Example 3

A spline interpolant

to a function

is constructed. Then, the values of the partial derivative $\frac{{\partial ^3 s\left( {x,y} \right)}}{{\partial x^2 2y}}$ and the error are computed on a 4 x 4 grid.


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

public class Spline2DInterpolateEx3 {

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

    private static double F21(double x, double y) {
        return (6.0 * x * 2.0 * y);
    }

    public static void main(String args[]) {
        int nData = 11;
        int outData = 2;
        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]);
            }
        }

        // Compute tensor-product interpolant
        Spline2DInterpolate spline
                = new Spline2DInterpolate(xData, yData, fData);

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

        // Print results
        System.out.println("   x        y     F21(x, y)   "
                + "21InterpDeriv   Error");
        for (int i = 0; i < outData; i++) {
            x = (double) (1 + i) / (double) (outData + 1);

            for (int j = 0; j < outData; j++) {
                y = (double) (1 + j) / (double) (outData + 1);
                z = spline.derivative(x, y, 2, 1);
                System.out.println(nf.format(x) + "   " + nf.format(y) + "    "
                        + nf.format(F21(x, y)) + "        " + nf.format(z)
                        + "       " + nf.format(Math.abs(F21(x, y) - z)));
            }
        }
    }
}

Output

   x        y     F21(x, y)   21InterpDeriv   Error
0.3333   0.3333    1.3333        1.3333       0.0000
0.3333   0.6667    2.6667        2.6667       0.0000
0.6667   0.3333    2.6667        2.6667       0.0000
0.6667   0.6667    5.3333        5.3333       0.0000

Link to Java source.