[ITensors] Use thin decomposition for factorize eigen backend (#1214)

src/tensor_operations/matrix_decomposition.jl

@@ -630,7 +630,7 @@ Perform a factorization of `A` into ITensors `L` and `R` such that `A ≈ L * R`
 
 For truncation arguments, see: [`svd`](@ref)
 """
-function factorize(A::ITensor, Linds...; kwargs...)
+function factorize(A::ITensor, Linds...; maxdim=nothing, kwargs...)
   ortho::String = get(kwargs, :ortho, "left")
   tags::TagSet = get(kwargs, :tags, "Link,fact")
   plev::Int = get(kwargs, :plev, 0)
@@ -661,9 +661,14 @@ function factorize(A::ITensor, Linds...; kwargs...)
   # Determines when to use eigen vs. svd (eigen is less precise,
   # so eigen should only be used if a larger cutoff is requested)
   automatic_cutoff = 1e-12
-  Lis = indices(Linds...)
-  dL, dR = dim(Lis), dim(indices(setdiff(inds(A), Lis)))
-  maxdim = get(kwargs, :maxdim, min(dL, dR))
+  Lis = commoninds(A, indices(Linds...))
+  Ris = uniqueinds(A, Lis)
+  dL, dR = dim(Lis), dim(Ris)
+  # maxdim is forced to be at most the max given SVD
+  if isnothing(maxdim)
+    maxdim = min(dL, dR)
+  end
+  maxdim = min(maxdim, min(dL, dR))
   might_truncate = !isnothing(cutoff) || maxdim < min(dL, dR)
 
   if isnothing(which_decomp)
@@ -677,13 +682,13 @@ function factorize(A::ITensor, Linds...; kwargs...)
   end
 
   if which_decomp == "svd"
-    LR = factorize_svd(A, Linds...; kwargs...)
+    LR = factorize_svd(A, Linds...; kwargs..., maxdim=maxdim)
     if isnothing(LR)
       return nothing
     end
     L, R, spec = LR
   elseif which_decomp == "eigen"
-    L, R, spec = factorize_eigen(A, Linds...; kwargs...)
+    L, R, spec = factorize_eigen(A, Linds...; kwargs..., maxdim=maxdim)
   elseif which_decomp == "qr"
     L, R = factorize_qr(A, Linds...; kwargs...)
     spec = Spectrum(nothing, 0.0)

test/base/test_decomp.jl

@@ -465,6 +465,20 @@ end
       @test blockdim(u, b) == blockdim(i, b) || blockdim(u, b) >= min_blockdim
     end
   end
+
+  @testset "factorize with mindim" begin
+    l = Index(8, "l")
+    s1 = Index(2, "s1")
+    s2 = Index(2, "s2")
+    r = Index(2, "r")
+
+    phi = randomITensor(l, s1, s2, r)
+
+    U, B = factorize(phi, (l, s1); ortho="left", mindim=8, which_decomp="eigen")
+
+    @test norm(U * B - phi) < 1E-5
+    @test dim(commonind(U, B)) <= 4
+  end
 end
 
 nothing