numpy.linalg.cond — NumPy v2.2 Manual (original) (raw)

linalg.cond(x, p=None)[source]#

Compute the condition number of a matrix.

This function is capable of returning the condition number using one of seven different norms, depending on the value of p (see Parameters below).

Parameters:

x(…, M, N) array_like

The matrix whose condition number is sought.

p{None, 1, -1, 2, -2, inf, -inf, ‘fro’}, optional

Order of the norm used in the condition number computation:

inf means the numpy.inf object, and the Frobenius norm is the root-of-sum-of-squares norm.

Returns:

c{float, inf}

The condition number of the matrix. May be infinite.

Notes

The condition number of x is defined as the norm of x times the norm of the inverse of x [1]; the norm can be the usual L2-norm (root-of-sum-of-squares) or one of a number of other matrix norms.

References

[1]

G. Strang, Linear Algebra and Its Applications, Orlando, FL, Academic Press, Inc., 1980, pg. 285.

Examples

import numpy as np from numpy import linalg as LA a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]]) a array([[ 1, 0, -1], [ 0, 1, 0], [ 1, 0, 1]]) LA.cond(a) 1.4142135623730951 LA.cond(a, 'fro') 3.1622776601683795 LA.cond(a, np.inf) 2.0 LA.cond(a, -np.inf) 1.0 LA.cond(a, 1) 2.0 LA.cond(a, -1) 1.0 LA.cond(a, 2) 1.4142135623730951 LA.cond(a, -2) 0.70710678118654746 # may vary (min(LA.svd(a, compute_uv=False)) * ... min(LA.svd(LA.inv(a), compute_uv=False))) 0.70710678118654746 # may vary