rocsolver_ssytd2_batched Interface Reference

rocsolver_ssytd2_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytd2_batched Interface Reference

SYTD2_BATCHED computes the tridiagonal form of a batch of real symmetric matrices A_j. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_ssytd2_batched_ (handle, uplo, n, A, lda, D, strideD, E, strideE, tau, strideP, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_ssytd2_batched_full_rank (handle, uplo, n, A, lda, D, strideD, E, strideE, tau, strideP, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_ssytd2_batched_rank_0 (handle, uplo, n, A, lda, D, strideD, E, strideE, tau, strideP, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_ssytd2_batched_rank_1 (handle, uplo, n, A, lda, D, strideD, E, strideE, tau, strideP, batch_count)

Detailed Description

SYTD2_BATCHED computes the tridiagonal form of a batch of real symmetric matrices A_j.

(This is the unblocked version of the algorithm).

The tridiagonal form of \(A_j\) is given by:

\[ T_j = Q_j' A_j Q_j \]

where \(T_j\) is symmetric tridiagonal and \(Q_j\) is an orthogonal matrix represented as the product of Householder matrices

\[ \begin{array}{cl} Q_j = H_{j_1}H_{j_2}\cdots H_{j_{n-1}} & \: \text{if uplo indicates lower, or}\newline Q_j = H_{j_{n-1}}H_{j_{n-2}}\cdots H_{j_1} & \: \text{if uplo indicates upper.} \end{array} \]

Each Householder matrix \(H_{j_i}\) is given by

\[ H_{j_i} = I - \text{tau}_j[i] \cdot v_{j_i} v_{j_i}' \]

where \(\text{tau}_j[i]\) is the corresponding Householder scalar. When uplo indicates lower, the first i elements of the Householder vector \(v_{j_i}\) are zero, and \(v_{j_i}[i+1] = 1\). If uplo indicates upper, the last n-i elements of the Householder vector \(v_{j_i}\) are zero, and \(v_{j_i}[i] = 1\).

Parameters

[in]	handle	rocblas_handle.
[in]	uplo	rocblas_fill. Specifies whether the upper or lower part of the symmetric matrix A_j 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 matrices A_j.
[in,out]	A	array of pointers to type. Each pointer points to an array on the GPU of dimension lda*n. On entry, the matrices A_j to be factored. On exit, if upper, then the elements on the diagonal and superdiagonal contain the tridiagonal form T_j; the elements above the superdiagonal contain the first i-1 elements of the Householder vectors v_(j_i) stored as columns. If lower, then the elements on the diagonal and subdiagonal contain the tridiagonal form T_j; the elements below the subdiagonal contain the last n-i-1 elements of the Householder vectors v_(j_i) stored as columns.
[in]	lda	rocblas_int. lda >= n. The leading dimension of A_j.
[out]	D	pointer to type. Array on the GPU (the size depends on the value of strideD). The diagonal elements of T_j.
[in]	strideD	rocblas_stride. Stride from the start of one vector D_j to the next one D_(j+1). There is no restriction for the value of strideD. Normal use case is strideD >= n.
[out]	E	pointer to type. Array on the GPU (the size depends on the value of strideE). The off-diagonal elements of T_j.
[in]	strideE	rocblas_stride. Stride from the start of one vector E_j to the next one E_(j+1). There is no restriction for the value of strideE. Normal use case is strideE >= n-1.
[out]	tau	pointer to type. Array on the GPU (the size depends on the value of strideP). Contains the vectors tau_j of corresponding Householder scalars.
[in]	strideP	rocblas_stride. Stride from the start of one vector tau_j to the next one tau_(j+1). There is no restriction for the value of strideP. Normal use is strideP >= n-1.
[in]	batch_count	rocblas_int. batch_count >= 0. Number of matrices in the batch.

Member Function/Subroutine Documentation