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

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