Fix behavior of factorize mindim

[ryanlevy]

Description

Fixes #1207

Minimal demonstration of previous behavior

Quick update, a more minimal example. Say we have a two-site tensor that we want to factorize

s  = Index(2)
s′ = Index(2)
l = Index(64)
r = Index(16)
T = randomITensor(l,s,s′,r)

The inconsistent behavior manifests as

> L,R,spec = factorize(T,l,s; cutoff=0,mindim=64)
> @show inds(L)
inds(L) = ((dim=64|id=719), (dim=2|id=499), (dim=32|id=847|"Link,fact"))

where we get the 64->32->16 stepdown. Or with cutoff

> L,R,spec = factorize(T,l,s; cutoff=1e-10,mindim=64)
> @show inds(L)
inds(L) = ((dim=64|id=444), (dim=2|id=941), (dim=64|id=961|"Link,fact"))

Where the factorize respects the mindim by padding the link dimension. I think the cutoff=0 behavior is best here.

Minimal demonstration of new behavior

using ITensors

s  = Index(2)
s′ = Index(2)
l = Index(64)
r = Index(16)
T = randomITensor(l,s,s′,r)

L,R,spec = factorize(T,l,s; cutoff=1e-10,maxdim=64,mindim=64)
@show inds(L)
@show inds(R)

> inds(L) = ((dim=64|id=96), (dim=2|id=968), (dim=32|id=502|"Link,fact"))
> inds(R) = ((dim=32|id=502|"Link,fact"), (dim=2|id=814), (dim=16|id=189))

How Has This Been Tested?

No new tests

Checklist:

• My code follows the style guidelines of this project. Please run using JuliaFormatter; format(".") in the base directory of the repository (~/.julia/dev/ITensors) to format your code according to our style guidelines.
• I have performed a self-review of my own code.
• I have commented my code, particularly in hard-to-understand areas.
• I have added tests that verify the behavior of the changes I made.
• I have made corresponding changes to the documentation.
• My changes generate no new warnings.
• Any dependent changes have been merged and published in downstream modules.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (b5d963e) 85.38% compared to head (d5f3168) 67.36%.
Report is 2 commits behind head on main.

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Additional details and impacted files

@@             Coverage Diff             @@
##             main    #1214       +/-   ##
===========================================
- Coverage   85.38%   67.36%   -18.02%     
===========================================
  Files          89       88        -1     
  Lines        8427     8392       -35     
===========================================
- Hits         7195     5653     -1542     
- Misses       1232     2739     +1507     

Files	Coverage Δ
src/tensor_operations/matrix_decomposition.jl	91.63% <100.00%> (-0.62%)	⬇️

... and 35 files with indirect coverage changes

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[mtfishman]

Thanks Ryan, could you add a test?

[mtfishman]

Thanks!