Print degenerate singular values warning only during derivation

[pbrehmer]

As suggested in #89, this PR will implement the degenerate singular value warning such that it is printed only when CTMRG is being differentiated.

This makes sense since degenerate values shouldn't really be problematic in the forward pass but in the reverse pass degenerate singular values will make the SVD adjoint diverge and thereby render the CTMRG gradient useless.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Files with missing lines	Coverage Δ
src/algorithms/ctmrg/ctmrg.jl	92.30% <100.00%> (+0.95%)	⬆️

[pbrehmer]

This can be tested e.g. using a product state PEPS which will lead to a singular value spectrum $S = (1, 0, 0, \dots)$. Correspondingly, the forward pass doesn't print any warnings:

julia> psi = product_peps(2, 2; noise_amp=0);
julia> leading_boundary(CTMRGEnv(psi, ComplexSpace(16)), psi, CTMRG());
[ Info: CTMRG init:     obj = +1.235387069986e-01 -7.116847020371e-02im err = 1.0000e+00
[ Info: CTMRG conv 66:  obj = +1.000000000000e+00       err = 3.3306690739e-16  time = 0.71 sec

But the reverse pass will warn and fail:

fixedpoint(psi, heisenberg_XYZ(InfiniteSquare()), PEPSOptimize(), CTMRGEnv(psi, ComplexSpace(16)))
[ Info: CTMRG init:     obj = +7.495770233902e-02 -1.901630443277e-01im err = 1.0000e+00
[ Info: CTMRG conv 83:  obj = +1.000000000000e+00       err = 2.2204460493e-16  time = 0.23 sec
┌ Warning: degenerate singular values detected: 
│   svals =
│    TensorKit.SortedVectorDict{Trivial, Vector{Float64}} with 1 entry:
│      Trivial() => [1.0, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17,…
└ @ PEPSKit ~/repos/PEPSKit.jl/src/algorithms/ctmrg/ctmrg.jl:280
┌ Warning: degenerate singular values detected: 
│   svals =
│    TensorKit.SortedVectorDict{Trivial, Vector{Float64}} with 1 entry:
│      Trivial() => [1.0, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17,…
└ @ PEPSKit ~/repos/PEPSKit.jl/src/algorithms/ctmrg/ctmrg.jl:280
┌ Warning: degenerate singular values detected: 
│   svals =
│    TensorKit.SortedVectorDict{Trivial, Vector{Float64}} with 1 entry:
│      Trivial() => [1.0, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17,…
└ @ PEPSKit ~/repos/PEPSKit.jl/src/algorithms/ctmrg/ctmrg.jl:280
┌ Warning: degenerate singular values detected: 
│   svals =
│    TensorKit.SortedVectorDict{Trivial, Vector{Float64}} with 1 entry:
│      Trivial() => [1.0, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17, 9.99201e-17,…
└ @ PEPSKit ~/repos/PEPSKit.jl/src/algorithms/ctmrg/ctmrg.jl:280
┌ Warning: Invariant subspace of dimension 2 (up to requested tolerance `tol = 1.0e-8`), which is smaller than the number of requested eigenvalues (i.e. `howmany == 16`); setting `howmany = 2`.
└ @ KrylovKit ~/.julia/packages/KrylovKit/Y0zG7/src/eigsolve/arnoldi.jl:350
┌ Warning: Invariant subspace of dimension 2 (up to requested tolerance `tol = 1.0e-8`), which is smaller than the number of requested eigenvalues (i.e. `howmany == 16`); setting `howmany = 2`.
└ @ KrylovKit ~/.julia/packages/KrylovKit/Y0zG7/src/eigsolve/arnoldi.jl:350
┌ Warning: Invariant subspace of dimension 2 (up to requested tolerance `tol = 1.0e-8`), which is smaller than the number of requested eigenvalues (i.e. `howmany == 16`); setting `howmany = 2`.
└ @ KrylovKit ~/.julia/packages/KrylovKit/Y0zG7/src/eigsolve/arnoldi.jl:350
┌ Warning: Invariant subspace of dimension 2 (up to requested tolerance `tol = 1.0e-8`), which is smaller than the number of requested eigenvalues (i.e. `howmany == 16`); setting `howmany = 2`.
└ @ KrylovKit ~/.julia/packages/KrylovKit/Y0zG7/src/eigsolve/arnoldi.jl:350
...

[lkdvos]

Great, thanks for getting this done! Fixes #89

[Yue-Zhengyuan]

Thanks! Now I know about Zygote.isderiving 😂