Generates the real orthogonal matrix Q or PT determined by gebrd. This routine belongs to the oneapi::mkl::lapacknamespace.


void orgbr(cl::sycl::queue &queue, mkl::generate gen, std::int64_t m, std::int64_t n, std::int64_t k, cl::sycl::buffer<T> &a, std::int64_t lda, cl::sycl::buffer<T> &tau, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)

orgbr supports the following precisions and devices:


Devices supported


Host and CPU


Host and CPU


The routine generates the whole or part of the orthogonal matrices Q and PT formed by the routines gebrd. Use this routine after a call to sgebrd/dgebrd. 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 PT:

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 PT if m < n:

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

Input Parameters


Device queue where calculations will be performed.


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 PT.


The number of rows in the matrix Q or PT to be returned (0≤m).

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

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


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


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.


Buffer holding memory returned by gebrd.


The leading dimension of a.


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


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


Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by the orgbr_scratchpad_size function.

Output Parameters


Overwritten by n leading columns of the m-by-m orthogonal matrix Q or PT (or the leading rows or columns thereof) as specified by gen, m, and n.



This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object: If info = -i, the i-th parameter had an illegal value. If info is equal to the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.