Example 4

using System;
using 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       
        Console.Out.WriteLine("   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);
                Console.Out.WriteLine(x.ToString("0.0000") + "  " + 
                    y.ToString("0.0000") + "    " + 
                    FI(x, y).ToString("0.0000") + "    " + 
                    z.ToString("0.0000") + "    " + 
                    Math.Abs(FI(x,y)-z).ToString("0.0000"));
            }
        }
    }
}

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