Contents

# ?upmtr

Multiplies a complex matrix by the unitary matrix Q determined by
?hptrd
.

## Syntax

Include Files
• mkl.h
Description
The routine multiplies a complex matrix
C
by
Q
or
Q
H
, where
Q
is the unitary matrix formed by hptrd when reducing a packed complex Hermitian matrix
A
to tridiagonal form:
A
=
Q*T*Q
H
. Use this routine after a call to
?hptrd
.
Depending on the parameters
side
and
trans
, the routine can form one of the matrix products
Q*C
,
Q
H
*C
,
C*Q
, or
C*Q
H
(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
H
is applied to
C
from the left.
If
side
=
'R'
,
Q
or
Q
H
is applied to
C
from the right.
uplo
Must be
'U'
or
'L'
.
Use the same
uplo
as supplied to
?hptrd
.
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
H
.
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
?hptrd
.
The size of
ap
must be at least max(1,
r
(
r
+1)/2).
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
.
ldc
c
;
ldc
max(1,
m
)
for column major layout and
ldc
max(1,
n
) for row major layout
.
Output Parameters
c
Overwritten by the product
Q*C
,
Q
H
*C
,
C*Q
, or
C*Q
H
(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
8*
m
2
*
n
if
side
=
'L'
or
8*
n
2
*
m
if
side
=
'R'
.
The real counterpart of this routine is opmtr.

#### Product and Performance Information

1

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