scipy.sparse.linalg.svds¶
- scipy.sparse.linalg.svds(A, k=6, ncv=None, tol=0, which='LM', v0=None, maxiter=None, return_singular_vectors=True, solver='arpack')[source]¶
Compute the largest or smallest k singular values/vectors for a sparse matrix. The order of the singular values is not guaranteed.
- Parameters
- A{sparse matrix, LinearOperator}
Array to compute the SVD on, of shape (M, N)
- kint, optional
Number of singular values and vectors to compute. Must be 1 <= k < min(A.shape).
- ncvint, optional
The number of Lanczos vectors generated ncv must be greater than k+1 and smaller than n; it is recommended that ncv > 2*k Default:
min(n, max(2*k + 1, 20))- tolfloat, optional
Tolerance for singular values. Zero (default) means machine precision.
- whichstr, [‘LM’ | ‘SM’], optional
Which k singular values to find:
‘LM’ : largest singular values
‘SM’ : smallest singular values
New in version 0.12.0.
- v0ndarray, optional
Starting vector for iteration, of length min(A.shape). Should be an (approximate) left singular vector if N > M and a right singular vector otherwise. Default: random
New in version 0.12.0.
- maxiterint, optional
Maximum number of iterations.
New in version 0.12.0.
- return_singular_vectorsbool or str, optional
True: return singular vectors (True) in addition to singular values.
New in version 0.12.0.
“u”: only return the u matrix, without computing vh (if N > M).
“vh”: only return the vh matrix, without computing u (if N <= M).
New in version 0.16.0.
- solverstr, optional
Eigenvalue solver to use. Should be ‘arpack’ or ‘lobpcg’. Default: ‘arpack’
- Returns
- undarray, shape=(M, k)
Unitary matrix having left singular vectors as columns. If return_singular_vectors is “vh”, this variable is not computed, and None is returned instead.
- sndarray, shape=(k,)
The singular values.
- vtndarray, shape=(k, N)
Unitary matrix having right singular vectors as rows. If return_singular_vectors is “u”, this variable is not computed, and None is returned instead.
Notes
This is a naive implementation using ARPACK or LOBPCG as an eigensolver on A.H * A or A * A.H, depending on which one is more efficient.
Examples
>>> from scipy.sparse import csc_matrix >>> from scipy.sparse.linalg import svds, eigs >>> A = csc_matrix([[1, 0, 0], [5, 0, 2], [0, -1, 0], [0, 0, 3]], dtype=float) >>> u, s, vt = svds(A, k=2) >>> s array([ 2.75193379, 5.6059665 ]) >>> np.sqrt(eigs(A.dot(A.T), k=2)[0]).real array([ 5.6059665 , 2.75193379])