rocsolver_sgesvd_batched Interface Reference

rocsolver_sgesvd_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgesvd_batched Interface Reference

The GESVD_BATCHED functions compute the singular values and optionally the singular vectors of a batch of general m-by-n matrices A_l (Singular Value Decomposition). More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgesvd_batched_ (handle, left_svect, right_svect, m, n, a, lda, s, strides, u, ldu, strideu, v, ldv, stridev, e, stridee, fast_alg, myinfo, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgesvd_batched_rank_0 (handle, left_svect, right_svect, m, n, a, lda, s, strides, u, ldu, strideu, v, ldv, stridev, e, stridee, fast_alg, myinfo, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgesvd_batched_rank_1 (handle, left_svect, right_svect, m, n, a, lda, s, strides, u, ldu, strideu, v, ldv, stridev, e, stridee, fast_alg, myinfo, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgesvd_batched_full_rank (handle, left_svect, right_svect, m, n, a, lda, s, strides, u, ldu, strideu, v, ldv, stridev, e, stridee, fast_alg, myinfo, batch_count)

Detailed Description

The GESVD_BATCHED functions compute the singular values and optionally the singular vectors of a batch of general m-by-n matrices A_l (Singular Value Decomposition).

The SVD of matrix A_l in the batch is given by:

\[ A_l^{} = U_l^{} S_l^{} V_l^H \]

where the m-by-n matrix \(S_l\) is zero except, possibly, for its min(m,n) diagonal elements, which are the singular values of \(A_l\). \(U_l\) and \(V_l\) are orthogonal (unitary) matrices. The first min(m,n) columns of \(U_l\) and \(V_l\) are the left and right singular vectors of \(A_l\), 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 \(V_l^H\).

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

rocblas_svect_all: the entire matrix \(U_l\) (or \(V_l^H\)) is computed,
rocblas_svect_singular: only the singular vectors (first min(m,n) columns of \(U_l\) or rows of \(V_l^H\)) are computed,
rocblas_svect_overwrite: the first columns (or rows) of \(A_l\) are overwritten with the singular vectors, or
rocblas_svect_none: no columns (or rows) of \(U_l\) (or \(V_l^H\)) are computed, that is, no singular vectors.

left_svect and right_svect cannot both be set to overwrite. When neither is set to overwrite, the contents of \(A_l\) are destroyed by the time the function returns.

Note: When m >> n (or n >> m) the algorithm could be sped up by compressing the matrix \(A_l\) via a QR (or LQ) factorization and working with the triangular factor afterwards (thin-SVD). If the singular vectors are also requested, its computation could be sped up as well via executing some intermediate operations out-of-place and relying more on matrix multiplications (GEMMs), but this will require a larger memory workspace. The parameter fast_alg controls whether the fast algorithm is executed or not. For more details, see the "rocSOLVER performance tuning" and "Memory model" sections of the documentation.; In order to carry out calculations, this method could potentially synchronize the stream contained within the rocblas_handle.; A hybrid (CPU+GPU) approach is available for GESVD_BATCHED, primarily intended for homogeneous architectures. Use rocsolver_set_alg_mode to enable it.

Parameters

[in]	handle	- rocblas_handle.
[in]	left_svect	- `rocblas_svect`. Specifies how the left singular vectors are computed.
[in]	right_svect	- `rocblas_svect`. Specifies how the right singular vectors are computed.
[in]	m	- rocblas_int. m >= 0. The number of rows of all matrices A_l in the batch.
[in]	n	- rocblas_int. n >= 0. The number of columns of all matrices A_l in the batch.
[in,out]	A	- Array of pointers to type. Each pointer points to an array on the GPU of dimension lda*n. On entry, the matrices A_l. On exit, if left_svect (or right_svect) is equal to overwrite, the first columns (or rows) of A_l contain the left (or right) corresponding singular vectors. Otherwise, the contents of A_l are destroyed.
[in]	lda	- rocblas_int. lda >= m. The leading dimension of A_l.
[out]	S	- pointer to real type. Array on the GPU (the size depends on the value of strideS). The singular values of A_l in decreasing order.
[in]	strideS	- rocblas_stride. Stride from the start of one vector S_l to the next one S_(l+1). There is no restriction for the value of strideS. The normal use case is strideS >= min(m,n).
[out]	U	- pointer to type. Array on the GPU (the side depends on the value of strideU). The matrices U_l of left singular vectors stored as columns. Not referenced if left_svect is set to overwrite or none.
[in]	ldu	- rocblas_int. ldu >= m if left_svect is all or singular, and ldu >= 1 otherwise. The leading dimension of U_l.
[in]	strideU	- rocblas_stride. Stride from the start of one matrix U_l to the next one U_(l+1). There is no restriction for the value of strideU. The normal use case is strideU >= ldumin(m,n) if left_svect is set to singular, or strideU >= ldum when left_svect is equal to all.
[out]	V	- pointer to type. Array on the GPU (the size depends on the value of strideV). The matrices V_l of right singular vectors stored as rows (transposed / conjugate-transposed). Not referenced if right_svect is set to overwrite or none.
[in]	ldv	- rocblas_int. ldv >= n if right_svect is all, and ldv >= min(m,n) if right_svect is set to singular or ldv >= 1 otherwise. The leading dimension of V_l.
[in]	strideV	- rocblas_stride. Stride from the start of one matrix V_l to the next one V_(l+1). There is no restriction for the value of strideV. The normal use case is strideV >= ldv*n.
[out]	E	- pointer to real type. Array on the GPU (the size depends on the value of strideE). This array is used to work internally with the bidiagonal matrix B_l associated with A_l (using BDSQR). On exit, if info[l] > 0, E_l contains the unconverged off-diagonal elements of B_l (or properly speaking, a bidiagonal matrix orthogonally equivalent to B_l). The diagonal elements of this matrix are in S_l. Those that converged correspond to a subset of the singular values of A_l (not necessarily ordered).
[in]	strideE	- rocblas_stride. Stride from the start of one vector E_l to the next one E_(l+1). There is no restriction for the value of strideE. The normal use case is strideE >= min(m,n)-1.
[in]	fast_alg	- `rocblas_workmode`. If set to rocblas_outofplace, the function will execute the fast thin-SVD version of the algorithm when possible.
[out]	myInfo	- pointer to a rocblas_int on the GPU. If info[l] = 0, successful exit. If info[l] = i > 0, BDSQR did not converge. i elements of E_l did not converge to zero.
[in]	batch_count	- rocblas_int. batch_count >= 0. Number of matrices in the batch.

Member Function/Subroutine Documentation