schur

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schur#

class brainunit.lax.schur(x, compute_schur_vectors=True, sort_eig_vals=False, select_callable=None)#

Schur decomposition.

Compute the Schur decomposition \(A = Q \cdot T \cdot Q^H\) where \(T\) is upper-triangular (quasi-triangular for real matrices) and \(Q\) is unitary.

Parameters:

  • x (saiunit.Quantity | Array | ndarray | number | bool) – A batch of square matrices with shape [..., n, n].

  • compute_schur_vectors (bool) – If True, compute the Schur vectors Q. Default is True.

  • sort_eig_vals (bool) – If True, sort eigenvalues. Default is False.

  • select_callable (Callable[..., Any] | None) – A function used to select eigenvalues for reordering. Default is None.

Return type:

tuple[saiunit.Quantity | Array, Array] | list[Array] | tuple[saiunit.Quantity | Array]

Returns:

  • t (Array or Quantity) – The Schur form. If x has a unit, t preserves that unit.

  • q (Array) – The Schur vectors (unitless). Only returned when compute_schur_vectors is True.

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]]) * u.second
>>> t, q = sulax.schur(A)
>>> u.get_unit(t) == u.second
True
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