## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?ppequ

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

## Syntax

Include Files
• mkl.fi
,
lapack.f90
Description
The routine computes row and column scalings intended to equilibrate a symmetric (Hermitian) positive definite matrix
A
in packed storage and reduce its condition number (with respect to the two-norm).
The output array
s
returns scale factors such that
s
(
i
)
s
[
i
+ 1]
contains These factors are chosen so that the scaled matrix
B
with elements
b
i
j
=
s
(i)*
a
i
j
*
s
(j)
has diagonal elements equal to 1.
This choice of
s
puts the condition number of
B
within a factor
n
of the smallest possible condition number over all possible diagonal scalings.
See
?laqsp
auxiliary function that uses scaling factors computed by
?ppequ
.
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates whether the upper or lower triangular part of
A
is packed in the array
ap
:
If
uplo
=
'U'
, the array
ap
stores the upper triangular part of the matrix
A
.
If
uplo
=
'L'
, the array
ap
stores the lower triangular part of the matrix
A
.
n
INTEGER
.
The order of matrix
A
;
n
0
.
ap
REAL
for
sppequ
DOUBLE PRECISION
for
dppequ
COMPLEX
for
cppequ
DOUBLE COMPLEX
for
zppequ
.
Array, size at least
max(1,
n
(
n
+1)/2)
. The array
ap
contains the upper or the lower triangular part of the matrix
A
(as specified by
uplo
) in packed storage (see Matrix Storage Schemes).
Output Parameters
s
REAL
for single precision flavors
DOUBLE PRECISION
for double precision flavors.
Array, size (
n
).
If
info
= 0
, the array
s
contains the scale factors for
A
.
scond
REAL
for single precision flavors
DOUBLE PRECISION
for double precision flavors.
If