/*      This example of the use of both BiCubicInterpolation and BiCubicSpline
        demonstrates interpolation within a calculated data set
            y = x + 2.x^2 - 3.x^3
        allowing a comparison of the use of gradients calculated  by numerical differentiation

        Michael Thomas Flanagan
        Created:    May 2003
        Updated:    1 May 2005, 15 January 2011
*/

import flanagan.interpolation.*;

public class CubicExampleOne{

        public static void main(String arg[]){


        // Array of x
        double[] x = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
        double[] y = new double[6];             // Array of y
        double[] dydx = new double[6];          // Array of gradients, dy/dx
        double xx = 0.0;                        // x value at interpolation point
        double y1 = 0.0;                        // interpolated y value using BiCubicInterpolation with user supplied
                                                //   analytically calculated gradients
        double y2 = 0.0;                        // interpolated y value using BiCubicInterpolation with
                                                //   numerical differencing using supplied data points
        double y3 = 0.0;                        // interpolated y value using BiCubicInterpolation with
                                                //   numerical differencing using interpolation
        double y4 = 0.0;                        // interpolated y value using BiCubicSpline
        double yt = 0.0;                        // true y value

        // Calculate the data
        for(int i=0; i<6; i++){
            y[i] = x[i] + 2.0*x[i]*x[i] - 3.0*x[i]*x[i]*x[i];
            dydx[i] = 1.0 + 4.0*x[i] - 9.0*x[i]*x[i];
        }

        // Create an instance of CubicInterpolation with supplied analytically determined derivatives
        CubicInterpolation ci1 = new CubicInterpolation(x, y, dydx);

        // Create an instance of CubicInterpolation with calculated derivatives
        // using supplied data points
        CubicInterpolation ci2 = new CubicInterpolation(x, y, 0);

        // Create an instance of CubicInterpolation with calculated derivatives
        // using numerical differencing and interpolation
        CubicInterpolation ci3 = new CubicInterpolation(x, y, 1);

        // Create an instance of CubicSpline
        CubicSpline cs = new CubicSpline(x, y);


        // interpolation
        xx = 0.5;
        for(int i=0; i<5; i++){
            yt = xx + 2.0*xx*xx - 3.0*xx*xx*xx;

            System.out.println("Interpolation at x = " + xx);
            System.out.println("The true y value is         " + yt);

            y1 = ci1.interpolate(xx);
            System.out.println(" CubicInterpolation with supplied analytical gradients:");
            System.out.println(" The interpolated y value is " + y1);

            y2 = ci2.interpolate(xx);
            System.out.println(" CubicInterpolation with numerical differencing of supplied data points:");
            System.out.println(" The interpolated y value is " + y2);

            y3 = ci3.interpolate(xx);
            System.out.println(" CubicInterpolation with numerical differencing using interpolation:");
            System.out.println(" The interpolated y value is " + y3);

            y4 = cs.interpolate(xx);
            System.out.println(" CubicSpline interpolation:");
            System.out.println(" The interpolated y value is " + y4);
            System.out.println(" ");

            xx += 1.0;
        }

     }
}