# 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(cl::sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::uplo upper_lower, oneapi::mkl::transpose trans, std::int64_t m, std::int64_t n, cl::sycl::buffer<T,1> &a, std::int64_t lda, cl::sycl::buffer<T,1> &tau, cl::sycl::buffer<T,1> &c, std::int64_t ldc, cl::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.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

oneapi::mkl::lapack::computation_error

Exception is thrown in case of problems during calculations. The info code of the problem can be obtained by info() method of exception object:

If $$\text{info}=-i$$, the $$i$$-th parameter had an illegal value.

If info equals to value passed as scratchpad size, and detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by detail() method of exception object.

## ormtr (USM Version)#

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event ormtr(cl::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<cl::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).

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

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

oneapi::mkl::lapack::computation_error

Exception is thrown in case of problems during calculations. The info code of the problem can be obtained by info() method of exception object:

If $$\text{info}=-i$$, the $$i$$-th parameter had an illegal value.

If info equals to value passed as scratchpad size, and detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by detail() method of exception object.

Return Values

Output event to wait on to ensure computation is complete.