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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.analysis.polynomials;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a> <FONT color="green">020</FONT> import java.util.Arrays;<a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> /**<a name="line.26"></a> <FONT color="green">027</FONT> * Immutable representation of a real polynomial function with real coefficients.<a name="line.27"></a> <FONT color="green">028</FONT> * <p><a name="line.28"></a> <FONT color="green">029</FONT> * <a href="http://mathworld.wolfram.com/HornersMethod.html">Horner's Method</a><a name="line.29"></a> <FONT color="green">030</FONT> * is used to evaluate the function.</p><a name="line.30"></a> <FONT color="green">031</FONT> *<a name="line.31"></a> <FONT color="green">032</FONT> * @version $Revision: 922714 $ $Date: 2010-03-13 20:35:14 -0500 (Sat, 13 Mar 2010) $<a name="line.32"></a> <FONT color="green">033</FONT> */<a name="line.33"></a> <FONT color="green">034</FONT> public class PolynomialFunction implements DifferentiableUnivariateRealFunction, Serializable {<a name="line.34"></a> <FONT color="green">035</FONT> <a name="line.35"></a> <FONT color="green">036</FONT> /** Message for empty coefficients array. */<a name="line.36"></a> <FONT color="green">037</FONT> private static final String EMPTY_ARRAY_MESSAGE =<a name="line.37"></a> <FONT color="green">038</FONT> "empty polynomials coefficients array";<a name="line.38"></a> <FONT color="green">039</FONT> <a name="line.39"></a> <FONT color="green">040</FONT> /**<a name="line.40"></a> <FONT color="green">041</FONT> * Serialization identifier<a name="line.41"></a> <FONT color="green">042</FONT> */<a name="line.42"></a> <FONT color="green">043</FONT> private static final long serialVersionUID = -7726511984200295583L;<a name="line.43"></a> <FONT color="green">044</FONT> <a name="line.44"></a> <FONT color="green">045</FONT> /**<a name="line.45"></a> <FONT color="green">046</FONT> * The coefficients of the polynomial, ordered by degree -- i.e.,<a name="line.46"></a> <FONT color="green">047</FONT> * coefficients[0] is the constant term and coefficients[n] is the<a name="line.47"></a> <FONT color="green">048</FONT> * coefficient of x^n where n is the degree of the polynomial.<a name="line.48"></a> <FONT color="green">049</FONT> */<a name="line.49"></a> <FONT color="green">050</FONT> private final double coefficients[];<a name="line.50"></a> <FONT color="green">051</FONT> <a name="line.51"></a> <FONT color="green">052</FONT> /**<a name="line.52"></a> <FONT color="green">053</FONT> * Construct a polynomial with the given coefficients. The first element<a name="line.53"></a> <FONT color="green">054</FONT> * of the coefficients array is the constant term. Higher degree<a name="line.54"></a> <FONT color="green">055</FONT> * coefficients follow in sequence. The degree of the resulting polynomial<a name="line.55"></a> <FONT color="green">056</FONT> * is the index of the last non-null element of the array, or 0 if all elements<a name="line.56"></a> <FONT color="green">057</FONT> * are null.<a name="line.57"></a> <FONT color="green">058</FONT> * <p><a name="line.58"></a> <FONT color="green">059</FONT> * The constructor makes a copy of the input array and assigns the copy to<a name="line.59"></a> <FONT color="green">060</FONT> * the coefficients property.