rocsolver_slabrd Interface Reference

rocsolver_slabrd Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_slabrd Interface Reference

LABRD computes the bidiagonal form of the first k rows and columns of a general m-by-n matrix A, as well as the matrices X and Y needed to reduce the remaining part of A. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_slabrd_ (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy)

integer(kind(rocblas_status_success)) function	rocsolver_slabrd_full_rank (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy)

integer(kind(rocblas_status_success)) function	rocsolver_slabrd_rank_0 (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy)

integer(kind(rocblas_status_success)) function	rocsolver_slabrd_rank_1 (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy)

Detailed Description

LABRD computes the bidiagonal form of the first k rows and columns of a general m-by-n matrix A, as well as the matrices X and Y needed to reduce the remaining part of A.

The reduced form is given by:

\[ B = Q'AP \]

where the leading k-by-k block of B is upper bidiagonal if m >= n, or lower bidiagonal if m < n. Q and P are orthogonal/unitary matrices represented as the product of Householder matrices

\[ \begin{array}{cl} Q = H_1H_2\cdots H_k, & \text{and} \newline P = G_1G_2\cdots G_k. \end{array} \]

Each Householder matrix \(H_i\) and \(G_i\) is given by

\[ \begin{array}{cl} H_i = I - \text{tauq}[i]\cdot v_iv_i', & \text{and} \newline G_i = I - \text{taup}[i]\cdot u_iu_i'. \end{array} \]

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

The unreduced part of the matrix A can be updated using the block update

\[ A = A - VY' - XU' \]

where V and U are the m-by-k and n-by-k matrices formed with the vectors \(v_i\) and \(u_i\), respectively.

Parameters

[in]	handle	rocblas_handle.
[in]	m	rocblas_int. m >= 0. The number of rows of the matrix A.
[in]	n	rocblas_int. n >= 0. The number of columns of the matrix A.
[in]	k	rocblas_int. min(m,n) >= k >= 0. The number of leading rows and columns of matrix A that will be reduced.
[in,out]	A	pointer to type. Array on the GPU of dimension lda*n. On entry, the m-by-n matrix to be reduced. On exit, the first k elements on the diagonal and superdiagonal (if m >= n), or subdiagonal (if m < n), contain the bidiagonal form B. If m >= n, the elements below the diagonal of the first k columns are the possibly non-zero elements of the Householder vectors associated with Q, while the elements above the superdiagonal of the first k rows are the n - i - 1 possibly non-zero elements of the Householder vectors related to P. If m < n, the elements below the subdiagonal of the first k columns are the m - i - 1 possibly non-zero elements of the Householder vectors related to Q, while the elements above the diagonal of the first k rows are the n - i possibly non-zero elements of the vectors associated with P.
[in]	lda	rocblas_int. lda >= m. specifies the leading dimension of A.
[out]	D	pointer to real type. Array on the GPU of dimension k. The diagonal elements of B.
[out]	E	pointer to real type. Array on the GPU of dimension k. The off-diagonal elements of B.
[out]	tauq	pointer to type. Array on the GPU of dimension k. The Householder scalars associated with matrix Q.
[out]	taup	pointer to type. Array on the GPU of dimension k. The Householder scalars associated with matrix P.
[out]	X	pointer to type. Array on the GPU of dimension ldx*k. The m-by-k matrix needed to update the unreduced part of A.
[in]	ldx	rocblas_int. ldx >= m. The leading dimension of X.
[out]	Y	pointer to type. Array on the GPU of dimension ldy*k. The n-by-k matrix needed to update the unreduced part of A.
[in]	ldy	rocblas_int. ldy >= n. The leading dimension of Y.

Member Function/Subroutine Documentation