scipy.linalg.svd¶
- scipy.linalg.svd(a, full_matrices=True, compute_uv=True, overwrite_a=False, check_finite=True)[source]¶
Singular Value Decomposition.
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.
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), where K = 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 : boolean, 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: 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 non-increasing 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, only s 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