svd(a, full_matrices=True, compute_uv=True, overwrite_a=False, check_finite=True, lapack_driver='gesdd')
Factorizes the matrix a
into two unitary matrices U
and Vh
, and a 1-D array s
of singular values (real, non-negative) such that a == U @ S @ Vh
, where S
is a suitably shaped matrix of zeros with main diagonal s
.
Matrix to decompose.
If True (default), U
and :None:None:`Vh`
are of shape (M, M)
, (N, N)
. If False, the shapes are (M, K)
and (K, N)
, where K = min(M, N)
.
Whether to compute also U
and Vh
in addition to s
. Default is True.
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.
Whether to use the more efficient divide-and-conquer approach ( 'gesdd'
) or general rectangular approach ( 'gesvd'
) to compute the SVD. MATLAB and Octave use the 'gesvd'
approach. Default is 'gesdd'
.
If SVD computation does not converge.
Unitary matrix having left singular vectors as columns. Of shape (M, M)
or (M, K)
, depending on :None:None:`full_matrices`
.
The singular values, sorted in non-increasing order. Of shape (K,), with K = min(M, N)
.
Unitary matrix having right singular vectors as rows. Of shape (N, N)
or (K, N)
depending on :None:None:`full_matrices`
.
Singular Value Decomposition.
diagsvd
Construct the Sigma matrix, given the vector s.
svdvals
Compute singular values of a matrix.
>>> from scipy import linalg
... from numpy.random import default_rng
... rng = default_rng()
... m, n = 9, 6
... a = rng.standard_normal((m, n)) + 1.j*rng.standard_normal((m, n))
... U, s, Vh = linalg.svd(a)
... U.shape, s.shape, Vh.shape ((9, 9), (6,), (6, 6))
Reconstruct the original matrix from the decomposition:
>>> sigma = np.zeros((m, n))
... for i in range(min(m, n)):
... sigma[i, i] = s[i]
... a1 = np.dot(U, np.dot(sigma, Vh))
... np.allclose(a, a1) True
Alternatively, use full_matrices=False
(notice that the shape of U
is then (m, n)
instead of (m, m)
):
>>> U, s, Vh = linalg.svd(a, full_matrices=False)
... U.shape, s.shape, Vh.shape ((9, 6), (6,), (6, 6))
>>> S = np.diag(s)
... np.allclose(a, np.dot(U, np.dot(S, Vh))) True
>>> s2 = linalg.svd(a, compute_uv=False)See :
... np.allclose(s, s2) True
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.null_space
scipy.linalg._decomp_svd.subspace_angles
scipy.linalg._decomp_svd.diagsvd
scipy.linalg._decomp_svd.svd
scipy.linalg._decomp_svd.orth
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