Developer Reference

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ormtr

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

Description

Q
T
, 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
).
The routine multiplies a real matrix
C
by
Q
or

API

Syntax
namespace oneapi::mkl::lapack { 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
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
Q
T
is applied to
C
from the left.
If
side = side::right
,
Q
or
Q
T
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
Q
T
.
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
Exception
Description
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.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.