SPPEQU(l) ) SPPEQU(l)
NAME
SPPEQU - compute row and column scalings intended to equilibrate a symmetric positive definite 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 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 small-
est 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 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) 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 i-th argument had an illegal value
> 0: if INFO = i, the i-th diagonal element is nonpositive.
LAPACK version 3.0 15 June 2000 SPPEQU(l)
