jax.lax.linalg.triangular_solve — JAX documentation (original) (raw)

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• triangular_solve()

jax.lax.linalg.triangular_solve#

jax.lax.linalg.triangular_solve(a, b, *, left_side=False, lower=False, transpose_a=False, conjugate_a=False, unit_diagonal=False)[source]#

Triangular solve.

Solves either the matrix equation

\[\mathit{op}(A) . X = B\]

if left_side is True or

\[X . \mathit{op}(A) = B\]

if left_side is False.

A must be a lower or upper triangular square matrix, and where\(\mathit{op}(A)\) may either transpose \(A\) if transpose_ais True and/or take its complex conjugate if conjugate_a is True.

Parameters:

• a (ArrayLike) – A batch of matrices with shape [..., m, m].
• b (ArrayLike) – A batch of matrices with shape [..., m, n] if left_side isTrue or shape [..., n, m] otherwise.
• left_side (bool) – describes which of the two matrix equations to solve; see above.
• lower (bool) – describes which triangle of a should be used. The other triangle is ignored.
• transpose_a (bool) – if True, the value of a is transposed.
• conjugate_a (bool) – if True, the complex conjugate of a is used in the solve. Has no effect if a is real.
• unit_diagonal (bool) – if True, the diagonal of a is assumed to be unit (all 1s) and not accessed.

Returns:

A batch of matrices the same shape and dtype as b.

Return type:

Array