# rocsolver_chetrd Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_chetrd Interface Reference
hipfort_rocsolver::rocsolver_chetrd Interface Reference

HETRD computes the tridiagonal form of a complex hermitian matrix A. More...

## Public Member Functions

integer(kind(rocblas_status_success)) function rocsolver_chetrd_ (handle, uplo, n, A, lda, D, E, tau)

integer(kind(rocblas_status_success)) function rocsolver_chetrd_full_rank (handle, uplo, n, A, lda, D, E, tau)

integer(kind(rocblas_status_success)) function rocsolver_chetrd_rank_0 (handle, uplo, n, A, lda, D, E, tau)

integer(kind(rocblas_status_success)) function rocsolver_chetrd_rank_1 (handle, uplo, n, A, lda, D, E, tau)

## Detailed Description

HETRD computes the tridiagonal form of a complex hermitian matrix A.

(This is the blocked version of the algorithm).

The tridiagonal form is given by:

$T = Q' A Q$

where T is hermitian tridiagonal and Q is an unitary 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 hermitian 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 real type. Array on the GPU of dimension n. The diagonal elements of T. [out] E pointer to real 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.

## ◆ rocsolver_chetrd_()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_chetrd::rocsolver_chetrd_ ( 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, complex(c_float_complex) tau )

## ◆ rocsolver_chetrd_full_rank()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_chetrd::rocsolver_chetrd_full_rank ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, complex(c_float_complex), dimension(:,:), target A, integer(c_int) lda, real(c_float), dimension(:), target D, real(c_float), dimension(:), target E, complex(c_float_complex) tau )

## ◆ rocsolver_chetrd_rank_0()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_chetrd::rocsolver_chetrd_rank_0 ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, complex(c_float_complex), target A, integer(c_int) lda, real(c_float), target D, real(c_float), target E, complex(c_float_complex) tau )

## ◆ rocsolver_chetrd_rank_1()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_chetrd::rocsolver_chetrd_rank_1 ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, complex(c_float_complex), dimension(:), target A, integer(c_int) lda, real(c_float), dimension(:), target D, real(c_float), dimension(:), target E, complex(c_float_complex) tau )

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