0_dp*s1%x(1) + s2%L%s(2,1)= 2.0_dp*s1%x(3) + s2%L%s(1,2)=-2.0_dp*s1%x(3) + s2%L%s(1,3)= 2.0_dp*s1%x(2) + s2%L%s(3,1)=-2.0_dp*s1%x(2) + + END SUBROUTINE c_EQUALVECqua + +SUBROUTINE c_EQUALcray(S2,S1) +!* + implicit none + type (c_ray),INTENT(inOUT)::S2 + integer,INTENT(IN)::S1 + + s2%x=0.0_dp + s2%n=0 +! s2%x0=0.0_dp + s2%s1=0.0_dp + s2%s2=0.0_dp + s2%s3=0.0_dp + s2%s1(1)=1 + s2%s2(2)=1 + s2%s3(3)=1 + s2%q=0.0_dp + s2%q%x(s1)=1.0_dp + END SUBROUTINE c_EQUALcray + + SUBROUTINE c_IdentityEQUALMAP(S2,S1) +!* + implicit none + type (c_damap),INTENT(inOUT)::S2 + integer,INTENT(IN)::S1 + integer i + real(dp) s1r + IF(.NOT.C_STABLE_DA) RETURN + + ! if(old) then + s2%s=s1 + s1r=s1 + s2%q=s1r + IF(S1.EQ.1) then + do i=1,s2%n + s2%v(i)=1.0_dp.cmono.i + enddo +! s2%s=1 + elseIF(S1.EQ.0) then + do i=1,s2%n + s2%v(i)=(0.0_dp,0.0_dp) + enddo +! s2%s=0 + endif + + s2%e_ij=0.0_dp +! s2%damps=0.0_dp +! s2%d_spin=0.0_dp +! s2%b_kin=0.0_dp +! s2%sm=0.0_dp +! do i=1,3 +! s2%sm(i,i)=1.0_dp +! enddo + END SUBROUTINE c_IdentityEQUALMAP + + + SUBROUTINE c_zero_constant_in_MAP(S2) +!* + implicit none + type (c_damap),INTENT(inOUT)::S2 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + do i=1,s2%n + s2%v(i)=s2%v(i)-(s2%v(i).sub.'0') + enddo + + END SUBROUTINE c_zero_constant_in_MAP + + + SUBROUTINE c_IdentityEQUALSPIN(S2,S1) +!* + implicit none + type (c_spinmatrix),INTENT(inOUT)::S2 + integer,INTENT(IN)::S1 + integer i,j + IF(.NOT.C_STABLE_DA) RETURN + + + + IF(S1.EQ.1) then + do i=1,3 + do j=1,3 + if(i/=j) then + s2%s(i,j)=(0.0_dp,0.0_dp) + else + s2%s(i,j)=(1.0_dp,0.0_dp) + endif + enddo + enddo + elseIF(S1.EQ.0) then + do i=1,3 + do j=1,3 + s2%s(i,j)=(0.0_dp,0.0_dp) + enddo + enddo + endif + + END SUBROUTINE c_IdentityEQUALSPIN + + SUBROUTINE c_IdentityEQUALSPINOR(S2,S1) +!* + implicit none + type (c_spinor),INTENT(inOUT)::S2 + integer,INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + do i=1,3 + s2%v(i)=(0.0_dp,0.0_dp) + enddo + + IF(S1>0.and.s1<=3) then + s2%v(s1)=(1.0_dp,0.0_dp) + endif + + + END SUBROUTINE c_IdentityEQUALSPINOR + + + SUBROUTINE c_IdentityEQUALVEC(S2,S1) +!* + implicit none + type (c_vector_field),INTENT(inOUT)::S2 + integer,INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + if(s1/=0) then + write(6,*) "c_IdentityEQUALVEC" + stop + endif + do i=1,s2%n + s2%v(i)=(0.0_dp,0.0_dp) + enddo + + if(use_quaternion) then + s2%q=0.0_dp + else + ! do i=1,3 + ! s2%h%v(i)=0.0_dp + ! enddo + S2%L=S1 + endif + END SUBROUTINE c_IdentityEQUALVEC + + + SUBROUTINE c_IdentityEQUALfactored(S2,S1) +!* + implicit none + type (c_factored_lie),INTENT(inOUT)::S2 + integer,INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + + if(s1/=0) then + s2%n=s1 + else + s2%n=no + endif + do i=1,size(s2%f) + s2%f(i)=0 !s1 + enddo + + END SUBROUTINE c_IdentityEQUALfactored + + SUBROUTINE matrixMAPr(S2,S1) +!* + implicit none + complex(dp),INTENT(inOUT)::S2(:,:) !(ndim2,ndim2) + type (c_damap),INTENT(IN)::S1 + integer i,j,JL(lnv) + IF(.NOT.C_STABLE_DA) RETURN + call c_check_snake + + do i=1,lnv + JL(i)=0 + enddo + ! if(old) then + do i=1,min(S1%n,size(s2,1)) + ! do j=1,min(S1%n,size(s2,2)) + do j=1,min(nv,size(s2,2)) + + JL(j)=1 + call c_dapek(S1%v(i)%i,JL,s2(i,j)) + JL(j)=0 + enddo + enddo + + END SUBROUTINE matrixMAPr + + SUBROUTINE r_matrixMAPr(S2,S1) +!* + implicit none + real(dp),INTENT(inOUT)::S2(:,:) !(ndim2,ndim2) + type (c_damap),INTENT(IN)::S1 + integer i,j,JL(lnv) + complex(dp) x + + IF(.NOT.C_STABLE_DA) RETURN + call c_check_snake + + do i=1,lnv + JL(i)=0 + enddo + + ! if(old) then + do i=1,min(S1%n,size(s2,1)) + do j=1,min(nv,size(s2,2)) +! do i=1,S1%n +! do j=1,S1%n + JL(j)=1 + call c_dapek(S1%v(i)%i,JL,x) + s2(i,j)=x + JL(j)=0 + enddo + enddo + + + END SUBROUTINE r_matrixMAPr + + + + + SUBROUTINE matrixvecfr(S2,S1) +!* + implicit none + complex(dp),INTENT(inOUT)::S2(:,:) !(ndim2,ndim2) + type (c_vector_field),INTENT(IN)::S1 + integer i,j,JL(lnv) + IF(.NOT.C_STABLE_DA) RETURN + call c_check_snake + + do i=1,lnv + JL(i)=0 + enddo + ! if(old) then + do i=1,min(S1%n,size(s2,1)) + ! do j=1,min(S1%n,size(s2,2)) + do j=1,min(nv,size(s2,2)) + + JL(j)=1 + call c_dapek(S1%v(i)%i,JL,s2(i,j)) + JL(j)=0 + enddo + enddo + + END SUBROUTINE matrixvecfr + + SUBROUTINE r_matrixvecfr(S2,S1) +!* + implicit none + real(dp),INTENT(inOUT)::S2(:,:) !(ndim2,ndim2) + type (c_vector_field),INTENT(IN)::S1 + integer i,j,JL(lnv) + complex(dp) x + + IF(.NOT.C_STABLE_DA) RETURN + call c_check_snake + + do i=1,lnv + JL(i)=0 + enddo + + ! if(old) then + do i=1,min(S1%n,size(s2,1)) + do j=1,min(nv,size(s2,2)) +! do i=1,S1%n +! do j=1,S1%n + JL(j)=1 + call c_dapek(S1%v(i)%i,JL,x) + s2(i,j)=x + JL(j)=0 + enddo + enddo + + + END SUBROUTINE r_matrixvecfr + + + SUBROUTINE MAPmatrixr(S1,S2) +!* + implicit none + complex(dp),INTENT(in)::S2(:,:) ! (ndim2,ndim2) + type (c_damap),INTENT(inout)::S1 + integer i,j,JL(lnv) + IF(.NOT.C_STABLE_DA) RETURN + do i=1,lnv + JL(i)=0 + enddo + + do i=1,s1%n + s1%v(i)=(0.0_dp,0.0_dp) + enddo + + ! if(old) then + do i=1,min(S1%n,size(s2,1)) + do j=1,min(nv,size(s2,2)) + + + ! do i=1,s1%n !size(s2,1) + ! do j=1,s1%n !,size(s2,2) + JL(j)=1 + call c_dapok(S1%v(i)%i,JL,s2(i,j)) + JL(j)=0 + enddo + enddo + + END SUBROUTINE MAPmatrixr + + SUBROUTINE r_MAPmatrixr(S1,S2) +!* + implicit none + real(dp),INTENT(in)::S2(:,:) ! (ndim2,ndim2) + type (c_damap),INTENT(inout)::S1 + integer i,j,JL(lnv) + complex(dp) x + IF(.NOT.C_STABLE_DA) RETURN + + do i=1,lnv + JL(i)=0 + enddo + + do i=1,s1%n + s1%v(i)=(0.0_dp,0.0_dp) + enddo + + + do i=1,min(S1%n,size(s2,1)) + do j=1,min(nv,size(s2,2)) + + + + ! if(old) then +! do i=1,s1%n !size(s2,1) +! do j=1,s1%n !,size(s2,2) + JL(j)=1 + x=s2(i,j) + call c_dapok(S1%v(i)%i,JL,x) + JL(j)=0 + enddo + enddo + + END SUBROUTINE r_MAPmatrixr + +!!!!!!!!!! TPSA LIE PART !!!!!!! + + +subroutine c_linear_a(xy,a1) +!#internal: normal +!# This routine linearises the linear part of the map ONLY. +!# For a full harmonic system the call c_linear_a(xy,a1) will result in +!# R=a1**(-1)*xy*a1. +!# The map R can be an amplitude dependent rotation, or a rotation followed by a drift +!# in the energy plane, or even a rotation sink if radiation is present. +!# R can also have rotations for clocks concerning AC modulation. (See Chap.4 of my Springer book) + implicit none + integer i,j + type(c_damap), intent(inout) :: xy,a1 + real(dp) reval(ndim2t),imval(ndim2t),vr(ndim2t,ndim2t),vi(ndim2t,ndim2t),vrt(ndim2t,ndim2t),vit(ndim2t,ndim2t) + real(dp) fm0(ndim2t,ndim2t),x(ndim2t/2),xx(ndim2t/2) + integer idef(ndim2t/2) + real(dp), allocatable :: fm(:,:),fmi(:,:),fmii(:,:) + type(c_damap) s1 + type(c_normal_form) n + + if(.not.c_stable_da) return + + + idef=0 + + allocate(fm(xy%n,xy%n),fmi(xy%n,xy%n),fmii(xy%n,xy%n)) + + + fm=xy + fm0=0 + + !!! To understand this, it is better to first understand ndpt=0 + !!! in PTC ndpt=0 includes : nd2=4 and nd2=6 (cavity on) + !!! Ndpt =5 is PTC's coasting beam normalisation + !!! if there are no magnet modulation,then the matrix massaging below will do very little + !!! see explanation below at the "else" + + !!! We are diagonalising a Lie map which is just the transposed + !!! of the matrix in the linear case + !!! The usual nonlinear map acts on rays and so does its matrix. + !!! Lie maps, Hamiltonian operators, act on functions. + !!! In the world of Linear maps, this involves taking the transposed of the matrix + !!! which represents the linear part of the map + if(ndpt==0) then + fm0(1:nd2,1:nd2)=transpose(fm(1:nd2,1:nd2)) + else + if(c_verbose) then + write(6,*) " nd2t,nd2,nd2harm " + write(6,*) nd2t,nd2,nd2harm + endif + ! Consider the following example + ! ndc2t,nd2t,nd2harm,nd2 + ! 2 4 6 8 + ! nd2= total size of phase space + ! + ! ndc2t=2 dimension of coasting phase space (2 or 0), here it is 2 + ! + ! nd2t=4 dimension of pseudo-harmonic phase space due to orbit (not magnet modulations) + ! here it is 4, which is a normal PTC run. + ! in accelerator physics, with mid-plane symmetry, it could be 2. But PTC only permits 4 and 6. + ! + ! nd2harm=6 Total size of pseudo-harmonic planes including magnet modulation. In the above case, + ! nd2-nd2harm=2 So there is a coasting plane. + ! + + !! The purpose of all the gymnastic below is to exchange the order of the planes + ! IF AND ONLY IF the longitudinal is coasting + ! The issue is that call c_eig6(fm0,reval,imval,vr,vi) should be called only on + ! matrix which is pseudo-harmonic. + fmi=0 + fmii=0 + do i=1,nd2t + fmi(i,i)=1 + fmii(i,i)=1 + enddo + fmi(nd2-1,nd2t+1)=1 + fmi(nd2,nd2t+2)=1 + fmii(nd2t+1,nd2-1)=1 + fmii(nd2t+2,nd2)=1 + + do i=1,2*rf + fmi(nd2t+i,nd2t+2+i)=1 + fmii(nd2t+2+i,nd2t+i)=1 + enddo + + ! fmi(1:nd2,1:nd2)=matmul(fmi(1:nd2,1:nd2),fmii(1:nd2,1:nd2)) + + fm0(1:nd2,1:nd2)=matmul( fm(1:nd2,1:nd2),fmii(1:nd2,1:nd2)) + fm0(1:nd2,1:nd2)=matmul( (fmi(1:nd2,1:nd2)),fm0(1:nd2,1:nd2)) + + + fm0(1:nd2harm,1:nd2harm)=transpose(fm0(1:nd2harm,1:nd2harm)) +! The diagonalisation is done only on the planes +! 1...nd2harm which are now in the front of the matrix +! Thus the Coasting beam is moved in the last plane (nd2-1,nd2) + + endif + +!###1 Find complex eigenvalues and eigenvectors + call c_eig6(fm0,reval,imval,vr,vi) + + !! This routine will locate the modulated plane + !! It assumes that the modulated plane are rotations + !! It will fail if some orbital planes are exactly rotations, say beta=1.00000000 and no coupling + call c_locate_modulated_magnet_planes(fm0,idef,reval) + + call alloc(s1) + + if(.not.c_normal_auto) then + + + if(c_verbose) then + write(6,*) " " + do i=1,nd2harm !t + write(6,'(i2,2(1x,G21.14))') i, reval(i),imval(i) + enddo + write(6,*) " " + do i=1,nd2harm !t + write(6,*) i + write(6,'(6(1x,G21.14))') vr(i,1:6) + write(6,'(6(1x,G21.14))') vi(i,1:6) + enddo + endif + +!###2 Trying to locate planes when almost mid-plane symmetric + + call c_locate_planes(vr,vi,idef) + + if(i_piotr(1)==0) then !.and.nd<=ndharm) then + write(6,'(a82)') " The order of the planes has been guessed using the algorithm in c_locate_planes " + write(6,'(a41)') " Hopefully it is correct! Please check! " + write(6,'(a18,100(i2,1x))') " Order guessed -> ",idef(1:ndharm) + + write(6,*) " Manually identify the location of distinct tunes in the order you like " + read(5,*) idef(1:ndharm) + else + + do j=1,size(i_piotr) + idef(j)=i_piotr(j) + enddo + + if(c_verbose) then + write(6,'(a82)') " The order of the planes has been defined by the user with i_piotr array " + write(6,'(a20,100(i2,1x))') " Order defuined -> ",idef(1:ndharm) + endif + + endif + else + !! c_locate_planes tries to locate the planes: important if there is little coupling + !! I suppose that this routine can be refined +!###3 Trying to locate planes when almost mid-plane symmetric + + call c_locate_planes(vr,vi,idef) + if(lielib_print(16)==1) then + do i=1,nd2harm !t + write(6,'(i2,2(1x,G21.14))') i, reval(i),imval(i) + enddo + + write(6,'(a82)') " The order of the planes has been guessed using the algorithm in c_locate_planes " + write(6,'(a41)') " Hopefully it is correct! Please check! " + write(6,'(a18,100(i2,1x))') " Order guessed -> ",idef(1:ndharm) + endif + endif + + +!!!! useless stuff for testing + if(c_mess_up_vector) then + vrt=a_mess*vr-b_mess*vi + vit=a_mess*vi+b_mess*vr + vr=vrt + vi=vit + endif + + x=0.0_dp + xx=1.0_dp + + +!###4 +! Enforce Poisson bracket = 1 +! Zero + + do i=1,ndharm !ndt + + x(i)=0.0_dp + xx(i)=1.0_dp + + !!! Here the Eigenvectors of the transposed matric (Lie map) + !!! are normalised so that the Poisson bracket is one. + !!! If the map is not Hamiltonian (radiation), no harm is done. + !!! If it is Hamiltonian, that alone will insure that the linear + !!! canonical transformation is symplectic. + + do j=1,ndharm !ndt + x(i)=vr(2*j-1,idef(i))*vi(2*j,idef(i))-vr(2*j,idef(i))*vi(2*j-1,idef(i))+x(i) + enddo + + enddo + + do i=1,ndharm !ndt + if(x(i).lt.0.0_dp) xx(i)=-1.0_dp + x(i)=SQRT(abs(x(i))) + enddo + + + fm=0 + do i=1,xy%n + fm(i,i)=1.0_dp + enddo + + do i=1,nd2harm !nd2t + do j=1,ndharm !ndt + fm(2*j-1,i)=vr(i,idef(j))*xx(j)/x(j) + fm(2*j,i)=vi(i,idef(j))/x(j) + enddo + enddo + + + a1 = fm + + !!!!! + + + if(ndpt/=0) then + fm=a1 + fm0(1:nd2,1:nd2)=matmul( fm(1:nd2,1:nd2),fmi(1:nd2,1:nd2)) + fm(1:nd2,1:nd2)=matmul( fmii(1:nd2,1:nd2),fm0(1:nd2,1:nd2)) + a1=fm + endif + + + + !!! In the case of a symplectic map, without magnet modulation, + !!! everything is done. + !!! However magnet modulations do not produce a symplectic matrix + !!! if there is a longitudinal coasting beam. + !!! Therefore time must be adjusted to make sure that the map + !!! is truly diagonalised. + a1%s=1 + a1%q=1.0_dp + a1=a1**(-1) + +!###5 Perhaps not necessary for new BMAD + !!!!! In the case of magnet modulations, planes are put back in their places. + + if(rf>0.and.ndpt>0.and.do_linear_ac_longitudinal) then + ! if(ndpt>0) then + call c_linear_ac_longitudinal(xy,a1,s1) + s1%s=1 + s1%q=1.0_dp + a1=a1*s1 + endif +! a1%s=1 ! make sure spin is non-zero + call kill(s1) + deallocate(fm,fmi,fmii) + + + return + end subroutine c_linear_a + +subroutine c_linear_a_stoch(xy,a1) +!#internal: normal +!# This routine linearises the linear part of the map ONLY. +!# For a full harmonic system the call c_linear_a(xy,a1) will result in +!# R=a1**(-1)*xy*a1. +!# The map R can be an amplitude dependent rotation, or a rotation followed by a drift +!# in the energy plane, or even a rotation sink if radiation is present. +!# R can also have rotations for clocks concerning AC modulation. (See Chap.4 of my Springer book) + implicit none + integer i,j,ier + type(c_damap), intent(inout) :: xy,a1 + real(dp) reval(ndim2t),imval(ndim2t),vr(ndim2t,ndim2t),vi(ndim2t,ndim2t),vrt(ndim2t,ndim2t),vit(ndim2t,ndim2t) + real(dp) fm0(ndim2t,ndim2t),x(ndim2t/2),xx(ndim2t/2) + integer idef(ndim2t/2) + real(dp), allocatable :: fm(:,:),fmi(:,:),fmii(:,:) + ! type(c_damap) s1 + real(dp) :: eps_eigen = 1.e-12_dp,norm + + if(.not.c_stable_da) return + + + idef=0 + + allocate(fm(xy%n,xy%n),fmi(xy%n,xy%n),fmii(xy%n,xy%n)) + + + fm=xy + fm0=0 + + !!! To understand this, it is better to first understand ndpt=0 + !!! in PTC ndpt=0 includes : nd2=4 and nd2=6 (cavity on) + !!! Ndpt =5 is PTC's coasting beam normalisation + !!! if there are no magnet modulation,then the matrix massaging below will do very little + !!! see explanation below at the "else" + + !!! We are diagonalising a Lie map which is just the transposed + !!! of the matrix in the linear case + !!! The usual nonlinear map acts on rays and so does its matrix. + !!! Lie maps, Hamiltonian operators, act on functions. + !!! In the world of Linear maps, this involves taking the transposed of the matrix + !!! which represents the linear part of the map + if(ndpt==0) then + fm0(1:nd2,1:nd2)=transpose(fm(1:nd2,1:nd2)) + else + if(c_verbose) then + write(6,*) " nd2t,nd2,nd2harm " + write(6,*) nd2t,nd2,nd2harm + endif + ! Consider the following example + ! ndc2t,nd2t,nd2harm,nd2 + ! 2 4 6 8 + ! nd2= total size of phase space + ! + ! ndc2t=2 dimension of coasting phase space (2 or 0), here it is 2 + ! + ! nd2t=4 dimension of pseudo-harmonic phase space due to orbit (not magnet modulations) + ! here it is 4, which is a normal PTC run. + ! in accelerator physics, with mid-plane symmetry, it could be 2. But PTC only permits 4 and 6. + ! + ! nd2harm=6 Total size of pseudo-harmonic planes including magnet modulation. In the above case, + ! nd2-nd2harm=2 So there is a coasting plane. + ! + + !! The purpose of all the gymnastic below is to exchange the order of the planes + ! IF AND ONLY IF the longitudinal is coasting + ! The issue is that call c_eig6(fm0,reval,imval,vr,vi) should be called only on + ! matrix which is pseudo-harmonic. + fmi=0 + fmii=0 + do i=1,nd2t + fmi(i,i)=1 + fmii(i,i)=1 + enddo + fmi(nd2-1,nd2t+1)=1 + fmi(nd2,nd2t+2)=1 + fmii(nd2t+1,nd2-1)=1 + fmii(nd2t+2,nd2)=1 + + do i=1,2*rf + fmi(nd2t+i,nd2t+2+i)=1 + fmii(nd2t+2+i,nd2t+i)=1 + enddo + + ! fmi(1:nd2,1:nd2)=matmul(fmi(1:nd2,1:nd2),fmii(1:nd2,1:nd2)) + + fm0(1:nd2,1:nd2)=matmul( fm(1:nd2,1:nd2),fmii(1:nd2,1:nd2)) + fm0(1:nd2,1:nd2)=matmul( (fmi(1:nd2,1:nd2)),fm0(1:nd2,1:nd2)) + + + fm0(1:nd2harm,1:nd2harm)=transpose(fm0(1:nd2harm,1:nd2harm)) +! The diagonalisation is done only on the planes +! 1...nd2harm which are now in the front of the matrix +! Thus the Coasting beam is moved in the last plane (nd2-1,nd2) + + endif + + + call c_eig6(fm0,reval,imval,vr,vi) + +norm=0.0_dp +do i=1,6 + norm=norm+ abs(reval(i))+abs(imval(i))-1.0_dp +enddo + +if(c_verbose) then +do i=1,6 +write(6,*) i,reval(i),imval(i) +enddo +write(6,*) " norm ",norm +do i=1,6 +write(6,'(i4,6(1x,g13.6))') i,vr(1:6,i) +write(6,'(i4,6(1x,g13.6))') i,vi(1:6,i) +enddo +endif + + +if(normrmax) then + rmax=r + jmax=j + endif + + enddo + + idef(k)=2*jmax-1 + enddo + + + !!!! checking maybe equal tunes.... + doit=.false. + do j=1,(nd2-ndc2t-irf*2*rf )/2 + do k=1,(nd2-ndc2t-irf*2*rf )/2 + + if(j==k) cycle + if(idef(j)==idef(k)) doit=.true. + + if(doit) exit + enddo + enddo + + if(doit) then + if(c_verbose) write(6,*) "warning : trouble locating planes, so chosen arbitrarily " + do k=1,(nd2-ndc2t-irf*2*rf )/2 + idef(k)=2*k-1 + enddo + endif +! if(abs(reval(j)-r) 1 (if c_gofix is used on its own). +!# c_canonise will take care of a1 if needed to higher order. + + implicit none + integer i,j,ndloc + type(c_damap), intent(inout) :: xy,a1 + type(c_damap) w,v,rel,x + type(c_taylor) t1 + real(dp), allocatable :: mt(:,:),mv(:) + integer, allocatable :: je(:) + type(c_universal_taylor) uf1 + type(c_vector_field) vf1 + ! ndct=iabs(ndpt-ndptb) ! 1 if coasting, otherwise 0 + ! ndc2t=2*ndct ! 2 if coasting, otherwise 0 + ! nd2t=nd2-2*rf-ndc2t ! size of harmonic oscillators minus modulated clocks + ! ndt=nd2t/2 ! ndt number of harmonic oscillators minus modulated clocks + ! nd2harm=nd2t+2*rf !!!! total dimension of harmonic phase space + ! ndharm=ndt+rf !!!! total number of harmonic planes +! write(6,*) " nd2,ndct,ndc2t,nd2t,ndt,nd2harm,rf,ndpt " +! write(6,'(8(1x,i4))') nd2,ndct,ndc2t,nd2t,ndt,nd2harm,rf,ndpt + + if(.not.c_stable_da) return + + ndloc=0 + + + ! COMPUTATION OF A1 AND A1I USING DAINV + rel%n=nv; w%n=nv; v%n=nv;x%n=nv + call alloc(rel);call alloc(w);call alloc(v);call alloc(x); + call alloc(t1); + + rel=1 + v=1 + + + x=xy + +!##1 +! v=map-identity in harmonic planes + do i=1,nd2 + if(i/=ndpt.and.i/=ndptb) then + v%v(i)=x%v(i)-rel%v(i) ! V= X-1 where X is the map + else + if(mod(i,2)==0) ndloc=i/2 ! degree of freedom of coasting plane + endif + enddo + +!##2 +! map is cut to order 2 or above + v=v.cut.(order_gofix+1) + + +!##3 +! map is inverted at least to order 1 + w=v**(-1) ! W= (Map-1)**-1 + + +!##4 +! a map x is created with dimension nv +! x is zero except for the parameters and delta if coasting + + x=0 + x%s=1 ! spin part is identity + x%q=1.0_dp + do i=nd2+1,nv + x%v(i)=1.0e0_dp.cmono.i ! Identity in all the parameter planes + enddo + if(ndpt/=0) x%v(ndpt)=1.0e0_dp.cmono.ndpt ! If coasting, then energy is a parameter + + ! a1=v + + + v=w*x ! v contains the fixed point, for example v(1)= eta_x * x_pt + ... + + a1=v + +!##5 if costing beam, a symplectic map is created from delta dependence +if(ndpt/=0) then + +allocate(je(nv)) +call alloc(vf1) +do i=1,nd2 +je=0 +je(i)=1 +a1%v(i)=a1%v(i)-(a1%v(i).sub.je)*(1.0_dp.cmono.je) !+(1.0_dp.cmono.je) +enddo + +do i=1,nd2 +vf1%v(i)=a1%v(i) +enddo + +call get_field_c_universal_taylor(vf1,uf1) + + +a1=1 +do i=1,nd + if(ndpt/=2*i-1.and.ndptb/=2*i-1) a1%v(2*i-1)=a1%v(2*i-1)-(uf1.d.(2*i)) + if(ndpt/=2*i.and.ndptb/=2*i) a1%v(2*i) =a1%v(2*i) +(uf1.d.(2*i-1)) +enddo + +if(mod(ndpt,2)==0) then + a1%v(ndptb)= a1%v(ndptb) - (uf1.d.ndpt) +else + a1%v(ndptb)= a1%v(ndptb) + (uf1.d.ndpt) +endif + +call kill(vf1) +call kill(uf1) +deallocate(je) +else + + do i=1,nd2 + a1%v(i)=(1e0_dp.cmono.i)+a1%v(i) ! ndpt is already identity + enddo + +endif + + call kill(t1); + call kill(v);call kill(w);call kill(rel);call kill(x); + return + end subroutine c_gofix + + ! dragt-finn +subroutine c_factor_map(m,l,f,dir) +!#general: manipulation +!# This routine factors a map m as: +!# m= l exp(f.grad) if dir=1 +!# m= exp(f.grad) l if dir =-1 +!# l is assumed to be a linear composition operator https://en.wikipedia.org/wiki/Composition_operator . +implicit none + type(c_damap) , intent(inout) :: m,l + type(c_vector_field), intent(inout) :: f + integer dir + type(c_damap) t,lin ! added lin 2021.8.11 + real(dp) epso + + call alloc(t,lin) + + t=m + + + lin=t.sub.(-1) + + + if(dir==1) then ! Dragt-Finn direction + t=t*lin**(-1) + else + t=lin**(-1)*t + endif + !epso=-no + f=c_logf_spin(t) !,epso=epso) + !call c_flofacg(t,f,epso) + l=lin + call kill(t,lin) + +end subroutine c_factor_map +!! no spin here +subroutine c_canonise(at,a_cs,a0,a1,a2,phase,irot) +!subroutine c_canonise(at,a_cs,a0,a1,a2,phase,nu_spin,irot) +!#general: manipulation +!# This routine is of great pedagogical importance. +!# It is restricted to the orbital motion, +!# c_full_canonise also includes spin. +!# It factors a canonical transformation as +!# at=a_cs o rotation(phase) as explaned in Chap.7 of my Springer book. +!# a_cs = a_0 o a_1 o a_2 +!# The flag courant_snyder_teng_edwards, defaulted to true, controls the linear part of a_cs. + implicit none + type(c_damap) , intent(inout) :: at,a_cs + type(c_damap) , optional, intent(inout) :: a2,a1,a0 + type(c_taylor) ,optional, intent(inout) :: phase(:) !,nu_spin + + integer ,optional, intent(in) :: irot + ! call c_full_canonise(at,a_cs,a0=a0,a1=a1,a2=a2,phase=phase,nu_spin,irot=irot) + call c_full_canonise(at,a_cs,a0=a0,a1=a1,a2=a2,phase=phase,irot=irot) + +end subroutine c_canonise + +! redundant +subroutine c_full_factor_map_old(U,Q,U_0,U_1,U_2) +!#general: manipulation +!# U = Q o U_0 o U_1 o U_2 + implicit none + type(c_damap) , intent(inout) :: U,Q,U_0,U_1,U_2 + type(c_damap) a + call alloc(a) + qphase=.false. + call c_full_canonise(U,a,Q,U_0,U_1,U_2,irot=0) + qphase=qphasedef + call kill(a) +end subroutine c_full_factor_map_old + +subroutine c_full_canonise(at,a_cs,as,a0,a1,a2,rotation,phase,nu_spin,irot) +!#general: manipulation +!# This routine is of great pedagogical importance. +!# It factors a canonical transformation as +!# at=a_cs o rotation(phase,nu_spin) as explained in Chap.7 of my Springer book. +!# a_cs = a_s o a_0 o a_1 o a_2 + implicit none + type(c_damap) , intent(inout) :: at,a_cs + type(c_damap) , optional, intent(inout) :: as,a2,a1,a0,rotation + type(c_taylor) ,optional, intent(inout) :: phase(:),nu_spin + integer ,optional, intent(in) :: irot + type(c_damap) ar,att,phi,a0t,a1t,a2t,ast,ri + type(c_taylor) pha,tune_spin + integer i,kspin,ir + real(dp) norm + ir=1 + if(present(irot)) ir=irot + call alloc(ar) + call alloc(att) + call alloc(a0t) + call alloc(a1t) + call alloc(a2t) + call alloc(ast) + call alloc(phi) + call alloc(pha,tune_spin) + call alloc(ri) + ! at= (a,s) = (a,I) o (I,s) + ! call c_full_norm_spin(at%s,kspin,norm) + + call c_full_norm_spin_map(at,kspin,norm) + + ! storing the spin because the code is careless (sets it to zero) + if(kspin==-1) then + att=at + att%s=1 + att%q=1.0_dp + ast=1 + ast%s=at%s + ast%q=at%q + else + att=at + ast=1 + endif + +! at= (a,s) = (att,I) o (I,ats) + + att%s=0 + att%q=0.0_dp + + ar=1 + + call extract_a0(att,a0t) + + phi=1 + + + if(ir/=1) then + call extract_a1(att,a1t) + else + call extract_a1(att,a1t,phi) + endif + +! if(present(phase)) ar=ar*phi +!call print(phi%v(6),6) +!pause 2 + if(ir/=1) then + call extract_a2(att) + else + call extract_a2(att,ar) + phi=ar*phi + endif + + a2t=att + if(kspin==-1) then + if(use_quaternion) THEN + ast%q=ast%q*phi**(-1) + else + ast%s=ast%s*phi**(-1) + endif + + endif + if(present(phase).or.present(rotation)) then + if(present(rotation)) then + rotation=phi + rotation%s=1 + rotation%q=1.0_dp + endif + ri=from_phasor(-1) + phi=c_simil(ri,phi,1) + endif + + if(use_quaternion) THEN + a0t%q=1.0_dp + a1t%q=1.0_dp + a2t%q=1.0_dp + else + a0t%s=1 + a1t%s=1 + a2t%s=1 + endif + if(kspin==-1.and.ir==1) then + + call c_remove_y_rot(ast,ar,tune_spin) + if(present(nu_spin) ) nu_spin=-tune_spin/twopi+nu_spin ! changed 2018.11.01 + if(present(rotation)) then + rotation=rotation*ar + endif + endif + a_cs=a0t*a1t*a2t + + if(kspin==-1) then + if(use_quaternion) then + ast%q=ast%q*a_cs**(-1) + else + ast%s=ast%s*a_cs**(-1) !! at= ast*a_cs * rotation + endif + endif + + a_cs=ast*a_cs + + if(present(phase).and.ir==1) then + do i=1,nd2t/2 + pha=(phi%v(2*i).k.(2*i)) + pha=(-i_*log(pha)/twopi).cut.no + phase(i)=pha+phase(i) + enddo + if(ndpt/=0) then + if(mod(ndpt,2)==0) then + i=ndpt/2 + else + i=ndptb/2 + endif + phase(i)=phase(i)+phi%v(ndptb)-(1.0_dp.cmono.ndptb) + endif + endif + + + if(present(a0)) a0=a0t + + if(present(a1)) a1=a1t + + if(present(a2)) a2=a2t + + if(present(as)) as=ast + + call kill(ri) + call kill(ar) + call kill(att) + call kill(a0t) + call kill(a1t) + call kill(a2t) + call kill(ast) + call kill(phi) + call kill(pha,tune_spin) +end subroutine c_full_canonise + + +subroutine c_full_canonise_linear(at,a_cs,a0,a1,phase) +!#general: manipulation +!# This routine is of great pedagogical importance. +!# It factors a canonical transformation as +!# at=a_cs o rotation(phase,nu_spin) as explained in Chap.7 of my Springer book. +!# a_cs = a_s o a_0 o a_1 o a_2 + implicit none + type(c_damap) , intent(inout) :: at,a_cs + type(c_damap) , optional, intent(inout) :: a1,a0 + type(c_taylor) ,optional, intent(inout) :: phase(:) + + type(c_damap) ar,att,phi,a0t,a1t,ri + type(c_taylor) pha + integer i,kspin,ir + real(dp) norm + + call alloc(ar) + call alloc(att) + call alloc(a0t) + call alloc(a1t) + + call alloc(phi) + call alloc(pha) + call alloc(ri) + ! at= (a,s) = (a,I) o (I,s) + ! call c_full_norm_spin(at%s,kspin,norm) + + call c_full_norm_spin_map(at,kspin,norm) + + ! storing the spin because the code is careless (sets it to zero) + + + att=at + + +! at= (a,s) = (att,I) o (I,ats) + + att%s=0 + att%q=0.0_dp + + ar=1 + + call extract_a0(att,a0t) + + phi=1 + + + + call extract_a1(att,a1t,phi) + + +! if(present(phase)) ar=ar*phi +!call print(phi%v(6),6) +!pause 2 + +ar=1 + + + + + + + + if(present(phase)) then + ri=from_phasor(-1) + phi=c_simil(ri,phi,1) + endif + + a_cs=a0t*a1t + + + + if(present(phase)) then + do i=1,nd2t/2 + pha=(phi%v(2*i).k.(2*i)) + pha=(-i_*log(pha)/twopi).cut.no + phase(i)=pha+phase(i) + enddo + if(ndpt/=0) then + if(mod(ndpt,2)==0) then + i=ndpt/2 + else + i=ndptb/2 + endif + phase(i)=phase(i)+phi%v(ndptb)-(1.0_dp.cmono.ndptb) + endif + endif + + + if(present(a0)) a0=a0t + + if(present(a1)) a1=a1t + + call kill(ri) + call kill(ar) + call kill(att) + call kill(a0t) + call kill(a1t) + call kill(phi) + call kill(pha) +end subroutine c_full_canonise_linear + +subroutine c_identify_resonance(j,n,c) + implicit none + integer, intent(inout) :: J(:) + complex(dp), intent(out) :: c + integer, intent(out) :: n + integer i + + do i=1,ndt*2 + if(j(i)/=0) exit + enddo + n=i + if(mod(n,2)==0) then + n=n-1 + else + n=n+1 + endif + c=1.0_dp/(j(i)*n_cai) + j(i)=j(i)-1 + + +end subroutine c_identify_resonance + +subroutine c_full_factorise(a,as,a0,a1,a2,dir) +!#general: manipulation +!# a_t = a_s o a_0 o a_1 o a_2 for dir=1 + implicit none + type(c_damap) , intent(inout) :: a + type(c_damap) , optional, intent(inout) :: as,a2,a1,a0 + integer,optional :: dir + + type(c_damap) att,a0t,a1t,a2t,ast,at + type(c_taylor) p + type(c_universal_taylor) u + type(c_vector_field) fv + integer i,kspin,ii,j,n,idir + real(dp) norm + complex(dp) value + integer, allocatable :: je(:) + + call alloc(at) + call alloc(att) + call alloc(a0t) + call alloc(a1t) + call alloc(a2t) + call alloc(ast) + call alloc(fv) + call alloc(p) + +at=a +idir=1 +if(present(dir)) idir=dir +if(idir==-1) at=a**(-1) + +as=1 +a2t=at +a2t%q=1.0_dp +if(use_quaternion) then +as%q=at%q*a2t**(-1) +else + as%s=at%s*a2t**(-1) +endif + + +att=as**(-1)*at + + + a1t=1 + do i=1,c_%nd2t + a1t%v(i)=0.0_dp + enddo + +a0t=1 + do i=1,c_%nd2t + a0t%v(i)=att%v(i)*a1t + if(c_%ndpt/=0) fv%v(i)=a0t%v(i) + a0t%v(i)=a0t%v(i) + (1.0_dp.cmono.i) + enddo + + + +if(c_%ndpt/=0) then +call get_field_c_universal_taylor(fv,U) + +fv=0 + +do i=1,c_%nd2t/2 + fv%v(2*i-1)=-(u.d.(2*i)) + fv%v(2*i) = (u.d.(2*i-1)) +enddo + fv%v(c_%ndptb) = (-1)**c_%ndptb*(u.d.(c_%ndpt)) + a0=exp(fv) + call kill(u) + +allocate(je(c_%nd2)) + je=0 + !a0%v(c_%ndptb)=a0%v(c_%ndptb) (at%v(c_%ndptb).par.je) +deallocate(je) + + else + a0=a0t +endif !!!!!!!!!!!! end c_%ndpt/=0 + + + + + att=a0**(-1)*att + + +if(c_%ndpt/=0) then + allocate(je(c_%nd2t)) + ast=1 + je=0 + p=(att%v(c_%ndptb).par.je)-(1.0_dp.cmono.c_%ndptb) + + ast%v(c_%ndptb)=ast%v(c_%ndptb) + p + deallocate(je) + +!!! extra iteration for parameters to vanish from time-like variable + a0=ast*a0 + att=a0**(-1)*as**(-1)*at + endif + + !!!!!!!!!!!!! linear part + +allocate(je(c_%nd2t)) +a1%q=1.0_dp +do i=1,c_%nd2t + do j=1,c_%nd2t + je=0 + je(j)=1 + a1%v(i)=(att%v(i).par.je)*(1.0_dp.cmono.j) + a1%v(i) + enddo +enddo + +deallocate(je) + +!!!!!!!!! removing the quadratic orbital part in the time-like variable +if(c_%ndpt/=0) then + +a1%v(c_%ndpt)=1.0_dp.cmono.c_%ndpt + +allocate(je(c_%nv)) + + call c_taylor_cycle(att%v(c_%ndptb),size=n) + + do i=1,n + call c_taylor_cycle(att%v(c_%ndptb),ii=i,value=value,j=je) + ii=0 + do j=1,c_%nd2t + ii=ii+je(j) + enddo + if(ii==2) a1%v(c_%ndptb)=a1%v(c_%ndptb)+(value.cmono.je) + enddo + + +deallocate(je) + + + a1%v(c_%ndptb)=a1%v(c_%ndptb)+(1.0_dp.cmono.c_%ndptb) +endif + a2=a1**(-1)*att + + + +if(idir==-1) then + as=as**(-1) + a0=a0**(-1) + a1=a1**(-1) + a2=a2**(-1) +endif + + + call kill(p) + call kill(att) + call kill(a0t) + call kill(a1t) + call kill(a2t) + call kill(ast) + call kill(fv) + call kill(at) + + + +end subroutine c_full_factorise + + + subroutine c_normal_spin_linear_quaternion(m_in,m_out,as,alpha) +!#restricted: normal +!# This routine normalises the constant part of the spin matrix. +!# m_out=as**(-1)*m_in*as + implicit none + type(c_damap), intent(inout) :: m_in,m_out,as + type(quaternion) q0,q1,e_y,q3,qs + real(dp) alpha,cosalpha,sinalpha,tone + type(c_damap) id + +q0=m_in%q.sub.0 + + as=1 + +q1=q0 +q1%x(0)=0.0_dp +qs=1.0_dp/sqrt(q1%x(1)**2+q1%x(2)**2+q1%x(3)**2) + + +q1=q1*qs ! q1=n + +e_y=0.0_dp +e_y%x(2)=1.0_dp +!call print(e_y) +!pause 5 + +q3=q1*e_y +!call print(q3) + +q3%x(0:3)=q3%x(0:3)/sqrt(q3%x(0)**2+q3%x(1)**2+q3%x(2)**2+q3%x(3)**2) +!pause 6 + ! q3 =-n.j + n x j . l + +cosalpha=-q3%x(0) + +sinalpha=sqrt(q3%x(1)**2+q3%x(2)**2+q3%x(3)**2) + + + +alpha= atan2(sinalpha,cosalpha) + + + +if(alpha==0.and.cosalpha/=-1.0_dp) then +! write(6,*)sinalpha,cosalpha +! write(6,*) "weird in c_normal_spin_linear_quaternion " +! pause 123 + q3=1.0_dp + +!call print(q3) +!pause 71 +else + +if(abs(cosalpha+1.0_dp)<=1.e-16_dp) then + q3=-1.0_dp +else + q3%x(0)=cos(alpha/2) + q3%x(1:3)=-sin(alpha/2)*q3%x(1:3)/sinalpha + +endif + +!call print(q3) +!pause 72 + +endif + +qs=2 +qs=q3*qs*q3**(-1) +tone=qs%x(2) +if(tone<0) then + qs=1 + q3=q3*qs +endif + +as%q=q3 +tone=AS%q%x(0) +if(tone<0) then + call alloc(id) + id=1 + id%q%x(0)=-1.0e0_dp + AS=id*AS + call kill(id) +endif + m_out=c_simil(AS,m_in,-1) +q0=m_out%q + +alpha=2*atan2(q0%x(2),q0%x(0)) + + + + end subroutine c_normal_spin_linear_quaternion + + + + + + subroutine c_normal_spin_linear(m_in,m_out,as,n0,as_ext) +!#restricted: normal +!# This routine normalises the constant part of the spin matrix. +!# m_out=as**(-1)*m_in*as +!# n0 is the invariant spin direction of type c_spinor. +!# Optional map as_ext is for a crazy Stern-Gerlach extension (not used). + implicit none + type(c_damap), intent(inout) :: m_in,m_out,as + type(c_damap), optional :: as_ext + type(c_spinor), intent (inout) :: n0 + type(c_taylor) s(3) + integer i +! as_ext is for crazy Stern-Gerlach extension + as=1 + call c_find_n0(m_in%s,n0,linear=my_true) + call c_find_as(n0,AS%s) + + m_out=c_simil(AS,m_in,-1) + + if(present(as_ext)) then + as_ext=1 + as_ext%s=AS%s**(-1) + do i=1,3 + call alloc(s(i)) + enddo + + s(1)=(1.0_dp.cmono.(nd2-1)) + s(3)=(1.0_dp.cmono.nd2) + s(2)= sqrt(1.0_dp-s(1)**2-s(3)**2) + + as_ext%v(nd2-1)=0.0_dp + as_ext%v(nd2)=0.0_dp + do i=1,3 + as_ext%v(nd2-1)=as_ext%v(nd2-1)+ as_ext%s%s(1,i)*s(i) + as_ext%v(nd2) =as_ext%v(nd2) + as_ext%s%s(3,i)*s(i) + enddo + as_ext%s=0 + + do i=1,3 + call kill(s(i)) + enddo + + endif + + end subroutine c_normal_spin_linear + + subroutine c_convert_spin(xy,m1) +!#general: Stern-Gerlach +!# Bizarre routine to convert a spectator spin +!# into a Stern-Gerlach type map. + implicit none + type(c_damap) , intent(inout) :: xy,m1 + type(c_taylor) s(3) + integer i + + do i=1,3 + call alloc(s(i)) + enddo + m1=xy + + s(1)=(1.0_dp.cmono.(nd2-1)) + s(3)=(1.0_dp.cmono.nd2) + s(2)= sqrt(1.0_dp-s(1)**2-s(3)**2) + + m1%v(nd2-1)=0.0_dp + m1%v(nd2)=0.0_dp + do i=1,3 + m1%v(nd2-1)=m1%s%s(1,i)*s(i)+m1%v(nd2-1) + m1%v(nd2)=m1%s%s(3,i)*s(i)+m1%v(nd2) + enddo + m1%s=0 + + do i=1,3 + call kill(s(i)) + enddo + + end subroutine c_convert_spin + + + function coast(l) + implicit none + logical(lp) coast + integer l + + coast=my_false + if(ndpt/=0) then + coast=l>nd2t.and.l=0 and =delta_ij +! then + + do i=1,6 + ki(i)=d(i,i) + enddo + do i=1,3 + if(ki(2*i-1)<0) then + if(c_verbose) then + write(6,*) "fluctuations ill defined in plane ",i + write(6,*) i,ki(2*i-1:2*i) + endif + ki(2*i-1)=0 + ki(2*i)=0 + endif + if(ki(2*i)<0) then + if(c_verbose) then + write(6,*) "fluctuations ill defined in plane ",i + write(6,*) i,ki(2*i-1:2*i) + endif + ki(2*i-1)=0 + ki(2*i)=0 + endif + if(ki(2*i-1)/=0.and.ki(2*i)/=0) then + if(ki(2*i-1)-ki(2*i)/=0) then + if(abs( (ki(2*i-1)-ki(2*i))/(abs(ki(2*i-1))+abs(ki(2*i))))>1.d-4) then + if(c_verbose) then + write(6,*) "fluctuations ill defined in plane ",i + write(6,*) i,ki(2*i-1:2*i) + endif + + ki(2*i-1)=0 + ki(2*i)=0 + endif + endif + endif + enddo + do i=1,6 + ki(i)=sqrt(ki(i)) + enddo +! construct z_i =ki(i) * r_i +! then x= Ait z is the appropriate kick +! in the original space. +! + + if(global_verbose) then + write(6,*)" Stochastic kick" + do i=1,6 + do j=1,6 + if(abs(d(i,j))>eps*norm) then + write(6,*) i,j,d(i,j) + endif + enddo + enddo +endif + + ai=-matmul(matmul(s,at),s) + ait=transpose(ai) + +! B= ait*d*ai + + call kill(vf) + call kill(id,as) + + +end subroutine c_stochastic_kick + + subroutine check_kernel(k,n,je,removeit) +!#internal: normal +!# This routine identifies terms in an orbital vector field that +!# are not in the kernel of a complete normalisation. +!# Namely it preserves generators of rotation. +!# Due to the vagueries of accelerator physics, +!# it leaves non-linear generators of rotations even in the +!# case of a damped oscillator. + implicit none + logical(lp) removeit + integer i,k,n,je(:),t,o + + if(remove_tune_shift) then + removeit=my_true + t=0 + if(k/=0) je(k)=je(k)-1 + o=0 + do i=1,n,2 + if(coast(i)) cycle + o=o+je(i)+je(i+1) + t=t+abs(je(i)-je(i+1)) + enddo + if(t==0.and.o==0) removeit=my_false + if(k/=0) je(k)=je(k)+1 + else + removeit=my_true + t=0 + if(k/=0) je(k)=je(k)-1 + do i=1,n,2 + if(coast(i)) cycle + t=t+abs(je(i)-je(i+1)) + enddo + if(t==0) removeit=my_false + if(k/=0) je(k)=je(k)+1 + endif + end subroutine check_kernel + + + + subroutine check_resonance(k,n,je,kr,m,removeit) +!#internal: normal +!# This routine identifies terms in an orbital vector field that +!# are left per user's request. +!# This is used if a resonance family is to be left in the map. +!# See Sec.5.4 of Springer book. + + implicit none + logical(lp) removeit + integer i,k,n,je(:),t1,t2,j,kr,m(:,:) + + + removeit=my_true + t1=0; t2=0; + je(k)=je(k)-1 + do i=1,n,2 + if(coast(i)) cycle + j=(i+1)/2 + t1=t1+abs(je(i)-je(i+1)+m(j,kr)) + t2=t2+abs(je(i)-je(i+1)-m(j,kr)) + enddo + if(t1==0.or.t2==0) removeit=my_false + je(k)=je(k)+1 + + end subroutine check_resonance + + subroutine check_resonance_spin(k,n,je,kr,ms,m,removeit) +!#internal: normal +!# This routine identifies terms in a spin-orbital orbital vector field that +!# are left per user's request. +!# This is used if a spin resonance family is to be left in the map. +!# See Sec.6.4 of Springer book. + implicit none + logical(lp) removeit + integer i,k,n,je(:),t1,t2,j,kr,ms(:),m(:,:) + + + removeit=my_true + t1=0; t2=0; + + do i=1,n,2 + if(coast(i)) cycle + j=(i+1)/2 + t2=t2+abs(je(i)-je(i+1)-m(j,kr)) + t1=t1+abs(je(i)-je(i+1)+m(j,kr)) + enddo +! if(k==1) then +! t1=t1+iabs(-spin_def_tune-ms(kr)) +! t2=t2+iabs(-spin_def_tune+ms(kr)) +! elseif(k==3) then +! t1=t1+iabs(spin_def_tune-ms(kr)) +! t2=t2+iabs(spin_def_tune+ms(kr)) +! else +! t1=t1+iabs(ms(kr)) +! t2=t2+iabs(ms(kr)) +! endif +if(spin_def_tune==-1) then + if(k==1) then + if(ms(kr)>0) then + if(t2==0) removeit=my_false + elseif(ms(kr)<0) then + if(t1==0) removeit=my_false + endif + elseif(k==3) then + if(ms(kr)>0) then + if(t1==0) removeit=my_false + elseif(ms(kr)<0) then + if(t2==0) removeit=my_false + endif + else + t1=t1+iabs(ms(kr)) + t2=t2+iabs(ms(kr)) + if(t1==0.or.t2==0) removeit=my_false + endif +else + if(k==1) then + if(ms(kr)>0) then + if(t1==0) removeit=my_false + elseif(ms(kr)<0) then + if(t2==0) removeit=my_false + endif + elseif(k==3) then + if(ms(kr)>0) then + if(t2==0) removeit=my_false + elseif(ms(kr)<0) then + if(t1==0) removeit=my_false + endif + else + t1=t1+iabs(ms(kr)) + t2=t2+iabs(ms(kr)) + if(t1==0.or.t2==0) removeit=my_false + endif +endif + + + end subroutine check_resonance_spin + + SUBROUTINE c_kernel(F,F_FLOQUET) +!#internal: normal +!# This routine extracts circles : equal powers of phasors + IMPLICIT NONE + TYPE(c_TAYLOR) F,F_FLOQUET,FQ + complex(dp) v + INTEGER I + logical(lp) removeit + integer, allocatable :: je(:) + + allocate(je(nv)) + + call alloc(fq) + + F_FLOQUET=F + + + i=1 + do while(.true.) + call c_cycle(F_FLOQUET,i,v ,je); if(i==0) exit; + call check_kernel(0,c_%nd2,je,removeit) + if(.not.removeit) then + fq=fq+(v.cmono.je) + endif + enddo + + f_floquet=fq + call kill(fq) + + deallocate(je) + + END SUBROUTINE c_kernel + + SUBROUTINE C_AVERAGE(F,A,F_FLOQUET,ergodic) +!#internal: normal +!# This routine averages a function F using the canonical trnsformation A. +!# This is explained in Sec.2.2.1 of my Springer book. +!# The result expressed in phasor's basis is in F_FLOQUET + IMPLICIT NONE + TYPE(c_damap) A + TYPE(c_TAYLOR) F,F_FLOQUET,FQ + complex(dp) v + INTEGER I,n_ergodic + logical(lp) removeit + logical,optional :: ergodic + integer, allocatable :: je(:) + + n_ergodic=A%n + allocate(je(nv)) + if(present(ergodic) ) then + n_ergodic =A%n - 2 + endif + call alloc(fq) + + F_FLOQUET=(F*A)*TO_PHASOR(-1) + + i=1 + do while(.true.) + call c_cycle(F_FLOQUET,i,v ,je); if(i==0) exit; + + call check_kernel(0,n_ergodic,je,removeit) + if(.not.removeit) then + fq=fq+(v.cmono.je) + endif + enddo + f_floquet=fq + call kill(fq) + + deallocate(je) + + END SUBROUTINE C_AVERAGE + + subroutine check_kernel_ergodic(n,je,removeit) +!#internal: normal +!# This routine identifies terms in an orbital vector field that +!# are not in the kernel of a complete normalisation. +!# Namely it preserves generators of rotation. +!# Due to the vagueries of accelerator physics, +!# it leaves non-linear generators of rotations even in the +!# case of a damped oscillator. + implicit none + logical(lp) removeit + integer i,n,je(:),t,o + + removeit=my_true + t=0 + do i=1,n,2 + if(coast(i)) cycle + t=t+abs(je(i)-je(i+1)) + enddo + if(t==0) removeit=my_false + + end subroutine check_kernel_ergodic + + + + function c_expflo_fac(h,x) !,eps,nrmax) + implicit none + ! DOES EXP( \VEC{H} ) X = Y + integer i,localmaster + type(c_damap) c_expflo_fac + type(c_damap),optional, intent(in):: x + type(c_factored_lie), intent(in) :: h + IF(.NOT.C_STABLE_DA) then + c_expflo_fac%v%i=0 + RETURN + endif + + localmaster=c_master + if(present(x)) then + c_expflo_fac%n=x%n + else + c_expflo_fac%n=nd2 + endif + call c_assmap(c_expflo_fac) + + if(present(x)) then + c_expflo_fac=x + else + c_expflo_fac=1 + endif + + if(h%dir==1) then + do i=h%n,1,-1 + c_expflo_fac=texp(h%f(i),c_expflo_fac) + enddo + else + do i=1,h%n + c_expflo_fac=texp(h%f(i),c_expflo_fac) + enddo + endif + if(present(x)) c_expflo_fac%x0=x%x0 + + c_master=localmaster + + end function c_expflo_fac + + + function c_expflo_fac_inv(h,x) !,eps,nrmax) + implicit none + ! DOES EXP( \VEC{H} ) X = Y + integer i,localmaster + type(c_damap) c_expflo_fac_inv + type(c_damap),optional, intent(in):: x + type(c_factored_lie), intent(in) :: h + IF(.NOT.C_STABLE_DA) then + c_expflo_fac_inv%v%i=0 + RETURN + endif + + localmaster=c_master + if(present(x)) then + c_expflo_fac_inv%n=x%n + else + c_expflo_fac_inv%n=nd2 + endif + call c_assmap(c_expflo_fac_inv) + + if(present(x)) then + c_expflo_fac_inv=x + else + c_expflo_fac_inv=1 + endif + + if(h%dir==-1) then + do i=h%n,1,-1 + c_expflo_fac_inv=texp(-h%f(i),c_expflo_fac_inv) + enddo + else + do i=1,h%n + c_expflo_fac_inv=texp(-h%f(i),c_expflo_fac_inv) + enddo + endif + + if(present(x)) c_expflo_fac_inv%x0=x%x0 + c_master=localmaster + + end function c_expflo_fac_inv + + + function c_add_map(s1,s2) !,eps,nrmax) + implicit none + + integer i,localmaster + type(c_damap) c_add_map + type(c_damap), intent(in):: s1 + type(c_damap), intent(in) :: s2 + type(c_taylor) tt + localmaster=c_master + + + c_add_map%n=s1%n + call alloc(tt) + call c_assmap(c_add_map) + + do i=1,s1%n + tt=s1%v(i)+ s2%v(i) + c_add_map%v(i)=tt + enddo + + c_add_map%q=s1%q+ s2%q + c_add_map%s=s1%s+ s2%s + c_add_map%e_ij=s1%e_ij+ s2%e_ij + + c_master=localmaster + call kill(tt) + end function c_add_map + + function c_sub_map(s1,s2) !,eps,nrmax) + implicit none + + integer i,localmaster + type(c_damap) c_sub_map + type(c_damap), intent(in):: s1 + type(c_damap), intent(in) :: s2 + type(c_taylor) tt + + localmaster=c_master + + + c_sub_map%n=s1%n + call alloc(tt) + call c_assmap(c_sub_map) + + do i=1,s1%n +! etienne was completely wrong fixed 1/5/2016 + tt=s1%v(i)- s2%v(i) + c_sub_map%v(i)=tt + enddo + c_sub_map%q=s1%q- s2%q + c_sub_map%s=s1%s- s2%s + c_sub_map%e_ij=s1%e_ij- s2%e_ij + + c_master=localmaster + call kill(tt) + end function c_sub_map + + + + FUNCTION c_logf_spin( s1,h,epso,n,tpsa ) + implicit none + TYPE (c_vector_field) c_logf_spin + TYPE (c_vector_field) , optional :: h + TYPE (c_damap), INTENT (INOUT) :: S1 + real(dp), optional :: epso + integer, optional :: n + logical, optional :: tpsa + logical da + integer localmaster,k,i + TYPE (c_vector_field) t,t2 + type(c_damap) mt,t_1,e2,s1t + real(dp) xnorm1,epsone,xn,xnorm2,r,r1(3) + + + IF(.NOT.C_STABLE_DA) then + c_logf_spin%v%i=0 + RETURN + endif +! da=.not.s1%tpsa + da=.true. + if(present(tpsa)) da=.not.tpsa + localmaster=c_master + t%n=s1%n;t2%n=s1%n;mt%n=s1%n;t_1%n=s1%n;e2%n=s1%n;s1t%n=s1%n; + call alloc(t);call alloc(t2);call alloc(mt,t_1,e2,s1t); + + c_logf_spin%n=s1%n + call c_ass_vector_field(c_logf_spin) + c_logf_spin=0 + if(present(h)) c_logf_spin=h + s1t=s1 + xnorm1=0.0_dp +if(use_quaternion) then + call c_full_norm_quaternion(s1t%q,k,xnorm1) +else + xnorm1=1.d0 + call c_full_norm_spin(s1t%s,k,xnorm1) +endif + do i=1,s1t%n + if(da) then + s1t%v(i)=s1t%v(i)-(s1t%v(i).sub.'0') + endif + r=full_abs(s1t%v(i)) + xnorm1=xnorm1+r + enddo + + if(present(epso)) then + epsone= epso + else + epsone= xnorm1/epso_factor + endif + if(lielib_print(3)==1) write(6,*) epsone,xnorm1 +! eps=abs(epsone)/2 !1.d5 + xn=1e36_dp + + k=1000 + if(present(n)) k=n + do i=1,k + + + mt=exp(-c_logf_spin,s1t) + + t=c_1_vf_q(mt) ! extracts mt-1 as a vector field including spin + + + t_1=1 + t_1=mt-t_1 ! same as a map + + + ! e2=(t*t_1) + + ! t2=(-0.5e0_dp)*c_1_vf_q(e2,0) + ! t=t+t2 + + call c_full_norm_vector_field(t,xnorm1) + if(lielib_print(3)==1) write(6,*) i,xn,xnorm1 + + + + if(xnorm1.lt.epsone) then !.and.i>=10) then + call c_full_norm_vector_field(t2,xnorm2) + + c_logf_spin=c_logf_spin+t +0.5e0_dp*(c_logf_spin.lb.t) + + if(xnorm1>=xn.and.