orgbr¶

Generates the real orthogonal matrix Q or P^T determined by gebrd.

orgbr supports the following precisions.

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-by-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-by-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

void onemkl::lapack::orgbr(cl::sycl::queue &queue, onemkl::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≤m).

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

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

n

The number of rows in the matrix Q or P^T to be returned (0≤n). See m for constraints.

k

If gen= generate::q, the number of columns in the original m-by-k matrix reduced by gebrd.

If gen= generate::p, the number of rows in the original k-by-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-by-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.

Throws

onemkl::lapack::exception

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

If info=-i, the i-th parameter had an illegal value.

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

orgbr (USM Version)¶