Computes the integral of the piecewise linear function through the given points (i, y[i]) using the trapezoidal method. - Java java.lang

Java examples for java.lang:Math Calculation

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Description

Computes the integral of the piecewise linear function through the given points (i, y[i]) using the trapezoidal method.

Demo Code

/**//from  w ww.j  a  va 2 s . com
 * Java Modular Image Synthesis Toolkit (JMIST)
 * Copyright (C) 2008-2013 Bradley W. Kimmel
 *
 * Permission is hereby granted, free of charge, to any person
 * obtaining a copy of this software and associated documentation
 * files (the "Software"), to deal in the Software without
 * restriction, including without limitation the rights to use,
 * copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following
 * conditions:
 *
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 * OTHER DEALINGS IN THE SOFTWARE.
 */
//package com.java2s;

import java.util.Iterator;

public class Main {
    /**
     * Computes the integral of the piecewise linear function through the given
     * points (<code>i</code>, <code>y[i]</code>) using the trapezoidal
     * method.
     * @param y The y-coordinates of the vertices of the piecewise linear
     *     function to integrate.
     * @return The integral of the piecewise linear function.
     * @throws IllegalArgumentException if <code>y.length == 0</code>.
     */
    public static double trapz(double[] y) {
        if (y.length == 0) {
            throw new IllegalArgumentException("y.length == 0");
        }
        double value = 0.0;
        double y0 = y[0];
        for (int i = 0; i < y.length; i++) {
            double y1 = y[i];
            double ym = y0 + y1;
            value += ym;
            y0 = y1;
        }
        return value / 2.0;
    }

    /**
     * Computes the integral of the piecewise linear function through the given
     * points (<code>x[i]</code>, <code>y[i]</code>) using the trapezoidal
     * method.
     * @param x The x-coordinates of the vertices of the piecewise linear
     *     function to integrate.
     * @param y The y-coordinates of the vertices of the piecewise linear
     *     function to integrate.
     * @return The integral of the piecewise linear function.
     * @throws IllegalArgumentException if <code>x.length != y.length</code>.
     * @throws IllegalArgumentException if <code>y.length == 0</code>.
     */
    public static double trapz(double[] x, double[] y) {
        if (x.length != y.length) {
            throw new IllegalArgumentException("x.length != y.length");
        }
        if (y.length == 0) {
            throw new IllegalArgumentException("y.length == 0");
        }
        double value = 0.0;
        double x0 = x[0];
        double y0 = y[0];
        for (int i = 1; i < y.length; i++) {
            double x1 = x[i];
            double y1 = y[i];
            double dx = x1 - x0;
            double ym = y0 + y1;
            value += dx * ym;
            x0 = x1;
            y0 = y1;
        }
        return value / 2.0;
    }

    /**
     * Computes the integral of the piecewise linear function through the given
     * points (<code>i</code>, <code>y[i]</code>) using the trapezoidal
     * method.
     * @param y The y-coordinates of the vertices of the piecewise linear
     *     function to integrate.
     * @return The integral of the piecewise linear function.
     * @throws IllegalArgumentException if <code>y</code> is empty.
     */
    public static double trapz(Iterable<Double> y) {
        Iterator<Double> ys = y.iterator();
        if (!ys.hasNext()) {
            throw new IllegalArgumentException("y is empty.");
        }
        double value = 0.0;
        double y0 = ys.next();
        while (ys.hasNext()) {
            double y1 = ys.next();
            double ym = y0 + y1;
            value += ym;
            y0 = y1;
        }
        return value / 2.0;
    }

    /**
     * Computes the integral of the piecewise linear function through the given
     * points (<code>x[i]</code>, <code>y[i]</code>) using the trapezoidal
     * method.
     * @param x The x-coordinates of the vertices of the piecewise linear
     *     function to integrate.
     * @param y The y-coordinates of the vertices of the piecewise linear
     *     function to integrate.
     * @return The integral of the piecewise linear function.
     * @throws IllegalArgumentException if the lengths of <code>x</code> and
     *     <code>y</code> differ.
     * @throws IllegalArgumentException if <code>y</code> is empty.
     */
    public static double trapz(Iterable<Double> x, Iterable<Double> y) {
        Iterator<Double> xs = x.iterator();
        Iterator<Double> ys = y.iterator();
        if (!ys.hasNext()) {
            throw new IllegalArgumentException("y is empty.");
        }
        if (!xs.hasNext()) {
            throw new IllegalArgumentException("Lengths of x and y differ.");
        }
        double value = 0.0;
        double x0 = xs.next();
        double y0 = ys.next();
        while (ys.hasNext()) {
            if (!xs.hasNext()) {
                throw new IllegalArgumentException(
                        "Lengths of x and y differ.");
            }
            double x1 = xs.next();
            double y1 = ys.next();
            double dx = x1 - x0;
            double ym = y0 + y1;
            value += dx * ym;
            x0 = x1;
            y0 = y1;
        }
        if (xs.hasNext()) {
            throw new IllegalArgumentException("Lengths of x and y differ.");
        }
        return value / 2.0;
    }
}

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