# ormtr¶

Multiplies a real matrix by the real orthogonal matrix $$Q$$ determined by sytrd.

Description

ormtr supports the following precisions.

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

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).

Buffer holding scratchpad memory to be used by routine for storing intermediate results.

## ormtr (USM Version)¶

Syntax

namespace oneapi::mkl::lapack {
sycl::event 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, T *a, std::int64_t lda, T *tau, T *c, std::int64_t ldc, T *scratchpad, std::int64_t scratchpad_size, const std::vector<sycl::event> &events = {})
}


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 pointer to a as returned by sytrd.

lda

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

tau

The buffer tau as returned by sytrd. 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 $$(\max(1, n) \le \text{ldc})$$.

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.

events

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

Output Parameters

c

Overwritten by the product $$QC$$, $$Q^TC$$, $$CQ$$, or $$CQ^T$$ (as specified by side and trans).