sytrd

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

Syntax

void sytrd(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, cl::sycl::buffer<T> &a, std::int64_t lda, cl::sycl::buffer<T> &d, cl::sycl::buffer<T> &e, cl::sycl::buffer<T> &tau, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)

sytrd supports the following precisions and devices:

T

Devices supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

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 .

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

Buffer holding 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

Buffer holding 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.

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 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 buffer tau, represent the orthogonal matrix Q as a product of elementary reflectors.

d

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

e

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

tau

Buffer holding 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

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.