Commons Math example source code file (PolynomialFunction.java)

This example Commons Math source code file (PolynomialFunction.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" ^TM.

Java - Commons Math tags/keywords

differentiableunivariaterealfunction, empty_array_message, io, override, override, polynomialfunction, polynomialfunction, serializable, string, string, stringbuffer, stringbuffer, univariaterealfunction, util

The Commons Math PolynomialFunction.java source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math.analysis.polynomials;

import java.io.Serializable;
import java.util.Arrays;

import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
import org.apache.commons.math.analysis.UnivariateRealFunction;

/**
 * Immutable representation of a real polynomial function with real coefficients.
 * <p>
 * <a href="http://mathworld.wolfram.com/HornersMethod.html">Horner's Method
 *  is used to evaluate the function.</p>
 *
 * @version $Revision: 922714 $ $Date: 2010-03-13 20:35:14 -0500 (Sat, 13 Mar 2010) $
 */
public class PolynomialFunction implements DifferentiableUnivariateRealFunction, Serializable {

    /** Message for empty coefficients array. */
    private static final String EMPTY_ARRAY_MESSAGE =
        "empty polynomials coefficients array";

    /**
     * Serialization identifier
     */
    private static final long serialVersionUID = -7726511984200295583L;

    /**
     * The coefficients of the polynomial, ordered by degree -- i.e.,
     * coefficients[0] is the constant term and coefficients[n] is the
     * coefficient of x^n where n is the degree of the polynomial.
     */
    private final double coefficients[];

    /**
     * Construct a polynomial with the given coefficients.  The first element
     * of the coefficients array is the constant term.  Higher degree
     * coefficients follow in sequence.  The degree of the resulting polynomial
     * is the index of the last non-null element of the array, or 0 if all elements
     * are null.
     * <p>
     * The constructor makes a copy of the input array and assigns the copy to
     * the coefficients property.</p>
     *
     * @param c polynomial coefficients
     * @throws NullPointerException if c is null
     * @throws IllegalArgumentException if c is empty
     */
    public PolynomialFunction(double c[]) {
        super();
        if (c.length < 1) {
            throw MathRuntimeException.createIllegalArgumentException(EMPTY_ARRAY_MESSAGE);
        }
        int l = c.length;
        while ((l > 1) && (c[l - 1] == 0)) {
            --l;
        }
        this.coefficients = new double[l];
        System.arraycopy(c, 0, this.coefficients, 0, l);
    }

    /**
     * Compute the value of the function for the given argument.
     * <p>
     *  The value returned is <br>
     *   <code>coefficients[n] * x^n + ... + coefficients[1] * x  + coefficients[0]
     * </p>
     *
     * @param x the argument for which the function value should be computed
     * @return the value of the polynomial at the given point
     * @see UnivariateRealFunction#value(double)
     */
    public double value(double x) {
       return evaluate(coefficients, x);
    }


    /**
     *  Returns the degree of the polynomial
     *
     * @return the degree of the polynomial
     */
    public int degree() {
        return coefficients.length - 1;
    }

    /**
     * Returns a copy of the coefficients array.
     * <p>
     * Changes made to the returned copy will not affect the coefficients of
     * the polynomial.</p>
     *
     * @return  a fresh copy of the coefficients array
     */
    public double[] getCoefficients() {
        return coefficients.clone();
    }

    /**
     * Uses Horner's Method to evaluate the polynomial with the given coefficients at
     * the argument.
     *
     * @param coefficients  the coefficients of the polynomial to evaluate
     * @param argument  the input value
     * @return  the value of the polynomial
     * @throws IllegalArgumentException if coefficients is empty
     * @throws NullPointerException if coefficients is null
     */
    protected static double evaluate(double[] coefficients, double argument) {
        int n = coefficients.length;
        if (n < 1) {
            throw MathRuntimeException.createIllegalArgumentException(EMPTY_ARRAY_MESSAGE);
        }
        double result = coefficients[n - 1];
        for (int j = n -2; j >=0; j--) {
            result = argument * result + coefficients[j];
        }
        return result;
    }

    /**
     * Add a polynomial to the instance.
     * @param p polynomial to add
     * @return a new polynomial which is the sum of the instance and p
     */
    public PolynomialFunction add(final PolynomialFunction p) {

        // identify the lowest degree polynomial
        final int lowLength  = Math.min(coefficients.length, p.coefficients.length);
        final int highLength = Math.max(coefficients.length, p.coefficients.length);

        // build the coefficients array
        double[] newCoefficients = new double[highLength];
        for (int i = 0; i < lowLength; ++i) {
            newCoefficients[i] = coefficients[i] + p.coefficients[i];
        }
        System.arraycopy((coefficients.length < p.coefficients.length) ?
                         p.coefficients : coefficients,
                         lowLength,
                         newCoefficients, lowLength,
                         highLength - lowLength);

        return new PolynomialFunction(newCoefficients);

    }

    /**
     * Subtract a polynomial from the instance.
     * @param p polynomial to subtract
     * @return a new polynomial which is the difference the instance minus p
     */
    public PolynomialFunction subtract(final PolynomialFunction p) {

