rocsolver_sgebrd Interface Reference

rocsolver_sgebrd Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgebrd Interface Reference

GEBRD computes the bidiagonal form of a general m-by-n matrix A. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgebrd_ (handle, m, n, A, lda, D, E, tauq, taup)

integer(kind(rocblas_status_success)) function	rocsolver_sgebrd_full_rank (handle, m, n, A, lda, D, E, tauq, taup)

integer(kind(rocblas_status_success)) function	rocsolver_sgebrd_rank_0 (handle, m, n, A, lda, D, E, tauq, taup)

integer(kind(rocblas_status_success)) function	rocsolver_sgebrd_rank_1 (handle, m, n, A, lda, D, E, tauq, taup)

Detailed Description

GEBRD computes the bidiagonal form of a general m-by-n matrix A.

(This is the blocked version of the algorithm).

The bidiagonal form is given by:

\[ B = Q' A P \]

where B is upper bidiagonal if m >= n and lower bidiagonal if m < n, and Q and P are orthogonal/unitary matrices represented as the product of Householder matrices

\[ \begin{array}{cl} Q = H_1H_2\cdots H_n\: \text{and} \: P = G_1G_2\cdots G_{n-1}, & \: \text{if}\: m >= n, \:\text{or}\newline Q = H_1H_2\cdots H_{m-1}\: \text{and} \: P = G_1G_2\cdots G_{m}, & \: \text{if}\: m < n. \end{array} \]

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

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

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 \(u_i[i] = 1\).

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,out]	A	pointer to type. Array on the GPU of dimension lda*n. On entry, the m-by-n matrix 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. If m >= n, the elements below the diagonal are the last m - i elements of Householder vector v_i, and the elements above the superdiagonal are the last n - i - 1 elements of Householder vector u_i. If m < n, the elements below the subdiagonal are the last m - i - 1 elements of Householder vector v_i, and the elements above the diagonal are the last n - i elements of Householder vector u_i.
[in]	lda	rocblas_int. lda >= m. specifies the leading dimension of A.
[out]	D	pointer to real type. Array on the GPU of dimension min(m,n). The diagonal elements of B.
[out]	E	pointer to real type. Array on the GPU of dimension min(m,n)-1. The off-diagonal elements of B.
[out]	tauq	pointer to type. Array on the GPU of dimension min(m,n). The Householder scalars associated with matrix Q.
[out]	taup	pointer to type. Array on the GPU of dimension min(m,n). The Householder scalars associated with matrix P.

Member Function/Subroutine Documentation