Contents

# ?ormtr

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

## 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 when reducing a real symmetric matrix
A
to tridiagonal form:
A
=
Q*T*Q
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
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
?sytrd
.
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
).
a
,
c
,
tau
a
(size max(1,
lda
*
r
))
and
tau
are the arrays returned by
?sytrd
.
The size 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
.
lda
a
;
lda
max(1,
r
)
.
ldc
c
;
ldc
max(1,
m
)
for column major layout and at least max(1,
n
) 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
.
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 unmtr.

#### Product and Performance Information

1

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