rocsolver_sgebrd Interface Reference

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]handlerocblas_handle.
[in]mrocblas_int. m >= 0.
The number of rows of the matrix A.
[in]nrocblas_int. n >= 0.
The number of columns of the matrix A.
[in,out]Apointer 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]ldarocblas_int. lda >= m.
specifies the leading dimension of A.
[out]Dpointer to real type. Array on the GPU of dimension min(m,n).
The diagonal elements of B.
[out]Epointer to real type. Array on the GPU of dimension min(m,n)-1.
The off-diagonal elements of B.
[out]tauqpointer to type. Array on the GPU of dimension min(m,n).
The Householder scalars associated with matrix Q.
[out]tauppointer to type. Array on the GPU of dimension min(m,n).
The Householder scalars associated with matrix P.

Member Function/Subroutine Documentation

◆ 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: