Contents

# p?gerqf

Computes the
RQ
factorization of a general rectangular matrix.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?gerqf
function
forms the
Q
R
factorization of a general
m
-by-
n
distributed matrix sub(
A
)=
A
(
ia
:
ia
+
m
-1,
ja
:
ja
+
n
-1) as
A
=
R
*
Q
Input Parameters
m
(global) The number of rows in the distributed matrix sub(
A
);
(
m
0)
.
n
(global) The number of columns in the distributed matrix sub(
A
);
(
n
0)
.
a
(local)
Pointer into the local memory to an array of local size
lld_a
*
LOCc
(
ja
+
n
-1)
.
Contains the local pieces of the distributed matrix sub(
A
) to be factored.
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
work
(local).
Workspace array of size
lwork
.
lwork
(local or global) size of
work
, must be at least
lwork
mb_a
*(
mp
0+
nq
0+
mb_a
)
, where
iroff
=
mod
(
ia
-1,
mb_a
)
,
icoff
=
mod
(
ja
-1,
nb_a
)
,
iarow
=
indxg2p
(
ia
,
mb_a
,
MYROW
,
rsrc_a
,
NPROW
)
,
iacol
=
indxg2p
(
ja
,
nb_a
,
MYCOL
,
csrc_a
,
NPCOL
)
,
mp
0 =
numroc
(
m
+
iroff
,
mb_a
,
MYROW
,
iarow
,
NPROW
)
,
mod(
x
,
y
)
is the integer remainder of
x
/
y
.
nq
0 =
numroc
(
n
+
icoff
,
nb_a
,
MYCOL
,
iacol
,
NPCOL
)
and
numroc
,
indxg2p
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
On exit, if
m
n
, the upper triangle of
A
(
ia
:
ia
+
m
-1,
ja
:
ja
+
n
-1) contains the
m
-by-
m
upper triangular matrix
R
; if
m
n
, the elements on and above the (
m
-
n
)-th subdiagonal contain the
m
-by-
n
upper trapezoidal matrix
R
; the remaining elements, with the array
tau
, represent the orthogonal/unitary matrix
Q
as a product of elementary reflectors
(see
Application Notes
below)
.
tau
(local)
Array of size
LOCr
(
ia
+
m
-1)
.
Contains the scalar factor of elementary reflectors.
tau
is tied to the distributed matrix
A
.
work
[0]
On exit,
work
[0]
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,
info
= -(
i
*100+
j
); if the
i-
th argument is a scalar and had an illegal value, then
info
=
-i
.
Application Notes
The matrix
Q
is represented as a product of elementary reflectors
Q
=
H
(
ia
)*
H
(
ia
+1)*...*
H
(
ia
+
k
-1),
where
k
= min(
m
,
n
)
.
Each
H
(
i
) has the form
H
(
i
) =
I
-
tau
*
v
*
v'
where
tau
is a real/complex scalar, and
v
is a real/complex vector with
v
(
n
-
k
+
i
+1:
n
) = 0 and
v
(
n
-
k
+
i
) = 1;
v
(1:
n
-
k
+
i
-1) is stored on exit in
A
(
ia
+
m
-
k
+
i
-1,
ja
:
ja
+
n
-
k
+
i
-2), and
tau
in
tau
[
ia
+
m
-
k
+
i
-2]
.

#### Product and Performance Information

1

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