NAME

       cppequ.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)
           CPPEQU

Function/Subroutine Documentation

   subroutine cppequ (characterUPLO, integerN, complex, dimension( * )AP, real, dimension( * )S,
       realSCOND, realAMAX, integerINFO)
       CPPEQU

       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.

       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 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

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

           SCOND

                     SCOND is 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

                     AMAX is 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

                     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

       Definition at line 118 of file cppequ.f.

Author

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