</p><a name="line.60"></a> <FONT color="green">061</FONT> *<a name="line.61"></a> <FONT color="green">062</FONT> * @param c polynomial coefficients<a name="line.62"></a> <FONT color="green">063</FONT> * @throws NullPointerException if c is null<a name="line.63"></a> <FONT color="green">064</FONT> * @throws IllegalArgumentException if c is empty<a name="line.64"></a> <FONT color="green">065</FONT> */<a name="line.65"></a> <FONT color="green">066</FONT> public PolynomialFunction(double c[]) {<a name="line.66"></a> <FONT color="green">067</FONT> super();<a name="line.67"></a> <FONT color="green">068</FONT> if (c.length < 1) {<a name="line.68"></a> <FONT color="green">069</FONT> throw MathRuntimeException.createIllegalArgumentException(EMPTY_ARRAY_MESSAGE);<a name="line.69"></a> <FONT color="green">070</FONT> }<a name="line.70"></a> <FONT color="green">071</FONT> int l = c.length;<a name="line.71"></a> <FONT color="green">072</FONT> while ((l > 1) && (c[l - 1] == 0)) {<a name="line.72"></a> <FONT color="green">073</FONT> --l;<a name="line.73"></a> <FONT color="green">074</FONT> }<a name="line.74"></a> <FONT color="green">075</FONT> this.coefficients = new double[l];<a name="line.75"></a> <FONT color="green">076</FONT> System.arraycopy(c, 0, this.coefficients, 0, l);<a name="line.76"></a> <FONT color="green">077</FONT> }<a name="line.77"></a> <FONT color="green">078</FONT> <a name="line.78"></a> <FONT color="green">079</FONT> /**<a name="line.79"></a> <FONT color="green">080</FONT> * Compute the value of the function for the given argument.<a name="line.80"></a> <FONT color="green">081</FONT> * <p><a name="line.81"></a> <FONT color="green">082</FONT> * The value returned is <br><a name="line.82"></a> <FONT color="green">083</FONT> * <code>coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]</code><a name="line.83"></a> <FONT color="green">084</FONT> * </p><a name="line.84"></a> <FONT color="green">085</FONT> *<a name="line.85"></a> <FONT color="green">086</FONT> * @param x the argument for which the function value should be computed<a name="line.86"></a> <FONT color="green">087</FONT> * @return the value of the polynomial at the given point<a name="line.87"></a> <FONT color="green">088</FONT> * @see UnivariateRealFunction#value(double)<a name="line.88"></a> <FONT color="green">089</FONT> */<a name="line.89"></a> <FONT color="green">090</FONT> public double value(double x) {<a name="line.90"></a> <FONT color="green">091</FONT> return evaluate(coefficients, x);<a name="line.91"></a> <FONT color="green">092</FONT> }<a name="line.92"></a> <FONT color="green">093</FONT> <a name="line.93"></a> <FONT color="green">094</FONT> <a name="line.94"></a> <FONT color="green">095</FONT> /**<a name="line.95"></a> <FONT color="green">096</FONT> * Returns the degree of the polynomial<a name="line.96"></a> <FONT color="green">097</FONT> *<a name="line.97"></a> <FONT color="green">098</FONT> * @return the degree of the polynomial<a name="line.98"></a> <FONT color="green">099</FONT> */<a name="line.99"></a> <FONT color="green">100</FONT> public int degree() {<a name="line.100"></a> <FONT color="green">101</FONT> return coefficients.length - 1;<a name="line.101"></a> <FONT color="green">102</FONT> }<a name="line.102"></a> <FONT color="green">103</FONT> <a name="line.103"></a> <FONT color="green">104</FONT> /**<a name="line.104"></a> <FONT color="green">105</FONT> * Returns a copy of the coefficients array.<a name="line.105"></a> <FONT color="green">106</FONT> * <p><a name="line.106"></a> <FONT color="green">107</FONT> * Changes made to the returned copy will not affect the coefficients of<a name="line.107"></a> <FONT color="green">108</FONT> * the polynomial.</p><a name="line.108"></a> <FONT color="green">109</FONT> *<a name="line.109"></a> <FONT color="green">110</FONT> * @return a fresh copy of the coefficients array<a name="line.110"></a> <FONT color="green">111</FONT> */<a name="line.111"></a> <FONT color="green">112</FONT> public double[] getCoefficients() {<a name="line.112"></a> <FONT color="green">113</FONT> return coefficients.clone();<a name="line.113"></a> <FONT color="green">114</FONT> }<a name="line.114"></a> <FONT color="green">115</FONT> <a name="line.115"></a> <FONT color="green">116</FONT> /**<a name="line.116"></a> <FONT color="green">117</FONT> * Uses Horner's Method to evaluate the polynomial with the given coefficients at<a name="line.117"></a> <FONT color="green">118</FONT> * the argument.