
SPPEQU(l) ) SPPEQU(l)
NAME
SPPEQU  compute row and column scalings intended to equilibrate a symmetric positive def
inite matrix A in packed storage and reduce its condition number (with respect to the two
norm)
SYNOPSIS
SUBROUTINE SPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
CHARACTER UPLO
INTEGER INFO, N
REAL AMAX, SCOND
REAL AP( * ), S( * )
PURPOSE
SPPEQU computes row and column scalings intended to equilibrate a symmetric positive defi
nite 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) REAL array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed columnwise in a lin
ear array. The jth column of A is stored in the array AP as follows: if UPLO =
'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j1)*(2nj)/2)
= A(i,j) for j<=i<=n.
S (output) REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND (output) REAL
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) REAL
Absolute value of largest matrix element. If AMAX is very close to overflow or
very close to underflow, the matrix should be scaled.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, the ith diagonal element is nonpositive.
LAPACK version 3.0 15 June 2000 SPPEQU(l) 
