feat: reintroduce iscentrosymmetric function from v1.x.x (#94)

- Add default iscentrosymmetric(::AbstractKernel) = false with docstring
- Specialize for LogisticKernel and RegularizedBoseKernel to return true
- Export iscentrosymmetric function
- Add unit tests for iscentrosymmetric

Author: shinaoka

src/SparseIR.jl

@@ -13,6 +13,7 @@ export FiniteTempBasis, FiniteTempBasisSet
 export DiscreteLehmannRepresentation
 export overlap
 export LogisticKernel, RegularizedBoseKernel
+export iscentrosymmetric
 export AugmentedBasis, TauConst, TauLinear, MatsubaraConst
 export TauSampling, MatsubaraSampling, evaluate, fit, evaluate!, fit!,
        sampling_points, npoints

src/abstract.jl

@@ -197,6 +197,17 @@ iswellconditioned(::AbstractBasis) = true
 
 ###############################################################################
 
+"""
+    iscentrosymmetric(kernel::AbstractKernel)
+
+Return whether the kernel satisfies `K(x, y) == K(-x, -y)` for all values of x and y.
+Defaults to `false`.
+
+A centrosymmetric kernel can be block-diagonalized, speeding up the singular value
+expansion by a factor of 4.
+"""
+iscentrosymmetric(::AbstractKernel) = false
+
 Base.broadcastable(kernel::AbstractKernel) = Ref(kernel)
 
 Base.broadcastable(sampling::AbstractSampling) = Ref(sampling)

src/kernel.jl

@@ -67,3 +67,6 @@ end
 
 Λ(kernel::LogisticKernel) = kernel.Λ
 Λ(kernel::RegularizedBoseKernel) = kernel.Λ
+
+iscentrosymmetric(::LogisticKernel) = true
+iscentrosymmetric(::RegularizedBoseKernel) = true

test/spir/kernel_tests.jl

@@ -5,11 +5,13 @@
         lam = 42
         kernel = LogisticKernel(lam)
         @test SparseIR.Λ(kernel) == lam
+        @test iscentrosymmetric(kernel)
     end
 
     @testset "Regularized Bose kernel" begin
         lam = 42
         kernel = RegularizedBoseKernel(lam)
         @test SparseIR.Λ(kernel) == lam
+        @test iscentrosymmetric(kernel)
     end
 end