package calculator;
import java.util.*;



public class Calc1 {

     public static final String ERR_NUMIN = "Non numerical input!";

     public static double function(double[] a, double x) {

         return a[3]*Math.pow(x, 5) + a[4]*Math.pow(x, 4) + a[5]*Math.pow(x, 3) + a[6]*Math.pow(x, 2) + a[7]*x + a[8];

     }

     public static double exact(double[] a) {
         return (((a[3]*Math.pow(a[0], 6))/6) + ((a[4]*Math.pow(a[0], 5))/5) + ((a[5]*Math.pow(a[0], 4))/4) + ((a[6]*Math.pow(a[0], 3))/3) + ((a[7]*Math.pow(a[0], 2))/2) + (a[8]*a[0])) - (((a[3]*Math.pow(a[1], 6))/6) + ((a[4]*Math.pow(a[1], 5))/5) + ((a[5]*Math.pow(a[1], 4))/4) + ((a[6]*Math.pow(a[1], 3))/3) + ((a[7]*Math.pow(a[1], 2))/2) + (a[8]*a[1]));
     }

     public static  double simpsons(double midpoint, double trapezoid) {
        double total = ((2.0*midpoint)+trapezoid)/3;
        return total;
     }

     public static double trapezoid(double[] a) {
          double interval = 0;
          double looped = 0;
          double x = 0;

          interval = (a[0] - a[1]) / a[2];

          looped = 0.5 * (function(a, a[1]) + function(a, a[0]));

          for (int i = 1; i < a[2]; i++) {
             x = a[1] + i * interval;
             looped += function(a, x);
          }

          return looped * interval;
     }

     public static double midpoint(double[] a) {

         double dx = 0;
         double looped = 0;
         double total = 0;

         dx = (a[0]-a[1])/a[2];

         for(int i = (int) a[1]+1; i<a[0]; i += dx) {
             looped += function(a, i);
         }

         total = dx*looped;


        return total;
     }

     public static double percentError(double Exact, double Theoretical) {
         return Math.abs(((Theoretical-Exact)/Exact)*100);
     }

    public static void main(String[] args) {

        double[] userData = new double[9];
        Scanner input = new Scanner(System.in);

        System.out.printf("%s", "Input the limits of integration(maximum first):");
        try {
            userData[0] = input.nextDouble();
            userData[1] = input.nextDouble();
        }
        catch(Exception e) {
            System.out.printf("%s%n", "ERR_NUMIN");
        }

        System.out.printf("%s%n", "Enter the number of sub intervals");
        try {
            userData[2] = input.nextDouble();
        }
        catch(Exception e) {
            System.out.printf("%s%n", "ERR_NUMIN");
        }

        System.out.printf("%s%n", "Enter the coefficients for a 5th degree polynomial");
        try {
            userData[3] = input.nextDouble();
            userData[4] = input.nextDouble();
            userData[5] = input.nextDouble();
            userData[6] = input.nextDouble();
            userData[7] = input.nextDouble();
            userData[8] = input.nextDouble();
        }
        catch(Exception e) {
            System.out.printf("%s%n", "ERR_NUMIN");
        }

        System.out.printf("%n%s%.2f%n%n", "Exact Value: ", exact(userData));
        System.out.printf("%s%.2f%n%s%.2f%s%n%n", "Trapezoid Rule: ", trapezoid(userData), "Percent Error: ", percentError(exact(userData), trapezoid(userData)), "%");
        System.out.printf("%s%.2f%n%s%.2f%s%n%n", "Simpsons: ", simpsons(midpoint(userData), trapezoid(userData)), "Percent Error: ", percentError(exact(userData), simpsons(midpoint(userData), trapezoid(userData))), "%");
        System.out.printf("%s%.2f%n%s%.2f%s%n", "Midpoint Rule: ", midpoint(userData), "Percent Error: ", percentError(exact(userData), midpoint(userData)), "%");

        input.close();

    }

}