rocsolver_ssytrf_batched Interface Reference

rocsolver_ssytrf_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytrf_batched Interface Reference

SYTRF_BATCHED computes the factorization of a batch of symmetric 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_full_rank (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

SYTRF_BATCHED computes the factorization of a batch of symmetric indefinite matrices using Bunch-Kaufman diagonal pivoting.

(This is the blocked version of the algorithm).

The factorization has the form

\[ \begin{array}{cl} A_i = U_i D_i U_i^T & \: \text{or}\newline A_i = L_i D_i L_i^T & \end{array} \]

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

Specifically, \(U_i\) and \(L_i\) are computed as

\[ \begin{array}{cl} U_i = P_i(n) U_i(n) \cdots P_i(k) U_i(k) \cdots & \: \text{and}\newline L_i = P_i(1) L_i(1) \cdots P_i(k) L_i(k) \cdots & \end{array} \]

where \(k\) decreases from \(n\) to 1 (increases from 1 to \(n\)) in steps of 1 or 2, depending on the order of block \(D_i(k)\), and \(P_i(k)\) is a permutation matrix defined by \(ipiv_i[k]\). If we let \(s\) denote the order of block \(D_i(k)\), then \(U_i(k)\) and \(L_i(k)\) are unit upper/lower triangular matrices defined as

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

and

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

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

Parameters

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

Member Function/Subroutine Documentation