# orgtr¶

Generates the real orthogonal matrix $$Q$$ determined by sytrd.

Description

orgtr supports the following precisions.

T

float

double

The routine explicitly generates the $$n \times n$$ orthogonal matrix $$Q$$ formed by sytrd when reducing a real symmetric matrix $$A$$ to tridiagonal form: $$A = QTQ^T$$. Use this routine after a call to sytrd.

## orgtr (Buffer Version)¶

Syntax

namespace oneapi::mkl::lapack {
void orgtr(sycl::queue &queue, oneapi::mkl::uplo upper_lower, std::int64_t n, sycl::buffer<T,1> &a, std::int64_t lda, sycl::buffer<T,1> &tau, 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. Uses the same upper_lower as supplied to sytrd.

n

The order of the matrix $$Q$$ $$(0 \le n)$$.

a

The buffer a as returned by sytrd. The second dimension of a must be at least $$\max(1,n)$$.

lda

The leading dimension of a $$(n \le \text{lda})$$.

tau

The buffer tau as returned by sytrd. The dimension of tau must be at least $$\max(1, n-1)$$.

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

Output Parameters

a

Overwritten by the orthogonal matrix $$Q$$.

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

## orgtr (USM Version)¶

Syntax

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


Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Must be uplo::upper or uplo::lower. Uses the same upper_lower as supplied to sytrd.

n

The order of the matrix $$Q$$ $$(0 \le n)$$.

a

The pointer to a as returned by sytrd. The second dimension of a must be at least $$\max(1,n)$$.

lda

The leading dimension of a $$(n \le \text{lda})$$.

tau

The pointer to tau as returned by sytrd. The dimension of tau must be at least $$\max(1, n-1)$$.

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

events

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

Output Parameters

a

Overwritten by the orthogonal matrix $$Q$$.