//interpolation
//this takes experimental data for x and f(x)
//the data is used to calculate the values for 
//the function in areas where we have no data


//this example uses hardcoded data
//f(x) = cube root of x


public class interpolation
{
    
    public static void main ( String args[] )
    {
	int arraysize = 5;
	double x[] = { 4.0, 4.5, 5.5, 6.0, 7.0 };
	double f_of_x[] = { 1.58740, 1.65096, 1.76517, 1.81712, 1.91293 };
	
	double x1[] = new double[arraysize];
	double x2[] = new double[arraysize];
	double x3[] = new double[arraysize];
	double x4[] = new double[arraysize];
		
	//initialize stuff
	for ( int i=0; i<arraysize; i++){
	    x1[i] = 0.0;
	    x2[i] = 0.0;
	    x3[i] = 0.0;
	    x4[i] = 0.0;
	
	}
	
	//calculate differences
	for ( int i=0; i<(arraysize-1); i++ ){
	    x1[i] = (f_of_x[i] - f_of_x[i+1])/(x[i] - x[i+1]);
	}
	
	for ( int i=0; i<(arraysize-2); i++ ){
	    x2[i] = (x1[i] - x1[i+1])/(x[i] - x[i+2]);
	}
	
	for ( int i=0; i<(arraysize-3); i++ ){
	    x3[i] = (x2[i] - x2[i+1])/(x[i] - x[i+3]);
	}
	
	for ( int i=0; i<(arraysize-4); i++ ){
	    x4[i] = (x3[i] - x3[i+1])/(x[i] - x[i+4]);
	}
	
	
	System.out.println();
	System.out.println ( "Interpolation of cube root of x for x=5 " );
	System.out.println ( " x " + "\t" + "f(x)" );
	
	for ( int i=0; i<arraysize; i++){
	    System.out.println ( x[i] + "\t" + f_of_x[i]);
	    
	    if ( x1[i] != 0 ) System.out.println ( "\t\t" + x1[i] );
	    if ( x2[i] != 0 ) System.out.println ( "\t\t\t" + x2[i] );
	    if ( x3[i] != 0 ) System.out.println ( "\t\t\t\t" + x3[i] );
	    if ( x4[i] != 0 ) System.out.println ( "\t\t\t\t\t" + x4[i] );
	}
	
	
	//now using that data calclulate f(5)
	double q = 5.0;
	double result = 0.0;
	
	result = f_of_x[0] + ( q - x[0] ) * ( x1[0] ) +
	    ( q - x[0] ) * ( q - x[1] ) * ( x2[0] ) +
	    ( q - x[0] ) * ( q - x[1] ) * ( q - x[2] ) * ( x3[0] ) +
	    ( q - x[0] ) * ( q - x[1] ) * ( q - x[2] ) * ( q - x[3] ) * ( x4[0] );
	
	System.out.println();
	System.out.println ( "result = " + f_of_x[0] + " + " + ( q - x[0] ) + " * " + ( x1[0] ) + " + " );
	System.out.println ( "\t\t " + ( q - x[0] ) + " * " +  ( q - x[1] ) + " * " + ( x2[0] ) + " + " );
	System.out.println ( "\t\t " + ( q - x[0] ) + " * " + ( q - x[1] ) + " * " +  ( q - x[2] ) + " * " + ( x3[0] ) + " + " );
	System.out.println ( "\t\t" + ( q - x[0] ) + " * " +  ( q - x[1] ) + " * " +  ( q - x[2] ) + " * " +  ( q - x[3] ) + " * " + ( x4[0] ));
	System.out.println ();
	System.out.println ( "Result: " + result );
	System.out.println();
	
	
    
    }
    
    
}