unmrq#

Multiplies a complex matrix by the unitary matrix \(Q\) of the RQ factorization formed by gerqf.

Description

unmrq supports the following precisions.

T

std::complex<float>

std::complex<double>

T
`std::complex<float>`
`std::complex<double>`

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

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

unmrq (Buffer Version)#

Syntax

namespace oneapi::mkl::lapack {
  void unmrq(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 \(Q^{H}\) is applied to \(C\) from the left.

If side = oneapi::mkl::side::right, \(Q\) or \(Q^{H}\) 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::conjtrans, the routine multiplies \(C\) by \(Q^{H}\).

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.

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 unmrq_scratchpad_size function.

Output Parameters

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

unmrq (USM Version)#