unmtr

ultiplies a complex matrix by the complex unitary matrix Q determined by hetrd. This routine belongs to the oneapi::mkl::lapack namespace.

Description

The routine multiplies a complex matrix C by Q or QH, where Q is the unitary matrix Q formed by hetrd when reducing a complex Hermitian matrix A to tridiagonal form: A = Q*T*QH. Use this routine after a call to hetrd.

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

API

Syntax

namespace oneapi::mkl::lapack {
  void unmtr(sycl::queue &queue,
  mkl::side side,
  mkl::uplo uplo,
  mkl::transpose trans,
  std::int64_t m,
  std::int64_t n,
  sycl::buffer<T> &a,
  std::int64_t lda,
  sycl::buffer<T> &tau,
  sycl::buffer<T> &c,
  std::int64_t ldc,
  sycl::buffer<T> &scratchpad,
  std::int64_t scratchpad_size)
}

unmtr supports the following precisions and devices:

T

Devices supported

std::complex<float>

CPU

std::complex<double>

CPU

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

Device queue where calculations will be performed.

side

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

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

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

uplo

Must be either uplo::upper or uplo::lower. Uses the same uplo as supplied to hetrd (USM Version).

trans

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

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

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

m

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

n

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

a

Buffer holding array returned by hetrd (USM Version).

lda

The leading dimension of a (lda max(1, r)).

tau

Buffer holding tau returned by hetrd (USM Version). The dimension of tau must be at least max(1, r-1).

c

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

ldc

The leading dimension of c (ldc max(1, m)).

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 unmtr_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.