Contents

# p?orm2l/p?unm2l

Multiplies a general matrix by the orthogonal/unitary matrix from a QL factorization determined by
p?geqlf
(unblocked algorithm).

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?orm2l/p?unm2l
function
overwrites the general real/complex
m
-by-
n
distributed matrix sub (
C
)=
C
(
ic
:
ic
+
m
-1
,jc
:
jc
+
n
-1)
with
Q
*sub(
C
) if
side
=
'L'
and
trans
=
'N'
, or
Q
T
*sub(
C
) /
Q
H
*sub(
C
) if
side
=
'L'
and
trans
=
'T'
(for real flavors) or
trans
=
'C'
(for complex flavors), or
sub(
C
)*
Q
if
side
=
'R
' and
trans
=
'N'
, or
sub(
C
)*
Q
T
/ sub(
C
)*
Q
H
if
side
=
'R'
and
trans
=
'T'
(for real flavors) or
trans
=
'C'
(for complex flavors).
where
Q
is a real orthogonal or complex unitary distributed matrix defined as the product of
k
elementary reflectors
Q = H
(
k
)*...*
H
(2)*
H
(1) as returned by
p?geqlf
.
Q
is of order
m
if
side
=
'L'
and of order
n
if
side
=
'R'
.
Input Parameters
side
(global)
=
'L'
: apply
Q
or
Q
T
for real flavors (
Q
H
for complex flavors) from the left,
=
'R'
: apply
Q
or
Q
T
for real flavors (
Q
H
for complex flavors) from the right.
trans
(global)
=
'N'
: apply
Q
(no transpose)
=
'T'
: apply
Q
T
(transpose, for real flavors)
=
'C'
: apply
Q
H
(conjugate transpose, for complex flavors)
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
.
k
(global)
The number of elementary reflectors whose product defines the matrix
Q
.
If
side
=
'L'
,
m
k
0
;
if
side
=
'R'
,
n
k
0
.
a
(local)
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
k
-1)
.
On entry, the
j
-th row
of the matrix stored in
a
must contain the vector that defines the elementary reflector
H
(
j
),
ja
j
ja
+
k
-1
, as returned by
p?geqlf
in the
k
columns of its distributed matrix argument
A
(
ia
:*,
ja
:
ja
+
k
-1)
. The argument
A
(
ia
:*,
ja
:
ja
+
k
-1)
is modified by the
function
but restored on exit.
If
side
=
'L'
, lld_a
max(1,
LOCr
(
ia
+
m
-1))
,
if
side
=
'R'
, lld_a
max(1,
LOCr
(
ia
+
n
-1))
.
ia
(global)
The row index in the global matrix
A
indicating the first row of sub(
A
).
ja
(global)
The column index in the global matrix
A
indicating the first column of sub(
A
).
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
tau
(local)
Array of size
LOCc
(
ja
+
n
-1)
.
tau
[
j
]
contains the scalar factor of the elementary reflector
H
(
j
+1),
j
= 0, 1, ...,
LOCc
(
ja
+
n
-1)
-1
, as returned by
p?geqlf
. This array is tied to the distributed matrix
A
.
c
(local)
Pointer into the local memory to an array of size
lld_c
*
LOCc
(
jc
+
n
-1)
.On entry, the local pieces of the distributed matrix sub (
C
).
ic
(global)
The row index in the global matrix
C
indicating the first row of sub(
C
).
jc
(global)
The column index in the global matrix
C
indicating the first column of sub(
C
).
descc
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
C
.
work
(local)
Workspace array of size
lwork
.
On exit,
work
(1)
returns the minimal and optimal
lwork
.
lwork
(local or global)
The size of the array
work
.
lwork
is local input and must be at least
if
side
=
'L'
,
lwork
mpc
0 + max(1,
nqc
0)
,
if
side
=
'R'
,
lwork
nqc
0 + max(max(1,
mpc
0), numroc(
numroc
(
n
+
icoffc
,
nb_a
, 0, 0,
npcol
),
nb_a
, 0, 0,
lcmq
))
,
where
lcmq
=
lcm
/
npcol
,
lcm = iclm(
nprow
,
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
)
,
Mqc0
=
numroc
(
m
+
icoffc
,
nb_c
,
mycol
,
icrow
,
nprow
)
,
Npc0
=
numroc
(
n
+
iroffc
,
mb_c
,
myrow
,
iccol
,
npcol
)
,
ilcm
,
indxg2p
, and
numroc
are ScaLAPACK tool functions;
myrow
,
mycol
,
nprow
, and
npcol
can be determined by calling the
function
blacs_gridinfo
.
If
lwork
= -1
, then
lwork
is global input and a workspace query is assumed; the
function
only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by
pxerbla
.
Output Parameters
c
On exit,
c
is overwritten by
Q
*sub(
C
), or
Q
T
*sub(
C
)/
Q
H
*sub(
C
), or sub(
C
)*
Q
, or sub(
C
)*
Q
T
/ sub(
C
)*
Q
H
work
On exit,
work

returns the minimal and optimal
lwork
.
info
(local)
= 0
: successful exit
< 0
: if the
i
-th argument is an array and the
j
-th entry
, indexed
j
-1,
then
info
= - (
i
*100 +
j
),
if the
i
-th argument is a scalar and had an illegal value,
then
info
= -
i
.
The distributed submatrices
A
(
ia
:*,
ja
:*)
and
C
(
ic
:
ic
+
m
-1,
jc
:
jc
+
n
-1)
must verify some alignment properties, namely the following expressions should be true:
If
side
=
'L'
,
(
mb_a
==
mb_c
&&
iroffa
==
iroffc
&&
iarow
==
icrow
)
If
side
=
'R'
,
(
mb_a
==
nb_c
&&
iroffa
==
iroffc
)
.

#### 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