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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(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 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 \(\max(1, n-1)\).

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 ungtr_scratchpad_size function.

Output Parameters

a

Overwritten by the unitary matrix \(Q\).

scratchpad

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

ungtr (USM Version)

Syntax

namespace oneapi::mkl::lapack {
  sycl::event ungtr(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 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 \(\max(1, n-1)\).

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 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 \(Q\).

scratchpad

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

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: LAPACK Singular Value and Eigenvalue Problem Routines

ungbr_scratchpad_size ungtr_scratchpad_size