(.not.present(n))) exit + xn=xnorm1 + else + c_logf_spin=c_logf_spin+t + xn=xnorm1 + endif + + enddo + if(i>k-10.and.(.not.present(n))) then + write(6,*) " no convergence in c_logf_spin " + ! stop 1984 + endif +!write(6,*) " i",i + call kill(t);call kill(t2);call kill(mt,t_1,e2,s1t); +! call c_flofacg(s1,c_logf_spin,epso,n) + ! if(complex_extra_order==1.and.special_extra_order_1) c_logf_spin=c_logf_spin.cut.no + c_master=localmaster + if(.not.c_stable_da) then + write(6,*) "Unstable in c_logf_spin" + write(6,*) "Perhaps map to far from Identity" + endif + + END FUNCTION c_logf_spin + + + + + function c_1_vf_q(s1,c) !,eps,nrmax) + implicit none + ! extracts mt-1 as a vector field including spin + integer i,localmaster,ci,k,j + type(c_vector_field) c_1_vf_q + type(c_damap), intent(in):: s1 + type(c_taylor) tt + real(dp) norm + integer, optional :: c + localmaster=c_master + ci=1 + if(present(c)) ci=c + c_1_vf_q%n=s1%n + call alloc(tt) + call c_ass_vector_field(c_1_vf_q) + + do i=1,s1%n + tt=s1%v(i)-ci*(1.0e0_dp.cmono.i) + c_1_vf_q%v(i)=tt + enddo + + if(use_quaternion) then + call c_full_norm_quaternion(s1%q,i,norm) + if(i/=0) then + do k=1,3 + c_1_vf_q%q%x(k)=s1%q%x(k) + enddo + c_1_vf_q%q%x(0)=0.0_dp !s1%q%x(0)-1.0_dp + endif + else +! call c_full_norm_spinor(c_1_vf_q%h,norm) + +! c_1_vf_q%h%v(1)=-(s1%s%s(3,2)-s1%s%s(2,3))/2.0_dp +! c_1_vf_q%h%v(2)=-(s1%s%s(1,3)-s1%s%s(3,1))/2.0_dp +! c_1_vf_q%h%v(3)=-(s1%s%s(2,1)-s1%s%s(1,2))/2.0_dp + +!if(.not.correct_quaternion_field) c_1_vf_q%h=-c_1_vf_q%h + ! do k=1,3 + ! c_1_vf_q%h%v(k)=s1%h%v(k) + ! enddo + !call c_full_norm_spinMATRIX(c_1_vf_q%L,norm) + DO I=1,3 + DO j=1,3 + if(i==j) then + c_1_vf_q%L%S(I,j)=s1%s%s(I,J)-1.0_DP + else + c_1_vf_q%L%S(I,j)=s1%s%s(I,J) + endif + ENDDO + ENDDO + + endif + + c_master=localmaster + call kill(tt) + end function c_1_vf_q + + + + + + + function c_1_map(s1,c) !,eps,nrmax) + implicit none + + integer i,j,localmaster,ci + type(c_damap) c_1_map + type(c_damap), intent(in):: s1 + type(c_taylor) tt + real(dp) norm + integer, optional :: c + localmaster=c_master + ci=-1 + if(present(c)) ci=c + c_1_map%n=s1%n + call alloc(tt) + call c_assmap(c_1_map) + c_1_map=s1 + do i=1,s1%n + tt=s1%v(i)+ci*(1.0e0_dp.cmono.i) + c_1_map%v(i)=tt + enddo + + call c_full_norm_spin(s1%s,i,norm) + if(i/=0) then + do j=1,3 + c_1_map%s%s(j,j)=c_1_map%s%s(j,j)+ci + enddo + endif + + c_master=localmaster + call kill(tt) + end function c_1_map + + + function c_add_vf(s1,s2) !,eps,nrmax) + implicit none + + integer i,localmaster + type(c_vector_field) c_add_vf + type(c_vector_field), intent(in):: s1 + type(c_vector_field), intent(in) :: s2 + type(c_taylor) tt + localmaster=c_master + + + c_add_vf%n=s1%n + call alloc(tt) + call c_ass_vector_field(c_add_vf) + + do i=1,s1%n + tt=s1%v(i)+ s2%v(i) + c_add_vf%v(i)=tt + enddo + if(use_quaternion) then + c_add_vf%q=s1%q+s2%q + else +! c_add_vf%h=s1%h+s2%h + c_add_vf%L=s1%L+s2%L + endif + + c_add_vf%nrmax=max(s1%nrmax,s2%nrmax) + c_add_vf%eps=min(s1%eps,s2%eps) + c_master=localmaster + call kill(tt) + end function c_add_vf + + function c_sub_vf(s1,s2) !,eps,nrmax) + implicit none + + integer i,localmaster + type(c_vector_field) c_sub_vf + type(c_vector_field), intent(in):: s1 + type(c_vector_field), intent(in) :: s2 + type(c_taylor) tt + localmaster=c_master + + + c_sub_vf%n=s1%n + call alloc(tt) + call c_ass_vector_field(c_sub_vf) + + do i=1,s1%n + tt=s1%v(i)- s2%v(i) + c_sub_vf%v(i)=tt + enddo + if(use_quaternion) then + c_sub_vf%q=s1%q-s2%q + else +! c_sub_vf%h=s1%h-s2%h + c_sub_vf%L=s1%L-s2%L + endif + + c_sub_vf%nrmax=max(s1%nrmax,s2%nrmax) + c_sub_vf%eps=min(s1%eps,s2%eps) + c_master=localmaster + call kill(tt) + end function c_sub_vf + + + FUNCTION real_mul_map( r,S1 ) + implicit none + TYPE (c_damap) real_mul_map + real(dp),intent(in):: r + TYPE (c_damap), INTENT (IN) :: S1 + integer localmaster,i,j + + IF(.NOT.C_STABLE_DA) then + real_mul_map%v%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + real_mul_map%n=s1%n + call c_assmap(real_mul_map) + + do i=1,s1%n + real_mul_map%v(i)=r*s1%v(i) + enddo + + + do i=1,3 + do j=1,3 + real_mul_map%s%s(i,j)=r*s1%s%s(i,j) + enddo + enddo + + do i=0,3 + real_mul_map%q%x(i)=r*s1%q%x(i) + enddo + + c_master=localmaster + + END FUNCTION real_mul_map + + FUNCTION complex_mul_map( r,S1 ) + implicit none + TYPE (c_damap) complex_mul_map + complex(dp),intent(in):: r + TYPE (c_damap), INTENT (IN) :: S1 + integer localmaster,i,j + + IF(.NOT.C_STABLE_DA) then + complex_mul_map%v%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + complex_mul_map%n=s1%n + call c_assmap(complex_mul_map) + + do i=1,s1%n + complex_mul_map%v(i)=r*s1%v(i) + enddo + + + do i=1,3 + do j=1,3 + complex_mul_map%s%s(i,j)=r*s1%s%s(i,j) + enddo + enddo + + do i=0,3 + complex_mul_map%q%x(i)=r*s1%q%x(i) + enddo + + + c_master=localmaster + + END FUNCTION complex_mul_map + + + FUNCTION real_mul_vec( r,S1 ) + implicit none + TYPE (c_vector_field) real_mul_vec + real(dp),intent(in):: r + TYPE (c_vector_field), INTENT (IN) :: S1 + integer localmaster,i + + IF(.NOT.C_STABLE_DA) then + real_mul_vec%v%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + real_mul_vec%n=s1%n + call c_ass_vector_field(real_mul_vec) + + do i=1,s1%n + real_mul_vec%v(i)=r*s1%v(i) + enddo + + + if(use_quaternion) then + do i=0,3 + real_mul_vec%q%x(i)=r*s1%q%x(i) + enddo + else + ! real_mul_vec%h=r*s1%h + real_mul_vec%L=r*s1%L + endif + + + real_mul_vec%nrmax=s1%nrmax + real_mul_vec%eps=s1%eps + + c_master=localmaster + + END FUNCTION real_mul_vec + + FUNCTION complex_mul_vec( r,S1 ) + implicit none + TYPE (c_vector_field) complex_mul_vec + complex(dp),intent(in):: r + TYPE (c_vector_field), INTENT (IN) :: S1 + integer localmaster,i + + IF(.NOT.C_STABLE_DA) then + complex_mul_vec%v%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + complex_mul_vec%n=s1%n + call c_ass_vector_field(complex_mul_vec) + + do i=1,s1%n + complex_mul_vec%v(i)=r*s1%v(i) + enddo + + + if(use_quaternion) then + do i=0,3 + complex_mul_vec%q%x(i)=r*s1%q%x(i) + enddo + else + ! complex_mul_vec%h=r*complex_mul_vec%h + complex_mul_vec%L=r*complex_mul_vec%L + endif +! do i=1,3 +! complex_mul_vec%q%x(i)=r*s1%q%x(i) + ! enddo + + complex_mul_vec%nrmax=s1%nrmax + complex_mul_vec%eps=s1%eps + + c_master=localmaster + + END FUNCTION complex_mul_vec + + FUNCTION c_taylor_mul_vec( r,S1 ) + implicit none + TYPE (c_vector_field) c_taylor_mul_vec + type(c_taylor),intent(in):: r + TYPE (c_vector_field), INTENT (IN) :: S1 + integer localmaster,i + + IF(.NOT.C_STABLE_DA) then + c_taylor_mul_vec%v%i=0 + RETURN + endif + localmaster=c_master + + ! call check(s1) + c_taylor_mul_vec%n=s1%n + call c_ass_vector_field(c_taylor_mul_vec) + + do i=1,s1%n + c_taylor_mul_vec%v(i)=r*s1%v(i) + enddo + + + if(use_quaternion) then + do i=0,3 + c_taylor_mul_vec%q%x(i)=r*s1%q%x(i) + enddo + else + ! c_taylor_mul_vec%h=r*c_taylor_mul_vec%h + c_taylor_mul_vec%L=r*c_taylor_mul_vec%L + endif + + c_taylor_mul_vec%nrmax=s1%nrmax + c_taylor_mul_vec%eps=s1%eps + + c_master=localmaster + + END FUNCTION c_taylor_mul_vec + + + FUNCTION map_mul_vec_q( A,S1 ) + implicit none + TYPE (c_vector_field) map_mul_vec_q + type(c_damap),intent(in):: A + TYPE (c_vector_field), INTENT (IN) :: S1 + integer localmaster,i,k + TYPE (c_vector_field) f_orb + TYPE (c_quaternion) alpha_inv + TYPE (c_spinmatrix) A_inv + IF(.NOT.C_STABLE_DA) then + map_mul_vec_q%v%i=0 + RETURN + endif + localmaster=c_master + map_mul_vec_q%n=s1%n + call c_ass_vector_field(map_mul_vec_q) + f_orb%n=s1%n + call alloc(f_orb) + call alloc(alpha_inv) + +!!!! ???? equates quaternion too??? YES + f_orb=s1 + + + alpha_inv=A%q**(-1) + +!!!!! map_mul_vec wipes out quaternion in f_orb??? NO, just copies + f_orb=map_mul_vec( A,f_orb ) + f_orb%q=0.0_dp !!! now removes + map_mul_vec_q=f_orb !!! Only orbital is now transformed + + do i=0,3 + f_orb%q%x(i)=f_orb*alpha_inv%x(i) + enddo + + map_mul_vec_q%q=(alpha_inv*(s1%q*A)+f_orb%q)*A%q + + + map_mul_vec_q%nrmax=s1%nrmax + map_mul_vec_q%eps=s1%eps + call kill(alpha_inv) + call kill(f_orb) + c_master=localmaster + END FUNCTION map_mul_vec_q + + + FUNCTION map_mul_vec( r,S1 ) + implicit none + TYPE (c_vector_field) map_mul_vec + type(c_damap),intent(in):: r + type(c_damap) ri,r0 + TYPE (c_vector_field), INTENT (IN) :: S1 + integer localmaster,i,k + + IF(.NOT.C_STABLE_DA) then + map_mul_vec%v%i=0 + RETURN + endif + localmaster=c_master + call alloc(ri,r0) + r0=r + ri=r0**(-1) + + ! call check(s1) + map_mul_vec%n=s1%n + call c_ass_vector_field(map_mul_vec) + + map_mul_vec=0 + + do i=1,s1%n + do k=1,s1%n + map_mul_vec%v(k)=s1%v(i)*(ri%v(k).d.i)+map_mul_vec%v(k) + enddo + enddo + do k=1,s1%n + map_mul_vec%v(k)=map_mul_vec%v(k)*r0 + enddo + + map_mul_vec%nrmax=s1%nrmax + map_mul_vec%eps=s1%eps + + map_mul_vec%q=s1%q + c_master=localmaster + call kill(ri,r0) + END FUNCTION map_mul_vec + + function exp_ad(h,x,m) ! exp(Lie bracket) + implicit none + ! DOES EXP( \VEC{H} ) X = Y + + integer i,j,localmaster + type(c_vector_field) exp_ad,ft + type(c_vector_field), intent(in):: x + type(c_vector_field), intent(in) :: h + complex(dp), optional, intent(in) :: m + real(dp) prec,xnorm,r,xnorma + complex(dp) m0 + IF(.NOT.C_STABLE_DA) then + exp_ad%v%i=0 + RETURN + endif + m0=0 + if(present(m)) m0=m +prec=1.d-8 + localmaster=c_master + + + exp_ad%n=x%n + ft%n=x%n + call alloc(ft) + call c_ass_vector_field(exp_ad) + + exp_ad=x + ! c=1.0_dp + ft=x + + xnorm=0.0_dp + do j=1,ft%n + r=full_abs(ft%v(j)) + xnorm=xnorm+r + enddo + + do i=1,x%nrmax + + ft=(1.0_dp/i)*((h.lb.ft)+(m0*ft)) + exp_ad=exp_ad+ ft + + xnorma=0.0_dp + do j=1,ft%n + r=full_abs(ft%v(j)) + xnorma=xnorma+r + enddo + + if(xnorma>=xnorm.and.i > 20) then + + exit + endif + xnorm=xnorma + enddo + + + + + call kill(ft) + + c_master=localmaster + + end function exp_ad + + function iexp_ad(h,x,m) ! (exp(Lie bracket)- 1)/Lie bracket + implicit none + ! DOES EXP( \VEC{H} ) X = Y + + integer i,j,localmaster + type(c_vector_field) iexp_ad,ft + type(c_vector_field), intent(in):: x + type(c_vector_field), intent(in) :: h + complex(dp), optional, intent(in) :: m + real(dp) prec,xnorm,r,xnorma + complex(dp) m0 + IF(.NOT.C_STABLE_DA) then + iexp_ad%v%i=0 + RETURN + endif + m0=0 + if(present(m)) m0=m +prec=1.d-8 + localmaster=c_master + + + iexp_ad%n=x%n + ft%n=x%n + call alloc(ft) + call c_ass_vector_field(iexp_ad) + + iexp_ad=x + ! c=1.0_dp + ft=x + + xnorm=0.0_dp + do j=1,ft%n + r=full_abs(ft%v(j)) + xnorm=xnorm+r + enddo + + do i=2,x%nrmax + + ft=(1.0_dp/i)*((h.lb.ft)+(m0*ft)) + iexp_ad=iexp_ad+ ft + + xnorma=0.0_dp + do j=1,ft%n + r=full_abs(ft%v(j)) + xnorma=xnorma+r + enddo + + if(xnorma>=xnorm.and.i > 20) then + + exit + endif + xnorm=xnorma + enddo + + + + + call kill(ft) + + c_master=localmaster + + end function iexp_ad + + + +!eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee + + function c_expflo_map(h,x) !,eps,nrmax) + implicit none + ! DOES EXP( \VEC{H} ) X = Y + + integer i,j,localmaster,jj,k + type(c_damap) c_expflo_map + type(c_damap), optional, intent(in):: x + type(c_vector_field), intent(in) :: h + real(dp) coe,r,rbefore + type(c_damap) m1,mtemp + logical more + IF(.NOT.C_STABLE_DA) then + c_expflo_map%v%i=0 + RETURN + endif + call alloc(m1,mtemp) + localmaster=c_master + + if(present(x)) then + c_expflo_map%n=x%n + else + c_expflo_map%n=nd2 + endif + + call c_assmap(c_expflo_map) +jj=c_nda_dab + + if(present(x)) then + c_expflo_map=x + else + c_expflo_map=1 + endif + + + more=.true. + rbefore=1e30_dp + +m1=c_expflo_map + + +mtemp=m1 + +do i=1,h%nrmax +coe=i +mtemp=((1.d0/coe)*(h*mtemp)) + m1=mtemp + m1 + r=0 + do j=1,mtemp%n + r=full_abs(mtemp%v(j))+r + enddo +!!!! added in 2024.8.10 + if(use_quaternion) then + do j=0,3 + r=full_abs(mtemp%q%x(j))+r + enddo + else + do j=1,3 + do k=1,3 + r=full_abs(mtemp%s%s(j,k))+r + enddo + enddo + endif +!!!! added in 2024.8.10 + + if(more) then + if(r.gt.h%eps) then + rbefore=r + goto 100 + else + rbefore=r + more=.false. + endif + else + if(r.ge.rbefore) then + c_expflo_map=m1 + if(present(x)) c_expflo_map%x0=x%x0 + + c_master=localmaster + call kill(m1,mtemp) + + + return + endif + rbefore=r + endif + 100 continue + +enddo + + + call kill(m1,mtemp) + if(present(x)) c_expflo_map%x0=x%x0 + + c_master=localmaster + write(6,*) "r,rbefore",r,rbefore + write(6,*) "eps,nrmax",h%eps,h%nrmax + write(6,*) "Convergence not achieved in c_expflo_map " + write(6,*) "Try changing eps or nrmax in the vector field " + c_stable_da=.false. + end function c_expflo_map + + function c_expflo(h,x) !,eps,nrmax) + implicit none + ! DOES EXP( \VEC{H} ) X = Y + logical(lp) more + integer i ,localmaster + type(c_taylor) c_expflo + type(c_taylor), intent(in):: x + type(c_vector_field), intent(in) :: h + type(c_damap) m + IF(.NOT.C_STABLE_DA) then + c_expflo%i=0 + RETURN + endif + localmaster=c_master + + call ass(c_expflo) + + call alloc(m) + + m=0 + m%v(1)=x + m=exp(h,m) + + c_expflo=m%v(1) + + call kill(m) + + c_master=localmaster + end function c_expflo + + + subroutine c_flofacg(xy0,h,epso,n) +!#internal: manipulation +!# Use preferably function c_logf or its interface + implicit none + ! GENERAL ONE EXPONENT FACTORIZATION + logical(lp) more + integer i,k,nrmax,k1,n1,nn,n2 +! integer,dimension(:)::xy,h +! integer,dimension(ndim2)::x,v,w,t,z + type(c_damap), intent(inout) :: xy0 + type(c_vector_field), intent(inout) :: h + type(c_vector_field) t,z,z3,e2,e3,e4,e5 + type(c_damap) x,v,xy + real(dp), optional :: epso + integer, optional :: n + integer,dimension(lnv)::jj + real(dp) eps,epsone,r,xn,xnbefore,xnorm,xnorm1 + + n1=1 + if(present(n)) n1=n + + if(.not.c_stable_da) return + jj=0 + jj(1)=1 + ! + xy%n=xy0%n + call alloc(xy); + x%n=xy%n;v%n=xy%n; z%n=xy%n; t%n=xy%n; + call alloc(x);call alloc(v); call alloc(z);call alloc(t); + z3%n=xy%n;call alloc(z3); + + e2%n=xy%n;call alloc(e2); + e3%n=xy%n;call alloc(e3); + e4%n=xy%n;call alloc(e4); + e5%n=xy%n;call alloc(e5); + + + v=1 + do n2=2,2 ! put two for extra convergence + do nn=1,n1 + ! write(6,*) n2,nn + if(n2==1) then + do k1=1,xy0%n + xy%v(k1)=v%v(k1)+ nn*((xy0%v(k1).sub.1)-v%v(k1))/n1 + enddo + else + do k1=1,xy0%n + xy%v(k1)=(xy0%v(k1).sub.1) + nn*(xy0%v(k1)-(xy0%v(k1).sub.1))/n1 + enddo + endif + + xnorm1=0.0_dp + do i=1,xy%n + r=full_abs(xy%v(i)) + xnorm1=xnorm1+r + enddo + if(present(epso)) then + epsone= epso + else + epsone= xnorm1/epso_factor + endif + xnbefore=1e36_dp + more=.false. +! eps=1e-5_dp + + nrmax=1000 + xn=1e4_dp + if(lielib_print(3)==1) write(6,*) "epsone,xnorm1 ",epsone,xnorm1 + + + if(epsone>0.0_dp) then !epsone>zero + do k=1,nrmax + if(.not.(check_stable.and.C_STABLE_DA)) then + write(6,*) " unstable in map logarithm " + check_stable=.false. + call kill(x) + call kill(xy) + call kill(e2) + call kill(e3) + call kill(e4) + call kill(e5) + call kill(z3) + call kill(v) + call kill(t) + call kill(z) + return + return + endif + t=-h + + x=texp(t,xy) + do k1=1,xy%n + t%v(k1)=x%v(k1)-v%v(k1) + enddo +!if(k==1) write(6,*)k, full_abs(t%v(1)),full_abs(t%v(2)) + + + if(xn.lt.epsone) then !!! Quasi quadratic after some convergence obtained + if(lielib_print(3)==1) then + write(6,'(a28,i4,g21.14,1x,g21.14)') " Norm of CBH iteration # ",k,xn,epsone + endif + + do k1=1,xy%n + e2%v(k1)=-0.5_dp*(t*t%v(k1)) + enddo + do k1=1,xy%n + e3%v(k1)=-0.5_dp*(e2*t%v(k1))-(1.0_dp/6.0_dp)*(t*e2%v(k1)) + enddo + + do k1=1,xy%n + t%v(k1)=t%v(k1)+e2%v(k1)+e3%v(k1) ! t is now tau + enddo + + z=h.lb.t ! + e2=h.lb.z ! > + e3=t.lb.z ! > + do k1=1,xy%n + t%v(k1)=t%v(k1)+0.5_dp*z%v(k1) +(1.0_dp/12.0_dp)*(e2%v(k1)-e3%v(k1)) + enddo + e4=t.lb.e2 ! (tau,>> (0) + do k1=1,xy%n + t%v(k1)=t%v(k1)-(1.0_dp/24.0_dp)*e4%v(k1) + enddo + if(extra_terms_log) then + e4=h.lb.e2 ! >> (1) + e5=h.lb.e4 + do k1=1,xy%n + t%v(k1)=t%v(k1)-(1.0_dp/720.0_dp)*e5%v(k1) + enddo + e5=t.lb.e4 ! (2) + do k1=1,xy%n + t%v(k1)=t%v(k1)+(1.0_dp/360.0_dp)*e5%v(k1) + enddo + e4=t.lb.e2 ! >> + e5=h.lb.e4 ! >> (3) + do k1=1,xy%n + t%v(k1)=t%v(k1)-(1.0_dp/120.0_dp)*e5%v(k1) + enddo + e4=h.lb.e3 ! >> + e5=t.lb.e4 ! >> (4) + do k1=1,xy%n + t%v(k1)=t%v(k1)+(1.0_dp/120.0_dp)*e5%v(k1) + enddo + e4=t.lb.e3 ! >> + e5=h.lb.e4 ! >> (5) + do k1=1,xy%n + t%v(k1)=t%v(k1)-(1.0_dp/360.0_dp)*e5%v(k1) + enddo + e5=t.lb.e4 ! >> (6) + do k1=1,xy%n + t%v(k1)=t%v(k1)+(1.0_dp/720.0_dp)*e5%v(k1) + enddo + endif + endif !!!! end of quasi quadratic + + do k1=1,xy%n + h%v(k1)=t%v(k1)+h%v(k1) + enddo + + xnorm=0.0_dp + do i=1,xy%n + r=full_abs(t%v(i)) + xnorm=xnorm+r + enddo + xn=xnorm/xnorm1 + if(xn.ge.epsone.and.(lielib_print(3)==1)) then + write(6,'(a28,i4,g21.14,1x,g21.14)') " Norm of linear iteration # ",k,xn,epsone + endif + ! if(xn.lt.eps.or.more) then + if(xn.lt.epsone.or.more) then + + more=.true. + if(xn.ge.xnbefore) goto 1000 + xnbefore=xn + endif + enddo + +1000 continue + ! write(6,*) "k",k + else !epsone>zero + + do k=1,nint(abs(epsone))-1 + if(lielib_print(3)==1) then + xnorm=0.0_dp + do i=1,xy%n + r=full_abs(t%v(i)) + xnorm=xnorm+r + enddo + xn=xnorm/xnorm1 + write(6,'(a20,g21.14)') " norm of correction ",xn + endif + t=-h + + x=texp(t,xy) + + do k1=1,xy%n + t%v(k1)=x%v(k1)-v%v(k1) + enddo + + + do k1=1,xy%n + h%v(k1)=t%v(k1)+h%v(k1) + enddo + + enddo + endif + ! if(lielib_print(3)==1) WRITE(6,*) " K ", K,epsone + if(lielib_print(3)==1) then + write(6,'(a11,i4)') " iteration " , k-1 + endif + + + enddo ! nn + + enddo ! n2 + + call kill(x) + call kill(xy) + call kill(e2) + call kill(e3) + call kill(e4) + call kill(e5) + call kill(z3) + call kill(v) + call kill(t) + call kill(z) + return + end subroutine c_flofacg + + + +!!!!!!!!!!!!!!!!!!!!! spin + + subroutine c_find_n0(s0,n0,linear) +!#general: manipulation & normal +!# This routine finds the invariant vector n0 +!# if the rotation s0 of type c_spinmatrix. +!# If linear is true, only the constant part of +!# s0 is used. Thus s0_constant =exp(theta n0.L) where n0 is a +!# vector of length one. This is the n0 of the normal form. +!# If linear is false, then s0=exp(theta n0.L) but this is NOT +!# the invariant ISF n. See Sec.6.3.2. where I explained why this n0 +!# cannot be the ISF vector n. + implicit none + type(c_spinmatrix),intent(inout) :: s0 + type(c_spinor), intent(inout) :: n0 + type(c_taylor) norm0 + type(c_taylor) det,detm + type(c_spinmatrix) ss + logical(lp), optional :: linear + logical(lp) linear0 + integer i,is,j + + linear0=my_false + if(present(linear)) linear0=linear + call alloc(det) + call alloc(detm) + call alloc(norm0) + call alloc(ss) + +! ss=s0 + + + do i=1,3 + do j=1,3 + if(linear0) then + ss%s(i,j)=(s0%s(i,j).sub.'0') + else + ss%s(i,j)=s0%s(i,j) + endif + enddo + enddo + + + + do i=1,3 + ss%s(i,i)=ss%s(i,i)-1.0_dp + enddo + + det=(ss%s(2,2)*ss%s(3,3)-ss%s(2,3)*ss%s(3,2)) + + is=1 + detm=(ss%s(1,1)*ss%s(3,3)-ss%s(1,3)*ss%s(3,1)) + + if(abs(detm)>=abs(det)) then + det=detm + is=2 + endif + + detm=ss%s(1,1)*ss%s(2,2)-ss%s(1,2)*ss%s(2,1) + if(abs(detm)>=abs(det)) then + det=detm + is=3 + endif + + + n0%v(is)=1.0_dp + if(is==1) then + n0%v(2)=(-ss%s(3,3)*ss%s(2,1)+ss%s(2,3)*ss%s(3,1))/det + n0%v(3)=(-ss%s(2,2)*ss%s(3,1)+ss%s(2,1)*ss%s(3,2))/det + elseif(is==2) then + n0%v(1)=(-ss%s(3,3)*ss%s(1,2)+ss%s(3,2)*ss%s(1,3))/det + n0%v(3)=(-ss%s(1,1)*ss%s(3,2)+ss%s(1,2)*ss%s(3,1))/det + else + n0%v(1)=(-ss%s(2,2)*ss%s(1,3)+ss%s(2,3)*ss%s(1,2))/det + n0%v(2)=(-ss%s(1,1)*ss%s(2,3)+ss%s(1,3)*ss%s(2,1))/det + endif + + norm0=sqrt(n0%v(1)**2+n0%v(2)**2+n0%v(3)**2) + + + + do i=1,3 + n0%v(i)=n0%v(i)/norm0 + enddo + + + call kill(det) + call kill(detm) + call kill(norm0) + call kill(ss) + + end subroutine c_find_n0 + + subroutine c_n0_to_nr(n0,nr) +!#general: manipulation & normal +!# Puts an vector n0 into the eigenoperators of L_y +!# nt%v(2)=n0%v(2) +!# nt%v(1)=n0%v(1)-i_*n0%v(3) ! coefficient of 1/2(L_x + i L_z) +!# nt%v(3)=n0%v(1)+i_*n0%v(3) ! coefficient of 1/2(L_x - i L_z) +!# The inverse routine is c_nr_to_n0 + + implicit none + TYPE(c_spinor), INTENT(INout) :: n0,nr + TYPE(c_spinor) nt + + call alloc(nt) + + nt%v(2)=n0%v(2) + nt%v(1)=n0%v(1)-i_*n0%v(3) ! coefficient of 1/2(L_x + i L_z) + nt%v(3)=n0%v(1)+i_*n0%v(3) ! coefficient of 1/2(L_x - i L_z) + nr=nt + call kill(nt) + + end subroutine c_n0_to_nr + + subroutine c_nr_to_n0(nr,n0) +!#general: manipulation & normal +!# Puts an eigenoperators vector nr into the cartesian basis +!# (L_x,L_y,L_z). +!# nt%v(2)=nr%v(2) +!# nt%v(1)=(nr%v(1)+nr%v(3))/2.0_dp ! coefficient of L_x +!# nt%v(3)=i_*(nr%v(1)-nr%v(3))/2.0_dp ! coefficient of L_z +!# The inverse routine is c_n0_to_nr. + implicit none + TYPE(c_spinor), INTENT(INout) :: n0,nr + TYPE(c_spinor) nt + + call alloc(nt) + + nt%v(2)=nr%v(2) + nt%v(1)=(nr%v(1)+nr%v(3))/2.0_dp ! coefficient of L_x + nt%v(3)=i_*(nr%v(1)-nr%v(3))/2.0_dp ! coefficient of L_z + n0=nt + call kill(nt) + + end subroutine c_nr_to_n0 + + subroutine c_q0_to_qr(n0,nr) +!#general: manipulation & normal +!# same as c_nr_to_n0 + + + implicit none + TYPE(c_quaternion), INTENT(INout) :: n0,nr + TYPE(c_quaternion) nt + + call alloc(nt) + + nt%x(2)=n0%x(2) + nt%x(1)=n0%x(1)-i_*n0%x(3) ! coefficient of 1/2(i + sqrt(-1) k) + nt%x(3)=n0%x(1)+i_*n0%x(3) ! coefficient of 1/2(i - sqrt(-1) k) + nr=nt + call kill(nt) + + end subroutine c_q0_to_qr + + subroutine c_qr_to_q0(nr,n0) +!#general: manipulation & normal +!# same as c_nr_to_n0 + + implicit none + TYPE(c_quaternion), INTENT(INout) :: n0,nr + TYPE(c_quaternion) nt + + call alloc(nt) + + nt%x(2)=nr%x(2) + nt%x(1)=(nr%x(1)+nr%x(3))/2.0_dp ! coefficient of i quaternion + nt%x(3)=i_*(nr%x(1)-nr%x(3))/2.0_dp ! coefficient of k quaternion + n0=nt + call kill(nt) + + end subroutine c_qr_to_q0 + + subroutine c_find_om_da(S,om,n) +!#restricted : normal +!# This routine finds om such that the c_spinmatrix S= exp(om.L). +!# However it does it in "n" steps if n is specified. +!# Otherwise it does it in no steps, no is the order of the complex +!# TPSA package. +!# This routine works only if the matrix S does not have constant parts. +!# It is used in the normal form algorithm for the spin. + implicit none + TYPE(c_spinmatrix), INTENT(INout) :: S + TYPE(c_spinor), INTENT(INout) :: om + integer, optional :: n + TYPE(c_spinmatrix) h + integer i,nr + TYPE(c_spinmatrix) dh,dhn,di + complex(dp) c,cl + real(dp) depsb,depsa + logical pre + call alloc(h) + call alloc(dh) + call alloc(dhn) + call alloc(di) + ! this only works with a da-map + nr=no + pre=present(n) + if(present(n)) then + nr=n + endif + dh=S + h=0 + dhn=1 + dh%s(1,1)=dh%s(1,1)-1.0_dp + dh%s(2,2)=dh%s(2,2)-1.0_dp + dh%s(3,3)=dh%s(3,3)-1.0_dp + depsb=1.e38_dp + c=1.0_dp + do i=1,nr + dhn=dhn*dh + cl=c/i + di=cl*dhn + h=h+di + c=-c + call c_norm_spinmatrix(di,depsa) + if(lielib_print(3)==1) write(6,*) i,depsa + if(pre.and.i>nr/2) then + if(depsa>=depsb) exit + depsb=depsa + endif + enddo + + if(pre.and.i>nr-1) then + write(6,*) " did not converged in c_find_om_da ",i + write(6,*) " Norms ",depsb,depsa + stop + endif + + om%v(1)=h%s(3,2) + om%v(2)=h%s(1,3) + om%v(3)=h%s(2,1) + + call kill(h) + call kill(dh) + call kill(dhn) + call kill(di) + end subroutine c_find_om_da + + subroutine c_find_as(n22,a) +!#general : normal & manipulation +!# Find the c_spinmatrix "a" such that +!# e_y = (0,1,0)= a**(-1)*n0 +!# because a*exp(theta n0.L)*a**(-1)= exp(theta (a*n0).L). See Sec.6.5.2. + + implicit none + type(c_spinor), intent(inout) :: n22 + type(c_spinmatrix), intent(inout) :: a + type(c_spinor) n1 ,n3,n2 + type(c_taylor) s,n + real(dp) x + integer i,is + + call alloc(n1) + call alloc(n2) + call alloc(n3) + call alloc(s,n) + + n2=n22 + + x=n2.dot.n2 + + x=sqrt(x) + + do i=1,3 + n2%v(i)=n2%v(i)/x + enddo + + ! here we find smallest value of n2 + is=2 + if(abs(n2%v(1))< abs(n2%v(2))) is=1 + + if(is==1) then + if(abs(n2%v(3))abs(n3%v(1))) then + do i=1,3 + a%s(i,1)=n1%v(i) + a%s(i,2)=n2%v(i) + a%s(i,3)=n3%v(i) + enddo +else +x=n3%v(1).sub.'0' + +if(x<0) then + do i=1,3 + a%s(i,1)=-n3%v(i) + a%s(i,2)=n2%v(i) + a%s(i,3)=n1%v(i) + enddo +else + do i=1,3 + a%s(i,1)=n3%v(i) + a%s(i,2)=n2%v(i) + a%s(i,3)=-n1%v(i) + enddo +endif + +endif + + + + call kill(n1) + call kill(n2) + call kill(n3) + call kill(s,n) + end subroutine c_find_as + + subroutine c_inv_as(m,mi) +!#internal : manipulation +!# Trivially inverts an O(3) rotation by taking the transpose. +!# mi=m**(-1)=m^t. + implicit none + integer i,j + TYPE (c_spinmatrix), intent (inout):: m,mi + TYPE (c_spinmatrix) n + + call alloc(n) + + do i=1,3 + do j=1,3 + n%s(j,i)=m%s(i,j) + enddo + enddo + + do i=1,3 + do j=1,3 + mi%s(i,j)=n%s(i,j) + enddo + enddo + + call kill(n) + + end subroutine c_inv_as + + + + subroutine c_find_spin_angle(S,tune,radian) +!#restricted : normal +!# Find the tune of a spin rotation S +!# which is a rotation around the y-axis. + implicit none + + TYPE (c_spinmatrix), intent (inout):: S + TYPE (c_taylor) tune + logical(lp),optional :: radian + logical(lp) rad + + rad=my_true + if(present(radian)) rad=radian + tune=S%s(1,1)+i_*S%s(1,3) + + tune=-i_*log(tune) + + if(.not.rad) tune=tune/twopi + + end subroutine c_find_spin_angle + + function c_log_spinmatrix(s,exact,n) ! spin routine + implicit none + TYPE(c_spinor) c_log_spinmatrix + TYPE(c_spinmatrix), INTENT(INout) :: s + type(c_taylor) tune + type(c_damap) as + logical(lp), optional :: exact + integer, optional :: n + logical(lp) exa,useq + integer localmaster + real(dp) d + integer k,n1 + IF(.NOT.C_STABLE_DA) then + c_log_spinmatrix%v%i=0 + RETURN + endif +useq=use_quaternion +use_quaternion=.false. + exa=my_false + n1=no + if(present(exact)) exa=exact + localmaster=c_master + + call c_ass_spinor(c_log_spinmatrix) + + if(present(n)) then + call c_find_om_da(s,c_log_spinmatrix,n) + else + + if(.not.exa) then + call c_norm_spin(s,k,EPS=d) + if(d<1.d-2) then + n1=no+20000 + k=1 + endif + else + k=0 + endif +! write(6,*) " k, d ",k,d +!pause +!etienne + if(k==1) then + call c_find_om_da(s,c_log_spinmatrix,n1) + else + call alloc(as) + call alloc(tune) + + as=1 + + call c_find_n0(s,c_log_spinmatrix) + + call c_find_as(c_log_spinmatrix,AS%s) + + AS%s= AS%s**(-1)*s*as%s + + + call c_find_spin_angle(as%s,tune) + + + c_log_spinmatrix=tune*c_log_spinmatrix + + + call kill(as) + call kill(tune) + endif + + endif + c_master=localmaster +use_quaternion=useq + end function c_log_spinmatrix + +! now useless, use quaternion if needed +! function c_spinor_spinmatrix(h_axis,ds) ! spin routine +! implicit none +! TYPE(c_spinmatrix) c_spinor_spinmatrix +! TYPE(c_spinmatrix), INTENT(IN) :: DS +! TYPE(c_spinor), INTENT(IN) :: h_axis + + ! integer localmaster + ! TYPE(c_spinmatrix) dh + ! real(dp) eps,norm1,norm2 + ! + ! logical check + ! IF(.NOT.C_STABLE_DA) then + ! c_spinor_spinmatrix%s%i=0 + ! RETURN + ! endif + ! + ! localmaster=c_master + ! + ! call c_ass_spinmatrix(c_spinor_spinmatrix) + ! call alloc(dh) + ! + ! dh%s(3,1)=-h_axis%v(2) + ! dh%s(2,1)=h_axis%v(3) + ! dh%s(1,3)=h_axis%v(2) + ! dh%s(3,2)=h_axis%v(1) + ! dh%s(1,2)=-h_axis%v(3) + ! dh%s(2,3)=-h_axis%v(1) + +! c_spinor_spinmatrix=dh*ds +! Lie operator order +! c_spinor_spinmatrix=ds*dh + + + + +! call kill(dh) +! +! c_master=localmaster +! +! end function c_spinor_spinmatrix + + + +function c_vector_field_quaternion(h,ds) ! spin routine + implicit none + TYPE(c_quaternion) c_vector_field_quaternion + TYPE(c_quaternion), INTENT(IN) :: DS + TYPE(c_vector_field), INTENT(IN) :: h + integer nmax + integer i,j,localmaster + IF(.NOT.C_STABLE_DA) then + c_vector_field_quaternion%x(1)%i=0 + RETURN + endif + + localmaster=c_master + + call c_ass_quaternion(c_vector_field_quaternion) + + do i=0,3 + c_vector_field_quaternion%x(i)=h*ds%x(i) + enddo + ! order reversed for compositional map considerations + if(correct_quaternion_field) then + c_vector_field_quaternion=c_vector_field_quaternion+ (ds*h%q) + else + c_vector_field_quaternion=c_vector_field_quaternion+ ( h%q*ds) + endif + c_master=localmaster + + end function c_vector_field_quaternion + +function c_vector_field_so3(h,ds) ! spin routine + implicit none + TYPE(c_spinmatrix) c_vector_field_so3 + TYPE(c_spinmatrix), INTENT(IN) :: DS + TYPE(c_vector_field), INTENT(IN) :: h + integer nmax + integer i,j,localmaster + TYPE(c_spinmatrix) sh + IF(.NOT.C_STABLE_DA) then + c_vector_field_so3%s(1,1)%i=0 + RETURN + endif + + localmaster=c_master + + call c_ass_spinmatrix(c_vector_field_so3) + call alloc(sh) + do i=1,3 + do j=1,3 + c_vector_field_so3%s(i,j)=h*ds%s(i,j) + enddo + enddo + ! order reversed for compositional map considerations + + + + + if(correct_quaternion_field) then + c_vector_field_so3= ds*h%L + c_vector_field_so3 + else + c_vector_field_so3= h%L*ds + c_vector_field_so3 + endif + c_master=localmaster + + call kill(sh) + + end function c_vector_field_so3 + + + + function c_exp_spinmatrix(h_axis,ds) ! spin routine + implicit none + TYPE(c_spinmatrix) c_exp_spinmatrix + TYPE(c_spinmatrix),optional, INTENT(INout) :: DS + TYPE(c_spinor), INTENT(IN) :: h_axis + integer nmax + integer i,localmaster + TYPE(c_spinmatrix) dh,dhn,dr,dst + real(dp) eps,norm1,norm2 + complex(dp) c + logical check + IF(.NOT.C_STABLE_DA) then + c_exp_spinmatrix%s%i=0 + RETURN + endif + + localmaster=c_master + + call c_ass_spinmatrix(c_exp_spinmatrix) + + + + + check=.true. + eps=1.d-5 + nmax=1000 + + call alloc(dh) + call alloc(dhn) + call alloc(dr) + + + ! this works with a tpsa-map + + + c_exp_spinmatrix=1 + + dh=0 + dh%s(2,1)=h_axis%v(3) + dh%s(1,3)=h_axis%v(2) + dh%s(3,2)=h_axis%v(1) + dh%s(1,2)=-h_axis%v(3) + dh%s(3,1)=-h_axis%v(2) + dh%s(2,3)=-h_axis%v(1) + + dhn=1 + c=1.0_dp + norm1=mybig + do i=1,nmax + dhn=dhn*dh + c=c/i + + dr=c_exp_spinmatrix + c_exp_spinmatrix=c_exp_spinmatrix+c*dhn + + dr=c_exp_spinmatrix+(-1.0_dp,0.0_dp)*dr + + call c_full_norm_spinmatrix(dr,norm2) + + if(check) then + if(norm210) then + check=.false. + endif + else + if(norm2>=norm1) exit + endif + norm1=norm2 + enddo + + if(i>nmax-10) then + write(6,*) "no convergence in c_exp_spinmatrix, enter 0 to stop " + read(5,*) norm1 + if(norm1==0) stop 1066 + endif + if(present(ds)) c_exp_spinmatrix=c_exp_spinmatrix*ds + + call kill(dh) + call kill(dhn) + call kill(dr) + + c_master=localmaster + end function c_exp_spinmatrix + + function c_exp_quaternion(h_axis,ds,n) ! spin routine + implicit none + TYPE(c_quaternion) c_exp_quaternion + TYPE(c_quaternion),optional, INTENT(INout) :: DS + TYPE(c_quaternion), INTENT(IN) :: h_axis + integer nmax,nnmax + integer , optional ::n + integer i,localmaster,k + TYPE(c_quaternion) dh,dhn,dr,dst + real(dp) eps,norm1,norm2 + complex(dp) c + logical check + IF(.NOT.C_STABLE_DA) then + c_exp_quaternion%x(1)%i=0 + RETURN + endif + + localmaster=c_master + + call c_ass_quaternion(c_exp_quaternion) + + check=.true. + eps=1.d-5 + nmax=1000 + nnmax=nmax + if(present(n)) nnmax=n + call alloc(dh) + call alloc(dhn) + call alloc(dr) + + c_exp_quaternion=1.0_dp + + dh=h_axis + + + dhn=1.0_dp + c=1.0_dp + norm1=mybig + do i=1,min(nmax,nnmax) + dhn=dhn*dh + c=1.0_dp/i + dhn=c*dhn + + dr=c_exp_quaternion + + c_exp_quaternion=c_exp_quaternion+dhn + + dr=c_exp_quaternion+(-1.0_dp,0.0_dp)*dr + + call c_full_norm_quaternion(dr,k,norm2) + + + if(check) then + if(norm210) then + check=.false. + endif + else + if(norm2>=norm1) exit + endif + norm1=norm2 + enddo + + if(i>nmax-10) then + write(6,*) "no convergence in c_exp_quaternion, enter 0 to stop " + read(5,*) norm1 + if(norm1==0) stop 1066 + endif + if(present(ds)) c_exp_quaternion=c_exp_quaternion*ds + + call kill(dh) + call kill(dhn) + call kill(dr) + + c_master=localmaster + end function c_exp_quaternion + + + + function c_exp_vectorfield_on_quaternion(h,ds) ! spin routine + implicit none + TYPE(c_quaternion) c_exp_vectorfield_on_quaternion + TYPE(c_quaternion), INTENT(INout) :: DS + TYPE(c_vector_field), INTENT(IN) :: h + integer nmax,k + integer i,localmaster + TYPE(c_quaternion) dh,dr + real(dp) eps,norm1,norm2 + complex(dp) c + logical check + IF(.NOT.C_STABLE_DA) then + c_exp_vectorfield_on_quaternion%x(1)%i=0 + RETURN + endif + + localmaster=c_master + + call c_ass_quaternion(c_exp_vectorfield_on_quaternion) + + + + check=.true. + eps=1.d-10 + nmax=1000 + + call alloc(dh) + + call alloc(dr) + + + ! this works with a tpsa-map + + + c_exp_vectorfield_on_quaternion=ds + + + ! if(present(ds)) then + dh=ds + ! else + ! dh=1 + ! dh=h.lb.dh + ! endif + + + c=1.0_dp + norm1=mybig + do i=1,nmax + + dh=h*dh + c=c/i + + dr=c_exp_vectorfield_on_quaternion + c_exp_vectorfield_on_quaternion=c_exp_vectorfield_on_quaternion+c*dh + + dr=c_exp_vectorfield_on_quaternion+(-1.0_dp,0.0_dp)*dr + + call c_full_norm_quaternion(dr,k,norm2) + + if(check) then + if(norm210) then + check=.false. + endif + else + if(norm2>=norm1) exit + endif + norm1=norm2 + enddo + + if(i>nmax-10) then + write(6,*) "no convergence in c_exp_vectorfield_on_quaternion, enter 0 to stop " + read(5,*) norm1 + if(norm1==0) stop 1066 + endif + + + call kill(dh) + call kill(dr) + + c_master=localmaster + end function c_exp_vectorfield_on_quaternion + + + subroutine c_full_norm_damap(m,norm) ! spin routine + implicit none + TYPE(c_damap), INTENT(IN) :: m + real(dp) norm + integer i,j + + norm=0.0_dp + do i=1,m%n + norm=norm+full_abs( m%v(i) ) + enddo + if(use_quaternion) then + do i=0,3 + norm=norm+full_abs( m%q%x(i) ) + enddo + else + do i=1,3 + do j=1,3 + norm=norm+full_abs( m%s%s(i,j) ) + enddo + enddo + endif + end subroutine c_full_norm_damap + + + subroutine c_full_norm_spin_map(m,k,norm) ! spin routine + implicit none + TYPE(c_damap), INTENT(IN) :: m + real(dp) norm + integer i,k + + norm=0.0_dp + if(use_quaternion) then + call c_full_norm_quaternion(m%q,k,norm) + else + call c_full_norm_spin(m%s,k,norm) + endif + + end subroutine c_full_norm_spin_map + + subroutine c_full_norm_spinmatrix(s,norm) ! spin routine + implicit none + TYPE(c_spinmatrix), INTENT(IN) :: S + real(dp) norm + integer i,j + + norm=0.0_dp + + do i=1,3 + do j=1,3 + norm=norm+full_abs( s%s(i,j) ) + enddo + enddo + + end subroutine c_full_norm_spinmatrix + + subroutine c_full_norm_quaternion(q,k,norm) ! spin routine + implicit none + TYPE(c_quaternion), INTENT(IN) :: q + real(dp) norm,normn,nr + integer i,k + k=-1 + norm=0.0_dp + + do i=1,3 + + norm=norm+full_abs( q%x(i) ) + + enddo + normn=norm + norm=norm+full_abs( q%x(0) ) + + if(norm==0) k=0 + nr=q%x(0) + if(norm==1.and.normn==0.and.nr==1) k=1 + + end subroutine c_full_norm_quaternion + + subroutine c_norm_spinmatrix(s,norm) ! spin routine + implicit none + TYPE(c_spinmatrix), INTENT(IN) :: S + real(dp) norm + integer i,j + + norm=0.0_dp + + do i=1,3 + do j=1,3 + norm=norm+abs( s%s(i,j) ) + enddo + enddo + + end subroutine c_norm_spinmatrix + + subroutine c_full_norm_vector_field(s,norm) ! spin routine + implicit none + TYPE(c_vector_field), INTENT(IN) :: S + real(dp) norm,norms + integer i,k + + norm=0.0_dp + + do i=1,s%n + norm=norm+full_abs( s%v(i) ) + enddo + norms=0.0_dp + if(use_quaternion) then + call c_full_norm_quaternion(s%q,k,norms) + else + call c_full_norm_spinmatrix(s%L,norms) + ! call c_full_norm_spinor(s%h,norms) + endif + norm=norm+norms + end subroutine c_full_norm_vector_field + + subroutine c_full_norm_spinor(s,norm) ! spin routine + implicit none + TYPE(c_spinor), INTENT(IN) :: S + real(dp) norm + integer i + + norm=0.0_dp + + do i=1,3 + norm=norm+full_abs( s%v(i) ) + enddo + + end subroutine c_full_norm_spinor + + subroutine c_full_norm_fourier(s,norm) ! spin routine + implicit none + TYPE(c_vector_field_fourier), INTENT(IN) :: S + real(dp) norm,nor1 + integer i + + norm=0.0_dp + + do i=-n_fourier,n_fourier + call c_full_norm_vector_field(s%f(i),nor1) + norm=norm+nor1 + enddo + + end subroutine c_full_norm_fourier + +!!!! radiation + + subroutine c_check_rad(e_ij,rad_in) + implicit none + logical(lp), INTENT(INout) :: rad_in + complex(dp) e_ij(6,6) + integer i,j + real(dp) norm + + rad_in=my_true + norm=0.0_dp + do i=1,min(c_%nd2,6) + do j=1,min(c_%nd2,6) + norm=norm+abs(e_ij(i,j)) + enddo + enddo + + if(norm==0.0_dp) then + rad_in=.false. + endif + + end subroutine c_check_rad + + subroutine c_check_rad_spin(e_ij,rad_in) + implicit none + logical(lp), INTENT(INout) :: rad_in + real(dp) e_ij(3,3) + integer i,j + real(dp) norm + + rad_in=my_true + norm=0.0_dp + do i=1,3 + do j=1,3 + norm=norm+abs(e_ij(i,j)) + enddo + enddo + + if(norm==0.0_dp) then + rad_in=.false. + endif + + end subroutine c_check_rad_spin + + subroutine c_exp_mat_(f,m) + implicit none + complex(dp), intent(inout) :: f(:,:) + complex(dp), intent(inout) :: m(:,:) + integer i,n + real(dp) norma,normb,x,y + complex(dp), allocatable :: t(:,:),ft(:,:) + y=1.d-7 + + n=size(m,1) + allocate(t(n,n)) + allocate(ft(n,n)) +ft=f + t=0 + m=0 + do i=1,n + m(i,i)=1 + t(i,i)=1 + enddo + normb=c_norm_matrix(ft) + x=1 + do i=1,10000 + t=matmul(ft,t)/x + norma=c_norm_matrix(t) + m= m+t + x=x+1 + + if(norma=normb.and.i>100) exit + normb=norma + enddo + if(i>10000-10) write(6,*) "c_exp_mat",i + deallocate(t) + deallocate(ft) + end subroutine c_exp_mat_ + + function c_norm_matrix(f) + implicit none + real(dp) c_norm_matrix + complex(dp), intent(in) :: f(:,:) + integer i,j,n + + + c_norm_matrix=0 + n=size(f,1) + + do i=1,n + do j=1,n + c_norm_matrix=c_norm_matrix+abs(f(i,j)) + enddo + enddo + + end function c_norm_matrix + + subroutine exp_mat_(f,m) + implicit none + real(dp), intent(inout) :: f(:,:) + real(dp), intent(inout) :: m(:,:) + integer i,n + real(dp) norma,normb,x,y + real(dp), allocatable :: t(:,:),ft(:,:) + y=1.d-7 + + n=size(m,1) + allocate(t(n,n)) + allocate(ft(n,n)) +ft=f + t=0 + m=0 + do i=1,n + m(i,i)=1 + t(i,i)=1 + enddo + normb=norm_matrix(ft) + x=1 + do i=1,10000 + t=matmul(ft,t)/x + norma=norm_matrix(t) + m= m+t + x=x+1 + + if(norma=normb.and.i>100) exit + normb=norma + enddo + if(i>10000-10) write(6,*) "exp_mat",i + deallocate(t) + deallocate(ft) + end subroutine exp_mat_ + + function norm_matrix(f) + implicit none + real(dp) norm_matrix + real(dp), intent(in) :: f(:,:) + integer i,j,n + + + norm_matrix=0 + n=size(f,1) + + do i=1,n + do j=1,n + norm_matrix=norm_matrix+abs(f(i,j)) + enddo + enddo + + end function norm_matrix + + +!!!!!!!!!!!!!!!!!!!!!!! eig6 + + + subroutine c_eig6(fm,reval,aieval,revec,aievec) +!* + implicit none + !************************************************************************** + + ! Diagonalization routines of NERI + + !ccccccccccccccccc + ! + ! this routine finds the eigenvalues and eigenvectors + ! of the full matrix fm. + ! the eigenvectors are normalized so that the real and + ! imaginary part of vectors 1, 3, and 5 have +1 antisymmetric + ! product: + ! revec1 J aivec1 = 1 ; revec3 J aivec3 = 1 ; + ! revec5 J aivec5 = one + ! the eigenvectors 2 ,4, and 6 have the opposite normalization. + ! written by F. Neri, Feb 26 1986. + ! + integer jet,nn,i,i1,ilo,ihi,mdim,info + real(dp),dimension(ndim2t)::reval,aieval,ort + real(dp),dimension(ndim2t,ndim2t)::revec,aievec,fm,aa,vv + real(dp) eig2 + if(.not.C_STABLE_DA) return + + Eigenvalues_off_unit_circle=1 + ! copy matrix to temporary storage (the matrix aa is destroyed) + do i=1,nd2harm !nd2t !-ndc2t + do i1=1,nd2harm !,nd2t !-ndc2t + aa(i1,i) = fm(i1,i) + enddo + enddo + + ilo = 1 + ihi = nd2harm !nd2t !-ndc2t + mdim = ndim2t + nn = nd2harm !nd2t !-ndc2t + ! compute eigenvalues and eigenvectors using double + ! precision Eispack routines: + call ety(mdim,nn,ilo,ihi,aa,ort) + call etyt(mdim,nn,ilo,ihi,aa,ort,vv) + call ety2(mdim,nn,ilo,ihi,aa,reval,aieval,vv,info) + + if ( info .ne. 0 ) then + write(6,*) ' ERROR IN C_EIG6' + stop 999 + endif + ! call neigv(vv,pbkt) + + do i=1,ndharm !ndt !-ndct + do jet=1,nd2harm !nd2t !-ndc2t + revec(jet,2*i-1)=vv(jet,2*i-1) + revec(jet,2*i)=vv(jet,2*i-1) + aievec(jet,2*i-1)=vv(jet,2*i) + aievec(jet,2*i)=-vv(jet,2*i) + enddo + enddo + +! do i=1,nd2harm !nd2t !-ndc2t +! if(abs(reval(i)**2+aieval(i)**2 -1.0_dp).gt.eps_Eigenvalues_off_unit_circle) then +! if(lielib_print(4)==1) then +! write(6,*) ' EIG6: Eigenvalues off the unit circle!' +! write(6,*) sqrt(reval(i)**2+aieval(i)**2) +! endif +! Eigenvalues_off_unit_circle=.false. +! endif +! enddo + + do i=1,nd2harm !nd2t !-ndc2t + eig2 = reval(i)**2+aieval(i)**2 + if(abs(eig2 -1.0_dp).gt.eps_eigenvalues_off_unit_circle) then + if(mod(i,2)==0.and.abs(aieval(i))=1) COSLIKE=.false. +if(gamma>=0) then + gam=sqrt(a(1,1)) + r_te=1 + R_TE%v(1)=gam*dz_c(1) + do i=2,4 + R_TE%v(i)=gam*dz_c(i) + enddo + do i=1,2 + do j=3,4 + R_TE%v(i)=-a(i,j)/gam*dz_c(j)+R_TE%v(i) + R_TE%v(j)=a(j,i)/gam*dz_c(i)+R_TE%v(j) + enddo + enddo + t_e=.true. +else + t_e=.false. +endif + +do i=1,4 +do j=1,4 + call kill(A(i,j)) + call kill(Ai(i,j)) + call kill(h1(i,j)) +enddo +enddo + +if(.not.t_e) goto 100 +! symplectifying if delta is a variable +if(c_%ndpt/=0) then +f_R_TE=ln(R_TE) +call get_field_c_universal_taylor(f_R_TE,uf) + + +do i=1,c_%nd + f_R_TEs%v(2*i-1)=-(uf.d.(2*i)) + f_R_TEs%v(2*i)=(uf.d.(2*i-1)) +enddo + + R_TE=exp(f_R_TEs) + +endif + +100 call kill(gam) +call kill(f_R_TE,f_R_TEs) + +if(.not.t_e) return + + +CS_TE=R_TE**(-1)*a1 + + +end subroutine teng_edwards_a1 + + + subroutine c_int_partial(v,h,nd0) + implicit none + ! IF SCA=-one + ! \VEC{V}.GRAD = J GRAD H . GRAD = :H: + ! + ! IF SCA=one + ! \VEC{V}.GRAD = GRAD H . GRAD + integer i,nd0 + type(c_vector_field) v + type(c_taylor) h + type(c_taylor) b4,b3,b2,b1 + type(c_damap) x + + if(.not.C_STABLE_DA) return + + + nd_used=nd0 + call alloc(x) + call alloc(b4,b3,b2,b1) + + x=1 + + do i=1,nd_used + call cfu(v%v(2*i-1),dlie,b3) + call cfu(v%v(2*i),dlie,b1) + b2=b1*x%v(2*i-1) + b1=b3*x%v(2*i) + b3=b2-b1 + b2=b3+b4 + b4=b2 + enddo + h=b4 + + + call kill(b4,b3,b2,b1) + call kill(x) + + + end subroutine c_int_partial + + complex(dp) function dlie(j) + implicit none + integer i + ! INTEGER J(NTT) + integer,dimension(:)::j + dlie=0.0_dp + if(.not.C_STABLE_DA) return + + + do i=1,nd_used + dlie=REAL(j(2*i-1)+j(2*i),kind=DP)+dlie + enddo + dlie=dlie+1.0_dp + dlie=1.0_dp/dlie + return + end function dlie + + subroutine copy_damap_matrix(mi,a) + implicit none + type(c_taylor), intent(inout) :: a(4,4) + type(c_damap), intent(in) :: mi + type(c_damap) m + + integer i,j,nt + + integer, allocatable :: jl(:) + + call alloc(m) + + m=mi + + nt=4 + + allocate(jl(nt)) + jl=0 + do i=1,nt + do j=1,nt + jl(j)=1 + a(i,j)=m%v(i).par.jl + jl(j)=0 + enddo + enddo + + call kill(m) + deallocate(jl) + + end subroutine copy_damap_matrix + + subroutine invert_22(a,ai) +!* + implicit none + type(c_taylor) a(2,2),ai(2,2),t(2,2) + type(c_taylor) det + call alloc_nn(t) + call alloc(det) + + det=a(1,1)*a(2,2)-a(1,2)*a(2,1) + t(1,1)=a(2,2)/det + t(2,2)=a(1,1)/det + t(1,2)=-a(1,2)/det + t(2,1)=-a(2,1)/det + + call copy_matrix_matrix(t,ai) + + call kill_nn(t) + call kill(det) + + end subroutine invert_22 + + subroutine dagger_22(a,ai) +!* + implicit none + type(c_taylor) a(2,2),ai(2,2),t(2,2),at(2,2) + + call alloc_nn(t) + call alloc_nn(at) + + t(1,2)=1.0_dp + t(2,1)=-1.0_dp + + at(1,1)=a(1,1) + at(2,2)=a(2,2) + at(1,2)=a(2,1) + at(2,1)=a(1,2) + + call matmul_nn(t,at,at) + call matmul_nn(at,t,at,-1.0_dp) + + call copy_matrix_matrix(at,ai) + + call kill_nn(t) + call kill_nn(at) + + end subroutine dagger_22 + + subroutine matmulr_33(m,mo,sc0) +!* +! mo=sc m.n + implicit none + type(c_taylor) m(:,:),mo(:,:) + real(dp) sc0 + integer i,j,k + + do i=1,size(m,dim=1) + do j=1,size(m,dim=2) + mo(i,j)=m(i,j)*sc0 + enddo + enddo + end subroutine matmulr_33 + + subroutine matmult_33(m,mo,sc0) +!