ormtr

Multiplies a real matrix by the real orthogonal matrix Q determined by sytrd. This routine belongs to the oneapi::mkl::lapacknamespace.

Syntax

void ormtr(cl::sycl::queue &queue, mkl::side side, mkl::uplo uplo, mkl::transpose trans, std::int64_t m, std::int64_t n, cl::sycl::buffer<T> &a, std::int64_t lda, cl::sycl::buffer<T> &tau, cl::sycl::buffer<T> &c, std::int64_t ldc, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)

ormtr supports the following precisions and devices:

T

Devices supported

float

Host and CPU

double

Host and CPU

Description

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

Depending on the parameters left_right 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).

Input Parameters

In the descriptions below, r denotes the order of Q:

r = m

if left_right = side::left

r = n

if left_right = 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.

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 sytrd.

lda

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

tau

Buffer holding tau returned by sytrd. 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(max(1, n) ldc).

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 ormtr_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

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.