/*	File:	Richardson.cpp



			Christer Karlsson

This code implements Richardson Extrapolation.



    Allowed inputs are real numbers (long double).

    Define f in the function procedure.

    x equals the point where the derivative is evaluated.

    h is the step values.

    n is the amount of itterations.



	NOTE!  All arrays have an upper limit of n = 10.	*/



#include <iostream>

#include <cmath>

#include <iomanip>		// Needed too manipulate the display



using namespace std;





// the function

long double f(long double x)

{

    long double f;

    f=sin(x);

    return f;

}



// The Derivative function

void Derivative(long double x, int n, long double h, long double D[10][10])

{

    int i, j;



    for (i=0; i<n; i++)

    {

        D[i][0]=(f(x+h)-f(x-h))/(2*h);



        for (j=0; j<=(i-1); j++)

        {

            D[i][j+1]=D[i][j]+(D[i][j]-D[i-1][j])/(pow(4.0,double(j+1))-1);

        }

        h=h/2;

    }

}

int main(int argc, char *argv[])

{

    long double D[10][10];

    int n=10, digits=5;

    long double h=1, x=0;



    Derivative(x, n, h, D);



    // Set a fixed amount of digits to show

    cout.setf(ios::fixed );

    cout.setf(ios::showpoint);

    cout <<  setprecision(digits) << endl;



    // Printout the diagram

    for(int i=0; i<n; i++)

    {

        for(int j=0;j<i+1;j++)

        {

            cout << setw(digits+2) << D[i][j] << " ";

        }



        cout << endl;

    }



    // Unset the fixed point

    cout.unsetf(ios::fixed);

    cout.unsetf(ios::showpoint);



    system("PAUSE");

    return 0;

}