Add SDDMM example

[mtsokol]

Hi @hameerabbasi,

This PR adds SDDMM example and upgrades Finch to the latest version.

[UPDATED 14.05.2024]
For my machine, running:

python examples/sddmm_example.py

gives:

Finch
Took 8.787564675013224 s.

Numba
Took 22.904020706812542 s.

SciPy
Took 22.59452811876933 s.

[github-actions]

Test Results

5 923 tests  ±0   5 892 ✅ ±0   9m 24s ⏱️ + 2m 33s
    1 suites ±0      31 💤 ±0 
    1 files   ±0       0 ❌ ±0 

Results for commit 0f52367. ± Comparison against base commit 79b9d71.

This pull request skips 1 and un-skips 1 tests.

sparse.numba_backend.tests.test_compressed ‑ test_reductions_float16[i8-None-sum-kwargs0]

sparse.numba_backend.tests.test_compressed ‑ test_reductions_float16[f8-None-sum-kwargs0]

♻️ This comment has been updated with latest results.

[mtsokol]

I think density could be increased to 0.0001 so we have 100 non-zeros (more realistic?) - I get same performance.

[hameerabbasi]

Two final changes then this is ready.

[hameerabbasi]

I'd actually like to test the examples as well, to make sure they always work. Can we add something like the following to CI:

# test_examples.sh
for example in $(find ./examples/ -iname *.py); do
  python $example
done

# in CI
source test_examples.sh

Alternatively (and preferably) let's move this to the benchmarks.

[mtsokol]

I added a CI stage for running it.

I can add SDDMM also to the benchmarks, but I prefer to also have examples separately that can be quickly shared with others and executed in repl, instead of unwrapping asv-specific benchmark code.

[mtsokol]

Blocked by finch-tensor/Finch.jl#534

[mtsokol]

Here's a debug output for Finch lazy mode plan:

Executing:
:(function var"##compute#410"(prgm)
      begin
          V = (((((((((((((((((((prgm.children[1]).children[2]).children[2]).children[3]).children[1]).children[1]).children[1]).children[2]).children[1]).children[2]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[2]).tns.val::Tensor{SparseCOOLevel{2, Tuple{Int64, Int64}, Vector{Int64}, Tuple{PlusOneVector{Int32}, PlusOneVector{Int32}}, ElementLevel{0.0, Float64, Int64, PyArray{Float64, 1, true, true, Float64}}}}
          V_2 = ((((((((((((((((((((((((((((prgm.children[1]).children[2]).children[2]).children[3]).children[1]).children[1]).children[1]).children[2]).children[1]).children[3]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[2]).children[1]).children[2]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[2]).tns.val::Tensor{DenseLevel{Int64, DenseLevel{Int64, ElementLevel{0.0, Float64, Int64, PyArray{Float64, 1, true, true, Float64}}}}}
          V_3 = ((((((((((((((((((((((((((((prgm.children[1]).children[2]).children[2]).children[3]).children[1]).children[1]).children[1]).children[2]).children[1]).children[3]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[2]).children[1]).children[3]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[1]).children[2]).tns.val::Tensor{DenseLevel{Int64, DenseLevel{Int64, ElementLevel{0.0, Float64, Int64, PyArray{Float64, 1, true, true, Float64}}}}}
          A0 = V::Tensor{SparseCOOLevel{2, Tuple{Int64, Int64}, Vector{Int64}, Tuple{PlusOneVector{Int32}, PlusOneVector{Int32}}, ElementLevel{0.0, Float64, Int64, PyArray{Float64, 1, true, true, Float64}}}}
          A0_2 = Tensor(Dense(SparseDict(Element{0.0, Float64}())))::Tensor{DenseLevel{Int64, SparseLevel{Int64, Finch.DictTable{Int64, Int64, Vector{Int64}, Vector{Int64}, Vector{Int64}, Dict{Tuple{Int64, Int64}, Int64}}, ElementLevel{0.0, Float64, Int64, Vector{Float64}}}}}
          @finch mode = :fast begin
                  A0_2 .= 0.0
                  for i1 = _
                      for i0 = _
                          A0_2[i1, i0] = A0[i0, i1]
                      end
                  end
                  return A0_2
              end
          A2 = V_2::Tensor{DenseLevel{Int64, DenseLevel{Int64, ElementLevel{0.0, Float64, Int64, PyArray{Float64, 1, true, true, Float64}}}}}
          A4 = V_3::Tensor{DenseLevel{Int64, DenseLevel{Int64, ElementLevel{0.0, Float64, Int64, PyArray{Float64, 1, true, true, Float64}}}}}
          A8 = Tensor(Dense(SparseDict(Element{0.0, Float64}())))::Tensor{DenseLevel{Int64, SparseLevel{Int64, Finch.DictTable{Int64, Int64, Vector{Int64}, Vector{Int64}, Vector{Int64}, Dict{Tuple{Int64, Int64}, Int64}}, ElementLevel{0.0, Float64, Int64, Vector{Float64}}}}}
          @finch mode = :fast begin
                  A8 .= 0.0
                  for i52 = _
                      for i51 = _
                          for i50 = _
                              A8[i50, i51] << + >>= (*)(A0_2[i50, i51], (*)(A2[1, i52], A4[1, i52]))
                          end
                      end
                  end
                  return A8
              end
          return (A8,)
      end
  end)

[willow-ahrens]

Let's keep working on this until we see a speedup from fusion. I believe a fusion-based speedup should be achievable here, so it's a good goal to work towards.

[mtsokol]

Right now in the latest Finch version we have precompilation of a few kernels. This causes a timeout of the first benchmark. Let me fix it.

[hameerabbasi]

Thanks for all the hard work on this, @mtsokol!

[willow-ahrens]

Thanks @mtsokol!