package com.imsl.test.example.math;

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

/**
 * <p>
 * Spline2DInterpolate Example 1: Computes a 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.
 *
 * @see <a href="Spline2DInterpolateEx1.java">Code</a>
 * @see <a href="doc-files/Spline2DInterpolateEx1.out">Output</a>
 */
public class Spline2DInterpolateEx1 {

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