* +! mo=sc m.n + implicit none + type(c_taylor) m(:,:),mo(:,:) + type(c_taylor) sc0 + integer i,j,k + + do i=1,size(m,dim=1) + do j=1,size(m,dim=2) + mo(i,j)=m(i,j)*sc0 + enddo + enddo + end subroutine matmult_33 + + subroutine matmul_33(m,n,mo,sc) +!* +! mo=sc m.n + implicit none + type(c_taylor) m(:,:),n(:,:),mo(:,:) + type(c_taylor), allocatable :: a(:,:) + real(dp), optional :: sc + real(dp) sc0 + integer i,j,k + sc0=1.0_dp + allocate(a(size(m,dim=1),size(n,dim=2))) + + call alloc_nn(a) + + do i=1,size(m,dim=1) + do j=1,size(m,dim=2) + do k=1,size(n,dim=2) + a(i,k)=m(i,j)*n(j,k)+a(i,k) + enddo + enddo + enddo + + if(present(sc)) sc0=sc + do i=1,size(mo,dim=1) + do j=1,size(mo,dim=2) + mo(i,j)=sc0*a(i,j) + enddo + enddo + call kill_nn(a) + deallocate(a) + end subroutine matmul_33 + + subroutine dalloc_33t(a) +!* + implicit none + type(c_taylor) a(:,:) + integer i,j + + do i=1,size(a,dim=1) + do j=1,size(a,dim=2) + call alloc(a(i,j)) + enddo + enddo + + end subroutine dalloc_33t + + subroutine prin_33t(a,mf,prec) +!* + implicit none + type(c_taylor) a(:,:) + integer i,j,mf + real(dp), optional :: prec + + do i=1,size(a,dim=1) + do j=1,size(a,dim=2) + write(mf,*) i,j + call print(a(i,j),mf,prec) + enddo + enddo + + end subroutine prin_33t + + + subroutine dkill_33t(a) +!* + implicit none + type(c_taylor) a(:,:) + integer i,j + + do i=1,size(a,dim=1) + do j=1,size(a,dim=2) + call kill(a(i,j)) + enddo + enddo + + end subroutine dkill_33t + + subroutine copy_matrix_matrix(ma,a) +!* + implicit none + type(c_taylor), intent(inout) :: a(:,:) + type(C_taylor), intent(in) :: ma(:,:) + integer i,j + + do i=1,size(a,dim=1) + do j=1,size(a,dim=2) + a(i,j)=ma(i,j) + enddo + enddo + + end subroutine copy_matrix_matrix + + + + +subroutine extract_linear_from_normalised(m,a1,phi1,f1,f2,integer_part,dospin) + implicit none + type(c_damap) , intent(inout) :: m,a1,phi1 + type(c_vector_field) , intent(inout) :: f1,f2 + real(dp), intent(IN):: integer_part(:) + !real(dp), optional ,intent(IN):: integer_part_spin + logical, optional :: dospin + type(c_damap) b1,a + type(taylor) t(2) + complex(dp) v + real(dp) dd,rr(2) + logical dos + integer i,j,k,kr + integer, allocatable :: je(:) + dos=.false. + if(present(dospin)) dos=dospin + + + call alloc(a) + call alloc(b1) + + a=to_phasor()*m*from_phasor() + + allocate(je(nv)) + je=0 + + + +!! extract the linear part as a function parameters (delta included) + + do i=1,nd2 + j=1 + do while(.true.) + + + call c_cycle(a%v(i),j,v ,je); if(j==0) exit; + kr=0 + do k=1,nd2 + if(k==ndpt) cycle + kr=je(k)+kr + enddo + if(i==ndptb) then + if(kr<=2) then + b1%v(i)=b1%v(i)+(v.cmono.je) + endif + else + if(kr==1) then + b1%v(i)=b1%v(i)+(v.cmono.je) + endif + endif + enddo + enddo + + + if(ndpt/=0) then + b1%v(ndpt)=1.0_dp.cmono.ndpt + f1%v(ndptb)=b1%v(ndptb)-(1.0_dp.cmono.ndptb) + endif + + if(dos) then + do i=0,3 + j=1 + do while(.true.) + + + call c_cycle(a%q%x(i),j,v ,je); if(j==0) exit; + kr=0 + do k=1,nd2 + if(k==ndpt) cycle + kr=je(k)+kr + enddo + + if(kr==0) then + b1%q%x(i)=b1%q%x(i)+(v.cmono.je) + endif + + enddo + enddo + endif ! spin + + + a1=a*b1**(-1) + + phi1=b1 + + do i=1,nd2t + f1%v(i)=(log(b1%v(i).d.i).cut.c_%no) *(1.0_dp.cmono.i) + enddo + if(dos) then + call alloc(t) + t(2)=b1%q%x(2) + t(1)=b1%q%x(0) + t(1)=-atan2(t(2),t(1))/pi + + v=integer_part(nd2/2+1) + + f1%q%x(2)=-spin_def_tune*(v+t(1))*pi + call kill(t) + endif + + + + do i=1,nd2t/2 + f1%v(2*i-1)=-(i_*twopi*integer_part(i).cmono.(2*i-1))+ f1%v(2*i-1) + f1%v(2*i)=(i_*twopi*integer_part(i).cmono.(2*i))+ f1%v(2*i) + enddo + + +!if(dos) then + f2=ln(a1) +!else +! f2=log(a1) +!endif + + f2=to_phasor()*f2 !transform_vector_field_by_map(f2,to_phasor()) + f1=to_phasor()*f1 !transform_vector_field_by_map(f1,to_phasor()) + + + deallocate(je) + call kill(b1) + + +end subroutine extract_linear_from_normalised + +subroutine extract_a0(a,a0) +!#internal: manipulation +!# This routines extracts a0: the full fixed point map. + implicit none + type(c_damap) , intent(inout) :: a,a0 + + type(c_damap) a0t,at,ai,x,v + type(c_taylor) t1 + integer i + integer np_pos + + + ! a0 is for the fixed point + + at%n=nv + call alloc(at) + call alloc(ai) + call alloc(a0t) + call alloc(t1) + call alloc(x) + call alloc(v) + ai=a + +!! extract the dispersion + if(ndpt/=0) at%v(ndpt)=1.0_dp.cmono.ndpt + np_pos=nv-np+1 + do i=np_pos,nv + at%v(i)=1.0_dp.cmono.i + enddo + + a0t=ai*at + + + +!!! Force the symplectic condition in the time variable + if(ndpt/=0) then + t1=0 + do i=1,ndt + x%v(2*i) =(-1)**(2*i-1)*(a0t%v(2*i-1)) + x%v(2*i-1)=(-1)**(2*i )*(a0t%v(2*i)) + v%v(2*i)= x%v(2*i).d.ndpt + v%v(2*i-1)= x%v(2*i-1).d.ndpt + enddo + do i=1,ndt + t1=-(1.0_dp.cmono.(2*i-1))*v%v(2*i-1)+t1 ! first order + t1=-(1.0_dp.cmono.(2*i))*v%v(2*i)+t1 ! first order + t1=-0.5_dp*(x%v(2*i-1)*v%v(2*i)-x%v(2*i)*v%v(2*i-1))+t1 ! second order + enddo + t1=(-1)**ndpt*t1 + a0t%v(ndptb)=(1.0_dp.cmono.ndptb)+t1 !!! effect on time added to identity map in the time-energy plane + a0t%v(ndpt)=1.0_dp.cmono.ndpt + + endif + + + do i=1,nd2 + if(i/=ndpt.and.i/=ndptb) a0t%v(i)=a0t%v(i)+(1.0_dp.cmono.i) + enddo + if(ndpt/=0) then + if(.not.time_lie_choice) then + t1=0.0_dp + do i=1,nd2-ndc2t + t1=t1+(1.0_dp.cmono.i)*(a0t%v(ndptb).d.i) + enddo + a0t%v(ndptb)=(1.0_dp.cmono.ndptb)+t1 + endif + endif + + + a0=a0t + a=a0**(-1)*a + + + + + call kill(at) + call kill(ai) + call kill(t1) + call kill(a0t) + call kill(x) + call kill(v) +end subroutine extract_a0 + +subroutine extract_only_a0(a,a0) +!#internal: manipulation +!# This routines extracts a0: the full fixed point map. + implicit none + type(c_damap) , intent(inout) :: a,a0 + + type(c_damap) a0t,at,ai,x,v + type(c_taylor) t1 + integer i + integer np_pos + + + ! a0 is for the fixed point + + at%n=nv + call alloc(at) + call alloc(ai) + call alloc(a0t) + call alloc(t1) + call alloc(x) + call alloc(v) + ai=a + +!! extract the dispersion + if(ndpt/=0) at%v(ndpt)=1.0_dp.cmono.ndpt + np_pos=nv-np+1 + do i=np_pos,nv + at%v(i)=1.0_dp.cmono.i + enddo + + a0t=ai*at + + + +!!! Force the symplectic condition in the time variable + if(ndpt/=0) then + t1=0 + do i=1,ndt + x%v(2*i) =(-1)**(2*i-1)*(a0t%v(2*i-1)) + x%v(2*i-1)=(-1)**(2*i )*(a0t%v(2*i)) + v%v(2*i)= x%v(2*i).d.ndpt + v%v(2*i-1)= x%v(2*i-1).d.ndpt + enddo + do i=1,ndt + t1=-(1.0_dp.cmono.(2*i-1))*v%v(2*i-1)+t1 ! first order + t1=-(1.0_dp.cmono.(2*i))*v%v(2*i)+t1 ! first order + t1=-0.5_dp*(x%v(2*i-1)*v%v(2*i)-x%v(2*i)*v%v(2*i-1))+t1 ! second order + enddo + t1=(-1)**ndpt*t1 + a0t%v(ndptb)=(1.0_dp.cmono.ndptb)+t1 !!! effect on time added to identity map in the time-energy plane + a0t%v(ndpt)=1.0_dp.cmono.ndpt + + endif + + + do i=1,nd2 + if(i/=ndpt.and.i/=ndptb) a0t%v(i)=a0t%v(i)+(1.0_dp.cmono.i) + enddo + + + + a0=a0t + a=a0**(-1)*a + + ! if(ndpt/=0) then + ! call print(a%v(ndpt),6) + ! at=0 + ! at%v(ndpt)=(1.0_dp.cmono.ndpt) + ! ai=a*at + ! at=1 + ! at%v(ndpt)=ai%v(ndpt) + ! call print(at%v(ndpt),6) + ! a=at**(-1)*a + ! a0=a0*at + ! endif + + + + call kill(at) + call kill(ai) + call kill(t1) + call kill(a0t) + call kill(x) + call kill(v) +end subroutine extract_only_a0 + + subroutine extract_a1(a,a1,phi1) +!#internal: manipulation +!# This routines extracts a1: the full linear canonical transformation. +!# Teng-Edward A_12=0 is imposed or, for fun, Anti-Teng-Edwards A_21=0 +!# based on the flag courant_snyder_teng_edwards (defaulted to true). +!# See Sec.7.4 of my Springer book. Phi1 is the phase advanced induced +!# by the choice of canonical transformation. Sec 2.4 gives a review in 1-d-f. + implicit none + type(c_damap) , intent(inout) :: a,a1 + type(c_damap),optional , intent(inout) :: phi1 + type(c_damap) b1 + type(c_taylor) cphi,sphi,t + complex(dp) v + + integer i,j,k,kr + integer, allocatable :: je(:) + + + call alloc(b1) + call alloc(cphi,sphi,t) + + allocate(je(nv)) + je=0 + + + +!! extract the linear part as a function parameters (delta included) + + do i=1,nd2 + j=1 + do while(.true.) + + + call c_cycle(a%v(i),j,v ,je); if(j==0) exit; + kr=0 + do k=1,nd2 + if(k==ndpt) cycle + kr=je(k)+kr + enddo + if(kr==1) then + b1%v(i)=b1%v(i)+(v.cmono.je) + endif + enddo + enddo + if(ndpt/=0) then + b1%v(ndpt)=b1%v(ndpt)+(1.0_dp.cmono.ndpt) + + j=1 + do while(.true.) + + + call c_cycle(a%v(ndptb),j,v ,je); if(j==0) exit; + kr=0 + do k=1,nd2t + kr=je(k)+kr + enddo + if(kr==2) then + b1%v(ndptb)=b1%v(ndptb)+(v.cmono.je) + endif + enddo + + endif + + + a=b1**(-1)*a + + a1=b1 + +! imposed Teng-Edward A_12=0 or, for fun, Anti-Teng-Edwards A_21=0 + + + if(present(phi1)) then + + phi1=1 + + do i=1,nd2/2 + if((i<=ndt).or.(i>nd-rf)) then + if(courant_snyder_teng_edwards) then + + t=sqrt((b1%v(2*i-1).d.(2*i))**2+(b1%v(2*i-1).d.(2*i-1))**2) + + cphi=(b1%v(2*i-1).d.(2*i-1))/t + sphi=(b1%v(2*i-1).d.(2*i))/t + else + t=sqrt((b1%v(2*i).d.(2*i-1))**2+(b1%v(2*i).d.(2*i))**2) + cphi=(b1%v(2*i).d.(2*i))/t + sphi=-(b1%v(2*i).d.(2*i-1))/t + endif + phi1%v(2*i-1) =cphi*(1.0_dp.cmono.(2*i-1))+sphi*(1.0_dp.cmono.(2*i)) + phi1%v(2*i) =cphi*(1.0_dp.cmono.(2*i))-sphi*(1.0_dp.cmono.(2*i-1)) + +!!! Corrects the time variable with the d/dp_t term + if(ndpt/=0) then + t= cphi + i_*sphi + t=-i_*log(t) + t=-(t.d.ndpt)/(2.0_dp,0.0_dp) + phi1%v(ndptb)=phi1%v(ndptb)+(-1)**(ndptb)*t*((1.0_dp.cmono.(2*i-1))**2+(1.0_dp.cmono.(2*i))**2) + endif + + endif + enddo + + + + a1=a1*phi1**(-1) + a=phi1*a*phi1**(-1) + + + endif + + + + + deallocate(je) + call kill(b1) + call kill(cphi,sphi,t) +end subroutine extract_a1 + + subroutine extract_only_a1(a,a1) +!#internal: manipulation +!# This routines extracts a1 + + implicit none + type(c_damap) , intent(inout) :: a,a1 + type(c_damap) b1 + type(c_taylor) t + complex(dp) v + + integer i,j,k,kr + integer, allocatable :: je(:) + + + call alloc(b1) + call alloc(t) + + allocate(je(nv)) + je=0 + + + +!! extract the linear part as a function parameters (delta included) + + do i=1,nd2 + j=1 + do while(.true.) + + + call c_cycle(a%v(i),j,v ,je); if(j==0) exit; + kr=0 + do k=1,nd2 + + kr=je(k)+kr + enddo + if(kr==1) then + b1%v(i)=b1%v(i)+(v.cmono.je) + endif + enddo + enddo + + + + a=b1**(-1)*a + + a1=b1 + +! imposed Teng-Edward A_12=0 or, for fun, Anti-Teng-Edwards A_21=0 + + + + + deallocate(je) + call kill(b1) + call kill(t) +end subroutine extract_only_a1 + + + +subroutine extract_a2(a,phi2) + implicit none + type(c_damap) , intent(inout) :: a + type(c_damap),optional , intent(inout) :: phi2 + type(c_damap) b1,ri + type(c_vector_field) h,hr,hf + + real(dp) eps + complex(dp) v + + integer j,k,kr + integer, allocatable :: je(:) + logical(lp) removeit + + if(.not.present(phi2)) return + + call alloc(b1) + call alloc(h) + call alloc(hr) + call alloc(hf) + call alloc(ri) + + + + allocate(je(nv)) + je=0 + + + ri=from_phasor(-1) + b1=c_simil(ri,a,1) + + + eps=-no-1 !1.0e-7_dp + + !! Here I assume that in a single Lie exponent representation there are NO kernel terms + !do kr=2,no + do kr=1,no + + hr=0 + call c_flofacg(b1,h,eps) + + + do k=1,nd2 + j=1 + do while(.true.) + + call c_cycle(h%v(k),j,v ,je); if(j==0) exit; + call check_kernel(k,nd2,je,removeit) + if(.not.removeit) then + hr%v(k)=hr%v(k)+(v.cmono.je) + endif + + enddo + hf%v(k)=hf%v(k)+hr%v(k) + enddo + b1=texp(-hr,b1) + + enddo + + + a=c_simil(ri,b1,-1) + phi2=texp(hf) + phi2=c_simil(ri,phi2,-1) + + + + deallocate(je) + + + + call kill(b1) + call kill(h) + call kill(hr) + call kill(hf) + call kill(ri) + +end subroutine extract_a2 + + + ! spin routine + subroutine factor_ely_rest(as_xyz,as_y,r_y,n_y,n_r) !r_y in normal units, tune in phasors as_xyz= r_y o as_xyz + implicit none + type(c_damap), intent(inout) :: as_xyz,as_y + type(c_damap) , intent(inout) :: r_y + type(c_spinor), intent(inout) :: n_y + type(c_spinor), intent(inout) :: n_r + type(c_damap) temp,as_nl,rot_y + type(c_spinor) n_expo,n_tune,tune0 + type(c_taylor) tr + type(c_taylor) t + integer i + integer nmax + real(dp) eps,norm1,norm2,d + logical check +!!! original as_xyz = as_xyz*r_y = a_y*a_nl*r_y on exit + check=.true. + eps=1.d-6 + nmax=1000 + + call alloc(n_expo) + call alloc(n_tune) + call alloc(tune0) + call alloc(temp,as_nl,rot_y) + call alloc(tr) + call alloc(t) + tune0=0 + as_y=as_xyz + as_y= as_y + norm1=mybig + rot_y=1 + temp=1 + check=.true. + norm1=mybig + + ! call c_full_norm_spin(as_xyz%s,i,EPS=d) + call c_full_norm_spin_map(as_xyz,i,d) + + eps=d*eps +! write(6,*) eps + + +!pause 1256 + + do i=1,nmax + ! call find_exponent_only(as_y,n_expo) + + + + n_expo=log(as_y%s,exact=my_false) + + + + + ! call dalog_spinor_8(as_y,n_expo) + norm2=0.0_dp + ! call c_n0_to_nr(n_expo,n_tune) ! not necessary + + n_tune=n_expo + + n_tune%v(1)=0.0_dp + n_tune%v(3)=0.0_dp + + + ! call cfu(n_tune%v(2),c_phase_shift,n_tune%v(2)) + + + tune0%v(2)=tune0%v(2)+n_tune%v(2) + norm2=FULL_ABS(n_tune%v(2)) + + temp%s=exp(n_tune) + + + rot_y=rot_y*temp + ! call inv_as(temp%s%s,temp%s%s) + as_y=temp**(-1)*as_y + ! write(6,*) norm1, norm2,i + if(check) then + if(norm210) then + check=.false. + endif + else + if(norm2>=norm1) exit !.and.i>40) exit + endif + norm1=norm2 + enddo + + if(i>nmax-10) then + write(6,*) "no convergence in factor_ely_rest " + !stop 1067 + endif + + ! as_xyz= as_y + + r_y= rot_y + + n_r=log(as_y%s,exact=my_false) + + n_y=0 + + n_y%v(2)= tune0%v(2) ! in phasors + + + call kill(n_expo) + call kill(temp,as_nl,rot_y) + call kill(tune0) + call kill(tr) + call kill(n_tune) + call kill(t) + + end subroutine factor_ely_rest + + ! spin routine + subroutine c_remove_y_rot(as_xyz,r_y,tune) !r_y in normal units, tune in phasors as_xyz= as_xyz o r_y + implicit none + type(c_damap), intent(inout) :: as_xyz + type(c_damap), optional , intent(inout) ::r_y + type(c_taylor), optional ,intent(inout) :: tune + type(c_damap) temp,as_y,as_nl,rot_y + type(c_spinor) n_expo,n_tune,tune0 + type(c_taylor) tr +! type(taylor) si,co + real(dp) si0,co0 + type(c_taylor) t + type(c_quaternion) qnr + type(c_linear_map) q,qr + integer i + integer nmax + real(dp) eps,norm1,norm2,d,dt,aq + logical check +!!! original as_xyz = as_xyz*r_y = a_y*a_nl*r_y on exit + check=.true. + eps=1.d-9 + nmax=1000 + + call alloc(n_expo) + call alloc(n_tune) + call alloc(tune0) + call alloc(temp,as_y,as_nl,rot_y) + call alloc(tr) +! call alloc(si,co) + call alloc(t) + call alloc(qnr) + tune0=0 + as_y=as_xyz + as_y=from_phasor(-1)*as_y*from_phasor() + norm1=mybig + rot_y=1 + temp=1 + check=.true. + norm1=mybig +dt=0 +! call c_full_norm_spin(as_xyz%s,i,EPS=d) + call c_full_norm_spin_map(as_xyz,i,d) + + eps=d*eps +! write(6,*) eps + +!pause 1256 + + do i=1,nmax + ! call find_exponent_only(as_y,n_expo) + + + if(use_quaternion) then + + + if(i==1.and.qphase) then + q=1 + q=as_y%q + ! make sure isf not below y plane + aq=q%q(0,0)**2-(q%q(1,0)**2+q%q(2,0)**2+q%q(3,0)**2) +if(aq<0) then + temp%q=1 ! = i + as_y%q=as_y%q*temp%q + q=as_y%q +endif + + aq=-atan2(real(q%q(2,0)),real(q%q(0,0))) + temp%q=1.0_dp + temp%q%x(0)= cos(aq) + temp%q%x(2)= -sin(aq) + + n_tune%v(1)=0.0_dp + n_tune%v(3)=0.0_dp + n_tune%v(2)=-aq*2.0_dp + + else + + temp%q=1.0_dp + si0=as_y%q%x(2) + co0=as_y%q%x(0) +!call print(as_y%q,16) + n_expo=as_y%q + call c_n0_to_nr(n_expo,n_tune) ! not necessary + + n_tune=n_expo + + n_tune%v(1)=0.0_dp + n_tune%v(3)=0.0_dp + + + call cfu(n_tune%v(2),c_phase_shift,n_tune%v(2)) + qnr=n_tune + temp%q=exp(qnr) + n_tune%v(2)=n_tune%v(2)*2.0_dp + endif + + else + n_expo=log(as_y%s,exact=my_false) + ! call dalog_spinor_8(as_y,n_expo) + norm2=0.0_dp + call c_n0_to_nr(n_expo,n_tune) ! not necessary + + n_tune=n_expo + + n_tune%v(1)=0.0_dp + n_tune%v(3)=0.0_dp + + + call cfu(n_tune%v(2),c_phase_shift,n_tune%v(2)) + temp%s=exp(n_tune) + endif + + + dt=dt+n_tune%v(2) + tune0%v(2)=tune0%v(2)+n_tune%v(2) + + + norm2=FULL_ABS(n_tune%v(2)) + + ! call c_nr_to_n0(n_tune,n_expo) + ! enddo + + + + + + + rot_y=temp*rot_y + ! call inv_as(temp%s%s,temp%s%s) + as_y=as_y*temp**(-1) + ! write(6,*) norm1, norm2,i +if(use_quaternion) then + if(check) then + if(norm2=norm1) goto 123 !.and.i>40) exit + endif +else + if(check) then + if(norm2=norm1) exit !.and.i>40) exit + endif +endif + norm1=norm2 + + enddo + + if(i>nmax-10) then + write(6,*) "no convergence in remove_y_rot ",norm2,norm1,eps,i,norm2>=norm1 + !stop 1067 + endif + +123 as_xyz=from_phasor()*as_y*from_phasor(-1) + + + if(present(r_y)) then + r_y=from_phasor()*rot_y*from_phasor(-1) + endif + if(present(tune)) then + tune=0.0_dp + tune=spin_def_tune*tune0%v(2) ! in phasors + endif + + + + call kill(n_expo) + call kill(temp,as_y,as_nl,rot_y) + call kill(tune0) +! call kill(si,co) + call kill(tr) + call kill(n_tune) + call kill(t) + call kill(qnr) + + + end subroutine c_remove_y_rot + + complex(dp) function c_phase_shift(j) + implicit none + + ! INTEGER J(NTT) + integer,dimension(:)::j + + logical(lp) removeit + + c_phase_shift=0.0_dp + if(.not.C_STABLE_DA) return + + + call check_kernel(0,nd2,j,removeit) + + if(.not.removeit) c_phase_shift=1.0_dp + + return + end function c_phase_shift + ! + complex(dp) function c_zeroth(j) + implicit none + integer i,k + ! keeps in regular harmonic planes zeroth order + integer,dimension(:)::j + + + c_zeroth=0.0_dp + if(.not.C_STABLE_DA) return + + k=0 + do i=1,nd2t + k=k+abs(j(i)) + enddo + + if(k==0) c_zeroth=1.0_dp + + return + end function c_zeroth +!!!!!!!!!!!!!!!!!!!!! tracking unitary !!!!!!!!!!!!!!!!!!!!!!!! + + ! spin routine +subroutine produce_orthogonal(n,ray,s) +implicit none +type(c_spinor),intent(inout) :: n +type(c_spinmatrix),intent(inout) :: s +type(c_ray),intent(inout):: ray +type(c_spinor) nt + +call alloc(nt) + +nt=n.o.ray + + s=exp(nt) + +call kill(nt) +end subroutine produce_orthogonal + + + + + ! spin routine + + + ! spin routine + subroutine orthogonalise_ray(ray) + implicit none + type(c_ray),intent(inout):: ray + real(dp)n + integer i + + n=0.0_dp + do i=1,3 + n=n+abs(ray%s1(i))**2 + enddo + ray%s1=ray%s1/sqrt(n) + + + + n=0.0_dp + + DO I=1,3 + n=n+ray%s1(i)*ray%s2(i) + ENDDO + + DO I=1,3 + ray%s2(i)=ray%s2(i)-n*ray%s1(i) + ENDDO + + n=0.0_dp + do i=1,3 + n=n+abs(ray%s2(i))**2 + enddo + + ray%s2=ray%s2/sqrt(n) + + ray%s3(1)=ray%s1(2)*ray%s2(3)-ray%s1(3)*ray%s2(2) + ray%s3(2)=ray%s1(3)*ray%s2(1)-ray%s1(1)*ray%s2(3) + ray%s3(3)=ray%s1(1)*ray%s2(2)-ray%s1(2)*ray%s2(1) + + n=0.0_dp + do i=1,3 + n=n+abs(ray%s3(i))**2 + enddo + ray%s3=ray%s3/sqrt(n) + + end subroutine orthogonalise_ray + + SUBROUTINE c_IdentityEQUALVECfourier(S2,S1) +!* + implicit none + type (c_vector_field_fourier),INTENT(inOUT)::S2 + integer,INTENT(IN)::S1 + integer i + IF(.NOT.C_STABLE_DA) RETURN + if(s1/=0) then + write(6,*) "c_IdentityEQUALVECfourier" + stop + endif + do i=-s2%n,s2%n + s2%f(i)=0 + enddo + + END SUBROUTINE c_IdentityEQUALVECfourier + +SUBROUTINE equal_c_vector_field_fourier(S1,s2) +!* + implicit none + type (c_vector_field_fourier),INTENT(INOUT) :: S1 + type (c_vector_field_fourier),INTENT(IN) :: S2 + INTEGER i + + do i=-n_fourier,n_fourier + s1%f(i)=s2%f(i) + enddo + s1%n=s2%n + +end SUBROUTINE equal_c_vector_field_fourier + + SUBROUTINE alloc_c_vector_field_fourier(S1,N) +!* + implicit none + type (c_vector_field_fourier),INTENT(INOUT) :: S1 + integer,optional :: n + INTEGER i + ! logical existed + + ! existed=.false. + ! if(s1%n/=0) existed=.true. + + ! if(present(n)) then + ! s1%n=n + ! else + s1%n=n_fourier + ! endif + + if(associated(s1%f) ) then + deallocate(s1%f) + nullify(s1%f) + endif + allocate(s1%f(-s1%n:s1%n)) + + do i=-s1%n,s1%n + s1%f(i)%n=0 + if(present(n)) s1%f(i)%n=n + call alloc(s1%f(i)) + enddo + + + END SUBROUTINE alloc_c_vector_field_fourier + + SUBROUTINE kill_c_vector_field_fourier(S1) +!* + implicit none + type (c_vector_field_fourier),INTENT(INOUT) :: S1 + INTEGER i + + + ! if(present(n)) then + ! s1%n=n + ! else + ! s1%n=0 + ! endif + + + + + do i=-s1%n,s1%n + call kill(s1%f(i)) + enddo + s1%n=0 + deallocate(s1%f) + + END SUBROUTINE kill_c_vector_field_fourier + + subroutine transform_vector_field_fourier_by_map(s1,s2,m) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: S1 ,s2 + TYPE (c_damap), INTENT (IN) :: m + + integer i + + + IF(.NOT.C_STABLE_DA) then + RETURN + endif +!!! The tunes are stored for the nonlinear normal form recursive algorithm + + + do i=-n_fourier,n_fourier + s2%f(i)=m*s1%f(i) ! transform_vector_field_by_map(s1%f(i),m) + enddo + +end subroutine transform_vector_field_fourier_by_map + + subroutine transform_vector_field_fourier_to_qr(s1,s2) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: S1 ,s2 + + + integer i + + + IF(.NOT.C_STABLE_DA) then + RETURN + endif +!!! The tunes are stored for the nonlinear normal form recursive algorithm + + + do i=-n_fourier,n_fourier + call c_q0_to_qr(s1%f(i)%q,s2%f(i)%q ) + enddo + +end subroutine transform_vector_field_fourier_to_qr + + subroutine transform_vector_field_fourier_to_q0(s1,s2) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: S1 ,s2 + + + integer i + + + IF(.NOT.C_STABLE_DA) then + RETURN + endif +!!! The tunes are stored for the nonlinear normal form recursive algorithm + + + do i=-n_fourier,n_fourier + call c_qr_to_q0(s1%f(i)%q,s2%f(i)%q ) + enddo + +end subroutine transform_vector_field_fourier_to_q0 +! etienne + +subroutine exp_vector_field_fourier(F,H,K,nlin) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: F,H,K + TYPE (c_vector_field_fourier) s3,t,dF_dt,dhs + integer, optional :: nlin + INTEGER I ,nl + real(dp) norm(3) + complex(dp) fac,fac1 + nl=0 + if(present(nlin)) nl=nlin + call alloc(s3) + call alloc(t) + call alloc(dhs) + call alloc(dF_dt) + + call ddt_vector_field_fourier(F,dF_dt) ! (1) + + s3=H ; t=H ; dhs=dF_dt; + fac=1.0_dp; fac1=1.0_dp; + + if(nl/=0) write(6,*) "Printing Iterations for convergence check " + do i=1,no+nl ! extra terms for cheap convergence + fac=1.0_dp/i + + call bra_vector_field_fourier(F,t,t) ! (2a) + call mulc_vector_field_fourier(t,fac,t) ! t=fac*t + call add_vector_field_fourier(s3,t,s3) ! (2b) + call bra_vector_field_fourier(F,dF_dt,dF_dt) ! (3a) + fac1=1.0_dp/(i+1) + call mulc_vector_field_fourier(dF_dt,fac1,dF_dt) + call add_vector_field_fourier(dhs,dF_dt,dhs) ! (3b) + if(i>no.and.i>no+nl-10) then + call c_full_norm_fourier(s3,norm(1)) + call c_full_norm_fourier(t,norm(2)) + call c_full_norm_fourier(dF_dt,norm(3)) + write(6,'(i4,1x,3(g23.16,1x))')i, norm + endif + enddo + fac=-1.0_dp + call add_vector_field_fourier(s3,dhs,s3,fac) ! (3c) + K=s3 + call kill(s3) + call kill(t) + call kill(dhs) + call kill(dF_dt) + +end subroutine exp_vector_field_fourier + + +subroutine ddt_vector_field_fourier(s1,ds1) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: S1,ds1 + INTEGER I + + ds1%f(0)=0 + do i=1,n_fourier + ds1%f(i)= (i*i_)*s1%f(i) + ds1%f(-i)= (-i*i_)*s1%f(-i) + enddo + +end subroutine ddt_vector_field_fourier + +subroutine print_vector_field_fourier(s1,mf,collated,non_zero_only) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: S1 + logical, optional :: collated,non_zero_only + logical usual,nonz + INTEGER I,mf,j + usual=.false. + if(present(collated)) usual=.not.collated + + write(mf,*) 0,"th mode" + call print(s1%f(0),mf) !,dospin=.false.) + nonz=.false. + if(present(non_zero_only)) nonz=non_zero_only + do i=1,n_fourier + + if(usual) then + write(mf,*) i,"th mode followed by,",-i, "th mode" + call print(s1%f(i),mf) !,dospin=.false.) + call print(s1%f(-i),mf) !,dospin=.false.) + else + do j=1,s1%f(i)%n + if(nonz) then + write(mf,*) i,"th mode orbital",j + if(full_abs(s1%f(i)%v(j))/=0) call print(s1%f(i)%v(j),mf) !,dospin=.false.) + write(mf,*) -i,"th orbital",j + if(full_abs(s1%f(-i)%v(j))/=0) call print(s1%f(-i)%v(j),mf) !,dospin=.false.) + else + write(mf,*) i,"th mode orbital",j + call print(s1%f(i)%v(j),mf) !,dospin=.false.) + write(mf,*) -i,"th orbital",j + call print(s1%f(-i)%v(j),mf) !,dospin=.false.) + endif + enddo + do j=0,3 + if(nonz) then + write(mf,*) i,"th quaternion",j + if(full_abs(s1%f(i)%q%x(j))/=0) call print(s1%f(i)%q%x(j),mf) !,dospin=.false.) + write(mf,*) -i,"th mode quaternion",j + if(full_abs(s1%f(-i)%q%x(j))/=0) call print(s1%f(-i)%q%x(j),mf) !,dospin=.false.) + else + write(mf,*) i,"th quaternion",j + call print(s1%f(i)%q%x(j),mf) !,dospin=.false.) + write(mf,*) -i,"th mode quaternion",j + call print(s1%f(-i)%q%x(j),mf) !,dospin=.false.) + endif + enddo + + endif + enddo + +end subroutine print_vector_field_fourier + + + +subroutine print_poisson_bracket_fourier(s1,mf) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: S1 + type(c_taylor) h + INTEGER I,mf + call alloc(h) + write(mf,*) 0,"th mode" +! call print(s1%f(0),mf) + h=cgetpb(s1%f(0)) + call print(h,mf) + do i=1,n_fourier + write(mf,*) i,"th mode" + h=cgetpb(s1%f(i)) + call print(h,mf) + h=cgetpb(s1%f(-i)) + call print(h,mf) + ! call print(s1%f(i),mf) + ! call print(s1%f(-i),mf) + enddo + call kill(h) +end subroutine print_poisson_bracket_fourier + +subroutine bra_vector_field_fourier(s1,s2,r) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: S1,s2,r + TYPE (c_vector_field_fourier) s3 + INTEGER I,J + call alloc(s3) + + DO I=-n_fourier,n_fourier + DO J=-n_fourier,n_fourier + IF(ABS(I+J)>n_fourier) CYCLE + S3%F(I+J)=S3%F(I+J) + (s1%f(i).lb.s2%f(j)) + ENDDO + ENDDO + + r=s3 + call kill(s3) + +end subroutine bra_vector_field_fourier + +subroutine add_vector_field_fourier(s1,s2,r,fac) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: S1,s2,r + TYPE (c_vector_field_fourier) s3 + complex(dp), optional :: fac + INTEGER I + call alloc(s3) + + if(present(fac) ) then + DO I=-n_fourier,n_fourier + + S3%F(I)=s1%f(i)+fac*s2%f(i) + + ENDDO + else + DO I=-n_fourier,n_fourier + + S3%F(I)=s1%f(i)+s2%f(i) + + ENDDO + endif + r=s3 + call kill(s3) + +end subroutine add_vector_field_fourier + +subroutine mulc_vector_field_fourier(s1,fac,r) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: S1,r + TYPE (c_vector_field_fourier) s3 + complex(dp) fac + INTEGER I + call alloc(s3) + + DO I=-n_fourier,n_fourier + + S3%F(I)=fac*s1%f(i) + + ENDDO + + r=s3 + call kill(s3) + +end subroutine mulc_vector_field_fourier + + SUBROUTINE c_clean_vector_field_fourier(S1,S2,prec,relative) + implicit none + type (c_vector_field_fourier),INTENT(INOUT)::S2 + type (c_vector_field_fourier), intent(INOUT):: s1 + real(dp) prec + logical, optional :: relative + integer i + + do i=-n_fourier,n_fourier + call c_clean_vector_field(s1%f(i),s2%f(i),prec,relative) + enddo + + END SUBROUTINE c_clean_vector_field_fourier + + SUBROUTINE c_clean_taylors(S1,S2,prec,relative) + implicit none + type (c_taylor),INTENT(INOUT)::S2(:) + type (c_taylor), intent(INOUT):: s1(:) + real(dp) prec + logical, optional :: relative + + integer i + + do i=lbound(s1,1),ubound(s1,1) + call clean(s1(i),s2(i),prec,relative) + enddo + + END SUBROUTINE c_clean_taylors + + SUBROUTINE c_evaluate_vector_field_fourier(S1,theta,S2) + implicit none + type (c_vector_field_fourier),INTENT(INOUT)::S1 + type (c_vector_field), intent(INOUT):: s2 + real(dp) theta + integer i + + S2=0 + do i=lbound(s1%f,1),ubound(s1%f,1) + + S2=S2+(exp(i_*i*theta))*S1%f(i) + + enddo + + END SUBROUTINE c_evaluate_vector_field_fourier + + + +subroutine create_rotation_linear_field( f1, integer_part,damping,dospin) + implicit none + type(c_vector_field) , intent(inout) :: f1 + real(dp), intent(IN):: integer_part(:) + real(dp),optional, intent(IN):: damping(:) + logical, optional :: dospin + complex(dp) v + logical dos + integer i + integer ndpt,ndt,ndptb + integer, allocatable :: je(:) + dos=.false. +ndt=c_%nd2t/2 +ndpt=c_%ndpt +ndptb=c_%ndptb +f1=0 + if(present(dospin)) dos=dospin + + + + + + if(ndpt/=0) then + f1%v(ndptb)=integer_part(c_%nd).cmono.ndpt + endif + + + + + do i=1,ndt + f1%v(2*i-1)=-i_*integer_part(i)*(1.0_dp.cmono.(2*i-1)) + f1%v(2*i)=i_*integer_part(i)*(1.0_dp.cmono.(2*i)) + enddo + if(present(damping)) then + do i=1,ndt + f1%v(2*i-1)= f1%v(2*i-1) - (damping(i).cmono.(2*i-1))/twopi + f1%v(2*i) = f1%v(2*i) - (damping(i).cmono.(2*i))/twopi + enddo + endif + if(dos) then + + v=integer_part(c_%nd2/2+1) + f1%q%x(2)=-spin_def_tune*v/2.0_dp + + endif + + + + + + f1=to_phasor()*f1 !transform_vector_field_by_map(f1,to_phasor()) + + + + + +end subroutine create_rotation_linear_field + + + + +subroutine symplectify_for_sethna(m,ms,a1,a2,eps_and_norm) +implicit none +TYPE(c_damap),intent(inout):: m,ms +TYPE(c_damap),optional,intent(inout):: a1,a2 ! to get phase advance +real(dp),optional:: eps_and_norm +TYPE(c_damap) mt,l,b1,b2 +type(damap) mm +type(c_vector_field) f,fs +complex(dp) v +type(c_taylor) t,dt +real(dp),allocatable:: mat(:,:), matt(:,:),S(:,:),id(:,:) +integer i,j,k,n(11),nv,nd2,al,ii,a +integer, allocatable :: je(:) +real(dp) dm,norm,normb,norma + +call c_get_indices(n,0) +nv=n(4) +nd2=n(3) + +call alloc(mt,l,b1,b2);call alloc(f);call alloc(fs); +call alloc(mm);call alloc(t,dt) + +b1=1 +b2=1 +if(present(a1)) b1=a1 +if(present(a2)) then +b2=a2 +else + b2=b1 +endif +m=b2**(-1)*m*b1 +allocate(mat(m%n,m%n),matt(m%n,m%n),S(m%n,m%n),id(m%n,m%n)) +mat=0 +matt=0 +id=0 +S=0 +do i=1,nd2/2 + S(2*I-1,2*I)=1 ; S(2*I,2*I-1)=-1; + Id(2*I-1,2*I-1)=1 ; id(2*I,2*I)=1; +enddo + + +if(nv-nd2==0) then +mt=m + call c_factor_map(mt,l,f,dir=-1) +mat=l +else +mat=m +l=mat +mt=l**(-1)*m +f=log(mt) +endif + + + +matt=transpose(mat) + +mm=l + + +! constructing Furman's contracting matrix from my review sec.3.8.2 + + +call checksymp(mm,normb) + +do i=1,1000 +mat=matmul((1.5e0_dp*id+0.5e0_dp*matmul(mat,matmul(s,matmul(matt,S)))),mat) +matt=transpose(mat) +mm=matt +call checksymp(mm,norm) +if(norm>=normb) exit + normb=norm +enddo +if(i>=999) then + Write(6,*) "procedure did not converge in symplectify_for_sethna" +stop +endif + +l=mat +mm=l +fs=0 + +! Integrating a symplectic operator using the hypercube's diagonal + +allocate(je(nv)) +je=0 +do i=1,f%n + + j=1 + + do while(.true.) + + call c_cycle(f%v(i),j,v ,je); if(j==0) exit; + dm=1 + do ii=1,nd2 + dm=dm+je(ii) + enddo + t=v.cmono.je + do a=1,nd2 + dt=t.d.a + do al=1,nd2 + do k=1,nd2 + fs%v(al)=fs%v(al)+s(a,al)*s(k,i)*(id(k,a)*t+(1.0_dp.cmono.k)*dt)/dm + enddo ! k + enddo ! al + enddo ! a + enddo + +enddo + +mt=exp(fs,l) + + +if(present(eps_and_norm)) then + m=m-(m.sub.0) + + l=m-mt + norma=0.0_dp + k=0 + +do i=1,l%n + + j=1 + + do while(.true.) + + call c_cycle(l%v(i),j,v ,je); if(j==0) exit; + + normb=abs(m%v(i).sub.je) + norm=abs(v) + ! if(norm>eps_and_norm) then + ! norma=norm/normb+norma + norma=norm+norma + ! write(16,*) je + ! write(16,*) norma,norm,normb + k=k+1 + ! endif + + + enddo + +enddo +!write(6,*) k +eps_and_norm=norma/k + +endif + + + +ms=mt + + +ms=b2*ms*b1**(-1) +m=b2*m*b1**(-1) + + +deallocate(mat,matt,S,id) +deallocate(je) +call kill(mt,l,b1,b2); call kill(f);call kill(fs); +call kill(mm);call kill(t,dt) + +end subroutine symplectify_for_sethna + +subroutine nth_root(m,mr,n) +implicit none +TYPE(c_damap) m,mr +TYPE(c_damap) dm +type(c_vector_field) f +integer, parameter :: nn=36 +real(dp) mt(nn,nn),ma(6,6),bb(nn),im(nn,nn),mm(nn,nn) +integer i,n,nt,k,a,b,j +real(dp) xn,norm +integer ind(6,6),k1(nn),k2(nn) + +if(n==1) then +mr=m +return +endif +call alloc(dm) +call alloc(f) +k=0 +do i=1,c_%nd2 +do j=1,c_%nd2 + k=k+1 + ind(i,j)=k +k1(k)=i +k2(k)=j +enddo +enddo + + +f=c_logf_spin(m) + +xn=1.0_dp/n +f=xn*f + +dm=exp(f) + + + +nt=nn + +ma=dm + + +do i=1,c_%nd2 +do j=1,c_%nd2 + bb(ind(i,j))=m%e_ij(i,j) +do a=1,c_%nd2 +do b=1,c_%nd2 + mt(ind(i,j),ind(a,b))=ma(i,a)*ma(j,b) +enddo +enddo +enddo +enddo + +im=0;mm=0; +do i=1,nt + im(i,i)=1 +enddo + + +do i=0,n-1 +mm=im+mm +im=matmul(im,mt) +enddo + + + call matinv(mm,im,nt,nt,i) +if(i/=0) then + write(6,*) "Could not inverse in nth_root",i + stop +endif +bb=matmul(im,bb) + +do i=1,nt + dm%e_ij(k1(i),k2(i))=bb(i) +enddo + +mr=dm + +call kill(f) +call kill(dm) + +end subroutine nth_root + +!!!!! stuff for arrays of nodes + + subroutine alloc_node_array_tpsa(a) + implicit none + type(node_array), allocatable :: a(:) + integer i + + do i=1,size(a) + call alloc(a(i)%f) + call alloc(a(i)%m) + enddo + + end subroutine alloc_node_array_tpsa + + subroutine kill_node_array_tpsa(a) + implicit none + type(node_array), allocatable :: a(:) + integer i + + do i=1,size(a) + call kill(a(i)%f) + call kill(a(i)%m) + enddo + + end subroutine kill_node_array_tpsa + + subroutine kill_node_array(a) + implicit none + type(node_array), allocatable :: a(:) + integer i + + do i=1,size(a) + deallocate(a(i)%pos,a(i)%f) + deallocate(a(i)%v,a(i)%vmax,a(i)%err,a(i)%s) + enddo + + end subroutine kill_node_array + + subroutine alloc_node_array(a,n,m) + implicit none + type(node_array), allocatable :: a(:) + integer i,n,m + + allocate(a(n)) + + do i=1,n + allocate(a(i)%pos,a(i)%f,a(i)%m) + allocate(a(i)%v,a(i)%vmax,a(i)%err,a(i)%s(m)) + a(i)%s=0.0_dp + a(i)%v=0.0_dp;a(i)%vmax=1.d38; + a(i)%pos=0 + enddo + + end subroutine alloc_node_array + +!!!!!!!!!!!!!!!!!! Yu Li Hua factorization !!!!!!!!!!!!!!!!!! + +subroutine get_c_yu_w(n,yu,a0,a1,a2,ugiven) +implicit none +type(c_normal_form), intent(inout) :: n +type(c_yu_w), intent(inout) :: yu +type(c_damap),optional :: ugiven,a0,a1,a2 +type(c_damap) u,b0,b1,bn,ui +type(c_vector_field) f +type(c_taylor) t,p +integer i,j,k +complex(dp), allocatable :: mu(:) +integer, allocatable :: js(:) + +!!! + +allocate(mu(nd2t),js(nd2t)) + + + +!nd2t # harmonic planes +if(yu%n/=0) then + call kill(yu) +endif +call alloc(yu) + + ! + +call alloc(u,b0,b1,bn,ui) +call alloc(f);call alloc(t,p); + +if(present(ugiven) ) then + call c_canonise(n%a_t,u,a0=b0,a1=b1,a2=bn) +ui=ci_phasor()*bn*c_phasor() +u=ui**(-1) +f=n%ker +f=u*f + u=ugiven +else + call c_canonise(n%a_t,u,a0=b0,a1=b1,a2=bn) +n%a_t=u +ui=ci_phasor()*bn*c_phasor() +u=ui**(-1) +f=n%ker +f=u*f +endif + + + + +do i=1,nd2t/2 +js=0 +js(2*i-1)=1 + mu(2*i-1)=f%v(2*i-1).sub.js +js=0 +js(2*i)=1 + mu(2*i)=f%v(2*i).sub.js +enddo + + +js=0 + +do i=1,size(yu%w,1) ! should be nd2t # harmonic planes + yu%w(i,0)=u%v(i) + t=yu%w(i,0) + p=1.e0_dp + do j=1,yu%n + t=f*t + p=p*(1.0e0_dp+(1.0e0_dp.cmono.1)) + yu%w(i,j)=t + do k=0,j-1 + js(1)=j-k + yu%w(i,j)=yu%w(i,j)-(p.sub.js)*mu(i)**(j-k)*yu%w(i,k) + enddo +enddo +enddo + +if(.not.present(ugiven)) then + +if(present(a0) ) a0=b0 +if(present(a1) ) a1=b1 +if(present(a2) ) a2=bn + +endif + + +call kill(u,b0,b1,bn,ui) +call kill(f);call kill(t,p); +deallocate(mu,js) +end subroutine get_c_yu_w + +subroutine transform_c_yu_w(yu,a) +implicit none +type(c_yu_w), intent(inout) :: yu +type(c_damap) a +integer i,j + +do i=1,size(yu%w,1) + do j=0,yu%n + yu%w(i,j)=yu%w(i,j)*a + enddo +enddo + +end subroutine transform_c_yu_w + +!!!!!!!!!!!!!!!!!! End of Yu Li Hua factorization !!!!!!!!!!!!!!!!!! +subroutine c_fast_canonise(u,u_c,phase,damping,q_cs,q_as,q_orb,q_rot,spin_tune ,dospin) +implicit none +type(c_damap), intent(inout) :: u,u_c +real(dp), optional, intent(inout) :: phase(:),damping(:) +real(dp), optional, intent(inout) :: spin_tune(2) +type(c_linear_map), optional :: q_cs,q_as,q_rot,q_orb ! q_c is properly factorised +real(dp) b(6,6),b0(6,6),ri(6,6),id(6,6),st(6,6),ang,damp(3),t,cphi,sphi,s(6,6),aq,daq +type(c_linear_map) q ,qr,qc,qrot +complex(dp) cri(6,6) +integer i +logical dos,rota +logical, optional :: dospin +type(c_damap) uct + +call alloc(uct) +rota=.not.(present(phase)) +rota=.true. + +dos=.false. +if(present(dospin)) then + dos=dospin +else + if(force_spin_input_normal) then + write(6,*) " your default forces you to include dospin in the input of c_fast_canonise" + stop + endif +endif +s=0 +b0=0 +id=0 +do i=1,nd +b0(2*i-1,2*i-1)=1 +b0(2*i,2*i)=1 +s(2*i-1,2*i)=1 +s(2*i,2*i-1)=-1 +enddo +if(present(q_rot) ) then +qrot=0 ! actually makes identity +endif +b=0 +id=b0 +ri=0 +b=u + +if(ndpt/=0) call extract_a0_mat(b,b0) + + +!else + damp=1 +!endif +!det=FindDet(b(1:nd2,1:nd2), nd2)**(1.0_dp/nd2) +!write(6,*) damp + + + do i=1,ndt + if((i<=ndt)) then !.or.(i>nd-rf)) then + ! damp(i)=sqrt(b(2*i-1,2*i-1)*b(2*i,2*i)-b(2*i-1,2*i)*b(2*i,2*i-1)) + if(courant_snyder_teng_edwards) then + t=sqrt(b(2*i-1,2*i-1)**2+b(2*i-1,2*i)**2) + cphi=b(2*i-1,2*i-1)/t + sphi=b(2*i-1,2*i)/t +! if(cphi*b(2*i-1,2*i)+sphi*b(2*i-1,2*i-1)< 0.and.rota) then + if(sphi*b(2*i-1,2*i)+cphi*b(2*i-1,2*i-1)< 0.and.rota) then !2023.12.10 bug in China? + cphi=-cphi + sphi=-sphi + endif + + else + if(K_phase_choice==1) then !2023.12.10 + t=sqrt(b(2*i,2*i-1)**2+b(2*i,2*i)**2) + + cphi=b(2*i,2*i)/t + sphi=-b(2*i,2*i-1)/t + if(cphi*b(2*i,2*i)-sphi*b(2*i,2*i-1)< 0.and.rota) then + cphi=-cphi + sphi=-sphi + endif + else ! mengyu + t=sqrt(b(2*i-1,2*i-1)**2+b(2*i-1,2*i)**2) + sphi=-b(2*i-1,2*i-1)/t + cphi=b(2*i-1,2*i)/t + if(cphi*b(2*i-1,2*i)-sphi*b(2*i-1,2*i-1)< 0.and.rota) then + cphi=-cphi + sphi=-sphi + endif + endif + endif + + ri(2*i-1,2*i-1)=cphi + ri(2*i,2*i)=cphi + ri(2*i-1,2*i)=-sphi + ri(2*i,2*i-1)=sphi + endif + + if(present(phase)) then + ang=-atan2(sphi,cphi) + phase(i)=phase(i)-ang/twopi + endif + + + enddo + + + +if(ndpt/=0) then + ri(5,5)=1 + ri(6,6)=1 + ri(ndptb,ndpt)=- b(ndptb,ndpt) + if(mod(ndpt,2)==0) then + i=ndpt/2 + else + i=ndptb/2 + endif + if(present(phase)) phase(i)=phase(i)+b(ndptb,ndpt) + if(present(q_rot) ) then + qrot%mat(ndptb,ndpt)=-ri(ndptb,ndpt) + qrot%mat(5,5)=ri(5,5) + qrot%mat(6,6)=ri(6,6) + endif +endif + + + st=matmul(b,ri) + st=matmul(b0,st) +if(do_damping) then +!b0=matmul(matmul(st,s),transpose(st)) + + ! id gets filled with diagonal +call canonize_damping(st,id,damp) + ! matrix multiplication +write(*,*) "diagonal ====" +write(*,*) id +write(*,*) "a before ====" +write(*,*) st + st=matmul(st,id) + !b0=matmul(matmul(st,s),transpose(st)) + write(*,*) "a after ====" + write (*,*) st + +if(present(damping)) then + do i=1,ndt + damping(i)=damping(i)+log(damp(i)) + enddo +endif + +endif + +if(present(q_rot) ) then +if(ndpt/=0) then !2023.12.10 + do i=1,2 + qrot%mat(2*i-1,2*i-1)=ri(2*i-1,2*i-1)/damp(i) + qrot%mat(2*i,2*i)=ri(2*i,2*i)/damp(i) + qrot%mat(2*i-1,2*i)=-ri(2*i-1,2*i)/damp(i) + qrot%mat(2*i,2*i-1)=-ri(2*i,2*i-1)/damp(i) + enddo + else + do i=1,3 + qrot%mat(2*i-1,2*i-1)=ri(2*i-1,2*i-1)/damp(i) + qrot%mat(2*i,2*i)=ri(2*i,2*i)/damp(i) + qrot%mat(2*i-1,2*i)=-ri(2*i-1,2*i)/damp(i) + qrot%mat(2*i,2*i-1)=-ri(2*i,2*i-1)/damp(i) + enddo + endif +endif + + uct=st +if(use_quaternion.and.dos) then +q=1 + q=u%q +! make sure isf not below y plane + ! aq=q%q(0,0)**2-(q%q(1,0)**2+q%q(2,0)**2+q%q(3,0)**2) + ! aq=real(q%q(2,0)) + +!if(aq<0) then +! qr=1 ! = i +! qr=0.0_dp +! qr%q(1,0)=1.0_dp +! q=q*qr +!endif + + qr=1 + qr=0.0_dp + + + aq=-atan2(real(q%q(2,0)),real(q%q(0,0))) + + qr%q(0,0)= cos(aq) + qr%q(2,0)= sin(aq) + + daq=0 + if(ndpt/=0) then + + daq=(q%q(0,ndpt)*qr%q(2,0)+q%q(2,ndpt)*qr%q(0,0))/(q%q(2,0)*qr%q(2,0)-q%q(0,0)*qr%q(0,0)) + qr%q(0,ndpt)= -daq*qr%q(2,0) + qr%q(2,ndpt)= daq*qr%q(0,0) + endif + qc=q*qr + + if(present(spin_tune).and.dos) then + spin_tune(1)=spin_tune(1)+aq/pi ! changed 2018.11.01 + endif +cri=ri +qc=qc*cri + uct%q=qc + + +if(present(q_as) ) then +q_as=1 + if(abs(damp(1))+abs(damp(2))+abs(damp(3))<1.d-10) then + cri=inv_symplectic66(s) + else + call matinv(s,s,6,6,i) + cri=s + endif +q_as=qc*cri +endif + +endif + + if(present(spin_tune).and.dos) then + spin_tune(2)=spin_tune(2)+daq/pi ! changed 2018.11.01 + endif + +if(present(q_cs) ) then +q_cs=uct +endif +if(present(q_orb)) then +q_orb=uct +q_orb=1.0_dp +endif +if(present(q_rot) ) then + qrot%q=qr%q + qrot%q(1:3,0:6)=-qrot%q(1:3,0:6) +endif + +if(present(q_rot) ) then + q_rot=qrot !*q_rot 2023.12.10 +endif +write(*,*) "a end ===" +write(*,*) uct +u_c=uct + call kill(uct) + +end subroutine c_fast_canonise + +subroutine canonize_damping(b0,sd,damp) +implicit none +real(dp) b0(6,6),damp(3),sd(6,6) +real(dp) a(3,3),v(3) +integer i +a=0 +!!!! makes J/= AJtranspose(A) _12,34,56 = 1 +do i=1,3 + a(i,i)=b0(2*i-1,2*i-1)*b0(2*i,2*i)-b0(2*i-1,2*i)*b0(2*i,2*i-1) +enddo + a(1,2)=b0(1,3)*b0(2,4)-b0(1,4)*b0(2,3) + a(1,3)=b0(1,5)*b0(2,6)-b0(1,6)*b0(2,5) + a(2,1)=b0(3,1)*b0(4,2)-b0(3,2)*b0(4,1) + a(2,3)=b0(3,5)*b0(4,6)-b0(3,6)*b0(4,5) + a(3,1)=b0(5,1)*b0(6,2)-b0(5,2)*b0(6,1) + a(3,2)=b0(5,3)*b0(6,4)-b0(5,4)*b0(6,3) + + call matinv(a,a,3,3,i) + if(i/=0) stop 250 + v=1 + v=matmul(a,v) + sd=0 + do i=1,3 + sd(2*i-1,2*i-1)=sqrt(v(i)) + sd(2*i,2*i)=sd(2*i-1,2*i-1) + damp(i)=sd(2*i-1,2*i-1) + enddo + +end subroutine canonize_damping + + + + +subroutine extract_a0_mat(a,a0) +!#internal: manipulation +!# This routines extracts a0: the full fixed point map. + implicit none + real(dp), intent(inout) :: a(6,6),a0(6,6) + type(c_damap) aa,aa0 + call alloc(aa,aa0) + aa=a + aa0=a0 + call extract_a0(aa,aa0) + a=aa + a0=aa0 + call kill(aa,aa0) +end subroutine extract_a0_mat + + + + +!Function to find the determinant of a square matrix +!Author : Louisda16th a.k.a Ashwith J. Rego +!Description: The subroutine is based on two key points: +!1] A determinant is unaltered when row operations are performed: Hence, using this principle, +!row operations (column operations would work as well) are used +!to convert the matrix into upper traingular form +!2]The determinant of a triangular matrix is obtained by finding the product of the diagonal elements +! +REAL(dp) FUNCTION FindDet(mat, n) + IMPLICIT NONE + REAL(dp), DIMENSION(n,n) :: matrix,mat + INTEGER, INTENT(IN) :: n + REAL(dp) :: m, temp + INTEGER :: i, j, k, l + LOGICAL :: DetExists = .TRUE. + matrix=mat + l = 1 + !Convert to upper triangular form + DO k = 1, n-1 + IF (matrix(k,k) == 0) THEN + DetExists = .FALSE. + DO i = k+1, n + IF (matrix(i,k) /= 0) THEN + DO j = 1, n + temp = matrix(i,j) + matrix(i,j)= matrix(k,j) + matrix(k,j) = temp + END DO + DetExists = .TRUE. + l=-l + EXIT + ENDIF + END DO + IF (DetExists .EQV. .FALSE.) THEN + FindDet = 0 + return + END IF + ENDIF + DO j = k+1, n + m = matrix(j,k)/matrix(k,k) + DO i = k+1, n + matrix(j,i) = matrix(j,i) - m*matrix(k,i) + END DO + END DO + END DO + + !Calculate determinant by finding product of diagonal elements + FindDet = l + DO i = 1, n + FindDet = FindDet * matrix(i,i) + END DO + +END FUNCTION FindDet + +!!!!!!!!!!!!!!!!!!!! tree tracking for Zhe : independent program + + SUBROUTINE SET_TREE_G_complex_zhe(T,Ma) + IMPLICIT NONE + TYPE(TREE_ELEMENT), INTENT(INOUT) :: T(:) + TYPE(c_damap), INTENT(INOUT) :: Ma + INTEGER N,NP,i,k,j,kq,mf + + real(dp) norm,mat(6,6) + TYPE(taylor), ALLOCATABLE :: M(:), MG(:) + TYPE(damap) ms + integer js(6) + type(c_damap) L_r , N_r , N_s , L_s + + + + + call alloc(L_r , N_r , N_s , L_s) + +!!! default sagan_gen=.true. + if(.not.sagan_gen.or.symplectify_map) call symplectify_for_zhe(ma,L_r , N_r, L_s , N_s ) + + !!! + if(symplectify_map) then + L_r=1 + N_r=1 + endif + + +! np=ma%n+18 + if(ma%n/=6) then + write(6,*) " you need a 6-d map in SET_TREE_G_complex for PTC " + stop + endif + np=size_tree +! initialized in ptc ini + ! ind_spin(1,1)=1+ma%n;ind_spin(1,2)=2+ma%n;ind_spin(1,3)=3+ma%n; + ! ind_spin(2,1)=4+ma%n;ind_spin(2,2)=5+ma%n;ind_spin(2,3)=6+ma%n; + ! ind_spin(3,1)=7+ma%n;ind_spin(3,2)=8+ma%n;ind_spin(3,3)=9+ma%n; + ! k1_spin(1)=1;k2_spin(1)=1; + ! k1_spin(2)=1;k2_spin(2)=2; + ! k1_spin(3)=1;k2_spin(3)=3; + ! k1_spin(4)=2;k2_spin(4)=1; + ! k1_spin(5)=2;k2_spin(5)=2; + ! k1_spin(6)=2;k2_spin(6)=3; + ! k1_spin(7)=3;k2_spin(7)=1; + ! k1_spin(8)=3;k2_spin(8)=2; + ! k1_spin(9)=3;k2_spin(9)=3; + + + ALLOCATE(M(NP)) + CALL ALLOC(M,NP) + ALLOCATE(Mg(NP)) + CALL ALLOC(mg,NP) + do i=1,np + m(i)=0.e0_dp + mg(i)=0.e0_dp + enddo + +if(.not.sagan_gen.or.symplectify_map) then + L_r = L_r*N_r +else + ! T(x)=T0 +L(x) + T2(x) + L_s=ma.sub.1 ! L_s=L + L_r=L_s**(-1)*ma ! T=L_s o L_r + +endif + +if(.not.sagan_gen.or.symplectify_map) then + + do i=1,L_r%n + m(i)=L_r%v(i) ! orbital part + enddo +else + do i=1,L_r%n ! dimension of phase space + m(i)= 1.0_dp.mono.i + enddo + +endif + + +if(use_quaternion) then + call c_full_norm_quaternion(Ma%q,kq,norm) + if(kq==-1) then + do i=0,3 + m(ind_spin(1,1)+i)=ma%q%x(i) + enddo + elseif(kq/=-1) then + m(ind_spin(1,1))=1.0_dp + do i=ind_spin(1,1)+1,size_tree + m(i)=0.0_dp + enddo + endif +else + call c_full_norm_spin(Ma%s,k,norm) + + if(k==-1) then + do i=1,3 + do j=1,3 + m(ind_spin(i,j))=ma%s%s(i,j) + enddo + enddo + else + do i=1,3 + m(ind_spin(i,i))=1.0e0_dp + enddo + endif +endif + js=0 + js(1)=1;js(3)=1;js(5)=1; ! q_i(q_f,p_i) and p_f(q_f,p_i) + call alloc(ms) + + +if(.not.sagan_gen.or.symplectify_map) then + + ms=n_s + +else + + ms = L_r + +endif + + + + + ms=ms**js +! do i=1,3 +! mg(i)=ms%v(2*i-1) ! q_i(q_f,p_i) +! mg(3+i)=ms%v(2*i) ! p_f(q_f,p_i) +! enddo + do i=1,6 + mg(i)=ms%v(i) + enddo + do i=1,3 + do j=1,3 + mg(ind_spin(i,j))=ms%v(2*i-1).d.