rocsolver_ssytd2 Interface Reference

rocsolver_ssytd2 Interface Reference#

HIPFORT API 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]	handle	rocblas_handle.
[in]	uplo	rocblas_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]	n	rocblas_int. n >= 0. The number of rows and columns of the matrix A.
[in,out]	A	pointer 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]	lda	rocblas_int. lda >= n. The leading dimension of A.
[out]	D	pointer to type. Array on the GPU of dimension n. The diagonal elements of T.
[out]	E	pointer to type. Array on the GPU of dimension n-1. The off-diagonal elements of T.
[out]	tau	pointer to type. Array on the GPU of dimension n-1. The Householder scalars.

Member Function/Subroutine Documentation