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.
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: