Contents

# ?opmtr

Multiplies a real matrix by the real orthogonal matrix Q determined by
?sptrd
.

## Syntax

Include Files
• mkl.h
Description
The routine multiplies a real matrix
C
by
Q
or
Q
T
, where
Q
is the orthogonal matrix
Q
formed by sptrd when reducing a packed real symmetric matrix
A
to tridiagonal form:
A
=
Q
*
T
*
Q
T
. Use this routine after a call to
?sptrd
.
Depending on the parameters
side
and
trans
, the routine can form one of the matrix products
Q
*
C
,
Q
T
*
C
,
C
*
Q
, or
C
*
Q
T
(overwriting the result on
C
).
Input Parameters
In the descriptions below,
r
denotes the order of
Q
:
If
side
=
'L'
,
r
=
m
; if
side
=
'R'
,
r
=
n
.
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
side
Must be either
'L'
or
'R'
.
If
side
=
'L'
,
Q
or
Q
T
is applied to
C
from the left.
If
side
=
'R'
,
Q
or
Q
T
is applied to
C
from the right.
uplo
Must be
'U'
or
'L'
.
Use the same
uplo
as supplied to
?sptrd
.
trans
Must be either
'N'
or
'T'
.
If
trans
=
'N'
, the routine multiplies
C
by
Q
.
If
trans
=
'T'
, the routine multiplies
C
by
Q
T
.
m
The number of rows in the matrix
C
(
m
0
).
n
The number of columns in
C
(
n
0
).
ap
,
tau
,
c
ap
and
tau
are the arrays returned by
?sptrd
.
The dimension of
ap
must be at least max(1,
r
(
r
+1)/2).
The dimension of
tau
must be at least max(1,
r
-1).
c
(size max(1,
ldc
*
n
) for column major layout and max(1,
ldc
*
m
) for row major layout)
contains the matrix
C
.
ldc
c
;
ldc
max(1,
n
)
for column major layout and
ldc
max(1,
m
) for row major layout
.
Output Parameters
c
Overwritten by the product
Q
*
C
,
Q
T
*
C
,
C
*
Q
, or
C
*
Q
T
(as specified by
side
and
trans
).
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
Application Notes
The computed product differs from the exact product by a matrix
E
such that
||
E
||
2
=
O
(
ε
) ||
C
||
2
, where
ε
is the machine precision.
The total number of floating-point operations is approximately
2*
m
2
*
n
if
side
=
'L'
, or
2*
n
2
*
m
if
side
=
'R'
.
The complex counterpart of this routine is upmtr.

#### Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804