rocsolver_ssytd2 Interface Reference

rocsolver_ssytd2 Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytd2 Interface Reference
hipfort_rocsolver::rocsolver_ssytd2 Interface Reference

SYTD2 computes the tridiagonal form of a real symmetric matrix A. More...

Public Member Functions

integer(kind(rocblas_status_success)) function rocsolver_ssytd2_ (handle, uplo, n, A, lda, D, E, tau)
 
integer(kind(rocblas_status_success)) function rocsolver_ssytd2_full_rank (handle, uplo, n, A, lda, D, E, tau)
 
integer(kind(rocblas_status_success)) function rocsolver_ssytd2_rank_0 (handle, uplo, n, A, lda, D, E, tau)
 
integer(kind(rocblas_status_success)) function rocsolver_ssytd2_rank_1 (handle, uplo, n, A, lda, D, E, tau)
 

Detailed Description

SYTD2 computes the tridiagonal form of a real symmetric matrix A.

(This is the unblocked version of the algorithm).

The tridiagonal form is given by:

\[ T = Q' A Q \]

where T is symmetric tridiagonal and Q is an orthogonal matrix represented as the product of Householder matrices

\[ \begin{array}{cl} Q = H_1H_2\cdots H_{n-1} & \: \text{if uplo indicates lower, or}\newline Q = H_{n-1}H_{n-2}\cdots H_1 & \: \text{if uplo indicates upper.} \end{array} \]

Each Householder matrix \(H_i\) is given by

\[ H_i = I - \text{tau}[i] \cdot v_i v_i' \]

where tau[i] is the corresponding Householder scalar. When uplo indicates lower, the first i elements of the Householder vector \(v_i\) are zero, and \(v_i[i+1] = 1\). If uplo indicates upper, the last n-i elements of the Householder vector \(v_i\) are zero, and \(v_i[i] = 1\).

Parameters
[in]handlerocblas_handle.
[in]uplorocblas_fill.
Specifies whether the upper or lower part of the symmetric matrix A is stored. If uplo indicates lower (or upper), then the upper (or lower) part of A is not used.
[in]nrocblas_int. n >= 0.
The number of rows and columns of the matrix A.
[in,out]Apointer to type. Array on the GPU of dimension lda*n.
On entry, the matrix to be factored. On exit, if upper, then the elements on the diagonal and superdiagonal contain the tridiagonal form T; the elements above the superdiagonal contain the first i-1 elements of the Householder vectors v_i stored as columns. If lower, then the elements on the diagonal and subdiagonal contain the tridiagonal form T; the elements below the subdiagonal contain the last n-i-1 elements of the Householder vectors v_i stored as columns.
[in]ldarocblas_int. lda >= n.
The leading dimension of A.
[out]Dpointer to type. Array on the GPU of dimension n.
The diagonal elements of T.
[out]Epointer to type. Array on the GPU of dimension n-1.
The off-diagonal elements of T.
[out]taupointer to type. Array on the GPU of dimension n-1.
The Householder scalars.

Member Function/Subroutine Documentation

◆ rocsolver_ssytd2_()

integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytd2::rocsolver_ssytd2_ ( type(c_ptr), value  handle,
integer(kind(rocblas_fill_upper)), value  uplo,
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,
real(c_float)  tau 
)

◆ rocsolver_ssytd2_full_rank()

integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytd2::rocsolver_ssytd2_full_rank ( type(c_ptr)  handle,
integer(kind(rocblas_fill_upper))  uplo,
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)  tau 
)

◆ rocsolver_ssytd2_rank_0()

integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytd2::rocsolver_ssytd2_rank_0 ( type(c_ptr)  handle,
integer(kind(rocblas_fill_upper))  uplo,
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)  tau 
)

◆ rocsolver_ssytd2_rank_1()

integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytd2::rocsolver_ssytd2_rank_1 ( type(c_ptr)  handle,
integer(kind(rocblas_fill_upper))  uplo,
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)  tau 
)

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