(2*j-1) ! Jacobian for Newton search + enddo + enddo + call kill(ms) + + call SET_TREE_g(T(1),m(1:6)) + ! do i=1,ma%n + ! m(i)=1.0_dp.cmono.i + ! enddo + ! do i=ma%n+1,6 + ! m(i)=0.0_dp + ! enddo + call SET_TREE_g(T(2),m(7:15)) + + ! call SET_TREE_g(T(2),m(1:size_tree)) + call SET_TREE_g(T(3),mg(1:size_tree)) + + + +! write(6,*) " mul ",mul + if(.not.sagan_gen.or.symplectify_map) then + t(3)%rad=L_s + else + t(3)%rad=L_s + endif + + + mat=ma**(-1) + t(1)%e_ij=ma%e_ij !matmul(matmul(mat,ma%e_ij),transpose(mat)) not necessary I think + +if(.false.) then !!!! annoying prints +call kanalnummer(mf,"taylor_series.txt") + +write(mf,*)" equation 20 " +do i=1,6 +call print(mg(i),mf) +enddo + write(mf,*)" 9 derivatives of equation 20" +do i=1,9 +write(mf,*) k1_spin(i),k2_spin(i) +call print(mg(i),mf) +enddo + write(mf,*)" linear part" +call print(l_s,mf) + write(mf,*)" Quantum fluctuation" +do i=1,6 +do j=1,6 + write(mf,*) ma%e_ij(i,j) +enddo +enddo + +close(mf) +endif + call kill(m); call kill(mg); + deallocate(M); deallocate(Mg); + call kill(L_r , N_r , N_s , L_s) + + END SUBROUTINE SET_TREE_G_complex_zhe + + + SUBROUTINE SET_TREE_G_complex_zhe_as_is(T,Ma) + IMPLICIT NONE + TYPE(TREE_ELEMENT), INTENT(INOUT) :: T(:) + TYPE(c_damap), INTENT(INOUT) :: Ma + INTEGER N,NP,i,k,j,kq + + real(dp) norm,mat(6,6) + TYPE(taylor), ALLOCATABLE :: M(:), MG(:) + TYPE(damap) ms + integer js(6) + type(c_damap) L_ns , N_pure_ns , N_s , L_s + + + + + call alloc(L_ns , N_pure_ns , N_s , L_s) + + ! call symplectify_for_zhe(ma,L_ns , N_pure_ns, L_s , N_s ) + +! np=ma%n+18 + if(ma%n/=6) then + write(6,*) " you need a 6-d map in SET_TREE_G_complex for PTC " + stop + endif + np=size_tree + + + ALLOCATE(M(NP)) + CALL ALLOC(M,NP) + ALLOCATE(Mg(NP)) + CALL ALLOC(mg,NP) + do i=1,np + m(i)=0.e0_dp + mg(i)=0.e0_dp + enddo + + + L_s=ma + do i=1,L_ns%n + m(i)=L_s%v(i) ! orbital part full + enddo + + + +if(use_quaternion) then + call c_full_norm_quaternion(Ma%q,kq,norm) + if(kq==-1) then + do i=0,3 + mg(ind_spin(1,1)+i)=ma%q%x(i) + enddo + elseif(kq/=-1) then + mg(ind_spin(1,1))=1.0_dp + do i=ind_spin(1,1)+1,size_tree + mg(i)=0.0_dp + enddo + endif +else + call c_full_norm_spin(Ma%s,k,norm) + if(k==-1) then + do i=1,3 + do j=1,3 + mg(ind_spin(i,j))=ma%s%s(i,j) + enddo + enddo + else + do i=1,3 + mg(ind_spin(i,i))=1.0e0_dp + enddo + endif +endif + + + call SET_TREE_g(T(1),m(1:6)) + ! do i=1,ma%n + ! m(i)=1.0_dp.cmono.i + ! enddo + ! do i=ma%n+1,6 + ! m(i)=0.0_dp + ! enddo + call SET_TREE_g(T(2),mg(7:15)) + + do i=1,np + mg(i)=0.e0_dp + enddo + call SET_TREE_g(T(3),mg(1:size_tree)) + +!T(3)%ng=mul +! write(6,*) " mul ",mul + t(3)%rad=L_s !linear + + + mat=ma**(-1) + t(1)%e_ij=ma%e_ij !matmul(matmul(mat,ma%e_ij),transpose(mat)) not necessary I think + + + + call kill(m); call kill(mg); + deallocate(M); deallocate(Mg); + call kill(L_ns , N_pure_ns , N_s , L_s) + + END SUBROUTINE SET_TREE_G_complex_zhe_as_is + + +subroutine fill_tree_element_line_zhe_outside_map(minput ,filef,fix0,as_is,stochprec,tree_zhe) ! fix0 is the initial condition for the maps +implicit none +logical, optional :: as_is +real(dp), optional :: fix0(6),stochprec +complex(dp)v +logical as_is0 +integer no1 + +real(dp) fix(6),mat(6,6) ,f0(6),stoch,r2,coe +!real(dp), allocatable :: mm(:,:),vm(:) +type(c_damap) m,minput +type(c_taylor) t +integer i,inf,j !,mberz +type(tree_element_zhe), optional :: tree_zhe(:) + +character(255) file_berz + +type(tree_element), pointer :: forward(:) =>null() +character(*),optional :: filef + + as_is0=.false. +!file_berz="zhe1_berz" +! call kanalnummer(mberz,file_berz) + +if(present(as_is)) as_is0=as_is + + allocate(forward(3)) + + +mat=0 +do i=1,size(mat,1) +mat(i,i)=1 +enddo + + +!call init_all(state,no,0) + call alloc(m); + + +!! +fix=minput +f0=minput%x0(1:6) +if(present(fix0)) f0=fix0 + + +m=minput + +do i=1,6 + m%v(i)=m%v(i)-(m%v(i).sub.0) +enddo + + + +if( as_is0) then + call SET_TREE_G_complex_zhe_as_is(forward,m) +else + call SET_TREE_G_complex_zhe(forward,m) +endif + + stoch=-1.0_dp +if(present(stochprec)) stoch=stochprec + +if(stoch>=0) then + call c_stochastic_kick(m,forward(2)%rad,forward(2)%fix0,stoch) +endif + +forward(1)%usenonsymp=as_is0 +forward(1)%rad=mat +forward(1)%fix0(1:6)=f0 ! entrance +forward(1)%fixr(1:6)=fix +forward(1)%fix(1:6)=fix ! exit +forward(3)%fix0(1:6)=f0 ! entrance +forward(3)%fixr(1:6)=fix +forward(3)%fix(1:6)=fix ! exit + + forward(1)%ds=0.0_dp + + + forward(1)%ds=0 + +forward(1)%beta0=1.0_dp +if(present(tree_zhe)) then + do i=1,3 + CALL ALLOC_TREE_zhe(tree_zhe(i),forward(i)%N,forward(i)%NP) + tree_zhe(i)=forward(i) + enddo +endif + + + + if(present(filef)) then + call kanalnummer(inf,filef) + call print_tree_elements(forward,inf) + close(inf) + call KILL(forward) + deallocate(forward) +endif + +!call print(minput) + call kill(m) +!close(mberz) +end subroutine fill_tree_element_line_zhe_outside_map + + subroutine compute_lie_map_matrix_complex(T) !,spin + implicit none + integer NO1,ND11,i + type(c_damap) mtotal,T + no1=c_%no + nd11=c_%nd + + if(c_%nd>3) stop 100 + call init_moment_map(NO1,nd11) + + call create_moment_map_one_complex(T,nd11) + t%cm=transpose(T%cm) + + + end subroutine compute_lie_map_matrix_complex + + subroutine compute_lie_map_matrix(T) !,spin + implicit none + integer NO1,ND11,i + type(c_damap) mtotal,T + real(dp) sig(6,6) + no1=c_%no + nd11=c_%nd + sig=0 + if(c_%nd>3) stop 100 + call init_moment_map(NO1,nd11) + call alloc(mtotal) + allocate(mtotal%m(nmono_from_moment,nmono_from_moment)) + mtotal=0 + do i=1,nmono_from_moment + mtotal%m(i,i)=1 + enddo + call create_moment_map_one(mtotal,T,sig,nd11,fin=.false.) + allocate(t%m(nmono_from_moment,nmono_from_moment)) + t%m=transpose(mtotal%m) + + call kill(mtotal) + + end subroutine compute_lie_map_matrix + + +subroutine create_taylor_vector(t,v,vc) ! fix0 is the initial condition for the maps +implicit none +complex(dp) w +integer je(6),i,k,j + real(dpn),optional:: v(:) + complex(dpn),optional:: vc(:) +type(c_taylor) t + +if(present(v)) v=0 +if(present(vc)) vc=0 + j=1 + + do while(.true.) + + call c_cycle(t,j,w ,je); if(j==0) exit; + k=hash(je(1),je(2),je(3),je(4),je(5),je(6)) + if(present(v)) v(k)=w + if(present(vc)) vc(k)=w + enddo + + +end subroutine create_taylor_vector + +subroutine create_vector_taylor(v,vc,w) ! fix0 is the initial condition for the maps +implicit none + + + real(dpn),optional:: v(:) + complex(dpn),optional:: vc(:) +complex(dp) vcc +type(c_taylor) t,w +integer i + + +call alloc(t) +w=0 + + +do i=1,nmono + + t= dz_c(1)**in1(i) + t=t*dz_c(2)**in2(i) + if(c_%nd>1) then + t= dz_c(3)**in3(i) + t=t*dz_c(4)**in4(i) + endif + if(c_%nd>2) then + t= dz_c(5)**in5(i) + t=t*dz_c(6)**in6(i) + endif + if(present(v)) then + w=t*v(i)+w + elseif(present(vc)) then +vcc=vc(i) + w=t*vcc+w + else + + write(6,*) "error in create_vector_taylor " + stop 476 + endif +enddo + +call kill(t) + + +end subroutine create_vector_taylor + +subroutine create_vector_field(finput,f) ! fix0 is the initial condition for the maps +implicit none + + +complex(dp)v +integer i1,i2,i3,i4,i5,i6,je(6),k !,mi,nz,noo,no1 + +complex(dp) coe ,eps +!complex(dpn) r2 +complex(dpn) f(:,:) +type(c_vector_field) finput +type(c_taylor) t +integer i,inf,j,nd1 + + + nd1=c_%nd + + + nmono=size(in1) + + + +f=0 + +call alloc(t) + + f=0 + + + + do i=1,nmono + + t= dz_c(1)**in1(i) + t=t*dz_c(2)**in2(i) + if(nd1>1) then + t= dz_c(3)**in3(i) + t=t*dz_c(4)**in4(i) + endif + if(nd1>2) then + t= dz_c(5)**in5(i) + t=t*dz_c(6)**in6(i) + endif + + t=finput*t + + j=1 + + do while(.true.) + + call c_cycle(t,j,v ,je); if(j==0) exit; + k=hash(je(1),je(2),je(3),je(4),je(5),je(6)) + f(k,i)=v+f(k,i) + enddo + enddo + +call kill(t) + + +end subroutine create_vector_field + + + subroutine init_moment_map(NO1,nd11) !,spin + implicit none + integer, intent(in) :: NO1,ND11 + integer i,i1,i2,i3,i4,i5,i6,noo,j,nd1 + + +if(associated(in1)) then + deallocate(in1,in2,in3,in4,in5,in6,posin,sigdis,sigdis0,dfac,pascal,hash,mono_order,vsol) +endif + +nd1=iabs(nd11) + nmono=0 + do noo=0,NO1 + if(nd1==3) then + do i1=0,noo + do i2=0,noo + if(i1+i2>noo)cycle + do i3=0,noo + if(i1+i2+i3>noo)cycle + do i4=0,noo + if(i1+i2+i3+i4>noo)cycle + do i5=0,noo + if(i1+i2+i3+i4+i5>noo)cycle + do i6=0,noo + if(i1+i2+i3+i4+i5+i6/=noo)cycle + nmono=nmono+1 + enddo + enddo + enddo + enddo + enddo + enddo + + elseif(nd1==2) then + do i1=0,noo + do i2=0,noo + if(i1+i2>noo)cycle + do i3=0,noo + if(i1+i2+i3>noo)cycle + do i4=0,noo + if(i1+i2+i3+i4/=noo)cycle + nmono=nmono+1 + enddo + enddo + enddo + enddo + elseif(nd1==1) then + do i1=0,noo + do i2=0,noo + if(i1+i2/=noo)cycle + nmono=nmono+1 + + enddo + enddo +else + +stop 888 +endif + enddo + ! write(6,*) "nmono original",nmono + +nmono_from_moment=nmono + + allocate(in1(nmono),in2(nmono),in3(nmono),in4(nmono),in5(nmono),in6(nmono),posin(0:no1),mono_order(nmono),vsol(nmono)) +if(nd1==3) then + allocate(sigdis(nmono),sigdis0(nmono),dfac(0:no1),pascal(0:no1,0:no1),hash(0:no1,0:no1,0:no1,0:no1,0:no1,0:no1)) +elseif(nd1==2) then + allocate(sigdis(nmono),sigdis0(nmono),dfac(0:no1),pascal(0:no1,0:no1),hash(0:no1,0:no1,0:no1,0:no1,0:0,0:0)) +elseif(nd1==1) then + allocate(sigdis(nmono),sigdis0(nmono),dfac(0:no1),pascal(0:no1,0:no1),hash(0:no1,0:no1,0:0,0:0,0:0,0:0)) +endif +pascal=0 +vsol=0 + +pascal(0,0)=1 +pascal(1,0)=1 +pascal(1,1)=1 + +if(no1>=2) then + pascal(2,0)=1 + pascal(2,1)=2 + pascal(2,2)=1 + + do i=3,no1 + do j=1,i-1 + pascal(i,j)=pascal(i-1,j-1)+pascal(i-1,j) + enddo + pascal(i,0)=1 + pascal(i,i)=1 + enddo +endif +!do i=1,no1 +!write(6,"(7(i2,1x))") pascal(i,0:i) +!enddo + +hash=0 + dfac=0 + dfac(0)=1 +if(use_gaussian_zhe) then + if(no1>=2) dfac(2)=1 + do i=4,no1,2 + dfac(i)=(i-1)*dfac(i-2) + enddo +else + do i=2,no1,2 + dfac(i)=1 + enddo +endif + !write(6,*) "dfac " + !write(6,*) dfac + sigdis0=0 + sigdis=0 + + nmono=0 + do noo=0,NO1 + if(nd1==3) then + do i1=0,noo + do i2=0,noo + if(i1+i2>noo)cycle + do i3=0,noo + if(i1+i2+i3>noo)cycle + do i4=0,noo + if(i1+i2+i3+i4>noo)cycle + do i5=0,noo + if(i1+i2+i3+i4+i5>noo)cycle + do i6=0,noo + if(i1+i2+i3+i4+i5+i6/=noo)cycle + nmono=nmono+1 + in1(nmono)=i6 + in2(nmono)=i5 + in3(nmono)=i4 + in4(nmono)=i3 + in5(nmono)=i2 + in6(nmono)=i1 + mono_order(nmono)=noo + + ! hash(i1,i2,i3,i4,i5,i6)=nmono + hash(i6,i5,i4,i3,i2,i1)=nmono + + + enddo + enddo + enddo + enddo + enddo + enddo + elseif(nd1==2) then + do i1=0,noo + do i2=0,noo + if(i1+i2>noo)cycle + do i3=0,noo + if(i1+i2+i3>noo)cycle + do i4=0,noo + if(i1+i2+i3+i4/=noo)cycle + nmono=nmono+1 + in1(nmono)=i4 + in2(nmono)=i3 + in3(nmono)=i2 + in4(nmono)=i1 + in5(nmono)=0 + in6(nmono)=0 + mono_order(nmono)=noo + + hash(i4,i3,i2,i1,0,0)=nmono +! hash(i1,i2,i3,i4,0,0)=nmono + + enddo + enddo + enddo + enddo + elseif(nd1==1) then + do i1=0,noo + do i2=0,noo + if(i1+i2/=noo)cycle + nmono=nmono+1 + in1(nmono)=i2 + in2(nmono)=i1 + in3(nmono)=0 + in4(nmono)=0 + in5(nmono)=0 + in6(nmono)=0 + mono_order(nmono)=noo + +! hash(i1,i2,0,0,0,0)=nmono + hash(i2,i1,0,0,0,0)=nmono + + enddo + enddo +else + +stop 888 +endif + + + +enddo + + + end subroutine init_moment_map + + + +subroutine create_moment_map_one(mtotal,minput,sig,nd11,fin) !,equilibrium_moments) ! fix0 is the initial condition for the maps +implicit none + + +complex(dp)v +integer i1,i2,i3,i4,i5,i6,no1,je(6),noo,k,mi,ouch,nz + +real(dp) coe,radkick(6,6),a(6,6),sig(6,6),ki(6),eps +real(dpn) r2 +real(dpn), allocatable :: mm(:,:),vm(:),db(:,:) +type(c_damap) m,minput,mtotal +type(c_taylor) t +integer i,inf,j,nd1,nd11 + logical,optional :: fin +!real(dp),optional :: equilibrium_moments(:) +logical ende + +ende=.false. +if(present(fin)) ende=fin + nd1=iabs(nd11) + + call alloc(m); + sig=0 + a=real(minput%e_ij) + call cholesky_dt(A, radkick) ! in back + + + + +m=minput + + +sigdis0=0 + + +m=0 +m=radkick + +call alloc(t) + +nmono=size(in1) + do i = 1,nmono + + if(nd1==3) then + t=dz_c(1)**in1(i)*dz_c(2)**in2(i)*dz_c(3)**in3(i)*dz_c(4)**in4(i)*dz_c(5)**in5(i)*dz_c(6)**in6(i) + elseif(nd1==2) then + t=dz_c(1)**in1(i)*dz_c(2)**in2(i)*dz_c(3)**in3(i)*dz_c(4)**in4(i) + +elseif(nd1==1) then + t=dz_c(1)**in1(i)*dz_c(2)**in2(i) + + else + stop 889 +endif + + t=t*m + + j=1 + + do while(.true.) +je=0 + call c_cycle(t,j,v ,je); if(j==0) exit; + + sigdis0(i)=sigdis0(i)+dfac(je(1))*dfac(je(2))*dfac(je(3))*dfac(je(4))*dfac(je(5))*dfac(je(6))*v + + enddo + + enddo + + + + ! allocate(minput%db(nmono,nmono),minput%m(nmono,nmono)) + allocate(db(nmono,nmono),minput%m(nmono,nmono)) + ! minput%db=0 + db=0 + minput%m=0 + + if(nd1==3) then + do i=1,nmono + noo=mono_order(i) + + do i6=0,in6(i) + + do i5=0,in5(i) + + do i4=0,in4(i) + + do i3=0,in3(i) + + do i2=0,in2(i) + do i1=0,in1(i) + ouch=i6+i5+i4+i3+i2+i1 + + if(mod(ouch,2)==1)cycle + + coe=pascal(in1(i),i1)*pascal(in2(i),i2)*pascal(in3(i),i3)*pascal(in4(i),i4)*pascal(in5(i),i5)*pascal(in6(i),i6) + mi=hash(in1(i)-i1,in2(i)-i2,in3(i)-i3,in4(i)-i4,in5(i)-i5,in6(i)-i6) + + k=hash(i1,i2,i3,i4,i5,i6) + + coe=coe*sigdis0(k) + ! minput%db(i,mi)=minput%db(i,mi)+coe + db(i,mi)=db(i,mi)+coe + + enddo + enddo + enddo + enddo + enddo + enddo + + enddo + + elseif(nd1==2) then + do i=1,nmono + noo=mono_order(i) + + do i4=0,in4(i) + + do i3=0,in3(i) + do i2=0,in2(i) + do i1=0,in1(i) + ouch=i4+i3+i2+i1 + + if(mod(ouch,2)==1)cycle + coe=pascal(in1(i),i1)*pascal(in2(i),i2)*pascal(in3(i),i3)*pascal(in4(i),i4) + mi=hash(in1(i)-i1,in2(i)-i2,in3(i)-i3,in4(i)-i4,0,0) + + k=hash(i1,i2,i3,i4,0,0) + coe=coe*sigdis0(k) + db(i,mi)=db(i,mi)+coe + enddo + enddo + enddo + enddo + + + enddo + + elseif(nd1==1) then + do i=1,nmono + noo=mono_order(i) + + do i2=0,in2(i) + + do i1=0,in1(i) + ouch=i2+i1 + + + coe=pascal(in1(i),i1)*pascal(in2(i),i2) + + mi=hash(in1(i)-i1,in2(i)-i2,0,0,0,0) + + k=hash(i1,i2,0,0,0,0) + coe=coe*sigdis0(k) + db(i,mi)=db(i,mi)+coe + enddo + enddo + + + enddo + +endif ! nd1==3 + +m=minput +do i=1,nd2 +m%v(i)=m%v(i)-(m%v(i).sub.0) +enddo + do i=1,nmono + + t= m%v(1)**in1(i) + t=t*m%v(2)**in2(i) + if(nd1>1) then + t=t*m%v(3)**in3(i) + t=t*m%v(4)**in4(i) + endif + if(nd1>2) then + + t=t*m%v(5)**in5(i) + t=t*m%v(6)**in6(i) + endif + j=1 + + do while(.true.) + + call c_cycle(t,j,v ,je); if(j==0) exit; + k=hash(je(1),je(2),je(3),je(4),je(5),je(6)) + minput%m(i,k)=v + enddo + enddo + + + +minput%m=matmul(db,minput%m) + +mtotal%m=matmul(minput%m,mtotal%m) + + +deallocate(db) + +deallocate(minput%m) + + +if(ende) then +nz=nmono-1 + + +allocate(mm(nz,nz),vm(nz)) + + + +mm=0 + + +do i=1,nz + vm(i)=mtotal%m(i+1,1) + mm(i,i)=1 +enddo + +do i=1,nz +do j=1,nz + mm(i,j)=mm(i,j)-mtotal%m(1+i,1+j) +enddo +enddo + + + + +call matinvn(mm,mm,nz,nz,i) + +write(6,*) " success = ",i + +vm=matmul(mm,vm) +vsol(2:nmono)=vm + + +write(6,*) "Quadratic moments to order ", no +do i=1,2*nd1 +je=0 +je(i)=je(i)+1 +do j=1,2*nd1 +je(j)=je(j)+1 +sig(i,j)=vm(hash(je(1),je(2),je(3),je(4),je(5),je(6))-1) +je(j)=je(j)-1 + +if(i<=j) write(6,*) i,j,sig(i,j) +enddo +enddo + + deallocate(mm,vm) + +endif ! final + +call kill(t) + call kill(m) + +end subroutine create_moment_map_one + + + +subroutine create_moment_map_one_complex(minput,nd11) ! fix0 is the initial condition for the maps +implicit none +complex(dp)v +integer i1,i2,i3,i4,i5,i6,no1,je(6),k !,mi,nz,noo + +complex(dp) coe ,eps +!complex(dpn) r2 +complex(dpn), allocatable :: mm(:,:) +type(c_damap) minput , m +type(c_taylor) t +integer i,inf,j,nd1,nd11 + + + nd1=iabs(nd11) + + call alloc(m); + nmono=size(in1) + if(.not.associated(minput%cm)) allocate(minput%cm(nmono,nmono)) + +m=minput + + +call alloc(t) + + + minput%cm=0 + + + +m=minput +do i=1,nd2 +m%v(i)=m%v(i)-(m%v(i).sub.0) +enddo + do i=1,nmono + + t= m%v(1)**in1(i) + t=t*m%v(2)**in2(i) + if(nd1>1) then + t=t*m%v(3)**in3(i) + t=t*m%v(4)**in4(i) + endif + if(nd1>2) then + + t=t*m%v(5)**in5(i) + t=t*m%v(6)**in6(i) + endif + j=1 + + do while(.true.) + + call c_cycle(t,j,v ,je); if(j==0) exit; + k=hash(je(1),je(2),je(3),je(4),je(5),je(6)) + minput%cm(i,k)=v + enddo + enddo + + + + + +call kill(t) + call kill(m) + +end subroutine create_moment_map_one_complex + +subroutine create_moment_map(minput,sig,nd11,radk) ! fix0 is the initial condition for the maps +implicit none + + +complex(dp)v +integer i1,i2,i3,i4,i5,i6,no1,je(6),noo,k,mi,ouch,nz +real(dp), optional :: radk(6,6) +real(dp) coe,radkick(6,6),a(6,6),sig(6,6),ki(6),eps +real(dpn) r2 +real(dpn), allocatable :: mm(:,:),vm(:),db(:,:) +type(c_damap) m,minput +type(c_taylor) t +integer i,inf,j,nd1,nd11 + + nd1=iabs(nd11) + + call alloc(m); + sig=0 + a=real(minput%e_ij) + call cholesky_dt(A, radkick) ! in back +! call c_stochastic_kick(minput,a,ki,eps) ! in front +! call c_stochastic_kick(minput,radkick,ki,eps) ! in front + +if(present(radk)) radk=radkick + +m=minput + + +sigdis0=0 + + +m=0 +m=radkick + +call alloc(t) + +nmono=size(in1) + do i = 1,nmono + + if(nd1==3) then + t=dz_c(1)**in1(i)*dz_c(2)**in2(i)*dz_c(3)**in3(i)*dz_c(4)**in4(i)*dz_c(5)**in5(i)*dz_c(6)**in6(i) + elseif(nd1==2) then + t=dz_c(1)**in1(i)*dz_c(2)**in2(i)*dz_c(3)**in3(i)*dz_c(4)**in4(i) + +elseif(nd1==1) then + t=dz_c(1)**in1(i)*dz_c(2)**in2(i) + + else + stop 889 +endif + +! if(in1(i)==n1_.and.in2(i)==n2_) then +! write(mf_,*) " in create map" +!call print(t,mf_) +!call print(m,mf_) +! write(mf_,*) " in cycle" + +!endif +! t=t.o.m + t=t*m + + j=1 + + do while(.true.) +je=0 + call c_cycle(t,j,v ,je); if(j==0) exit; +! k=hash(j(1),j(2),j(3),j(4),j(5),j(6)) +! if(in1(i)==n1_.and.in2(i)==n2_) then +!write(mf_,*) v +!write(mf_,"(6(1x,i4))") je(1:6) +!write(mf_,format6) dfac(je(1)),dfac(je(2)),dfac(je(3)),dfac(je(4)),dfac(je(5)),dfac(je(6)) + +!endif + sigdis0(i)=sigdis0(i)+dfac(je(1))*dfac(je(2))*dfac(je(3))*dfac(je(4))*dfac(je(5))*dfac(je(6))*v + + enddo +! if(in1(i)==n1_.and.in2(i)==n2_) then + +! call print(t,mf_) +! endif + enddo + +! do j=1,nmono +!if( sigdis0(j)/=0) then +! write(mf_,*) in1(j),in2(j),j +! write(mf_,*) sigdis0(j) +!endif +! enddo + + allocate(db(nmono,nmono),minput%m(nmono,nmono)) + db=0 + minput%m=0 + + if(nd1==3) then + do i=1,nmono + noo=mono_order(i) + + do i6=0,in6(i) + + do i5=0,in5(i) + + do i4=0,in4(i) + + do i3=0,in3(i) + + do i2=0,in2(i) + do i1=0,in1(i) + ouch=i6+i5+i4+i3+i2+i1 + + if(mod(ouch,2)==1)cycle + + coe=pascal(in1(i),i1)*pascal(in2(i),i2)*pascal(in3(i),i3)*pascal(in4(i),i4)*pascal(in5(i),i5)*pascal(in6(i),i6) + mi=hash(in1(i)-i1,in2(i)-i2,in3(i)-i3,in4(i)-i4,in5(i)-i5,in6(i)-i6) + + k=hash(i1,i2,i3,i4,i5,i6) + + coe=coe*sigdis0(k) + db(i,mi)=db(i,mi)+coe + + enddo + enddo + enddo + enddo + enddo + enddo + + enddo + + elseif(nd1==2) then + do i=1,nmono + noo=mono_order(i) + + do i4=0,in4(i) + + do i3=0,in3(i) + do i2=0,in2(i) + do i1=0,in1(i) + ouch=i4+i3+i2+i1 + + if(mod(ouch,2)==1)cycle + coe=pascal(in1(i),i1)*pascal(in2(i),i2)*pascal(in3(i),i3)*pascal(in4(i),i4) + mi=hash(in1(i)-i1,in2(i)-i2,in3(i)-i3,in4(i)-i4,0,0) + + k=hash(i1,i2,i3,i4,0,0) + coe=coe*sigdis0(k) + db(i,mi)=db(i,mi)+coe + enddo + enddo + enddo + enddo + + + enddo + + elseif(nd1==1) then + do i=1,nmono + noo=mono_order(i) + + do i2=0,in2(i) + + do i1=0,in1(i) + ouch=i2+i1 + + ! if(ouch>noo)cycle + ! if(mod(ouch,2)==1)cycle + + coe=pascal(in1(i),i1)*pascal(in2(i),i2) + + mi=hash(in1(i)-i1,in2(i)-i2,0,0,0,0) + + k=hash(i1,i2,0,0,0,0) + coe=coe*sigdis0(k) + db(i,mi)=db(i,mi)+coe + enddo + enddo + + + enddo + +endif ! nd1==3 + +m=minput +do i=1,nd2 +m%v(i)=m%v(i)-(m%v(i).sub.0) +enddo + do i=1,nmono + + t= m%v(1)**in1(i) + t=t*m%v(2)**in2(i) + if(nd1>1) then + t=t*m%v(3)**in3(i) + t=t*m%v(4)**in4(i) + endif + if(nd1>2) then + + t=t*m%v(5)**in5(i) + t=t*m%v(6)**in6(i) + endif + j=1 + + do while(.true.) + + call c_cycle(t,j,v ,je); if(j==0) exit; + k=hash(je(1),je(2),je(3),je(4),je(5),je(6)) + minput%m(i,k)=v + enddo + enddo + + + + +!minput%m=matmul(minput%m,minput%db) +minput%m=matmul(db,minput%m) + + + + if(nd11<0) then + db=minput%m + + do i=1,100 + + db=matmul(db,db) + enddo + + + do i=1,nmono + write(6,*) i + if(nd1==1) then + write(6,"(6(1x,i2))") in1(i),in2(i) +elseif(nd1==2) then +write(6,"(6(1x,i2))") in1(i),in2(i),in3(i),in4(i) +else +write(6,"(6(1x,i2))") in1(i),in2(i),in3(i),in4(i),in5(i),in6(i) +endif +write(6,*) db(i,1) + enddo +endif +deallocate(db) +nz=nmono-1 + +allocate(mm(nz,nz),vm(nz)) + +mm=0 + + +do i=1,nz + vm(i)=minput%m(i+1,1) + mm(i,i)=1 +enddo + +do i=1,nz +do j=1,nz + mm(i,j)=mm(i,j)-minput%m(1+i,1+j) +enddo +enddo + +do i=1,100,-1 +minput%m=matmul(minput%m,minput%m) + call norm_moment_matrix(minput%m,r2) +enddo +deallocate(minput%m) +call matinvn(mm,mm,nz,nz,i) + +write(6,*) " success = ",i + +vm=matmul(mm,vm) +vsol(2:nmono)=vm + + +write(6,*) "Quadratic moments to order ", no +do i=1,2*nd1 +je=0 +je(i)=je(i)+1 +do j=1,2*nd1 +je(j)=je(j)+1 +sig(i,j)=vm(hash(je(1),je(2),je(3),je(4),je(5),je(6))-1) +je(j)=je(j)-1 + +if(i<=j) write(6,*) i,j,sig(i,j) +enddo +enddo +!return + + deallocate(mm,vm) +call kill(t) + call kill(m) + +end subroutine create_moment_map + + +subroutine create_yu_map(minput,nd11) ! fix0 is the initial condition for the maps +implicit none + + +complex(dp)v +integer i1,i2,i3,i4,i5,i6,no1,je(6),noo,k,mi,ouch,nz +real(dp) coe,ki(6),eps +real(dpn) r2 +!real(dpn), allocatable :: mm(:,:),vm(:) +type(c_damap) m,minput +type(c_taylor) t +integer i,inf,j,nd1,nd11 + + nd1=iabs(nd11) + + call alloc(m); + + +m=minput + + +sigdis0=0 + + +m=0 + + +call alloc(t) + +nmono=size(in1) + + + + + allocate(minput%cm(nmono,nmono)) + + minput%cm=0 + + +m=minput +do i=1,nd2 +m%v(i)=m%v(i)-(m%v(i).sub.0) +enddo + do i=1,nmono + + t= m%v(1)**in1(i) + t=t*m%v(2)**in2(i) + if(nd1>1) then + t=t*m%v(3)**in3(i) + t=t*m%v(4)**in4(i) + endif + if(nd1>2) then + + t=t*m%v(5)**in5(i) + t=t*m%v(6)**in6(i) + endif + j=1 + + do while(.true.) + + call c_cycle(t,j,v ,je); if(j==0) exit; + k=hash(je(1),je(2),je(3),je(4),je(5),je(6)) +! minput%cm(i,k)=v + minput%cm(k,i)=v + enddo + enddo + + + + +call kill(t) + call kill(m) + +end subroutine create_yu_map + + + +subroutine norm_moment_matrix(m,norm) +implicit none +real(dpn) norm,m(:,:) +integer i,j + +norm=0 + +do i=1,size(m,1) +do j=2,size(m,1) + +norm=norm+abs(m(i,j) ) + +enddo +enddo + +end subroutine norm_moment_matrix +!$$$$$$$$$$$$$$ + subroutine matinvn(a,ai,n,nmx,ier) + + implicit none + + integer i,ier,j,n,nmx + integer,allocatable ::indx(:) + real(dpn) d + real(dpn),dimension(nmx,nmx)::a,ai + real(dpn),allocatable :: aw(:,:) + ! + ! if((.not.C_%STABLE_DA)) then + ! if(c_%watch_user) then + ! write(6,*) "big problem in dabnew ", sqrt(crash) + ! endif + ! return + ! endif + allocate(aw(n,n),indx(n)) + aw(1:n,1:n) = a(1:n,1:n) + + ! call ludcmp_nr0n(aw,n,nmaxn,indx,d,ier) + call ludcmp_nr0n(aw,n,n,indx,d,ier) + if (ier .eq. 132) return + + ai(1:n,1:n) = 0.0_dp + ! forall (i = 1:n) ai(i,i) = one + do i=1,n + ai(i,i) = 1.0_dp + enddo + + do j=1,n + call lubksb_nr0n(aw,n,n,indx,ai(1,j),nmx) +! call lubksb_nr0n(aw,n,nmaxn,indx,ai(1,j),nmx) + enddo + deallocate(aw,indx) + end subroutine matinvn + + + ! + subroutine ludcmp_nr0n(a,n,np,indx,d,ier) + implicit none + ! ************************************ + ! + ! THIS SUBROUTINE DECOMPOSES A MATRIX INTO LU FORMAT + ! INPUT A: NXN MATRIX - WILL BE OVERWRITTEN BY THE LU DECOMP. + ! NP: PHYSICAL DIMENSION OF A + ! INDX: ROW PERMUTATION VECTOR + ! D: EVEN OR ODD ROW INTERCHANGES + ! + ! REFERENCE: NUMERICAL RECIPIES BY PRESS ET AL (CAMBRIDGE) PG. 35 + ! + !----------------------------------------------------------------------------- + ! + integer i,ier,imax,j,k,n,np + integer,dimension(np)::indx + real(dpn) aamax,d,dum,sum + real(dpn),dimension(np,np)::a + real(dpn),allocatable ::vv(:) + ! + ! if((.not.C_%STABLE_DA)) then + ! if(c_%watch_user) then + ! write(6,*) "big problem in dabnew ", sqrt(crash) + ! endif + ! return + ! endif + allocate(vv(n)) + ier=0 + d=1.0_dp + do i=1,n + aamax=0.0_dp + do j=1,n + if(abs(a(i,j)).gt.aamax) aamax=abs(a(i,j)) + enddo + if(aamax.eq.0.0_dp) then + ier=132 + return + endif + vv(i)=1.0_dp/aamax + enddo + do j=1,n + if(j.gt.1) then + do i=1,j-1 + sum=a(i,j) + if(i.gt.1) then + do k=1,i-1 + sum=sum-a(i,k)*a(k,j) + enddo + a(i,j)=sum + endif + enddo + endif + aamax=0.0_dp + do i=j,n + sum=a(i,j) + if (j.gt.1) then + do k=1,j-1 + sum=sum-a(i,k)*a(k,j) + enddo + a(i,j)=sum + endif + dum=vv(i)*abs(sum) + if(dum.ge.aamax) then + imax=i + aamax=dum + endif + enddo + if (j.ne.imax) then + do k=1,n + dum=a(imax,k) + a(imax,k)=a(j,k) + a(j,k)=dum + enddo + d=-d + vv(imax)=vv(j) + endif + indx(j)=imax + if(j.ne.n) then + if(a(j,j).eq.0.0_dp) a(j,j)=tiny + dum=1.0_dp/a(j,j) + do i=j+1,n + a(i,j)=a(i,j)*dum + enddo + endif + enddo + if(a(n,n).eq.0.0_dp) a(n,n)=tiny + deallocate(vv) + return + end subroutine ludcmp_nr0n + ! + subroutine lubksb_nr0n(a,n,np,indx,b,nmx) + implicit none + ! ************************************ + ! + ! THIS SUBROUTINE SOLVES SET OF LINEAR EQUATIONS AX=B, + ! INPUT A: NXN MATRIX IN lu FORM GIVEN BY ludcmp_nr + ! NP: PHYSICAL DIMENSION OF A + ! INDX: ROW PERMUTATION VECTOR + ! D: EVEN OR ODD ROW INTERCHANGES + ! B: RHS OF LINEAR EQUATION - WILL BE OVERWRITTEN BY X + ! + ! REFERENCE: NUMERICAL RECIPIES BY PRESS ET AL (CAMBRIDGE) PG. 36 + ! + !----------------------------------------------------------------------------- + ! + integer i,ii,j,ll,n,nmx,np + integer,dimension(np)::indx + real(dpn) sum + real(dpn),dimension(np,np)::a + real(dpn),dimension(nmx)::b + ! + ! if((.not.C_%STABLE_DA)) then + ! if(c_%watch_user) then + ! write(6,*) "big problem in dabnew ", sqrt(crash) + ! endif + ! return + ! endif + ii = 0 + do i=1,n + ll = indx(i) + sum = b(ll) + b(ll) = b(i) + if(ii.ne.0) then + do j=ii,i-1 + sum = sum-a(i,j)*b(j) + enddo + else if (sum.ne.0.0_dp) then + ii = i + endif + b(i)=sum + enddo + do i=n,1,-1 + sum=b(i) + if(i.lt.n) then + do j=i+1,n + sum = sum-a(i,j)*b(j) + enddo + endif + + b(i)=sum/a(i,i) + + enddo + return + end subroutine lubksb_nr0n +!$$$$$$$$$$$$$$$$$$$$ +subroutine copy_tree_into_tree_zhe(tree_zhe,t) +implicit none +type(tree_element), intent(in) :: t +type(tree_element_zhe), intent(out) :: tree_zhe + + tree_zhe%cc=t%cc + tree_zhe%fixr=t%fixr + tree_zhe%fix=t%fix + tree_zhe%fix0=t%fix0 + tree_zhe%jl=t%jl + tree_zhe%jv=t%jv + tree_zhe%n=t%n + tree_zhe%np=t%np + tree_zhe%no=t%no + tree_zhe%e_ij=t%e_ij + tree_zhe%rad=t%rad + tree_zhe%ds=t%ds + tree_zhe%beta0=t%beta0 + tree_zhe%eps=t%eps + tree_zhe%symptrack=t%symptrack + tree_zhe%usenonsymp=t%usenonsymp + tree_zhe%factored=t%factored + +end subroutine copy_tree_into_tree_zhe + +subroutine print_tree_element(t,mf) +implicit none +type(tree_element) t + +integer i,mf +! write(mf,'(a204)') t%file +write(mf,'(3(1X,i8))') t%N,t%NP,t%no +do i=1,t%n + write(mf,'(1X,G20.13,1x,i8,1x,i8)') t%cc(i),t%jl(i),t%jv(i) +enddo +write(mf,'(2(1X,L1))') t%symptrack,t%usenonsymp,t%factored +write(mf,'(18(1X,G20.13))') t%fix0,t%fix,t%fixr +do i=1,6 + write(mf,'(6(1X,G20.13))') t%e_ij(i,1:6) +enddo +do i=1,6 + write(mf,'(6(1X,G20.13))') t%rad(i,1:6) +enddo + write(mf,'(3(1X,G20.13))') t%ds,t%beta0,t%eps + +end subroutine print_tree_element + +subroutine print_tree_elements(t,mf) +implicit none +type(tree_element) t(:) + +integer i,mf + + do i=1,size(t) + call print_tree_element(t(i),mf) + enddo + +end subroutine print_tree_elements + +subroutine read_tree_element(t,mf) +implicit none +type(tree_element) t + +integer i,mf + + ! read(mf,'(a204)') t%file +!read(mf,*) t%N,t%NP,t%no +do i=1,t%n + read(mf,*) t%cc(i),t%jl(i),t%jv(i) +enddo +read(mf,*) t%symptrack,t%usenonsymp,t%factored +read(mf,'(18(1X,G20.13))') t%fix0,t%fix,t%fixr +do i=1,6 + read(mf,*) t%e_ij(i,1:6) +enddo +do i=1,6 + read(mf,*) t%rad(i,1:6) +enddo + read(mf,*) t%ds,t%beta0,t%eps + +end subroutine read_tree_element + +subroutine read_tree_elements(t,mf) +implicit none +type(tree_element) t(:) + +integer i,mf + + do i=1,size(t) + call read_tree_element(t(i),mf) + enddo + +end subroutine read_tree_elements + +subroutine symplectify_for_zhe(m,L_r , N_r , L_s, N_s ) +implicit none +TYPE(c_damap),intent(inout):: m ,L_r , N_r , N_s , L_s +type(c_vector_field) f,fs,ft +complex(dp) v +type(c_taylor) t,dt +real(dp),allocatable:: mat(:,:) +integer i,j,k,n(11),nv,nd2,al,ii,a,mul +integer, allocatable :: je(:) +real(dp) dm,norm,normb,norma,h(4) +TYPE(c_damap) mt,ids,m4,ml +real(dp),allocatable:: S(:,:),id(:,:) + +! m = L_r o N_r o L_s o N_s +! d= = L_r o N_r +! ms= L_s o N_s + +allocate(S(m%n,m%n),id(m%n,m%n)) + +call c_get_indices(n,0) +nv=n(4) +nd2=n(3) + +S=0 +id=0 +do i=1,nd2/2 + S(2*I-1,2*I)=1 ; S(2*I,2*I-1)=-1; + Id(2*I-1,2*I-1)=1 ; id(2*I,2*I)=1; +enddo + + + + + call alloc(f);call alloc(fs);call alloc(ft); +call alloc(t,dt);call alloc(mt,ids,m4,ml); + +allocate(mat(m%n,m%n)) + +mat=0 + + +! constructing Furman's contracting matrix from my review sec.3.8.2 + +if(nv-nd2==0) then +mat=m.sub.1 +else +write(6,*) " this map should not have parameters or modulated magnets " +stop 444 +endif + + + +if(hypercube_integration) then + if(nv-nd2==0) then + mat=m.sub.1 + else + write(6,*) " this map should not have parameters or modulated magnets " + stop 444 + endif + + call furman_symp(mat) + L_s=mat +else + if(nv-nd2==0) then + mt=m.sub.1 +ids=1 +ids%v(5)=0.0_dp +ids%v(6)=0.0_dp + m4=1 + do i=1,4 + m4%v(i)=mt%v(i)*ids + enddo + mat=m4 + call furman_symp(mat) + m4=mat + mt=mt*m4**(-1) + if(ndpt_bmad==0) then + h(1)= mt%v(2).sub.'000010' + h(2)= -mt%v(1).sub.'000010' + h(3)= mt%v(4).sub.'000010' + h(4)= -mt%v(3).sub.'000010' + ml=1 + ml%v(1)=ml%v(1)-(h(2).cmono.5) + ml%v(2)=ml%v(2)+(h(1).cmono.5) + ml%v(3)=ml%v(3)-(h(4).cmono.5) + ml%v(4)=ml%v(4)+(h(3).cmono.5) + do i=1,4 + ml%v(6)=ml%v(6)+(h(i).cmono.i) + enddo + else + h(1)= mt%v(2).sub.'000001' + h(2)=-mt%v(1).sub.'000001' + h(3)= mt%v(4).sub.'000001' + h(4)=-mt%v(3).sub.'000001' + ml=1 + ml%v(1)=ml%v(1)-(h(2).cmono.6) + ml%v(2)=ml%v(2)+(h(1).cmono.6) + ml%v(3)=ml%v(3)-(h(4).cmono.6) + ml%v(4)=ml%v(4)+(h(3).cmono.6) + do i=1,4 + ml%v(5)=ml%v(5)-(h(i).cmono.i) + enddo + endif + + mt=mt*ml**(-1) + mat=mt + call furman_symp(mat) + mt=mat +L_s=mt*ml*m4 + + + else + write(6,*) " this map should not have parameters or modulated magnets " + stop 445 + endif + +endif + + +mt=m*L_s**(-1) +L_r=mt.sub.1 + +mt=L_r**(-1)*mt + +f=log(mt) + +fs=0 + +if(hypercube_integration) then +! Integrating a symplectic operator using the hypercube's diagonal + +allocate(je(nv)) +je=0 +do i=1,f%n + + j=1 + + do while(.true.) + + call c_cycle(f%v(i),j,v ,je); if(j==0) exit; + dm=1 + do ii=1,nd2 + dm=dm+je(ii) + enddo + t=v.cmono.je + do a=1,nd2 + dt=t.d.a + do al=1,nd2 + do k=1,nd2 + fs%v(al)=fs%v(al)+s(a,al)*s(k,i)*(id(k,a)*t+(1.0_dp.cmono.k)*dt)/dm + enddo ! k + enddo ! al + enddo ! a + enddo + +enddo + +else + + + +allocate(je(nv)) + +do i=1,nd2 +ft%v(i)=f%v(i) +enddo +f%v(5)=0.0_dp +f%v(6)=0.0_dp + + +!!! over the transverse +je=0 +do i=1,f%n + + j=1 + + do while(.true.) + + call c_cycle(f%v(i),j,v ,je); if(j==0) exit; + dm=1 + do ii=1,nd2-2 + dm=dm+je(ii) + enddo + t=v.cmono.je + do a=1,nd2 + dt=t.d.a + do al=1,nd2 + do k=1,nd2 + fs%v(al)=fs%v(al)+s(a,al)*s(k,i)*(id(k,a)*t+(1.0_dp.cmono.k)*dt)/dm + enddo ! k + enddo ! al + enddo ! a + enddo + +enddo + +do i=1,4 + f%v(i)=0.0_dp +enddo + f%v(5)=ft%v(5) + f%v(6)=ft%v(6) +ids=0 +ids%v(5)=1.0_dp.cmono.5 +ids%v(6)=1.0_dp.cmono.6 + + f%v(5)= f%v(5)*ids + f%v(6)= f%v(6)*ids + +!!! over the logitudinal +je=0 +do i=1,f%n + + j=1 + + do while(.true.) + + call c_cycle(f%v(i),j,v ,je); if(j==0) exit; + dm=1 + do ii=5,6 + dm=dm+je(ii) + enddo + t=v.cmono.je + do a=1,nd2 + dt=t.d.a + do al=1,nd2 + do k=1,nd2 + fs%v(al)=fs%v(al)+s(a,al)*s(k,i)*(id(k,a)*t+(1.0_dp.cmono.k)*dt)/dm + enddo ! k + enddo ! al + enddo ! a + enddo + +enddo + + +endif + + +N_s=exp(fs) +N_r= mt*N_s**(-1) + +N_s= L_s**(-1)*N_s*L_s + +!norma=1.d0/mul +!fs=norma*log(n_s) +!N_s=exp(fs) + + +deallocate(je);deallocate(s,id); + call kill(f);call kill(fs);call kill(ft); +call kill(t,dt);call kill(mt,ids,m4,ml); +deallocate(mat) +end subroutine symplectify_for_zhe + + + SUBROUTINE furman_symp(r) + implicit none + real(dp) r(:,:) + real(dp), allocatable::rt(:,:) + real(dp) eps,a,ab + integer nmax,i,j,k,n +! Furmanizing the rotation + n=size(r,1) + allocate(rt(n,n)) + + rt=0 + eps=1.d-8 + nmax=1000 + + ab=1.d8 + do i=1,nmax + ! rt=matmul(r,transpose(r)) + ! r= matmul((id-0.5e0_dp*rt),r) + + call furman_step(r,r,rt) + + a=-n + do j=1,n + do k=1,n + a=a+abs(rt(j,k)) + enddo + enddo + a=abs(a) + if(a=ab) exit + ab=a + endif + enddo + if(i>nrmax-10) then + write(6,*) i, a, "did not converge in orthonormalisep 1" + read(5,*) i + + ! stop + endif + deallocate(rt) + end SUBROUTINE furman_symp + + SUBROUTINE furman_step(r,s,rt) + implicit none + real(dp) r(:,:),s(:,:),rt(:,:) + real(dp), allocatable :: id(:,:),ik(:,:), j(:,:),ji(:,:) + integer i,n + + n=size(r,1) + +allocate(id(n,n),ik(n,n), j(n,n),ji(n,n)) + id=0 + ik=0 + j=0 + ji=0 + do i=1,n/2 + j(2*i-1,2*i)=1 + j(2*i,2*i-1)=-1 + enddo + ji=-j + do i=1,n + ik(i,i)=1.5e0_dp + enddo + + + id=matmul(ik-0.5_dp* matmul( matmul(r,j),matmul(transpose(r),ji) ) , r) + + + + + s=id + + rt=matmul(r,matmul(j,transpose(r)) ) +deallocate(id,ik, j,ji) +end SUBROUTINE furman_step + + subroutine checksympn(s1,norm,orthogonal) !,normt) + implicit none + TYPE (c_damap) s1 + real(dp) norm1,mat(8,8),xj(8,8),normt1 + real(dp), optional :: norm + integer i,j + logical(lp), optional :: orthogonal + ! real(dp), optional :: normt + logical(lp) nn + ! checks symplectic conditions on linear map + nn=.not.present(norm) + mat=0.d0 + mat=s1 + + xj=0.d0 + if(present(orthogonal)) then + if(orthogonal) then + do i=1,nd + xj(2*i-1,2*i-1)=1.0_dp + xj(2*i,2*i)=1.0_dp + enddo + else + do i=1,nd + xj(2*i-1,2*i)=1.0_dp + xj(2*i,2*i-1)=-1.0_dp + enddo + endif + else + do i=1,nd + xj(2*i-1,2*i)=1.0_dp + xj(2*i,2*i-1)=-1.0_dp + enddo + endif + xj= MATMUL( transpose(mat),MATMUL(xj,mat)) + + norm1=0.0_dp + normt1=0.0_dp + do i=1,nd2 + if(lielib_print(9)==1.or.nn) write(6,'(6(1x,E15.8))') xj(i,1:nd2) + do j=1,nd2 + norm1=norm1+abs(xj(i,j)) + if(i<5.and.j<5) normt1=normt1+abs(xj(i,j)) + enddo + enddo + norm1=abs(norm1-nd2) + if(lielib_print(9)==1.or.nn) write(6,'(a29,(1x,E15.8))')"deviation from symplecticity ", norm1 + if(present(norm)) norm=abs(norm1) + + end subroutine checksympn + + +! cholesky_d.f -*-f90-*- +! Using Cholesky decomposition, cholesky_d.f solve a linear equation Ax=b, +! where A is a n by n positive definite real symmetric matrix, x and b are +! real*8 vectors length n. +! +! Time-stamp: <2015-06-25 18:05:47 takeshi> +! Author: Takeshi NISHIMATSU +! Licence: GPLv3 +! +! [1] A = G tG, where G is a lower triangular matrix and tG is transpose of G. +! [2] Solve Gy=b with forward elimination +! [3] Solve tGx=y with backward elimination +! +! Reference: Taketomo MITSUI: Solvers for linear equations [in Japanese] +! http://www2.math.human.nagoya-u.ac.jp/~mitsui/syllabi/sis/info_math4_chap2.pdf +! +! Comment: This Cholesky decomposition is used in src/elastic.F and +! src/optimize-inho-strain.F of feram http://loto.sourceforge.net/feram/ . +!! +! modified by Etienne Forest and David Sagan +subroutine cholesky_dt(A, G) + implicit none + real(dp), intent(in) :: A(:,:) + real(dp), intent(out) :: G(:,:) + real(dp) gg + integer :: i,j + + + G(:,:)=0 + do j = 1, size(A,1) + gg = A(j,j) - dot_product(G(j,1:j-1),G(j,1:j-1)) + if (gg <= 0) then + G(j,j) = 0 + else + G(j,j) = sqrt(gg) + do i = j+1, size(A,1) + G(i,j) = ( A(i,j) - dot_product(G(i,1:j-1),G(j,1:j-1)) ) / G(j,j) + end do + endif + end do + +end subroutine cholesky_dt + + + ! Complex Universal Taylor Routines (Sagan's Stuff made complex) + + SUBROUTINE c_kill_uni(S2) + implicit none + type (c_UNIVERSAL_TAYLOR),INTENT(INOUT)::S2 + + DEALLOCATE(S2%N,S2%Nd2,S2%NV,S2%C,S2%J) + NULLIFY(S2%N,S2%Nd2,S2%NV,S2%C,S2%J) + + END SUBROUTINE c_kill_uni + + SUBROUTINE c_kill_Unis(S2) + implicit none + type (C_UNIVERSAL_TAYLOR),INTENT(INOUT)::S2(:) + integer k,i + k=size(s2) + do i=1,k + call c_kill_uni(S2(i)) + enddo + + END SUBROUTINE c_kill_Unis + + + + SUBROUTINE c_null_uni(S2,S1) + implicit none + type (c_UNIVERSAL_TAYLOR),INTENT(INOUT)::S2 + integer, intent(in):: s1 + IF(S1==0) THEN + NULLIFY(S2%N,S2%NV,S2%C,S2%J) + ELSEIF(S1==-1) THEN + DEALLOCATE(S2%N,S2%NV,S2%C,S2%J,S2%nd2) + NULLIFY(S2%N,S2%NV,S2%C,S2%J,S2%nd2) + ENDIF + END SUBROUTINE c_null_uni + + + SUBROUTINE c_ALLOC_U(S2,N,NV,nd2,order) + implicit none + type (C_UNIVERSAL_TAYLOR),INTENT(INOUT)::S2 + integer, intent(in):: N,NV,nd2 + logical, optional :: order + + ALLOCATE(S2%N,S2%NV,S2%nd2) + if(N==0) then + allocate(S2%C(1),S2%J(1,NV));S2%C(1)=0.0_dp;S2%J(:,:)=0; + else + allocate(S2%C(N),S2%J(N,NV)) + endif + S2%N=N + S2%NV=NV + S2%nd2=nd2 + + + + END SUBROUTINE c_ALLOC_U + + SUBROUTINE c_ALLOC_Us(S2,N,NV,nd2,order) + implicit none + type (C_UNIVERSAL_TAYLOR),INTENT(INOUT)::S2(:) + integer, intent(in):: N,NV,nd2 + integer k,i + logical, optional :: order + k=size(s2) + do i=1,k + ALLOCATE(S2(i)%N,S2(i)%NV,S2(i)%nd2) + if(N==0) then + allocate(S2(i)%C(1),S2(i)%J(1,NV));S2(i)%C(1)=0.0_dp;S2(i)%J(:,:)=0; + else + allocate(S2(i)%C(N),S2(i)%J(N,NV)) + endif + S2(i)%N=N + S2(i)%NV=NV + S2(i)%nd2=nd2 + + enddo + + END SUBROUTINE c_ALLOC_Us + + + function c_get_coeff(S1,Jj) !new sagan + implicit none + type (C_UNIVERSAL_TAYLOR),INTENT(IN)::S1 + integer,INTENT(IN)::Jj(:) + integer, allocatable ::J(:) + + complex (dp)c_get_coeff + INTEGER i,n,done + + allocate(J(S1%NV)) + J=0 + j(1:size(JJ))=jj + + c_get_coeff=0 + do i=1,s1%n + done=0 + DO N=1,S1%NV + done=iabs(S1%j(i,n)-J(n))+done + ENDDO + if(done==0) then + c_get_coeff=s1%c(i) + exit + endif + enddo + deallocate(j) + + END function c_get_coeff + + + + + SUBROUTINE c_fill_uni_r(S2,S1) !new sagan + implicit none + type (C_UNIVERSAL_TAYLOR),INTENT(INOUT)::S2 + complex (dp), intent(in):: s1 + INTEGER n,J(LNV) + + + IF(ASSOCIATED(S2%N)) S2=-1 + S2=0 + CALL c_ALLOC_U(S2,1,nv,nd2) + J=0 + DO N=1,S2%NV + S2%J(1,N)=J(N) + ENDDO + S2%C(1)=S1 + + END SUBROUTINE c_fill_uni_r + + SUBROUTINE c_FILL_UNI(S2,S1) + implicit none + type (c_UNIVERSAL_TAYLOR),INTENT(INOUT)::S2 + type (c_TAYLOR), intent(in):: s1 + INTEGER ipresent,k,n,I + complex(dp) value + INTEGER, allocatable :: j(:) + call c_check_snake + + ! if(old) then + ! if(s1%i==0) call crap1("FILL_N 1") + ! else + ! IF (.NOT. ASSOCIATED(s1%j%r)) call crap1("FILL_N 2") + ! endif + + + IF(ASSOCIATED(S2%N)) S2=-1 + S2=0 + ipresent=1 + call c_taylor_cycle(S1,n) + CALL c_ALLOC_U(S2,N,c_%nv,c_%nd2) + allocate(j(c_%nv)) + + do i=1,N + call c_taylor_cycle(S1,ii=i,value=value,j=j) + S2%C(I)=value + DO k=1,S2%NV + S2%J(i,k)=J(k) + ENDDO + ENDDO + + deallocate(j) + + END SUBROUTINE c_FILL_UNI + + SUBROUTINE c_FILL_UNI_complextaylor(s2,S1) + implicit none + type (c_UNIVERSAL_TAYLOR),INTENT(INOUT)::S2 + type (complextaylor), intent(in):: s1 + type (taylor) t,t_tot + INTEGER k,n,I + complex(dp) value + real(dp) v + INTEGER, allocatable :: j(:) + +call alloc(t,t_tot) + allocate(j(c_%nv)) +t=s1%r + call taylor_cycle(t,size=n) + + do i=1,n + call taylor_cycle(t,ii=i,value=v,j=j) + t_tot= t_tot + (abs(v).mono.j) + + enddo +t=s1%i + call taylor_cycle(t,size=n) + + do i=1,n + call taylor_cycle(t,ii=i,value=v,j=j) + t_tot= t_tot + (abs(v).mono.j) + + enddo + + IF(ASSOCIATED(S2%N)) S2=-1 + S2=0 + call taylor_cycle(t_tot,n) + CALL c_ALLOC_U(S2,N,c_%nv,c_%nd2) + + S2%C=0 + + do i=1,N + call taylor_cycle(t_tot,ii=i,value=v,j=j) + value=s1.sub.j + S2%C(I)=value + DO k=1,S2%NV + S2%J(i,k)=J(k) + ENDDO + + ENDDO + + call c_uni_reorder(s2) + +call kill(t,t_tot) + + deallocate(j) + + END SUBROUTINE c_FILL_UNI_complextaylor + + FUNCTION c_concat_c_uni_ray( S1, S2 ) + implicit none + complex(dp) c_concat_c_uni_ray,c + TYPE (c_UNIVERSAL_TAYLOR), INTENT (IN) :: S1 + TYPE (c_ray), INTENT (IN) :: S2 + integer i,j,k + + + c_concat_c_uni_ray=0.0_dp + + do i=1,s1%n + c=1 + k=0 + do j=1,s1%nv + k=k+s1%J(i,j) + c=c*s2%x(j)**s1%J(i,j) + enddo + if(k<=no_uni) then + c_concat_c_uni_ray=c_concat_c_uni_ray+s1%c(i)*c + endif + enddo + + ! TYPE c_UNIVERSAL_TAYLOR + ! INTEGER, POINTER:: N,NV,nd2 ! Number of coeeficients and number of variables + ! complex(DP), POINTER,dimension(:)::C ! Coefficients C(N) + ! INTEGER, POINTER,dimension(:,:)::J ! Exponents of each coefficients J(N,NV) + ! END TYPE c_UNIVERSAL_TAYLOR + + END FUNCTION c_concat_c_uni_ray + + + + FUNCTION c_concat_c_uni_rays( S1, S2 ) + implicit none + TYPE (c_ray) c_concat_c_uni_rays + TYPE (c_UNIVERSAL_TAYLOR), INTENT (IN) :: S1(:) + TYPE (c_ray), INTENT (IN) :: S2 + integer i,j + + + c_concat_c_uni_rays%x=0.0_dp + + do i=1,size(s1) + c_concat_c_uni_rays%x(i)= S1(i).o.s2 + enddo + + + END FUNCTION c_concat_c_uni_rays + + SUBROUTINE c_equal_UNI(S1,S2) + implicit none + type (c_UNIVERSAL_TAYLOR),INTENT(IN)::S2 + type (c_UNIVERSAL_TAYLOR), intent(inOUT):: s1 + + IF(.not.ASSOCIATED(S1%N)) THEN + call alloc(S1,s2%n,s2%NV,s2%nd2) + else + call kill(S1) + call alloc(S1,s2%n,s2%NV,s2%nd2) + endif + S1%n=S2%n + S1%nv=S2%nv + S1%nd2=S2%nd2 + S1%c=S2%c + S1%j=S2%j + + end SUBROUTINE c_equal_UNI + + + SUBROUTINE c_REFILL_UNI(S1,S2) + implicit none + type (c_UNIVERSAL_TAYLOR),INTENT(IN)::S2 + type (c_TAYLOR), intent(inOUT):: s1 + INTEGER I,K,J(LNV) + logical(lp) DOIT + + ! if(old) then + !if(s1%i==0) call crap1("REFILL_N 1") + ! else + ! IF (.NOT. ASSOCIATED(s1%j%r)) call crap1("REFILL_N 2") + ! endif + + + S1=0.0_dp + + IF(.not.ASSOCIATED(S2%N)) THEN + + write(6,*) " ERROR IN REFILL_N: UNIVERSAL_TAYLOR DOES NOT EXIST" + ! call !write_e(123) + ENDIF + + DO I=1,S2%N + J=0 + DOIT=.TRUE. + IF(S2%NV>NV) THEN + K=NV + DO WHILE(DOIT.AND.K<=S2%NV) + IF(S2%J(I,K)/=0) DOIT=.FALSE. + K=K+1 + ENDDO + ENDIF + + IF(DOIT) THEN + !DO K=1,NV + ! J(K)=S2%J(I,K) + !ENDDO + + s1=s1+(S2%C(I).cmono.S2%J(I,1:S2%nv)) ! bug 2023.10.16 + ! CALL c_POK(S1,S2%J(I,1:nv),S2%C(I)) + !CALL c_POK(S1,J,S2%C(I)) + ENDIF + ENDDO + + END SUBROUTINE c_REFILL_UNI + + + !_________________________________________________________________________________ + + subroutine c_printunitaylors(ut,iunit,print_abs,prec) + implicit none + type(c_universal_taylor) :: ut(:) + integer, optional :: iunit + integer :: i,k + logical, optional :: print_abs + real(dp), optional ::prec + k=size(ut) + + do i=1,k + call c_printunitaylor_old(ut(i),iunit,print_abs,prec, ind=i) + enddo + end subroutine c_printunitaylors + + + subroutine c_printunitaylor_old(ut,iunit,print_abs,prec,ind) + implicit none + type(c_universal_taylor) :: ut + integer, optional :: iunit, ind + integer :: i,ii,inde,no1,nomax + logical, optional :: print_abs + logical abst + integer iunit0 + real(dp) xr,prec0 + real(dp), optional ::prec + complex(dp) v + iunit0=6 + abst=.false. + prec0=0 +nomax=0 + do i=1,ut%n + no1=0 + do ii=1,ut%nv + no1=no1+iabs(ut%J(i,ii)) + enddo + if(no1>nomax) nomax=no1 + enddo + if(present(prec)) prec0=prec + if(present(print_abs)) abst=print_abs + if(present(iunit)) iunit0=iunit + if (.not. associated(ut%n)) then + write(iunit0,'(A)') ' C_UNIVERSAL_TAYLOR IS EMPTY (NOT ASSOCIATED)' + write(6,'(A)') ' C_UNIVERSAL_TAYLOR IS EMPTY (NOT ASSOCIATED)' + return + endif + + if (nice_taylor_print) then + inde = 0 + if (present(ind)) inde = ind + if (inde < 2) write (iunit, '(a)') 'Out Order Coef Exponents' + write (iunit, '(a)') '-----------------------------------------------------------------------------------' + else + write(iunit0,'(/1X,A,I5,A,I5,A/1X,A/)') 'UNIV_TAYLOR NO_max =',nomax,', NV =',ut%nv,', INA = unita',& + '*********************************************' + if(ut%n /= 0) then + write(iunit0,'(A)') ' I COEFFICIENT ORDER EXPONENTS' + else + write(iunit0,'(A)') ' ALL COMPONENTS 0.0_dp ' + endif + endif + + do i = 1,ut%n + v=0 + if(abs(real(ut%c(i)))>prec0) then + v=real(ut%c(i)) + endif + if(abs(aimag(ut%c(i)))>prec0) then + v=i_*aimag(ut%c(i))+v + endif + + if(abs(v)<=prec0) cycle + + if (nice_taylor_print) then + if (inde > 0) then + write(iunit, '(i3,a,i6,2(1x,g23.16),1x,100(2x,i2))') inde, ':', sum(ut%j(i,:)), v, (ut%j(i,ii),ii=1,ut%nv) + else + write(iunit, '(4x,i6,2(1x,g23.16),1x,100(2x,i2))') sum(ut%j(i,:)), v, (ut%j(i,ii),ii=1,ut%nv) + endif + elseif(abst) then + xr=sqrt(real(ut%c(i))**2+aimag(ut%c(i))**2) + write(iunit0,'(I6,2X,(G21.14,1x,G21.14,3x,G21.14),I5,4X,18(2I2,1X))') i,v,xr, & + sum(ut%j(i,:)),(ut%j(i,ii),ii=1,ut%nv) + else + write(iunit0,'(I6,2X,(G21.14,1x,G21.14),I5,4X,18(I2,2X))') i,v,sum(ut%j(i,:)),(ut%j(i,ii),ii=1,ut%nv) + endif + if( .not. print77) then + write(iunit0,*) ut%c(i) + endif + enddo + + if (.not. nice_taylor_print) write(iunit0,'(A)') ' ' + + end subroutine c_printunitaylor_old + +subroutine r_field_for_demin(f,ut) +implicit none +type(c_vector_field),intent(inout):: f +type(c_universal_taylor), target :: ut +complex(dp) ncai + +ncai=n_cai +n_cai=1 + +call d_field_for_demin(f,ut) + +n_cai=ncai + + +end subroutine r_field_for_demin + + +subroutine d_field_for_demin(f,ut,norm,reorder) +implicit none +type(c_vector_field),intent(inout):: f +type(c_normal_form), optional :: norm +logical, optional :: reorder +complex(dp) v +type(c_taylor) t +integer i,j,k,n(11),nv,nd2,Nu,i1 +integer, allocatable :: je(:),jf(:) +type(c_vector_field) fs +!type(universal_taylor), target :: Re, Im +type(c_universal_taylor), target :: ut +type(c_universal_taylor) ut0 +real(dp) prec +complex(dp) zilch +integer, allocatable :: ord(:) +integer maxord,max,kmax +!type(c_universal_taylor), allocatable :: u(:) +logical normal,keep,tune, re_order +complex(dp), allocatable :: ncai(:) +normal=.false. +tune=.false. +re_order=.true. +if(present(norm)) normal=.true. +if(present(reorder)) re_order=reorder + allocate(ncai(c_%nd2)) +ncai=n_cai + + +if(c_%ndpt/=0) then + ncai(c_%ndpt)=1 + ncai(c_%ndptb)=1 +endif + + +prec=1.d-7 +zilch=0.0_dp +call alloc(fs) +call alloc(t) + +allocate(ord(0:no+1)) + +ord=0 + + +!!! counting only +fs=f + +call c_get_indices(n,0) +nv=n(4) +nd2=n(3) + + +allocate(je(nv),jf(nv)) +je=0 +fs=f + + nu=0 + +maxord=0 + +do i=1,fs%n + + j=1 + + do while(.true.) +je=0 + call c_cycle(fs%v(i),j,v ,je); if(j==0) exit; +!write(6,*) i,je +!pause 123 + k=d_mod_demin(i) + jf=je + jf(k)=jf(k)+1 + + v=-(-1)**k*v/ncai(i)/jf(k) + if(normal) then + call check_re(norm,jf,keep,tune) + if(.not.keep) v=0 + endif + + + + if(abs(v)>0) nu=nu+1 + + + + do i1=i+1,fs%n !,-1 + k=d_mod_demin(i1) + jf(k)=jf(k)-1 + if(jf(k)>=0) CALL c_pok(fs%v(i1),jf,zilch) + jf(k)=jf(k)+1 + enddo + + enddo + + + enddo + + +call ALLOC(ut0,Nu,NV,nd2) + + +fs=f + + nu=0 + +je=0 +do i=1,fs%n + + j=1 + + do while(.true.) + + call c_cycle(fs%v(i),j,v ,je); if(j==0) exit; + + k=d_mod_demin(i) + jf=je + jf(k)=jf(k)+1 + + v=-(-1)**k*v/ncai(i)/jf(k) + + if(normal) then + call check_re(norm,jf,keep,tune) + if(tune) v=real(v) + if(.not.keep) v=0 + endif + +if(abs(v)>0) then + nu=nu+1 + ut0%c(nu)=v + + ut0%J(nu,1:nv)=jf + endif + + + do i1=i+1,fs%n !,-1 + k=d_mod_demin(i1) + jf(k)=jf(k)-1 + if(jf(k)>=0) CALL c_pok(fs%v(i1),jf,zilch) + jf(k)=jf(k)+1 + enddo + enddo + + enddo +! write(6,*) "nu ",nu +!pause 112 + +call ALLOC(ut,Nu,NV,nd2) + + + +ut=ut0 + +if(re_order) call c_uni_reorder(ut) + +!call kill(u) +call kill(fs) +call kill(t) +call kill(ut0) +deallocate(je,jf,ord,ncai); + + +end subroutine d_field_for_demin + + subroutine c_uni_reorder(ut) + implicit none + type(c_UNIVERSAL_TAYLOR) ut + type(c_universal_taylor), allocatable :: u(:) + integer, allocatable :: ord(:) + integer i,k,nu,max,kmax + + +allocate(ord(0:c_%no+1)) + +ord=0 + + + do i=1,ut%n + max=0 + do kmax=1,c_%nv + max=ut%J(i,kmax)+max + enddo + + ord(max)=ord(max)+1 + enddo + +!write(6,*) ord + + + + + allocate(u(0:c_%no+1)) +do i=0,c_%no+1 + k=ord(i) + if(k==0) k=1 + + call ALLOC(u(i),k,c_%NV,c_%nd2) +! write(6,*) i,u(i)%n + u(i)%n=0 +enddo + + !sum(ut%j(i,:)) + + !call print(ut0,6) + +!pause 111 +do nu=1,ut%n + i=sum(ut%j(nu,1:c_%nv)) + + u(i)%n=u(i)%n+1 + u(i)%j(u(i)%n,1:c_%nv)=ut%j(nu,1:c_%nv) + u(i)%c(u(i)%n)=ut%c(nu) +enddo + +ut%n=0 +ut%c=0 +ut%j=0 +do nu=0,c_%no+1 + do i=1,u(nu)%n + if(abs(u(nu)%c(i))/=0) then + ut%n=ut%n+1 + ut%j(ut%n,1:c_%nv)= u(nu)%j(i,1:c_%nv) + ut%c(ut%n)=u(nu)%c(i) + endif + enddo +enddo + + +call kill(u) + deallocate(ord,u) + + end subroutine c_uni_reorder + + + integer function d_mod_demin(i) + implicit none + integer i + + d_mod_demin=mod(i,2) + if(d_mod_demin==0) then + d_mod_demin=i-1 + else + d_mod_demin=i+1 + endif + + end function d_mod_demin + + + + subroutine check_re(norm,je,keep,tune) + implicit none + type(c_normal_form) norm + logical keep,tune + integer i,j,ir,it,ndt, je(:) + integer, allocatable :: me(:) + keep=.false. + tune=.false. + + ndt= ND2/2 + allocate(me(ndt) ) + + me=0 +ir=0 + do i=1,ndt + me(i)=je(2*i-1)-je(2*i) + ir=iabs(me(i))+ir + enddo + + + + if(ir==0) then + keep=.true. + tune=.true. + deallocate(me) + return +endif + +do j=1,norm%nres + +ir=0 + do i=1,ndt + ir=ir+iabs(me(i)-norm%m(i,j)) + enddo + + if(ir==0) then + keep=.true. + deallocate(me) + return + endif + +ir=0 + do i=1,ndt + ir=ir+iabs(me(i)+norm%m(i,j)) + enddo + + if(ir==0) then + keep=.true. + deallocate(me) + return + endif +enddo + + +deallocate(me) + end subroutine check_re + + ! End of Universal complex Taylor Routines + +subroutine symplectify_general(m1,L_r , N_r , L_s, N_s,Q_s ) +implicit none +TYPE(c_damap),intent(inout):: m1 ,L_r , N_r , N_s , L_s,Q_s +type(c_vector_field) f,fs,ft +complex(dp) v +type(c_taylor) t,dt +real(dp),allocatable:: mat(:,:) +integer i,j,k,n(11),nv,nd2,al,ii,a,mul +integer, allocatable :: je(:) +real(dp) dm,norm,normb,norma,h(4) +TYPE(c_damap) mt,ids,m4,ml,m +real(dp),allocatable:: S(:,:),id(:,:) + +! Q_s is a normalized quaternion +! m = L_r o N_r o L_s o N_s o Q_s +! d= = L_r o N_r +! ms= L_s o N_s o Q_s + +allocate(S(m1%n,m1%n),id(m1%n,m1%n)) + +call c_get_indices(n,0) +nv=n(4) +nd2=n(3) + +S=0 +id=0 +do i=1,nd2/2 + S(2*I-1,2*I)=1 ; S(2*I,2*I-1)=-1; + Id(2*I-1,2*I-1)=1 ; id(2*I,2*I)=1; +enddo + + +call alloc(m) +m=m1 +Q_s=1 +Q_s%q=m%q +m%q=1.0_dp + + call alloc(f);call alloc(fs);call alloc(ft); +call alloc(t,dt);call alloc(mt,ids,m4,ml); + +allocate(mat(m%n,m%n)) + + t=Q_s%q%x(0)**2+Q_s%q%x(1)**2+Q_s%q%x(2)**2+Q_s%q%x(3)**2 + dm=t + + if(dm/=0) then + t=1.0_dp/sqrt(t) + do i=0,3 + Q_s%q%x(i)=t*Q_s%q%x(i) + enddo + endif + + +mat=0 + + +! constructing Furman's contracting matrix from my review sec.3.8.2 + + mat=m.sub.1 + + + call furman_symp(mat) + + +allocate(je(nv)) + + L_s=m.sub.1 + L_s%q=1.0_dp + do i=1,nd2 + do j=1,nd2 + je=0 + je(j)=1 + L_s%v(i)=L_s%v(i)+(-(L_s%v(i).sub.je)+mat(i,j))*dz_c(j) + enddo + enddo + + +mt=m*L_s**(-1) + + +L_r=mt.sub.1 + + +mt=L_r**(-1)*mt + +f=log(mt) + +fs=0 + +! Integrating a symplectic operator using the hypercube's diagonal + +je=0 +do i=1,f%n + + j=1 + + do while(.true.) + + call c_cycle(f%v(i),j,v ,je); if(j==0) exit; + dm=1 + do ii=1,nd2 + dm=dm+je(ii) + enddo + t=v.cmono.je + do a=1,nd2 + dt=t.d.a + do al=1,nd2 + do k=1,nd2 + fs%v(al)=fs%v(al)+s(a,al)*s(k,i)*(id(k,a)*t+(1.0_dp.cmono.k)*dt)/dm + enddo ! k + enddo ! al + enddo ! a + enddo + +enddo + + + + +N_s=exp(fs) + + +N_r= mt*N_s**(-1) + + +N_s= L_s**(-1)*N_s*L_s + +L_r%q=1.0_dp +N_r%q=1.0_dp +L_s%q=1.0_dp +N_s%q=1.0_dp + + +deallocate(je);deallocate(s,id); + call kill(f);call kill(fs);call kill(ft); +call kill(t,dt);call kill(mt,ids,m4,ml); +deallocate(mat) +call kill(m) + +end subroutine symplectify_general + + + +!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ + +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + subroutine normalise_vector_field_fourier(H,Fc,K,F1,dospin,mres,h_comoving) + implicit none + TYPE (c_vector_field_fourier), INTENT (INout) :: H,Fc,K + TYPE (c_vector_field_fourier),optional, INTENT (INout) :: F1 + TYPE (c_vector_field),optional, INTENT (INout) :: h_comoving + TYPE (c_taylor) temp + TYPE (c_quaternion) qtemp,qtempf + integer,optional :: mres(-1:ndim) ! -1 has the spin + + integer ki,n,m,j,l,o,nl,i1,kr,i,nv,no + complex(dp), allocatable :: eg(:) + real(dp), allocatable :: nu(:),da(:) + integer, allocatable :: je(:) + complex(dp) v,lam + logical(lp) removeit,dos + type(c_vector_field_fourier) ht,H1 + logical,optional :: dospin + real(dp) nus(-1:1),xmr2 + integer jq,mf,ires + + + nv=c_%nv + no=c_%no + dos=.false. + + + if(present(dospin)) dos=dospin + + IF(.NOT.C_STABLE_DA) then + RETURN + endif + call alloc(temp) + call alloc(qtemp) + call alloc(qtempf) + call alloc(ht) + call alloc(h1) + + Fc=0 + H1=H + ht=H + n=H%f(0)%n + i1=2 + if(present(F1)) i1=1 + allocate(eg(n),je(nv)); + allocate(nu(n/2),da(n/2)); + eg=0.0_dp + je=0 + do ki=1,n + if(coast(ki)) then + eg(ki)=0 + else + je=0 + je(ki)=1 + eg(ki)=H%f(0)%v(ki).sub.je ! (1) + if(mod(ki,2)==0) then + nu(ki/2)=aimag(eg(ki)) + da(ki/2)=real(eg(ki)) + endif + endif + enddo + + if(dos) then + nus(1)=-2*spin_def_tune*H%f(0)%q%x(2) + nus(0)=0 + nus(-1)=2*spin_def_tune*H%f(0)%q%x(2) + endif + i1=2 ;if(present(F1)) i1=1 ;nl=0; nl=n_extra; + + + + do o=i1,no+1 +!!!!!!!!!!!!!!! + ht=H1 + do i=-n_fourier,n_fourier + call c_qr_to_q0(Fc%f(i)%q,Fc%f(i)%q) + enddo + !!!!!!!!!!!!!!!!!!!!!! + + +IF(O>1) call exp_vector_field_fourier(Fc,Ht,Ht) ! (2) + + + do i=-n_fourier,n_fourier + call c_q0_to_qr(Fc%f(i)%q,Fc%f(i)%q) + enddo + do m=-n_fourier,n_fourier + + do ki=1,n ! do-looping over size of a vector field (6 for example for BMAD) + temp=ht%f(m)%v(ki).sub.o + + j=1 + do while(.true.) + + call c_cycle(temp,j,v ,je); if(j==0) exit; + + +jq=0 + call check_kernel_ham(ki,n,je,nu,da,removeit,m,nus,jq) + +!!! m.nu+k=0 => k=-p + if(removeit.and.present(mres)) then + je(ki)=je(ki)-1 + ires=0 + do l=1,c_%nd + ires=iabs(mres(L)-(je(2*L)-je(2*L-1)))+ires + enddo +! ires=iabs(mres(-1)-jq)+ires + ires=iabs(-mres(0)-m)+ires !k=-p + if(ires==0) removeit=.false. +je(ki)=je(ki)+1 + endif + if(removeit.and.present(mres)) then +je(ki)=je(ki)-1 + ires=0 + do l=1,c_%nd + ires=iabs(-mres(L)-(je(2*L)-je(2*L-1)))+ires + enddo +! ires=iabs(-mres(-1)-jq)+ires + ires=iabs(mres(0)-m)+ires !k=-p + if(ires==0) removeit=.false. +je(ki)=je(ki)+1 + endif + + if(removeit) then + lam=-i_*m ! (3a) + je(ki)=je(ki)-1 + do l=1,n + if(coast(l)) cycle + lam=lam-eg(l)*je(l) ! (3b) + enddo + je(ki)=je(ki)+1 + Fc%f(m)%v(ki)=Fc%f(m)%v(ki)-(v.cmono.je)/lam ! (4) + endif + + enddo ! over monomials + enddo ! over vector index + + qtemp=ht%f(m)%q.sub.(o-1) + + qtempf=0.0_dp + call c_q0_to_qr(qtemp,qtempF) + + do ki=1,3 !,-1 ! do-looping over quaterion 0,3 + if(ki==1) jq=1 + if(ki==2) jq=0 + if(ki==3) jq=-1 + + j=1 + temp=qtempF%x(ki) + + + + do while(.true.) + + call c_cycle(temp,j,v ,je); if(j==0) exit; + + + call check_kernel_ham(0,n,je,nu,da,removeit,m,nus,jq) +!!! m.nu+k=0 => k=-p + if(removeit.and.present(mres)) then + ires=0 + do l=1,c_%nd + ires=iabs(mres(L)-(je(2*L)-je(2*L-1)))+ires + enddo + ires=iabs(mres(-1)-jq)+ires + ires=iabs(-mres(0)-m)+ires !k=-p + if(ires==0) removeit=.false. + endif + if(removeit.and.present(mres)) then + ires=0 + do l=1,c_%nd + ires=iabs(-mres(L)-(je(2*L)-je(2*L-1)))+ires + enddo + ires=iabs(-mres(-1)-jq)+ires + ires=iabs(mres(0)-m)+ires !k=-p + if(ires==0) removeit=.false. + endif + + + if(removeit) then + lam=-i_*m ! (3a) + + do l=1,n + if(coast(l)) cycle + lam=lam -eg(l)*je(l) ! (3b) + enddo + + lam=lam -nus(jq)*i_ + + Fc%f(m)%q%x(ki)=Fc%f(m)%q%x(ki)-(v.cmono.je)/lam ! (4) + + + endif + + enddo ! over monomials + + enddo + + enddo ! over fourier mode + + IF(o==1) THEN + do i=-n_fourier,n_fourier + call c_qr_to_q0(Fc%f(i)%q,Fc%f(i)%q) + enddo + + call exp_vector_field_fourier(Fc,Ht,H1,nlin=nl) ! (5) + do i=-n_fourier,n_fourier + call c_q0_to_qr(Fc%f(i)%q,Fc%f(i)%q) + enddo + + F1=Fc; Fc=0;NL=0; + ENDIF + + enddo ! over order o + + ht=H1 + do i=-n_fourier,n_fourier + call c_qr_to_q0(Fc%f(i)%q,Fc%f(i)%q) + enddo + + + call exp_vector_field_fourier(Fc,Ht,Ht) ! (6) + + K=ht + + + +if(present(h_comoving) ) then + + if(present(mres)) then + xmr2=0 + do l=1,c_%nd + xmr2=mres(l)**2+xmr2 + enddo + xmr2=xmr2+mres(-1)**2 + lam=mres(0) + lam=-lam/xmr2 + endif + + h_comoving=0 + do i=1,c_%nd + h_comoving%v(2*i-1) = -i_*lam* mres(i)*(1.0_dp.cmono.(2*i-1)) + h_comoving%v(2*i ) = i_*lam* mres(i)*(1.0_dp.cmono.(2*i )) + + enddo + if(mres(-1)/=0) then + h_comoving%q%x(2)=-lam *mres(-1)/2.0_dp + endif + + + + do i=-n_fourier,n_fourier + h_comoving = K%f(i)+h_comoving + enddo + + + + +endif + + + + deallocate(eg,je,nu) + call kill(temp) + call kill(qtemp) + call kill(ht) + call kill(h1) + call kill(qtempf) + +end subroutine normalise_vector_field_fourier + + subroutine check_kernel_ham(k,n,je,nu,da,removeit,ktheta,nus,jq) +!#internal: normal +!# This routine identifies terms in an orbital vector field that +!# are left per user's request. +!# This is used if a resonance family is to be left in the map. +!# See Sec.5.4 of Springer book. + + implicit none + logical(lp) removeit + integer i,k,n,je(:),j ,jj,ktheta,mr(ndim),jq,ires + real(dp) nu(:),nus(-1:1),da(:) + real(dp) tr1,t2 + complex(dp) t1 + + + removeit=my_true + t1=0; t2=0; + ! if(k/=0) je(k)=je(k)-1 + do i=1,n,2 + if(coast(i)) cycle + j=(i+1)/2 + jj=0 + if(k==i) jj=1 + if(k==i+1) jj=-1 + mr(j)=(je(i+1)-je(i)+jj) + + t1=t1+ nu(j)*(je(i+1)-je(i)+jj)+nus(jq) + t1=t1 !- i_*da(J)*(je(i+1)+je(i)+iabs(jj)) + t2=t2-da(J)*(je(i+1)+je(i)+iabs(jj)) + enddo + t1=t1-ktheta + if(remove_tune_shift) t1=t1+i_*t2 + + tr1=abs(t1) + ires=0 + + if(tr1<=0) removeit=my_false + +! if(k/=0) je(k)=je(k)+1 + + end subroutine check_kernel_ham !_new + + subroutine check_kernel_spin1(k,n,je,da,removeit) +!#internal: normal +!# This routine identifies terms in spin-orbital vector field that +!# are not in the kernel of a complete normalisation. + + implicit none + logical(lp) removeit + integer i,k,n,je(:),t,j + real(dp) da(:),ts + removeit=my_true + if(mod(k,2)/=0) return + t=0 + ts=0 + do i=1,n,2 + if(coast(i)) cycle + t=t+abs(je(i)-je(i+1)) + j=(i+1)/2 + ts=ts+da(j)*abs(je(i)*je(i+1)) + enddo + + ! if(k==1) then + ! t=t+iabs(1) ! k is +/- 1 for spin s1 and s3 + ! elseif(k==3) then + ! t=t+iabs(-1) ! k is +/- 1 for spin s1 and s3 + ! endif + if(ts/=0.0_dp.and.remove_tune_shift) t=t+1 + if(t==0) removeit=my_false + + end subroutine check_kernel_spin1 + +subroutine gramschmidt(v) +use gauss_dis +implicit none +real(dp) w,v(:,:) +!complex(dp) w,v(:,:) +integer n,k,i + +n=size(v,1) + +v(1,1:n)=v(1,1:n)/sqrt(dot_product(v(1,1:n),v(1,1:n))) + +do k=2,n + +do i=1,n +v(k,i)=RANF() +enddo + +do i=1,k-1 +v(k,1:n)= v(k,1:n)-dot_product(v(i,1:n),v(k,1:n))*v(i,1:n) +enddo +v(k,1:n)=( 1.0_dp/sqrt(dot_product(v(k,1:n),v(k,1:n))) )*v(k,1:n) + +enddo !k +end subroutine gramschmidt + + + +subroutine c_normal(xyso3,n,dospin,no_used,rot,phase,nu_spin,canonize) +!#general: normal +!# This routine normalises the map xy +!# xy = n%a_t**(-1)*r*n%a_t +!# The linear part of r is described in Chap.4 for the orbital part +!# and in Chap.6 for the spin. The nonlinear parts are in Chap.5 and 6. +!# Dospin must be set to .true. if spin is to be normalised. +!# Resonances can be left in the map. Their number is in n%nres. +!# They are nres resonances The kth resonance is n%m(i,k).Q_i+n%ms(k)=integer +!# canonize=.true. Then it is put into courant-snyder form or anti- courant-snyder form +!# depending on the logical courant_snyder_teng_edwards=true or false. (See blue or yellow book) +!# The map in phasors is exp(n%H_l.grad) exp(n%H_nl.grad) +!# if fully normalized into a rotation then the map is exp(n%h.grad) + + implicit none + type(c_damap) , intent(inout) :: xyso3 + type(c_damap) m1,ri,nonl,a1,a2,mt,AS,xy,Nf,N_cut_2,N_nl + type(c_normal_form), intent(inout) :: n + type(c_damap), optional :: rot + type(c_taylor), optional :: phase(:),nu_spin + type(taylor) c1,s1 + integer,optional :: no_used + integer i,j,k,l,kr,not,ncoast + integer, allocatable :: je(:) + logical(lp) removeit,rad_in + complex(dp) v,lam,egspin(3) + complex(dp), allocatable :: eg(:) + real(dp) norm,alpha,prec !,cx,sx + logical(lp), optional :: dospin,canonize + logical dospinr,change + type(c_spinor) n0,nr + type(c_quaternion) qnr + integer mker, mkers,mdiss,mdis,ndptbmad + real(dp), allocatable :: da(:) + + + call kill(n%ker) + call kill(n%g) + call alloc(n%ker) + call alloc(n%g) +n%unstable=.false. +unstable=.false. +!hyperbolic=n%hyperbolic + n%g%dir=-1 + n%ker%dir=1 + + if(lielib_print(13)/=0) then + call kanalnummer(mker,"kernel.txt") + call kanalnummer(mdis,"distortion.txt") + call kanalnummer(mkers,"kernel_spin.txt") + call kanalnummer(mdiss,"distortion_spin.txt") + endif + + dospinr=.false. + if(present(dospin)) then + dospinr=dospin + else + if(force_spin_input_normal) then + write(6,*) " your default forces you to include dospin in the input of c_normal" + stop + endif + endif + + +if(bmad_automatic) then + if(nd2t+ndc2t/=6) then + write(6,*) " nd2t , ndc2t ",nd2t,ndc2t + write(6,*) " not BMAD on entrance, suspicious" + endif + ndptbmad=0 + alpha=abs(xyso3%v(6).sub.'000001') + norm=full_abs(xyso3%v(6)) + alpha=abs(alpha-1.0_dp)+abs(norm-1.0_dp) + if(alpha<1.d-12) then + ndptbmad=6 + call in_bmad_units + endif + alpha=abs(xyso3%v(5).sub.'000010') + norm=full_abs(xyso3%v(5)) + alpha=abs(alpha-1.0_dp)+abs(norm-1.0_dp) + if(alpha<1.d-12) then + ndptbmad=5 + call in_ptc_units + endif + call c_bmad_reinit(ndptbmad) + + + if(use_quaternion) then + call c_full_norm_quaternion(xyso3%q,k,norm) + if(k==-1) dospinr=.true. + else + call c_full_norm_spin(xyso3%s,k,norm) + if(k==-1) dospinr=.true. + endif +endif + +if(spin_automatic) then + dospinr=.false. + if(use_quaternion) then + call c_full_norm_quaternion(xyso3%q,k,norm) + if(k==-1) dospinr=.true. + else + call c_full_norm_spin(xyso3%s,k,norm) + if(k==-1) dospinr=.true. + endif +write(6,*)"dospin ", dospinr +endif + +inside_normal=.true. +!call c_count_da(i_alloc) +!write(6,*)" entering c_normal ", i_alloc + change=.false. + not=no + if(present(no_used)) then + not=no_used ! sometimes only linear stuff is needed + else + if(complex_extra_order==1.and.special_extra_order_1) not=not-1 + endif + + call alloc(xy); + xy=xyso3 + if(use_quaternion_in_so3.and.(.not.use_quaternion.and.dospinr)) then + call makequaternion(xy) + use_quaternion=.true. + change=.true. + endif + call alloc(m1);call alloc(nonl);call alloc(a1);call alloc(a2);call alloc(ri); + + allocate(je(nv)) + allocate(eg(xyso3%n)) + allocate(da(c_%nd)) + da=0.0_dp + + m1=xy + + ! Brings the map to the parameter dependent fixed point + ! including the coasting beam gymnastic: time-energy is canonical + ! but energy is constant. (Momentum compaction, phase slip etc.. falls from there) + ! etienne + + if(c_skip_gofix) then + a1=1 +else + call c_gofix(m1,a1) + +endif + + + m1=c_simil(a1,m1,-1) + + + + ! Does the the diagonalisation into a rotation + call c_linear_a(m1,a2) + + + + + !!! Now the linear map is normalised + m1=c_simil(a2,m1,-1) + + + !!! We go into the phasors' basis + ri=from_phasor(-1) + + m1=c_simil(ri,m1,1) + + +!stop 999 + ri=(m1.sub.-1)**(-1) + + ri%s=1 ! make spin identity + ri%q=1.0_dp ! make spin identity + + + + !!! The tunes are stored for the nonlinear normal form recursive algorithm + do k=1,xy%n + if(coast(k)) then + eg(k)=1 + else + je=0 + je(k)=1 + eg(k)=ri%v(k).sub.je + if(mod(k,2)==0) then + da(k/2)=log(abs(eg(k))) + endif + endif + enddo + + + n%ker=0 ! In case reusing normal form + + do i=2,not + if(lielib_print(13)/=0) then + write(mdis,*) " **************************************** " + write(mdis,*) "Order ",i + write(mker,*) " **************************************** " + write(mker,*) "Order ",i + endif + + nonl=(m1*ri) + nonl= exp_inv(n%ker,nonl) + nonl=nonl.sub.i + + + + do k=1,xy%n + if(lielib_print(13)/=0) then + write(mdis,*) " **************************************** " + write(mdis,*) "field component ",k + write(mker,*) " **************************************** " + write(mker,*) "field component ",k + endif + + n%g%f(i)%v(k)=0.0_dp + n%ker%f(i)%v(k)=0.0_dp + + + j=1 + + do while(.true.) + + call c_cycle(nonl%v(k),j,v ,je); if(j==0) exit; + call check_kernel(k,xy%n,je,removeit) + + if(n%nres>0.and.removeit) then + do kr=1,n%nres + if(n%ms(kr)/=0) cycle ! a spin resonance + call check_resonance(k,xy%n,je,kr,n%m,removeit) + if(.not.removeit) then + exit + endif + enddo + endif + + if(removeit) then + + lam=1.0_dp + je(k)=je(k)-1 + do l=1,xy%n + if(coast(l)) cycle + lam=lam*eg(l)**je(l) + enddo + + if(lielib_print(13)/=0) then + write(mdis,*) k + write(mdis,'(6(1x,i4))') je(1:nd2) + write(mdis,*) v + write(mdis,*) abs(v/(1-lam)) + endif + + je(k)=je(k)+1 + + n%g%f(i)%v(k)=n%g%f(i)%v(k)+(v.cmono.je)/(1.0_dp-lam) + + else ! Put in the kernel + + if(lielib_print(13)/=0) then + je(k)=je(k)-1 + write(mker,*) k + write(mker,'(6(1x,i4))') je(1:nd2) + write(mker,*) v + write(mker,*) abs(v/(1-lam)) + je(k)=je(k)+1 + endif + n%ker%f(i)%v(k)=n%ker%f(i)%v(k)+(v.cmono.je) + endif + + enddo ! over monomial + enddo ! over vector index + + m1=c_simil(n%g%f(i),m1,-1) +!call c_full_norm_vector_field(n%g%f(i),norm) +!write(6,*) " old ",i,norm + enddo + + ! if(dospinr)then + do i=1,size(n%g%f) + n%g%f(i)%q=0.0_dp ! makes identity 2024.1.2 + enddo + do i=1,size(n%ker%f) + n%ker%f(i)%q=0.0_dp + enddo + ! endif + + + n%a_t=a1*a2*from_phasor()*texp(n%g)*from_phasor(-1) + ! + n%a1=a1 + n%a2=a2 + + +!!!!! here we put the normalised linear part into the factored vector field +!!!!! not necessary but useful + do k=1,xy%n + if(.not.coast(k)) then + je=0 + je(k)=1 + n%ker%f(1)%v(k)=n%ker%f(1)%v(k)-(log(eg(k)).cmono.je) + + if(mod(k,2)==1) then + + if(.not.unstable((k+1)/2) ) then + n%tune((k+1)/2)=aimag(log(eg(k)))/twopi + n%damping((k+1)/2)=real(log(eg(k))) + if(n%tune((k+1)/2)<0.and.n%positive) n%tune((k+1)/2)=n%tune((k+1)/2)+1.0_dp + if(n%tune((k+1)/2)<-0.5_dp.and.(.not.n%positive)) n%tune((k+1)/2)=n%tune((k+1)/2)+1.0_dp + if(n%tune((k+1)/2)> 0.5_dp.and.(.not.n%positive)) n%tune((k+1)/2)=n%tune((k+1)/2)-1.0_dp + else + n%tune((k+1)/2)=log(eg(k)) + n%damping((k+1)/2)= log(eg(k)*eg(k+1))/2.0_dp + endif + + + endif + endif + enddo + + if(c_skip_gofix) then + do k=1,xy%n + if(mod(k,2)==1) then + if(n%tune((k+1)/2)>0.50_dp) n%tune((k+1)/2)=n%tune((k+1)/2)-1.0_dp + endif + enddo + endif + if(nd2t==6) then + if(n%tune(3)>0.50_dp.and.negative_synchrotron_tune) n%tune(3)=n%tune(3)-1.0_dp + endif + + if(ndpt/=0) then + je=0 + je(ndpt)=1 + lam=(ri%v(ndptb).sub.je) + n%ker%f(1)%v(ndptb)=n%ker%f(1)%v(ndptb)-(lam.cmono.je) + if(mod(ndpt,2)==0) then + n%tune(ndpt/2)=-lam + else + n%tune(ndptb/2)=-lam + endif + endif + + + if(dospinr) then + +if(use_quaternion)then + call c_full_norm_quaternion(m1%q,k,norm) +else + call c_full_norm_spin(m1%s,k,norm) +endif + if(k>=0) then + dospinr=.false. + if(use_quaternion) then + write(6,*) " no quaternion spin in map: dospin command ignored " + else + write(6,*) " no spin matrix in map: dospin command ignored " + endif + endif + endif + + + if(dospinr) then + call alloc(n0) + call alloc(nr) + call alloc(mt) + call alloc(AS) + call alloc(qnr) + n%AS=1 + + +if(use_quaternion)then + + call c_normal_spin_linear_quaternion(m1,m1,n%AS,alpha) + + n%quaternion_angle=alpha/2.0_dp + ri=1 ; ri%q=m1%q.sub.0 ; ! exp(theta_0 L_y) (2) +! sx=sqrt(ri%q%x(1)**2+ri%q%x(2)**2+ri%q%x(3)**2) +! cx=ri%q%x(0) +!write(6,*) alpha +! alpha=-(-2*atan2(sx,cx)) +!write(6,*) alpha +!pause 723 + egspin(3)=cos(alpha)-i_*sin(alpha) + egspin(2)=1.0_dp + egspin(1)=cos(alpha)+i_*sin(alpha) +else + call c_normal_spin_linear(m1,m1,n%AS,n0) ! (1) + ri=1 ; ri%s=m1%s.sub.0 ; ! exp(theta_0 L_y) (2) + egspin(3)=ri%s%s(1,1)-i_*ri%s%s(1,3) + egspin(2)=1.0_dp + egspin(1)=ri%s%s(1,1)+i_*ri%s%s(1,3) +endif + + + + + + + if(lielib_print(13)/=0) then + write(mdiss,*) " eg(1:4),spin_def_tune" ,spin_def_tune + write(mdiss,*)eg(1) + write(mdiss,*)eg(2) + write(mdiss,*)eg(3) + write(mdiss,*)eg(4) + write(mdiss,*) " egspin(1:3)" + write(mdiss,*)egspin(1) + write(mdiss,*)egspin(2) + write(mdiss,*)egspin(3) + endif + if(lielib_print(13)/=0) then + write(mkers,*) " eg(1:4),spin_def_tune" ,spin_def_tune + write(mkers,*)eg(1) + write(mkers,*)eg(2) + write(mkers,*)eg(3) + write(mkers,*)eg(4) + write(mkers,*) " egspin(1:3)" + write(mkers,*)egspin(1) + write(mkers,*)egspin(2) + write(mkers,*)egspin(3) + endif + + !!! tune is taken from egspin(1) or egspin(3) spin_def_tune= +/- 1 + n%spin_tune=aimag(log(egspin(2+spin_def_tune))/twopi) + + + + ! because exp(a L_y) x = x- a z + O(a**2) + ri=ri**(-1) ! exp(-alpha_0 L_y) (3) + + +if(use_quaternion)then + nonl=m1.sub.1 ; nonl%q=1.0_dp ;nonl=nonl**(-1) ! R_0^-1 (4) +else + nonl=m1.sub.1 ; nonl%s=1 ;nonl=nonl**(-1) ! R_0^-1 (4) +endif +! nonl=m1.sub.1 ; nonl%s=1 ;nonl=nonl**(-1) ! R_0^-1 (4) + + + do i=1,no !+2 + if(lielib_print(13)/=0) then + write(mdiss,*) " **************************************** " + write(mdiss,*) "Order ",i + write(mkers,*) " **************************************** " + write(mkers,*) "Order ",i + endif + + + + mt=m1*ri ! S*exp(-theta_0 L_y) (5) + + +if(use_quaternion)then + n0=mt%q +else + call c_find_om_da(mt%s,n0) ! (4) +endif + + call c_n0_to_nr(n0,n0) ! n0 = > eigen-operator of spin (7) + + + + n0=n0*nonl ! no * R^-1 (8) + + + nr=0 + + do k=1,3 + if(lielib_print(13)/=0) then + write(mdiss,*) " $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ " + write(mdiss,*) "Spin component ",k + write(mdiss,*) " " + write(mkers,*) " $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ " + write(mkers,*) "Spin component ",k + write(mkers,*) " " + endif + + j=1 + do while(.true.) + call c_cycle(n0%v(k),j,v ,je); if(j==0) exit; + call check_kernel_spin1(k,xy%n,je,da,removeit) + if(n%nres>0.and.removeit) then + do kr=1,n%nres + call check_resonance_spin(k,xy%n,je,kr,n%ms,n%m,removeit) + if(.not.removeit) then + exit + endif + enddo + endif + + if(removeit) then + lam=egspin(k) + do l=1,xy%n + if(coast(l)) cycle + lam=lam*eg(l)**je(l) + enddo + + if(lielib_print(13)/=0) then + !do kr=1,nd2 + !je(kr)=-(-1)**kr*je(kr) + !enddo + write(mdiss,'(6(1x,i4))') je(1:nd2) + write(mdiss,*)lam + write(mdiss,*) v + write(mdiss,*) abs(v/(1-lam)) + !do kr=1,nd2 + !je(kr)=-(-1)**kr*je(kr) + !enddo + endif + nr%v(k)=nr%v(k) +(v.cmono.je)/(1.0_dp-lam) ! (9) + else + if(lielib_print(13)/=0) then + do kr=1,nd2 + je(kr)=-(-1)**kr*je(kr) + enddo + write(mkers,'(6(1x,i4))') je(1:nd2) + write(mkers,*) v + do kr=1,nd2 + je(kr)=-(-1)**kr*je(kr) + enddo + endif + endif + enddo ! cycle + enddo ! k + + + call c_nr_to_n0(nr,nr) ! (10) + + + + + +if(use_quaternion)then +qnr=nr + AS=1 ; +AS%q=exp(qnr,n=c_%no) +else + AS=1 ; AS%s=exp(nr)*AS%s +endif + + + + + n%AS=n%AS*AS ! (12) + + + + m1=c_simil(AS,m1,-1) + + + enddo + + n%AS=from_phasor()*n%AS*from_phasor(-1) + + n%AS=n%A_t*n%AS*n%a_t**(-1) + + call kill(AS) + call kill(mt) + call kill(n0) + call kill(nr) + call kill(qnr) + endif + + call c_check_rad(m1%e_ij,rad_in) + if(rad_in) call c_normal_radiation(m1,n) + + ri=from_phasor() + n%n=c_simil(ri,m1,1) + n%Atot=n%as*n%a_t + + if(present(canonize)) then + if(canonize) call c_full_canonise(n%atot,n%atot) + endif + + + + if(present(rot)) then + rot=n%Atot**(-1)*xy*n%Atot + endif + + if(present(nu_spin)) nu_spin=0.0_dp + if(present(phase)) then + do i=1,size(phase) + phase(i)=0.0_dp + enddo +endif + if((present(phase).or.present(nu_spin)).and.old_phase_calculation) then + + + + if(present(rot)) then + m1=rot + else + m1=n%Atot**(-1)*xy*n%Atot + endif + + + + + qphase=.false. + call c_full_canonise(m1,a1,phase=phase,nu_spin=nu_spin) + ! if(dospinr.and.present(nu_spin)) then + ! if(real(nu_spin.sub.'0')<0) nu_spin=-nu_spin ! 2018.11.01 to match phase advance + ! endif + qphase=qphasedef + endif + +! error because m1 was reutilized in present(rot) +! call c_check_rad(m1%e_ij,rad_in) + !! if(rad_in) call c_normal_radiation(m1,n) + ! call c_check_rad(m1%e_ij,rad_in) + !! if(rad_in) call c_normal_radiation(m1,n) + + call kill(m1);call kill(nonl);call kill(a1);call kill(a2);call kill(ri); + + deallocate(eg) + deallocate(da) + deallocate(je) + + if(lielib_print(13)/=0) then + close(mker) + close(mdis) + close(mdiss) + close(mkers) + endif + + if(change) then + call makeso3(n%a1) + call makeso3(n%a2) + call makeso3(n%a_t) + call makeso3(n%atot) + call makeso3(n%as) + call makeso3(n%n) + n%a1%q=0.0_dp + n%a2%q=0.0_dp + n%a_t%q=0.0_dp + n%atot%q=0.0_dp + n%as%q=0.0_dp + n%n%q=0.0_dp + use_quaternion=.false. + endif + call kill(xy) +!call c_count_da(i_alloc) +!write(6,*) " exiting c_normal ",i_alloc +inside_normal=.false. +!!!! finding a Lie exponent + +! if(use_quaternion.and.rf==0) then + call alloc(Nf,N_cut_2,N_nl ) + Nf=n%atot**(-1)*xyso3*n%atot + N_cut_2=Nf.cut.(-2) + +! creating the linear vector field in phasors variables +ncoast=0 +if(c_%ndpt/=0) ncoast=1 +!!!! create a full vector field for N_cut_2 + +do i=1,(c_%nd-ncoast) + + ! IF(.not.hyperbolic.or..not.unstable(i) ) then + IF( .not.unstable(i) ) then + +lam=n%tune(i) +if(n%tune(i)>0.5e0_dp) lam=lam-1.0_dp + n%H_l%v(2*i-1)=-(i_*twopi*lam)*dz_c(2*i-1)-n%damping(i)*dz_c(2*i-1) + n%H_l%v(2*i)=(i_*twopi*lam)*dz_c(2*i)-n%damping(i)*dz_c(2*i) +ELSE + n%H_l%v(2*i-1)= (-n%damping(i)-n%tune(i))*dz_c(2*i-1) + n%H_l%v(2*i)=(-n%damping(i)+n%tune(i))*dz_c(2*i-1) + +ENDIF ! HYPERBOLIC + +enddo + +if(ncoast/=0) then + n%H_l%v(c_%ndptb)=n%tune(c_%nd)*dz_c(c_%ndpt) +endif +if(dospinr) then + n%H_l%q=0.0_dp + n%H_l%q%x(2)=n%quaternion_angle +endif +!!!! Going into variables moving on a circle +n%H_l=ci_phasor()*n%H_l + +!!! Reverse-Dragt-Finn order for Lie map +N_nl=N_cut_2**(-1)*nf + +n%H_nl=ln(N_nl) + +n%H_l=c_phasor()*n%H_l +n%H_nl=c_phasor()*n%H_nl + + n%H=n%H_l+n%H_nl + call kill(Nf,N_cut_2,N_nl ) +! endif + +if(.not.old_phase_calculation) then +if(present(phase)) then +! ncoast=0 + !if(c_%ndpt/=0) ncoast=1 + do i=1,c_%nd !-ncoast + ! IF(.not.hyperbolic.or..not.unstable(i) ) then + IF( .not.unstable(i) ) then + + phase(i)=aimag(n%h%v(2*i).k.(2*i))/twopi + + ELSE + phase(i)=(n%h%v(2*i).k.(2*i)) + + ENDIF + enddo + + if(c_%ndptb/=0) then + phase(c_%nd)=n%h%v(c_%ndptb) ! overwrites if necessary + endif +endif + +if(present(nu_spin)) nu_spin=-spin_def_tune*n%h%q%x(2)/pi + +endif + + + end subroutine c_normal !_with_quaternion + +subroutine c_normal_new(xyso3,n,dospin,no_used,rot,phase,nu_spin,canonize) +!#general: normal +!# This routine normalises the map xy +!# xy = n%a_t**(-1)*r*n%a_t +!# The linear part of r is described in Chap.4 for the orbital part +!# and in Chap.6 for the spin. The nonlinear parts are in Chap.5 and 6. +!# Dospin must be set to .true. if spin is to be normalised. +!# Resonances can be left in the map. Their number is in n%nres. +!# They are nres resonances The kth resonance is n%m(i,k).Q_i+n%ms(k)=integer +!# canonize=.true. Then it is put into courant-snyder form or anti- courant-snyder form +!# depending on the logical courant_snyder_teng_edwards=true or false. (See blue or yellow book) +!# The map in phasors is exp(n%H_l.grad) exp(n%H_nl.grad) +!# if fully normalized into a rotation then the map is exp(n%h.grad) + + implicit none + type(c_damap) , intent(inout) :: xyso3 + type(c_damap) m1,ri,nonl,a0,a1,mt,AS,xy,Nf,N_cut_2,N_nl,rispin + type(c_normal_form), intent(inout) :: n + type(c_damap), optional :: rot + type(c_taylor), optional :: phase(:),nu_spin + type(taylor) c1,s1 + integer,optional :: no_used + integer i,j,k,l,kr,not,ncoast + integer, allocatable :: je(:) + logical(lp) removeit,rad_in + complex(dp) v,lam,egspin(3) + complex(dp), allocatable :: eg(:) + real(dp) norm,alpha,prec !,cx,sx + logical(lp), optional :: dospin,canonize + logical dospinr + + integer mker, mkers,mdiss,mdis,ndptbmad + type(c_vector_field) F + real(dp), allocatable :: da(:) + + call kill(n%ker) + call kill(n%g) + call alloc(n%ker) + call alloc(n%g) + n%g%dir=-1 + n%ker%dir=1 + + if(.not.use_quaternion) then + call c_normal(xyso3,n,dospin,no_used,rot,phase,nu_spin,canonize) + return + endif + + + dospinr=.false. + if(present(dospin)) then + dospinr=dospin + else + if(force_spin_input_normal) then + write(6,*) " your default forces you to include dospin in the input of c_normal" + stop + endif + endif + + + +if(bmad_automatic) then + if(nd2t+ndc2t/=6) then + write(6,*) " nd2t , ndc2t ",nd2t,ndc2t + write(6,*) " not BMAD on entrance, suspicious" + endif + ndptbmad=0 + alpha=abs(xyso3%v(6).sub.'000001') + norm=full_abs(xyso3%v(6)) + alpha=abs(alpha-1.0_dp)+abs(norm-1.0_dp) + if(alpha<1.d-12) then + ndptbmad=6 + call in_bmad_units + endif + alpha=abs(xyso3%v(5).sub.'000010') + norm=full_abs(xyso3%v(5)) + alpha=abs(alpha-1.0_dp)+abs(norm-1.0_dp) + if(alpha<1.d-12) then + ndptbmad=5 + call in_ptc_units + endif + call c_bmad_reinit(ndptbmad) + + + ! if(use_quaternion) then + call c_full_norm_quaternion(xyso3%q,k,norm) + if(k==-1) dospinr=.true. +endif + + +if(spin_automatic) then + dospinr=.false. + call c_full_norm_quaternion(xyso3%q,k,norm) + if(k==-1) dospinr=.true. +endif + +inside_normal=.true. + + not=no + if(present(no_used)) then + not=no_used ! sometimes only linear stuff is needed + else + if(complex_extra_order==1.and.special_extra_order_1) not=not-1 + endif + + call alloc(xy); + xy=xyso3 + + call alloc(m1);call alloc(nonl);call alloc(a0);call alloc(a1);call alloc(ri,rispin); + + allocate(je(nv)) + allocate(eg(xyso3%n)) + allocate(da(c_%nd)) + da=0.0_dp + + m1=xy + + ! Brings the map to the parameter dependent fixed point + ! including the coasting beam gymnastic: time-energy is canonical + ! but energy is constant. (Momentum compaction, phase slip etc.. falls from there) + ! etienne + +if(c_skip_gofix) then + a0=1 +else +!#1 Go to fix point + + call c_gofix(m1,a0) + + endif + + m1=c_simil(a0,m1,-1) + + + + ! Does the the diagonalisation into a rotation + +!#2 doing the linear normal form exactly + + call c_linear_a(m1,a1) + + + + + !!! Now the linear map is normalised + m1=c_simil(a1,m1,-1) + + !#3 + !!! We go into the phasors' basis + ri=from_phasor(-1) + + m1=c_simil(ri,m1,1) + + + + if(dospinr) then + + call c_full_norm_quaternion(m1%q,k,norm) + + if(k>=0) then + dospinr=.false. + if(use_quaternion) then + write(6,*) " no quaternion spin in map: dospin command ignored " + else + write(6,*) " no spin matrix in map: dospin command ignored " + endif + endif + endif + + +if(dospinr) then + + + n%AS=1 + +!#4 Linear part of spin + call c_normal_spin_linear_quaternion(m1,m1,n%AS,alpha) + + n%quaternion_angle=alpha/2.0_dp + rispin=1 ; rispin%q=m1%q.sub.0 ; ! exp(theta_0 L_y) (2) + + egspin(3)=cos(alpha)-i_*sin(alpha) + egspin(2)=1.0_dp + egspin(1)=cos(alpha)+i_*sin(alpha) + + +endif + +!#5 Linear part of the orbit map and zeroth order of quaternion + + ri=(m1.sub.-1)**(-1) + + + + + !!! The tunes are stored for the nonlinear normal form recursive algorithm + do k=1,xy%n + if(coast(k)) then + eg(k)=1 + else + je=0 + je(k)=1 + eg(k)=ri%v(k).sub.je + if(mod(k,2)==0) then + da(k/2)=log(abs(eg(k))) + endif + endif + enddo + + + n%ker=0 ! In case reusing normal form +call alloc(F) + do i=1,not + +!#6 + nonl=(m1*ri) + nonl= exp_inv(n%ker,nonl) + +!#7 vector field of nonlinear part computed + F=0 + F=ln(nonl,tpsa=.false.) +if(dospinr) then + !#8 the basis is changed to + ! e_x = 1/2(i + sqrt(-1) k) + ! e_z = 1/2(i - sqrt(-1) k) + ! e_y = j + call c_q0_to_qr(F%q,F%q) +endif + + + +!!!!!!!!!!!!!!!!! doing the orbital !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + do k=1,xy%n + + + n%g%f(i)%v(k)=0.0_dp + n%ker%f(i)%v(k)=0.0_dp + + + j=1 + + do while(.true.) + + call c_cycle(F%v(k),j,v ,je); if(j==0) exit; + call check_kernel(k,xy%n,je,removeit) + + if(n%nres>0.and.removeit) then + do kr=1,n%nres + if(n%ms(kr)/=0) cycle ! a spin resonance + call check_resonance(k,xy%n,je,kr,n%m,removeit) + if(.not.removeit) then + exit + endif + enddo + endif + + if(removeit) then + + lam=1.0_dp + je(k)=je(k)-1 + do l=1,xy%n + if(coast(l)) cycle + lam=lam*eg(l)**je(l) + enddo + + + je(k)=je(k)+1 +!#9 Removing the "resonances " + n%g%f(i)%v(k)=n%g%f(i)%v(k)+(v.cmono.je)/(1.0_dp-lam) + + else ! Put in the kernel + + !#10 Leaving the Kernel which might include resonances in the one-resonance model + n%ker%f(i)%v(k)=n%ker%f(i)%v(k)+(v.cmono.je) + endif + + enddo ! over monomial + enddo ! over vector index +!!!!!!!!!!!!!!!!! end of doing the orbital !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +if(dospinr) then + + + do k=1,3 + + + j=1 + + do while(.true.) + + call c_cycle(F%q%x(k),j,v ,je); if(j==0) exit; + call check_kernel_spin1(k,xy%n,je,da,removeit) + if(n%nres>0.and.removeit) then + do kr=1,n%nres + call check_resonance_spin(k,xy%n,je,kr,n%ms,n%m,removeit) + if(.not.removeit) then + exit + endif + enddo + endif + + + if(removeit) then + + lam=egspin(k) + do l=1,xy%n + if(coast(l)) cycle + lam=lam*eg(l)**je(l) + enddo +!#11 Removing the "resonances " + n%g%f(i)%q%x(k)=n%g%f(i)%q%x(k) +(v.cmono.je)/(1.0_dp-lam) ! (9) + else ! Put in the kernel + !#12 Leaving the Kernel which might include resonances in the one-resonance model + n%ker%f(i)%q%x(k)=n%ker%f(i)%q%x(k)+(v.cmono.je) + endif + + + + enddo ! over monomial + enddo ! over quaternion index + + !#13 the quaternion basis is changed back to i,j,k inverting \#8 + + call c_qr_to_q0(n%g%f(i)%q,n%g%f(i)%q) ! (10) + +endif + + m1=c_simil(n%g%f(i),m1,-1) + + + enddo + + +call kill(F) + + + !#14 n%a_t contains everything + + n%a_t=a0*a1*from_phasor()*texp(n%g,n%as)*from_phasor(-1) + + +! not so useful + n%a1=a0 + n%a2=a1 + + +!#15 + +!!!!! here we put the normalised linear part into the factored vector field +!!!!! not necessary but very useful + do k=1,xy%n + if(.not.coast(k)) then + je=0 + je(k)=1 + n%ker%f(1)%v(k)=n%ker%f(1)%v(k)-(log(eg(k)).cmono.je) + + if(mod(k,2)==1) then + n%tune((k+1)/2)=aimag(log(eg(k)))/twopi + n%damping((k+1)/2)=real(log(eg(k))) + if(n%tune((k+1)/2)<0.and.n%positive) n%tune((k+1)/2)=n%tune((k+1)/2)+1.0_dp + if(n%tune((k+1)/2)<-0.5_dp.and.(.not.n%positive)) n%tune((k+1)/2)=n%tune((k+1)/2)+1.0_dp + if(n%tune((k+1)/2)> 0.5_dp.and.(.not.n%positive)) n%tune((k+1)/2)=n%tune((k+1)/2)-1.0_dp + + endif + endif + enddo + +!!!! Not used except for moments + if(c_skip_gofix) then + do k=1,xy%n + if(mod(k,2)==1) then + if(n%tune((k+1)/2)>0.50_dp) n%tune((k+1)/2)=n%tune((k+1)/2)-1.0_dp + endif + enddo + endif +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +!#16 The synchrotron tune should be a small negative number if necessary + if(nd2t==6) then + if(n%tune(3)>0.50_dp.and.negative_synchrotron_tune) n%tune(3)=n%tune(3)-1.0_dp + endif + + if(ndpt/=0) then + je=0 + je(ndpt)=1 + lam=(ri%v(ndptb).sub.je) + n%ker%f(1)%v(ndptb)=n%ker%f(1)%v(ndptb)-(lam.cmono.je) + if(mod(ndpt,2)==0) then + n%tune(ndpt/2)=-lam + else + n%tune(ndptb/2)=-lam + endif + endif + + !#17 Checking for fluctuation, ie, stochastic radiation + ! c_normal_radiation normalizes the stochastic map + call c_check_rad(m1%e_ij,rad_in) + if(rad_in) call c_normal_radiation(m1,n) + + ri=from_phasor() + n%n=c_simil(ri,m1,1) + + +! backward compatibility + n%Atot= n%a_t + +! not necessary + if(present(canonize)) then + if(canonize) call c_full_canonise(n%atot,n%atot) + endif + + + + if(present(rot)) then + rot=n%Atot**(-1)*xy*n%Atot + endif + + if(present(nu_spin)) nu_spin=0.0_dp + if(present(phase)) then + do i=1,size(phase) + phase(i)=0.0_dp + enddo +endif + + + + call kill(m1);call kill(nonl);call kill(a0);call kill(a1);call kill(ri);call kill(rispin); + + deallocate(eg) + deallocate(da) + deallocate(je) + + + + + call kill(xy) +!call c_count_da(i_alloc) +!write(6,*) " exiting c_normal ",i_alloc +inside_normal=.false. +!!!! finding a Lie exponent + +!#18 Normalized vector fields are computed or created (linear) + +! if(use_quaternion.and.rf==0) then + call alloc(Nf,N_cut_2,N_nl ) + Nf=n%atot**(-1)*xyso3*n%atot + N_cut_2=Nf.cut.(-2) + +! creating the linear vector field in phasors variables +ncoast=0 +if(c_%ndpt/=0) ncoast=1 + +!!!! create a full vector field for N_cut_2 +!#19 Linear vector field for orbital and constant quaternion computed +do i=1,(c_%nd-ncoast) + n%H_l%v(2*i-1)=-(i_*twopi*n%tune(i))*dz_c(2*i-1)-n%damping(i)*dz_c(2*i-1) + n%H_l%v(2*i)=(i_*twopi*n%tune(i))*dz_c(2*i)-n%damping(i)*dz_c(2*i) +enddo +if(ncoast/=0) then + n%H_l%v(c_%ndptb)=n%tune(c_%nd)*dz_c(c_%ndpt) +endif +if(dospinr) then + n%H_l%q=0.0_dp + n%H_l%q%x(2)=n%quaternion_angle +endif + + +! Put in ordinary Floquet (x,p) +!!!! Going into variables moving on a circle +n%H_l=ci_phasor()*n%H_l + +!!! Reverse-Dragt-Finn order for Lie map +N_nl=N_cut_2**(-1)*nf + +!#20 Put in phasors + +n%H_nl=c_logf_spin(N_nl) + +!#21 Put in ordinary Floquet (x,p) + +n%H_l=c_phasor()*n%H_l +n%H_nl=c_phasor()*n%H_nl + +!#22 Only valid without damping and no resonance left in + + n%H=n%H_l+n%H_nl + call kill(Nf,N_cut_2,N_nl ) +! endif + +if(.not.old_phase_calculation) then +if(present(phase)) then +! ncoast=0 + !if(c_%ndpt/=0) ncoast=1 + do i=1,c_%nd !-ncoast + phase(i)=aimag(n%h%v(2*i).k.(2*i))/twopi + enddo + + if(c_%ndptb/=0) then + phase(c_%nd)=n%h%v(c_%ndptb) ! overwrites if necessary + endif +endif + +if(present(nu_spin)) nu_spin=-spin_def_tune*n%h%q%x(2)/pi + +endif + + + end subroutine c_normal_new !_with_quaternion + + +subroutine c_normal_new_no_fac(xyso3,n,dospin,no_used,rot,phase,nu_spin,canonize,doberz) +!#general: normal +!# This routine normalises the map xy +!# xy = n%a_t**(-1)*r*n%a_t +!# The linear part of r is described in Chap.4 for the orbital part +!# and in Chap.6 for the spin. The nonlinear parts are in Chap.5 and 6. +!# Dospin must be set to .true. if spin is to be normalised. +!# Resonances can be left in the map. Their number is in n%nres. +!# They are nres resonances The kth resonance is n%m(i,k).Q_i+n%ms(k)=integer +!# canonize=.true. Then it is put into courant-snyder form or anti- courant-snyder form +!# depending on the logical courant_snyder_teng_edwards=true or false. (See blue or yellow book) +!# The map in phasors is exp(n%H_l.grad) exp(n%H_nl.grad) +!