rocsolver_sgebd2_batched Interface Reference

rocsolver_sgebd2_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgebd2_batched Interface Reference

GEBD2_BATCHED computes the bidiagonal form of a batch of general m-by-n matrices. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgebd2_batched_ (handle, m, n, A, lda, D, strideD, E, strideE, tauq, strideQ, taup, strideP, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgebd2_batched_full_rank (handle, m, n, A, lda, D, strideD, E, strideE, tauq, strideQ, taup, strideP, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgebd2_batched_rank_0 (handle, m, n, A, lda, D, strideD, E, strideE, tauq, strideQ, taup, strideP, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgebd2_batched_rank_1 (handle, m, n, A, lda, D, strideD, E, strideE, tauq, strideQ, taup, strideP, batch_count)

Detailed Description

GEBD2_BATCHED computes the bidiagonal form of a batch of general m-by-n matrices.

(This is the unblocked version of the algorithm).

For each instance in the batch, the bidiagonal form is given by:

\[ B_j = Q_j' A_j P_j \]

where \(B_j\) is upper bidiagonal if m >= n and lower bidiagonal if m < n, and \(Q_j\) and \(P_j\) are orthogonal/unitary matrices represented as the product of Householder matrices

\[ \begin{array}{cl} Q_j = H_{j_1}H_{j_2}\cdots H_{j_n}\: \text{and} \: P_j = G_{j_1}G_{j_2}\cdots G_{j_{n-1}}, & \: \text{if}\: m >= n, \:\text{or}\newline Q_j = H_{j_1}H_{j_2}\cdots H_{j_{m-1}}\: \text{and} \: P_j = G_{j_1}G_{j_2}\cdots G_{j_m}, & \: \text{if}\: m < n. \end{array} \]

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

\[ \begin{array}{cl} H_{j_i} = I - \text{tauq}_j[i] \cdot v_{j_i} v_{j_i}', & \: \text{and}\newline G_{j_i} = I - \text{taup}_j[i] \cdot u_{j_i}' u_{j_i}. \end{array} \]

If m >= n, the first i-1 elements of the Householder vector \(v_{j_i}\) are zero, and \(v_{j_i}[i] = 1\); while the first i elements of the Householder vector \(u_{j_i}\) are zero, and \(u_{j_i}[i+1] = 1\). If m < n, the first i elements of the Householder vector \(v_{j_i}\) are zero, and \(v_{j_i}[i+1] = 1\); while the first i-1 elements of the Householder vector \(u_{j_i}\) are zero, and \(u_{j_i}[i] = 1\).

Parameters

[in]	handle	rocblas_handle.
[in]	m	rocblas_int. m >= 0. The number of rows of all the matrices A_j in the batch.
[in]	n	rocblas_int. n >= 0. The number of columns of all the matrices A_j 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 m-by-n matrices A_j to be factored. On exit, the elements on the diagonal and superdiagonal (if m >= n), or subdiagonal (if m < n) contain the bidiagonal form B_j. If m >= n, the elements below the diagonal are the last m - i elements of Householder vector v_(j_i), and the elements above the superdiagonal are the last n - i - 1 elements of Householder vector u_(j_i). If m < n, the elements below the subdiagonal are the last m - i - 1 elements of Householder vector v_(j_i), and the elements above the diagonal are the last n - i elements of Householder vector u_(j_i).
[in]	lda	rocblas_int. lda >= m. Specifies the leading dimension of matrices A_j.
[out]	D	pointer to real type. Array on the GPU (the size depends on the value of strideD). The diagonal elements of B_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 >= min(m,n).
[out]	E	pointer to real type. Array on the GPU (the size depends on the value of strideE). The off-diagonal elements of B_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 >= min(m,n)-1.
[out]	tauq	pointer to type. Array on the GPU (the size depends on the value of strideQ). Contains the vectors tauq_j of Householder scalars associated with matrices Q_j.
[in]	strideQ	rocblas_stride. Stride from the start of one vector tauq_j to the next one tauq_(j+1). There is no restriction for the value of strideQ. Normal use is strideQ >= min(m,n).
[out]	taup	pointer to type. Array on the GPU (the size depends on the value of strideP). Contains the vectors taup_j of Householder scalars associated with matrices P_j.
[in]	strideP	rocblas_stride. Stride from the start of one vector taup_j to the next one taup_(j+1). There is no restriction for the value of strideP. Normal use is strideP >= min(m,n).
[in]	batch_count	rocblas_int. batch_count >= 0. Number of matrices in the batch.

Member Function/Subroutine Documentation