pymc-devs / pymc-devs/pytensor

Rewrite `Solve` involving `Kron`

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graph rewriting linalg performance
Dominant language
Python
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Forks
208
Avg merge
2d 14h
Merged PRs (30d)
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Description

Description

Define $\text{vec}(X)$ as the ravel operator that works column-wise (that's the math convention, so in code it's x.reshape(-1, order="F").

Given $(A \otimes B)x = y$. If $y = \text{vec}(Y)$, then $x = \text{vec}(B^{-1}YA^{-T})$

This identity suggests a rewrite for solve Ops involving Kron:

import pytensor.tensor as pt
import pytensor
import numpy as np

A, B = pt.dmatrices('A', 'B')
y = pt.dvector('y')

n, m = A.shape[0], B.shape[0]

x1 = pt.linalg.solve(pt.linalg.kron(A, B), y)
x2 = pt.linalg.solve(A, 
                     pt.linalg.solve(B, y.reshape((n, m)).T).T).ravel()

fn1 = pytensor.function([A, B, y], x1)
fn2 = pytensor.function([A, B, y], x2)

# Show equivalence
rng = np.random.default_rng()
n = 50
a_val, b_val = rng.normal(size=(2, n, n))
y_val = rng.normal(size=(n * n))    

np.allclose(fn1(a_val, b_val, y_val), fn2(a_val, b_val, y_val)) # True

Timings:

%timeit fn1(a_val, b_val, y_val) # 83.9 ms ± 626 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)
%timeit fn2(a_val, b_val, y_val) # 178 μs ± 8.41 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

Contributor guide

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start by tracing the Solve and Kron Ops and the rewrite machinery that handles them; the issue names no files or tests. Use the provided fn1 and fn2 expressions to verify equivalent results, then confirm that the rewrite avoids explicitly solving the Kronecker-product system and preserves the expected behavior.

Written by the indexing model from the issue text.

Assessment

Tech stack
numpy, python
Domain
backend-api-design, performance
Issue type
Refactor
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
45/100

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