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# dppequ

```
NAME
DPPEQU - compute row and column scalings intended to equili-
brate a symmetric positive definite matrix A in packed
storage and reduce its condition number (with respect to the
two-norm)

SYNOPSIS
SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )

CHARACTER      UPLO

INTEGER        INFO, N

DOUBLE         PRECISION AMAX, SCOND

DOUBLE         PRECISION AP( * ), S( * )

PURPOSE
DPPEQU computes row and column scalings intended to equili-
brate a symmetric positive definite matrix A in packed
storage and reduce its condition number (with respect to the
two-norm).  S contains the scale factors,
S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
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.

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array.  The j-th
column of A is stored in the array AP as follows: if
UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for
j<=i<=n.

S       (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND   (output) DOUBLE PRECISION
If INFO = 0, S contains the ratio of the smallest
S(i) to the largest S(i).  If SCOND >= 0.1 and AMAX
is neither too large nor too small, it is not worth

scaling by S.

AMAX    (output) DOUBLE PRECISION
Absolute value of largest matrix element.  If AMAX
is very close to overflow or very close to under-
flow, the matrix should be scaled.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
> 0:  if INFO = i, the i-th diagonal entry is nonpo-
sitive.
```