Mathematical Recipes: Newton Raphson Method

[sumitmehta]

Here is a program in C# for Newton Raphson Method. Hope it is useful for somebody.

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Text;
using System.Windows.Forms;

namespace NRMethod
{
    public partial class Form1 : Form
    {
        public struct Polynomial
        {
            public int Exponent;
            public int Coefficient;
            public bool isVariable;
        };
        Polynomial[] polynomial;

        public Form1()
        {
            //This constructor initializes the polynomial
            //It can also be initialized at runtime
            InitializeComponent();

            int polyCount = 0;
            initPoly(out polynomial,2);

            addTerm(ref polynomial,polyCount,1, 2, true);
            polyCount++;
            addTerm(ref polynomial, polyCount, -10, 1, false);
            polyCount++; 
        }

        public void initPoly(out Polynomial[] Poly,int termCount) {

            Poly = new Polynomial[termCount];
        }
        public void addTerm(ref Polynomial[] Poly,int index,int Coefficient, int Exponent, bool isVariable) {

            Poly[index].Coefficient = Coefficient;
            Poly[index].Exponent = Exponent;
            Poly[index].isVariable = isVariable;
        }
        public float CalculateValue(Polynomial[] Poly,float value) {

            float val=0;
            float e=1;
            int polyCount = Poly.Length;

            for (int i = 0; i < polyCount; i++) {

                if (Poly[i].isVariable==true)
                {
                    for (int j = 0; j < Poly[i].Exponent; j++)
                        e *= value;

                    e *= Poly[i].Coefficient;
                    val += e;
                    
                }
                else {
                    val += Poly[i].Coefficient;
                }
                e = 1;
            }
            return val;
        }
        public Polynomial[] Derivative(Polynomial[] Poly) {

            Polynomial[] d;
            int tCount = 0;
            int polyCount = Poly.Length;

            for (int i = 0; i < polyCount; i++) {

                if (Poly[i].isVariable)
                    tCount++;
            }
            d = new Polynomial[tCount];
            tCount = 0;

            for (int i = 0; i < polyCount; i++)
            {
                int coeff, exp;
                bool isvar = true;

                if (Poly[i].isVariable)
                {
                    coeff = Poly[i].Coefficient * Poly[i].Exponent;
                    exp = Poly[i].Exponent - 1;

                    if (exp == 0)
                        isvar = false;

                    addTerm(ref d, tCount, coeff, exp, isvar);
                    tCount++;
                }
            }
            return d;
        }
        public float FindInitialValue(Polynomial[] Poly)
        {
            float init=0;
            int[] roots = new int[2];
            roots[0]=0;

            float c = CalculateValue(Poly,0);

            for (int i = 0; ; i++) {

                float v = CalculateValue(Poly,i);

                if ((v < 0 && c < 0) | (v > 0 && c > 0))
                {
                    c = v;
                    roots[0] = i;
                    continue;
                }
                else if ((c < 0 && v > 0) | (c > 0 && v < 0))
                {
                    roots[1] = i;
                    break;
                }
            }

            if(Math.Abs(0-roots[0])>Math.Abs(0-roots[1]))
                init=roots[1];
            else
                init=roots[0];

            return init;
        }
        public float NR(Polynomial[] Poly) {

            float nr = 0, n = 0;
            float x = FindInitialValue(Poly);
            Polynomial[] der = Derivative(Poly);
            n = x - (CalculateValue(Poly, x) / CalculateValue(der, x));

            do
            {
                nr = n;
                x = n;
                n = x - (CalculateValue(Poly, x) / CalculateValue(der, x));
            }
            while ((Math.Abs(nr - n) >= 0.00001f));

            return n;
        }
        private void button1_Click(object sender, EventArgs e)
        {
            float n = NR(polynomial);
            MessageBox.Show(n.ToString());
        }
    }
}