qr

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qr#

class brainunit.linalg.qr(a, mode='reduced', **kwargs)#

Compute the QR decomposition of a matrix.

SaiUnit implementation of numpy.linalg.qr().

The QR decomposition of a matrix A is:

\[A = QR\]

where Q is a unitary matrix (\(Q^HQ=I\)) and R is upper-triangular. The unit of A is carried by R; Q is always dimensionless.

Parameters:

  • a (saiunit.Quantity | Array | ndarray | bool | number | bool | int | float | complex) – Input of shape (..., M, N).

  • mode (str) –

    Computational mode (default: "reduced").

    • "reduced" – Q has shape (..., M, K), R has shape (..., K, N) with K = min(M, N).

    • "complete" – Q has shape (..., M, M), R has shape (..., M, N).

    • "r" – only R is returned.

Return type:

Array | saiunit.Quantity

Returns:

  • Q (ndarray) – Orthogonal factor (omitted when mode="r").

  • R (ndarray or Quantity) – Upper-triangular factor carrying the unit of a.

Examples

>>> import saiunit as u
>>> import jax.numpy as jnp
>>> a = jnp.array([[1., 2., 3., 4.],
...                [5., 4., 2., 1.],
...                [6., 3., 1., 5.]]) * u.meter
>>> Q, R = u.linalg.qr(a)
>>> Q.shape
(3, 3)
>>> R.unit
meter
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