Example 2

A tensor-product spline interpolant to a function $f(x,y) = x^{3} + y^2$ is computed. The values of the interpolant and the error on a 4 x 4 grid are displayed. Notice that the first interpolant with order = 3 does not reproduce the cubic data, while the second interpolant with order = 6 does reproduce the data.


import java.text.*;
import com.imsl.math.*;

public class Spline2DInterpolateEx2 {

    private static double F(double x, double y) {
        return (x * x * x + y * y);
    }

    public static void main(String args[]) {
        int nData = 7;
        int outData = 4;
        double[][] fData = new double[nData][nData];
        double[] xData = new double[nData];
        double[] yData = new double[nData];
        double x, y, z;

        // Set up grid
        for (int i = 0; i < nData; i++) {
            xData[i] = yData[i] = (double) i / ((double) (nData - 1));
        }

        for (int i = 0; i < nData; i++) {
            for (int j = 0; j < nData; j++) {
                fData[i][j] = F(xData[i], yData[j]);
            }
        }

        NumberFormat nf = NumberFormat.getInstance();
        nf.setMaximumFractionDigits(4);
        nf.setMinimumFractionDigits(4);

        for (int order = 3; order < 7; order += 3) {
            // Compute tensor-product interpolant
            Spline2DInterpolate spline
                    = new Spline2DInterpolate(xData, yData,
                            fData, order, order);

            // Print results
            System.out.println("\nThe order of the spline is " + order);
            System.out.println("   x        y     F(x, y)   "
                    + "Interpolant   Error");

            for (int i = 0; i < outData; i++) {
                x = (double) i / (double) (outData);

                for (int j = 0; j < outData; j++) {
                    y = (double) j / (double) (outData);
                    z = spline.value(x, y);

                    System.out.println(nf.format(x) + "   " + nf.format(y)
                            + "   " + nf.format(F(x, y)) + "       "
                            + nf.format(z) + "     "
                            + nf.format(Math.abs(F(x, y) - z)));
                }
            }
        }
    }
}

Output


The order of the spline is 3
   x        y     F(x, y)   Interpolant   Error
0.0000   0.0000   0.0000       0.0000     0.0000
0.0000   0.2500   0.0625       0.0625     0.0000
0.0000   0.5000   0.2500       0.2500     0.0000
0.0000   0.7500   0.5625       0.5625     0.0000
0.2500   0.0000   0.0156       0.0158     0.0002
0.2500   0.2500   0.0781       0.0783     0.0002
0.2500   0.5000   0.2656       0.2658     0.0002
0.2500   0.7500   0.5781       0.5783     0.0002
0.5000   0.0000   0.1250       0.1250     0.0000
0.5000   0.2500   0.1875       0.1875     0.0000
0.5000   0.5000   0.3750       0.3750     0.0000
0.5000   0.7500   0.6875       0.6875     0.0000
0.7500   0.0000   0.4219       0.4217     0.0002
0.7500   0.2500   0.4844       0.4842     0.0002
0.7500   0.5000   0.6719       0.6717     0.0002
0.7500   0.7500   0.9844       0.9842     0.0002

The order of the spline is 6
   x        y     F(x, y)   Interpolant   Error
0.0000   0.0000   0.0000       0.0000     0.0000
0.0000   0.2500   0.0625       0.0625     0.0000
0.0000   0.5000   0.2500       0.2500     0.0000
0.0000   0.7500   0.5625       0.5625     0.0000
0.2500   0.0000   0.0156       0.0156     0.0000
0.2500   0.2500   0.0781       0.0781     0.0000
0.2500   0.5000   0.2656       0.2656     0.0000
0.2500   0.7500   0.5781       0.5781     0.0000
0.5000   0.0000   0.1250       0.1250     0.0000
0.5000   0.2500   0.1875       0.1875     0.0000
0.5000   0.5000   0.3750       0.3750     0.0000
0.5000   0.7500   0.6875       0.6875     0.0000
0.7500   0.0000   0.4219       0.4219     0.0000
0.7500   0.2500   0.4844       0.4844     0.0000
0.7500   0.5000   0.6719       0.6719     0.0000
0.7500   0.7500   0.9844       0.9844     0.0000

Link to Java source.