package tscore;

/* File :Simpson1_3Integration.java

* Project: Math Tools in Java

* Author : Wachara R.

* First Released: Thu 8 Mar 2007.

* Last Updated : Thu 8 Mar 2007.

*/

//import common.Function;

/** Integration of given function from lower limit

to upper limit using the Simpson 1/3 method.

*/

public class Simpson1_3Integration extends Integrator{

/** Constructor.

* @param function the function to integration.

* @param lower the lower limit of integration.

* @param upper the upper limit of integration.

* @param intervals the number of equal-width intervals

*/

public Simpson1_3Integration (Function function, double lower, double upper, int intervals){

super(function, lower, upper,intervals);

try {

IntegrationResult = integrate();

} catch (IntegrationException msg) {

System.out.println( "Error : "+ msg);

}

}

double integrate() throws IntegrationException {

if(intervals <=0) throw new IntegrationException(IntegrationException.INVALID_INTERVALS);

double h = (upper - lower)/(2*intervals); // half of interval width

double area = 0;

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

double x1 = lower + 2*i*h;

area += findAreaUnderCurve(x1,h);

}

return area;

}

/** Evaluate the area under parabolic curve

* @param x1 the left bound of the region

* @param h the interval width

*/

double findAreaUnderCurve(double x1, double h){

// area of the parabolic region = h/3(f(-h) +4f(0) +f(h))

double x2 = x1 + h; // middle point

double x3 = x2 + h; // rightmost point

double y1 = function.Of(x1);

double y2 = function.Of(x2);

double y3 = function.Of(x3);

return (h*(y1 + 4*y2 +y3)/3); // area under parabolic curve element

}

}