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Merged
mattsignorelli merged 2 commits into from
Dec 29, 2025
Merged

NNF inverter #69

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c0d95bb
NNF inverter
mattsignorelli Dec 18, 2025
66ef809
own inv, fix sagan-rubin
mattsignorelli Dec 19, 2025
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55 changes: 54 additions & 1 deletion src/map.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -547,13 +547,66 @@ function inv!(
m::TaylorMap,
m1::TaylorMap;
do_spin::Bool=true,
work_vs::NTuple{3}=m.v isa StaticArray ?
ntuple(t->StaticArrays.sacollect(MVector{nvars(m)}, zero(first(m.v)) for i in 1:nvars(m)), Val{3}()) :
ntuple(t->zero.(view(m.v, 1:nvars(m))), Val{3}()),
work_q::Union{Nothing,Quaternion}=isnothing(m.q) ? nothing : zero(m.q)
)

checkinplace(m, m1)
!(m === m1) || error("Cannot inv!(m, m1) with m === m1")

TI.inv!(m.v, m1.v)
# Following Dragt book:
# We can use the equation on Wikipedia
# for inverse of block matrices: https://en.wikipedia.org/wiki/Block_matrix#Inversion
A = jacobian(m1, VARS)
B = jacobian(m1, PARAMS)
Ri = hcat(inv(A), -inv(A)*B)

clear!(m)
setray!(m.v, v_matrix=Ri)

mo = maxord(m1)
if mo > 1
nn = ndiffs(m)
nv = nvars(m)
np = nparams(m)

ri = work_vs[1]
Ntilde = work_vs[2]
tmp = work_vs[3]

# Put N-not-tilde in tmp
for j in 1:nv
TI.clear!(ri[j])
TI.clear!(Ntilde[j])
TI.cutord!(tmp[j], m1.v[j], -1)
end

# (nv x nn) * (nn x 1) = (nv x 1)
# Use first TPSA in ri as temporary
tt = first(ri)
for j in 1:nv
for i in 1:nv
TI.mul!(tt, -Ri[i,j], tmp[j])
TI.add!(Ntilde[i], Ntilde[i], tt)
end
end

# now can set ri, tt dead
TI.clear!(tt)
setray!(ri, v_matrix=Ri)

# At each step in iteration, m should contain the result up to
# that order
for i in 2:mo
TI.compose!(view(tmp, 1:nv), view(Ntilde, 1:nv), m.v)
for j in 1:nv
TI.cutord!(tmp[j], tmp[j], mo+1)
TI.add!(m.v[j], ri[j], tmp[j])
end
end
end

# Now do quaternion: inverse of q(z0) is q^-1(M^-1(zf))
if !isnothing(m.q)
Expand Down
40 changes: 28 additions & 12 deletions src/sagan_rubin.jl
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Expand Up @@ -12,6 +12,22 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V

# If we are coasting, then we will not return any dispersion stuff, since
# that is all well-defined in the parameter-dependent fixed point.

# Note: generators (for i in _ for j in _) act in ORDER. So this would be like
# for i in _
# for j in _
# ...

# Then, if a matrix is constructed from this result, it is filled in column-major order
#= Observe:
julia> StaticArrays.sacollect(SMatrix{2,2}, (i, j) for j=1:2 for i=1:2)
2×2 SMatrix{2, 2, Tuple{Int64, Int64}, 4} with indices SOneTo(2)×SOneTo(2):
(1, 1) (1, 2)
(2, 1) (2, 2)

The tuple of indices works when COLUMN is first
So the order is basically for col in cols for row in rows
=#
nv = nvars(a1)
nhv = nhvars(a1)
coast = iscoasting(a1)
Expand All @@ -20,12 +36,12 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V
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))
gamma_c = sqrt(H[1][1,1])
C = nv > 2 ? StaticArrays.sacollect(SMatrix{2,2,eltype(H[1])}, H[1][i,j] for i in 3:4 for j in 3:4) : 0
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[i,j] for i in 1:nvm for j in 1:nvm)
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,i+1]*N[i,i] 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))
# 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))
Expand All @@ -40,12 +56,12 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V
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))
gamma_c = sqrt(H[1][1,1])
C = nv > 2 ? StaticArrays.sacollect(SMatrix{2,2,eltype(H[1])}, H[1][i,j] for i in 3:4 for j in 3:4) : 0
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[i,j] for i in 1:nhv for j in 1:nhv)
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,i+1]*N[i,i] 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)
return (; beta=beta, alpha=alpha, gamma_c=gamma_c, C=C)
end
end
Expand All @@ -61,12 +77,12 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V
)
mo = maxord(a1)
gamma_c = TI.cutord(sqrt(factor_out(H[1].v[1], 1)), mo)
C = nv > 2 ? StaticArrays.sacollect(SMatrix{2,2,eltype(H[1].v)}, factor_out(H[1].v[i], j) for i in 3:4 for j in 3:4) : 0
C = nv > 2 ? StaticArrays.sacollect(SMatrix{2,2,eltype(H[1].v)}, TI.cutord(-factor_out(H[1].v[row], col)/gamma_c, mo) 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 = TI.cutord.(Vi*StaticArrays.sacollect(SMatrix{nvm,nvm,eltype(a1.v)}, factor_out(a1.v[i], j) for i in 1:nvm for j in 1:nvm), mo)
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,i+1]*N[i,i], 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))
# 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))
Expand All @@ -93,12 +109,12 @@ function compute_sagan_rubin(a1::DAMap{V0}, ::Val{linear}=Val{false}()) where {V
)
mo = maxord(a1)
gamma_c = TI.cutord(sqrt(factor_out(H[1].v[1], 1)), mo)
C = nv > 2 ? StaticArrays.sacollect(SMatrix{2,2,eltype(H[1].v)}, factor_out(H[1].v[i], j) for i in 3:4 for j in 3:4) : 0
C = nv > 2 ? StaticArrays.sacollect(SMatrix{2,2,eltype(H[1].v)}, TI.cutord(-factor_out(H[1].v[row], col)/gamma_c, mo) 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 = TI.cutord.(Vi*StaticArrays.sacollect(SMatrix{nhv,nhv,eltype(a1.v)}, factor_out(a1.v[i], j) for i in 1:nhv for j in 1:nhv), mo)
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,i+1]*N[i,i], 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))
return (; beta=beta, alpha=alpha, gamma_c=gamma_c, C=C)
end
end
Expand Down