Contents

# p?geequ

Computes row and column scaling factors intended to equilibrate a general rectangular distributed matrix and reduce its condition number.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?geequ
function
computes row and column scalings intended to equilibrate an
m
-by-
n
distributed matrix sub(
A
) =
A
(
ia
:
ia
+
m
-1,
ja
:
ja
+
n
-1) and reduce its condition number. The output array
r
returns the row scale factors
r
i
, and the array
c
returns the column scale factors
c
j
. These factors are chosen to try to make the largest element in each row and column of the matrix
B
with elements
b
i
j
=
r
i
*
a
i
j
*
c
j
have absolute value 1.
r
i
and
c
j
are restricted to be between
SMLNUM
= smallest safe number and
BIGNUM
= largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of sub(
A
) but works well in practice.
SMLNUM
and
BIGNUM
are parameters representing machine precision. You can use the
?lamch
routines to compute them. For example, compute single precision values of
SMLNUM
and
BIGNUM
as follows:
```SMLNUM = slamch ('s')
BIGNUM = 1 / SMLNUM```
The auxiliary function p?laqge uses scaling factors computed by
p?geequ
to scale a general rectangular matrix.
Input Parameters
m
(global) The number of rows to be operated on, that is, the number of rows of the distributed matrix sub(
A
)
(
m
0)
.
n
(global) The number of columns to be operated on, that is, the number of columns of 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)
.
The array
a
contains the local pieces of the
m
-by-
n
distributed matrix whose equilibration factors are to be computed.
ia
,
ja
(global) The row and column indices in the global matrix
A
indicating the first row and the first column of the matrix sub(
A
), respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
Output Parameters
r
,
c
(local)
Arrays of sizes
LOCr
(
m_a)
and
LOCc
(
n_a)
, respectively.
If
info
= 0
, or
info
>
ia+m-1
,
r
[
i
] contain
the row scale factors for sub(
A
)
for
ia
-1≤
i
<
ia
+
m
-1
.
r
is aligned with the distributed matrix
A
, and replicated across every process column.
r
is tied to the distributed matrix
A
.
If
info
= 0
,
c
[
i
] contain
the column scale factors for sub(
A
)
for
ja
-1≤
i
<
ja
+
n
-1
.
c
is aligned with the distributed matrix
A
, and replicated down every process row.
c
is tied to the distributed matrix
A
.
rowcnd
,
colcnd
(global)
If
info
= 0
or
info
>
ia+m-1
,
rowcnd
contains the ratio of the smallest
r
i
to the largest
r
i
(i
a
i
ia
+
m
-1). If
rowcnd
0.1
and
amax
is neither too large nor too small, it is not worth scaling by
r
i
.
If
info
= 0
,
colcnd
contains the ratio of the smallest
c
j
to the largest
c
j
(
ja
j
ja
+
n
-1).
If
colcnd
0.1
, it is not worth scaling by
c
j
.
amax
(global)
Absolute value of the largest matrix element. If
amax
is very close to overflow or very close to underflow, the matrix should be scaled.
info
(global) If
info
=0
, the execution is successful.
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
.
info
>
0
:
If
info
=
i
and
i
m
, the
i
-th row of the distributed matrix
sub(
A
) is exactly zero;
i
>
m
, the (
i
-
m
)-th column of the distributed
matrix sub(
A
) is exactly zero.

#### 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