/*     Example of the use of the class Integration demonstrating
       the use of several of the numerical integration methods
       in integrating one of two functions, y = a + x*x and y = b + c*x
       using the static methods.

       Michael Thomas Flanagan

       July 2006
*/

import flanagan.integration.Integration;
import flanagan.integration.IntegralFunction;

// Class to evaluate the function y = a + x*x for a given value of x (function 1).
class Funct1 implements IntegralFunction{

    private double a = 0.0D;

    public double function(double x){
        double y = a + x*x;
        return y;
    }

    public void setA(double a){
        this.a = a;
    }
}

// Class to evaluate the function y = b + c*x for a given value of x (function 2).
class Funct2 implements IntegralFunction{

    private double b = 0.0D, c = 1.0D;

    public double function(double x){
        double y = b + c*x;
        return y;
    }

    public void setB(double b){
        this.b = b;
    }

    public void setC(double c){
        this.c = c;
    }
}


// Class to demonstrate numerical integration methods in class Integration.
public class IntegrationExample2{

    public static void main(String[] arg){

        // Create instances of the classes holding the function evaluation methods
        Funct1 f1 = new Funct1();
        Funct2 f2 = new Funct2();

        // Assign values to constants in the functions
        f1.setA(10.5);

        f2.setB(7.0);
        f2.setC(-2.3);

        // Variable declarations
        double lowerLimit = 1.0D;
        double upperLimit = 3.0D;
        int nPoints = 32;
        int nIntervals = 1;

        // Example of Gauss-Legendre quadrature on function 1
        // Call Gauss-Legendre quadrature method to operate on function 1
        double integralSum0 = Integration.gaussQuad(f1, lowerLimit, upperLimit, nPoints);

        // Output the result
        System.out.println("The " + nPoints + " point Gausian-Legendre integral of function 1 between the limits " + lowerLimit + " and " + upperLimit + " is " + integralSum0);

        // Call Gauss-Legendre quadrature method to operate on function 2 with the same limits and twice the number of points
        nPoints *= 2;
        integralSum0 = Integration.gaussQuad(f2, lowerLimit, upperLimit, nPoints);
        System.out.println("The  " + nPoints + " point Gausian-Legendre integral of function 2 between the limits " + lowerLimit + " and " + upperLimit + " is " + integralSum0);

        // Example of Gauss-Legendre Quadrature and Trapeziodal rule applied to function 1
        // Reset limits and number of points or intervals
        lowerLimit = 0.0D;
        upperLimit = 5.0D;
        nPoints = 16;
        nIntervals = 1000;

        // Call both methods to operate on function 1
        double integralSum1 = Integration.gaussQuad(f1, lowerLimit, upperLimit, nPoints);
        double integralSum2 = Integration.trapezium(f1, lowerLimit, upperLimit, nIntervals);

        System.out.println("The " + nPoints + " point Gausian-Legendre integral of function 1 between the limits " + lowerLimit + " and " + upperLimit + " is " + integralSum1);
        System.out.println("The " + nIntervals + " interval trapezium integral of function 1 between the limits " + lowerLimit + " and " + upperLimit + " is " + integralSum2);

        // Example of Trapeziodal rule and backward rectangular rule applied to function 2 after function constants have been altered
        // Reset b and c
        f2.setB(3.1D);
        f2.setC(5.5D);

        // Reset limits and number of intervals
        lowerLimit = 0.0D;
        upperLimit = 10.0D;
        nIntervals = 5000;

        // Call both methods to operate on function 2
        integralSum1 = Integration.trapezium(f2, lowerLimit, upperLimit, nIntervals);
        integralSum2 = Integration.backward(f2, lowerLimit, upperLimit, nIntervals);

        System.out.println("The " + nIntervals + " interval trapezium integral of function 2 between the limits " + lowerLimit + " and " + upperLimit + " is " + integralSum1);
        System.out.println("The " + nIntervals + " interval backward rectangular integral of function 2 between the limits " + lowerLimit + " and " + upperLimit + " is " + integralSum2);
    }
}