sytrd

Reduces a real symmetric matrix to tridiagonal form.

sytrd supports the following precisions.

T
float
double

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 .

sytrd (BUFFER Version)

Syntax

void onemkl::lapack::sytrd(cl::sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, cl::sycl::buffer<T, 1> &a, std::int64_t lda, cl::sycl::buffer<T, 1> &d, cl::sycl::buffer<T, 1> &e, cl::sycl::buffer<T, 1> &tau, cl::sycl::buffer<T, 1> &scratchpad, std::int64_t scratchpad_size)

Input Parameters

queue

The queue where the routine should be executed.

upper_lower

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

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

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

n

The order of the matrices A(0≤n).

a

The buffer a, size (lda,*). Contains the upper or lower triangle of the symmetric matrix A, as specified by upper_lower.

The second dimension of a must be at least max(1,n).

lda

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

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 sytrd_scratchpad_size function.

Output Parameters

a

On exit,

if upper_lower = 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 upper_lower = 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 containing the diagonal elements of the matrix T. The dimension of d must be at least max(1, n).

e

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

tau

Buffer, 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.

scratchpad

Buffer holding scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of exception object:

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

If info equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

sytrd (USM Version)

Syntax

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

Input Parameters

queue

The queue where the routine should be executed.

upper_lower

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

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

If upper_lower = 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 of the symmetric matrix A, as specified by upper_lower. The second dimension of a must be at least max(1,n).

lda

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

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 sytrd_scratchpad_size function.

events

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

Output Parameters

a

On exit,

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

e

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

tau

Pointer to 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.

scratchpad

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

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of exception object:

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

If info equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: LAPACK Singular Value and Eigenvalue Problem Routines