DPPEQU(3F)DPPEQU(3F)NAME
DPPEQU - 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 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 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) 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 underflow, the matrix should be
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DPPEQU(3F)DPPEQU(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.
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