<a name="line.118"></a> <FONT color="green">119</FONT> *<a name="line.119"></a> <FONT color="green">120</FONT> * @param coefficients the coefficients of the polynomial to evaluate<a name="line.120"></a> <FONT color="green">121</FONT> * @param argument the input value<a name="line.121"></a> <FONT color="green">122</FONT> * @return the value of the polynomial<a name="line.122"></a> <FONT color="green">123</FONT> * @throws IllegalArgumentException if coefficients is empty<a name="line.123"></a> <FONT color="green">124</FONT> * @throws NullPointerException if coefficients is null<a name="line.124"></a> <FONT color="green">125</FONT> */<a name="line.125"></a> <FONT color="green">126</FONT> protected static double evaluate(double[] coefficients, double argument) {<a name="line.126"></a> <FONT color="green">127</FONT> int n = coefficients.length;<a name="line.127"></a> <FONT color="green">128</FONT> if (n < 1) {<a name="line.128"></a> <FONT color="green">129</FONT> throw MathRuntimeException.createIllegalArgumentException(EMPTY_ARRAY_MESSAGE);<a name="line.129"></a> <FONT color="green">130</FONT> }<a name="line.130"></a> <FONT color="green">131</FONT> double result = coefficients[n - 1];<a name="line.131"></a> <FONT color="green">132</FONT> for (int j = n -2; j >=0; j--) {<a name="line.132"></a> <FONT color="green">133</FONT> result = argument * result + coefficients[j];<a name="line.133"></a> <FONT color="green">134</FONT> }<a name="line.134"></a> <FONT color="green">135</FONT> return result;<a name="line.135"></a> <FONT color="green">136</FONT> }<a name="line.136"></a> <FONT color="green">137</FONT> <a name="line.137"></a> <FONT color="green">138</FONT> /**<a name="line.138"></a> <FONT color="green">139</FONT> * Add a polynomial to the instance.<a name="line.139"></a> <FONT color="green">140</FONT> * @param p polynomial to add<a name="line.140"></a> <FONT color="green">141</FONT> * @return a new polynomial which is the sum of the instance and p<a name="line.141"></a> <FONT color="green">142</FONT> */<a name="line.142"></a> <FONT color="green">143</FONT> public PolynomialFunction add(final PolynomialFunction p) {<a name="line.143"></a> <FONT color="green">144</FONT> <a name="line.144"></a> <FONT color="green">145</FONT> // identify the lowest degree polynomial<a name="line.145"></a> <FONT color="green">146</FONT> final int lowLength = Math.min(coefficients.length, p.coefficients.length);<a name="line.146"></a> <FONT color="green">147</FONT> final int highLength = Math.max(coefficients.length, p.coefficients.length);<a name="line.147"></a> <FONT color="green">148</FONT> <a name="line.148"></a> <FONT color="green">149</FONT> // build the coefficients array<a name="line.149"></a> <FONT color="green">150</FONT> double[] newCoefficients = new double[highLength];<a name="line.150"></a> <FONT color="green">151</FONT> for (int i = 0; i < lowLength; ++i) {<a name="line.151"></a> <FONT color="green">152</FONT> newCoefficients[i] = coefficients[i] + p.coefficients[i];<a name="line.152"></a> <FONT color="green">153</FONT> }<a name="line.153"></a> <FONT color="green">154</FONT> System.arraycopy((coefficients.length < p.coefficients.length) ?