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.
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: