`dpnp.linalg.lu_factor()` - Feature request. Implemeted but not a public method

[abagusetty]

I was looking for a port of from cupyx.scipy.linalg import lu_factor, lu_solve for LU factorization & eq. solve via LU factorization

Apparently `lu_factor does exist luckily (thanks!) but not exposed since it is a private function: https://github.com/IntelPython/dpnp/blob/master/dpnp/linalg/dpnp_utils_linalg.py#L874

I would like to request a feature to expose this method and also implement a lu_solve feature possibly via getrs: Ref: https://github.com/cupy/cupy/blob/v13.4.1/cupyx/scipy/linalg/_decomp_lu.py#L259

[abagusetty]

With the following, the results differ between the L, U and pivots. This is sort of expected as it depends on the pivoting steps. If there is a way to support similar to scipy API (ie., the args): lu_factor(a, overwrite_a=False, check_finite=True)

import dpnp as dp
A = dp.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]], dtype=dp.float64)
lu, piv, dev_info = dp.linalg.dpnp_utils_linalg._lu_factor(A, A.dtype)
print("LU from dpnp:\n", lu)
print("Pivots from dpnp:\n", piv)
print("Dev info:\n", dev_info)


import numpy as np
from scipy.linalg import lu_factor
Anp = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
lu_np, piv_np = lu_factor(Anp)
print("LU from scipy:\n", lu_np)
print("Pivots from scipy:\n", piv_np)

output:

LU from dpnp:
 [[8.         0.875      0.25       0.625     ]
 [2.         6.25       0.72       0.12      ]
 [6.         0.75       4.96       0.23387097]
 [4.         4.5        0.76       0.78225806]]
Pivots from dpnp:
 [3 4 3 4]
Dev info:
 [0]
LU from scipy:
 [[ 7.          5.          6.          6.        ]
 [ 0.28571429  3.57142857  6.28571429  5.28571429]
 [ 0.71428571  0.12       -1.04        3.08      ]
 [ 0.71428571 -0.44       -0.46153846  7.46153846]]
Pivots from scipy:
 [2 2 3 3]

[vlad-perevezentsev]

Hi @abagusetty and thank you for the feature request

The function _lu_factor() was originally designed for internal use in dpnp.linalg.det() and dpnp.linalg.slogdet() so we did not make it public.
To maintain functional completeness of DPNP with CuPy and SciPy where lu_factor is part of the public API, we plan to add dpnp.linalg.lu_factor as a public function in a future release including support for arguments like overwrite_a and check_finite

Your request for lu_solve() makes sense as the next logical step and will be implemented in the same upcoming release.

Regarding the differences in LU and pivot outputs. This is expected.
LU factorization is not unique and results may vary depending on the pivoting strategy used by the underlying library

I will keep this issue updated as soon as development begins.