# 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

The leading dimension of a.

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

The leading dimension of c.

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

The leading dimension of a.

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

The leading dimension of c.

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).

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

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: LAPACK Linear Equation Routines