Interpolation

import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.Arrays;


/**
 * <p>Static methods for doing useful math</p><hr>
 *
 * @author  : $Author: brian $
 * @version : $Revision: 1.1 $
 *
 * <hr><p><font size="-1" color="#336699"><a href="http://www.mbari.org">
 * The Monterey Bay Aquarium Research Institute (MBARI)</a> provides this
 * documentation and code &quot;as is&quot;, with no warranty, express or
 * implied, of its quality or consistency. It is provided without support and
 * without obligation on the part of MBARI to assist in its use, correction,
 * modification, or enhancement. This information should not be published or
 * distributed to third parties without specific written permission from
 * MBARI.</font></p><br>
 *
 * <font size="-1" color="#336699">Copyright 2002 MBARI.<br>
 * MBARI Proprietary Information. All rights reserved.</font><br><hr><br>
 *
 */

public class Util{


    public static final double[] interpLinear(double[] x, double[] y, double[] xi) throws IllegalArgumentException {

        if (x.length != y.length) {
            throw new IllegalArgumentException("X and Y must be the same length");
        }
        if (x.length == 1) {
            throw new IllegalArgumentException("X must contain more than one value");
        }
        double[] dx = new double[x.length - 1];
        double[] dy = new double[x.length - 1];
        double[] slope = new double[x.length - 1];
        double[] intercept = new double[x.length - 1];

        // Calculate the line equation (i.e. slope and intercept) between each point
        for (int i = 0; i < x.length - 1; i++) {
            dx[i] = x[i + 1] - x[i];
            if (dx[i] == 0) {
                throw new IllegalArgumentException("X must be montotonic. A duplicate " + "x-value was found");
            }
            if (dx[i] < 0) {
                throw new IllegalArgumentException("X must be sorted");
            }
            dy[i] = y[i + 1] - y[i];
            slope[i] = dy[i] / dx[i];
            intercept[i] = y[i] - x[i] * slope[i];
        }

        // Perform the interpolation here
        double[] yi = new double[xi.length];
        for (int i = 0; i < xi.length; i++) {
            if ((xi[i] > x[x.length - 1]) || (xi[i] < x[0])) {
                yi[i] = Double.NaN;
            }
            else {
                int loc = Arrays.binarySearch(x, xi[i]);
                if (loc < -1) {
                    loc = -loc - 2;
                    yi[i] = slope[loc] * xi[i] + intercept[loc];
                }
                else {
                    yi[i] = y[loc];
                }
            }
        }

        return yi;
    }

    public static final BigDecimal[] interpLinear(BigDecimal[] x, BigDecimal[] y, BigDecimal[] xi) {
        if (x.length != y.length) {
            throw new IllegalArgumentException("X and Y must be the same length");
        }
        if (x.length == 1) {
            throw new IllegalArgumentException("X must contain more than one value");
        }
        BigDecimal[] dx = new BigDecimal[x.length - 1];
        BigDecimal[] dy = new BigDecimal[x.length - 1];
        BigDecimal[] slope = new BigDecimal[x.length - 1];
        BigDecimal[] intercept = new BigDecimal[x.length - 1];

        // Calculate the line equation (i.e. slope and intercept) between each point
        BigInteger zero = new BigInteger("0");
        BigDecimal minusOne = new BigDecimal(-1);

        for (int i = 0; i < x.length - 1; i++) {
            //dx[i] = x[i + 1] - x[i];
            dx[i] = x[i + 1].subtract(x[i]);
            if (dx[i].equals(new BigDecimal(zero, dx[i].scale()))) {
                throw new IllegalArgumentException("X must be montotonic. A duplicate " + "x-value was found");
            }
            if (dx[i].signum() < 0) {
                throw new IllegalArgumentException("X must be sorted");
            }
            //dy[i] = y[i + 1] - y[i];
            dy[i] = y[i + 1].subtract(y[i]);
            //slope[i] = dy[i] / dx[i];
            slope[i] = dy[i].divide(dx[i]);
            //intercept[i] = y[i] - x[i] * slope[i];
            intercept[i] = x[i].multiply(slope[i]).subtract(y[i]).multiply(minusOne);
            //intercept[i] = y[i].subtract(x[i]).multiply(slope[i]);
        }

        // Perform the interpolation here
        BigDecimal[] yi = new BigDecimal[xi.length];
        for (int i = 0; i < xi.length; i++) {
            //if ((xi[i] > x[x.length - 1]) || (xi[i] < x[0])) {
            if (xi[i].compareTo(x[x.length - 1]) > 0 || xi[i].compareTo(x[0]) < 0) {
                yi[i] = null; // same as NaN
            }
            else {
                int loc = Arrays.binarySearch(x, xi[i]);
                if (loc < -1) {
                    loc = -loc - 2;
                    //yi[i] = slope[loc] * xi[i] + intercept[loc];
                    yi[i] = slope[loc].multiply(xi[i]).add(intercept[loc]);
                }
                else {
                    yi[i] = y[loc];
                }
            }
        }

        return yi;
    }

    public static final double[] interpLinear(long[] x, double[] y, long[] xi) throws IllegalArgumentException {

        double[] xd = new double[x.length];
        for (int i = 0; i < x.length; i++) {
            xd[i] = (double) x[i];
        }

        double[] xid = new double[xi.length];
        for (int i = 0; i < xi.length; i++) {
            xid[i] = (double) xi[i];
        }

        return interpLinear(xd, y, xid);
    }
}