package com.imsl.test.example.math;

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

/**
 * <p>
 * Computes a tensor-product cubic spline least squares fit to a function.</p>
 *
 * The data for this example comes from the function \(e^x sin(x + y)\) on the
 * rectangle \([0, 3] \times [0, 5]\). This function is first sampled on a \(50
 * \times 25\) grid. Next, an attempt to recover it by using tensor-product
 * cubic splines is performed. The values of the function \(e^x sin(x + y)\) are
 * printed on a \(2 \times 2\) grid and compared with the values of the
 * tensor-product spline least-squares fit.
 *
 * @see <a href="Spline2DLeastSquaresEx1.java">Code</a>
 * @see <a href="doc-files/Spline2DLeastSquaresEx1.out">Output</a>
 */
public class Spline2DLeastSquaresEx1 {

    private static double F(double x, double y) {
        return (Math.exp(x) * Math.sin(x + y));
    }

    public static void main(String args[]) {
        int nxData = 50, nyData = 25, outData = 2;
        double[] xData = new double[nxData];
        double[] yData = new double[nyData];
        double[][] fData = new double[nxData][nyData];
        double x, y, z;

        // Set up grid
        for (int i = 0; i < nxData; i++) {
            xData[i] = 3. * (double) i / ((double) (nxData - 1));
        }
        for (int i = 0; i < nyData; i++) {
            yData[i] = 5. * (double) i / ((double) (nyData - 1));
        }

        // Compute function values on grid
        for (int i = 0; i < nxData; i++) {
            for (int j = 0; j < nyData; j++) {
                fData[i][j] = F(xData[i], yData[j]);
            }
        }

        // Compute tensor-product approximant
        Spline2DLeastSquares spline
                = new Spline2DLeastSquares(xData, yData, fData, 5, 7);

        spline.compute();
        x = spline.getErrorSumOfSquares();

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

        // Print results
        System.out.println("The error sum of squares is "
                + nf.format(x) + "\n");

        double[][] output = new double[outData * outData][5];
        for (int i = 0, idx = 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);
                output[idx][0] = x;
                output[idx][1] = y;
                output[idx][2] = F(x, y);
                output[idx][3] = z;
                output[idx][4] = Math.abs(F(x, y) - z);
                idx++;
            }
        }

        String[] labels = {"x", "y", "F(x, y)", "Fitted Values", "Error"};
        PrintMatrixFormat pmf = new PrintMatrixFormat();
        pmf.setNumberFormat(nf);
        pmf.setColumnLabels(labels);
        new PrintMatrix().print(pmf, output);
    }
}