# rocsolver_sgebrd Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgebrd Interface Reference
hipfort_rocsolver::rocsolver_sgebrd Interface Reference

GEBRD computes the bidiagonal form of a general m-by-n matrix A. More...

## Public Member Functions

integer(kind(rocblas_status_success)) function rocsolver_sgebrd_ (handle, m, n, A, lda, D, E, tauq, taup)

integer(kind(rocblas_status_success)) function rocsolver_sgebrd_full_rank (handle, m, n, A, lda, D, E, tauq, taup)

integer(kind(rocblas_status_success)) function rocsolver_sgebrd_rank_0 (handle, m, n, A, lda, D, E, tauq, taup)

integer(kind(rocblas_status_success)) function rocsolver_sgebrd_rank_1 (handle, m, n, A, lda, D, E, tauq, taup)

## Detailed Description

GEBRD computes the bidiagonal form of a general m-by-n matrix A.

(This is the blocked version of the algorithm).

The bidiagonal form is given by:

$B = Q' A P$

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

$\begin{array}{cl} Q = H_1H_2\cdots H_n\: \text{and} \: P = G_1G_2\cdots G_{n-1}, & \: \text{if}\: m >= n, \:\text{or}\newline Q = H_1H_2\cdots H_{m-1}\: \text{and} \: P = G_1G_2\cdots G_{m}, & \: \text{if}\: m < n. \end{array}$

Each Householder matrix $$H_i$$ and $$G_i$$ is given by

$\begin{array}{cl} H_i = I - \text{tauq}[i] \cdot v_i v_i', & \: \text{and}\newline G_i = I - \text{taup}[i] \cdot u_i' u_i. \end{array}$

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.

## ◆ rocsolver_sgebrd_()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgebrd::rocsolver_sgebrd_ ( 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 D, type(c_ptr), value E, type(c_ptr), value tauq, type(c_ptr), value taup )

## ◆ rocsolver_sgebrd_full_rank()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgebrd::rocsolver_sgebrd_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 D, real(c_float), dimension(:), target E, real(c_float), dimension(:), target tauq, real(c_float), dimension(:), target taup )

## ◆ rocsolver_sgebrd_rank_0()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgebrd::rocsolver_sgebrd_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 D, real(c_float), target E, real(c_float), target tauq, real(c_float), target taup )

## ◆ rocsolver_sgebrd_rank_1()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgebrd::rocsolver_sgebrd_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 D, real(c_float), dimension(:), target E, real(c_float), dimension(:), target tauq, real(c_float), dimension(:), target taup )

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