# ungqr¶

Generates the complex unitary matrix $$Q$$ of the QR factorization formed by geqrf.

Description

ungqr supports the following precisions.

T

std::complex<float>

std::complex<double>

The routine generates the whole or part of $$m \times m$$ unitary matrix $$Q$$ of the QR factorization formed by the routines geqrf.

Usually $$Q$$ is determined from the QR factorization of an $$m \times p$$ matrix $$A$$ with $$m \ge p$$. To compute the whole matrix $$Q$$, use:

oneapi::mkl::lapack::ungqr(queue, m, m, p, a, lda, tau, scratchpad, scratchpad_size)


To compute the leading $$p$$ columns of $$Q$$ (which form an orthonormal basis in the space spanned by the columns of $$A$$):

oneapi::mkl::lapack::ungqr(queue, m, p, p, a, lda, tau, scratchpad, scratchpad_size)


To compute the matrix $$Q^{k}$$ of the QR factorization of the leading $$k$$ columns of the matrix $$A$$:

oneapi::mkl::lapack::ungqr(queue, m, m, k, a, lda, tau, scratchpad, scratchpad_size)


To compute the leading $$k$$ columns of $$Q^{k}$$ (which form an orthonormal basis in the space spanned by the leading $$k$$ columns of the matrix $$A$$):

oneapi::mkl::lapack::ungqr(queue, m, k, k, a, lda, tau, scratchpad, scratchpad_size)


## ungqr (Buffer Version)¶

Syntax

namespace oneapi::mkl::lapack {
void ungqr(sycl::queue &queue, 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.

m

The number of rows in the matrix $$A$$ ($$0 \le m$$).

n

The number of columns in the matrix $$A$$ ($$0 \le n$$).

k

The number of elementary reflectors whose product defines the matrix $$Q$$ ($$0 \le k \le n$$).

a

The buffer a as returned by geqrf.

lda

The leading dimension of a ($$\text{lda} \le m$$).

tau

The buffer tau as returned by geqrf.

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

Output Parameters

a

Overwritten by $$n$$ leading columns of the $$m \times m$$ orthogonal matrix $$Q$$.

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

## ungqr (USM Version)¶

Syntax

namespace oneapi::mkl::lapack {
sycl::event ungqr(sycl::queue &queue, 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<sycl::event> &events = {})
}


Input Parameters

queue

The queue where the routine should be executed.

m

The number of rows in the matrix $$A$$ ($$0 \le m$$).

n

The number of columns in the matrix $$A$$ ($$0 \le n$$).

k

The number of elementary reflectors whose product defines the matrix $$Q$$ ($$0 \le k \le n$$).

a

The pointer to a as returned by geqrf.

lda

The leading dimension of a ($$\text{lda} \le m$$).

tau

The pointer to tau as returned by geqrf.

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