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)[source]¶
Compute the largest k singular values/vectors for a sparse matrix.
Parameters: A : {sparse matrix, LinearOperator}
Array to compute the SVD on, of shape (M, N)
k : int, optional
Number of singular values and vectors to compute. Must be 1 <= k < min(A.shape).
ncv : int, 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))
tol : float, optional
Tolerance for singular values. Zero (default) means machine precision.
which : str, [‘LM’ | ‘SM’], optional
Which k singular values to find:
- ‘LM’ : largest singular values
- ‘SM’ : smallest singular values
New in version 0.12.0.
v0 : ndarray, 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.
maxiter : int, optional
Maximum number of iterations.
New in version 0.12.0.
return_singular_vectors : bool 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.
Returns: u : ndarray, 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.
s : ndarray, shape=(k,)
The singular values.
vt : ndarray, 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 as an eigensolver on A.H * A or A * A.H, depending on which one is more efficient.