rocsolver_slarfg Interface Reference#
The LARFG functions generate a Householder reflector H of order n.
More...
Public Member Functions | |
| integer(kind(rocblas_status_success)) function | rocsolver_slarfg_ (handle, n, alpha, x, incx, tau) |
| integer(kind(rocblas_status_success)) function | rocsolver_slarfg_rank_0 (handle, n, alpha, x, incx, tau) |
| integer(kind(rocblas_status_success)) function | rocsolver_slarfg_rank_1 (handle, n, alpha, x, incx, tau) |
Detailed Description
The LARFG functions generate a Householder reflector H of order n.
The reflector H is such that:
\[ H^H\left[\begin{array}{c} \text{alpha}\\% x \end{array}\right]=\left[\begin{array}{c} \text{beta}\\% 0 \end{array}\right] \]
where x is an n-1 vector and alpha and beta are scalars. Matrix H can be generated as
\[ H = I - \text{tau}\left[\begin{array}{c} 1\\% v \end{array}\right]\left[\begin{array}{cc} 1 & v^H \end{array}\right] \]
where v is an n -1 vector, and tau is a scalar known as the Householder scalar. The vector
\[ \bar{v}=\left[\begin{array}{c} 1\\% v \end{array}\right] \]
is the Householder vector associated with the reflection.
- Note
- The matrix H is orthogonal/unitary (that is, \(H^H H=H H^H=I\)). It is symmetric when real (that is, \(H^T=H\)), but not Hermitian when complex (that is, \(H^H≠ H\) in general).
- Parameters
-
[in] handle - rocblas_handle. [in] n - rocblas_int. n >= 0. The order (size) of reflector H. [in,out] alpha - pointer to type. A scalar on the GPU. On entry, the scalar alpha. On exit, it is overwritten with beta. [in,out] x - pointer to type. Array on the GPU of size at least n-1 (size depends on the value of incx). On entry, the vector x, On exit, it is overwritten with vector v. [in] incx - rocblas_int. incx > 0. The distance between two consecutive elements of x. [out] tau - pointer to type. A scalar on the GPU. The Householder scalar tau.
Member Function/Subroutine Documentation
◆ rocsolver_slarfg_()
| integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slarfg::rocsolver_slarfg_ | ( | type(c_ptr), value | handle, |
| integer(c_int), value | n, | ||
| real(c_float) | alpha, | ||
| type(c_ptr), value | x, | ||
| integer(c_int), value | incx, | ||
| real(c_float) | tau | ||
| ) |
◆ rocsolver_slarfg_rank_0()
| integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slarfg::rocsolver_slarfg_rank_0 | ( | type(c_ptr) | handle, |
| integer(c_int) | n, | ||
| real(c_float) | alpha, | ||
| real(c_float), target | x, | ||
| integer(c_int) | incx, | ||
| real(c_float) | tau | ||
| ) |
◆ rocsolver_slarfg_rank_1()
| integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slarfg::rocsolver_slarfg_rank_1 | ( | type(c_ptr) | handle, |
| integer(c_int) | n, | ||
| real(c_float) | alpha, | ||
| real(c_float), dimension(:), target | x, | ||
| integer(c_int) | incx, | ||
| real(c_float) | tau | ||
| ) |
The documentation for this interface was generated from the following file: