# 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 $$m \times m$$ 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(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, $$m \le n \le \min(m, k)$$.

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.

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.

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

## orgbr (USM Version)¶

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event orgbr(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 $$(0 \le m)$$.

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

Pointer to array a as returned by gebrd.

lda

The leading dimension of a.

tau

Pointer to array of 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.

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.

events

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

Output Parameters

a

Overwritten by n leading columns of the $$m \times m$$ orthogonal matrix $$Q$$ or $$P^{T}$$ (or the leading rows or columns thereof) as specified by gen, m, and n.