scipy.linalg.svd¶

scipy.linalg.
svd
(a, full_matrices=True, compute_uv=True, overwrite_a=False, check_finite=True, lapack_driver='gesdd')[source]¶ Singular Value Decomposition.
Factorizes the matrix a into two unitary matrices U and Vh, and a 1D array s of singular values (real, nonnegative) such that
a == U*S*Vh
, where S is a suitably shaped matrix of zeros with main diagonal s.Parameters: a : (M, N) array_like
Matrix to decompose.
full_matrices : bool, optional
If True, U and Vh are of shape
(M,M)
,(N,N)
. If False, the shapes are(M,K)
and(K,N)
, whereK = min(M,N)
.compute_uv : bool, optional
Whether to compute also U and Vh in addition to
s
. Default is True.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, nontermination) if the inputs do contain infinities or NaNs.
lapack_driver : {‘gesdd’, ‘gesvd’}, optional
Whether to use the more efficient divideandconquer approach (
'gesdd'
) or general rectangular approach ('gesvd'
) to compute the SVD. MATLAB and Octave use the'gesvd'
approach. Default is'gesdd'
.New in version 0.18.
Returns: U : ndarray
Unitary matrix having left singular vectors as columns. Of shape
(M,M)
or(M,K)
, depending on full_matrices.s : ndarray
The singular values, sorted in nonincreasing order. Of shape (K,), with
K = min(M, N)
.Vh : ndarray
Unitary matrix having right singular vectors as rows. Of shape
(N,N)
or(K,N)
depending on full_matrices.For
compute_uv=False
, onlys
is returned.Raises: LinAlgError
If SVD computation does not converge.
See also
Examples
>>> from scipy import linalg >>> a = np.random.randn(9, 6) + 1.j*np.random.randn(9, 6) >>> U, s, Vh = linalg.svd(a) >>> U.shape, Vh.shape, s.shape ((9, 9), (6, 6), (6,))
>>> U, s, Vh = linalg.svd(a, full_matrices=False) >>> U.shape, Vh.shape, s.shape ((9, 6), (6, 6), (6,)) >>> S = linalg.diagsvd(s, 6, 6) >>> np.allclose(a, np.dot(U, np.dot(S, Vh))) True
>>> s2 = linalg.svd(a, compute_uv=False) >>> np.allclose(s, s2) True