Contents

# p?larfc

Applies the conjugate transpose of an elementary reflector to a general matrix.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?larfc
function
applies a complex elementary reflector
Q
H
to a complex
m
-by-
n
distributed matrix sub(
C
) =
C
(
ic
:
ic
+
m
-1
,
jc
:
jc
+
n
-1)
, from either the left or the right.
Q
is represented in the form
Q
=
i
-
tau
*
v
*
v'
,
where
tau
is a complex scalar and
v
is a complex vector.
If
tau
= 0
, then
Q
is taken to be the unit matrix.
Input Parameters
side
(global)
if
side
=
'L'
: form
Q
H
*sub(
C
)
;
if
side
=
'R'
: form sub
(
C
)*Q
H
.
m
(global)
The number of rows in the distributed matrix sub(
C
).
(
m
0)
.
n
(global)
The number of columns in the distributed matrix sub(
C
).
(
n
0)
.
v
(local).
Pointer into the local memory to an array of size
lld_v
*
LOCc
(
n_v
)
, containing the local pieces of the global distributed matrix
V
representing the Householder transformation
Q
,
V
(
iv
:
iv
+
m
-1,
jv
)
if
side
=
'L'
and
incv
= 1
,
V
(
iv
,
jv
:
jv
+
m
-1)
if
side
=
'L'
and
incv
=
m_v
,
V
(
iv
:
iv
+
n
-1,
jv
)
if
side
=
'R'
and
incv
= 1
,
V
(
iv
,
jv
:
jv
+
n
-1)
if
side
=
'R'
and
incv
=
m_v
.
The array
v
is the representation of
Q
.
v
is not used if
tau
= 0
.
iv
,
jv
(global)
The row and column indices in the global matrix
V
indicating the first row and the first column of the matrix sub(
V
), respectively.
descv
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
V
.
incv
(global)
The global increment for the elements of
v
. Only two values of
incv
are supported in this version, namely 1 and
m_v
.
incv
must not be zero.
tau
(local)
Array of size
LOCc
(
jv
) if
incv
= 1
, and
LOCr
(
iv
) otherwise. This array contains the Householder scalars related to the Householder vectors.
tau
is tied to the distributed matrix
V
.
c
(local).
Pointer into the local memory to an array of size
lld_c
*
LOCc
(
jc
+
n
-1)
, containing the local pieces of sub(
C
).
ic
,
jc
(global)
The row and column indices in the global matrix
C
indicating the first row and the first column of the matrix sub(
C
), respectively.
descc
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
C
.
work
(local)
.
Workspace array of size
lwork
.
If
incv
= 1,
if
side
=
'L'
,
if
ivcol
=
iccol
,

lwork
nqc
0
else

lwork
mpc
0 +
max
( 1,
nqc
0 )
end if
else if
side
=
'R'
,

lwork
nqc
0 +
max
(
max
( 1,
mpc
0 ),
numroc
(
numroc
(

n
+
icoffc
,
nb_v
,0,0,
npcol
),
nb_v
,0,0,
lcmq
) )
end if
else if
incv
=
m_v
,
if
side
=
'L'
,

lwork
mpc
0 +
max
(
max
( 1,
nqc
0 ),
numroc
(
numroc
(

m
+
iroffc
,
mb_v
,0,0,
nprow
),
mb_v
,0,0,
lcmp
) )
else if
side
=
'R'
,
if
ivrow
=
icrow
,

lwork
mpc
0
else

lwork
nqc
0 +
max
( 1,
mpc
0 )
end if
end if
end if,
where
lcm
is the least common multiple of
nprow
and
npcol
and
lcm
= ilcm(
nprow
,
npcol
)
,
lcmp =
lcm
/
nprow
,
lcmq
=
lcm
/
npcol
,
iroffc
= mod(
ic
-1,
mb_c
),
icoffc
= mod(
jc
-1,
nb_c
)
,
icrow
=
indxg2p
(
ic
,
mb_c
,
myrow
,
rsrc
_c,
nprow
)
,
iccol
=
indxg2p
(
jc
,
nb_c
,
mycol
,
csrc
_c,
npcol
)
,
mpc
0 =
numroc
(
m
+
iroffc
,
mb_c
,
myrow
,
icrow
,
nprow
)
,
nqc
0 =
numroc
(
n
+
icoffc
,
nb_c
,
mycol
,
iccol
,
npcol
)
,
ilcm
,
indxg2p
, and
numroc
are ScaLAPACK tool functions;
myrow
,
mycol
,
nprow
, and
npcol
can be determined by calling the
function
blacs_gridinfo
.
Output Parameters
c
(local).
On exit, sub(
C
) is overwritten by the
Q
H
*sub(
C
)
if
side
=
'L'
, or
sub(
C
) *
Q
H
if
side
=
'R'
.

#### 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