rocsolver_slarfb Interface Reference

rocsolver_slarfb Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_slarfb Interface Reference

The LARFB functions apply a block reflector H to a general m -by-n matrix A. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_slarfb_ (handle, side, trans, mydirect, storev, m, n, k, v, ldv, t, ldt, a, lda)

integer(kind(rocblas_status_success)) function	rocsolver_slarfb_rank_0 (handle, side, trans, mydirect, storev, m, n, k, v, ldv, t, ldt, a, lda)

integer(kind(rocblas_status_success)) function	rocsolver_slarfb_rank_1 (handle, side, trans, mydirect, storev, m, n, k, v, ldv, t, ldt, a, lda)

integer(kind(rocblas_status_success)) function	rocsolver_slarfb_full_rank (handle, side, trans, mydirect, storev, m, n, k, v, ldv, t, ldt, a, lda)

Detailed Description

The LARFB functions apply a block reflector H to a general m -by-n matrix A.

The block reflector H is applied in one of the following forms, depending on the values of side and trans:

\[ \begin{array}{cl} HA & \: \text{(No transpose from the left),}\\% H^H A & \: \text{(Transpose or conjugate transpose from the left),}\\% AH & \: \text{(No transpose from the right), or}\\% AH^H & \: \text{(Transpose or conjugate transpose from the right).} \end{array} \]

The block reflector H is defined as the product of k Householder matrices as

\[ \begin{array}{cl} H = H(1)H(2)\cdots H(k) & \: \text{if direct indicates forward direction, or} \\% H = H(k)\cdots H(2)H(1) & \: \text{if direct indicates backward direction} \end{array} \]

H is never stored. It is calculated as

\[ H = I - VTV^H \]

where the \(j\)th column of matrix V contains the Householder vector associated with \(H(j)\), if storev is column-wise, or

\[ H = I - V^H T V \]

where the \(i\)th row of matrix V contains the Householder vector associated with \(H(i)\), if storev is row-wise. T is the associated triangular factor as computed by LARFT.

Parameters

[in]	handle	- rocblas_handle.
[in]	side	- rocblas_side. Specifies from which side to apply H.
[in]	trans	- rocblas_operation. Specifies whether the block reflector or its transpose/conjugate transpose is to be applied.
[in]	myDirect	- `rocblas_direct`. Specifies the direction in which the Householder matrices are to be applied to generate H.
[in]	storev	- `rocblas_storev`. Specifies how the Householder vectors are stored in matrix V.
[in]	m	- rocblas_int. m >= 0. Number of rows of matrix A.
[in]	n	- rocblas_int. n >= 0. Number of columns of matrix A.
[in]	k	- rocblas_int. k >= 1. The number of Householder matrices.
[in]	V	- pointer to type. Array on the GPU of size ldvk if column-wise, ldvn if row-wise and applying from the right, or ldv*m if row-wise and applying from the left. The matrix of Householder vectors.
[in]	ldv	- rocblas_int. ldv >= k if row-wise, ldv >= m if column-wise and applying from the left, or ldv >= n if column-wise and applying from the right. The leading dimension of V.
[in]	T	- pointer to type. Array on the GPU of dimension ldt*k. The triangular factor of the block reflector.
[in]	ldt	- rocblas_int. ldt >= k. The leading dimension of T.
[in,out]	A	- pointer to type. Array on the GPU of size lda*n. On entry, the matrix A. On exit, it is overwritten with \(HA\), \(AH\), \(H^H A\), or \(AH^H\).
[in]	lda	- rocblas_int. lda >= m. The leading dimension of A.

Member Function/Subroutine Documentation