ungbr#

Generates the complex unitary matrix \(Q\) or \(P^{t}\) determined by gebrd.

Description

ungbr supports the following precisions.

T

std::complex<float>

std::complex<double>

T
`std::complex<float>`
`std::complex<double>`

The routine generates the whole or part of the unitary matrices \(Q\) and \(P^{H}\) formed by the routines gebrd. All valid combinations of arguments are described in Input Parameters; in most cases you need the following:

To compute the whole \(m \times m\) matrix \(Q\), use:

oneapi::mkl::lapack::ungbr(queue, generate::q, m, m, n, a, ...)

(note that the buffer a must have at least \(m\) columns).

To form the \(n\) leading columns of \(Q\) if \(m > n\), use:

oneapi::mkl::lapack::ungbr(queue, generate::q, m, n, n, a, ...)

To compute the whole \(n \times n\) matrix \(P^{T}\), use:

oneapi::mkl::lapack::ungbr(queue, generate::p, n, n, m, a, ...)

(note that the array a must have at least \(n\) rows).

To form the \(m\) leading rows of \(P^{T}\) if \(m < n\), use:

oneapi::mkl::lapack::ungbr(queue, generate::p, m, n, m, a, ...)

ungbr (Buffer Version)#

Syntax

namespace oneapi::mkl::lapack {
  void ungbr(sycl::queue &queue, oneapi::mkl::generate gen, std::int64_t m, std::int64_t n, std::int64_t k, 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.

gen

Must be generate::q or generate::p.

If gen = generate::q, the routine generates the matrix \(Q\).

If gen = generate::p, the routine generates the matrix \(P^{T}\).

m

The number of rows in the matrix \(Q\) or \(P^{T}\) to be returned \((0 \le m)\).

If gen = generate::q, \(m \ge n \ge \min(m, k)\).

If gen = generate::p, \(n \ge m \ge \min(n, k)\).

n

The number of columns in the matrix \(Q\) or \(P^{T}\) to be returned \((0 \le n)\). See m for constraints.

k

If gen = generate::q, the number of columns in the original \(m \times k\) matrix returned by gebrd.

If gen = generate::p, the number of rows in the original \(k \times n\) matrix returned by gebrd.

a

The buffer a as returned by gebrd.

lda

The leading dimension of a.

tau

For gen = generate::q, the array tauq as returned by gebrd. For gen = generate::p, the array taup as returned by gebrd.

The dimension of tau must be at least \(\max(1, \min(m, k))\) for gen = generate::q, or \(\max(1, \min(m, k))\) for gen = generate::p.

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 ungbr_scratchpad_size function.

Output Parameters

a: Overwritten by \(n\) leading columns of the \(m \times m\) unitary matrix \(Q\) or \(P^{T}\), (or the leading rows or columns thereof) as specified by gen, m, and n.
scratchpad: Buffer holding scratchpad memory to be used by routine for storing intermediate results.

ungbr (USM Version)#