# if fully normalized into a rotation then the map is exp(n%h.grad) + + implicit none + type(c_damap) , intent(inout) :: xyso3 + type(c_damap) m1,ri,nonl,a1,a2,mt,AS,xy,Nf,N_cut_2,N_nl,an,ant,ker,kert + type(c_normal_form), intent(inout) :: n + type(c_damap), optional :: rot + type(c_taylor), optional :: phase(:),nu_spin + type(taylor) c1,s1 + integer,optional :: no_used + integer i,j,k,l,kr,not,ncoast + integer, allocatable :: je(:) + logical(lp) removeit,rad_in + complex(dp) v,lam,egspin(3) + complex(dp), allocatable :: eg(:) + real(dp) norm,alpha,prec !,cx,sx + logical(lp), optional :: dospin,canonize,doberz + logical dospinr,change + type(c_spinor) n0,nr + type(c_quaternion) qnr + type(c_vector_field) kerf,gf + integer mker, mkers,mdiss,mdis,ndptbmad + real(dp), allocatable :: da(:) + + + call kill(n%ker) + call kill(n%g) + call alloc(n%ker) + call alloc(n%g) + call alloc(kerf,gf) + n%g%dir=-1 + n%ker%dir=1 + + if(lielib_print(13)/=0) then + call kanalnummer(mker,"kernel.txt") + call kanalnummer(mdis,"distortion.txt") + call kanalnummer(mkers,"kernel_spin.txt") + call kanalnummer(mdiss,"distortion_spin.txt") + endif + + dospinr=.false. + if(present(dospin)) then + dospinr=dospin + else + if(force_spin_input_normal) then + write(6,*) " your default forces you to include dospin in the input of c_normal" + stop + endif + endif + + +if(bmad_automatic) then + if(nd2t+ndc2t/=6) then + write(6,*) " nd2t , ndc2t ",nd2t,ndc2t + write(6,*) " not BMAD on entrance, suspicious" + endif + ndptbmad=0 + alpha=abs(xyso3%v(6).sub.'000001') + norm=full_abs(xyso3%v(6)) + alpha=abs(alpha-1.0_dp)+abs(norm-1.0_dp) + if(alpha<1.d-12) then + ndptbmad=6 + call in_bmad_units + endif + alpha=abs(xyso3%v(5).sub.'000010') + norm=full_abs(xyso3%v(5)) + alpha=abs(alpha-1.0_dp)+abs(norm-1.0_dp) + if(alpha<1.d-12) then + ndptbmad=5 + call in_ptc_units + endif + call c_bmad_reinit(ndptbmad) + + + if(use_quaternion) then + call c_full_norm_quaternion(xyso3%q,k,norm) + if(k==-1) dospinr=.true. + else + call c_full_norm_spin(xyso3%s,k,norm) + if(k==-1) dospinr=.true. + endif +endif + +if(spin_automatic) then + dospinr=.false. + if(use_quaternion) then + call c_full_norm_quaternion(xyso3%q,k,norm) + if(k==-1) dospinr=.true. + else + call c_full_norm_spin(xyso3%s,k,norm) + if(k==-1) dospinr=.true. + endif +write(6,*)"dospin ", dospinr +endif + +inside_normal=.true. +!call c_count_da(i_alloc) +!write(6,*)" entering c_normal ", i_alloc + change=.false. + not=no + if(present(no_used)) then + not=no_used ! sometimes only linear stuff is needed + else + if(complex_extra_order==1.and.special_extra_order_1) not=not-1 + endif + + call alloc(xy); + xy=xyso3 + if(use_quaternion_in_so3.and.(.not.use_quaternion.and.dospinr)) then + call makequaternion(xy) + use_quaternion=.true. + change=.true. + endif + call alloc(m1);call alloc(nonl);call alloc(a1);call alloc(a2);call alloc(ri); + call alloc(an,ant,ker,kert) + allocate(je(nv)) + allocate(eg(xyso3%n)) + allocate(da(c_%nd)) + da=0.0_dp + + m1=xy + + ! Brings the map to the parameter dependent fixed point + ! including the coasting beam gymnastic: time-energy is canonical + ! but energy is constant. (Momentum compaction, phase slip etc.. falls from there) + ! etienne + + if(c_skip_gofix) then + a1=1 +else + call c_gofix(m1,a1) + +endif + + + m1=c_simil(a1,m1,-1) + + + + ! Does the the diagonalisation into a rotation + call c_linear_a(m1,a2) + + + + + !!! Now the linear map is normalised + m1=c_simil(a2,m1,-1) + + + !!! We go into the phasors' basis + ri=from_phasor(-1) + + m1=c_simil(ri,m1,1) + + +!stop 999 + ri=(m1.sub.-1)**(-1) + + ri%s=1 ! make spin identity + ri%q=1.0_dp ! make spin identity + + + + !!! The tunes are stored for the nonlinear normal form recursive algorithm + do k=1,xy%n + if(coast(k)) then + eg(k)=1 + else + je=0 + je(k)=1 + eg(k)=ri%v(k).sub.je + if(mod(k,2)==0) then + da(k/2)=log(abs(eg(k))) + endif + endif + enddo + + n%ker=0 ! In case reusing normal form +an=1 +ker=1 + do i=2,not +ant=1 +kert=1 + if(lielib_print(13)/=0) then + write(mdis,*) " **************************************** " + write(mdis,*) "Order ",i + write(mker,*) " **************************************** " + write(mker,*) "Order ",i + endif + + nonl=(m1*ri) + nonl= nonl*ker**(-1) !exp_inv(n%ker,nonl) +! nonl= exp_inv(n%ker,nonl) + nonl=nonl.sub.i + + + + do k=1,xy%n + if(lielib_print(13)/=0) then + write(mdis,*) " **************************************** " + write(mdis,*) "field component ",k + write(mker,*) " **************************************** " + write(mker,*) "field component ",k + endif + + ! n%g%f(i)%v(k)=0.0_dp + ! n%ker%f(i)%v(k)=0.0_dp +kerf%v(k)=0.0_dp +gf%v(k)=0.0_dp + + + j=1 + + do while(.true.) + + call c_cycle(nonl%v(k),j,v ,je); if(j==0) exit; + call check_kernel(k,xy%n,je,removeit) + + if(n%nres>0.and.removeit) then + do kr=1,n%nres + if(n%ms(kr)/=0) cycle ! a spin resonance + call check_resonance(k,xy%n,je,kr,n%m,removeit) + if(.not.removeit) then + exit + endif + enddo + endif + + if(removeit) then + + lam=1.0_dp + je(k)=je(k)-1 + do l=1,xy%n + if(coast(l)) cycle + lam=lam*eg(l)**je(l) + enddo + + if(lielib_print(13)/=0) then + write(mdis,*) k + write(mdis,'(6(1x,i4))') je(1:nd2) + write(mdis,*) v + write(mdis,*) abs(v/(1-lam)) + endif + + je(k)=je(k)+1 + + ! n%g%f(i)%v(k)=n%g%f(i)%v(k)+(v.cmono.je)/(1.0_dp-lam) + gf%v(k)=gf%v(k)+(v.cmono.je)/(1.0_dp-lam) + + else ! Put in the kernel + + if(lielib_print(13)/=0) then + je(k)=je(k)-1 + write(mker,*) k + write(mker,'(6(1x,i4))') je(1:nd2) + write(mker,*) v + write(mker,*) abs(v/(1-lam)) + je(k)=je(k)+1 + endif + kerf%v(k)=kerf%v(k)+(v.cmono.je) + endif + + enddo ! over monomial + enddo ! over vector index +!kert=exp(n%ker%f(i)) + +if(present(doberz)) then +do l=1,ant%n + kert%v(l)=kerf%v(l)+(1.0_dp.cmono.l) +enddo +else +kert=exp(kerf) +endif + +ker=kert*ker +if(present(doberz)) then +do l=1,ant%n + ant%v(l)=gf%v(l)+(1.0_dp.cmono.l) +enddo +else +ant=exp(gf) +endif +an=an*ant + m1=c_simil(ant,m1,-1) +!call c_full_norm_vector_field(n%g%f(i),norm) +!write(6,*) " old ",i,norm + enddo + + ! if(dospinr)then + ! endif + + + ! n%a_t=a1*a2*from_phasor()*texp(n%g)*from_phasor(-1) + n%a_t=a1*a2*from_phasor()*an*from_phasor(-1) + ! + n%a1=a1 + n%a2=a2 + + +!!!!! here we put the normalised linear part into the factored vector field +!!!!! not necessary but useful + + do k=1,xy%n + if(.not.coast(k)) then + je=0 + je(k)=1 + n%ker%f(1)%v(k)=n%ker%f(1)%v(k)-(log(eg(k)).cmono.je) + + if(mod(k,2)==1) then + n%tune((k+1)/2)=aimag(log(eg(k)))/twopi + n%damping((k+1)/2)=real(log(eg(k))) + if(n%tune((k+1)/2)<0.and.n%positive) n%tune((k+1)/2)=n%tune((k+1)/2)+1.0_dp + if(n%tune((k+1)/2)<-0.5_dp.and.(.not.n%positive)) n%tune((k+1)/2)=n%tune((k+1)/2)+1.0_dp + if(n%tune((k+1)/2)> 0.5_dp.and.(.not.n%positive)) n%tune((k+1)/2)=n%tune((k+1)/2)-1.0_dp + + endif + endif + enddo + + if(c_skip_gofix) then + do k=1,xy%n + if(mod(k,2)==1) then + if(n%tune((k+1)/2)>0.50_dp) n%tune((k+1)/2)=n%tune((k+1)/2)-1.0_dp + endif + enddo + endif + if(nd2t==6) then + if(n%tune(3)>0.50_dp.and.negative_synchrotron_tune) n%tune(3)=n%tune(3)-1.0_dp + endif + + if(ndpt/=0) then + je=0 + je(ndpt)=1 + lam=(ri%v(ndptb).sub.je) + n%ker%f(1)%v(ndptb)=n%ker%f(1)%v(ndptb)-(lam.cmono.je) + if(mod(ndpt,2)==0) then + n%tune(ndpt/2)=-lam + else + n%tune(ndptb/2)=-lam + endif + endif + + + if(dospinr) then + +if(use_quaternion)then + call c_full_norm_quaternion(m1%q,k,norm) +else + call c_full_norm_spin(m1%s,k,norm) +endif + if(k>=0) then + dospinr=.false. + if(use_quaternion) then + write(6,*) " no quaternion spin in map: dospin command ignored " + else + write(6,*) " no spin matrix in map: dospin command ignored " + endif + endif + endif + + + if(dospinr) then + call alloc(n0) + call alloc(nr) + call alloc(mt) + call alloc(AS) + call alloc(qnr) + n%AS=1 + + +if(use_quaternion)then + + call c_normal_spin_linear_quaternion(m1,m1,n%AS,alpha) + + n%quaternion_angle=alpha/2.0_dp + ri=1 ; ri%q=m1%q.sub.0 ; ! exp(theta_0 L_y) (2) +! sx=sqrt(ri%q%x(1)**2+ri%q%x(2)**2+ri%q%x(3)**2) +! cx=ri%q%x(0) +!write(6,*) alpha +! alpha=-(-2*atan2(sx,cx)) +!write(6,*) alpha +!pause 723 + egspin(3)=cos(alpha)-i_*sin(alpha) + egspin(2)=1.0_dp + egspin(1)=cos(alpha)+i_*sin(alpha) +else + call c_normal_spin_linear(m1,m1,n%AS,n0) ! (1) + ri=1 ; ri%s=m1%s.sub.0 ; ! exp(theta_0 L_y) (2) + egspin(3)=ri%s%s(1,1)-i_*ri%s%s(1,3) + egspin(2)=1.0_dp + egspin(1)=ri%s%s(1,1)+i_*ri%s%s(1,3) +endif + + + + + + + if(lielib_print(13)/=0) then + write(mdiss,*) " eg(1:4),spin_def_tune" ,spin_def_tune + write(mdiss,*)eg(1) + write(mdiss,*)eg(2) + write(mdiss,*)eg(3) + write(mdiss,*)eg(4) + write(mdiss,*) " egspin(1:3)" + write(mdiss,*)egspin(1) + write(mdiss,*)egspin(2) + write(mdiss,*)egspin(3) + endif + if(lielib_print(13)/=0) then + write(mkers,*) " eg(1:4),spin_def_tune" ,spin_def_tune + write(mkers,*)eg(1) + write(mkers,*)eg(2) + write(mkers,*)eg(3) + write(mkers,*)eg(4) + write(mkers,*) " egspin(1:3)" + write(mkers,*)egspin(1) + write(mkers,*)egspin(2) + write(mkers,*)egspin(3) + endif + + !!! tune is taken from egspin(1) or egspin(3) spin_def_tune= +/- 1 + n%spin_tune=aimag(log(egspin(2+spin_def_tune))/twopi) + + if(n%spin_tune <0.and.n%positive) n%spin_tune=n%spin_tune+1.0_dp + if(n%spin_tune <-0.5_dp.and.(.not.n%positive)) n%spin_tune=n%spin_tune+1.0_dp + if(n%spin_tune> 0.5_dp.and.(.not.n%positive)) n%spin_tune=n%spin_tune-1.0_dp + + + + ! because exp(a L_y) x = x- a z + O(a**2) + ri=ri**(-1) ! exp(-alpha_0 L_y) (3) + + +if(use_quaternion)then + nonl=m1.sub.1 ; nonl%q=1.0_dp ;nonl=nonl**(-1) ! R_0^-1 (4) +else + nonl=m1.sub.1 ; nonl%s=1 ;nonl=nonl**(-1) ! R_0^-1 (4) +endif +! nonl=m1.sub.1 ; nonl%s=1 ;nonl=nonl**(-1) ! R_0^-1 (4) + + + do i=1,no !+2 + if(lielib_print(13)/=0) then + write(mdiss,*) " **************************************** " + write(mdiss,*) "Order ",i + write(mkers,*) " **************************************** " + write(mkers,*) "Order ",i + endif + + + + mt=m1*ri ! S*exp(-theta_0 L_y) (5) + + +if(use_quaternion)then + n0=mt%q +else + call c_find_om_da(mt%s,n0) ! (4) +endif + + call c_n0_to_nr(n0,n0) ! n0 = > eigen-operator of spin (7) + + + + n0=n0*nonl ! no * R^-1 (8) + + + nr=0 + + do k=1,3 + if(lielib_print(13)/=0) then + write(mdiss,*) " $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ " + write(mdiss,*) "Spin component ",k + write(mdiss,*) " " + write(mkers,*) " $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ " + write(mkers,*) "Spin component ",k + write(mkers,*) " " + endif + + j=1 + do while(.true.) + call c_cycle(n0%v(k),j,v ,je); if(j==0) exit; + call check_kernel_spin1(k,xy%n,je,da,removeit) + if(n%nres>0.and.removeit) then + do kr=1,n%nres + call check_resonance_spin(k,xy%n,je,kr,n%ms,n%m,removeit) + if(.not.removeit) then + exit + endif + enddo + endif + + if(removeit) then + lam=egspin(k) + do l=1,xy%n + if(coast(l)) cycle + lam=lam*eg(l)**je(l) + enddo + + if(lielib_print(13)/=0) then + !do kr=1,nd2 + !je(kr)=-(-1)**kr*je(kr) + !enddo + write(mdiss,'(6(1x,i4))') je(1:nd2) + write(mdiss,*)lam + write(mdiss,*) v + write(mdiss,*) abs(v/(1-lam)) + !do kr=1,nd2 + !je(kr)=-(-1)**kr*je(kr) + !enddo + endif + nr%v(k)=nr%v(k) +(v.cmono.je)/(1.0_dp-lam) ! (9) + else + if(lielib_print(13)/=0) then + do kr=1,nd2 + je(kr)=-(-1)**kr*je(kr) + enddo + write(mkers,'(6(1x,i4))') je(1:nd2) + write(mkers,*) v + do kr=1,nd2 + je(kr)=-(-1)**kr*je(kr) + enddo + endif + endif + enddo ! cycle + enddo ! k + + + call c_nr_to_n0(nr,nr) ! (10) + + + + + +if(use_quaternion)then +qnr=nr + AS=1 ; +AS%q=exp(qnr) +else + AS=1 ; AS%s=exp(nr)*AS%s +endif + + + + + n%AS=n%AS*AS ! (12) + + + + m1=c_simil(AS,m1,-1) + + + enddo + + n%AS=from_phasor()*n%AS*from_phasor(-1) + + n%AS=n%A_t*n%AS*n%a_t**(-1) + + call kill(AS) + call kill(mt) + call kill(n0) + call kill(nr) + call kill(qnr) + endif + + call c_check_rad(m1%e_ij,rad_in) + if(rad_in) call c_normal_radiation(m1,n) + + ri=from_phasor() + n%n=c_simil(ri,m1,1) + n%Atot=n%as*n%a_t + + if(present(canonize)) then + if(canonize) call c_full_canonise(n%atot,n%atot) + endif + + + + if(present(rot)) then + rot=n%Atot**(-1)*xy*n%Atot + endif + + if(present(nu_spin)) nu_spin=0.0_dp + if(present(phase)) then + do i=1,size(phase) + phase(i)=0.0_dp + enddo +endif + if((present(phase).or.present(nu_spin)).and.old_phase_calculation) then + + + + if(present(rot)) then + m1=rot + else + m1=n%Atot**(-1)*xy*n%Atot + endif + + + + + qphase=.false. + call c_full_canonise(m1,a1,phase=phase,nu_spin=nu_spin) + ! if(dospinr.and.present(nu_spin)) then + ! if(real(nu_spin.sub.'0')<0) nu_spin=-nu_spin ! 2018.11.01 to match phase advance + ! endif + qphase=qphasedef + endif + +! error because m1 was reutilized in present(rot) +! call c_check_rad(m1%e_ij,rad_in) + !! if(rad_in) call c_normal_radiation(m1,n) + ! call c_check_rad(m1%e_ij,rad_in) + !! if(rad_in) call c_normal_radiation(m1,n) + + call kill(m1);call kill(nonl);call kill(a1);call kill(a2);call kill(ri); + call kill(an,ant,ker,kert); + call kill(kerf,gf) + + deallocate(eg) + deallocate(da) + deallocate(je) + + if(lielib_print(13)/=0) then + close(mker) + close(mdis) + close(mdiss) + close(mkers) + endif + + if(change) then + call makeso3(n%a1) + call makeso3(n%a2) + call makeso3(n%a_t) + call makeso3(n%atot) + call makeso3(n%as) + call makeso3(n%n) + n%a1%q=0.0_dp + n%a2%q=0.0_dp + n%a_t%q=0.0_dp + n%atot%q=0.0_dp + n%as%q=0.0_dp + n%n%q=0.0_dp + use_quaternion=.false. + endif + call kill(xy) +!call c_count_da(i_alloc) +!write(6,*) " exiting c_normal ",i_alloc +inside_normal=.false. +!!!! finding a Lie exponent + +! if(use_quaternion.and.rf==0) then + call alloc(Nf,N_cut_2,N_nl ) + Nf=n%atot**(-1)*xyso3*n%atot + N_cut_2=Nf.cut.(-2) + +! creating the linear vector field in phasors variables +ncoast=0 +if(c_%ndpt/=0) ncoast=1 +!!!! create a full vector field for N_cut_2 +do i=1,(c_%nd-ncoast) + n%H_l%v(2*i-1)=-(i_*twopi*n%tune(i))*dz_c(2*i-1)-n%damping(i)*dz_c(2*i-1) + n%H_l%v(2*i)=(i_*twopi*n%tune(i))*dz_c(2*i)-n%damping(i)*dz_c(2*i) +enddo +if(ncoast/=0) then + n%H_l%v(c_%ndptb)=n%tune(c_%nd)*dz_c(c_%ndpt) +endif +if(dospinr) then + n%H_l%q=0.0_dp + n%H_l%q%x(2)=n%quaternion_angle +endif +!!!! Going into variables moving on a circle +n%H_l=ci_phasor()*n%H_l + +!!! Reverse-Dragt-Finn order for Lie map +N_nl=N_cut_2**(-1)*nf + +n%H_nl=ln(N_nl) + +n%H_l=c_phasor()*n%H_l +n%H_nl=c_phasor()*n%H_nl + + n%H=n%H_l+n%H_nl + call kill(Nf,N_cut_2,N_nl ) +! endif + +if(.not.old_phase_calculation) then +if(present(phase)) then +! ncoast=0 + !if(c_%ndpt/=0) ncoast=1 + do i=1,c_%nd !-ncoast + phase(i)=aimag(n%h%v(2*i).k.(2*i))/twopi + enddo + + if(c_%ndptb/=0) then + phase(c_%nd)=n%h%v(c_%ndptb) ! overwrites if necessary + endif +endif + + if(present(nu_spin)) then + nu_spin=-spin_def_tune*n%h%q%x(2)/pi + nu_spin=nu_spin-(nu_spin.sub.'0')+n%spin_tune + endif +endif + + + end subroutine c_normal_new_no_fac !_with_quaternion + +real(dp) function DET(aa0) +implicit none +real(dp) aa0(:,:),aa(size(aa0,dim=1),size(aa0,dim=2)) +real(dp) tmp,c(size(aa0,dim=1),size(aa0,dim=2)) +real(dp) max + integer i,j,k,l,m,num(size(aa0,dim=1)),n + + aa=aa0 + n=size(aa,dim=1) + det=1 + do k=1,n + max=aa(k,k);num(k)=k; + do i=k+1,n + if(abs(max) 0 M_hvars = jacobian(m, HVARS) M_hparams = jacobian(m, HPARAMS) A0_12 = -inv(M_hvars-I)*M_hparams - a0 = one(m) setray!(a0.v, v_matrix=A0_12, v_matrix_offset=nv) # offset to parameters part # if we are coasting, then we need to include the effect of the variables on the time-like coordinate @@ -81,13 +86,11 @@ function normal(m::DAMap, order::Integer=maxord(m); res=nothing, spin_res=nothin # And so we can capture this just by adding the Poisson bracket. # But in the nonlinear part (where we "factorize" we have to actually exponentiate # the Poisson bracket captured in F to handle this properly.) - for i in 1:Int(nhv/2) + for i in 1:div(nhv, 2) TI.seti!(a0.v[nt], TI.geti(a0.v[2*i-1], ndpt), 2*i) TI.seti!(a0.v[nt], -TI.geti(a0.v[2*i], ndpt), 2*i-1) end end - else - a0 = I end if mo == 0 @@ -334,7 +337,7 @@ function factorize(a) t2 = zero(t1) tm = zero(t1) # set the timelike variable so poisson bracket does not change - for i in 1:Int(nhv/2) + for i in 1:div(nhv, 2) TI.clear!(tm) TI.deriv!(t1, vf.v[2*i-1], ndpt) TI.seti!(tm, 1, 2*i) @@ -477,8 +480,8 @@ function is_orbital_resonance(varidx, ords, nhv, res, spin_res) t2 = 0 for k in 1:2:nhv # ignore coasting plane - t1 += abs(ords[k]-ords[k+1]+res[Int((k+1)/2),curresidx]) - t2 += abs(ords[k]-ords[k+1]-res[Int((k+1)/2),curresidx]) + t1 += abs(ords[k]-ords[k+1]+res[div(k+1, 2),curresidx]) + t2 += abs(ords[k]-ords[k+1]-res[div(k+1, 2),curresidx]) end if t1 == 0 || t2 == 0 ords[varidx] += 1 @@ -518,8 +521,8 @@ function is_spin_resonance(spinidx, ords, nhv, res, spin_res) t2 = 0 for k in 1:2:nhv # ignore coasting plane - t1 += abs(ords[k]-ords[k+1]+res[Int((k+1)/2),curresidx]) - t2 += abs(ords[k]-ords[k+1]-res[Int((k+1)/2),curresidx]) + t1 += abs(ords[k]-ords[k+1]+res[div(k+1, 2),curresidx]) + t2 += abs(ords[k]-ords[k+1]-res[div(k+1, 2),curresidx]) end m = spin_res[curresidx] @@ -598,11 +601,12 @@ end # Returns the rotation map to put a in Courant Snyder form # The phase advance can be acquired from this map by atan(r11,r22), etc etc function canonize( - a::DAMap, + a::DAMap{V0}, ::Val{linear}=Val{true}(); - phase=nothing, - damping::Bool=!isnothing(a.s) -) where {linear} + phase=nothing, + damping::Bool=!isnothing(a.s), + damp=nothing +) where {V0<:StaticArray,linear} nv = nvars(a) nhv = nhvars(a) coast = iscoasting(a) @@ -612,7 +616,7 @@ function canonize( if linear a_matrix = real.(jacobian(a, VARS)) canonizer = zero(a) - for i in 1:Int(nhv/2) # for each harmonic oscillator + for i in 1:div(nhv, 2) # for each harmonic oscillator t = sqrt(a_matrix[2*i-1,2*i-1]^2 + a_matrix[2*i-1,2*i]^2) cphi = a_matrix[2*i-1,2*i-1]/t sphi = a_matrix[2*i-1,2*i]/t @@ -640,8 +644,6 @@ function canonize( phase[end] += -TI.geti(a.v[nt], ndpt) end end - #a_rot = a_matrix*ri - #return a_rot # Now we have rotated a so that a_12, a_34, a_56, etc are 0 (Courant Snyder) # But if we have damping, we also have @@ -649,28 +651,41 @@ function canonize( # We can multiply the normalizing map A by some dilation to make it so that, # even though we don't have exactly A*S*transpose(A) == S, that # we atleast have (A*S*transpose(A))[1,2] == 1, (A*S*transpose(A))[2,1] == -1, etc + # NOTE THAT THIS IS NOT 0 FOR "SYMPLECTIC ANGLE" BETWEEN EIGENVECTORS THO! # note that with damping we have M as # A*Λ*R*A^-1 where R is the amplitude dependent rotation (diagonal matrix with # complex values on unit circle) and Λ is a diagonal matrix with real values # which correspond to the damping (same in each plane, Diagonal(lambda1, lambda1, lambda2, lambda2, etc) + # Basically want to multiply the matrix A by some diagonal real matrix D so that + # (AD)*S*transpose(AD) = S + # So we have to include this in the canonizer if damping - error("Canonization including damping is not implemented yet") - damp = zeros(Int(nvars(a)/2)) - tmp = zeros(Int(nvars(a)/2), Int(nvars(a)/2)) - for i in 1:Int(nvars(a)/2) - tmp[i,i] = a_rot[2*i-1,2*i-1]*a_rot[2*i,2*i]-a_rot[2*i-1,2*i]*a_rot[2*i,2*i-1] - for j in 1:Int(nvars(a)/2) - if i != j - tmp[i,j] = a_rot[2*i-1,2*j-1]*a_rot[2*i,2*j]-a_rot[2*i-1,2*j]*a_rot[2*i,2*j-1] - end + if coast + error("Canonization including damping and coasting beam is not supported") + end + #a_matrix = jacobian(a, VARS)*jacobian(canonizer, VARS) + tmp = StaticArrays.sacollect(SMatrix{div(nhv, 2),div(nhv, 2)}, begin + a_matrix[2*i-1,2*j-1]*a_matrix[2*i,2*j]-a_matrix[2*i-1,2*j]*a_matrix[2*i,2*j-1] + end for j in 1:div(nhv, 2) for i in 1:div(nhv, 2)) + tmp2 = inv(tmp) + + dampt = sqrt.(sum(tmp2, dims=2)) + Λi = StaticArrays.sacollect(SMatrix{nhv,nhv}, begin + if j == i + dampt[floor(Int, (i-1)/2)+1] + else + 0 end + end for j in 1:nhv for i in 1:nhv) + + # now multiply canonizer matrix by this one + a_rot = jacobian(canonizer, VARS)*Λi + if !isnothing(damp) + damp .+= log.(dampt) end - tmp = inv(tmp) - damp .= sqrt.(sum(tmp, dims=2)) - a_rot = a_rot*Diagonal(repeat(damp,inner=2)) - damp .= log.(damp) + setray!(canonizer.v, v_matrix=a_rot) end return canonizer else @@ -679,7 +694,7 @@ function canonize( id = one(a) lin_canonizer = zero(a) # linear part separately to speed up exponent canonizerf = zero(VectorField, a) - for i in 1:Int(nhv/2) # for each harmonic oscillator + for i in 1:div(nhv, 2) # for each harmonic oscillator # Need to include parameter dependence if nonlinear, so "var-par" t1 = fast_var_slice(a.v[2*i-1], 2*i-1, nv; par=true) t2 = fast_var_slice(a.v[2*i-1], 2*i, nv; par=true) @@ -719,8 +734,7 @@ function canonize( # so for time like variable we have # -\partial_\delta (mu_x(delta)(x^2+px^2) + mu_y(delta)(y^2+py^2)) # = -dmu_x/ddelta*(x^2+px^2) - dmu_y/ddelta(y^2+py^2) - for i in 1:Int(nhv/2) - #TI.add!(canonizerf.v[nt], canonizerf.v[nt], tm) + for i in 1:div(nhv, 2) TI.clear!(tmp3) TI.deriv!(tmp1, canonizerf.v[2*i-1], ndpt) TI.seti!(tmp3, 1, 2*i) @@ -749,34 +763,74 @@ function canonize( # set linear part to zero for nonlinear part TI.seti!(slip, 0, ndpt) TI.add!(canonizerf.v[nt], canonizerf.v[nt], -slip) - - #= - TI.seti!(canonizer.v[nt], 1, nt) - TI.seti!(canonizer.v[ndpt], 1, ndpt) - TI.seti!(canonizer.v[nt], -TI.geti(a.v[nt], ndpt), ndpt) - if !isnothing(phase) - phase[end] += -TI.geti(a.v[nt], ndpt) - end - =# end + # linear === + # AS IN THIS IS NOT COMPLETE IN THE ===== + # IT WAS COPIED FROM LINEAR AND I STARTED IT BUT DON'T HAVE TIME RN if damping - error("Canonization including damping is not implemented yet") - damp = zeros(Int(nvars(a)/2)) - tmp = zeros(Int(nvars(a)/2), Int(nvars(a)/2)) - for i in 1:Int(nvars(a)/2) - tmp[i,i] = a_rot[2*i-1,2*i-1]*a_rot[2*i,2*i]-a_rot[2*i-1,2*i]*a_rot[2*i,2*i-1] - for j in 1:Int(nvars(a)/2) - if i != j - tmp[i,j] = a_rot[2*i-1,2*j-1]*a_rot[2*i,2*j]-a_rot[2*i-1,2*j]*a_rot[2*i,2*j-1] - end + if coast + error("Canonization including damping and coasting beam is not supported") + end + + error("Nonlinear canonization including damping not implemented yet") + # Note: here are are doing something a bit strange + # We need to invert a (nhv/2) x (nhv/2) MAP (for linear we can do matrix) + # Therefore we will so something a bit strange + tmpmap = one(canonizer) + tmp1 = zero(tmpmap.v[1]) + tmp2 = zero(tmpmap.v[1]) + tmp3 = zero(tmpmap.v[1]) + tmp4 = zero(tmpmap.v[1]) + + for i in 1:div(nhv, 2) + TI.clear!(tmpmap.v[i]) + for j in 1:div(nhv, 2) + TI.clear!(tmp1) + TI.clear!(tmp2) + TI.clear!(tmp3) + TI.clear!(tmp4) + fast_var_slice!(tmp1, a.v[2*i-1], 2*j-1, nhv; par=true) + fast_var_slice!(tmp2, a.v[2*i], 2*j, nhv; par=true) + TI.mul!(tmp3, tmp1, tmp2) + TI.clear!(tmp1) + TI.clear!(tmp2) + fast_var_slice!(tmp1, a.v[2*i-1], 2*j, nhv; par=true) + fast_var_slice!(tmp2, a.v[2*i], 2*j-1, nhv; par=true) + TI.mul!(tmp4, tmp1, tmp2) + TI.clear!(tmp1) + TI.sub!(tmp1, tmp3, tmp4) + TI.clear!(tmp2) + TI.cutord!(tmp2, tmp1, mo) + TI.factor_in!(tmpmap.v[i], tmp2, j) end end - tmp = inv(tmp) - damp .= sqrt.(sum(tmp, dims=2)) - a_rot = a_rot*Diagonal(repeat(damp,inner=2)) - damp .= log.(damp) + #= + tmp = StaticArrays.sacollect(SMatrix{div(nhv, 2),div(nhv, 2)}, begin + a_matrix[2*i-1,2*j-1]*a_matrix[2*i,2*j]-a_matrix[2*i-1,2*j]*a_matrix[2*i,2*j-1] + end for j in 1:div(nhv, 2) for i in 1:div(nhv, 2)) + =# + tmp2 = inv(tmpmap) + + dampt = sqrt.(sum(tmp2, dims=2)) + Λi = StaticArrays.sacollect(SMatrix{nhv,nhv}, begin + if j == i + dampt[floor(Int, (i-1)/2)+1] + else + 0 + end + end for j in 1:nhv for i in 1:nhv) + + # now multiply canonizer matrix by this one + a_rot = jacobian(canonizer, VARS)*Λi + if !isnothing(damp) + damp .+= log.(dampt) + end + setray!(canonizer.v, v_matrix=a_rot) end + return canonizer + # linear === + return lin_canonizer ∘ exp(canonizerf, id) end end diff --git a/src/sagan_rubin.jl b/src/sagan_rubin.jl index 110cfe6..1a04538 100644 --- a/src/sagan_rubin.jl +++ b/src/sagan_rubin.jl @@ -34,34 +34,34 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V if linear if !coast let a1_mat = jacobian(a1, HVARS), a1i_mat = inv(a1_mat), nvm = nv-2 - H = StaticArrays.sacollect(SVector{Int(nv/2),typeof(a1_mat)}, a1_mat*ip_mat(a1, i)*a1i_mat for i in 1:Int(nv/2)) + H = StaticArrays.sacollect(SVector{div(nv, 2),typeof(a1_mat)}, a1_mat*ip_mat(a1, i)*a1i_mat for i in 1:div(nv, 2)) gamma_c = sqrt(H[1][1,1]) C = nv > 2 ? StaticArrays.sacollect(SMatrix{2,2,eltype(H[1])}, -H[1][row,col]/gamma_c for col in 3:4 for row in 1:2) : 0 Ct = nv > 2 ? SA[C[2,2] -C[1,2]; -C[2,1] C[1,1]] : 0 Vi = gamma_c*I + vcat(hcat(zero(C), -C), hcat(Ct, zero(Ct))) N = Vi*StaticArrays.sacollect(SMatrix{nvm,nvm,eltype(a1_mat)}, a1_mat[row,col] for col in 1:nvm for row in 1:nvm) - beta = StaticArrays.sacollect(SVector{Int(nvm/2),eltype(N)}, N[i,i]^2 for i in 1:2:Int(nvm)) - alpha = StaticArrays.sacollect(SVector{Int(nvm/2),eltype(N)}, -N[i+1,i]*N[i,i] for i in 1:2:Int(nvm)) + beta = StaticArrays.sacollect(SVector{div(nvm, 2),eltype(N)}, N[i,i]^2 for i in 1:2:nvm) + alpha = StaticArrays.sacollect(SVector{div(nvm, 2),eltype(N)}, -N[i+1,i]*N[i,i] for i in 1:2:nvm) # Note that eta and zeta here are in x,px,y,py, not in a,pa,b,pb eta = StaticArrays.sacollect(SVector{nvm,eltype(H[1])}, H[end][i,nv] for i in 1:(nvm)) zeta = StaticArrays.sacollect(SVector{nvm,eltype(H[1])}, H[end][i,nv-1] for i in 1:(nvm)) # we also return B[3][5,6], which can then be multiplied by sin(mu_3) to approximate the # phase slip - approx_slip = (a1_mat*jp_mat(a1, Int(nv/2))*a1i_mat)[5,6] + approx_slip = (a1_mat*jp_mat(a1, div(nv, 2))*a1i_mat)[5,6] # I don't really understand the utility of this, but for consistency with Sagan-Rubin # multiply by Vi to put in "normalized" coordinates return (; beta=beta, alpha=alpha, gamma_c=gamma_c, C=C, eta=Vi*eta, zeta=Vi*zeta, approx_slip=approx_slip) end else let a1_mat = jacobian(a1, HVARS), a1i_mat = inv(a1_mat) - H = StaticArrays.sacollect(SVector{Int(nhv/2),typeof(a1_mat)}, a1_mat*ip_mat(a1, i)*a1i_mat for i in 1:Int(nhv/2)) + H = StaticArrays.sacollect(SVector{div(nhv, 2),typeof(a1_mat)}, a1_mat*ip_mat(a1, i)*a1i_mat for i in 1:div(nhv, 2)) gamma_c = sqrt(H[1][1,1]) C = nv > 2 ? StaticArrays.sacollect(SMatrix{2,2,eltype(H[1])}, -H[1][row,col]/gamma_c for col in 3:4 for row in 1:2) : 0 Ct = nv > 2 ? SA[C[2,2] -C[1,2]; -C[2,1] C[1,1]] : 0 Vi = gamma_c*I + vcat(hcat(zero(C), -C), hcat(Ct, zero(Ct))) N = Vi*StaticArrays.sacollect(SMatrix{nhv,nhv,eltype(a1_mat)}, a1_mat[row,col] for col in 1:nhv for row in 1:nhv) - beta = StaticArrays.sacollect(SVector{Int(nhv/2),eltype(N)}, N[i,i]^2 for i in 1:2:nhv) - alpha = StaticArrays.sacollect(SVector{Int(nhv/2),eltype(N)}, -N[i+1,i]*N[i,i] for i in 1:2:nhv) + beta = StaticArrays.sacollect(SVector{div(nhv, 2),eltype(N)}, N[i,i]^2 for i in 1:2:nhv) + alpha = StaticArrays.sacollect(SVector{div(nhv, 2),eltype(N)}, -N[i+1,i]*N[i,i] for i in 1:2:nhv) return (; beta=beta, alpha=alpha, gamma_c=gamma_c, C=C) end end @@ -70,10 +70,10 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V let nvm = nv-2 tmp = zero(a1) a1i = inv(a1) - H = StaticArrays.sacollect(SVector{Int(nhv/2)}, begin + H = StaticArrays.sacollect(SVector{div(nhv, 2)}, begin setray!(tmp.v, v_matrix=ip_mat(a1, i)) a1∘tmp∘a1i - end for i in 1:Int(nhv/2) + end for i in 1:div(nhv, 2) ) mo = maxord(a1) gamma_c = TI.cutord(sqrt(factor_out(H[1].v[1], 1)), mo) @@ -81,8 +81,8 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V Ct = nv > 2 ? SA[C[2,2] -C[1,2]; -C[2,1] C[1,1]] : 0 Vi = gamma_c*I + vcat(hcat(zero(C), -C), hcat(Ct, zero(Ct))) N = TI.cutord.(Vi*StaticArrays.sacollect(SMatrix{nvm,nvm,eltype(a1.v)}, factor_out(a1.v[row], col) for col in 1:nvm for row in 1:nvm), mo) - beta = StaticArrays.sacollect(SVector{Int(nvm/2),eltype(N)}, TI.cutord(N[i,i]^2, mo) for i in 1:2:Int(nvm)) - alpha = StaticArrays.sacollect(SVector{Int(nvm/2),eltype(N)}, TI.cutord(-N[i+1,i]*N[i,i], mo) for i in 1:2:Int(nvm)) + beta = StaticArrays.sacollect(SVector{div(nvm, 2),eltype(N)}, TI.cutord(N[i,i]^2, mo) for i in 1:2:nvm) + alpha = StaticArrays.sacollect(SVector{div(nvm, 2),eltype(N)}, TI.cutord(-N[i+1,i]*N[i,i], mo) for i in 1:2:nvm) # Note that eta and zeta here are in x,px,y,py, not in a,pa,b,pb eta = StaticArrays.sacollect(SVector{nvm,eltype(H[1].v)}, factor_out(H[end].v[i], nv) for i in 1:(nvm)) zeta = StaticArrays.sacollect(SVector{nvm,eltype(H[1].v)}, factor_out(H[end].v[i], nv-1) for i in 1:(nvm)) @@ -102,10 +102,10 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V let tmp = zero(a1) a1i = inv(a1) - H = StaticArrays.sacollect(SVector{Int(nhv/2)}, begin + H = StaticArrays.sacollect(SVector{div(nhv, 2)}, begin setray!(tmp.v, v_matrix=ip_mat(a1, i)) a1∘tmp∘a1i - end for i in 1:Int(nhv/2) + end for i in 1:div(nhv, 2) ) mo = maxord(a1) gamma_c = TI.cutord(sqrt(factor_out(H[1].v[1], 1)), mo) @@ -113,8 +113,8 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V Ct = nv > 2 ? SA[C[2,2] -C[1,2]; -C[2,1] C[1,1]] : 0 Vi = gamma_c*I + vcat(hcat(zero(C), -C), hcat(Ct, zero(Ct))) N = TI.cutord.(Vi*StaticArrays.sacollect(SMatrix{nhv,nhv,eltype(a1.v)}, factor_out(a1.v[row], col) for col in 1:nhv for row in 1:nhv), mo) - beta = StaticArrays.sacollect(SVector{Int(nhv/2),eltype(N)}, TI.cutord(N[i,i]^2, mo) for i in 1:2:Int(nhv)) - alpha = StaticArrays.sacollect(SVector{Int(nhv/2),eltype(N)}, TI.cutord(-N[i+1,i]*N[i,i], mo) for i in 1:2:Int(nhv)) + beta = StaticArrays.sacollect(SVector{div(nhv, 2),eltype(N)}, TI.cutord(N[i,i]^2, mo) for i in 1:2:nhv) + alpha = StaticArrays.sacollect(SVector{div(nhv, 2),eltype(N)}, TI.cutord(-N[i+1,i]*N[i,i], mo) for i in 1:2:nhv) return (; beta=beta, alpha=alpha, gamma_c=gamma_c, C=C) end end diff --git a/src/utils.jl b/src/utils.jl index eee6900..53203e1 100644 --- a/src/utils.jl +++ b/src/utils.jl @@ -76,6 +76,8 @@ fast_var_slice(t, var::Int, nv::Int; par::Bool=false, all_ords::Bool=false) = (o # This will par out the polynomial with only # 1st order dependence on variable, nonlinear # parameter dependence +# all_ords means beyond first order variable dependence +# par removes a variable function fast_var_slice!(out, t, var::Int, nv::Int; par::Bool=false, all_ords::Bool=false) TI.is_tps_type(typeof(t)) isa TI.IsTPSType || error("Function only accepts TPS types") TI.is_tps_type(typeof(out)) isa TI.IsTPSType || error("Function only accepts TPS types") @@ -230,7 +232,7 @@ function ci_jacobian(m::TaylorMap{V0,V,Q,S}, ::T=VARS) where {V0,V,Q,S,T<:Union{ n = T == HarmonicVariables ? nhv : nv CI = similar(m.v0, complex(eltype(m.v0)), n, n) CI .= 0 - for i in 1:Int(nhv/2) + for i in 1:div(nhv, 2) # x_new = 1/sqrt(2)*(v+im*p) CI[2*i-1,2*i-1] = 1/sqrt(2) CI[2*i-1,2*i] = complex(0,1/sqrt(2)) @@ -295,7 +297,7 @@ function c_jacobian(m::TaylorMap{V0,V,Q,S}, ::T=VARS) where {V0,V,Q,S,T<:Union{H n = T == HarmonicVariables ? nhv : nv C = similar(m.v0, complex(eltype(m.v0)), n, n) C .= 0 - for i in 1:Int(nhv/2) + for i in 1:div(nhv, 2) C[2*i-1,2*i-1] = 1/sqrt(2) C[2*i-1,2*i] = 1/sqrt(2) diff --git a/test/.ipynb_checkpoints/Untitled-checkpoint.ipynb b/test/.ipynb_checkpoints/Untitled-checkpoint.ipynb new file mode 100644 index 0000000..363fcab --- /dev/null +++ b/test/.ipynb_checkpoints/Untitled-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/test/.ipynb_checkpoints/canonize_rad3-checkpoint.ipynb b/test/.ipynb_checkpoints/canonize_rad3-checkpoint.ipynb new file mode 100644 index 0000000..c35e9a8 --- /dev/null +++ b/test/.ipynb_checkpoints/canonize_rad3-checkpoint.ipynb @@ -0,0 +1,214 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 7, + "id": "d7186c9a-6d16-4e6d-8d5b-0431822f3323", + "metadata": {}, + "outputs": [], + "source": [ + "using Revise\n", + "using NonlinearNormalForm, TPSAInterface, GTPSA, JET, BenchmarkTools\n", + "import TPSAInterface as TI\n", + "import NonlinearNormalForm as NNF\n", + "using LinearAlgebra" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "5826f509-423e-4f25-89d6-65f2405a24a6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0e-9" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "GTPSA.show_eps=1e-9" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "8019c020-2efb-4aae-82c7-02c486d43cb9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "read_fpp_map (generic function with 1 method)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"test/readfpp.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ccfff21d-4873-430b-974e-24bc23a35089", + "metadata": {}, + "outputs": [], + "source": [ + "m = real(read_fpp_map(\"test/canonize_rad3/test.map\", spin=false, stochastic=false));\n", + "ac_norad_fpp = real(read_fpp_map(\"test/canonize_rad3/ac_norad.map\", spin=false, stochastic=false));\n", + "#ac_fpp = real(read_fpp_map(\"test/canonize_rad3/ac.map\", spin=false, stochastic=false));" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "8e958ba8-d3b5-4f79-be50-e21cb242160b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4.2092546059575386e-15" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = normal(m)\n", + "ac_norad = a∘canonize(a)\n", + "norm(NNF.jacobian(ac_norad-ac_norad_fpp))" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "8e7c9272-7d37-455d-a61f-4520044f229c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7.021651535476685e-16" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ac = a∘canonize(a; damping=true)\n", + "a_end = m∘ac\n", + "damp=zeros(3)\n", + "ac_end = a_end∘canonize(a_end; damping=true, damp=damp)\n", + "norm(damp-[0.1531583287271725E-05, 0.2817861217457402E-05, 0.2142167833506887E-05])" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "d2785066-6105-4752-9030-a9f00e94e4db", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.084545602475685e-15" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "norm(NNF.jacobian(ac_end - ac))" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "92af3f73-7715-4749-b3dc-b276486fb610", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-1.5315832873166573e-6 - 2.366801815732135im" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = c_map(a)\n", + "reallog((inv(c)∘inv(ac_norad)∘m∘ac_norad∘c).v[1][1])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "effb66e9-f812-4f78-a8bf-bf1a61821ca7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 5.6974835447389954e-8\n", + " -2.1736512048935732e-8\n", + " -3.55658602232123e-8" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "\n", + "damp" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0e7858db-c6dc-4df9-9606-cd3a81561c41", + "metadata": {}, + "outputs": [], + "source": [ + "0.1531583287271725E-05 0.2817861217457402E-05 0.2142167833506887E-05" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/test/Untitled.ipynb b/test/Untitled.ipynb new file mode 100644 index 0000000..9f4fae5 --- /dev/null +++ b/test/Untitled.ipynb @@ -0,0 +1,198 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "3f298f09-b988-4d37-87c0-78947945ca37", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m packages...\n", + " 692.0 ms\u001b[32m ✓ \u001b[39mNonlinearNormalForm\n", + " 1 dependency successfully precompiled in 1 seconds. 10 already precompiled.\n", + "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m packages...\n", + " 809.7 ms\u001b[32m ✓ \u001b[39mNonlinearNormalForm → NonlinearNormalFormGTPSAExt\n", + " 1 dependency successfully precompiled in 1 seconds. 33 already precompiled.\n" + ] + } + ], + "source": [ + "using Revise\n", + "using NonlinearNormalForm, TPSAInterface, GTPSA, JET, BenchmarkTools\n", + "import TPSAInterface as TI\n", + "import NonlinearNormalForm as NNF\n", + "using LinearAlgebra" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "12e689f9-60b7-497b-82aa-c703e4ec55ef", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0e-9" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "GTPSA.show_eps=1e-9" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "1c7f94cc-8da7-4705-b696-d6d70f51e3bb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "read_fpp_map (generic function with 1 method)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"readfpp.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b093e110-27da-4840-a707-663c2d3c82b0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "true" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m = read_fpp_map(\"spin1/test.map\")\n", + "a_fpp = include(\"spin1/a.jl\")\n", + "r_fpp = read_fpp_map(\"spin1/R.map\")\n", + "c = c_map(m)\n", + "a = normal(m,res=[0; 1], spin_res=[-1])\n", + "norm(TI.norm_tps.((inv(c)*inv(a)*m*a*c).v .- r_fpp.v)) < 4e-9" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "1feb39c2-647e-4882-bd0c-f113c414f341", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "DAMap{StaticArraysCore.MVector{4, ComplexF64}, StaticArraysCore.MVector{4, ComplexTPS64{Descriptor(NV=4, MO=3)}}, Quaternion{ComplexTPS64{Descriptor(NV=4, MO=3)}}, Nothing}(ComplexF64[0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im], 4-element StaticArraysCore.MVector{4, ComplexTPS64{Descriptor(NV=4, MO=3)}}:\n", + " Index Real Imag Order Exponent\n", + "--------------------------------------------------------------------------------\n", + " 1: 4.8678129941965171e-05 0.0000000000000000e+00 0 0 0 0 ⋯\n", + " 1: -3.1963072438129640e+00 0.0000000000000000e+00 1 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0.0000000000000000e+00 3 1 1 1 ⋯\n", + " ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱\n", + "\u001b[36m 2 columns and 119 rows omitted\u001b[0m\n", + ", nothing)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "R_rot = jacobian(a, NonlinearNormalForm.HVARS)\\jacobian(a_fpp, NonlinearNormalForm.HVARS) \n", + "r_rot = one(a_fpp)\n", + "NonlinearNormalForm.setray!(r_rot.v, v_matrix=R_rot)\n", + "a = a ∘ r_rot" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6e318e4a-0797-4a29-aeda-246dd39d8b7f", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/test/canonize_rad-Copy1.ipynb b/test/canonize_rad-Copy1.ipynb new file mode 100644 index 0000000..c10acc8 --- /dev/null +++ b/test/canonize_rad-Copy1.ipynb @@ -0,0 +1,479 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 37, + "id": "0d376b20-40c6-4722-8a9a-61975bad5c9d", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m packages...\n", + " 345.7 ms\u001b[32m ✓ \u001b[39m\u001b[90mAccessors → TestExt\u001b[39m\n", + " 1 dependency successfully precompiled in 1 seconds. 11 already precompiled.\n", + "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m packages...\n", + " 342.3 ms\u001b[32m ✓ \u001b[39m\u001b[90mRecursiveArrayTools → RecursiveArrayToolsStatisticsExt\u001b[39m\n", + " 1 dependency successfully precompiled in 0 seconds. 30 already precompiled.\n" + ] + } + ], + "source": [ + "using Revise\n", + "using NonlinearNormalForm, BeamTracking, Beamlines, GTPSA\n", + "import NonlinearNormalForm as NNF\n", + "using JET, BenchmarkTools\n", + "using SciBmad" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "7e0afcee-4bb6-46c8-b36f-8c17fa436a3a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6-element Vector{Float64}:\n", + " -2.6000686032132613e-7\n", + " 1.5303928131191435e-5\n", + " -3.556902826710349e-9\n", + " 3.9231617960303014e-8\n", + " -0.02704383542507716\n", + " -0.0003522717640595932" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"../SciBmad/lattices/esr-v6.3.1.jl\");\n", + "# Set RF for 0.05 synch tune (from previous optimization)\n", + "cavities = ring.line[findall(x->x.kind==\"RFCavity\", ring.line)];\n", + "foreach(x->x.voltage=3.355606790694894e6, cavities);\n", + "\n", + "# Set all elements radiation damping, second order Yoshida\n", + "foreach(x->x.tracking_method=Yoshida(order=2, radiation_damping_on=true), ring.line);\n", + "\n", + "t = twiss(ring)\n", + "co = [t.orbit_x[1], t.orbit_px[1], t.orbit_y[1], t.orbit_py[1], t.orbit_z[1], t.orbit_pz[1]]\n", + "# Closed orbit from previous check:\n", + "#co = [-2.6000686032132613e-7, 1.5303928131191435e-5, -3.556902826710349e-9, 3.9231617960303014e-8, -0.02704383542507716, -0.0003522717640595932];" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "66edee15-0027-4c2d-9e40-88540b921c64", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Setting bunch.species = Species(electron, charge=-1.0e, mass=510998.95069 eV/c², spin=0.5ħ) (reference species from the Beamline)\n", + "Setting bunch.R_ref = -59.5287244902766 (reference R_ref from the Beamline)\n" + ] + }, + { + "data": { + "text/plain": [ + "true" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d4 = Descriptor(6, 4);\n", + "b0 = Bunch(co+vars(d4));\n", + "track!(b0, ring);\n", + "m = DAMap(v0=co, v=b0.coords.v)\n", + "norm(scalar.(m.v) .- co) < 1e-12 || println(\"not on closed orbit\")" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "eda0dab2-567f-49c4-bd76-7d55895cf07e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.590660168880395\n", + "Setting bunch.species = Species(electron, charge=-1.0e, mass=510998.95069 eV/c², spin=0.5ħ) (reference species from the Beamline)\n", + "Setting bunch.R_ref = -59.5287244902766 (reference R_ref from the Beamline)\n", + "0.5906601688803629\n" + ] + } + ], + "source": [ + "# Check symplectic error:\n", + "a = normal(m)\n", + "a0, a1, a2 = factorize(a)\n", + "ac = a ∘ canonize(a1, damping=true);\n", + "a0, a1, a2 = factorize(ac)\n", + "println(compute_sagan_rubin(a1, Val{true}()).beta[1])\n", + "ba = Bunch(ac.v[1:6])\n", + "track!(ba, ring)\n", + "a_end = DAMap(v=ba.coords.v)\n", + "damp = [0.,0.,0.]\n", + "ac_end = a_end∘canonize(a_end, damping=true, damp=damp)\n", + "a0end, a1end, a2end = factorize(ac_end)\n", + "println(compute_sagan_rubin(a1end, Val{true}()).beta[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "72d296f7-2e22-4f01-aee4-0076d2ca417d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 0.0010461401064894994\n", + " 0.0010538510381837948\n", + " 0.002115411357111029" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "damp" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "f5ab98cb-ebf4-4736-b7bd-d692ad6b8afc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " -4.8693687970668975e-15\n", + " 4.908540674614104e-10\n", + " -2.454139677934841e-10" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = c_map(a)\n", + "r = inv(c)*inv(a)*m*a*c\n", + "damp+[real(log(r.v[2][2])), real(log(r.v[4][4])), real(log(r.v[6][6]))]" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "6b431774-bd11-4dfc-833a-64a1e9c0a59e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "\u001b[92mNo errors detected\u001b[39m\n" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "@report_opt canonize(a1,damping=true,damp=damp)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "387f653a-65f2-4cfa-ba61-5d7d86b83bce", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6-element StaticArraysCore.SVector{6, Float64} with indices SOneTo(6):\n", + " -2.093187819254827e-16\n", + " 1.3822561259653476e-16\n", + " 5.995405079784345e-20\n", + " 1.7336713022376396e-18\n", + " 1.056932319443149e-13\n", + " 2.770732861895331e-15" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "NNF.getscalar(a0∘a1∘a2)-co" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "99b04451-d62d-4eed-9e0d-31b1d7f9a513", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6-element StaticArraysCore.MVector{6, Float64} with indices SOneTo(6):\n", + " -6.169199653776737e-6\n", + " -1.4400708388299533e-5\n", + " 8.68066056709423e-9\n", + " -1.0499466453552429e-7\n", + " 0.02508424340287435\n", + " 0.0010955002803866903" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a_end2 = DAMap(v0=co,v=ba.coords.v)\n", + "scalar.(a_end2.v) - co" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "be522bbf-2048-4f3e-b328-7fd708629f44", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6×6 StaticArraysCore.SMatrix{6, 6, Float64, 36} with indices SOneTo(6)×SOneTo(6):\n", + " 0.691096 0.33439 0.000609166 … -0.00021779 0.00484671\n", + " -0.498014 1.20303 -0.001456 0.00580697 0.00109282\n", + " -0.000155324 -0.000291939 0.139188 4.63464e-7 1.80551e-6\n", + " -0.00129553 -0.00170724 -3.36416 3.16731e-6 -6.26364e-5\n", + " -0.00640813 0.0043149 -1.39552e-5 2.77704 -0.791761\n", + " -0.000705994 0.000194329 -9.7348e-9 … 0.0829852 0.334915" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "NNF.jacobian(a_end)" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "id": "ca132cbd-7f45-4ce4-9b42-b54681051494", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.590660168880395" + ] + }, + "execution_count": 89, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "scalar(compute_sagan_rubin(factorize(a).a1∘canonize(factorize(a).a1,damping=true)).beta[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "id": "50b10794-6ccc-4db6-ad0f-d5848ee59048", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.590660168880395" + ] + }, + "execution_count": 86, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "scalar(compute_sagan_rubin(a1∘r_c).beta[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "id": "55544a66-17f8-48de-ac45-cd456a265010", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5866968053123066" + ] + }, + "execution_count": 91, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b0.coords.v .