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
andVh
, and a 1D arrays
of singular values (real, nonnegative) such thata == U @ S @ Vh
, whereS
is a suitably shaped matrix of zeros with main diagonals
. Parameters
 a(M, N) array_like
Matrix to decompose.
 full_matricesbool, optional
If True (default), 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_uvbool, optional
Whether to compute also
U
andVh
in addition tos
. Default is True. overwrite_abool, optional
Whether to overwrite a; may improve performance. Default is False.
 check_finitebool, 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
 Undarray
Unitary matrix having left singular vectors as columns. Of shape
(M, M)
or(M, K)
, depending on full_matrices. sndarray
The singular values, sorted in nonincreasing order. Of shape (K,), with
K = min(M, N)
. Vhndarray
Unitary matrix having right singular vectors as rows. Of shape
(N, N)
or(K, N)
depending on full_matrices. For ``compute_uv=False``, only ``s`` is returned.
 Raises
 LinAlgError
If SVD computation does not converge.
See also
Examples
>>> from scipy import linalg >>> m, n = 9, 6 >>> a = np.random.randn(m, n) + 1.j*np.random.randn(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 ofU
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) >>> np.allclose(s, s2) True