unmtr#

Multiplies a complex matrix by the complex unitary matrix Q determined by hetrd.

Description

unmtr supports the following precisions.

T

std::complex<float>

std::complex<double>

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

The routine multiplies a complex matrix \(C\) by \(Q\) or \(Q^{H}\), where \(Q\) is the unitary matrix \(Q\) formed by hetrd when reducing a complex Hermitian matrix \(A\) to tridiagonal form: \(A = QTQ^H\). Use this routine after a call to hetrd.

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

unmtr (Buffer Version)#

Syntax

namespace oneapi::mkl::lapack {
  void unmtr(sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::uplo upper_lower, oneapi::mkl::transpose trans, std::int64_t m, std::int64_t n, 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

In the descriptions below, r denotes the order of \(Q\):

\(r\)=\(m\)	if `side = side::left`
\(r\)=\(n\)	if `side = side::right`

queue

The queue where the routine should be executed.

side

Must be either side::left or side::right.

If side=side::left, \(Q\) or \(Q^{H}\) is applied to \(C\) from the left.

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

upper_lower

Must be either uplo::upper or uplo::lower. Uses the same upper_lower as supplied to hetrd.

trans

Must be either transpose::nontrans or transpose::conjtrans.

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

If trans=transpose::conjtrans, the routine multiplies \(C\) by \(Q^{H}\).

m

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

n

The number of columns the matrix \(C\) (\(n \ge 0\)).

k

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

a

The buffer a as returned by hetrd.

lda

The leading dimension of a \((\max(1,r) \le \text{lda})\).

tau

The buffer tau as returned by hetrd. The dimension of tau must be at least \(\max(1,r-1)\).

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 \((\max(1,n) \le \text{ldc})\).

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 unmtr_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.

unmtr (USM Version)#