Is it possible to implement Newton's method *once* in VBA? - vba

Question

I need to use Newton's method on closures.
Function f (x as Double, y as Double) as Double
f = x^3-y
End Function
I get the value of y from a cell and then I would like to find out when f is zero. In the toy example above, if the cell contains y=8, then I would expect Newton's method to find a solution close to x=2.
My solution was to make a newton_solve_f function:
Function newton_solve_f (y as Double as Double) as Double
Dim x as Double
x = 0 'initial guess for x
'do Newton's method to find x
...
newton_solve_f = x
End Function
so in effect, I copy paste my code for Newton's method (taken from here) into newton_solve_f.
The problem is that I have several such fs (some with more than two arguments), and it would be really neat if I didn't have to make a separate almost identical newton_solve_f for every one of them.
How would you solve this in VBA?
In Python, for example, it's possible to solve this problem as follows:
def f(y):
def g(x):
return x^3-y
return g
def newton_solve(f):
#do newton's method on f(x)
newton_solve(f(3))
Here f(3) is a function, a closure of one variable. (The closure example on wikipedia is almost identical to this one.)
ps. I know Newton's method also needs the (partial) derivative of f, I'm actually doing something that's more like the secant method, but that's irrelevant for what I'm asking about

Answer 1

Closures are not part of VBA. But you can use static variables within a method scope. They cannot be used outside the method. If you want a variable to visible outside, then you have to use global variable. Preferable declare it public in a module.
We cannot define function inside function in VB. Tried to convert the code given in the link you have mentioned. I hope it helps you. Not well versed with php, but you can see the approach below and make changes accordingly.
Sub Test()
Dim x As Double
Dim y As Double
Dim z As Double
x = Cells(1, 1).Value
y = Cells(1, 2).Value
z = NewtRap("Fun1", "dFun1", x, y)
Cells(1, 3).Value = z
End Sub
Private Function NewtRap(fname As String, dfname As String, x_guess As Double, y_value As Double) As Double
Dim cur_x As Double
Dim Maxiter As Double
Dim Eps As Double
Maxiter = 500
Eps = 0.00001
cur_x = x_guess
For i = 1 To Maxiter
If (fname = "Fun1") Then
fx = Fun1(cur_x)
ElseIf (fname = "dFun1") Then
fx = dFun1(cur_x)
ElseIf (fname = "f") Then
fx = f(cur_x, y_value)
End If
If (dfname = "Fun1") Then
fx = Fun1(cur_x)
ElseIf (dfname = "dFun1") Then
fx = dFun1(cur_x)
ElseIf (dfname = "f") Then
fx = f(cur_x, y_value)
End If
If (Abs(dx) < Eps) Then Exit For
cur_x = cur_x - (fx / dx)
Next i
NewtRap = cur_x
End Function
Function f(x As Double, y As Double) As Double
f = x ^ 3 - y
End Function
Function Fun1(x As Double) As Double
Fun1 = x ^ 2 - 7 * x + 10
End Function
Function dFun1(x As Double) As Double
dFun1 = 2 * x - 7
End Function

Answer 2

So to first summarise: You want to create a function that will find (using Newton-Raphson method) the roots of a function. You already have this written and working for certain functions but would like help expanding your code so it will work with a variety of functions with varying numbers of parameters?
I think you first need to think about what input functions you want it to cover. If you are only dealing with polynomials (as your example suggests), this should be fairly straightforward.
You could have general functions of:
Function fnGeneralCase (x, y, z, w, a1, a2, a3, b1, b2, b3, c1, c2, c3 as Double) as Double
fnGeneralCase = a1*x^3 + a2*x^2 + a3*x + b1*y^3 + b2*y^2 + b3*y + c1*z^3 + c2*z^2 + c3*z + w
End Function
Function fnDerivGeneralCase (x, y, z, w, a1, a2, a3, b1, b2, b3, c1, c2, c3 as Double) as Double
fnDerivGeneralCase = a1*3*x^2 + a2*2*x + a3 + b1*3*y^2 + b2*2*y + b3 + c1*3*z^2 + c2*2*z + c3
End Function
And just set the inputs to zero when you don't need them (which will be for the majority of the time).
So for your example calling:
answer = fnGeneralCase(guess, 0, 0, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0)
basically gives:
function = x^3-8
If you want to include more than polynomials, this will get more complicated but you could still use the above approach...

Answer 3

This seems to be asking 2 related questions:
how to pass a function as an argument in vba.
how to create a closure out of an existing function.
Unfortunately neither of these are really supported, however,
for 1 you can generally work around this by passing a string function name and using 'Application.Run' to invoke the function.
2 is trickier if you have lots of functions with different numbers of parameters, but for a set number of parameters you could add extra parameters to the newton_solve function or maybe use global variables.
e.g.
Public Function f(x as Double, y as Double) as Double
f = x^3-y
End Function
Function newton_solve_f (function_name as String, y as Double) as Double
Dim x as Double
x = 0 'initial guess for x
'do Newton's method to find x
...
' invoke function_name
x = Application.Run(function_name, x, y)
...
newton_solve_f = x
End Function
Assuming f is in a module called 'Module1' you can call this with:
x = newton_solve('Module1.f', 3)
Note that the function you want to call must be public.