Sparse#

This page provides pylibraft class references for the publicly-exposed elements of the pylibraft.sparse.linalg package.

pylibraft.sparse.linalg.eigsh( A, k=6, which='LM', v0=None, ncv=None, maxiter=None, tol=0, seed=None, handle=None, )[source]#

Find k eigenvalues and eigenvectors of the real symmetric square matrix or complex Hermitian matrix A.

Solves Ax = wx, the standard eigenvalue problem for w eigenvalues with corresponding eigenvectors x.

Args:

a (spmatrix): A symmetric square sparse CSR matrix with: dimension (n, n). a must be of type cupyx.scipy.sparse._csr.csr_matrix
k (int): The number of eigenvalues and eigenvectors to compute. Must be: 1 <= k < n.
which (str): ‘LM’ or ‘LA’ or ‘SA’.: ‘LM’: finds k largest (in magnitude) eigenvalues. ‘LA’: finds k largest (algebraic) eigenvalues. ‘SA’: finds k smallest (algebraic) eigenvalues. ‘SM’: finds k smallest (in magnitude) eigenvalues.
v0 (ndarray): Starting vector for iteration. If None, a random: unit vector is used.
ncv (int): The number of Lanczos vectors generated. Must be: k + 1 < ncv < n. If None, default value is used.
maxiter (int): Maximum number of Lanczos update iterations.: If None, default value is used.
tol (float): Tolerance for residuals ||Ax - wx||. If 0, machine: precision is used.

Returns:

tuple:: It returns w and x where w is eigenvalues and x is eigenvectors.

See also

scipy.sparse.linalg.eigsh() cupyx.scipy.sparse.linalg.eigsh()

Note

This function uses the thick-restart Lanczos methods (https://sdm.lbl.gov/~kewu/ps/trlan.html).

pylibraft.sparse.linalg.svds( A, k=6, n_oversamples=10, n_power_iters=2, seed=None, return_singular_vectors=True, handle=None, solver='randomized', ncv=None, tol=1e-4, maxiter=None, orthogonalization='cgs2', )[source]#

Compute the largest k singular values and corresponding singular vectors of a sparse matrix.

Computes the truncated SVD: A ~ U @ diag(S) @ Vt.

Args:

A (cupyx.scipy.sparse.csr_matrix): Sparse CSR matrix of shape

(m, n). Must be of type cupyx.scipy.sparse.csr_matrix.

k (int): Number of singular values and vectors to compute. Must be

1 <= k < min(m, n). Default 6.

n_oversamples (int): Number of extra random vectors for better

approximation. Total subspace dimension is k + n_oversamples. Used only when solver="randomized". Default 10.

n_power_iters (int): Number of power iteration passes. More

iterations improve accuracy for matrices with slowly decaying singular values. Used only when solver="randomized". Default 2.

seed (int or None): Random seed for reproducibility. If None,

a non-deterministic seed is used.

return_singular_vectors (bool or {“u”, “vh”}): Controls which

singular vectors are returned (matches scipy.sparse.linalg.svds()).

True (default): return (U, S, Vt).
False: skip both vector matrices, return (None, S, None).
"u": skip Vt, return (U, S, None).
"vh": skip U, return (None, S, Vt).

Skipping a side avoids the corresponding output buffer. Depending on the selected solver, some intermediate vector products may still be required for numerical refinement.

handle: RAFT resource handle. If None, a default is created. solver ({ “randomized”, “lanczos” }): Solver to use. The default

"randomized" preserves the existing approximate randomized SVD behavior. "lanczos" uses Lanczos bidiagonalization and is the higher-accuracy, ARPACK-like sparse SVD path.

ncv (int or None): Number of Lanczos vectors. Used only when: solver="lanczos". If None, a default is selected. Larger values can improve convergence margin and orthogonality for difficult spectra, but increase sparse matrix-vector work. The value is clamped to [k + 10, min(A.shape) - 1]; the extra subspace slack is required for reliable convergence, in particular with repeated or tightly clustered singular values.
tol (float): Lanczos residual tolerance. Used only when: solver="lanczos".
maxiter (int or None): Maximum Lanczos restart iterations. Used only: when solver="lanczos". If None, defaults to 100. The Lanczos solver raises an error if all requested singular triplets do not converge within this limit.
orthogonalization ({ “cgs2”, “mgs2” }): Lanczos reorthogonalization: method. "cgs2" is the GPU-efficient default. "mgs2" is more launch-heavy and intended as an alternate path for difficult float32 spectra.

Returns:

tuple:: (U, S, Vt) where U is left singular vectors (m, k), S is singular values (k,) in descending order, and Vt is right singular vectors (k, n). U and/or Vt may be None depending on return_singular_vectors.