[NDTensors] Get more Array storage functionality working

[mtfishman]

This gets more functionality for Tensor directly wrapping an Array (as opposed to Dense) working, such as tensor contraction, QR, eigen, and SVD.

EDIT: This is now working:

using NDTensors
using ITensors

function heisenberg(n)
  os = OpSum()
  for j in 1:(n - 1)
    os += "Sz", j, "Sz", j + 1
    os += 0.5, "S+", j, "S-", j + 1
    os += 0.5, "S-", j, "S+", j + 1
  end
  return os
end

function main(; n=10, nsweeps=5, conserve_qns=false)
  s = siteinds("S=1/2", n; conserve_qns)
  H = MPO(heisenberg(n), s)
  ψ = randomMPS(s, j -> isodd(j) ? "↑" : "↓"; linkdims=4)
  ψ1, e1 = dmrg(NDTensors.to_arraystorage.((H, ψ))...; nsweeps, maxdim=10, cutoff=1e-12)
  ψ2, e2 = dmrg(H, ψ; nsweeps, maxdim=10, cutoff=1e-12)
  return e1, e2
end

main()

where NDTensors.to_arraystorage replaces Dense storage with Array.

This outputs:

After sweep 1 energy=-4.256581185494193  maxlinkdim=10 maxerr=2.11E-06 time=0.020
After sweep 2 energy=-4.258028428488432  maxlinkdim=10 maxerr=1.25E-06 time=0.020
After sweep 3 energy=-4.258028444854628  maxlinkdim=10 maxerr=8.24E-07 time=0.030
After sweep 4 energy=-4.258028445008366  maxlinkdim=10 maxerr=8.23E-07 time=0.020
After sweep 5 energy=-4.258028445013943  maxlinkdim=10 maxerr=8.23E-07 time=0.021
After sweep 1 energy=-4.2565811854942  maxlinkdim=10 maxerr=2.11E-06 time=0.021
After sweep 2 energy=-4.258028428488428  maxlinkdim=10 maxerr=1.25E-06 time=0.029
After sweep 3 energy=-4.258028444854625  maxlinkdim=10 maxerr=8.24E-07 time=0.021
After sweep 4 energy=-4.258028445008369  maxlinkdim=10 maxerr=8.23E-07 time=0.021
After sweep 5 energy=-4.258028445013948  maxlinkdim=10 maxerr=8.23E-07 time=0.021

so DMRG is running just as before, but with the Dense type completely removed.

[codecov-commenter]

Codecov Report

Attention: 4 lines in your changes are missing coverage. Please review.

Comparison is base (74095ef) 85.38% compared to head (514424f) 67.35%.

❗ Current head 514424f differs from pull request most recent head c14150c. Consider uploading reports for the commit c14150c to get more accurate results

❗ Your organization needs to install the Codecov GitHub app to enable full functionality.

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #1222       +/-   ##
===========================================
- Coverage   85.38%   67.35%   -18.03%     
===========================================
  Files          89       88        -1     
  Lines        8449     8415       -34     
===========================================
- Hits         7214     5668     -1546     
- Misses       1235     2747     +1512     

Files	Coverage Δ
src/itensor.jl	80.76% <0.00%> (-1.59%)	⬇️
src/mps/abstractmps.jl	49.35% <0.00%> (-37.74%)	⬇️

... and 34 files with indirect coverage changes

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[mtfishman]

@kmp5VT @emstoudenmire with this PR we would almost be able to remove the Dense type entirely. We might have to add a few more functions for the new Array storage type, but DMRG can be run entirely without the Dense type.

It may be worth just going ahead and doing that soon in a future PR since it will simplify the code base and make future work on removing EmptyStorage, Diag, and BlockSparse simpler. It would only be breaking for users who are reaching into internals (i.e. working at the storage level), and it would make reaching into internals much simpler since the type becomes simpler. We can think about how to coordinate with work like #1213 (which will lead to us being able to remove the EmptyStorage type) but I think they are mostly separate.

[mtfishman]

[test ITensors mps]

[github-actions]

Run ITensors mps tests from comment trigger: failed ❌
https://github.com/ITensor/ITensors.jl/actions/runs/6696637447

[github-actions]

Run ITensors mps tests from comment trigger: failed ❌
https://github.com/ITensor/ITensors.jl/actions/runs/6696637447

[mtfishman]

[test ITensors mps]

[github-actions]

Run ITensors mps tests from comment trigger: failed ❌
https://github.com/ITensor/ITensors.jl/actions/runs/6697351721

[github-actions]

Run ITensors mps tests from comment trigger: failed ❌
https://github.com/ITensor/ITensors.jl/actions/runs/6697351721

[emstoudenmire]

Nice – this is advancing really fast, and I see you're already on to the diagonal case.