SRC/zppequ.f(3)            Library Functions Manual            SRC/zppequ.f(3)

NAME
       SRC/zppequ.f

SYNOPSIS
   Functions/Subroutines
       subroutine zppequ (uplo, n, ap, s, scond, amax, info)
           ZPPEQU

Function/Subroutine Documentation
   subroutine zppequ (character uplo, integer n, complex*16, dimension( * )
       ap, double precision, dimension( * ) s, double precision scond, double
       precision amax, integer info)
       ZPPEQU

       Purpose:


            ZPPEQU 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*16 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 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.

       Definition at line 116 of file zppequ.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/zppequ.f(3)