ormrq

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::math::lapack {
  void ormrq(cl::sycl::queue &queue, oneapi::math::side side, oneapi::math::transpose trans, std::int64_t m, std::int64_t n, std::int64_t k, cl::sycl::buffer<T,1> &a, std::int64_t lda, cl::sycl::buffer<T,1> &tau, cl::sycl::buffer<T,1> &c, std::int64_t ldc, cl::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::math::side::left, \(Q\) or \(Q^{T}\) is applied to \(C\) from the left.

If side = oneapi::math::side::right, \(Q\) or \(Q^{T}\) is applied to \(C\) from the right.

trans

If trans = oneapi::math::transpose::nontrans, the routine multiplies \(C\) by \(Q\).

If trans = oneapi::math::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::math::side::left, \(0 \le k \le m\)

If side = oneapi::math::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.

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 \(QC\), \(Q^{T}C\), \(CQ\), or \(CQ^{T}\) (as specified by side and trans).
scratchpad: Buffer holding scratchpad memory to be used by routine for storing intermediate results.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::math::host_bad_alloc

oneapi::math::device_bad_alloc

oneapi::math::unimplemented

oneapi::math::unsupported_device

oneapi::math::lapack::invalid_argument

oneapi::math::lapack::computation_error

Exception is thrown in case of problems during calculations. The info code of the problem can be obtained by info() method of exception object:

If \(\text{info}=-i\), the \(i\)-th parameter had an illegal value.

If info equals to value passed as scratchpad size, and detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by detail() method of exception object.

ormrq (USM Version)#