Contents

sytrd (USM Version)

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

Description

The routine reduces a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation: A = Q*T*QT. The orthogonal matrix Q is not formed explicitly but is represented as a product of n-1 elementary reflectors. Routines are provided for working with Q in this representation.

API

Syntax

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

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

T

Devices supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

Input Parameters

queue

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

The pointer to 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 sytrd_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 array tau, represent the orthogonal 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 orthogonal 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 the off diagonal elements of the matrix T. The dimension of e must be at least max(1, n-1).

tau

Pointer to the 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.

Return Values

Output event to wait on to ensure computation is complete.

sytrd sytrd_scratchpad_size