NAME

       dppequ.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)
           DPPEQU

Function/Subroutine Documentation

   subroutine dppequ (character UPLO, integer N, double precision, dimension( * ) AP, double
       precision, dimension( * ) S, double precision SCOND, double precision AMAX, integer INFO)
       DPPEQU

       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.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           AP

                     AP is 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

                     S is DOUBLE PRECISION array, dimension (N)
                     If INFO = 0, S contains the scale factors for A.

           SCOND

                     SCOND is 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

                     AMAX is DOUBLE PRECISION
                     Absolute value of largest matrix element.  If AMAX is very
                     close to overflow or very close to underflow, the matrix
                     should be scaled.

           INFO

                     INFO is 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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

Author

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