rocsolver_slasyf Interface Reference

rocsolver_slasyf Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_slasyf Interface Reference

LASYF computes a partial factorization of a symmetric matrix \(A\) using Bunch-Kaufman diagonal pivoting. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_slasyf_ (handle, uplo, n, nb, kb, A, lda, ipiv, myInfo)

integer(kind(rocblas_status_success)) function	rocsolver_slasyf_full_rank (handle, uplo, n, nb, kb, A, lda, ipiv, myInfo)

integer(kind(rocblas_status_success)) function	rocsolver_slasyf_rank_0 (handle, uplo, n, nb, kb, A, lda, ipiv, myInfo)

integer(kind(rocblas_status_success)) function	rocsolver_slasyf_rank_1 (handle, uplo, n, nb, kb, A, lda, ipiv, myInfo)

Detailed Description

LASYF computes a partial factorization of a symmetric matrix \(A\) using Bunch-Kaufman diagonal pivoting.

The partial factorization has the form

\[ A = \left[ \begin{array}{cc} I & U_{12} \newline 0 & U_{22} \end{array} \right] \left[ \begin{array}{cc} A_{11} & 0 \newline 0 & D \end{array} \right] \left[ \begin{array}{cc} I & 0 \newline U_{12}^T & U_{22}^T \end{array} \right] \]

or

\[ A = \left[ \begin{array}{cc} L_{11} & 0 \newline L_{21} & I \end{array} \right] \left[ \begin{array}{cc} D & 0 \newline 0 & A_{22} \end{array} \right] \left[ \begin{array}{cc} L_{11}^T & L_{21}^T \newline 0 & I \end{array} \right] \]

depending on the value of uplo. The order of the block diagonal matrix \(D\) is either \(nb\) or \(nb-1\), and is returned in the argument \(kb\).

Parameters

[in]	handle	rocblas_handle.
[in]	uplo	rocblas_fill. Specifies whether the upper or lower part of the matrix A is stored. If uplo indicates lower (or upper), then the upper (or lower) part of A is not used.
[in]	n	rocblas_int. n >= 0. The number of rows and columns of the matrix A.
[in]	nb	rocblas_int. 2 <= nb <= n. The number of columns of A to be factored.
[out]	kb	pointer to a rocblas_int on the GPU. The number of columns of A that were actually factored (either nb or nb-1).
[in,out]	A	pointer to type. Array on the GPU of dimension lda*n. On entry, the symmetric matrix A to be factored. On exit, the partially factored matrix.
[in]	lda	rocblas_int. lda >= n. Specifies the leading dimension of A.
[out]	ipiv	pointer to rocblas_int. Array on the GPU of dimension n. The vector of pivot indices. Elements of ipiv are 1-based indices. If uplo is upper, then only the last kb elements of ipiv will be set. For n - kb < k <= n, if ipiv[k] > 0 then rows and columns k and ipiv[k] were interchanged and D[k,k] is a 1-by-1 diagonal block. If, instead, ipiv[k] = ipiv[k-1] < 0, then rows and columns k-1 and -ipiv[k] were interchanged and D[k-1,k-1] to D[k,k] is a 2-by-2 diagonal block. If uplo is lower, then only the first kb elements of ipiv will be set. For 1 <= k <= kb, if ipiv[k] > 0 then rows and columns k and ipiv[k] were interchanged and D[k,k] is a 1-by-1 diagonal block. If, instead, ipiv[k] = ipiv[k+1] < 0, then rows and columns k+1 and -ipiv[k] were interchanged and D[k,k] to D[k+1,k+1] is a 2-by-2 diagonal block.
[out]	info	pointer to a rocblas_int on the GPU. If info = 0, successful exit. If info[i] = j > 0, D is singular. D[j,j] is the first diagonal zero.

Member Function/Subroutine Documentation