package com.company;

import java.math.BigDecimal;
import java.math.RoundingMode;
import java.util.ArrayList;
import java.util.Collections;

public class Algorithm {
    //steps
    private static double t=0.05;
    //bounds
    private static final double a=3.0;
    private static final double b=4.0;
    //initial values
    private static final double t0=3.0;
    private static final double y10=3.0;
    private static final double y11=3.1525019829;
    private static final double y12=3.3100042804;
    private static final double y20=3.0;
    private static final double y21=3.1000093976;
    private static final double y22=3.2000185502;
    //

    //plases for rounding
    private static final int PLASES = 10;

    //Algorithm
    private void doAlgorithm(double t, double num, ArrayList<Double> y1Array, ArrayList<Double> y2Array,ArrayList<Double> tjArray){

        double y1,y2;

        y1Array.add(y10);
        y1Array.add(y11);
        y1Array.add(y12);
        y2Array.add(y20);
        y2Array.add(y21);
        y2Array.add(y22);

        double tj=t0;
        for(int i=0;i<3;i++, tj+=t){
            tjArray.add(tj);
        }
        //
        for(int j=2; j<num; j++, tj+=t){ //j=0,19
            tjArray.add(tj);
            //iteration
            y1=y11(y1Array.get(j),y2Array.get(j),y2Array.get(j-1),y2Array.get(j-2));
            y2=y21(tjArray.get(j),tjArray.get(j-1),tjArray.get(j-2), y1Array.get(j),y1Array.get(j-1),y1Array.get(j-2),y2Array.get(j),y2Array.get(j-1),y2Array.get(j-2));
            //add new elements
            y1Array.add(y1);
            y2Array.add(y2);
        }
    }
    //////////////////////////////////////// run algorithm
    public void run(){
        int num=(int)((b-a)/t); //(b-a)/t
        ArrayList<Double> y1Array=new ArrayList<>();
        ArrayList<Double> y2Array=new ArrayList<>();
        ArrayList<Double> tjArray=new ArrayList<>();
        doAlgorithm(t,num,y1Array,y2Array,tjArray);

        //calculate error
        ArrayList<Double> y1Error=new ArrayList<>();
        ArrayList<Double> y2Error=new ArrayList<>();
        calculateError(num,tjArray,y1Array,y2Array,y1Error,y2Error);
        double error = Math.max(Collections.max(y1Error),Collections.max(y2Error));

        //output
        print(num,tjArray,y1Array,y2Array, error);

    }
    private void calculateError(int num, ArrayList<Double> tjArray,ArrayList<Double> y1Array,ArrayList<Double> y2Array,ArrayList<Double> y1Error,ArrayList<Double> y2Error){
        double tj;
        for(int i=0;i<num;i++){
            tj=tjArray.get(i);
            y1Error.add(round(Math.abs(u(tj)-y1Array.get(i))));
            y2Error.add(round(Math.abs(du(tj)-y2Array.get(i))));

//            System.out.printf("%2s u %14s u'%14s \n",i, round(Math.abs(u(tj)-y1Array.get(i))),round(Math.abs(du(tj)-y2Array.get(i))));
        }
    }
    //////////////////////////////////////// print output
    private void print(int num, ArrayList<Double> tjArray,ArrayList<Double> y1Array,ArrayList<Double> y2Array, double error){
        System.out.printf("%2s%5s%14s%14s%14s%14s\n","j", "tj","u","u'", "y1", "y2");
        double tj;
        for(int i=0;i<num;i++){
            tj=tjArray.get(i);
            System.out.printf("%2s%5s%14s%14s%14s%14s\n",i, round(tj),round(u(tj)),round(du(tj)), round(y1Array.get(i)), round(y2Array.get(i)));
        }
        System.out.printf("Error is %14s\n",error);
    }
    //////////////////////////////////////// round
    private double round(double value) {
        if (PLASES < 0) throw new IllegalArgumentException();

        BigDecimal bd = new BigDecimal(Double.toString(value));
        bd = bd.setScale(PLASES, RoundingMode.HALF_UP);
        return bd.doubleValue();
    }
    //////////////////////////////////////// u(t)
    public double u(double t){
        return t*t-3.0*t+3.0;
    }
    //////////////////////////////////////// u'(t)
    public double du(double t){
        return 2.0*t-3.0;
    }
    ////////////////////////////////////////   y1.j+1,y2.j+1
    //y1.j+1=F(y1.j,y2.j,y2.j-1,y2.j-2)
    public double y11(double y1a,double y2a,double y2b,double y2c){
        return y1a+t/12.0*(23.0*y2a-16.0*y2b+5.0*y2c);
    }
    //y2.j+1=F(y2.j,q1,q2,q3)
    public double y21(double tja,double tjb,double tjc, double y1a, double y1b, double y1c,double y2a,double y2b,double y2c){
        return y2a+t/12.0*(23.0*f2(tja, y1a,y2a)-16.0*f2(tjb, y1b,y2b)+5.0*f2(tjc, y1c,y2c));
    }
    ////////////////////////////////////////   f1,f2
    //f1=y2.j
    public double f1(double y2){
        return y2;
    }
    //f2=...
    public double f2(double tj, double y1, double y2){
        double numerator=tj+2.0+3.0*(tj-2.0)*y2-4.0*y1;
        double denumenator=(tj-2.0)*(tj-2.0);
        return numerator/denumenator;
    }
}