rocsolver_sgesvd Interface Reference#
GESVD computes 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_sgesvd_ (handle, left_svect, right_svect, m, n, A, lda, S, U, ldu, V, ldv, E, fast_alg, myInfo) |
integer(kind(rocblas_status_success)) function | rocsolver_sgesvd_full_rank (handle, left_svect, right_svect, m, n, A, lda, S, U, ldu, V, ldv, E, fast_alg, myInfo) |
integer(kind(rocblas_status_success)) function | rocsolver_sgesvd_rank_0 (handle, left_svect, right_svect, m, n, A, lda, S, U, ldu, V, ldv, E, fast_alg, myInfo) |
integer(kind(rocblas_status_success)) function | rocsolver_sgesvd_rank_1 (handle, left_svect, right_svect, m, n, A, lda, S, U, ldu, V, ldv, E, fast_alg, myInfo) |
Detailed Description
GESVD computes 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:
\[ A = U S V' \]
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 it 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, i.e. the rows of V'.
left_svect and right_svect are rocblas_svect enums that can take the following values:
- rocblas_svect_all: the entire matrix U (or V') is computed,
- rocblas_svect_singular: only the singular vectors (first min(m,n) columns of U or rows of V') are computed,
- rocblas_svect_overwrite: the first columns (or rows) of A are overwritten with the singular vectors, or
- rocblas_svect_none: no columns (or rows) of U (or V') are computed, i.e. no singular vectors.
left_svect and right_svect cannot both be set to overwrite. When neither is set to overwrite, the contents of A 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 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); this will require, however, a larger memory workspace. The parameter fast_alg controls whether the fast algorithm is executed or not. For more details, see the "Tuning rocSOLVER performance" and "Memory model" sections of the documentation.
- 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 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, if left_svect (or right_svect) is equal to overwrite, the first columns (or rows) contain the left (or right) singular vectors; otherwise, the contents of A are destroyed.[in] lda rocblas_int. lda >= m.
The leading dimension of A.[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 ldu*min(m,n) if left_svect is set to singular, or ldu*m when left_svect is equal to all.
The matrix 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; 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 overwrite or none.[in] ldv rocblas_int. ldv >= n if right_svect is all; ldv >= min(m,n) if right_svect is set to singular; or ldv >= 1 otherwise.
The leading dimension of V.[out] E pointer to real type. Array on the GPU of dimension min(m,n)-1.
This array is used to work internally with the bidiagonal matrix B associated with A (using BDSQR). On exit, if info > 0, it contains the unconverged off-diagonal elements of B (or properly speaking, a bidiagonal matrix orthogonally equivalent to B). The diagonal elements of this matrix are in S; those that converged correspond to a subset of the singular values of A (not necessarily ordered).[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] info pointer to a rocblas_int on the GPU.
If info = 0, successful exit. If info = i > 0, BDSQR did not converge. i elements of E did not converge to zero.
Member Function/Subroutine Documentation
◆ rocsolver_sgesvd_()
integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgesvd::rocsolver_sgesvd_ | ( | type(c_ptr), value | handle, |
integer(kind(rocblas_svect_all)), value | left_svect, | ||
integer(kind(rocblas_svect_all)), value | right_svect, | ||
integer(c_int), value | m, | ||
integer(c_int), value | n, | ||
type(c_ptr), value | A, | ||
integer(c_int), value | lda, | ||
type(c_ptr), value | S, | ||
type(c_ptr), value | U, | ||
integer(c_int), value | ldu, | ||
type(c_ptr), value | V, | ||
integer(c_int), value | ldv, | ||
type(c_ptr), value | E, | ||
integer(kind(rocblas_outofplace)), value | fast_alg, | ||
integer(c_int) | myInfo | ||
) |
◆ rocsolver_sgesvd_full_rank()
integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgesvd::rocsolver_sgesvd_full_rank | ( | type(c_ptr) | handle, |
integer(kind(rocblas_svect_all)) | left_svect, | ||
integer(kind(rocblas_svect_all)) | right_svect, | ||
integer(c_int) | m, | ||
integer(c_int) | n, | ||
real(c_float), dimension(:,:), target | A, | ||
integer(c_int) | lda, | ||
real(c_float), dimension(:), target | S, | ||
real(c_float), dimension(:,:), target | U, | ||
integer(c_int) | ldu, | ||
real(c_float), dimension(:,:), target | V, | ||
integer(c_int) | ldv, | ||
real(c_float), dimension(:), target | E, | ||
integer(kind(rocblas_outofplace)) | fast_alg, | ||
integer(c_int) | myInfo | ||
) |
◆ rocsolver_sgesvd_rank_0()
integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgesvd::rocsolver_sgesvd_rank_0 | ( | type(c_ptr) | handle, |
integer(kind(rocblas_svect_all)) | left_svect, | ||
integer(kind(rocblas_svect_all)) | right_svect, | ||
integer(c_int) | m, | ||
integer(c_int) | n, | ||
real(c_float), target | A, | ||
integer(c_int) | lda, | ||
real(c_float), target | S, | ||
real(c_float), target | U, | ||
integer(c_int) | ldu, | ||
real(c_float), target | V, | ||
integer(c_int) | ldv, | ||
real(c_float), target | E, | ||
integer(kind(rocblas_outofplace)) | fast_alg, | ||
integer(c_int) | myInfo | ||
) |
◆ rocsolver_sgesvd_rank_1()
integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgesvd::rocsolver_sgesvd_rank_1 | ( | type(c_ptr) | handle, |
integer(kind(rocblas_svect_all)) | left_svect, | ||
integer(kind(rocblas_svect_all)) | right_svect, | ||
integer(c_int) | m, | ||
integer(c_int) | n, | ||
real(c_float), dimension(:), target | A, | ||
integer(c_int) | lda, | ||
real(c_float), dimension(:), target | S, | ||
real(c_float), dimension(:), target | U, | ||
integer(c_int) | ldu, | ||
real(c_float), dimension(:), target | V, | ||
integer(c_int) | ldv, | ||
real(c_float), dimension(:), target | E, | ||
integer(kind(rocblas_outofplace)) | fast_alg, | ||
integer(c_int) | myInfo | ||
) |
The documentation for this interface was generated from the following file: