rocsolver_slabrd Interface Reference

rocsolver_slabrd Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_slabrd Interface Reference

The LABRD functions 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_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)

integer(kind(rocblas_status_success)) function	rocsolver_slabrd_full_rank (handle, m, n, k, a, lda, d, e, tauq, taup, x, ldx, y, ldy)

Detailed Description

The LABRD functions 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:

\[ B = Q^H A P \]

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:

\[ \begin{array}{cl} Q = H(1)H(2)\cdots H(k), & \text{and} \\% P = G(1)G(2)\cdots G(k). \end{array} \]

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

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

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

\[ A = A - VY^H - XU^H \]

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