rocsolver_ssytrf_batched Interface Reference

rocsolver_ssytrf_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytrf_batched Interface Reference

The SYTRF_BATCHED functions compute the factorization of a batch of symmetric and maybe indefinite matrices using Bunch-Kaufman diagonal pivoting. More...

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

integer(kind(rocblas_status_success)) function	rocsolver_ssytrf_batched_rank_0 (handle, uplo, n, a, lda, ipiv, stridep, myinfo, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_ssytrf_batched_rank_1 (handle, uplo, n, a, lda, ipiv, stridep, myinfo, batch_count)

Detailed Description

The SYTRF_BATCHED functions compute the factorization of a batch of symmetric and maybe indefinite matrices using Bunch-Kaufman diagonal pivoting.

(This is the blocked version of the algorithm.)

The factorization has the form

\[ \begin{array}{cl} A_l^{} = U_l^{} D_l^{} U_l^T & \: \text{or}\\% A_l^{} = L_l^{} D_l^{} L_l^T & \end{array} \]

where \(U_l\) or \(L_l\) is a product of permutation and unit upper/lower triangular matrices (depending on the value of uplo), and \(D_l\) is a symmetric block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks \(D_{kl}\).

Specifically, \(U_l\) and \(L_l\) are computed as

\[ \begin{array}{cl} U_l = P_l(n) U_l(n) \cdots P_l(k) U_l(k) \cdots & \: \text{and}\\% L_l = P_l(1) L_l(1) \cdots P_l(k) L_l(k) \cdots & \end{array} \]

where \(k\) decreases from \(n\) to 1 (increases from 1 to \(n\)) in steps of 1 or 2, depending on the order of block \(D_{kl}\), and \(P_l(k)\) is a permutation matrix defined by \(ipiv_l[k]\). If \(s\) denotes the order of block \(D_{kl}\), then \(U_l(k)\) and \(L_l(k)\) are unit upper/lower triangular matrices defined as

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

and

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

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

Parameters

[in]	handle	- rocblas_handle.
[in]	uplo	- rocblas_fill. Specifies whether the upper or lower part of the matrices A_l are stored. If uplo indicates lower (or upper), then the upper (or lower) part of A_l is not used.
[in]	n	- rocblas_int. n >= 0. The number of rows and 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 symmetric matrices A_l to be factored. On exit, the block diagonal matrices D_l and the multipliers needed to compute U_l or L_l.
[in]	lda	- rocblas_int. lda >= n. Specifies the leading dimension of matrices A_l.
[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_l[k] > 0, then rows and columns k and ipiv_l[k] were interchanged, and D_l[k,k] is a 1-by-1 diagonal block. If, instead, ipiv_l[k] = ipiv_l[k-1] < 0 and uplo is upper (or ipiv_l[k] = ipiv_l[k+1] < 0 and uplo is lower), then rows and columns k-1 and -ipiv_l[k] (or rows and columns k+1 and -ipiv_l[k]) were interchanged, and D_l[k-1,k-1] to D_l[k,k] (or D_l[k,k] to D_l[k+1,k+1]) is a 2-by-2 diagonal block.
[in]	strideP	- rocblas_stride. Stride from the start of one vector ipiv_l to the next one ipiv_(l+1). There is no restriction for the value of strideP. The normal use case is strideP >= n.
[out]	myInfo	- pointer to rocblas_int. Array of batch_count integers on the GPU. If info[l] = 0, successful exit for factorization of A_l. If info[l] = i > 0, D_l is singular. D_l[i,i] is the first diagonal zero.
[in]	batch_count	- rocblas_int. batch_count >= 0. Number of matrices in the batch.

Member Function/Subroutine Documentation