Add pagerank example

[mtsokol]

Hi @hameerabbasi,

Here I share initial pagerank implementation (following scipy_pagerank).

A few comments:

• It's slower than scipy implementation.
• spdiag is still missing in finch-tensor, therefore I use SciPy diag to create it.

[github-actions]

Test Results

5 923 tests  ±0   5 891 ✅ ±0   9m 24s ⏱️ -7s
    1 suites ±0      32 💤 ±0 
    1 files   ±0       0 ❌ ±0 

Results for commit b2e63af. ± Comparison against base commit c12b29e.

This pull request skips 2 and un-skips 2 tests.

sparse.numba_backend.tests.test_compressed ‑ test_reductions_float16[f4-None-sum-kwargs0]
sparse.numba_backend.tests.test_coo ‑ test_reductions_float16[f8-None-sum-kwargs0]

sparse.numba_backend.tests.test_compressed ‑ test_reductions_float16[i4-None-sum-kwargs0]
sparse.numba_backend.tests.test_coo ‑ test_reductions_float16[i4-None-sum-kwargs0]

♻️ This comment has been updated with latest results.

[hameerabbasi]

IIUC This is equivalent to https://data-apis.org/array-api/latest/extensions/generated/array_api.linalg.diagonal.html#diagonal, which is supported by the Numba backend. Let's use that instead.

Suggested change

	Q = sparse.asarray(sp.csc_array(sp.spdiags(S.todense(), 0, *A.shape)))
	A = Q @ A
	Q = sparse.diagonal(S)
	A *= Q

[hameerabbasi]

For Finch, we can add support for it later, as the example only needs to work on Numba for now.

[hameerabbasi]

You might need Q[None, :] to match the results, but otherwise this is equivalent.

[mtsokol]

But the pagerank example is run either with Finch or Numba backend. when we run with Finch backend (and I think it should be runnable with Finch) then we can't execute one line with Numba.

[mtsokol]

I would prefer to keep these examples Finch and Numba ready, and update implementation once both backends support something new.

[hameerabbasi]

I would prefer to keep these examples Finch and Numba ready, and update implementation once both backends support something new.

According to the deliverable, we just need a script that will demonstrate a speedup against the "old" code. If you would prefer, we can always keep this PR open until xp.diagonal is supported by Finch, but I wouldn't densify.

[hameerabbasi]

@mtsokol Is this still relevant?

[mtsokol]

@mtsokol Is this still relevant?

Let's leave it open for now. For power iteration we have HITS example, but once we have diagonal this will be a fine addition to the examples docs.