`scipy.linalg._decomp_svd:svdvals`

source: /scipy/linalg/_decomp_svd.py:215

Signature

def svdvals(a, overwrite_a = False, check_finite = True)

Summary

Compute singular values of a matrix.

Parameters

a : (M, N) array_like: Matrix to decompose.
overwrite_a : bool, optional: Whether to overwrite data in a (may improve performance). Default is False. See tutorial_linalg_overwrite for details.
check_finite : bool, 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.

Notes

Array argument of this function, a, may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details.

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([4.281, 1.635])

If the input matrix has more than two dimensions, it is interpreted as a batch of two-dimensional matrices:

mm = np.stack((m, 2*m))

✓

svdvals(mm)

✗

array([[4.281, 1.635],
       [8.562, 3.27 ]])

We can verify the maximum singular value of `m` by computing the maximum length of `m @ 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 @ u, axis=0).max()

✗

np.float64(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., 0., 0., 0.])

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

from scipy.stats import ortho_group
orth = ortho_group.rvs(4)

✓

svdvals(orth)

✗

array([1., 1., 1., 1.])

Aliases

scipy.linalg.svdvals