rocsolver_sgesvdj Interface Reference

rocsolver_sgesvdj Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgesvdj Interface Reference

The GESVDJ functions compute the singular values and optionally the singular vectors of a general m-by-n matrix A (Singular Value Decomposition). More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgesvdj_ (handle, left_svect, right_svect, m, n, a, lda, abstol, residual, max_sweeps, n_sweeps, s, u, ldu, v, ldv, myinfo)

Detailed Description

The GESVDJ functions compute the singular values and optionally the singular vectors of a general m-by-n matrix A (Singular Value Decomposition).

The SVD of matrix A is given by:

\[ A = U S V^H \]

where the m-by-n matrix S is zero except, possibly, for its min(m,n) diagonal elements, which are the singular values of A. U and V are orthogonal (unitary) matrices. The first min(m,n) columns of U and V are the left and right singular vectors of A, respectively.

The computation of the singular vectors is optional and is controlled by the function arguments left_svect and right_svect, as described below. When computed, this function returns the transpose (or transpose conjugate) of the right singular vectors, that is, the rows of \(V^H\).

left_svect and right_svect are rocblas_svect enums that can take the following values:

rocblas_svect_all: the entire matrix U (or \(V^H\)) is computed,
rocblas_svect_singular: the singular vectors (first min(m,n) columns of U or rows of \(V^H\)) are computed, or
rocblas_svect_none: no columns (or rows) of U (or \(V^H\)) are computed, that is, no singular vectors.

The singular values are computed by applying QR factorization to \(AV\) if \(m ≥ n\) (resp. LQ factorization to \(U^H A\) if \(m < n\)), where \(V\) (resp. \(U\)) is found as the eigenvectors of \(A^H A\) (resp. \(A A^H\)) using the Jacobi eigenvalue algorithm.

Note: In order to carry out calculations, this method could potentially synchronize the stream contained within the rocblas_handle.

Parameters

[in]	handle	- rocblas_handle.
[in]	left_svect	- `rocblas_svect`. Specifies how the left singular vectors are computed. rocblas_svect_overwrite is not supported.
[in]	right_svect	- `rocblas_svect`. Specifies how the right singular vectors are computed. rocblas_svect_overwrite is not supported.
[in]	m	- rocblas_int. m >= 0. The number of rows of matrix A.
[in]	n	- rocblas_int. n >= 0. The number of columns of matrix A.
[in,out]	A	- pointer to type. Array on the GPU of dimension lda*n. On entry, the matrix A. On exit, the contents of A are destroyed.
[in]	lda	- rocblas_int. lda >= m. The leading dimension of A.
[in]	abstol	- real type. The absolute tolerance. The algorithm is considered to have converged once \(\mathrm{off}(A^H A) ≤ \mathrm{norm}(A^H A) \cdot \mathrm{abstol}\) [resp. \(\mathrm{off}(A A^H) ≤ \mathrm{norm}(A A^H) \cdot \mathrm{abstol}\)]. If abstol <= 0, then the tolerance will be set to machine precision.
[out]	residual	- pointer to real type on the GPU. The Frobenius norm of the off-diagonal elements of \(A^H A\) (resp. \(A A^H\)) at the final iteration.
[in]	max_sweeps	- rocblas_int. max_sweeps > 0. Maximum number of sweeps (iterations) to be used by the algorithm.
[out]	n_sweeps	- pointer to a rocblas_int on the GPU. The actual number of sweeps (iterations) used by the algorithm.
[out]	S	- pointer to real type. Array on the GPU of dimension min(m,n). The singular values of A in decreasing order.
[out]	U	- pointer to type. Array on the GPU of dimension ldumin(m,n) if left_svect is set to singular, or ldum when left_svect is equal to all. The matrix of left singular vectors stored as columns. Not referenced if left_svect is set to none.
[in]	ldu	- rocblas_int. ldu >= m if left_svect is set to all or singular, and ldu >= 1 otherwise. The leading dimension of U.
[out]	V	- pointer to type. Array on the GPU of dimension ldv*n. The matrix of right singular vectors stored as rows (transposed / conjugate-transposed). Not referenced if right_svect is set to none.
[in]	ldv	- rocblas_int. ldv >= n if right_svect is set to all, and ldv >= min(m,n) if right_svect is set to singular; or ldv >= 1 otherwise. The leading dimension of V.
[out]	myInfo	- pointer to a rocblas_int on the GPU. If info = 0, successful exit. If info = 1, the algorithm did not converge.

Member Function/Subroutine Documentation