package labs import utils Point import utils Spline Spline interpolati

package labs;

import utils.Point;
import utils.Spline;

/*
 * Spline interpolation of function
 */

public class Lab1 {
	private static double function(double arg) {
		return Math.sin(arg)*Math.cos(arg);
	}
	
	private static void printDiv(Spline[] splines, Point[] nodes){
		for(Integer i = 0; i < splines.length; i++) {	
			System.out.println(" " + i.toString() + "\t" + 
						Double.toString(
							Math.abs(
									function(nodes[i].x) - splines[i].calc(nodes[i].x)			
					)));
		}
		if(splines.length != nodes.length)
			System.out.println(" " + Integer.toString(splines.length).toString() + "\t" + 
					Double.toString(
						Math.abs(
								function(nodes[splines.length].x) - splines[splines.length-1].calc(nodes[splines.length].x)
				)));
	}
	private static void print(Spline[] splines, Point[] nodes){
		for(Integer i = 0; i < splines.length; i++) {
			System.out.println(" " + i.toString() + "\t" + 
								Double.toString(function(nodes[i].x)) + "\t" + 
								Double.toString(splines[i].calc(nodes[i].x)));
		}
		
		if(splines.length != nodes.length)
			System.out.println(" " + Integer.toString(splines.length) + "\t" + 
				Double.toString(function(nodes[splines.length].x)) + "\t" + 
				Double.toString(splines[splines.length-1].calc(nodes[splines.length].x)));
	}
	
	private static Spline[] progon(Point[] nodes, double h){
		Spline[] splines = new Spline[nodes.length-1];
		for(int i = 0; i < nodes.length-1; i++) splines[i] = new Spline();
		
		for(int i = 0; i < splines.length; i++) {
			splines[i].a = nodes[i].y;
		}
		
		
		double[] alpha = new double[splines.length];
		double[] betta = new double[splines.length];
		
		for(int i = 1; i < splines.length; i++) {
			alpha[i] = (-1)/(alpha[i-1] + 4);
			betta[i] = ((3*(nodes[i-1].y - 2*nodes[i].y + nodes[i+1].y))/(h*h) - betta[i-1])/(alpha[i-1] + 4);
		}
		
		
		
		splines[splines.length-1].c = ((3*(nodes[splines.length-2].y - 2*nodes[splines.length-1].y + nodes[splines.length].y))/(h*h) - betta[splines.length-1])/(4 + alpha[splines.length-1]);
		for(int i = splines.length-2; i > 0; i--) {
			splines[i].c = alpha[i+1]*splines[i+1].c + betta[i+1];
		}
		return splines;
	}
	
	public static void start(int steps) {
		System.out.println("Steps: " + Integer.toString(steps));
		
		double start = 0.0;
		double finish = Math.PI / 2;
		
		Point[] nodes = new Point[steps+1];
		for(int i = 0; i < steps+1; i++) nodes[i] = new Point();
			
		for(int i = 0; i <= steps; i++) {
			nodes[i].x = ((finish - start)*i) / steps;
			nodes[i].y = function(nodes[i].x);
		}
		Point[] mediansFunc = new Point[steps];
		for(int i = 0; i < steps; i++) mediansFunc[i] = new Point();
		
		for(int i = 0; i < steps; i++) {
			mediansFunc[i].x = (nodes[i].x + nodes[i+1].x)/2;
			mediansFunc[i].y = function(mediansFunc[i].x);
		}
		
		double h = (finish - start)/steps;
		//fill A and C
		Spline[] splines = progon(nodes, h);
		
		//fill X
		for(int i = 0; i < steps; i++) {
			splines[i].x = nodes[i].x;
		}
		
		//fill D
		for(int i = 0; i < steps; i++) {
			splines[i].d = ( splines[ (i+1)%steps ].c - splines[i].c) / (3 * h);
		}
		
		//fill B
		for(int i = 0; i < steps; i++) {
			splines[i].b = (nodes[i+1].y - nodes[i].y)/h - (h/3)*(splines[(i+1)%steps].c + 2*splines[i].c);  
		}
		
		print(splines, nodes);
		System.out.println();
		printDiv(splines, nodes);
		System.out.println();
		print(splines, mediansFunc);
		System.out.println();
		printDiv(splines, mediansFunc);
	}
}