svdvals — SciPy v1.15.2 Manual (original) (raw)

scipy.linalg.

scipy.linalg.svdvals(a, overwrite_a=False, check_finite=True)[source]#

Compute singular values of a matrix.

Parameters:

a(M, N) array_like

Matrix to decompose.

overwrite_abool, optional

Whether to overwrite a; may improve performance. Default is False.

check_finitebool, optional

Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns:

s(min(M, N),) ndarray

The singular values, sorted in decreasing order.

Raises:

LinAlgError

If SVD computation does not converge.

See also

svd

Compute the full singular value decomposition of a matrix.

diagsvd

Construct the Sigma matrix, given the vector s.

Examples

import numpy as np from scipy.linalg import svdvals m = np.array([[1.0, 0.0], ... [2.0, 3.0], ... [1.0, 1.0], ... [0.0, 2.0], ... [1.0, 0.0]]) svdvals(m) array([ 4.28091555, 1.63516424])

We can verify the maximum singular value of m by computing the maximum length of m.dot(u) over all the unit vectors u in the (x,y) plane. We approximate “all” the unit vectors with a large sample. Because of linearity, we only need the unit vectors with angles in [0, pi].

t = np.linspace(0, np.pi, 2000) u = np.array([np.cos(t), np.sin(t)]) np.linalg.norm(m.dot(u), axis=0).max() 4.2809152422538475

p is a projection matrix with rank 1. With exact arithmetic, its singular values would be [1, 0, 0, 0].

v = np.array([0.1, 0.3, 0.9, 0.3]) p = np.outer(v, v) svdvals(p) array([ 1.00000000e+00, 2.02021698e-17, 1.56692500e-17, 8.15115104e-34])

The singular values of an orthogonal matrix are all 1. Here, we create a random orthogonal matrix by using the rvs() method ofscipy.stats.ortho_group.

from scipy.stats import ortho_group orth = ortho_group.rvs(4) svdvals(orth) array([ 1., 1., 1., 1.])