Example 4

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

public class Spline2DInterpolateEx4 {
    
    // Define function
    private static double F(double x, double y) {
        return (x*x*x+y*y);
    }
    
    // The integral of F from 0 to x and 0 to y
    private static double FI(double x, double y) {
        return (y*x*x*x*x/4.0 + x*y*y*y/3.0);
    }
    
    public static void main(String args[]) {
        int nData = 11, 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);
        
        // Print results
        NumberFormat nf = NumberFormat.getInstance();
        nf.setMaximumFractionDigits(4);
        nf.setMinimumFractionDigits(4);
        
        System.out.println("   x       y     FI(x, y)  Integral   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.integral(0.0, x, 0.0, y);
                System.out.println(nf.format(x) + "  " + nf.format(y) + 
                        "    " + nf.format(FI(x, y)) + "    " + 
                        nf.format(z) + "    " + 
                        nf.format(Math.abs(FI(x,y)-z)));
            }
        }
    }
}

Output

   x       y     FI(x, y)  Integral   Error
0.3333  0.3333    0.0051    0.0051    0.0000
0.3333  0.6667    0.0350    0.0350    0.0000
0.6667  0.3333    0.0247    0.0247    0.0000
0.6667  0.6667    0.0988    0.0988    0.0000