orgbr¶

Generates the real orthogonal matrix \(Q\) or \(P^{T}\) determined by gebrd.

orgbr supports the following precisions.

T

float

double

T
`float`
`double`

Description

The routine generates the whole or part of the orthogonal matrices \(Q\) and \(P^{T}\) 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 \(Q\):

orgbr(queue, generate::q, m, m, n, a, ...)

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

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

orgbr(queue, generate::q, m, n, n, a, ...)

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

orgbr(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 \(m < n\):

orgbr(queue, generate::p, m, n, m, a, ...)

orgbr (Buffer Version)¶

Syntax

namespace oneapi::mkl::lapack {
  void orgbr(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, \(m \le n \le \min(m, k)\).

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

n

The number of rows 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 reduced by gebrd.

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

a

The buffer a as returned by gebrd.

lda

The leading dimension of a.

tau

Buffer, size \(\min(m,k)\) if gen = generate::q, size \(\min(n,k)\) if gen = generate::p. Scalar factor of the elementary reflectors, as returned by gebrd in the array tauq or taup.

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 orgbr_scratchpad_size function.

Output Parameters

a: Overwritten by n leading columns of the \(m \times m\) orthogonal 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.

orgbr (USM Version)¶