SPPEQU(3F)SPPEQU(3F)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 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 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
Page 1
SPPEQU(3F)SPPEQU(3F)
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.
Page 2