rocsolver_sgebd2 Interface Reference

rocsolver_sgebd2 Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgebd2 Interface Reference

The GEBD2 functions compute the bidiagonal form of a general m -by-n matrix A. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgebd2_ (handle, m, n, a, lda, d, e, tauq, taup)

integer(kind(rocblas_status_success)) function	rocsolver_sgebd2_rank_0 (handle, m, n, a, lda, d, e, tauq, taup)

integer(kind(rocblas_status_success)) function	rocsolver_sgebd2_rank_1 (handle, m, n, a, lda, d, e, tauq, taup)

integer(kind(rocblas_status_success)) function	rocsolver_sgebd2_full_rank (handle, m, n, a, lda, d, e, tauq, taup)

Detailed Description

The GEBD2 functions compute the bidiagonal form of a general m -by-n matrix A.

(This is the unblocked version of the algorithm.)

The bidiagonal form is given by:

\[ B = Q^H A P \]

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

\[ \begin{array}{cl} Q = H(1)H(2)\cdots H(n)\: \text{and} \: P = G(1)G(2)\cdots G(n-1), & \: \text{if}\: m >= n, \:\text{or}\\% Q = H(1)H(2)\cdots H(m-1)\: \text{and} \: P = G(1)G(2)\cdots G(m), & \: \text{if}\: m < n. \end{array} \]

Each Householder matrix \(H(i)\) and \(G(i)\) is given by

\[ \begin{array}{cl} H(i) = I - \text{tauq}[i] \cdot v_i^{} v_i^H, & \: \text{and}\\% G(i) = I - \text{taup}[i] \cdot u_i^H u_i^{}. \end{array} \]

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