lu_factor_op

→std::vector<TensorImplPtr>

int lu_factor_op(const int & a)

source edit

Python wrappers

pylucid.linalg.lu_factorfunction

Compute the LU factorisation $PA = LU$ of a square matrix.

Shape

Input a: (..., n, n).
Output LU_packed: (..., n, n).
Output pivots: (..., n) with Dtype::I32.

References

LAPACK sgetrf/dgetrf; LAPACK Users' Guide §2.5.

See Also

[[lu_solve_op]] : Apply the factors to solve $Ax = b$ . [[solve_op]] : End-to-end differentiable linear solve.

Parameters

aconst TensorImplPtr&

Square float tensor of shape (..., n, n). Leading dimensions are treated as independent batch axes — one factorisation is produced per batch element.

Returns

std::vector<TensorImplPtr>

A two-element vector {LU_packed, pivots}: - LU_packed has the same shape and dtype as a; its upper triangle holds $U$ and its strict lower triangle holds the off-diagonal entries of $L$ (unit diagonal is implicit). - pivots has shape (..., n) and dtype I32; entries are 1-based row indices matching the LAPACK convention.

Raises

LinAlgError

When a is not square, not float-typed, or the LAPACK call reports a structural failure.