`scipy.sparse.linalg._svdp:_svdp`

source: /scipy/sparse/linalg/_svdp.py :64

Signature

   def     _svdp (    A    ,    k    ,    which    =  LM   ,    irl_mode    =  True   ,    kmax    =  None   ,    compute_u    =  True   ,    compute_v    =  True   ,    v0    =  None   ,    full_output    =  False   ,    tol    =  0   ,    delta    =  None   ,    eta    =  None   ,    anorm    =  0   ,    cgs    =  False   ,    elr    =  True   ,    min_relgap    =  0.002   ,    shifts    =  None   ,    maxiter    =  None   ,    rng    =  None     )

Summary

Compute the singular value decomposition of a linear operator using PROPACK

Parameters

A : array_like, sparse matrix, or LinearOperator: Operator for which SVD will be computed. If A is a LinearOperator object, it must define both matvec and rmatvec methods.
k : int: Number of singular values/vectors to compute
which : {"LM", "SM"}: Which singular triplets to compute: - 'LM': compute triplets corresponding to the k largest singular values - 'SM': compute triplets corresponding to the k smallest singular values which='SM' requires irl_mode=True. Computes largest singular values by default.
irl_mode : bool, optional: If True, then compute SVD using IRL (implicitly restarted Lanczos) mode. Default is True.
kmax : int, optional: Maximal number of iterations / maximal dimension of the Krylov subspace. Default is 10 * k.
compute_u : bool, optional: If True (default) then compute left singular vectors, u.
compute_v : bool, optional: If True (default) then compute right singular vectors, v.
tol : float, optional: The desired relative accuracy for computed singular values. If not specified, it will be set based on machine precision.
v0 : array_like, optional: Starting vector for iterations: must be of length A.shape[0]. If not specified, PROPACK will generate a starting vector.
full_output : bool, optional: If True, then return sigma_bound. Default is False.
delta : float, optional: Level of orthogonality to maintain between Lanczos vectors. Default is set based on machine precision.
eta : float, optional: Orthogonality cutoff. During reorthogonalization, vectors with component larger than eta along the Lanczos vector will be purged. Default is set based on machine precision.
anorm : float, optional: Estimate of ||A||. Default is 0.
cgs : bool, optional: If True, reorthogonalization is done using classical Gram-Schmidt. If False (default), it is done using modified Gram-Schmidt.
elr : bool, optional: If True (default), then extended local orthogonality is enforced when obtaining singular vectors.
min_relgap : float, optional: The smallest relative gap allowed between any shift in IRL mode. Default is 0.001. Accessed only if irl_mode=True.
shifts : int, optional: Number of shifts per restart in IRL mode. Default is determined to satisfy k <= min(kmax-shifts, m, n). Must be >= 0, but choosing 0 might lead to performance degradation. Accessed only if irl_mode=True.
maxiter : int, optional: Maximum number of restarts in IRL mode. Default is 1000. Accessed only if irl_mode=True.
rng : `numpy.random.Generator`, optional: Pseudorandom number generator state. When rng is None, a new numpy.random.Generator is created using entropy from the operating system. Types other than numpy.random.Generator are passed to numpy.random.default_rng to instantiate a Generator.

Returns

u : ndarray: The k largest (which="LM") or smallest (which="SM") left singular vectors, shape == (A.shape[0], 3), returned only if compute_u=True.
sigma : ndarray: The top k singular values, shape == (k,)
vt : ndarray: The k largest (which="LM") or smallest (which="SM") right singular vectors, shape == (3, A.shape[1]), returned only if compute_v=True.
sigma_bound : ndarray: the error bounds on the singular values sigma, returned only if full_output=True.

Aliases

scipy.sparse.linalg._svdp._svdp