ormtr#

Multiplies a real matrix by the real orthogonal matrix \(Q\) determined by sytrd.

Description

ormtr supports the following precisions.

T

float

double

T
`float`
`double`

The routine multiplies a real matrix \(C\) by \(Q\) or \(Q^{T}\), where \(Q\) is the orthogonal matrix \(Q\) formed by:ref:onemkl_lapack_sytrd when reducing a real symmetric matrix \(A\) to tridiagonal form: \(A = QTQ^T\). Use this routine after a call to sytrd.

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 on \(C\)).

ormtr (Buffer Version)#

Syntax

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

If side = side::right, \(Q\) or \(Q^{T}\) 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 sytrd.

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 \(Q^{T}\).

m

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

n

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

a

The buffer a as returned by sytrd.

lda

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

tau

The buffer tau as returned bya sytrd. 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 ormtr_scratchpad_size function.

Output Parameters

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

ormtr (USM Version)#