# ungtr#

Generates the complex unitary matrix $$Q$$ determined by hetrd.

Description

ungtr supports the following precisions.

T

std::complex<float>

std::complex<double>

The routine explicitly generates the $$n \times n$$ unitary matrix $$Q$$ formed by hetrd when reducing a complex Hermitian matrix $$A$$ to tridiagonal form: $$A = QTQ^H$$. Use this routine after a call to hetrd.

## ungtr (Buffer Version)#

Syntax

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

n

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

a

The buffer a as returned by hetrd. 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 hetrd. 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 ungtr_scratchpad_size function.

Output Parameters

a

Overwritten by the unitary matrix $$Q$$.

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

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

oneapi::mkl::lapack::computation_error

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

If $$\text{info}=-i$$, the $$i$$-th parameter had an illegal value.

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

## ungtr (USM Version)#

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event ungtr(cl::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<cl::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 hetrd.

n

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

a

The pointer to a as returned by hetrd. 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 hetrd. 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 ungtr_scratchpad_size function.

events

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

Output Parameters

a

Overwritten by the unitary matrix $$Q$$.

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

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

oneapi::mkl::lapack::computation_error

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

If $$\text{info}=-i$$, the $$i$$-th parameter had an illegal value.

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

Return Values

Output event to wait on to ensure computation is complete.