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ormrq

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

Description

The routine multiplies a real m-by-n matrix C by Q or QT, where Q is the real orthogonal matrix defined as a product of k elementary reflectors Hi : Q = H1H2 ... Hk as returned by the RQ factorization routine gerqf.

Depending on the parameters side and trans, the routine can form one of the matrix products Q*C, QT*C, C*Q, or C*QT (overwriting the result over C).

API

Syntax

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

ormrq supports the following precisions and devices:

T

Devices supported

float

Host and CPU

double

Host and CPU

Input Parameters

queue

Device queue where calculations will be performed.

side

If side = mkl::side::left, Q or QT is applied to C from the left. If side = mkl::side::right, Q or QT is applied to C from the right.

trans

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

If trans=mkl::transpose::nontrans, the routine multiplies C by QT.

m

The number of rows in the matrix A (0≤m).

n

The number of columns in the matrix A (0≤n≤m).

k

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

a

Buffer holding the result of the gerqf function. The second dimension of a must be at least max(1,k).

lda

The leading dimension of a.

tau

Buffer holding tau returned by the gerqf function.

c

Buffer holding the matrix C. The second dimension of c must be at least max(1,n).

ldc

The leading dimension of c.

scratchpad

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

scratchpad_size

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 Q*C, QT*C, C*Q, or C*QT (as specified by side and trans).

Exceptions

Exception

Description

mkl::lapack::exception

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.

Application Notes

The complex counterpart of this routine is unmrq.

ormqr_scratchpad_size ormrq (USM Version)