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] 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] k rocblas_int. min(m,n) >= k >= 0. The number of leading rows and columns of matrix A that will be reduced. [in,out] A pointer 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] lda rocblas_int. lda >= m. specifies the leading dimension of A. [out] D pointer to real type. Array on the GPU of dimension k. The diagonal elements of B. [out] E pointer to real type. Array on the GPU of dimension k. The off-diagonal elements of B. [out] tauq pointer to type. Array on the GPU of dimension k. The Householder scalars associated with matrix Q. [out] taup pointer to type. Array on the GPU of dimension k. The Householder scalars associated with matrix P. [out] X pointer to type. Array on the GPU of dimension ldx*k. The m-by-k matrix needed to update the unreduced part of A. [in] ldx rocblas_int. ldx >= m. The leading dimension of X. [out] Y pointer to type. Array on the GPU of dimension ldy*k. The n-by-k matrix needed to update the unreduced part of A. [in] ldy rocblas_int. ldy >= n. The leading dimension of Y.

◆ 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: