svdvals(a, overwrite_a=False, check_finite=True)
svdvals(a)
only differs from svd(a, compute_uv=False)
by its handling of the edge case of empty a
, where it returns an empty sequence:
>>> a = np.empty((0, 2)) >>> from scipy.linalg import svdvals >>> svdvals(a) array([], dtype=float64)
Matrix to decompose.
Whether to overwrite a; may improve performance. Default is False.
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.
If SVD computation does not converge.
The singular values, sorted in decreasing order.
Compute singular values of a matrix.
diagsvd
Construct the Sigma matrix, given the vector s.
svd
Compute the full singular value decomposition of a matrix.
>>> 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 :None:None:`m` by computing the maximum length of :None:None:`m.dot(u)` over all the unit vectors :None:None:`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
:None:None:`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 :None:None:`rvs()` method of :None:None:`scipy.stats.ortho_group`.
>>> from scipy.stats import ortho_groupSee :
... orth = ortho_group.rvs(4)
... svdvals(orth) array([ 1., 1., 1., 1.])
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._decomp_svd.svdvals
scipy.linalg._decomp_svd.svd
scipy.linalg._decomp_svd.diagsvd
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