rocsolver_sgelqf Interface Reference

rocsolver_sgelqf Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgelqf Interface Reference

GELQF computes a LQ factorization of a general m-by-n matrix A. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgelqf_ (handle, m, n, A, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_sgelqf_full_rank (handle, m, n, A, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_sgelqf_rank_0 (handle, m, n, A, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_sgelqf_rank_1 (handle, m, n, A, lda, ipiv)

Detailed Description

GELQF computes a LQ factorization of a general m-by-n matrix A.

(This is the blocked version of the algorithm).

The factorization has the form

\[ A = \left[\begin{array}{cc} L & 0 \end{array}\right] Q \]

where L is lower triangular (lower trapezoidal if m > n), and Q is a n-by-n orthogonal/unitary matrix represented as the product of Householder matrices

\[ Q = H_k'H_{k-1}' \cdots H_1', \quad \text{with} \: k = \text{min}(m,n). \]

Each Householder matrix \(H_i\) is given by

\[ H_i = I - \text{ipiv}[i] \cdot v_i' v_i \]

where the first i-1 elements of the Householder vector \(v_i\) are zero, and \(v_i[i] = 1\).

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 and below the diagonal contain the factor L; the elements above the diagonal are the last n - i elements of Householder vector v_i.
[in]	lda	rocblas_int. lda >= m. Specifies the leading dimension of A.
[out]	ipiv	pointer to type. Array on the GPU of dimension min(m,n). The Householder scalars.

Member Function/Subroutine Documentation