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>

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(cl::sycl::queue &queue, oneapi::mkl::generate gen, std::int64_t m, std::int64_t n, std::int64_t k, 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.

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)

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event ungbr(cl::sycl::queue &queue, oneapi::mkl::generate gen, std::int64_t m, std::int64_t n, std::int64_t k, T *a, std::int64_t lda, 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.

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 \((0 \ge m)\).

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 pointer to 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.

events

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

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

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