lu_solve_op

→TensorImplPtr

int lu_solve_op(const int & LU, const int & pivots, const int & b)

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Python wrappers

pylucid.linalg.lu_solvefunction

Solve $Ax = b$ given the packed LU factors and pivot vector.

Shape

LU: (..., n, n).
pivots: (..., n).
b: (..., n) or (..., n, k).
Output: same shape as b.

References

LAPACK sgetrs/dgetrs; LAPACK Users' Guide §2.5.1.

See Also

[[lu_factor_op]] : Produce the packed factors consumed here. [[solve_op]] : Differentiable one-shot solve (factor + apply).

Parameters

LUconst TensorImplPtr&

Packed LU matrix of shape (..., n, n) as returned by [[lu_factor_op]] — upper triangle holds

U

, strict lower triangle holds the off-diagonal entries of

L

pivotsconst TensorImplPtr&

1-based pivot indices of shape (..., n) and dtype I32.

bconst TensorImplPtr&

Right-hand side of shape (..., n) for a single RHS or (..., n, k) for

k

simultaneous RHS columns.

Returns

TensorImplPtr

Solution tensor with the same shape and dtype as b.

Raises

LinAlgError

When LU or b is not a float dtype, when any argument is null, or when shapes are inconsistent with the batched solve.