= view((a∘r_c).v, 1:6)'\n", + "#b0 = Bunch((co+a.v)');\n", + "track!(b0, ring);\n", + "aend = DAMap(v=b0.coords.v)\n", + "dampend = zeros(3)\n", + "rend = canonize(aend, damping=true, damp=dampend);\n", + "a0e, a1e, a2e = factorize(aend∘rend)\n", + "scalar(compute_sagan_rubin(factorize(aend).a1∘canonize(factorize(aend).a1,damping=true)).beta[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "e691ef6c-f3df-4af2-9d65-da31a19ac943", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 0.0008124780226362984\n", + " 0.0010549097317526213\n", + " 0.002351194915378987" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phase = [0.,0.,0.]\n", + "rend = canonize(aend, phase=phase, damping=true, damp=dampend);\n", + "dampend" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "3b399ded-000f-47fa-9a95-d10e4ad816c8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 0.0700700373959855\n", + " 0.15344937330719371\n", + " -0.04382444058656845" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phase" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "32439acd-a59e-4cc4-961d-1eb3f7694150", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6×6 StaticArraysCore.SMatrix{6, 6, ComplexF64, 36} with indices SOneTo(6)×SOneTo(6):\n", + " 0.899224-0.435093im … 5.04549e-18+1.43746e-18im\n", + " 9.99201e-16+1.94289e-16im -1.38955e-19+2.81743e-18im\n", + " 1.06005e-16-1.30363e-17im 1.94005e-18-4.95366e-17im\n", + " -6.81705e-17-7.37268e-17im 6.83323e-17+5.58629e-17im\n", + " -2.37277e-17+5.2132e-18im -1.66533e-16-3.05311e-16im\n", + " -2.93242e-17+6.59316e-18im … 0.959645-0.273604im" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "NNF.jacobian(ci_map(a)*inv(a)*m*a*c_map(a))" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "id": "696a6540-7dcb-482e-a4b3-d3aa334e2bc5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.0 + 0.0717227709692705im" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + " imag(log(0.899224-0.435093im ))/(2*pi*im)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5e6b05eb-9507-4460-b767-c2029c8f2c50", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/test/canonize_rad.ipynb b/test/canonize_rad.ipynb new file mode 100644 index 0000000..8a2b695 --- /dev/null +++ b/test/canonize_rad.ipynb @@ -0,0 +1,380 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 191, + "id": "0d376b20-40c6-4722-8a9a-61975bad5c9d", + "metadata": {}, + "outputs": [], + "source": [ + "using Revise\n", + "using NonlinearNormalForm, TPSAInterface, GTPSA, JET, BenchmarkTools\n", + "import TPSAInterface as TI\n", + "import NonlinearNormalForm as NNF\n", + "using LinearAlgebra" + ] + }, + { + "cell_type": "code", + "execution_count": 192, + "id": "7e0afcee-4bb6-46c8-b36f-8c17fa436a3a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0e-9" + ] + }, + "execution_count": 192, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "GTPSA.show_eps=1e-9" + ] + }, + { + "cell_type": "code", + "execution_count": 193, + "id": "8912351a-4bf9-49f6-83f4-502a7ef2a7a7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "read_fpp_map (generic function with 1 method)" + ] + }, + "execution_count": 193, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"test/readfpp.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 194, + "id": "5e6b05eb-9507-4460-b767-c2029c8f2c50", + "metadata": {}, + "outputs": [], + "source": [ + "m = real(read_fpp_map(\"test/canonize_rad2/test.map\", spin=false, stochastic=false));\n", + "a_fpp = real(read_fpp_map(\"test/canonize_rad2/a.map\", spin=false, stochastic=false));\n", + "ac_norad_fpp = real(read_fpp_map(\"test/canonize_rad2/ac_norad.map\", spin=false, stochastic=false));\n", + "ac_fpp = real(read_fpp_map(\"test/canonize_rad2/ac.map\", spin=false, stochastic=false));" + ] + }, + { + "cell_type": "code", + "execution_count": 195, + "id": "86db2524-8cb2-461e-aaa6-278eb5569a5a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.0270205354294195e-14" + ] + }, + "execution_count": 195, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = normal(m);\n", + "ac_norad = a ∘ canonize(a)\n", + "norm(NNF.jacobian(ac_norad - ac_norad_fpp)) # Identical" + ] + }, + { + "cell_type": "code", + "execution_count": 196, + "id": "c91339b0-d327-4e2b-96f7-7fec0c0a1efc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "diagonal: [1.000000007079415 0.0 0.0 0.0 0.0 0.0; 0.0 1.000000007079415 0.0 0.0 0.0 0.0; 0.0 0.0 1.0000003292721718 0.0 0.0 0.0; 0.0 0.0 0.0 1.0000003292721718 0.0 0.0; 0.0 0.0 0.0 0.0 1.0000005598543975 0.0; 0.0 0.0 0.0 0.0 0.0 1.0000005598543975]\n", + "a before:\n", + "[1.0 0.0 0.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0 0.0 0.0; 0.0 0.0 1.0 0.0 0.0 0.0; 0.0 0.0 0.0 1.0 0.0 0.0; 0.0 0.0 0.0 0.0 1.0 0.0; 0.0 0.0 0.0 0.0 0.0 1.0]\n", + "4.965067803394708e-16\n" + ] + }, + { + "data": { + "text/plain": [ + "6×6 StaticArraysCore.SMatrix{6, 6, Float64, 36} with indices SOneTo(6)×SOneTo(6):\n", + " -1.75415e-14 0.0 6.50521e-19 … 9.6494e-18 8.5652e-18\n", + " 2.17604e-14 8.88178e-15 6.05629e-19 -1.12757e-17 -1.89735e-17\n", + " -8.94467e-19 1.20617e-18 8.88178e-16 -1.72984e-16 5.02636e-16\n", + " -7.91468e-18 -2.1684e-18 1.27676e-15 8.25119e-16 4.74013e-16\n", + " 6.23416e-19 -4.55365e-18 -1.37233e-16 -1.11022e-16 1.92593e-34\n", + " -1.0842e-19 -5.47522e-18 1.22271e-16 … -2.22045e-15 -2.22045e-16" + ] + }, + "execution_count": 196, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "damp = zeros(3)\n", + "ac = ac_norad ∘ canonize(ac_norad; damping=true, damp=damp)\n", + "println(norm(damp - [ 7.0794145850303742E-009 , 3.2927211731860217E-007 , 5.5985424078986008E-007]))\n", + "NNF.jacobian(ac-ac_fpp)" + ] + }, + { + "cell_type": "code", + "execution_count": 197, + "id": "b7225fd1-16c7-4802-805b-1904ba72ac51", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7.021666937153402e-16" + ] + }, + "execution_count": 197, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lambdafpp = reshape([ 1.0000000070794146 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000070794146 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000003292721715 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000003292721715 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000005598543975 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000005598543975], (6,6))\n", + "norm(lambdafpp - [1.000000007079415 0.0 0.0 0.0 0.0 0.0; 0.0 1.000000007079415 0.0 0.0 0.0 0.0; 0.0 0.0 1.0000003292721718 0.0 0.0 0.0; 0.0 0.0 0.0 1.0000003292721718 0.0 0.0; 0.0 0.0 0.0 0.0 1.0000005598543975 0.0; 0.0 0.0 0.0 0.0 0.0 1.0000005598543975])" + ] + }, + { + "cell_type": "code", + "execution_count": 198, + "id": "a408590f-4955-401a-884f-c9bbeeda3168", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.0088927366606835e-14\n", + "5.169391260095872e-16\n" + ] + } + ], + "source": [ + "a_before = [ 1.4338964279515740 -1.0429846794179958 -2.3570745104877473E-004 2.6262433147074087E-004 -1.1622855493497868E-004 -2.4830774444213496E-004;\n", + " 0.0000000000000000 0.69740039709121038 -5.6963396668069055E-005 -2.5344223264124729E-004 -2.6963112129992518E-004 -4.4781540226155144E-004;\n", + " 3.2095498585761557E-004 -6.5644456769718596E-006 0.90954598906121942 0.31682388106900750 1.0873929838182747E-004 1.8075859732463265E-004;\n", + " -9.1093681800944834E-005 2.6038105865456624E-004 0.0000000000000000 1.0994483139658224 -2.6186501157691305E-004 1.5773820802234262E-003;\n", + " 9.2386297069853697E-004 -8.9967415302002584E-004 -2.5891049089962905E-004 3.3946102928534663E-005 0.78995961443071061 -0.51904306741849293 ;\n", + " -9.5435643284262238E-004 8.9108155914763970E-004 -1.1516106612173820E-003 -1.6357668265082929E-003 -1.9259299443872359E-034 1.2658858226033121 ]'\n", + "println(norm(NNF.jacobian(ac_norad) - a_before))\n", + "println(norm(a_before-NNF.jacobian(ac_norad_fpp)))" + ] + }, + { + "cell_type": "code", + "execution_count": 199, + "id": "3823b7e7-ce95-4cb2-b6de-decec9326dfc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6×6 Matrix{Float64}:\n", + " 2.22045e-16 0.0 5.42101e-20 … 0.0 0.0\n", + " 2.22045e-16 0.0 0.0 0.0 0.0\n", + " 0.0 6.77626e-21 0.0 -5.42101e-20 2.1684e-19\n", + " 0.0 -5.42101e-20 0.0 0.0 0.0\n", + " 0.0 0.0 -1.35525e-20 0.0 4.27642e-50\n", + " -5.42101e-20 -5.42101e-20 2.71051e-20 … 0.0 -2.22045e-16" + ] + }, + "execution_count": 199, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a_before*Diagonal(lambdafpp)-a_after" + ] + }, + { + "cell_type": "code", + "execution_count": 201, + "id": "1f076567-c58d-4544-9738-3f356b5dd70e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.9482741224155094e-14\n" + ] + } + ], + "source": [ + "a_after = [ 1.433896438102721 0.000000000000000 0.3209550915391607E-03 -0.9109371179555925E-04 0.9238634879272838E-03 -0.9543569671432681E-03;\n", + " -1.042984686801717 0.6974004020283969 -0.6564447838461143E-05 0.2603811443908029E-03 -0.8996746567065567E-03 0.8910820580235691E-03;\n", + " -0.2357074527174455E-03 -0.5696339707133656E-04 0.9095462885494023 0.000000000000000 -0.2589106358518059E-03 -0.1151611305951675E-02;\n", + " 0.2626243333299674E-03 -0.2534422344354699E-03 0.3168239853902948 1.099448675983556 0.3394612193340967E-04 -0.1635767742299544E-02;\n", + " -0.1162285557578088E-03 -0.2696311232087557E-03 0.1087393341866524E-03 -0.2618650978017741E-03 0.7899600566930746 -0.1925931022627585E-33;\n", + " -0.2483077462000084E-03 -0.4478154054318223E-03 0.1807586568434085E-03 0.1577382599611449E-02 -0.5190433580070367 1.265886531315057 ]\n", + "println(norm(a_after-NNF.jacobian(ac)))" + ] + }, + { + "cell_type": "markdown", + "id": "38b55bf8-5f17-4e88-8e55-77bfde004e1c", + "metadata": {}, + "source": [ + "# EOD NOTE FOR 1/13/26\n", + "THEY BOTH AGREE\n", + "REMEMBER THAT CANONIZE IN SCIBMAD RETURNS ROTATION UNLIKE IN FPP WHERE IT RETURNS A\n", + "REMEMBER THAT WE WILL NEED TO INCLUDE PARAMETERS SO CANNOT JUST DO CANONIZER * \\Lambda i\n", + "IT SEEMS FINE NOW? IDK WHY IT ISN'T PERIODIC...\n", + "IT DOES AGREE WITH FPP SO WE WILL HAVE TO SIMULATE AN EXAMPLE OR ASK ETIENNE :(" + ] + }, + { + "cell_type": "code", + "execution_count": 216, + "id": "52c61536-2deb-4d01-9ddd-bc096fae6801", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.541610881461082e-5 - 0.00018981135333548938im" + ] + }, + "execution_count": 216, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Mt = NNF.jacobiant(m)\n", + "V = mat_eigen(Mt; phase_modes=true).vectors\n", + "i=2\n", + "V[:,5]'*S*V[:,1]" + ] + }, + { + "cell_type": "code", + "execution_count": 185, + "id": "5b7e55b6-1ec5-4c75-ba94-4dc0e5e7aec5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "diagonal: [1.0000000070794148 0.0 0.0 0.0 0.0 0.0; 0.0 1.0000000070794148 0.0 0.0 0.0 0.0; 0.0 0.0 1.0000003292721718 0.0 0.0 0.0; 0.0 0.0 0.0 1.0000003292721718 0.0 0.0; 0.0 0.0 0.0 0.0 1.0000005598543975 0.0; 0.0 0.0 0.0 0.0 0.0 1.0000005598543975]\n", + "a before:\n", + "[1.0782589624650461e-7 0.9999999999999941 0.0 0.0 0.0 0.0; -0.9999999999999941 1.0782589624650461e-7 0.0 0.0 0.0 0.0; 0.0 0.0 -0.9608991686520796 0.27689851513459274 0.0 0.0; 0.0 0.0 -0.27689851513459274 -0.9608991686520796 0.0 0.0; 0.0 0.0 0.0 0.0 0.9252444168617395 0.379371544882032; 0.0 0.0 0.0 0.0 -0.379371544882032 0.9252444168617395]\n" + ] + }, + { + "data": { + "text/plain": [ + "3.400479869349483e-15" + ] + }, + "execution_count": 185, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = normal(m)\n", + "dampdec = zeros(3)\n", + "r_c = canonize(a; damp=dampdec, damping=true)\n", + "ac = a∘r_c\n", + "norm(NNF.jacobian(inv(ac)*m*ac) - NNF.jacobian(inv(ac_fpp)*m*ac_fpp))" + ] + }, + { + "cell_type": "code", + "execution_count": 128, + "id": "83afc05a-e743-445b-8382-d53d17cd10ba", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " -18.766074587024786\n", + " -14.92638132305711\n", + " -14.395589371400876" + ] + }, + "execution_count": 128, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "log.(dampdec)" + ] + }, + { + "cell_type": "code", + "execution_count": 124, + "id": "ad6d6465-fe3f-43f7-a86f-7bbcdd67d8be", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6×6 StaticArraysCore.SMatrix{6, 6, Float64, 36} with indices SOneTo(6)×SOneTo(6):\n", + " -1.21431 0.762561 0.000330239 … -0.0003392 0.00128424\n", + " 0.512381 -1.14527 -0.000112 0.000349042 -0.00121721\n", + " 0.000229906 -7.71115e-5 0.830759 0.000788974 0.00087793\n", + " -8.76237e-5 0.000354297 -0.15822 0.000770268 0.00144346\n", + " 0.000241822 0.000166529 0.000205929 -0.689072 0.386285\n", + " 0.000448436 0.000247186 -0.000477073 … -0.166255 -1.35803" + ] + }, + "execution_count": 124, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "NNF.jacobian(a_fpp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bf6a2aad-1a95-400b-9ca3-10ff96b23f7d", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/test/canonize_rad/.ipynb_checkpoints/ac-checkpoint.map b/test/canonize_rad/.ipynb_checkpoints/ac-checkpoint.map new file mode 100644 index 0000000..8605345 --- /dev/null +++ b/test/canonize_rad/.ipynb_checkpoints/ac-checkpoint.map @@ -0,0 +1,114 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 6, INA = 30 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 1.000894544903768 0.000000000000000 1 0 0 0 0 0 + 1 0.2898383785589784E-17 0.000000000000000 0 1 0 0 0 0 + 1 0.1072346651692552E-01 0.000000000000000 0 0 1 0 0 0 + 1 -0.2118694457370925E-02 0.000000000000000 0 0 0 1 0 0 + 1 0.4155138533233235E-02 0.000000000000000 0 0 0 0 1 0 + 1 0.4320889391311298E-02 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 29 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.5534977252960378E-02 0.000000000000000 1 0 0 0 0 0 + 1 0.9989852254957123 0.000000000000000 0 1 0 0 0 0 + 1 0.4877226259522432E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.9696261692589593E-02 0.000000000000000 0 0 0 1 0 0 + 1 0.4073349610091699E-02 0.000000000000000 0 0 0 0 1 0 + 1 0.5878736643683100E-02 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 28 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.9868705355824936E-02 0.000000000000000 1 0 0 0 0 0 + 1 -0.1911305556281594E-02 0.000000000000000 0 1 0 0 0 0 + 1 0.9951259751950008 0.000000000000000 0 0 1 0 0 0 + 1 0.1056616759159222E-16 0.000000000000000 0 0 0 1 0 0 + 1 0.3404645852057041E-01 0.000000000000000 0 0 0 0 1 0 + 1 0.5415262872270297E-02 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 27 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.4841735616146606E-02 0.000000000000000 1 0 0 0 0 0 + 1 -0.1083999771824625E-01 0.000000000000000 0 1 0 0 0 0 + 1 -0.2015817552930598E-02 0.000000000000000 0 0 1 0 0 0 + 1 1.003760231114819 0.000000000000000 0 0 0 1 0 0 + 1 0.1113831492740976E-01 0.000000000000000 0 0 0 0 1 0 + 1 0.3160996239353395E-01 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 26 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.5569338572082764E-02 0.000000000000000 1 0 0 0 0 0 + 1 0.4244735218630108E-02 0.000000000000000 0 1 0 0 0 0 + 1 -0.3138262218397136E-01 0.000000000000000 0 0 1 0 0 0 + 1 0.2869981996784570E-02 0.000000000000000 0 0 0 1 0 0 + 1 0.9993909397417949 0.000000000000000 0 0 0 0 1 0 + 1 -0.3987923281177374E-16 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 25 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.3741978177850075E-02 0.000000000000000 1 0 0 0 0 0 + 1 -0.3696953976953218E-02 0.000000000000000 0 1 0 0 0 0 + 1 0.1324810116270562E-01 0.000000000000000 0 0 1 0 0 0 + 1 -0.3377041744323566E-01 0.000000000000000 0 0 0 1 0 0 + 1 0.2012515017333046E-01 0.000000000000000 0 0 0 0 1 0 + 1 0.9995823175428081 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + No Spin Matrix + Quaternion + c_quaternion + + 1, NO = 3, NV = 6, INA = 15 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 0.9044197722704104 0.000000000000000 0 0 0 0 0 0 + -1 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 232 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 0.3632814512983805 0.000000000000000 0 0 0 0 0 0 + -1 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 233 + ********************************************* + + ALL COMPONENTS 0.0_dp + NO = 3 NV = 6 + -1 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 234 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 -0.2237218421810473 0.000000000000000 0 0 0 0 0 0 + -1 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + No Stochastic Radiation \ No newline at end of file diff --git a/test/canonize_rad2/a.map b/test/canonize_rad2/a.map new file mode 100644 index 0000000..adfc95b --- /dev/null +++ b/test/canonize_rad2/a.map @@ -0,0 +1,1066 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 8, INA = 610 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -1.214314410352367 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.7625611312562857 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.3302385559552847E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 0.4746217411246875E-04 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.3392002031880292E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 0.1284236042047263E-02 0.000000000000000 0 0 0 0 0 1 0 0 + 1 0.2453306346361718E-02 0.000000000000000 0 0 0 0 0 0 1 0 + 1 0.1185109441791654E-02 0.000000000000000 0 0 0 0 0 0 0 1 + 2 -0.1672096234631561E-01 0.000000000000000 2 0 0 0 0 0 0 0 + 2 -0.1113559244434609E-01 0.000000000000000 1 1 0 0 0 0 0 0 + 2 -0.2477418084340689E-02 0.000000000000000 0 2 0 0 0 0 0 0 + 2 0.1513359364113275E-03 0.8131516293641283E-19 1 0 1 0 0 0 0 0 + 2 -0.7955422379081106E-03 0.5421010862427522E-19 0 1 1 0 0 0 0 0 + 2 -0.4399049163683698E-02 -0.4336808689942018E-18 0 0 2 0 0 0 0 0 + 2 0.6672304958740190E-03 0.8131516293641283E-19 1 0 0 1 0 0 0 0 + 2 -0.7800751754362603E-03 -0.8131516293641283E-19 0 1 0 1 0 0 0 0 + 2 0.3697315924057349E-03 0.000000000000000 0 0 1 1 0 0 0 0 + 2 -0.5558397134432039E-02 -0.4336808689942018E-18 0 0 0 2 0 0 0 0 + 2 0.6213834864955292E-03 -0.5421010862427522E-19 1 0 0 0 1 0 0 0 + 2 0.2532156349462448E-03 0.1084202172485504E-18 0 1 0 0 1 0 0 0 + 2 -0.5598013117576559E-03 0.000000000000000 0 0 1 0 1 0 0 0 + 2 0.6944592088366885E-03 0.1084202172485504E-18 0 0 0 1 1 0 0 0 + 2 -0.9211157758484199E-03 0.1084202172485504E-18 1 0 0 0 0 1 0 0 + 2 -0.1570473314487640E-02 0.8131516293641283E-19 0 1 0 0 0 1 0 0 + 2 -0.1973585660882655E-02 -0.1219727444046192E-18 0 0 1 0 0 1 0 0 + 2 -0.1620353721629206E-03 -0.5421010862427522E-19 0 0 0 1 0 1 0 0 + 2 0.5468394577362431E-02 0.000000000000000 1 0 0 0 0 0 1 0 + 2 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-0.3120612745421403E-05 -0.8470329472543003E-21 0 0 0 0 0 1 0 2 + 3 0.9930082910200882E-05 0.000000000000000 0 0 0 0 0 0 1 2 + 3 0.6218114519720904E-05 -0.4235164736271502E-21 0 0 0 0 0 0 0 3 + -164 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + No Spin Matrix + c_quaternion is identity + Stochastic Radiation + 1 1 (4.78496700165581078E-309,4.77436088731941736E-309) + 1 2 (-1.15838638216516574E-309,-5.80001664303653428E-309) + 1 3 (-9.76232425915700699E-313,-5.94732259004214057E-313) + 1 4 (3.25156519626666156E-314,1.72019122731488058E-312) + 1 5 (-1.28563405530822329E-312,5.12769916318176359E-313) + 1 6 (-2.31967709791816693E-312,6.67601314091296342E-313) + 2 1 (-5.80362881340180161E-309,-1.14448839044724747E-309) + 2 2 (3.66478999250300401E-309,3.65517117825029391E-309) + 2 3 (9.99481184741796422E-313,-4.24228471160496846E-314) + 2 4 (-8.60670561876140763E-313,-1.23541359597585252E-312) + 2 5 (6.85640231209755736E-313,-9.98549605745421733E-313) + 2 6 (1.36244534201062515E-312,-1.61432094798323234E-312) + 3 1 (-2.99208306462214185E-309,-4.26951651612723026E-310) + 3 2 (1.96871997833640936E-309,1.76580672043292347E-309) + 3 3 (5.08807243364223477E-313,-4.86810118167993325E-314) + 3 4 (-4.72548938354854645E-313,-6.07050891021686479E-313) + 3 5 (3.22816163280530110E-313,-5.28026099713089522E-313) + 3 6 (6.51478659384259376E-313,-8.60512276573104353E-313) + 4 1 (-1.55522493229467097E-309,3.46771987796072537E-309) + 4 2 (2.81782206759188771E-309,-1.76593244150500246E-309) + 4 3 (1.17892058562068074E-313,-6.31815722845912785E-313) + 4 4 (-8.97768172847889730E-313,3.60240757637683954E-313) + 4 5 (-5.26009855287290632E-313,-5.73531739583687374E-313) + 4 6 (-8.13673815137568635E-313,-1.08621191151066656E-312) + 5 1 (2.74917870630199058E-313,-2.19919355361209576E-312) + 5 2 (-1.26958513129220458E-312,1.46593387805570995E-312) + 5 3 (4.21741401615694412E-317,3.72430359683536704E-316) + 5 4 (4.39061450887464944E-316,-3.54199875883548673E-316) + 5 5 (3.91254003875952360E-316,2.29957686930152705E-316) + 5 6 (6.39215284839553419E-316,4.66692877458139378E-316) + 6 1 (-6.70846376565985089E-313,2.78178752023638372E-312) + 6 2 (1.84092948610736473E-312,-1.69713320164698437E-312) + 6 3 (-2.34730588339176233E-319,-4.83927374322676039E-316) + 6 4 (-6.14551374638808181E-316,3.90923829686149572E-316) + 6 5 (-4.68712365844859015E-316,-3.51632231544081090E-316) + 6 6 (-7.52600346640992786E-316,-6.91231741316521542E-316) diff --git a/test/canonize_rad2/ac copy.map b/test/canonize_rad2/ac copy.map new file mode 100644 index 0000000..e2be04f --- /dev/null +++ b/test/canonize_rad2/ac copy.map @@ -0,0 +1,82 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 8, INA = 118 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 1.433896438102721 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.9045943127422253E-16 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.3209550915391607E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.9109371179555925E-04 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.9238634879272838E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.9543569671432681E-03 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 117 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -1.042984686801717 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.6974004020283968 0.000000000000000 0 1 0 0 0 0 0 0 + 1 -0.6564447838461139E-05 0.000000000000000 0 0 1 0 0 0 0 0 + 1 0.2603811443908029E-03 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.8996746567065567E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 0.8910820580235691E-03 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 116 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.2357074527174455E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.5696339707133657E-04 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.9095462885494023 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.1397530980785473E-16 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.2589106358518059E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1151611305951675E-02 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 115 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 0.2626243333299674E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.2534422344354699E-03 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.3168239853902948 0.000000000000000 0 0 1 0 0 0 0 0 + 1 1.099448675983556 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.3394612193340966E-04 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1635767742299544E-02 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 114 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.1162285557578088E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.2696311232087557E-03 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.1087393341866524E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.2618650978017741E-03 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.7899600566930746 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1654622519214764E-17 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 113 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.2483077462000084E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.4478154054318223E-03 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.1807586568434085E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 0.1577382599611449E-02 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.5190433580070367 0.000000000000000 0 0 0 0 1 0 0 0 + 1 1.265886531315057 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + No Spin Matrix + No c_quaternion + No Stochastic Radiation diff --git a/test/canonize_rad2/ac.map b/test/canonize_rad2/ac.map new file mode 100644 index 0000000..dde346c --- /dev/null +++ b/test/canonize_rad2/ac.map @@ -0,0 +1,80 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 8, INA = 137 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 1.433896438102721 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.3209550915391607E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.9109371179555925E-04 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.9238634879272838E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.9543569671432681E-03 0.000000000000000 0 0 0 0 0 1 0 0 + -5 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 136 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -1.042984686801717 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.6974004020283969 0.000000000000000 0 1 0 0 0 0 0 0 + 1 -0.6564447838461143E-05 0.000000000000000 0 0 1 0 0 0 0 0 + 1 0.2603811443908029E-03 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.8996746567065567E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 0.8910820580235691E-03 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 135 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.2357074527174455E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.5696339707133656E-04 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.9095462885494023 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.2589106358518059E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1151611305951675E-02 0.000000000000000 0 0 0 0 0 1 0 0 + -5 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 134 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 0.2626243333299674E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.2534422344354699E-03 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.3168239853902948 0.000000000000000 0 0 1 0 0 0 0 0 + 1 1.099448675983556 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.3394612193340967E-04 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1635767742299544E-02 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 133 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.1162285557578088E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.2696311232087557E-03 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.1087393341866524E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.2618650978017741E-03 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.7899600566930746 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1925931022627585E-33 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 132 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.2483077462000084E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.4478154054318223E-03 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.1807586568434085E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 0.1577382599611449E-02 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.5190433580070367 0.000000000000000 0 0 0 0 1 0 0 0 + 1 1.265886531315057 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + Spin Matrix is identity + No c_quaternion + No Stochastic Radiation diff --git a/test/canonize_rad2/ac_norad.map b/test/canonize_rad2/ac_norad.map new file mode 100644 index 0000000..8d77f80 --- /dev/null +++ b/test/canonize_rad2/ac_norad.map @@ -0,0 +1,82 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 8, INA = 118 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 1.433896427951574 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.9045943063382272E-16 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.3209549858576156E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.9109368180094483E-04 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.9238629706985370E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.9543564328426224E-03 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 117 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -1.042984679417996 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.6974003970912103 0.000000000000000 0 1 0 0 0 0 0 0 + 1 -0.6564445676971855E-05 0.000000000000000 0 0 1 0 0 0 0 0 + 1 0.2603810586545662E-03 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.8996741530200258E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 0.8910815591476397E-03 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 116 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.2357074510487747E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.5696339666806907E-04 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.9095459890612194 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.1397530520617564E-16 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.2589104908996291E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1151610661217382E-02 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 115 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 0.2626243314707409E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.2534422326412473E-03 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.3168238810690075 0.000000000000000 0 0 1 0 0 0 0 0 + 1 1.099448313965822 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.3394610292853466E-04 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1635766826508293E-02 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 114 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.1162285549349787E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.2696311212999252E-03 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.1087392983818275E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.2618650115769131E-03 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.7899596144307106 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1654621592867588E-17 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 113 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.2483077444421349E-03 0.000000000000000 1 0 0 0 0 0 0 0 + 1 -0.4478154022615514E-03 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.1807585973246327E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 0.1577382080223426E-02 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.5190430674184929 0.000000000000000 0 0 0 0 1 0 0 0 + 1 1.265885822603312 0.000000000000000 0 0 0 0 0 1 0 0 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + No Spin Matrix + No c_quaternion + No Stochastic Radiation diff --git a/test/canonize_rad2/test.map b/test/canonize_rad2/test.map new file mode 100644 index 0000000..788fa3a --- /dev/null +++ b/test/canonize_rad2/test.map @@ -0,0 +1,1066 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 8, INA = 137 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 0.8910372041775222 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.1376741773228439 0.000000000000000 0 1 0 0 0 0 0 0 + 1 -0.5536136885324756E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.4705508139691222E-04 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.5180705827569297E-04 0.000000000000000 0 0 0 0 1 0 0 0 + 1 0.1115890029217075E-02 0.000000000000000 0 0 0 0 0 1 0 0 + 1 0.1021997333870391E-02 0.000000000000000 0 0 0 0 0 0 1 0 + 1 0.3410596525327765E-03 0.000000000000000 0 0 0 0 0 0 0 1 + 2 0.1058179067056163E-02 0.000000000000000 2 0 0 0 0 0 0 0 + 2 0.3410880510950978E-02 0.000000000000000 1 1 0 0 0 0 0 0 + 2 0.7086616665419881E-03 0.000000000000000 0 2 0 0 0 0 0 0 + 2 -0.2894075789719156E-03 0.000000000000000 1 0 1 0 0 0 0 0 + 2 -0.1242027947192844E-02 0.000000000000000 0 1 1 0 0 0 0 0 + 2 0.1222776129203476E-02 0.000000000000000 0 0 2 0 0 0 0 0 + 2 0.5597898583092443E-03 0.000000000000000 1 0 0 1 0 0 0 0 + 2 -0.3797487844071057E-03 0.000000000000000 0 1 0 1 0 0 0 0 + 2 0.9872347411932309E-04 0.000000000000000 0 0 1 1 0 0 0 0 + 2 0.1266056665337754E-02 0.000000000000000 0 0 0 2 0 0 0 0 + 2 -0.7151159160332179E-03 0.000000000000000 1 0 0 0 1 0 0 0 + 2 -0.4969415412612374E-03 0.000000000000000 0 1 0 0 1 0 0 0 + 2 0.8159428348135991E-03 0.000000000000000 0 0 1 0 1 0 0 0 + 2 0.7545578735754189E-03 0.000000000000000 0 0 0 1 1 0 0 0 + 2 0.1203740311403586E-02 0.000000000000000 1 0 0 0 0 1 0 0 + 2 0.2078505916028268E-02 0.000000000000000 0 1 0 0 0 1 0 0 + 2 -0.9114756632480498E-03 0.000000000000000 0 0 1 0 0 1 0 0 + 2 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+ "cells": [ + { + "cell_type": "code", + "execution_count": 7, + "id": "d7186c9a-6d16-4e6d-8d5b-0431822f3323", + "metadata": {}, + "outputs": [], + "source": [ + "using Revise\n", + "using NonlinearNormalForm, TPSAInterface, GTPSA, JET, BenchmarkTools\n", + "import TPSAInterface as TI\n", + "import NonlinearNormalForm as NNF\n", + "using LinearAlgebra" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "5826f509-423e-4f25-89d6-65f2405a24a6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0e-9" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "GTPSA.show_eps=1e-9" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "8019c020-2efb-4aae-82c7-02c486d43cb9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "read_fpp_map (generic function with 1 method)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "include(\"test/readfpp.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ccfff21d-4873-430b-974e-24bc23a35089", + "metadata": {}, + "outputs": [], + "source": [ + "m = real(read_fpp_map(\"test/canonize_rad3/test.map\", spin=false, stochastic=false));\n", + "ac_norad_fpp = real(read_fpp_map(\"test/canonize_rad3/ac_norad.map\", spin=false, stochastic=false));\n", + "#ac_fpp = real(read_fpp_map(\"test/canonize_rad3/ac.map\", spin=false, stochastic=false));" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "8e958ba8-d3b5-4f79-be50-e21cb242160b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4.2092546059575386e-15" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = normal(m)\n", + "ac_norad = a∘canonize(a)\n", + "norm(NNF.jacobian(ac_norad-ac_norad_fpp))" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "8e7c9272-7d37-455d-a61f-4520044f229c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7.021651535476685e-16" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ac = a∘canonize(a; damping=true)\n", + "a_end = m∘ac\n", + "damp=zeros(3)\n", + "ac_end = a_end∘canonize(a_end; damping=true, damp=damp)\n", + "norm(damp-[0.1531583287271725E-05, 0.2817861217457402E-05, 0.2142167833506887E-05])" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "d2785066-6105-4752-9030-a9f00e94e4db", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.084545602475685e-15" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "norm(NNF.jacobian(ac_end - ac))" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "92af3f73-7715-4749-b3dc-b276486fb610", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-1.5315832873166573e-6 - 2.366801815732135im" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = c_map(a)\n", + "reallog((inv(c)∘inv(ac_norad)∘m∘ac_norad∘c).v[1][1])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "effb66e9-f812-4f78-a8bf-bf1a61821ca7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 5.6974835447389954e-8\n", + " -2.1736512048935732e-8\n", + " -3.55658602232123e-8" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "\n", + "damp" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0e7858db-c6dc-4df9-9606-cd3a81561c41", + "metadata": {}, + "outputs": [], + "source": [ + "0.1531583287271725E-05 0.2817861217457402E-05 0.2142167833506887E-05" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia Global (10 threads) 1.10", + "language": "julia", + "name": "julia-global-_10-threads_-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/test/canonize_rad3/ac_norad.map b/test/canonize_rad3/ac_norad.map new file mode 100644 index 0000000..36c5a96 --- /dev/null +++ b/test/canonize_rad3/ac_norad.map @@ -0,0 +1,82 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 6, INA = 319 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.9991617924790048 0.000000000000000 1 0 0 0 0 0 + 1 -0.1808455582616642E-17 0.000000000000000 0 1 0 0 0 0 + 1 0.1775562377462435E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.8693612418935089E-03 0.000000000000000 0 0 0 1 0 0 + 1 -0.4881649352221389E-02 0.000000000000000 0 0 0 0 1 0 + 1 -0.1519737248966161E-01 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 320 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.3633197946400632E-03 0.000000000000000 1 0 0 0 0 0 + 1 1.001032028356718 0.000000000000000 0 1 0 0 0 0 + 1 -0.1999448273180322E-02 0.000000000000000 0 0 1 0 0 0 + 1 -0.3584212613372295E-02 0.000000000000000 0 0 0 1 0 0 + 1 -0.1178349560867409E-01 0.000000000000000 0 0 0 0 1 0 + 1 0.1918582052009290E-02 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 321 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.3519167299401198E-02 0.000000000000000 1 0 0 0 0 0 + 1 0.7629666986330736E-03 0.000000000000000 0 1 0 0 0 0 + 1 1.002285851602522 0.000000000000000 0 0 1 0 0 0 + 1 0.7604336928300232E-16 0.000000000000000 0 0 0 1 0 0 + 1 0.8485941832027496E-02 0.000000000000000 0 0 0 0 1 0 + 1 0.4485200315040324E-02 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 322 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.2067226950472278E-02 0.000000000000000 1 0 0 0 0 0 + 1 -0.1682337190197596E-02 0.000000000000000 0 1 0 0 0 0 + 1 -0.7118708833742166E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.9976570229666665 0.000000000000000 0 0 0 1 0 0 + 1 -0.4787176517244352E-02 0.000000000000000 0 0 0 0 1 0 + 1 0.5349595855810138E-02 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 323 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.1928414659354402E-02 0.000000000000000 1 0 0 0 0 0 + 1 -0.1518707224150579E-01 0.000000000000000 0 1 0 0 0 0 + 1 -0.5363862417333338E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.4500207091177663E-02 0.000000000000000 0 0 0 1 0 0 + 1 0.9978362759867911 0.000000000000000 0 0 0 0 1 0 + 1 -0.8517674441934914E-16 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 324 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.1179860889517246E-01 0.000000000000000 1 0 0 0 0 0 + 1 0.4888117914499528E-02 0.000000000000000 0 1 0 0 0 0 + 1 -0.4762704135403215E-02 0.000000000000000 0 0 1 0 0 0 + 1 -0.8515155530063876E-02 0.000000000000000 0 0 0 1 0 0 + 1 0.6848329156037140E-03 0.000000000000000 0 0 0 0 1 0 + 1 1.002290256026178 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + No Spin Matrix + No c_quaternion + No Stochastic Radiation \ No newline at end of file diff --git a/test/canonize_rad3/test.map b/test/canonize_rad3/test.map new file mode 100644 index 0000000..79f6351 --- /dev/null +++ b/test/canonize_rad3/test.map @@ -0,0 +1,909 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 6, INA = 135 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.7142817816214686 0.000000000000000 1 0 0 0 0 0 + 1 0.6982378917890342 0.000000000000000 0 1 0 0 0 0 + 1 0.1488087117373118E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.1578883417181524E-02 0.000000000000000 0 0 0 1 0 0 + 1 -0.5455514982869485E-03 0.000000000000000 0 0 0 0 1 0 + 1 0.2847738493709066E-02 0.000000000000000 0 0 0 0 0 1 + 2 0.2700355123017907E-02 0.000000000000000 2 0 0 0 0 0 + 2 0.2092899742128830E-02 0.000000000000000 1 1 0 0 0 0 + 2 -0.4502673185823148E-02 0.000000000000000 0 2 0 0 0 0 + 2 -0.6961025414876449E-02 0.000000000000000 1 0 1 0 0 0 + 2 -0.3318663315591372E-02 0.000000000000000 0 1 1 0 0 0 + 2 -0.1848598087692178E-02 0.000000000000000 0 0 2 0 0 0 + 2 -0.4407857210635507E-02 0.000000000000000 1 0 0 1 0 0 + 2 -0.2349286559437702E-02 0.000000000000000 0 1 0 1 0 0 + 2 -0.5180756747168586E-03 0.000000000000000 0 0 1 1 0 0 + 2 0.6565402652764262E-02 0.000000000000000 1 0 0 0 1 0 + 2 0.1590511961398486E-02 0.000000000000000 0 1 0 0 1 0 + 2 0.5416858160765499E-02 0.000000000000000 0 0 1 0 1 0 + 2 0.5309803358754450E-03 0.000000000000000 1 0 0 0 0 1 + 2 -0.5494201843144654E-02 0.000000000000000 0 1 0 0 0 1 + 2 -0.6101931404964740E-03 0.000000000000000 0 0 1 0 0 1 + 2 -0.2571536495584966E-02 0.000000000000000 0 0 0 2 0 0 + 2 -0.4773322008921323E-03 0.000000000000000 0 0 0 1 1 0 + 2 0.5728766581469947E-03 0.000000000000000 0 0 0 0 2 0 + 2 0.2702370287440257E-03 0.000000000000000 0 0 0 1 0 1 + 2 -0.2942314964036645E-02 0.000000000000000 0 0 0 0 1 1 + 2 -0.8906502981398300E-02 0.000000000000000 0 0 0 0 0 2 + 3 0.2567954123134559E-03 0.000000000000000 3 0 0 0 0 0 + 3 0.2259671815581400E-03 0.000000000000000 2 1 0 0 0 0 + 3 0.3298532336316906E-03 0.000000000000000 1 2 0 0 0 0 + 3 0.3044202269423251E-03 0.000000000000000 0 3 0 0 0 0 + 3 -0.6295945782289577E-04 0.000000000000000 2 0 1 0 0 0 + 3 0.2665194134619220E-04 0.000000000000000 1 1 1 0 0 0 + 3 0.4329599649435814E-04 0.000000000000000 0 2 1 0 0 0 + 3 0.3011865756195327E-03 0.000000000000000 1 0 2 0 0 0 + 3 0.2253992137495027E-03 0.000000000000000 0 1 2 0 0 0 + 3 -0.1107442318134645E-04 0.000000000000000 0 0 3 0 0 0 + 3 -0.4394237475484951E-04 0.000000000000000 2 0 0 1 0 0 + 3 -0.4922883420818634E-04 0.000000000000000 1 1 0 1 0 0 + 3 -0.7736753457125401E-04 0.000000000000000 0 2 0 1 0 0 + 3 0.8938687892570289E-04 0.000000000000000 1 0 1 1 0 0 + 3 -0.1165493070759964E-03 0.000000000000000 0 1 1 1 0 0 + 3 -0.1422721599428304E-04 0.000000000000000 0 0 2 1 0 0 + 3 -0.4728027036557019E-05 0.000000000000000 2 0 0 0 1 0 + 3 -0.1368055491326370E-05 0.000000000000000 1 1 0 0 1 0 + 3 0.1081549301262227E-03 0.000000000000000 0 2 0 0 1 0 + 3 -0.3563606243051575E-04 0.000000000000000 1 0 1 0 1 0 + 3 -0.3214660159467110E-04 0.000000000000000 0 1 1 0 1 0 + 3 0.7243162365398792E-04 0.000000000000000 0 0 2 0 1 0 + 3 -0.5565703700983203E-04 0.000000000000000 2 0 0 0 0 1 + 3 0.1678910171220707E-03 0.000000000000000 1 1 0 0 0 1 + 3 0.1483634315691846E-03 0.000000000000000 0 2 0 0 0 1 + 3 -0.1750396462620445E-04 0.000000000000000 1 0 1 0 0 1 + 3 -0.3506277776701750E-04 0.000000000000000 0 1 1 0 0 1 + 3 0.7540798095101702E-04 0.000000000000000 0 0 2 0 0 1 + 3 0.3749186570469334E-03 0.000000000000000 1 0 0 2 0 0 + 3 0.3378812170686086E-03 0.000000000000000 0 1 0 2 0 0 + 3 -0.2925160316954292E-04 0.000000000000000 0 0 1 2 0 0 + 3 0.1046656735651302E-03 0.000000000000000 1 0 0 1 1 0 + 3 0.3831087273853212E-04 0.000000000000000 0 1 0 1 1 0 + 3 -0.6126562092732761E-05 0.000000000000000 0 0 1 1 1 0 + 3 0.3947579817582147E-03 0.000000000000000 1 0 0 0 2 0 + 3 0.4648398130047275E-03 0.000000000000000 0 1 0 0 2 0 + 3 -0.1018110919532747E-03 0.000000000000000 0 0 1 0 2 0 + 3 0.2956723894674087E-04 0.000000000000000 1 0 0 1 0 1 + 3 0.8747122296805315E-04 0.000000000000000 0 1 0 1 0 1 + 3 0.6409388664555764E-04 0.000000000000000 0 0 1 1 0 1 + 3 0.2875119151256485E-04 0.000000000000000 1 0 0 0 1 1 + 3 0.2119253489842015E-03 0.000000000000000 0 1 0 0 1 1 + 3 0.8507464463664613E-04 0.000000000000000 0 0 1 0 1 1 + 3 0.3551145195205590E-03 0.000000000000000 1 0 0 0 0 2 + 3 0.3250490138258245E-03 