C-----------------------------------------------------------------------
C IMSL Name:  NEQBF/DNEQBF (Single/Double precision version)
C
C Purpose:    Solve a system of nonlinear equations using factored
C             secant update with a finite-difference approximation to
C             the Jacobian.
C
C Usage:      CALL NEQBF (FCN, N, XGUESS, XSCALE, FSCALE, IPARAM,
C                         RPARAM, X, FVEC)
C
C Example 1:
C                                  Declare variables
      INTEGER    N
      PARAMETER  (N=3)
C
      INTEGER    IPARAM(6), K, NOUT
      REAL       FCN, FSCALE(N), FVEC(N), RPARAM(5), X(N), XGUESS(N),
     &           XSCALE(N)
      EXTERNAL   FCN, NEQBF, UMACH
C                                  Set values of initial guess
C                                  XGUESS = (  4.0  4.0  4.0 )
C
      DATA XGUESS/3*4.0/, XSCALE/3*1.0/, FSCALE/3*1.0/
C
C                                  Use the default setting
C
      IPARAM(1) = 0
C                                  Find the solution
      CALL NEQBF (FCN, N, XGUESS, XSCALE, FSCALE, IPARAM, RPARAM, X,
     &           FVEC)
C                                  Output
      CALL UMACH (2, NOUT)
      WRITE (NOUT,99999) (X(K),K=1,N)
99999 FORMAT ('  The solution to the system is', /, '  X = (', 3F8.3,
     &       ')')
C
      END
C                                  User-defined subroutine
      SUBROUTINE FCN (N, X, F)
      INTEGER    N
      REAL       X(N), F(N)
C
      REAL       EXP, SIN
      INTRINSIC  EXP, SIN
C
      F(1) = X(1) + EXP(X(1)-1.0) + (X(2)+X(3))*(X(2)+X(3)) - 27.0
      F(2) = EXP(X(2)-2.0)/X(1) + X(3)*X(3) - 10.0
      F(3) = X(3) + SIN(X(2)-2.0) + X(2)*X(2) - 7.0
      RETURN
      END
C   The solution to the system is
C   X = (   1.000   2.000   3.000)