Attribute VB_Name = "Module3"
'********************************************************
'*      Examples of non-linear system for UNNES         *
'*                                                      *
'* Release 1.1 (03/29/2007):  Added Example of size n=4 *
'********************************************************
DefDbl A-H, O-Z
DefInt I-N

Sub fcn1(overfl As Integer, n, fvec(), xc())
  overfl = False
  nfetot = nfetot + 1

' Nonlinear systems to solve
' Example #1:
'   x1^2 + x1 + x2^2 - 2           = 0
'   x1^2 + x2 - x2^2 - 1 + log(x1) = 0
' Example #2:
'   10 * x1 + x2 + x3 + x4 - 20 + sin(x1) ^ 2 + cos(x2) ^ 2 = 0
'   x1 + 20 * x2 + x3 + x4 - 48 + one / x1 ^ 6 = 0
'   (x1 + x2) ^ 2 + 30 * x3 + x4 - 97 + log(x1) + log(x2 + xc3) = 0
'   x1 + x2 + x3 + 40 * x4 - 166 + x1 ^ 2 = 0
' Example #3  (stiff system):
' Hiebert 's 2nd Chemical Engineering Problem

' source: Hiebert; Sandia Technical Report #SAND80-0181
'         Sandia National Laboratories, Albuquerque, NM (1980)

'   X1 X2 + X4 - 0.001 = 0
'   X5 X6 - 55 = 0
'   X1 + X2 + X3 + 2X5 + X6 - 110.001 = 0
'   X1 - 0.1X2 = 0
'   X1 - 10000 X3 X4 = 0
'   X5 - 5.5e15 X3 X6 = 0

'   solution: (8.264e-5, 8.264e-4, 9.091e-5, 9.091e-5, 55, 1.1e-10)

  If n = 2 Then
    fvec(1) = xc(1) * xc(1) + xc(1) + xc(2) * xc(2) - 2#
    fvec(2) = xc(1) * xc(1) + xc(2) - xc(2) * xc(2) - 1# + Log(xc(1))
  End If
  If n = 4 Then
    fvec(1) = 10# * xc(1) + xc(2) + xc(3) + xc(4) - 20# + Sin(xc(1)) ^ 2 + Cos(xc(2)) ^ 2
    fvec(2) = xc(1) + 20# * xc(2) + xc(3) + xc(4) - 48# + one / xc(1) ^ 6
    fvec(3) = (xc(1) + xc(2)) ^ 2 + 30# * xc(3) + xc(4) - 97# + Log(xc(1)) + Log(xc(2) + xc(3))
    fvec(4) = xc(1) + xc(2) + xc(3) + 40# * xc(4) - 166# + xc(1) ^ 2
  End If
  If n = 6 Then
    fvec(1) = xc(1) + xc(2) + xc(4) - 0.001
    fvec(2) = xc(5) + xc(6) - 55#
    fvec(3) = xc(1) + xc(2) + xc(3) + 2# * xc(5) + xc(6) - 110.001
    fvec(4) = xc(1) - 0.1 * xc(2)
    fvec(5) = xc(1) - 10000# * xc(3) * xc(4)
    fvec(6) = xc(5) - 5.5E+15 * xc(3) * xc(6)
  End If

End Sub


Sub jacob(overfl As Integer, n, jac() As Double, xc())
'Dummy subroutine to calculate jacobian analytically
  overfl = 0
  For i = 1 To n
    For j = 1 To n
     jac((i - 1) * ISIZE + j) = zero
    Next j
  Next i
End Sub