cond

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cond#

class saiunit.linalg.cond(x, p=None, **kwargs)#

Compute the condition number of a matrix.

SaiUnit implementation of numpy.linalg.cond().

The condition number is defined as norm(x, p) * norm(inv(x), p). For p = 2 (the default), the condition number is the ratio of the largest to the smallest singular value. The unit is stripped before computation and the result is a dimensionless JAX array.

Parameters:

  • x (Array | ndarray | bool | number | bool | int | float | complex | saiunit.Quantity) – Input of shape (..., M, N) for which to compute the condition number. If x carries a unit, the unit is removed before the computation.

  • p ({None, 1, -1, 2, -2, inf, -inf, 'fro'}, optional) – Order of the norm used in the condition number computation; see jax.numpy.linalg.norm(). The default p = None is equivalent to p = 2. If p is not in {None, 2, -2}, then x must be square (M = N).

Returns:

out – Condition number(s) of shape x.shape[:-2]. Always dimensionless.

Return type:

Array

See also

saiunit.linalg.matrix_rank

Rank of a matrix via SVD.

saiunit.linalg.slogdet

Sign and log-determinant of a matrix.

Notes

The condition number is a scalar measure of how sensitive a matrix inversion is to numerical errors. A large condition number indicates an ill-conditioned (nearly singular) matrix.

Examples

>>> import saiunit as u
>>> import jax.numpy as jnp
>>> x = jnp.array([[1., 2.],
...                [2., 1.]]) * u.meter
>>> u.linalg.cond(x)
Array(3., dtype=float32)

Ill-conditioned (rank-deficient) matrix:

>>> import saiunit as u
>>> import jax.numpy as jnp
>>> x = jnp.array([[1., 2.],
...                [0., 0.]]) * u.meter
>>> u.linalg.cond(x)
Array(inf, dtype=float32)
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