Contents

# p?poequ

Computes row and column scaling factors intended to equilibrate a symmetric (Hermitian) positive definite distributed matrix and reduce its condition number.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?poequ
function
computes row and column scalings intended to equilibrate a real symmetric or complex Hermitian positive definite distributed matrix sub(
A
) =
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1) and reduce its condition number (with respect to the two-norm). The output arrays
sr
and
sc
return the row and column scale factors These factors are chosen so that the scaled distributed matrix
B
with elements
b
i
j
=
s
(
i
)*
a
i
j
*
s
(
j
) has ones on the diagonal.
This choice of
sr
and
sc
puts the condition number of
B
within a factor
n
of the smallest possible condition number over all possible diagonal scalings.
The auxiliary function
p?laqsy
uses scaling factors computed by
p?geequ
to scale a general rectangular matrix.
Input Parameters
n
(global) The number of rows and columns to be operated on, that is, the order 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
n
-by-
n
symmetric/Hermitian positive definite distributed matrix sub(
A
) whose scaling factors are to be computed. Only the diagonal elements of sub(
A
) are referenced.
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
sr
,
sc
(local)
Arrays of sizes
LOCr
(
m_a)
and
LOCc
(
n_a)
, respectively.
If
info
= 0
, the array
sr
(
ia:ia+n-1
)
contains the row scale factors for sub(
A
).
sr
is aligned with the distributed matrix
A
, and replicated across every process column.
sr
is tied to the distributed matrix
A
.
If
info
= 0
, the array
sc
(
ja:ja+n-1
)
contains the column scale factors for sub(
A
).
sc
is aligned with the distributed matrix
A
, and replicated down every process row.
sc
is tied to the distributed matrix
A
.
scond
(global)
If
info
= 0
,
scond
contains the ratio of the smallest
sr
[
i
] ( or
sc
[
j
]) to the largest
sr
[
i
] ( or
sc
[
j
])
, with
ia
-1≤
i
<
ia
+
n
-1 and
ja
-1≤
j
<
ja
+
n
-1.
If
scond
0.1
and
amax
is neither too large nor too small, it is not worth scaling by
sr
( or
sc
).
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
=
k
, the
k
-th diagonal entry of sub(
A
) is nonpositive.

#### Product and Performance Information

1

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