cppequ(3F)

NAME
     CPPEQU - compute row and column scalings intended to equilibrate a
     Hermitian positive definite matrix A in packed storage and reduce its
     condition number (with respect to the two-norm)

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

         CHARACTER      UPLO

         INTEGER        INFO, N

         REAL           AMAX, SCOND

         REAL           S( * )

         COMPLEX        AP( * )

PURPOSE
     CPPEQU computes row and column scalings intended to equilibrate a
     Hermitian 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) COMPLEX array, dimension (N*(N+1)/2)
             The upper or lower triangle of the Hermitian 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.