householder_product

class saiunit.lax.householder_product(a, taus)

Product of elementary Householder reflectors.

Reconstruct the orthogonal (unitary) matrix \(Q\) from a set of elementary Householder reflectors and their scalar factors.

Parameters:

• a (saiunit.Quantity | Array | ndarray | bool | number | bool | int | float | complex) – A matrix with shape [..., m, n] whose lower triangle contains the elementary Householder reflectors. Units, if present, are stripped before computation.

• taus (saiunit.Quantity | Array | ndarray | bool | number | bool | int | float | complex) – A vector with shape [..., k] (k < min(m, n)) containing the scalar factors. Units, if present, are stripped.

Returns:

Q – The orthogonal (unitary) matrix with the same shape as a (always unitless).

Return type:

Array

See also

saiunit.lax.hessenberg

Produces reflectors consumed by this function.

Examples

>>> import jax.numpy as jnp
>>> import saiunit as u
>>> import saiunit.lax as sulax
>>> a = jnp.array([[1.0, 2.0], [3.0, 4.0]])
>>> taus = jnp.array([1.0])
>>> Q = sulax.householder_product(a, taus)
>>> Q.shape
(2, 2)