Contents

# ?unmql

Multiplies a complex matrix by the unitary matrix Q of the QL factorization formed by
?geqlf
.

## Syntax

Include Files
• mkl.h
Description
The routine multiplies a complex
m
-by-
n
matrix
C
by
Q
or
Q
H
, where
Q
is the unitary matrix
Q
of the
QL
factorization formed by the routine geqlf.
Depending on the parameters
side
and
trans
, the routine unmql can form one of the matrix products
Q*C
,
Q
H
*C
,
C*Q
, or
C*Q
H
(overwriting the result over
C
).
Input Parameters
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.
trans
Must be either
'N'
or
'C'
.
If
trans
=
'N'
, the routine multiplies
C
by
Q
.
If
trans
=
'C'
, 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
).
k
The number of elementary reflectors whose product defines the matrix
Q
. Constraints:
0
k
m
if
side
=
'L'
;
0
k
n
if
side
=
'R'
.
a
,
tau
,
c
Arrays:
a
,
tau
,
c
.
The size of
a
must be:
For column major layout regardless of
side
, max(1,
lda
*
k
).
For
side
= 'L' and row major layout, max(1,
lda
*
m
).
For
side
= 'R' and row major layout, max(1,
lda
*
n
).
On entry, the
i
-th column of
a
must contain the vector which defines the elementary reflector
H
(
i
)
, for i = 1,2,...,
k
, as returned by
cgeqlf
/
zgeqlf
in the last
k
columns of its array argument
a
.
tau
[
i
- 1]
must contain the scalar factor of the elementary reflector
H
(
i
)
, as returned by
cgeqlf
/
zgeqlf
.
The size of
tau
must be at least max(1,
k
).
c
(size max(1,
ldc
*
n
) for column major layout and max(1,
ldc
*
m
for row major layout)
contains the
m
-by-
n
matrix
C
.
lda
The leading dimension of
a
.
If
side
=
'L'
,
lda
max(1,
m
)
for column major layout and max(1,
k
) for row major layout
.
If
side
=
'R'
,
lda
max(1,
n
)
for column major layout and max(1,
k
) for row major layout
.
ldc
The leading dimension of
c
;
ldc
max(1,
m
)
for column major layout and 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 real counterpart of this routine is ormql.

#### Product and Performance Information

1

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