rocsolver_slabrd Interface Reference

rocsolver_slabrd Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_slabrd Interface Reference
hipfort_rocsolver::rocsolver_slabrd Interface Reference

LABRD computes the bidiagonal form of the first k rows and columns of a general m-by-n matrix A, as well as the matrices X and Y needed to reduce the remaining part of A. More...

Public Member Functions

integer(kind(rocblas_status_success)) function rocsolver_slabrd_ (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy)
 
integer(kind(rocblas_status_success)) function rocsolver_slabrd_full_rank (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy)
 
integer(kind(rocblas_status_success)) function rocsolver_slabrd_rank_0 (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy)
 
integer(kind(rocblas_status_success)) function rocsolver_slabrd_rank_1 (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy)
 

Detailed Description

LABRD computes the bidiagonal form of the first k rows and columns of a general m-by-n matrix A, as well as the matrices X and Y needed to reduce the remaining part of A.

The reduced form is given by:

\[ B = Q'AP \]

where the leading k-by-k block of B is upper bidiagonal if m >= n, or lower bidiagonal if m < n. Q and P are orthogonal/unitary matrices represented as the product of Householder matrices

\[ \begin{array}{cl} Q = H_1H_2\cdots H_k, & \text{and} \newline P = G_1G_2\cdots G_k. \end{array} \]

Each Householder matrix \(H_i\) and \(G_i\) is given by

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

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 \(u_i[i]=1\).

The unreduced part of the matrix A can be updated using the block update

\[ A = A - VY' - XU' \]

where V and U are the m-by-k and n-by-k matrices formed with the vectors \(v_i\) and \(u_i\), respectively.

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]krocblas_int. min(m,n) >= k >= 0.
The number of leading rows and columns of matrix A that will be reduced.
[in,out]Apointer to type. Array on the GPU of dimension lda*n.
On entry, the m-by-n matrix to be reduced. On exit, the first k 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 of the first k columns are the possibly non-zero elements of the Householder vectors associated with Q, while the elements above the superdiagonal of the first k rows are the n - i - 1 possibly non-zero elements of the Householder vectors related to P. If m < n, the elements below the subdiagonal of the first k columns are the m - i - 1 possibly non-zero elements of the Householder vectors related to Q, while the elements above the diagonal of the first k rows are the n - i possibly non-zero elements of the vectors associated with P.
[in]ldarocblas_int. lda >= m.
specifies the leading dimension of A.
[out]Dpointer to real type. Array on the GPU of dimension k.
The diagonal elements of B.
[out]Epointer to real type. Array on the GPU of dimension k.
The off-diagonal elements of B.
[out]tauqpointer to type. Array on the GPU of dimension k.
The Householder scalars associated with matrix Q.
[out]tauppointer to type. Array on the GPU of dimension k.
The Householder scalars associated with matrix P.
[out]Xpointer to type. Array on the GPU of dimension ldx*k.
The m-by-k matrix needed to update the unreduced part of A.
[in]ldxrocblas_int. ldx >= m.
The leading dimension of X.
[out]Ypointer to type. Array on the GPU of dimension ldy*k.
The n-by-k matrix needed to update the unreduced part of A.
[in]ldyrocblas_int. ldy >= n.
The leading dimension of Y.

Member Function/Subroutine Documentation

◆ rocsolver_slabrd_()

integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slabrd::rocsolver_slabrd_ ( type(c_ptr), value  handle,
integer(c_int), value  m,
integer(c_int), value  n,
integer(c_int), value  k,
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,
type(c_ptr), value  X,
integer(c_int), value  ldx,
type(c_ptr), value  Y,
integer(c_int), value  ldy 
)

◆ rocsolver_slabrd_full_rank()

integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slabrd::rocsolver_slabrd_full_rank ( type(c_ptr)  handle,
integer(c_int)  m,
integer(c_int)  n,
integer(c_int)  k,
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,
real(c_float), dimension(:,:), target  X,
integer(c_int)  ldx,
real(c_float), dimension(:,:), target  Y,
integer(c_int)  ldy 
)

◆ rocsolver_slabrd_rank_0()

integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slabrd::rocsolver_slabrd_rank_0 ( type(c_ptr)  handle,
integer(c_int)  m,
integer(c_int)  n,
integer(c_int)  k,
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,
real(c_float), target  X,
integer(c_int)  ldx,
real(c_float), target  Y,
integer(c_int)  ldy 
)

◆ rocsolver_slabrd_rank_1()

integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slabrd::rocsolver_slabrd_rank_1 ( type(c_ptr)  handle,
integer(c_int)  m,
integer(c_int)  n,
integer(c_int)  k,
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,
real(c_float), dimension(:), target  X,
integer(c_int)  ldx,
real(c_float), dimension(:), target  Y,
integer(c_int)  ldy 
)

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