mojolearn.lu_factor#

mojolearn.lu_factor(a, *, numeric_mode=None)[source]#

LU factorization of a square matrix with partial pivoting.

Follows scipy.linalg.lu_factor: returns (lu, piv), where lu holds the unit lower-triangular L (diagonal not stored) and U in one float32 matrix, and piv holds the 0-based row interchanges, applied in order. Pivoting picks the largest absolute value in the column; ties go to the lowest row. A zero pivot is kept and a RuntimeWarning is issued, as scipy does.

Parameters:

  • a (array-like of shape (n, n)) – The matrix to factor; must be finite.

  • numeric_mode ({“identical”, “fast”} or None, default None) – Numeric mode for this call. None uses the package default ("identical" unless changed). "identical" gives the same bits on NVIDIA and AMD GPUs; "fast" applies on Apple GPUs.

Returns:

  • lu (ndarray of shape (n, n), float32)

  • piv (ndarray of shape (n,), int32) – Pass the pair to lu_solve().

Raises:

ValueError – If a is not square, is empty, or contains NaN or infinity.

Examples

>>> import numpy as np, mojolearn
>>> A = np.random.default_rng(0).random((8, 8), dtype=np.float32) + 8 * np.eye(8, dtype=np.float32)
>>> lu, piv = mojolearn.lu_factor(A)
>>> x = mojolearn.lu_solve((lu, piv), np.ones(8, dtype=np.float32))
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