# ormrq¶

Multiplies a real matrix by the orthogonal matrix $$Q$$ of the RQ factorization formed by gerqf.

Description

ormrq supports the following precisions.

T

float

double

The routine multiplies a rectangular real $$m \times n$$ matrix $$C$$ by $$Q$$ or $$Q^T$$, where $$Q$$ is the complex unitary matrix defined as a product of $$k$$ elementary reflectors $$H(i)$$ of order $$n$$: $$Q = H(1)^TH(2)^T ... H(k)^T$$ as returned by the RQ factorization routine gerqf.

Depending on the parameters side and trans, the routine can form one of the matrix products $$QC$$, $$Q^TC$$, $$CQ$$, or $$CQ^T$$ (overwriting the result over $$C$$).

## ormrq (Buffer Version)¶

Syntax

namespace oneapi::mkl::lapack {
void ormrq(sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::transpose trans, 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> &c, std::int64_t ldc, sycl::buffer<T,1> &scratchpad, std::int64_t scratchpad_size)
}

Input Parameters

queue

The queue where the routine should be executed.

side

If side = oneapi::mkl::side::left, $$Q$$ or $$Q^{T}$$ is applied to $$C$$ from the left.

If side = oneapi::mkl::side::right, $$Q$$ or $$Q^{T}$$ is applied to $$C$$ from the right.

trans

If trans = oneapi::mkl::transpose::nontrans, the routine multiplies $$C$$ by $$Q$$.

If trans = oneapi::mkl::transpose::trans, the routine multiplies $$C$$ by $$Q^{T}$$.

m

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

n

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

k

The number of elementary reflectors whose product defines the matrix $$Q$$

If side = oneapi::mkl::side::left, $$0 \le k \le m$$

If side = oneapi::mkl::side::right, $$0 \le k \le n$$

a

The buffer a as returned by gerqf. The second dimension of a must be at least $$\max(1,k)$$.

lda

tau

The buffer tau as returned by gerqf.

c

The buffer c contains the matrix $$C$$. The second dimension of c must be at least $$\max(1,n)$$.

ldc

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 ormrq_scratchpad_size function.

Output Parameters

c

Overwritten by the product $$QC$$, $$Q^{T}C$$, $$CQ$$, or $$CQ^{T}$$ (as specified by side and trans).

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

## ormrq (USM Version)¶

Syntax

namespace oneapi::mkl::lapack {
sycl::event ormrq(sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::transpose trans, std::int64_t m, std::int64_t n, std::int64_t k, T *a, std::int64_t lda, T *tau, T *c, std::int64_t ldc, T *scratchpad, std::int64_t scratchpad_size, const std::vector<sycl::event> &events = {})
}

Input Parameters

queue

The queue where the routine should be executed.

side

If side = oneapi::mkl::side::left, $$Q$$ or $$Q^{T}$$ is applied to $$C$$ from the left.

If side = oneapi::mkl::side::right, $$Q$$ or $$Q^{T}$$ is applied to $$C$$ from the right.

trans

If trans = oneapi::mkl::transpose::nontrans, the routine multiplies $$C$$ by $$Q$$.

If trans = oneapi::mkl::transpose::trans, the routine multiplies $$C$$ by $$Q^{T}$$.

m

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

n

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

k

The number of elementary reflectors whose product defines the matrix $$Q$$

If side = oneapi::mkl::side::left, $$0 \le k \le m$$

If side = oneapi::mkl::side::right, $$0 \le k \le n$$

a

The pointer to a as returned by gerqf. The second dimension of a must be at least $$\max(1,k)$$.

lda

tau

The pointer to tau as returned by gerqf.

c

The pointer c points to the matrix $$C$$. The second dimension of c must be at least $$\max(1,n)$$.

ldc

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 ormrq_scratchpad_size function.

events

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

Output Parameters

c

Overwritten by the product $$QC$$, $$Q^{T}C$$, $$CQ$$, or $$CQ^{T}$$ (as specified by side and trans).