# 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.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

oneapi::mkl::lapack::computation_error

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

If $$\text{info}=-i$$, the $$i$$-th parameter had an illegal value.

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

## 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 std::vector<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.

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

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

oneapi::mkl::lapack::computation_error

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

If $$\text{info}=-i$$, the $$i$$-th parameter had an illegal value.

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

Return Values

Output event to wait on to ensure computation is complete.