Re: c++ Newton-Raphson problem

From:
James Kanze <james.kanze@gmail.com>
Newsgroups:
comp.lang.c++
Date:
Sat, 15 Nov 2008 02:16:01 -0800 (PST)
Message-ID:
<7f8e63bc-e1e6-484e-bd13-10e0e8fdd242@i18g2000prf.googlegroups.com>
On Nov 15, 9:53 am, pauldepst...@att.net wrote:

Let double NR( double x, double(*)(const double&) f ) be the
signature of a Newton-Raphson function NR.

Here, f is a function which returns a double and accepts a
const double&. The aim of the game is to find a zero of
this function f (the point at which f crosses the x-axis).
This zero-of-f which solves our problem is the double which NR
returns. It remains to explain what the "double x"
represents. This is the starting-guess that is required in
Newton-Raphson implementations.

In my case, I have the following amended Newton-Raphson
situation. I have a function of the form

double MyFunc(double x1, double x2, double x3, double x4, double x5)

I want to solve the following problem: Fix x1, x2, x3, and
x4. Then use Newton Raphson to return the double y such that
MyFunc(x1, x2, x3, x4, y) = 0.

I was unable to find a way of using the ready-made function NR
because it assumes f accepts 1 double and returns 1 double,
whereas My Func accepts 5 doubles and returns 1 double.


That's because the interface to the existing NR function is very
poorly designed. In C++, the "standard" solution for any
callback would be:

    class NRCallBack
    {
    public:
        virtual ~NRCallBack() {}
        virtual double operator()( double ) const = 0 ;
    } ;

So the signature of NR would be:

    double NR( double x, NRCallBack const& f ) ;

Rather than providing a function, you then derive from
NRCallBack, and define the appropriate operator.

In your precise case, it's probably a bit wordy, because we
don't have lambda classes, and you'd have to do something like:

    double
    NRforMyFunc( double x1, double x2, double x3, double x4 )
    {
        class F : public NRCallBack
        {
        public:
            NRCallBack( double x1, double x2, double x3, double x4 )
                : x1( x1 )
                , x2( x2 )
                , x3( x3 )
                , x4( x4 )
            {
            }
            virtual double operator()( double x ) const
            {
                return MyFunc( x1, x2, x3, x4, x ) ;
            }

        private:
            double x1 ;
            double x2 ;
            double x3 ;
            double x4 ;
        } ;
        return NR( 0.0, F() ) ;
    }

If (as may be the case), NR is in fact a C function, and must be
callable from C, the established convention is to pass an
additional void* with user data, i.e.:
    double NR( double x, double (*f)( double, void* ), void* ) ;
Again, you have to write a wrapper function which takes the
additional, fixed values as a void*, move these values into an
array, and pass the address of the array to NR.

My very-inelegant solution was to copy-paste the NR code and
adapt it so that the pointer-to-function parameter was of the
type I needed.


You may end up having to do this, if it's interface is broken.

Is there a more elegant approach that calls on the NR function
already present?


Depending on the context of what you're doing, you may be able
to use static variables and a wrapper function. IMHO, it's
playing with fire, however, and you'd be better off rewriting
the function to use one of the above interfaces, depending on
whether it is pure C++, or it must be callable from C as well.

--
James Kanze (GABI Software) email:james.kanze@gmail.com
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