rocsolver_sgesvdx Interface Reference

rocsolver_sgesvdx Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgesvdx Interface Reference

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

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgesvdx_ (handle, left_svect, right_svect, srange, m, n, a, lda, vl, vu, il, iu, nsv, s, u, ldu, v, ldv, ifail, myinfo)

Detailed Description

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

This function computes all the singular values of A, all the singular values in the half-open interval \([vl, vu)\), or the il -th through iu -th singular values, depending on the value of srange.

The full 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, for this function, can take the following values:

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

Parameters

[in]	handle	- rocblas_handle.
[in]	left_svect	- `rocblas_svect`. Specifies if the left singular vectors are computed.
[in]	right_svect	- `rocblas_svect`. Specifies if the right singular vectors are computed.
[in]	srange	- `rocblas_srange`. Specifies the type of range or interval of the singular values to be computed.
[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]	vl	- real type. 0 <= vl < vu. The lower bound of the search interval [vl, vu). Ignored if srange indicates to look for all the singular values of A or the singular values within a set of indices.
[in]	vu	- real type. 0 <= vl < vu. The upper bound of the search interval [vl, vu). Ignored if srange indicates to look for all the singular values of A or the singular values within a set of indices.
[in]	il	- rocblas_int. il = 1 if n = 0, and 1 <= il <= iu otherwise. The index of the largest singular value to be computed. Ignored if srange indicates to look for all the singular values of A or the singular values in a half-open interval.
[in]	iu	- rocblas_int. iu = 0 if n = 0, and 1 <= il <= iu otherwise. The index of the smallest singular value to be computed. Ignored if srange indicates to look for all the singular values of A or the singular values in a half-open interval.
[out]	nsv	- pointer to a rocblas_int on the GPU. The total number of singular values found. If srange is rocblas_srange_all, nsv = min(m,n). If srange is rocblas_srange_index, nsv = iu - il + 1. Otherwise, 0 <= nsv <= min(m,n).
[out]	S	- pointer to real type. Array on the GPU of dimension nsv. The first nsv elements contain the computed singular values in descending order. Note: If srange is rocblas_srange_value, then the value of nsv is not known in advance. In this case, the user should ensure that S is large enough to hold min(m,n) values.
[out]	U	- pointer to type. Array on the GPU of dimension ldu*nsv. The matrix of left singular vectors stored as columns. Not referenced if left_svect is set to none. Note: If srange is rocblas_srange_value, then the value of nsv is not known in advance. In this case, the user should ensure that U is large enough to hold min(m,n) columns.
[in]	ldu	- rocblas_int. ldu >= m if left_svect 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 >= nsv if right_svect is set to singular, or ldv >= 1 otherwise. The leading dimension of V. Note: If srange is rocblas_srange_value, then the value of nsv is not known in advance. In this case, the user should ensure that V is large enough to hold min(m,n) rows.
[out]	ifail	- pointer to rocblas_int. Array on the GPU of dimension min(m,n). If info = 0, the first nsv elements of ifail are zero. Otherwise, contains the indices of those eigenvectors that failed to converge, as returned by BDSVDX.
[out]	myInfo	- pointer to a rocblas_int on the GPU. If info = 0, successful exit. If info = i > 0, i eigenvectors did not converge in BDSVDX. Their indices are stored in ifail.

Member Function/Subroutine Documentation