BUG: `pt.linalg.solve` returns incorrect results when `mode = "NUMBA"`

[jessegrabowski]

Describe the issue:

This is identical to #382. When assume_a != 'gen' in pt.linalg.solve, the solve_triangular function is incorrectly invoked, and the resulting output is not correct.

Reproducable code example:

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

X = pt.dmatrix('X')
b = pt.dmatrix('b')
y1 = pt.linalg.solve(X, b, assume_a='gen')
y2 = pt.linalg.solve(X, b, assume_a='sym')

f1 = pytensor.function([X, b], y1)
f2 = pytensor.function([X, b], y2)
f1_nb = pytensor.function([X, b], y1, mode='NUMBA')
f2_nb = pytensor.function([X, b], y2, mode='NUMBA')

X_sym = np.random.normal(size=(3, 3))
X_sym = X_sym @ X_sym.T
X_inv_1 = f1(X_sym, np.eye(3))
X_inv_2 = f2(X_sym, np.eye(3))
X_inv_1_nb = f1_nb(X_sym, np.eye(3))
X_inv_2_nb = f2_nb(X_sym, np.eye(3))

# Passes, C backend, assume_a = 'gen'
np.testing.assert_allclose(X_inv_1 @ X_sym, np.eye(3), atol=1e-12)

# Passes, C backend, assume_a = 'sym'
np.testing.assert_allclose(X_inv_2 @ X_sym, np.eye(3), atol=1e-12)

# Passes, Numba backend, assume_a = 'gen'
np.testing.assert_allclose(X_inv_1_nb @ X_sym, np.eye(3), atol=1e-12)

# Fails, Numba backend, assuma_a = 'sym'
np.testing.assert_allclose(X_inv_2_nb @ X_sym, np.eye(3), atol=1e-12)

Error message:

```shell AssertionError: Not equal to tolerance rtol=1e-07, atol=1e-12 Mismatched elements: 6 / 9 (66.7%) Max absolute difference: 0.67369019 Max relative difference: 0.52399333 x: array([[ 4.760067e-01, -2.459194e-01, 9.939378e-18], [-3.325732e-01, 6.636944e-01, 1.353323e-18], [-1.317192e-01, 6.736902e-01, 1.000000e+00]]) y: array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]) ```

PyTensor version information:

Pytensor version 2.11.1

Context for the issue:

No response

[ricardoV94]

@jessegrabowski Is this one resolved?

[jessegrabowski]

No. I am working on a numba overload for solve but it's more work than I expected. Maybe in the meantime I could do a temporary quick fix that either errors if assume_a is not "gen", or silently force it to be?

[ricardoV94]

Yes you can treat it as if it was gen always while we don't have the alternatives working