## Developer Reference

• 2021.2
• 03/26/2021
• Public Content
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Contents

# p?orgql

Generates the orthogonal matrix
Q
of the
QL
factorization formed by
p?geqlf
.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?orgql
function
generates the whole or part of
m
-by-
n
real distributed matrix
Q
denoting
A
(
ia
:
ia
+
m
-1,
ja
:
ja
+
n
-1) with orthonormal rows, which is defined as the first
m
rows of a product of
k
elementary reflectors of order
n
Q
=
H
(
k
)*...*
H
(2)*
H
(1)
as returned by
p?geqlf
.
Input Parameters
m
(global) The number of rows in the matrix sub(
Q
),
(
m
0)
.
n
(global) The number of columns in the matrix sub(
Q
)
,(
m
n
0)
.
k
(global) The number of elementary reflectors whose product defines the matrix
Q
(
n
k
0)
.
a
(local)
Pointer into the local memory to an array of local size
lld_a
*
LOCc
(
ja
+
n
-1)
. On entry, the
j
-th column
of the matrix stored in
a
must contain the vector that defines the elementary reflector
H
(
j
),
ja
+
n
-
k
j
ja
+
n
-1, as returned by
p?geqlf
in the
k
columns of its distributed matrix argument
A
(
ia
:*,
ja
+
n
-
k
:
ja
+
n
-1).
ia
,
ja
(global) The row and column indices in the global matrix
A
indicating the first row and the first column of the submatrix
A
(
ia
:
ia
+
m
-1,
ja
:
ja
+
n
-1), respectively.
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)
.
Contains the scalar factors
tau
[
j
]
of elementary reflectors
H
(
j
+1), 0 ≤
j
<
LOCr
(
ia
+n-1)
.
tau
is tied to the distributed matrix
A
.
work
(local)
Workspace array of size of
lwork
.
lwork
(local or global) size of
work
, must be at least
lwork
nb_a
*(
nqa
0+
mpa
0+
nb_a
)
, where
iroffa
=
mod
(
ia
-1,
mb_a
)
,
icoffa
=
mod
(
ja
-1,
nb_a
)
,
iarow
=
indxg2p
(
ia
,
mb_a
,
MYROW
,
rsrc_a
,
NPROW
)
,
iacol
=
indxg2p
(
ja
,
nb_a
,
MYCOL
,
csrc_a
,
NPCOL
)
,
mpa
0 =
numroc
(
m
+
iroffa
,
mb_a
,
MYROW
,
iarow
,
NPROW
)
,
nqa
0 =
numroc
(
n
+
icoffa
,
nb_a
,
MYCOL
,
iacol
,
NPCOL
)
mod(
x
,
y
)
is the integer remainder of
x
/
y
.
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
a
Contains the local pieces of the
m
-by-
n
distributed matrix
Q
to be factored.
work

On exit,
work

contains the minimum value of
lwork
required for optimum performance.
info
(global)
= 0
: the execution is successful.
< 0
: if the
i
-th argument is an array and the
j-
th entry
, indexed
j
- 1,
had an illegal value, then
info
= -(
i
*100+
j
); if the
i-
th argument is a scalar and had an illegal value, then
info
=
-i
.

#### Product and Performance Information

1

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