package com.imsl.test.example.math;

import java.text.*;
import com.imsl.math.*;
/** 
 * <p>Spline2DInterpolate Example 2: Computes the tensor-product spline interpolant.</p>

* A tensor-product spline interpolant to the function 
* $$f(x,y) = x^{3} + y^2$$
* is computed. The values of the interpolant and the error on a \(4 \times 4\) 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.

 * @see <a href="Spline2DInterpolateEx2.java">Code</a>
 * @see <a href="doc-files/Spline2DInterpolateEx2.out">Output</a>
 */

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)));
                }
            }
        }
    }
}