        // identify the lowest degree polynomial
        int lowLength  = Math.min(coefficients.length, p.coefficients.length);
        int highLength = Math.max(coefficients.length, p.coefficients.length);

        // build the coefficients array
        double[] newCoefficients = new double[highLength];
        for (int i = 0; i < lowLength; ++i) {
            newCoefficients[i] = coefficients[i] - p.coefficients[i];
        }
        if (coefficients.length < p.coefficients.length) {
            for (int i = lowLength; i < highLength; ++i) {
                newCoefficients[i] = -p.coefficients[i];
            }
        } else {
            System.arraycopy(coefficients, lowLength, newCoefficients, lowLength,
                             highLength - lowLength);
        }

        return new PolynomialFunction(newCoefficients);

    }

    /**
     * Negate the instance.
     * @return a new polynomial
     */
    public PolynomialFunction negate() {
        double[] newCoefficients = new double[coefficients.length];
        for (int i = 0; i < coefficients.length; ++i) {
            newCoefficients[i] = -coefficients[i];
        }
        return new PolynomialFunction(newCoefficients);
    }

    /**
     * Multiply the instance by a polynomial.
     * @param p polynomial to multiply by
     * @return a new polynomial
     */
    public PolynomialFunction multiply(final PolynomialFunction p) {

        double[] newCoefficients = new double[coefficients.length + p.coefficients.length - 1];

        for (int i = 0; i < newCoefficients.length; ++i) {
            newCoefficients[i] = 0.0;
            for (int j = Math.max(0, i + 1 - p.coefficients.length);
                 j < Math.min(coefficients.length, i + 1);
                 ++j) {
                newCoefficients[i] += coefficients[j] * p.coefficients[i-j];
            }
        }

        return new PolynomialFunction(newCoefficients);

    }

    /**
     * Returns the coefficients of the derivative of the polynomial with the given coefficients.
     *
     * @param coefficients  the coefficients of the polynomial to differentiate
     * @return the coefficients of the derivative or null if coefficients has length 1.
     * @throws IllegalArgumentException if coefficients is empty
     * @throws NullPointerException if coefficients is null
     */
    protected static double[] differentiate(double[] coefficients) {
        int n = coefficients.length;
        if (n < 1) {
            throw MathRuntimeException.createIllegalArgumentException(EMPTY_ARRAY_MESSAGE);
        }
        if (n == 1) {
            return new double[]{0};
        }
        double[] result = new double[n - 1];
        for (int i = n - 1; i  > 0; i--) {
            result[i - 1] = i * coefficients[i];
        }
        return result;
    }

    /**
     * Returns the derivative as a PolynomialRealFunction
     *
     * @return  the derivative polynomial
     */
    public PolynomialFunction polynomialDerivative() {
        return new PolynomialFunction(differentiate(coefficients));
    }

    /**
     * Returns the derivative as a UnivariateRealFunction
     *
     * @return  the derivative function
     */
    public UnivariateRealFunction derivative() {
        return polynomialDerivative();
    }

    /** Returns a string representation of the polynomial.

     * <p>The representation is user oriented. Terms are displayed lowest
     * degrees first. The multiplications signs, coefficients equals to
     * one and null terms are not displayed (except if the polynomial is 0,
     * in which case the 0 constant term is displayed). Addition of terms
     * with negative coefficients are replaced by subtraction of terms
     * with positive coefficients except for the first displayed term
     * (i.e. we display <code>-3 for a constant negative polynomial,
     * but <code>1 - 3 x + x^2 if the negative coefficient is not
     * the first one displayed).</p>

     * @return a string representation of the polynomial

     */
    @Override
     public String toString() {

       StringBuffer s = new StringBuffer();
       if (coefficients[0] == 0.0) {
         if (coefficients.length == 1) {
           return "0";
         }
       } else {
         s.append(Double.toString(coefficients[0]));
       }

       for (int i = 1; i < coefficients.length; ++i) {

         if (coefficients[i] != 0) {

           if (s.length() > 0) {
             if (coefficients[i] < 0) {
               s.append(" - ");
             } else {
               s.append(" + ");
             }
           } else {
             if (coefficients[i] < 0) {
               s.append("-");
             }
           }

           double absAi = Math.abs(coefficients[i]);
           if ((absAi - 1) != 0) {
             s.append(Double.toString(absAi));
             s.append(' ');
           }

           s.append("x");
           if (i > 1) {
             s.append('^');
             s.append(Integer.toString(i));
           }
         }

       }

       return s.toString();

     }

    /** {@inheritDoc} */
    @Override
    public int hashCode() {
        final int prime = 31;
        int result = 1;
        result = prime * result + Arrays.hashCode(coefficients);
        return result;
    }

    /** {@inheritDoc} */
    @Override
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (!(obj instanceof PolynomialFunction))
            return false;
        PolynomialFunction other = (PolynomialFunction) obj;
        if (!Arrays.equals(coefficients, other.coefficients))
            return false;
        return true;
    }

}