0.000000000000000 0 1 0 0 0 2 + 3 -0.6435023517171525E-04 0.000000000000000 0 0 1 0 0 2 + 3 -0.2702040863387879E-04 0.000000000000000 0 0 0 3 0 0 + 3 -0.1334416144833931E-05 0.000000000000000 0 0 0 2 1 0 + 3 -0.9004451674721047E-04 0.000000000000000 0 0 0 1 2 0 + 3 0.1225348640975705E-04 0.000000000000000 0 0 0 0 3 0 + 3 -0.5062136160075650E-04 0.000000000000000 0 0 0 2 0 1 + 3 0.1189419252878742E-03 0.000000000000000 0 0 0 1 1 1 + 3 -0.4070358312505773E-04 0.000000000000000 0 0 0 0 2 1 + 3 -0.3699073504760294E-04 0.000000000000000 0 0 0 1 0 2 + 3 0.1114743092069898E-03 0.000000000000000 0 0 0 0 1 2 + 3 -0.1300607280635791E-04 0.000000000000000 0 0 0 0 0 3 + -83 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 134 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.7009168217145417 0.000000000000000 1 0 0 0 0 0 + 1 -0.7148179404495251 0.000000000000000 0 1 0 0 0 0 + 1 -0.2053893447811506E-04 0.000000000000000 0 0 1 0 0 0 + 1 0.2127017971784430E-02 0.000000000000000 0 0 0 1 0 0 + 1 -0.1280629034982933E-02 0.000000000000000 0 0 0 0 1 0 + 1 -0.3702639556398551E-02 0.000000000000000 0 0 0 0 0 1 + 2 -0.4365013733416068E-02 0.000000000000000 2 0 0 0 0 0 + 2 0.5127555668804009E-02 0.000000000000000 1 1 0 0 0 0 + 2 -0.7969544905378790E-02 0.000000000000000 0 2 0 0 0 0 + 2 0.9864623249735326E-02 0.000000000000000 1 0 1 0 0 0 + 2 -0.5946406126125567E-02 0.000000000000000 0 1 1 0 0 0 + 2 -0.3715657993777061E-02 0.000000000000000 0 0 2 0 0 0 + 2 0.4196681911675454E-02 0.000000000000000 1 0 0 1 0 0 + 2 -0.2003099626647655E-02 0.000000000000000 0 1 0 1 0 0 + 2 -0.2043042995602654E-02 0.000000000000000 0 0 1 1 0 0 + 2 -0.2586016166177442E-02 0.000000000000000 1 0 0 0 1 0 + 2 -0.2447859957129570E-02 0.000000000000000 0 1 0 0 1 0 + 2 -0.3462314563961911E-02 0.000000000000000 0 0 1 0 1 0 + 2 -0.2584401722273815E-02 0.000000000000000 1 0 0 0 0 1 + 2 -0.3441721208885898E-02 0.000000000000000 0 1 0 0 0 1 + 2 0.3441885289950285E-02 0.000000000000000 0 0 1 0 0 1 + 2 -0.2780093400696201E-02 0.000000000000000 0 0 0 2 0 0 + 2 0.5391497167159526E-04 0.000000000000000 0 0 0 1 1 0 + 2 -0.2915322812786569E-02 0.000000000000000 0 0 0 0 2 0 + 2 -0.1688593246705929E-02 0.000000000000000 0 0 0 1 0 1 + 2 0.6598451733747391E-02 0.000000000000000 0 0 0 0 1 1 + 2 -0.3329240762727633E-02 0.000000000000000 0 0 0 0 0 2 + 3 -0.2661218180845786E-03 0.000000000000000 3 0 0 0 0 0 + 3 0.2930394578267776E-03 0.000000000000000 2 1 0 0 0 0 + 3 -0.3336309636480156E-03 0.000000000000000 1 2 0 0 0 0 + 3 0.2909658521676586E-03 0.000000000000000 0 3 0 0 0 0 + 3 -0.2895107561121525E-04 0.000000000000000 2 0 1 0 0 0 + 3 0.1958091771008535E-04 0.000000000000000 1 1 1 0 0 0 + 3 0.1344999916151902E-03 0.000000000000000 0 2 1 0 0 0 + 3 -0.3181724565380951E-03 0.000000000000000 1 0 2 0 0 0 + 3 0.3622798490725315E-03 0.000000000000000 0 1 2 0 0 0 + 3 0.5253087383666481E-04 0.000000000000000 0 0 3 0 0 0 + 3 0.2387070353765828E-04 0.000000000000000 2 0 0 1 0 0 + 3 0.5312366729250464E-06 0.000000000000000 1 1 0 1 0 0 + 3 0.1903216672778962E-04 0.000000000000000 0 2 0 1 0 0 + 3 -0.6491427486064224E-04 0.000000000000000 1 0 1 1 0 0 + 3 -0.7079792013204298E-04 0.000000000000000 0 1 1 1 0 0 + 3 0.1300713375936838E-04 0.000000000000000 0 0 2 1 0 0 + 3 0.8679043433143914E-04 0.000000000000000 2 0 0 0 1 0 + 3 -0.4108219628742871E-04 0.000000000000000 1 1 0 0 1 0 + 3 -0.1382820610795186E-04 0.000000000000000 0 2 0 0 1 0 + 3 -0.2223709426782587E-04 0.000000000000000 1 0 1 0 1 0 + 3 -0.2406606034684807E-04 0.000000000000000 0 1 1 0 1 0 + 3 -0.1560033645607593E-04 0.000000000000000 0 0 2 0 1 0 + 3 0.1591943566139007E-03 0.000000000000000 2 0 0 0 0 1 + 3 -0.2044425861121398E-03 0.000000000000000 1 1 0 0 0 1 + 3 0.1597029761049402E-03 0.000000000000000 0 2 0 0 0 1 + 3 -0.5300856504258353E-04 0.000000000000000 1 0 1 0 0 1 + 3 -0.1773058698977742E-05 0.000000000000000 0 1 1 0 0 1 + 3 -0.2344306067779725E-04 0.000000000000000 0 0 2 0 0 1 + 3 -0.3591157348135088E-03 0.000000000000000 1 0 0 2 0 0 + 3 0.3232345353752056E-03 0.000000000000000 0 1 0 2 0 0 + 3 0.6447396332802285E-04 0.000000000000000 0 0 1 2 0 0 + 3 -0.1166044555882980E-03 0.000000000000000 1 0 0 1 1 0 + 3 -0.4635703210803932E-04 0.000000000000000 0 1 0 1 1 0 + 3 0.9939707705066442E-04 0.000000000000000 0 0 1 1 1 0 + 3 -0.2989367045689343E-03 0.000000000000000 1 0 0 0 2 0 + 3 0.3200857287650055E-03 0.000000000000000 0 1 0 0 2 0 + 3 0.2763781334052379E-04 0.000000000000000 0 0 1 0 2 0 + 3 0.7319644085908964E-04 0.000000000000000 1 0 0 1 0 1 + 3 0.6924082311204069E-04 0.000000000000000 0 1 0 1 0 1 + 3 -0.2532202074172650E-05 0.000000000000000 0 0 1 1 0 1 + 3 -0.6930082027833764E-04 0.000000000000000 1 0 0 0 1 1 + 3 0.3559729773566089E-04 0.000000000000000 0 1 0 0 1 1 + 3 -0.1135982724687012E-04 0.000000000000000 0 0 1 0 1 1 + 3 -0.2882013611559674E-03 0.000000000000000 1 0 0 0 0 2 + 3 0.4141482180753441E-03 0.000000000000000 0 1 0 0 0 2 + 3 0.7217838254866520E-04 0.000000000000000 0 0 1 0 0 2 + 3 -0.2176705532318229E-04 0.000000000000000 0 0 0 3 0 0 + 3 0.8391036695806742E-04 0.000000000000000 0 0 0 2 1 0 + 3 0.7042944442146817E-05 0.000000000000000 0 0 0 1 2 0 + 3 0.5312187200120939E-04 0.000000000000000 0 0 0 0 3 0 + 3 -0.1910614270333821E-04 0.000000000000000 0 0 0 2 0 1 + 3 0.2966368425361740E-04 0.000000000000000 0 0 0 1 1 1 + 3 -0.3989922695260037E-04 0.000000000000000 0 0 0 0 2 1 + 3 0.4624116360422495E-04 0.000000000000000 0 0 0 1 0 2 + 3 -0.4598728211513065E-04 0.000000000000000 0 0 0 0 1 2 + 3 0.3824558963900414E-04 0.000000000000000 0 0 0 0 0 3 + -83 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 133 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.8524539885100547E-03 0.000000000000000 1 0 0 0 0 0 + 1 0.1870784270878379E-02 0.000000000000000 0 1 0 0 0 0 + 1 -0.8963246816821581 0.000000000000000 0 0 1 0 0 0 + 1 -0.4519236966210469 0.000000000000000 0 0 0 1 0 0 + 1 0.1405075500263237E-02 0.000000000000000 0 0 0 0 1 0 + 1 -0.2270850461546340E-02 0.000000000000000 0 0 0 0 0 1 + 2 -0.2746165368586620E-04 0.000000000000000 2 0 0 0 0 0 + 2 -0.1067608106240198E-02 0.000000000000000 1 1 0 0 0 0 + 2 0.8809225526390025E-04 0.000000000000000 0 2 0 0 0 0 + 2 -0.2653785268026866E-03 0.000000000000000 1 0 1 0 0 0 + 2 0.1914509719759772E-02 0.000000000000000 0 1 1 0 0 0 + 2 0.1012485221842923E-02 0.000000000000000 0 0 2 0 0 0 + 2 -0.2308025533319226E-03 0.000000000000000 1 0 0 1 0 0 + 2 -0.5948654273507342E-02 0.000000000000000 0 1 0 1 0 0 + 2 0.1213382989973371E-02 0.000000000000000 0 0 1 1 0 0 + 2 -0.3131843428714933E-02 0.000000000000000 1 0 0 0 1 0 + 2 -0.9021190059762026E-03 0.000000000000000 0 1 0 0 1 0 + 2 -0.1443158088719974E-02 0.000000000000000 0 0 1 0 1 0 + 2 0.2593066301998239E-02 0.000000000000000 1 0 0 0 0 1 + 2 -0.1768503794360204E-02 0.000000000000000 0 1 0 0 0 1 + 2 -0.1186000110633304E-02 0.000000000000000 0 0 1 0 0 1 + 2 0.6628846217535213E-03 0.000000000000000 0 0 0 2 0 0 + 2 0.1156605810524671E-01 0.000000000000000 0 0 0 1 1 0 + 2 -0.1256247272747786E-02 0.000000000000000 0 0 0 0 2 0 + 2 -0.4374692897272686E-02 0.000000000000000 0 0 0 1 0 1 + 2 -0.2404351137461201E-02 0.000000000000000 0 0 0 0 1 1 + 2 0.1120916534857217E-02 0.000000000000000 0 0 0 0 0 2 + 3 -0.5182514292750895E-05 0.000000000000000 3 0 0 0 0 0 + 3 0.2226850489349788E-04 0.000000000000000 2 1 0 0 0 0 + 3 -0.4195374109684061E-04 0.000000000000000 1 2 0 0 0 0 + 3 -0.2343786076179539E-04 0.000000000000000 0 3 0 0 0 0 + 3 -0.1332616335470051E-03 0.000000000000000 2 0 1 0 0 0 + 3 0.2593015545818425E-04 0.000000000000000 1 1 1 0 0 0 + 3 -0.2276093689958150E-03 0.000000000000000 0 2 1 0 0 0 + 3 0.1217897356542363E-04 0.000000000000000 1 0 2 0 0 0 + 3 -0.4076451567293478E-04 0.000000000000000 0 1 2 0 0 0 + 3 -0.1801850583337344E-03 0.000000000000000 0 0 3 0 0 0 + 3 0.3843482150985183E-03 0.000000000000000 2 0 0 1 0 0 + 3 0.3818214092320124E-04 0.000000000000000 1 1 0 1 0 0 + 3 0.4774569615594513E-03 0.000000000000000 0 2 0 1 0 0 + 3 -0.3126469637818461E-04 0.000000000000000 1 0 1 1 0 0 + 3 0.2215053967296324E-05 0.000000000000000 0 1 1 1 0 0 + 3 0.3897971106763285E-03 0.000000000000000 0 0 2 1 0 0 + 3 -0.2383659330629772E-04 0.000000000000000 2 0 0 0 1 0 + 3 0.3787930234564966E-04 0.000000000000000 1 1 0 0 1 0 + 3 -0.7164291703717768E-04 0.000000000000000 0 2 0 0 1 0 + 3 -0.8770084369609669E-04 0.000000000000000 1 0 1 0 1 0 + 3 -0.7700615315938399E-04 0.000000000000000 0 1 1 0 1 0 + 3 -0.6426037089273762E-04 0.000000000000000 0 0 2 0 1 0 + 3 -0.1589515979145603E-04 0.000000000000000 2 0 0 0 0 1 + 3 0.2517252284781543E-04 0.000000000000000 1 1 0 0 0 1 + 3 0.5890668835973423E-04 0.000000000000000 0 2 0 0 0 1 + 3 -0.1363659311478538E-04 0.000000000000000 1 0 1 0 0 1 + 3 0.3144560085676609E-04 0.000000000000000 0 1 1 0 0 1 + 3 -0.1987230108760493E-04 0.000000000000000 0 0 2 0 0 1 + 3 0.4664967411067309E-04 0.000000000000000 1 0 0 2 0 0 + 3 -0.8162735779851945E-04 0.000000000000000 0 1 0 2 0 0 + 3 -0.1570394378447014E-03 0.000000000000000 0 0 1 2 0 0 + 3 -0.2884940051906093E-04 0.000000000000000 1 0 0 1 1 0 + 3 0.1317448669364831E-05 0.000000000000000 0 1 0 1 1 0 + 3 0.1326477818761857E-03 0.000000000000000 0 0 1 1 1 0 + 3 0.2888914607403040E-04 0.000000000000000 1 0 0 0 2 0 + 3 -0.1733555846560521E-05 0.000000000000000 0 1 0 0 2 0 + 3 -0.2304512409690210E-03 0.000000000000000 0 0 1 0 2 0 + 3 0.5007407817467228E-04 0.000000000000000 1 0 0 1 0 1 + 3 0.9554872601104254E-04 0.000000000000000 0 1 0 1 0 1 + 3 0.1246198815331438E-04 0.000000000000000 0 0 1 1 0 1 + 3 -0.6827702235759171E-04 0.000000000000000 1 0 0 0 1 1 + 3 0.1298174756162642E-04 0.000000000000000 0 1 0 0 1 1 + 3 -0.6878959511819220E-04 0.000000000000000 0 0 1 0 1 1 + 3 -0.2762775569706412E-04 0.000000000000000 1 0 0 0 0 2 + 3 -0.2256339620685598E-04 0.000000000000000 0 1 0 0 0 2 + 3 -0.1886318413200823E-03 0.000000000000000 0 0 1 0 0 2 + 3 0.4025144687555550E-03 0.000000000000000 0 0 0 3 0 0 + 3 -0.1371625581681857E-03 0.000000000000000 0 0 0 2 1 0 + 3 0.4400896094048144E-03 0.000000000000000 0 0 0 1 2 0 + 3 -0.7354513714139166E-04 0.000000000000000 0 0 0 0 3 0 + 3 0.1157420372946471E-03 0.000000000000000 0 0 0 2 0 1 + 3 -0.4805448085935450E-04 0.000000000000000 0 0 0 1 1 1 + 3 0.5094397240538925E-04 0.000000000000000 0 0 0 0 2 1 + 3 0.3955002994182848E-03 0.000000000000000 0 0 0 1 0 2 + 3 -0.6615158895035892E-04 0.000000000000000 0 0 0 0 1 2 + 3 0.2645765929566431E-04 0.000000000000000 0 0 0 0 0 3 + -83 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 132 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.7485991171002530E-03 0.000000000000000 1 0 0 0 0 0 + 1 -0.2103140434459037E-02 0.000000000000000 0 1 0 0 0 0 + 1 0.4477619168955018 0.000000000000000 0 0 1 0 0 0 + 1 -0.8898977662569922 0.000000000000000 0 0 0 1 0 0 + 1 -0.1045921313975443E-02 0.000000000000000 0 0 0 0 1 0 + 1 0.1364852746857127E-02 0.000000000000000 0 0 0 0 0 1 + 2 0.6673892411300398E-02 0.000000000000000 2 0 0 0 0 0 + 2 -0.1585582442364730E-02 0.000000000000000 1 1 0 0 0 0 + 2 0.3572197300007452E-02 0.000000000000000 0 2 0 0 0 0 + 2 -0.2890732269667287E-02 0.000000000000000 1 0 1 0 0 0 + 2 0.7757364805513355E-02 0.000000000000000 0 1 1 0 0 0 + 2 0.6301703137679499E-03 0.000000000000000 0 0 2 0 0 0 + 2 -0.1114525745594961E-02 0.000000000000000 1 0 0 1 0 0 + 2 0.4974301165282270E-02 0.000000000000000 0 1 0 1 0 0 + 2 -0.1976786155621691E-02 0.000000000000000 0 0 1 1 0 0 + 2 -0.5448138593581424E-02 0.000000000000000 1 0 0 0 1 0 + 2 -0.1168505514167141E-02 0.000000000000000 0 1 0 0 1 0 + 2 0.3025025414754935E-02 0.000000000000000 0 0 1 0 1 0 + 2 0.1951766713393564E-02 0.000000000000000 1 0 0 0 0 1 + 2 -0.1324481339512534E-02 0.000000000000000 0 1 0 0 0 1 + 2 0.2326507050042713E-02 0.000000000000000 0 0 1 0 0 1 + 2 -0.1427578542730562E-02 0.000000000000000 0 0 0 2 0 0 + 2 -0.2811902412766415E-02 0.000000000000000 0 0 0 1 1 0 + 2 0.1842341870535220E-02 0.000000000000000 0 0 0 0 2 0 + 2 0.4506372673168411E-02 0.000000000000000 0 0 0 1 0 1 + 2 -0.5702714787894246E-02 0.000000000000000 0 0 0 0 1 1 + 2 -0.1609476469712292E-02 0.000000000000000 0 0 0 0 0 2 + 3 0.2444580582844008E-04 0.000000000000000 3 0 0 0 0 0 + 3 -0.3302122534942095E-05 0.000000000000000 2 1 0 0 0 0 + 3 0.8580723679436340E-04 0.000000000000000 1 2 0 0 0 0 + 3 -0.3235607455120962E-04 0.000000000000000 0 3 0 0 0 0 + 3 -0.3640562829124676E-03 0.000000000000000 2 0 1 0 0 0 + 3 0.1099039406856618E-03 0.000000000000000 1 1 1 0 0 0 + 3 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INA = 131 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.3375726389921229E-02 0.000000000000000 1 0 0 0 0 0 + 1 0.3302213998354971E-03 0.000000000000000 0 1 0 0 0 0 + 1 -0.3479168603594852E-03 0.000000000000000 0 0 1 0 0 0 + 1 -0.3144002570262796E-02 0.000000000000000 0 0 0 1 0 0 + 1 -0.7969805946515344 0.000000000000000 0 0 0 0 1 0 + 1 -0.6006955499197988 0.000000000000000 0 0 0 0 0 1 + 2 -0.1015886622501391E-02 0.000000000000000 2 0 0 0 0 0 + 2 -0.2876929819692427E-02 0.000000000000000 1 1 0 0 0 0 + 2 -0.2303015566066642E-02 0.000000000000000 0 2 0 0 0 0 + 2 -0.6117321417523804E-02 0.000000000000000 1 0 1 0 0 0 + 2 0.7497482467949737E-03 0.000000000000000 0 1 1 0 0 0 + 2 0.2137457331022755E-04 0.000000000000000 0 0 2 0 0 0 + 2 0.1303865613491531E-02 0.000000000000000 1 0 0 1 0 0 + 2 -0.6061737722354680E-03 0.000000000000000 0 1 0 1 0 0 + 2 -0.5645283519594889E-04 0.000000000000000 0 0 1 1 0 0 + 2 -0.8326969887993169E-02 0.000000000000000 1 0 0 0 1 0 + 2 0.3918972085079738E-02 0.000000000000000 0 1 0 0 1 0 + 2 0.6255407288805448E-02 0.000000000000000 0 0 1 0 1 0 + 2 -0.2095613938881766E-02 0.000000000000000 1 0 0 0 0 1 + 2 -0.1531833391243228E-01 0.000000000000000 0 1 0 0 0 1 + 2 -0.2235716154617081E-02 0.000000000000000 0 0 1 0 0 1 + 2 -0.5825420394110148E-02 0.000000000000000 0 0 0 2 0 0 + 2 0.2681651357213832E-02 0.000000000000000 0 0 0 1 1 0 + 2 -0.8669835725822892E-02 0.000000000000000 0 0 0 0 2 0 + 2 0.2505853296335770E-02 0.000000000000000 0 0 0 1 0 1 + 2 0.4120502691419656E-02 0.000000000000000 0 0 0 0 1 1 + 2 -0.4659773559107403E-02 0.000000000000000 0 0 0 0 0 2 + 3 -0.5392972730348942E-04 0.000000000000000 3 0 0 0 0 0 + 3 0.2109334715151350E-04 0.000000000000000 2 1 0 0 0 0 + 3 -0.7205478393373613E-04 0.000000000000000 1 2 0 0 0 0 + 3 0.3122571331690538E-04 0.000000000000000 0 3 0 0 0 0 + 3 0.2577420076941614E-06 0.000000000000000 2 0 1 0 0 0 + 3 -0.9801524471496799E-05 0.000000000000000 1 1 1 0 0 0 + 3 -0.5690977913056824E-04 0.000000000000000 0 2 1 0 0 0 + 3 0.2753035178721820E-04 0.000000000000000 1 0 2 0 0 0 + 3 -0.5045382960995262E-04 0.000000000000000 0 1 2 0 0 0 + 3 -0.1350850128185882E-05 0.000000000000000 0 0 3 0 0 0 + 3 0.2965165507061937E-04 0.000000000000000 2 0 0 1 0 0 + 3 -0.1675992688746479E-04 0.000000000000000 1 1 0 1 0 0 + 3 0.1053921382043977E-03 0.000000000000000 0 2 0 1 0 0 + 3 0.6575880275452812E-04 0.000000000000000 1 0 1 1 0 0 + 3 0.8106060131886108E-04 0.000000000000000 0 1 1 1 0 0 + 3 0.4989906836273782E-04 0.000000000000000 0 0 2 1 0 0 + 3 -0.2576620590946497E-03 0.000000000000000 2 0 0 0 1 0 + 3 -0.6496572384343854E-04 0.000000000000000 1 1 0 0 1 0 + 3 -0.3698727535502254E-03 0.000000000000000 0 2 0 0 1 0 + 3 0.1615577385610975E-03 0.000000000000000 1 0 1 0 1 0 + 3 0.8147851161307147E-04 0.000000000000000 0 1 1 0 1 0 + 3 -0.3153865043022508E-03 0.000000000000000 0 0 2 0 1 0 + 3 0.1784217601871763E-03 0.000000000000000 2 0 0 0 0 1 + 3 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0.000000000000000 1 0 0 0 1 1 + 3 -0.2154544486708719E-03 0.000000000000000 0 1 0 0 1 1 + 3 0.5882788344142839E-04 0.000000000000000 0 0 1 0 1 1 + 3 -0.9675800343156708E-04 0.000000000000000 1 0 0 0 0 2 + 3 0.6902596264698091E-04 0.000000000000000 0 1 0 0 0 2 + 3 0.2864601851999181E-04 0.000000000000000 0 0 1 0 0 2 + 3 0.6978583069574244E-04 0.000000000000000 0 0 0 3 0 0 + 3 -0.3698173029087964E-03 0.000000000000000 0 0 0 2 1 0 + 3 0.2733018325473231E-04 0.000000000000000 0 0 0 1 2 0 + 3 -0.2811350961458392E-03 0.000000000000000 0 0 0 0 3 0 + 3 0.3462753773312862E-03 0.000000000000000 0 0 0 2 0 1 + 3 0.1301167557123534E-04 0.000000000000000 0 0 0 1 1 1 + 3 0.4312339223920099E-03 0.000000000000000 0 0 0 0 2 1 + 3 0.8352286907078042E-04 0.000000000000000 0 0 0 1 0 2 + 3 -0.3801230471238151E-03 0.000000000000000 0 0 0 0 1 2 + 3 0.4404468460691550E-03 0.000000000000000 0 0 0 0 0 3 + -83 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 130 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.3234814433454220E-02 0.000000000000000 1 0 0 0 0 0 + 1 0.1357883348001260E-02 0.000000000000000 0 1 0 0 0 0 + 1 -0.1149713691309673E-03 0.000000000000000 0 0 1 0 0 0 + 1 0.2338909601034744E-03 0.000000000000000 0 0 0 1 0 0 + 1 0.6061422287899446 0.000000000000000 0 0 0 0 1 0 + 1 -0.7978658493654193 0.000000000000000 0 0 0 0 0 1 + 2 -0.3246308766802652E-02 0.000000000000000 2 0 0 0 0 0 + 2 -0.1431197067135088E-02 0.000000000000000 1 1 0 0 0 0 + 2 0.2118257516480021E-02 0.000000000000000 0 2 0 0 0 0 + 2 -0.3250362816038322E-02 0.000000000000000 1 0 1 0 0 0 + 2 -0.2368245395905501E-02 0.000000000000000 0 1 1 0 0 0 + 2 0.1281775497310958E-02 0.000000000000000 0 0 2 0 0 0 + 2 -0.5765278084932161E-03 0.000000000000000 1 0 0 1 0 0 + 2 0.8171017546634266E-03 0.000000000000000 0 1 0 1 0 0 + 2 0.3383199168003160E-02 0.000000000000000 0 0 1 1 0 0 + 2 0.2835711170148060E-03 0.000000000000000 1 0 0 0 1 0 + 2 0.1076827874408290E-02 0.000000000000000 0 1 0 0 1 0 + 2 -0.2004588399164941E-02 0.000000000000000 0 0 1 0 1 0 + 2 0.1010950121609059E-01 0.000000000000000 1 0 0 0 0 1 + 2 0.8522548110680889E-02 0.000000000000000 0 1 0 0 0 1 + 2 -0.6080967806700334E-02 0.000000000000000 0 0 1 0 0 1 + 2 -0.2825874011842205E-02 0.000000000000000 0 0 0 2 0 0 + 2 0.2764711973510631E-02 0.000000000000000 0 0 0 1 1 0 + 2 -0.1306504434323557E-01 0.000000000000000 0 0 0 0 2 0 + 2 -0.2491990430453158E-02 0.000000000000000 0 0 0 1 0 1 + 2 -0.5479202090201884E-02 0.000000000000000 0 0 0 0 1 1 + 2 -0.6135265484633716E-03 0.000000000000000 0 0 0 0 0 2 + 3 0.5691693279830704E-04 0.000000000000000 3 0 0 0 0 0 + 3 -0.2373010945553241E-04 0.000000000000000 2 1 0 0 0 0 + 3 -0.3412205674119827E-04 0.000000000000000 1 2 0 0 0 0 + 3 -0.6530976971377357E-04 0.000000000000000 0 3 0 0 0 0 + 3 -0.1367274267061098E-05 0.000000000000000 2 0 1 0 0 0 + 3 0.3945886384983194E-04 0.000000000000000 1 1 1 0 0 0 + 3 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identity + Quaternion + c_quaternion + + 1, NO = 3, NV = 6, INA = 120 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 -0.1958201134215110 0.000000000000000 0 0 0 0 0 0 + 1 -4.332685575205621 0.000000000000000 1 0 0 0 0 0 + 1 12.24371391540661 0.000000000000000 0 1 0 0 0 0 + 1 0.1772263480198414 0.000000000000000 0 0 1 0 0 0 + 1 -6.541589039866645 0.000000000000000 0 0 0 1 0 0 + 1 -0.3475728424545270 0.000000000000000 0 0 0 0 1 0 + 1 -1.795757126692559 0.000000000000000 0 0 0 0 0 1 + 2 60.48851146040804 0.000000000000000 2 0 0 0 0 0 + 2 -40.92054131683324 0.000000000000000 1 1 0 0 0 0 + 2 -54.69890170438954 0.000000000000000 0 2 0 0 0 0 + 2 -42.22051380073097 0.000000000000000 1 0 1 0 0 0 + 2 52.83733049299954 0.000000000000000 0 1 1 0 0 0 + 2 112.1701698776015 0.000000000000000 0 0 2 0 0 0 + 2 105.1251537109505 0.000000000000000 1 0 0 1 0 0 + 2 265.2861956967640 0.000000000000000 0 1 0 1 0 0 + 2 2.626597866683241 0.000000000000000 0 0 1 1 0 0 + 2 -46.14988382499946 0.000000000000000 1 0 0 0 1 0 + 2 -172.9311651709200 0.000000000000000 0 1 0 0 1 0 + 2 129.4742873139263 0.000000000000000 0 0 1 0 1 0 + 2 94.43532638858250 0.000000000000000 1 0 0 0 0 1 + 2 1.427222153269181 0.000000000000000 0 1 0 0 0 1 + 2 -186.0190579147815 0.000000000000000 0 0 1 0 0 1 + 2 -106.7490735888826 0.000000000000000 0 0 0 2 0 0 + 2 299.6889865931734 0.000000000000000 0 0 0 1 1 0 + 2 -56.71906594970099 0.000000000000000 0 0 0 0 2 0 + 2 34.76381971188037 0.000000000000000 0 0 0 1 0 1 + 2 -71.76983000000314 0.000000000000000 0 0 0 0 1 1 + 2 61.92238508993285 0.000000000000000 0 0 0 0 0 2 + 3 47.68556704121434 0.000000000000000 3 0 0 0 0 0 + 3 -95.94381108470344 0.000000000000000 2 1 0 0 0 0 + 3 1163.702697166684 0.000000000000000 1 2 0 0 0 0 + 3 -1572.893089228891 0.000000000000000 0 3 0 0 0 0 + 3 172.3929440750692 0.000000000000000 2 0 1 0 0 0 + 3 -1587.700347864375 0.000000000000000 1 1 1 0 0 0 + 3 1154.405731098298 0.000000000000000 0 2 1 0 0 0 + 3 1549.273990286499 0.000000000000000 1 0 2 0 0 0 + 3 -41.16292989957799 0.000000000000000 0 1 2 0 0 0 + 3 -57.00952677664753 0.000000000000000 0 0 3 0 0 0 + 3 647.8652622442791 0.000000000000000 2 0 0 1 0 0 + 3 -1398.090963309525 0.000000000000000 1 1 0 1 0 0 + 3 5233.533042256353 0.000000000000000 0 2 0 1 0 0 + 3 1812.143089273384 0.000000000000000 1 0 1 1 0 0 + 3 -1653.252643055521 0.000000000000000 0 1 1 1 0 0 + 3 -385.2251334303332 0.000000000000000 0 0 2 1 0 0 + 3 219.4586127684631 0.000000000000000 2 0 0 0 1 0 + 3 -311.8979395815612 0.000000000000000 1 1 0 0 1 0 + 3 -505.2372306729944 0.000000000000000 0 2 0 0 1 0 + 3 -1117.045672213736 0.000000000000000 1 0 1 0 1 0 + 3 1226.112131659966 0.000000000000000 0 1 1 0 1 0 + 3 384.6191462889236 0.000000000000000 0 0 2 0 1 0 + 3 273.4828102943407 0.000000000000000 2 0 0 0 0 1 + 3 1862.549562327978 0.000000000000000 1 1 0 0 0 1 + 3 629.3258756772393 0.000000000000000 0 2 0 0 0 1 + 3 -2424.212404185655 0.000000000000000 1 0 1 0 0 1 + 3 513.5599720699952 0.000000000000000 0 1 1 0 0 1 + 3 274.9035838415575 0.000000000000000 0 0 2 0 0 1 + 3 1176.934007289864 0.000000000000000 1 0 0 2 0 0 + 3 -4197.237331665051 0.000000000000000 0 1 0 2 0 0 + 3 248.3461702523448 0.000000000000000 0 0 1 2 0 0 + 3 -1211.894612964393 0.000000000000000 1 0 0 1 1 0 + 3 1912.337942004780 0.000000000000000 0 1 0 1 1 0 + 3 -1019.161142087936 0.000000000000000 0 0 1 1 1 0 + 3 494.2177214186884 0.000000000000000 1 0 0 0 2 0 + 3 -450.1263222796902 0.000000000000000 0 1 0 0 2 0 + 3 424.4610559672201 0.000000000000000 0 0 1 0 2 0 + 3 -2334.179005812496 0.000000000000000 1 0 0 1 0 1 + 3 -256.0737927777349 0.000000000000000 0 1 0 1 0 1 + 3 840.6656423692909 0.000000000000000 0 0 1 1 0 1 + 3 1096.863641386835 0.000000000000000 1 0 0 0 1 1 + 3 -223.7212641308320 0.000000000000000 0 1 0 0 1 1 + 3 -930.6583884186667 0.000000000000000 0 0 1 0 1 1 + 3 2047.393050719109 0.000000000000000 1 0 0 0 0 2 + 3 -6.777724021085078 0.000000000000000 0 1 0 0 0 2 + 3 -377.8801297585310 0.000000000000000 0 0 1 0 0 2 + 3 2304.252177260119 0.000000000000000 0 0 0 3 0 0 + 3 -2147.504525280832 0.000000000000000 0 0 0 2 1 0 + 3 311.1770875512000 0.000000000000000 0 0 0 1 2 0 + 3 176.5981582426425 0.000000000000000 0 0 0 0 3 0 + 3 912.4425528314387 0.000000000000000 0 0 0 2 0 1 + 3 -821.0898744302617 0.000000000000000 0 0 0 1 1 1 + 3 242.8654889320730 0.000000000000000 0 0 0 0 2 1 + 3 576.3923252838508 0.000000000000000 0 0 0 1 0 2 + 3 -325.1526822505619 0.000000000000000 0 0 0 0 1 2 + 3 394.0002137042621 0.000000000000000 0 0 0 0 0 3 + -84 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 119 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 -0.9141356293737908 0.000000000000000 0 0 0 0 0 0 + 1 3.835606878752129 0.000000000000000 1 0 0 0 0 0 + 1 -2.426056589288625 0.000000000000000 0 1 0 0 0 0 + 1 -4.243970112261902 0.000000000000000 0 0 1 0 0 0 + 1 -0.3686827839065454E-01 0.000000000000000 0 0 0 1 0 0 + 1 0.1024710012201643 0.000000000000000 0 0 0 0 1 0 + 1 4.938607246491936 0.000000000000000 0 0 0 0 0 1 + 2 41.39283916878784 0.000000000000000 2 0 0 0 0 0 + 2 70.77162336903970 0.000000000000000 1 1 0 0 0 0 + 2 172.2488053328933 0.000000000000000 0 2 0 0 0 0 + 2 -176.8529193273664 0.000000000000000 1 0 1 0 0 0 + 2 -126.1127683651465 0.000000000000000 0 1 1 0 0 0 + 2 85.16976558656231 0.000000000000000 0 0 2 0 0 0 + 2 -179.4056678168968 0.000000000000000 1 0 0 1 0 0 + 2 -413.4457784024020 0.000000000000000 0 1 0 1 0 0 + 2 215.7159848073787 0.000000000000000 0 0 1 1 0 0 + 2 146.6546444572223 0.000000000000000 1 0 0 0 1 0 + 2 349.6544626461306 0.000000000000000 0 1 0 0 1 0 + 2 -175.8499060530543 0.000000000000000 0 0 1 0 1 0 + 2 178.2613407995911 0.000000000000000 1 0 0 0 0 1 + 2 145.0959655140650 0.000000000000000 0 1 0 0 0 1 + 2 -186.5114002790896 0.000000000000000 0 0 1 0 0 1 + 2 271.7671869470216 0.000000000000000 0 0 0 2 0 0 + 2 -453.4052044935634 0.000000000000000 0 0 0 1 1 0 + 2 198.5237137120463 0.000000000000000 0 0 0 0 2 0 + 2 -274.7935905844946 0.000000000000000 0 0 0 1 0 1 + 2 222.0372265210610 0.000000000000000 0 0 0 0 1 1 + 2 121.0788900655871 0.000000000000000 0 0 0 0 0 2 + 3 -909.4457355914601 0.000000000000000 3 0 0 0 0 0 + 3 177.2830441646231 0.000000000000000 2 1 0 0 0 0 + 3 -1829.772853547436 0.000000000000000 1 2 0 0 0 0 + 3 -823.0486346056667 0.000000000000000 0 3 0 0 0 0 + 3 573.3958875962210 0.000000000000000 2 0 1 0 0 0 + 3 -24.33195306866678 0.000000000000000 1 1 1 0 0 0 + 3 400.4277094112198 0.000000000000000 0 2 1 0 0 0 + 3 -463.0262751482569 0.000000000000000 1 0 2 0 0 0 + 3 596.1209611186006 0.000000000000000 0 1 2 0 0 0 + 3 551.4276110732444 0.000000000000000 0 0 3 0 0 0 + 3 55.76393725341632 0.000000000000000 2 0 0 1 0 0 + 3 2240.281789423460 0.000000000000000 1 1 0 1 0 0 + 3 2439.516900435840 0.000000000000000 0 2 0 1 0 0 + 3 -330.9878180447280 0.000000000000000 1 0 1 1 0 0 + 3 1137.014357866853 0.000000000000000 0 1 1 1 0 0 + 3 670.9060746461190 0.000000000000000 0 0 2 1 0 0 + 3 -188.1992112835325 0.000000000000000 2 0 0 0 1 0 + 3 -452.3836532326612 0.000000000000000 1 1 0 0 1 0 + 3 -2515.217508122940 0.000000000000000 0 2 0 0 1 0 + 3 513.1091694543032 0.000000000000000 1 0 1 0 1 0 + 3 -953.1829163178579 0.000000000000000 0 1 1 0 1 0 + 3 -1295.917811004144 0.000000000000000 0 0 2 0 1 0 + 3 -1986.479129297298 0.000000000000000 2 0 0 0 0 1 + 3 -945.8540224265096 0.000000000000000 1 1 0 0 0 1 + 3 -355.5510682577445 0.000000000000000 0 2 0 0 0 1 + 3 2255.443836082639 0.000000000000000 1 0 1 0 0 1 + 3 -2511.619639970775 0.000000000000000 0 1 1 0 0 1 + 3 -2002.217468816046 0.000000000000000 0 0 2 0 0 1 + 3 -1522.328355968220 0.000000000000000 1 0 0 2 0 0 + 3 -2125.862138063136 0.000000000000000 0 1 0 2 0 0 + 3 -27.86764702484800 0.000000000000000 0 0 1 2 0 0 + 3 881.3767572200693 0.000000000000000 1 0 0 1 1 0 + 3 3932.246836074172 0.000000000000000 0 1 0 1 1 0 + 3 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1127.033313653610 0.000000000000000 0 0 0 0 2 1 + 3 1266.334670198522 0.000000000000000 0 0 0 1 0 2 + 3 -1372.676567461959 0.000000000000000 0 0 0 0 1 2 + 3 -1914.747827429902 0.000000000000000 0 0 0 0 0 3 + -84 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 118 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 -0.1076369453110744 0.000000000000000 0 0 0 0 0 0 + 1 2.499162282282532 0.000000000000000 1 0 0 0 0 0 + 1 13.02891439453220 0.000000000000000 0 1 0 0 0 0 + 1 -3.421976033556220 0.000000000000000 0 0 1 0 0 0 + 1 -17.66187224392267 0.000000000000000 0 0 0 1 0 0 + 1 16.40791372914529 0.000000000000000 0 0 0 0 1 0 + 1 4.228965454014198 0.000000000000000 0 0 0 0 0 1 + 2 -68.34763724358122 0.000000000000000 2 0 0 0 0 0 + 2 -127.4365760655281 0.000000000000000 1 1 0 0 0 0 + 2 21.95360859719769 0.000000000000000 0 2 0 0 0 0 + 2 159.8698483419990 0.000000000000000 1 0 1 0 0 0 + 2 -11.47342757759136 0.000000000000000 0 1 1 0 0 0 + 2 -89.27774931136774 0.000000000000000 0 0 2 0 0 0 + 2 132.9629083209089 0.000000000000000 1 0 0 1 0 0 + 2 -101.7838648301049 0.000000000000000 0 1 0 1 0 0 + 2 -27.44589939244567 0.000000000000000 0 0 1 1 0 0 + 2 -74.49730084622999 0.000000000000000 1 0 0 0 1 0 + 2 -17.36529920312919 0.000000000000000 0 1 0 0 1 0 + 2 80.41534776056486 0.000000000000000 0 0 1 0 1 0 + 2 -252.8046727782150 0.000000000000000 1 0 0 0 0 1 + 2 -43.01972058448825 0.000000000000000 0 1 0 0 0 1 + 2 160.6696520155641 0.000000000000000 0 0 1 0 0 1 + 2 -34.01783889763676 0.000000000000000 0 0 0 2 0 0 + 2 72.65245074437955 0.000000000000000 0 0 0 1 1 0 + 2 -6.569847542161854 0.000000000000000 0 0 0 0 2 0 + 2 69.65772661697024 0.000000000000000 0 0 0 1 0 1 + 2 -61.22830144516571 0.000000000000000 0 0 0 0 1 1 + 2 -202.3259172013142 0.000000000000000 0 0 0 0 0 2 + 3 86.69449972070740 0.000000000000000 3 0 0 0 0 0 + 3 -122.8030993424216 0.000000000000000 2 1 0 0 0 0 + 3 -1681.762737057522 0.000000000000000 1 2 0 0 0 0 + 3 -974.4398854140386 0.000000000000000 0 3 0 0 0 0 + 3 381.7295307652059 0.000000000000000 2 0 1 0 0 0 + 3 2122.724562484363 0.000000000000000 1 1 1 0 0 0 + 3 1669.616689403860 0.000000000000000 0 2 1 0 0 0 + 3 -572.7918661364236 0.000000000000000 1 0 2 0 0 0 + 3 -97.95854190590234 0.000000000000000 0 1 2 0 0 0 + 3 -531.1394078799109 0.000000000000000 0 0 3 0 0 0 + 3 748.5745090932802 0.000000000000000 2 0 0 1 0 0 + 3 4632.487126588780 0.000000000000000 1 1 0 1 0 0 + 3 5213.128575734858 0.000000000000000 0 2 0 1 0 0 + 3 -2071.309753385420 0.000000000000000 1 0 1 1 0 0 + 3 -3185.453460902152 0.000000000000000 0 1 1 1 0 0 + 3 -177.2237706163904 0.000000000000000 0 0 2 1 0 0 + 3 -963.3339296245952 0.000000000000000 2 0 0 0 1 0 + 3 -3605.402268421945 0.000000000000000 1 1 0 0 1 0 + 3 -3989.850585083847 0.000000000000000 0 2 0 0 1 0 + 3 2475.041881772252 0.000000000000000 1 0 1 0 1 0 + 3 3649.349301942405 0.000000000000000 0 1 1 0 1 0 + 3 -1006.441566819659 0.000000000000000 0 0 2 0 1 0 + 3 329.4583642069102 0.000000000000000 2 0 0 0 0 1 + 3 -1523.316199800553 0.000000000000000 1 1 0 0 0 1 + 3 -983.7900198815418 0.000000000000000 0 2 0 0 0 1 + 3 1765.923551907984 0.000000000000000 1 0 1 0 0 1 + 3 649.1458956830157 0.000000000000000 0 1 1 0 0 1 + 3 921.8763168929461 0.000000000000000 0 0 2 0 0 1 + 3 -2761.287696708246 0.000000000000000 1 0 0 2 0 0 + 3 -5753.829754721616 0.000000000000000 0 1 0 2 0 0 + 3 777.6427054080920 0.000000000000000 0 0 1 2 0 0 + 3 4615.480797039757 0.000000000000000 1 0 0 1 1 0 + 3 11622.89680338953 0.000000000000000 0 1 0 1 1 0 + 3 -3851.117328237452 0.000000000000000 0 0 1 1 1 0 + 3 -1648.405707660532 0.000000000000000 1 0 0 0 2 0 + 3 -6430.622044063362 0.000000000000000 0 1 0 0 2 0 + 3 1125.357062542797 0.000000000000000 0 0 1 0 2 0 + 3 2387.242152777638 0.000000000000000 1 0 0 1 0 1 + 3 4554.355111732526 0.000000000000000 0 1 0 1 0 1 + 3 -729.1448838678496 0.000000000000000 0 0 1 1 0 1 + 3 -1121.803380435633 0.000000000000000 1 0 0 0 1 1 + 3 -3610.247907610883 0.000000000000000 0 1 0 0 1 1 + 3 1378.929982071900 0.000000000000000 0 0 1 0 1 1 + 3 -1642.999930582444 0.000000000000000 1 0 0 0 0 2 + 3 -2297.088755129128 0.000000000000000 0 1 0 0 0 2 + 3 -879.8587168530942 0.000000000000000 0 0 1 0 0 2 + 3 1816.161644051974 0.000000000000000 0 0 0 3 0 0 + 3 -6780.861716447980 0.000000000000000 0 0 0 2 1 0 + 3 6252.132505111543 0.000000000000000 0 0 0 1 2 0 + 3 -2149.706565587670 0.000000000000000 0 0 0 0 3 0 + 3 -2303.729902164059 0.000000000000000 0 0 0 2 0 1 + 3 4696.490999852344 0.000000000000000 0 0 0 1 1 1 + 3 -1942.912529857008 0.000000000000000 0 0 0 0 2 1 + 3 2120.660534871240 0.000000000000000 0 0 0 1 0 2 + 3 -1922.768353235656 0.000000000000000 0 0 0 0 1 2 + 3 620.8605214137242 0.000000000000000 0 0 0 0 0 3 + -84 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 117 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 -0.3382673828392587 0.000000000000000 0 0 0 0 0 0 + 1 -8.652445579342437 0.000000000000000 1 0 0 0 0 0 + 1 -4.677404050413464 0.000000000000000 0 1 0 0 0 0 + 1 12.45520871051883 0.000000000000000 0 0 1 0 0 0 + 1 9.506524881099613 0.000000000000000 0 0 0 1 0 0 + 1 -5.296722188983420 0.000000000000000 0 0 0 0 1 0 + 1 -13.65223085894155 0.000000000000000 0 0 0 0 0 1 + 2 44.25649918036787 0.000000000000000 2 0 0 0 0 0 + 2 -95.44556133772457 0.000000000000000 1 1 0 0 0 0 + 2 72.72902126489294 0.000000000000000 0 2 0 0 0 0 + 2 57.23614926518145 0.000000000000000 1 0 1 0 0 0 + 2 46.69640709076307 0.000000000000000 0 1 1 0 0 0 + 2 6.592741191478250 0.000000000000000 0 0 2 0 0 0 + 2 91.37870199001456 0.000000000000000 1 0 0 1 0 0 + 2 -52.12424373412836 0.000000000000000 0 1 0 1 0 0 + 2 -49.99723694340268 0.000000000000000 0 0 1 1 0 0 + 2 -83.57854713122062 0.000000000000000 1 0 0 0 1 0 + 2 -147.3716544064612 0.000000000000000 0 1 0 0 1 0 + 2 12.19621494405408 0.000000000000000 0 0 1 0 1 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3 -1861.594366772231 0.000000000000000 2 0 0 1 0 0 + 3 -518.9867414600877 0.000000000000000 1 1 0 1 0 0 + 3 23.42549345035889 0.000000000000000 0 2 0 1 0 0 + 3 2415.500303967344 0.000000000000000 1 0 1 1 0 0 + 3 2420.089862590135 0.000000000000000 0 1 1 1 0 0 + 3 -3133.754546726516 0.000000000000000 0 0 2 1 0 0 + 3 471.6886521998772 0.000000000000000 2 0 0 0 1 0 + 3 3311.991689659324 0.000000000000000 1 1 0 0 1 0 + 3 995.5298778348356 0.000000000000000 0 2 0 0 1 0 + 3 -2237.442878725181 0.000000000000000 1 0 1 0 1 0 + 3 -1527.166164359405 0.000000000000000 0 1 1 0 1 0 + 3 986.1795768580652 0.000000000000000 0 0 2 0 1 0 + 3 1602.386324054921 0.000000000000000 2 0 0 0 0 1 + 3 2409.400925184020 0.000000000000000 1 1 0 0 0 1 + 3 177.9019332473923 0.000000000000000 0 2 0 0 0 1 + 3 -4747.081329539311 0.000000000000000 1 0 1 0 0 1 + 3 -2510.038313974769 0.000000000000000 0 1 1 0 0 1 + 3 3082.096730521561 0.000000000000000 0 0 2 0 0 1 + 3 2220.318733525844 0.000000000000000 1 0 0 2 0 0 + 3 1700.364219896285 0.000000000000000 0 1 0 2 0 0 + 3 -3626.552484240502 0.000000000000000 0 0 1 2 0 0 + 3 -5081.298647999360 0.000000000000000 1 0 0 1 1 0 + 3 -3394.558150559058 0.000000000000000 0 1 0 1 1 0 + 3 2961.239272230329 0.000000000000000 0 0 1 1 1 0 + 3 1704.988569949293 0.000000000000000 1 0 0 0 2 0 + 3 2575.710975142705 0.000000000000000 0 1 0 0 2 0 + 3 -1887.267785685976 0.000000000000000 0 0 1 0 2 0 + 3 -3061.692592597084 0.000000000000000 1 0 0 1 0 1 + 3 -978.9456241093465 0.000000000000000 0 1 0 1 0 1 + 3 3609.004159307790 0.000000000000000 0 0 1 1 0 1 + 3 2316.279764370226 0.000000000000000 1 0 0 0 1 1 + 3 2710.732140435710 0.000000000000000 0 1 0 0 1 1 + 3 -1567.799001006000 0.000000000000000 0 0 1 0 1 1 + 3 3172.731014706633 0.000000000000000 1 0 0 0 0 2 + 3 1533.857274309677 0.000000000000000 0 1 0 0 0 2 + 3 -2230.617696932195 0.000000000000000 0 0 1 0 0 2 + 3 -1657.207198600324 0.000000000000000 0 0 0 3 0 0 + 3 2936.547714346649 0.000000000000000 0 0 0 2 1 0 + 3 -4288.907211425025 0.000000000000000 0 0 0 1 2 0 + 3 1411.617314932849 0.000000000000000 0 0 0 0 3 0 + 3 3418.564716693405 0.000000000000000 0 0 0 2 0 1 + 3 -5175.668449512717 0.000000000000000 0 0 0 1 1 1 + 3 2049.541560347549 0.000000000000000 0 0 0 0 2 1 + 3 -2411.660120183091 0.000000000000000 0 0 0 1 0 2 + 3 1548.120249007944 0.000000000000000 0 0 0 0 1 2 + 3 1879.312016813623 0.000000000000000 0 0 0 0 0 3 + -84 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + No Stochastic Radiation \ No newline at end of file diff --git a/test/radiation/.ipynb_checkpoints/R-checkpoint.map b/test/radiation/.ipynb_checkpoints/R-checkpoint.map new file mode 100644 index 0000000..6f7c7bb --- /dev/null +++ b/test/radiation/.ipynb_checkpoints/R-checkpoint.map @@ -0,0 +1,100 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 8, INA = 184 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 0.7908959332811654 -0.6695991550019673E-01 1 0 0 0 0 0 0 0 + 2 -0.2674551503347272E-03 -0.3158473553075905E-02 1 0 0 0 0 0 1 0 + 2 -0.2330304072250565E-03 -0.2751099950742762E-02 1 0 0 0 0 0 0 1 + 3 0.1295021869335785E-04 0.1538655889331663E-03 2 1 0 0 0 0 0 0 + 3 -0.1090507745644914E-05 -0.1283815559391832E-04 1 0 1 1 0 0 0 0 + 3 0.4872137818799815E-06 0.8597403640235870E-05 1 0 0 0 1 1 0 0 + 3 -0.5049442942341548E-05 0.1632852637248317E-04 1 0 0 0 0 0 2 0 + 3 -0.1126961263316189E-04 -0.2960336878691315E-06 1 0 0 0 0 0 1 1 + 3 -0.5466170471736421E-05 -0.5770808010332199E-05 1 0 0 0 0 0 0 2 + -9 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 183 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 0.7908959332811654 0.6695991550019673E-01 0 1 0 0 0 0 0 0 + 2 -0.2674551503347265E-03 0.3158473553075904E-02 0 1 0 0 0 0 1 0 + 2 -0.2330304072250561E-03 0.2751099950742763E-02 0 1 0 0 0 0 0 1 + 3 0.1295021869335756E-04 -0.1538655889331665E-03 1 2 0 0 0 0 0 0 + 3 -0.1090507745644899E-05 0.1283815559391830E-04 0 1 1 1 0 0 0 0 + 3 0.4872137818799518E-06 -0.8597403640235845E-05 0 1 0 0 1 1 0 0 + 3 -0.5049442942341412E-05 -0.1632852637248290E-04 0 1 0 0 0 0 2 0 + 3 -0.1126961263316196E-04 0.2960336878690118E-06 0 1 0 0 0 0 1 1 + 3 -0.5466170471736424E-05 0.5770808010332127E-05 0 1 0 0 0 0 0 2 + -9 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 182 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.5943538218748672 0.4655570859915613 0 0 1 0 0 0 0 0 + 2 0.1458046436420680E-02 0.1861082549789210E-02 0 0 1 0 0 0 1 0 + 2 0.8777678663247976E-03 0.1120303385786709E-02 0 0 1 0 0 0 0 1 + 3 0.3722436835540079E-05 0.4633500015660966E-05 1 1 1 0 0 0 0 0 + 3 -0.9645298769864392E-05 -0.1238272013865765E-04 0 0 2 1 0 0 0 0 + 3 -0.2456615421394505E-04 -0.3197190867475002E-04 0 0 1 0 1 1 0 0 + 3 -0.2850106343387933E-05 -0.9816202440784224E-05 0 0 1 0 0 0 2 0 + 3 -0.2037043132020785E-05 -0.1013959395523847E-04 0 0 1 0 0 0 1 1 + 3 -0.5316672881586423E-05 -0.9085044159686621E-05 0 0 1 0 0 0 0 2 + -9 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 181 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.5943538218748672 -0.4655570859915613 0 0 0 1 0 0 0 0 + 2 0.1458046436420680E-02 -0.1861082549789210E-02 0 0 0 1 0 0 1 0 + 2 0.8777678663247976E-03 -0.1120303385786709E-02 0 0 0 1 0 0 0 1 + 3 0.3722436835540121E-05 -0.4633500015660982E-05 1 1 0 1 0 0 0 0 + 3 -0.9645298769864392E-05 0.1238272013865764E-04 0 0 1 2 0 0 0 0 + 3 -0.2456615421394505E-04 0.3197190867475002E-04 0 0 0 1 1 1 0 0 + 3 -0.2850106343387928E-05 0.9816202440784224E-05 0 0 0 1 0 0 2 0 + 3 -0.2037043132020784E-05 0.1013959395523847E-04 0 0 0 1 0 0 1 1 + 3 -0.5316672881586421E-05 0.9085044159686624E-05 0 0 0 1 0 0 0 2 + -9 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 180 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.3293100781067481 -0.4019389664354702 0 0 0 0 1 0 0 0 + 2 -0.1104901043456016E-02 0.9050258856907777E-03 0 0 0 0 1 0 1 0 + 2 -0.1227908064067363E-02 0.1005769895510704E-02 0 0 0 0 1 0 0 1 + 3 0.2813502223841236E-04 -0.2324540912087560E-04 1 1 0 0 1 0 0 0 + 3 0.1650702165408676E-04 -0.1360304875828599E-04 0 0 1 1 1 0 0 0 + 3 0.4401333986152190E-04 -0.3632897685989845E-04 0 0 0 0 2 1 0 0 + 3 0.5505162202298586E-05 -0.2136010249235780E-05 0 0 0 0 1 0 2 0 + 3 0.4821285916781770E-05 0.1368000638527462E-05 0 0 0 0 1 0 1 1 + 3 0.5079389507815567E-05 -0.1228217232637109E-05 0 0 0 0 1 0 0 2 + -9 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 179 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.3293100781067481 0.4019389664354702 0 0 0 0 0 1 0 0 + 2 -0.1104901043456016E-02 -0.9050258856907777E-03 0 0 0 0 0 1 1 0 + 2 -0.1227908064067363E-02 -0.1005769895510704E-02 0 0 0 0 0 1 0 1 + 3 0.2813502223841236E-04 0.2324540912087568E-04 1 1 0 0 0 1 0 0 + 3 0.1650702165408676E-04 0.1360304875828599E-04 0 0 1 1 0 1 0 0 + 3 0.4401333986152191E-04 0.3632897685989844E-04 0 0 0 0 1 2 0 0 + 3 0.5505162202298583E-05 0.2136010249235782E-05 0 0 0 0 0 1 2 0 + 3 0.4821285916781775E-05 -0.1368000638527462E-05 0 0 0 0 0 1 1 1 + 3 0.5079389507815567E-05 0.1228217232637109E-05 0 0 0 0 0 1 0 2 + -9 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + Spin Matrix is identity + c_quaternion is identity + Stochastic Radiation \ No newline at end of file diff --git a/test/radiation/.ipynb_checkpoints/test-checkpoint.map b/test/radiation/.ipynb_checkpoints/test-checkpoint.map new file mode 100644 index 0000000..c7ba04a --- /dev/null +++ b/test/radiation/.ipynb_checkpoints/test-checkpoint.map @@ -0,0 +1,1066 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 8, INA = 184 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 0.8910372041775222 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.1376741773228439 0.000000000000000 0 1 0 0 0 0 0 0 + 1 -0.5536136885324756E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.4705508139691222E-04 0.000000000000000 0 0 0 1 0 0 0 0 + 1 -0.5180705827569297E-04 0.000000000000000 0 0 0 0 1 0 0 0 + 1 0.1115890029217075E-02 0.000000000000000 0 0 0 0 0 1 0 0 + 1 0.1021997333870391E-02 0.000000000000000 0 0 0 0 0 0 1 0 + 1 0.3410596525327765E-03 0.000000000000000 0 0 0 0 0 0 0 1 + 2 0.1058179067056163E-02 0.000000000000000 2 0 0 0 0 0 0 0 + 2 0.3410880510950978E-02 0.000000000000000 1 1 0 0 0 0 0 0 + 2 0.7086616665419881E-03 0.000000000000000 0 2 0 0 0 0 0 0 + 2 -0.2894075789719156E-03 0.000000000000000 1 0 1 0 0 0 0 0 + 2 -0.1242027947192844E-02 0.000000000000000 0 1 1 0 0 0 0 0 + 2 0.1222776129203476E-02 0.000000000000000 0 0 2 0 0 0 0 0 + 2 0.5597898583092443E-03 0.000000000000000 1 0 0 1 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-0.6232539999888361E-05 0.000000000000000 0 0 0 0 0 0 2 1 + 3 0.8324206210753609E-06 0.000000000000000 0 0 0 0 1 0 0 2 + 3 -0.4388778018072103E-05 0.000000000000000 0 0 0 0 0 1 0 2 + 3 -0.6187543607804073E-05 0.000000000000000 0 0 0 0 0 0 1 2 + 3 -0.1620275688674411E-05 0.000000000000000 0 0 0 0 0 0 0 3 + -164 0.000000000000000 0.000000000000000 0 0 0 0 0 0 0 0 + + 1, NO = 3, NV = 8, INA = 183 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 8 + 1 -0.1054078687710558 0.000000000000000 1 0 0 0 0 0 0 0 + 1 0.6907544923778413 0.000000000000000 0 1 0 0 0 0 0 0 + 1 0.2874869774793682E-03 0.000000000000000 0 0 1 0 0 0 0 0 + 1 -0.3087216790400928E-03 0.000000000000000 0 0 0 1 0 0 0 0 + 1 0.1199411601155604E-03 0.000000000000000 0 0 0 0 1 0 0 0 + 1 -0.1083308939758020E-02 0.000000000000000 0 0 0 0 0 1 0 0 + 1 -0.1435701141555291E-02 0.000000000000000 0 0 0 0 0 0 1 0 + 1 -0.3497656283358658E-03 0.000000000000000 0 0 0 0 0 0 0 1 + 2 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(6.01126470886281740E-005,0.0000000000000000) + 5 5 (1.00583982333440146E-004,0.0000000000000000) + 5 6 (1.20598560658544330E-004,0.0000000000000000) + 6 1 (9.76589477976747277E-005,0.0000000000000000) + 6 2 (8.54117454075056779E-006,0.0000000000000000) + 6 3 (6.07103751080318008E-005,0.0000000000000000) + 6 4 (5.28408796909018443E-005,0.0000000000000000) + 6 5 (1.20598560658544330E-004,0.0000000000000000) + 6 6 (5.66006422587618803E-005,0.0000000000000000) \ No newline at end of file diff --git a/test/runtests.jl b/test/runtests.jl index ba14737..93906df 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,4 +1,5 @@ using NonlinearNormalForm +using NonlinearNormalForm: NonlinearNormalForm as NNF using TPSAInterface using TPSAInterface: TPSAInterface as TI using Test, GTPSA @@ -121,7 +122,22 @@ end r_rot = one(a_fpp) NonlinearNormalForm.setray!(r_rot.v, v_matrix=R_rot) a = a ∘ r_rot + NonlinearNormalForm.setscalar!(a, 0) # bc FPP doesn't handle consistently @test norm(a - a_fpp) < 2e-7 + # Canonization with damping + m = real(read_fpp_map("canonize_rad2/test.map", spin=false, stochastic=false)); + a_fpp = real(read_fpp_map("canonize_rad2/a.map", spin=false, stochastic=false)); + ac_norad_fpp = real(read_fpp_map("canonize_rad2/ac_norad.map", spin=false, stochastic=false)); + ac_fpp = real(read_fpp_map("canonize_rad2/ac.map", spin=false, stochastic=false)); + + a = normal(m); + ac_norad = a ∘ canonize(a) + @test norm(NNF.jacobian(ac_norad - ac_norad_fpp)) < 1e-12 + + damp = zeros(3) + ac = ac_norad ∘ canonize(ac_norad; damping=true, damp=damp) + @test norm(damp - [ 7.0794145850303742E-009 , 3.2927211731860217E-007 , 5.5985424078986008E-007]) < 1e-12 + @test norm(NNF.jacobian(ac-ac_fpp)) < 1e-12 end