`local_det_chol` doesn't work

[jessegrabowski]

Description

A simple example:

import pytensor.tensor as pt 
import pytensor

x = pt.dmatrix('x')
out = pt.linalg.det(pt.linalg.cholesky(x))
fn = pytensor.function([x], out)
fn.dprint()

Det [id A] 1
 └─ Cholesky{lower=True, check_finite=False, on_error='raise', overwrite_a=False} [id B] 0
    └─ x [id C]

The expected output is prod(diag(cholesky(x)))

[jessegrabowski]

Ok I guess the graph has to have a cholesky lying around somewhere else for the rewrite to trigger. For example:

x = pt.dmatrix('x')
L = pt.linalg.cholesky(x)
d = pt.linalg.det(x)

fn = pytensor.function([x], [L, d])

Cholesky{lower=True, check_finite=False, on_error='raise', overwrite_a=False} [id A] 0
 └─ x [id B]
CAReduce{Composite{(i0 * sqr(i1))}, axis=0} [id C] 2
 └─ ExtractDiag{offset=0, axis1=0, axis2=1, view=True} [id D] 1
    └─ Cholesky{lower=True, check_finite=False, on_error='raise', overwrite_a=False} [id A] 0
       └─ ···

Inner graphs:

CAReduce{Composite{(i0 * sqr(i1))}, axis=0} [id C]
 ← mul [id E] 'o0'
    ├─ i0 [id F]
    └─ sqr [id G]
       └─ i1 [id H]

But it still seems like a bug that it doesn't trigger on the simpler case.

[ricardoV94]

Your original example is not what the rewrite targets. It targets det(x), not det(cholesky(x)), but yes no reason not to also apply it here

The determinant is just the product of the diagonals without the square though?