From 2fd20b06877c4111cad319f41db72374144edfff Mon Sep 17 00:00:00 2001
From: mtfishman <mfishman@flatironinstitute.org>
Date: Wed, 10 Jan 2024 11:49:35 -0500
Subject: [PATCH 1/3] [ITensors] Fix eigen_perturbation rank

---
 src/tensor_operations/matrix_decomposition.jl | 16 +++++++++++-----
 1 file changed, 11 insertions(+), 5 deletions(-)

diff --git a/src/tensor_operations/matrix_decomposition.jl b/src/tensor_operations/matrix_decomposition.jl
index c288b8348d..22622c3817 100644
--- a/src/tensor_operations/matrix_decomposition.jl
+++ b/src/tensor_operations/matrix_decomposition.jl
@@ -781,13 +781,19 @@ function factorize(
   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)
+  if isnothing(eigen_perturbation)
+    # 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))
+  else
+    if isnothing(maxdim)
+      maxdim = max(dL, dR)
+    end
+    maxdim = min(maxdim, max(dL, dR))
   end
-  maxdim = min(maxdim, min(dL, dR))
   might_truncate = !isnothing(cutoff) || maxdim < min(dL, dR)
-
   if isnothing(which_decomp)
     if !might_truncate && ortho != "none"
       which_decomp = "qr"

From 912fbfaa0301c5a12a98460d271a641015357b58 Mon Sep 17 00:00:00 2001
From: mtfishman <mfishman@flatironinstitute.org>
Date: Tue, 16 Jan 2024 12:30:02 -0500
Subject: [PATCH 2/3] Add test

---
 test/base/test_decomp.jl | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/test/base/test_decomp.jl b/test/base/test_decomp.jl
index a4c8fc1554..c43c900a28 100644
--- a/test/base/test_decomp.jl
+++ b/test/base/test_decomp.jl
@@ -136,6 +136,25 @@ end
     )
   end
 
+  @testset "factorize with eigen_perturbation dimensions" begin
+    elt = Float64
+    di = 10
+    dj = 5
+    maxdim = di - 1
+    i = Index(di, "i")
+    j = Index(dj, "j")
+    a = randomITensor(elt, i, j)
+    δ = randomITensor(elt, i, j)
+    δ² = prime(δ, i) * dag(δ)
+    a² = prime(a, i) * dag(a)
+    x, y = factorize(a, i; ortho="left", which_decomp="eigen", maxdim)
+    l = commonind(x, y)
+    @test dim(l) == dj
+    xδ, yδ = factorize(a, i; ortho="left", which_decomp="eigen", eigen_perturbation=δ², maxdim)
+    lδ = commonind(xδ, yδ)
+    @test dim(lδ) == maxdim
+  end
+
   @testset "QR/RQ/QL/LQ decomp on MPS dense $elt tensor with all possible collections on Q/R/L" for ninds in
                                                                                                     [
       0, 1, 2, 3

From 223a55091550c2011fa75edf1466a3f257f5dc21 Mon Sep 17 00:00:00 2001
From: Matt Fishman <mtfishman@users.noreply.github.com>
Date: Tue, 16 Jan 2024 12:33:35 -0500
Subject: [PATCH 3/3] Format

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 test/base/test_decomp.jl | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/test/base/test_decomp.jl b/test/base/test_decomp.jl
index c43c900a28..99c9781660 100644
--- a/test/base/test_decomp.jl
+++ b/test/base/test_decomp.jl
@@ -150,7 +150,9 @@ end
     x, y = factorize(a, i; ortho="left", which_decomp="eigen", maxdim)
     l = commonind(x, y)
     @test dim(l) == dj
-    xδ, yδ = factorize(a, i; ortho="left", which_decomp="eigen", eigen_perturbation=δ², maxdim)
+    xδ, yδ = factorize(
+      a, i; ortho="left", which_decomp="eigen", eigen_perturbation=δ², maxdim
+    )
     lδ = commonind(xδ, yδ)
     @test dim(lδ) == maxdim
   end