rocsolver_sgeqrf Interface Reference

rocsolver_sgeqrf Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgeqrf Interface Reference

The GEQRF functions compute a QR factorization of a general m -by-n matrix A. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgeqrf_ (handle, m, n, a, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_sgeqrf_rank_0 (handle, m, n, a, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_sgeqrf_rank_1 (handle, m, n, a, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_sgeqrf_full_rank (handle, m, n, a, lda, ipiv)

Detailed Description

The GEQRF functions compute a QR factorization of a general m -by-n matrix A.

(This is the blocked version of the algorithm.)

The factorization has the form

\[ A = Q\left[\begin{array}{c} R\\% 0 \end{array}\right] \]

where R is upper triangular (upper trapezoidal if m < n), and Q is an m -by-m orthogonal/unitary matrix represented as the product of Householder matrices

\[ Q = H(1)H(2)\cdots H(k), \quad \text{with} \: k = \text{min}(m,n) \]

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

\[ H(i) = I - \text{ipiv}[i] \cdot v_i^{} v_i^H \]

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 above the diagonal contain the factor R, and the elements below the diagonal are the last m - 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