# rocsolver_sgelqf Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgelqf Interface 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.

## ◆ rocsolver_sgelqf_()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgelqf::rocsolver_sgelqf_ ( type(c_ptr), value handle, integer(c_int), value m, integer(c_int), value n, type(c_ptr), value A, integer(c_int), value lda, type(c_ptr), value ipiv )

## ◆ rocsolver_sgelqf_full_rank()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgelqf::rocsolver_sgelqf_full_rank ( type(c_ptr) handle, integer(c_int) m, integer(c_int) n, real(c_float), dimension(:,:), target A, integer(c_int) lda, real(c_float), dimension(:), target ipiv )

## ◆ rocsolver_sgelqf_rank_0()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgelqf::rocsolver_sgelqf_rank_0 ( type(c_ptr) handle, integer(c_int) m, integer(c_int) n, real(c_float), target A, integer(c_int) lda, real(c_float), target ipiv )

## ◆ rocsolver_sgelqf_rank_1()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgelqf::rocsolver_sgelqf_rank_1 ( type(c_ptr) handle, integer(c_int) m, integer(c_int) n, real(c_float), dimension(:), target A, integer(c_int) lda, real(c_float), dimension(:), target ipiv )

The documentation for this interface was generated from the following file: