rocsolver_ssytd2_batched Interface Reference

rocsolver_ssytd2_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytd2_batched Interface Reference

The SYTD2_BATCHED functions compute the tridiagonal form of a batch of real symmetric matrices A_l. 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_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

The SYTD2_BATCHED functions compute the tridiagonal form of a batch of real symmetric matrices A_l.

(This is the unblocked version of the algorithm.)

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

\[ T_l^{} = Q_l^H A_l^{} Q_l^{} \]

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

\[ \begin{array}{cl} Q_l = H_l(1)H_l(2)\cdots H_l(n-1) & \: \text{if uplo indicates lower, or}\\% Q_l = H_l(n-1)H_l(n-2)\cdots H_l(1) & \: \text{if uplo indicates upper.} \end{array} \]

Each Householder matrix \(H_l(i)\) is given by

\[ H_l^{}(i) = I - \text{tau}_l^{}[i] \cdot v_{l_i}^{} v_{l_i}^H \]

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

Parameters

[in]	handle	- rocblas_handle.
[in]	uplo	- rocblas_fill. Specifies whether the upper or lower part of the symmetric matrix A_l is 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 the matrices A_l.
[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_l to be factored. On exit, if upper, then the elements on the diagonal and superdiagonal contain the tridiagonal form T_l, and the elements above the superdiagonal contain the first i-1 elements of the Householder vectors v_(l_i) stored as columns. If lower, then the elements on the diagonal and subdiagonal contain the tridiagonal form T_l, and the elements below the subdiagonal contain the last n-i-1 elements of the Householder vectors v_(l_i) stored as columns.
[in]	lda	- rocblas_int. lda >= n. The leading dimension of A_l.
[out]	D	- pointer to type. Array on the GPU (the size depends on the value of strideD). The diagonal elements of T_l.
[in]	strideD	- rocblas_stride. Stride from the start of one vector D_l to the next one D_(l+1). There is no restriction for the value of strideD. The 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_l.
[in]	strideE	- rocblas_stride. Stride from the start of one vector E_l to the next one E_(l+1). There is no restriction for the value of strideE. The 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_l of corresponding Householder scalars.
[in]	strideP	- rocblas_stride. Stride from the start of one vector tau_l to the next one tau_(l+1). There is no restriction for the value of strideP. Normal usage is strideP >= n-1.
[in]	batch_count	- rocblas_int. batch_count >= 0. Number of matrices in the batch.

Member Function/Subroutine Documentation