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ormtr (USM Version)

Multiplies a real matrix by the real orthogonal matrix Q determined by the sytrd (USM Version) function. This routine belongs to the oneapi::mkl::lapack namespace.

Description

The routine multiplies a real matrix C by Q or QT, where Q is the orthogonal matrix Q formed by sytrd (USM Version) when reducing a real symmetric matrix A to tridiagonal form: A = Q*T*QT. Use this routine after a call to sytrd (USM Version).

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 on C).

API

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event ormtr(cl::sycl::queue &queue,
  mkl::side side,
  mkl::uplo uplo,
  mkl::transpose trans,
  std::int64_t m,
  std::int64_t n,
  T *a,
  std::int64_t lda,
  T *tau,
  T *c,
  std::int64_t ldc,
  T *scratchpad,
  std::int64_t scratchpad_size,
  const std::vector<cl::sycl::event> &events = {})
}

ormtr (USM version) supports the following precisions and devices:

T

Devices supported

float

Host and CPU

double

Host and 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 sytrd (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

The pointer to memory returned by sytrd (USM Version).

lda

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

tau

The pointer to tau returned by sytrd (USM Version). The dimension of tau must be at least max(1, r-1).

c

The pointer to memory containing the matrix C. The second dimension of c must be at least max(1, n).

ldc

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

scratchpad

Pointer to 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 ormtr_scratchpad_size function.

events

List of events to wait for before starting computation. Defaults to empty list.

Output Parameters

c

Overwritten by 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.

Return Values

Output event to wait on to ensure computation is complete.

ormtr ormtr_scratchpad_size