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


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:


Devices supported


Host and CPU


Host and CPU


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


Device queue where calculations will be performed.


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.


Must be either uplo::upper or uplo::lower. Uses the same uplo as supplied to sytrd.


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.


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


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


Buffer holding array returned by sytrd.


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


Buffer holding tau returned by sytrd. The dimension of tau must be at least max(1, r-1).


Buffer holding the matrix C. The second dimension of c must be at least max(1, n).


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


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


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


Overwritten by the product Q*C, QT*C, C*Q, or C*QT (as specified by side and trans).



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.