package Maths;

import java.util.TreeMap;

public class SimpsonIntegration{

 /*
 * Calculate definite integrals by using Composite Simpson's rule.
 * Wiki: https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule
 * Given f a function and an even number N of intervals that divide the integration interval e.g. [a, b],
 * we calculate the step h = (b-a)/N and create a table that contains all the x points of
 * the real axis xi = x0 + i*h and the value f(xi) that corresponds to these xi.
 *
 * To evaluate the integral i use the formula below:
 * I = h/3 * {f(x0) + 4*f(x1) + 2*f(x2) + 4*f(x3) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)}
 *
 */

 public static void main(String[] args) {
 SimpsonIntegration integration = new SimpsonIntegration();

 // Give random data for the example purposes
 int N = 16;
 double a = 1;
 double b = 3;

 // Check so that N is even
 if(N%2 != 0){
 System.out.println("N must be even number for Simpsons method. Aborted");
 System.exit(1);
 }

 // Calculate step h and evaluate the integral
 double h = (b-a) / (double) N;
 double integralEvaluation = integration.simpsonsMethod(N, h, a);
 System.out.println("The integral is equal to: " + integralEvaluation);
 }

 /*
 * @param N: Number of intervals (must be even number N=2*k)
 * @param h: Step h = (b-a)/N
 * @param a: Starting point of the interval
 * @param b: Ending point of the interval
 *
 * The interpolation points xi = x0 + i*h are stored the treeMap data
 *
 * @return result of the integral evaluation
 */
 public double simpsonsMethod(int N, double h, double a){
 TreeMap<Integer, Double> data = new TreeMap<>(); // Key: i, Value: f(xi)
 double temp;
 double xi = a; // Initialize the variable xi = x0 + 0*h

 // Create the table of xi and yi points
 for(int i=0; i<=N; i++){
 temp = f(xi); // Get the value of the function at that point
 data.put(i, temp);
 xi += h; // Increase the xi to the next point
 }

 // Apply the formula
 double integralEvaluation = 0;
 for(int i=0; i<data.size(); i++){
 if(i == 0 || i == data.size()-1) {
 integralEvaluation += data.get(i);
 System.out.println("Multiply f(x" + i + ") by 1");
 }
 else if(i%2 == 1) {
 integralEvaluation += (double) 4 * data.get(i);
 System.out.println("Multiply f(x" + i + ") by 4");
 }
 else {
 integralEvaluation += (double) 2 * data.get(i);
 System.out.println("Multiply f(x" + i + ") by 2");
 }
 }

 // Multiply by h/3
 integralEvaluation = h/3 * integralEvaluation;

 // Return the result
 return integralEvaluation;
 }

 // Sample function f
 // Function f(x) = e^(-x) * (4 - x^2)
 public double f(double x){
 return Math.exp(-x) * (4 - Math.pow(x, 2));
// return Math.sqrt(x);
 }

}