rocsolver_ssytrf Interface Reference

rocsolver_ssytrf Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytrf Interface Reference

The SYTRF functions compute the factorization of a symmetric and maybe indefinite matrix \(A\) using Bunch-Kaufman diagonal pivoting. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_ssytrf_ (handle, uplo, n, a, lda, ipiv, myinfo)

integer(kind(rocblas_status_success)) function	rocsolver_ssytrf_rank_0 (handle, uplo, n, a, lda, ipiv, myinfo)

integer(kind(rocblas_status_success)) function	rocsolver_ssytrf_rank_1 (handle, uplo, n, a, lda, ipiv, myinfo)

integer(kind(rocblas_status_success)) function	rocsolver_ssytrf_full_rank (handle, uplo, n, a, lda, ipiv, myinfo)

Detailed Description

The SYTRF functions compute the factorization of a symmetric and maybe indefinite matrix \(A\) using Bunch-Kaufman diagonal pivoting.

(This is the blocked version of the algorithm.)

The factorization has the form

\[ \begin{array}{cl} A = U D U^T & \: \text{or}\\% A = L D L^T & \end{array} \]

where \(U\) or \(L\) is a product of permutation and unit upper/lower triangular matrices (depending on the value of uplo), and \(D\) is a symmetric block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks \(D_k\).

Specifically, \(U\) and \(L\) are computed as

\[ \begin{array}{cl} U = P(n) U(n) \cdots P(k) U(k) \cdots & \: \text{and}\\% L = P(1) L(1) \cdots P(k) L(k) \cdots & \end{array} \]

where \(k\) decreases from \(n\) to 1 (increases from 1 to \(n\)) in steps of 1 or 2, depending on the order of block \(D_k\), and \(P(k)\) is a permutation matrix defined by \(ipiv[k]\). If \(s\) denotes the order of block \(D_k\), then \(U(k)\) and \(L(k)\) are unit upper/lower triangular matrices defined as

\[ U(k) = \left[ \begin{array}{ccc} I_{k-s} & v & 0 \\% 0 & I_s & 0 \\% 0 & 0 & I_{n-k} \end{array} \right] \]

and

\[ L(k) = \left[ \begin{array}{ccc} I_{k-1} & 0 & 0 \\% 0 & I_s & 0 \\% 0 & v & I_{n-k-s+1} \end{array} \right]. \]

If \(s = 1\), then \(D_k\) is stored in \(A[k,k]\), and \(v\) is stored in the upper/lower part of column \(k\) of \(A\). If \(s = 2\) and uplo is upper, then \(D_k\) is stored in \(A[k-1,k-1]\), \(A[k-1,k]\), and \(A[k,k]\), and \(v\) is stored in the upper parts of columns \(k-1\) and \(k\) of \(A\). If \(s = 2\) and uplo is lower, then \(D_k\) is stored in \(A[k,k]\), \(A[k+1,k]\), and \(A[k+1,k+1]\), and \(v\) is stored in the lower parts of columns \(k\) and \(k+1\) of \(A\).

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,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 block diagonal matrix D and the multipliers needed to compute U or L.
[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. For 1 <= 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 and uplo is upper (or ipiv[k] = ipiv[k+1] < 0 and uplo is lower), then rows and columns k-1 and -ipiv[k] (or rows and columns k+1 and -ipiv[k]) were interchanged, and D[k-1,k-1] to D[k,k] (or D[k,k] to D[k+1,k+1]) is a 2-by-2 diagonal block.
[out]	myInfo	- pointer to a rocblas_int on the GPU. If info = 0, successful exit. If info = i > 0, D is singular. D[i,i] is the first diagonal zero.

Member Function/Subroutine Documentation