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Module « scipy.linalg »

Fonction svdvals - module scipy.linalg

Signature de la fonction svdvals

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

Description

help(scipy.linalg.svdvals)

Compute singular values of a matrix.

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.

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 of
`scipy.stats.ortho_group`.

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

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