`scipy.linalg._decomp_svd:svdvals`

source: /scipy/linalg/_decomp_svd.py :182

Signature

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

Summary

Compute singular values of a matrix.

Extended Summary

The documentation is written assuming array arguments are of specified "core" shapes. However, array argument(s) of this function 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. Note that calls with zero-size batches are unsupported and will raise a ValueError.

Parameters

a : (M, N) array_like: Matrix to decompose.
overwrite_a : bool, optional: Whether to overwrite a; may improve performance. Default is False.
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.

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)

✗

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()

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`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)

✗

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)

✗

Aliases

scipy.linalg.svdvals