Contents

# p?geqr2

Computes a QR factorization of a general rectangular matrix (unblocked algorithm).

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?geqr2
function
computes a
QR
factorization of a real/complex distributed
m
-by-
n
matrix
sub(
A
) =
A
(
ia
:
ia
+
m
-1,
ja
:
ja
+
n
-1)=
Q
*
R
.
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 size
lld_a
*
LOC
c
(
ja
+
n
-1)
.
On entry, this array contains the local pieces of the
m
-by-
n
distributed matrix sub(
A
) which is 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 sub(
A
), respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix A.
work
(local).
This is a workspace array of size
lwork
.
lwork
(local or global)
The size of the array
work
.
l
work
is local input and must be at least
lwork
mp
0+max(1,
nq
0)
,
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
)
,
nq
0 =
numroc
(
n
+
icoff
,
nb_a
,
mycol
,
iacol
,
npcol
)
.
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
(local).
On exit, the elements on and above the diagonal of sub(
A
) contain the min(
m,n
) by
n
upper trapezoidal matrix
R
(
R
is upper triangular if
m
n
); the elements below the diagonal, 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
LOCc
(
ja
+min(
m,n)
-1). This array contains the scalar factors of the elementary reflectors.
tau
is tied to the distributed matrix
A
.
work
On exit,
work[0]
returns the minimal and optimal
lwork
.
info
(local)
If
info = 0
, the execution is successful. if
info
< 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
(
ja
)*
H
(
ja
+1)*. . .*
H
(
ja
+
k
-1)
, where
k
= min(
m,n
)
.
Each
H
(
i
)
has the form
H
(
j
)=
I
-
tau
*
v
*
v'
,
where
tau
is a real/complex scalar, and
v
is a real/complex vector with
v
(1:
i
-1) = 0 and
v
(
i
) = 1;
v
(
i
+1:
m
) is stored on exit in
A
(
ia
+
i
:
ia
+
m
-1,
ja
+
i
-1), and
tau
in
tau
[
ja
+
i
-2]
.

#### Product and Performance Information

1

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