hetrd (USM Version)

oneMKL - Data Parallel C++ Developer Reference

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ID 772045

Date 6/24/2024

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hetrd (USM Version)

Reduces a complex Hermitian matrix to tridiagonal form. This routine belongs to the oneapi::mkl::lapack namespace.

Description
API

Description

The routine reduces a complex Hermitian matrix A to Hermitian tridiagonal form T by a unitary similarity transformation: A = Q*T*QH. The unitary matrix Q is not formed explicitly but is represented as a product of n-1 elementary reflectors. Routines are provided to work with Q in this representation.

API

Syntax

namespace oneapi::mkl::lapack {
  sycl::event hetrd(sycl::queue &queue,
  mkl::uplo uplo,
  int64_t n,
  T *a,
  int64_t lda,
  T *d,
  T *e,
  T *tau,
  T *scratchpad,
  int64_t scratchpad_size,
  const std::vector<sycl::event> &events = {})
}

hetrd (USM version) supports the following precisions and devices:

T	Devices supported
`std::complex<float>`	CPU and GPU*
`std::complex<double>`	CPU and GPU*

*Interface support only; all computations are performed on the CPU.

Input Parameters

queue

The device queue where calculations will be performed.

uplo

Must be uplo::upper or uplo::lower.

If uplo = uplo::upper, a stores the upper triangular part of A.

If uplo = uplo::lower, a stores the lower triangular part of A.

n

The order of the matrices A(0 ≤ n).

a

Pointer to the matrix A, size (lda,*). Contains the upper or lower triangle as specified by uplo.

lda

The leading dimension of a; at least max(1, n)

scratchpad

Pointer to scratchpad memory to be used by the routine for storing intermediate results.

scratchpad_size

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by the hetrd_scratchpad_size function.

events

List of events to wait for before starting computation. Defaults to empty list.

Output Parameters

a

On exit,

if uplo = uplo::upper, the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the buffer tau, represent the unitary matrix Q as a product of elementary reflectors;

if uplo = uplo::lower, the diagonal and first subdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array tau, represent the unitary matrix Q as a product of elementary reflectors.

d

Pointer to the diagonal elements of the matrix T. The dimension of d must be at least max(1, n).

e

Pointer to off diagonal elements of the matrix T. The dimension of e must be at least max(1, n-1).

tau

Pointer to memory array of size at least max(1, n). Stores (n-1) scalars that define elementary reflectors in decomposition of the unitary matrix Q in a product of n-1 elementary reflectors. tau(n) is used as workspace.

Exceptions

Exception	Description
`mkl::lapack::exception`	This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object: If `info = -i`, the `i`-th parameter had an illegal value. If `info` is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.

Exception

Description

mkl::lapack::exception

This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object:

If info = -i, the i-th parameter had an illegal value.

If info is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.

Return Values

Output event to wait on to ensure computation is complete.

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oneMKL - Data Parallel C++ Developer Reference

hetrd (USM Version)

Description

API