<a name="line.154"></a> <FONT color="green">155</FONT> p.coefficients : coefficients,<a name="line.155"></a> <FONT color="green">156</FONT> lowLength,<a name="line.156"></a> <FONT color="green">157</FONT> newCoefficients, lowLength,<a name="line.157"></a> <FONT color="green">158</FONT> highLength - lowLength);<a name="line.158"></a> <FONT color="green">159</FONT> <a name="line.159"></a> <FONT color="green">160</FONT> return new PolynomialFunction(newCoefficients);<a name="line.160"></a> <FONT color="green">161</FONT> <a name="line.161"></a> <FONT color="green">162</FONT> }<a name="line.162"></a> <FONT color="green">163</FONT> <a name="line.163"></a> <FONT color="green">164</FONT> /**<a name="line.164"></a> <FONT color="green">165</FONT> * Subtract a polynomial from the instance.<a name="line.165"></a> <FONT color="green">166</FONT> * @param p polynomial to subtract<a name="line.166"></a> <FONT color="green">167</FONT> * @return a new polynomial which is the difference the instance minus p<a name="line.167"></a> <FONT color="green">168</FONT> */<a name="line.168"></a> <FONT color="green">169</FONT> public PolynomialFunction subtract(final PolynomialFunction p) {<a name="line.169"></a> <FONT color="green">170</FONT> <a name="line.170"></a> <FONT color="green">171</FONT> // identify the lowest degree polynomial<a name="line.171"></a> <FONT color="green">172</FONT> int lowLength = Math.min(coefficients.length, p.coefficients.length);<a name="line.172"></a> <FONT color="green">173</FONT> int highLength = Math.max(coefficients.length, p.coefficients.length);<a name="line.173"></a> <FONT color="green">174</FONT> <a name="line.174"></a> <FONT color="green">175</FONT> // build the coefficients array<a name="line.175"></a> <FONT color="green">176</FONT> double[] newCoefficients = new double[highLength];<a name="line.176"></a> <FONT color="green">177</FONT> for (int i = 0; i < lowLength; ++i) {<a name="line.177"></a> <FONT color="green">178</FONT> newCoefficients[i] = coefficients[i] - p.coefficients[i];<a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> if (coefficients.length < p.coefficients.length) {<a name="line.180"></a> <FONT color="green">181</FONT> for (int i = lowLength; i < highLength; ++i) {<a name="line.181"></a> <FONT color="green">182</FONT> newCoefficients[i] = -p.coefficients[i];<a name="line.182"></a> <FONT color="green">183</FONT> }<a name="line.183"></a> <FONT color="green">184</FONT> } else {<a name="line.184"></a> <FONT color="green">185</FONT> System.arraycopy(coefficients, lowLength, newCoefficients, lowLength,<a name="line.185"></a> <FONT color="green">186</FONT> highLength - lowLength);<a name="line.186"></a> <FONT color="green">187</FONT> }<a name="line.187"></a> <FONT color="green">188</FONT> <a name="line.188"></a> <FONT color="green">189</FONT> return new PolynomialFunction(newCoefficients);<a name="line.189"></a> <FONT color="green">190</FONT> <a name="line.190"></a> <FONT color="green">191</FONT> }<a name="line.191"></a> <FONT color="green">192</FONT> <a name="line.192"></a> <FONT color="green">193</FONT> /**<a name="line.193"></a> <FONT color="green">194</FONT> * Negate the instance.<a name="line.194"></a> <FONT color="green">195</FONT> * @return a new polynomial<a name="line.195"></a> <FONT color="green">196</FONT> */<a name="line.196"></a> <FONT color="green">197</FONT> public PolynomialFunction negate() {<a name="line.197"></a> <FONT color="green">198</FONT> double[] newCoefficients = new double[coefficients.length];<a name="line.198"></a> <FONT color="green">199</FONT> for (int i = 0; i < coefficients.length; ++i) {<a name="line.199"></a> <FONT color="green">200</FONT> newCoefficients[i] = -coefficients[i];<a name="line.200"></a> <FONT color="green">201</FONT> }<a name="line.201"></a> <FONT color="green">202</FONT> return new PolynomialFunction(newCoefficients);<a name="line.202"></a> <FONT color="green">203</FONT> }<a name="line.203"></a> <FONT color="green">204</FONT> <a name="line.204"></a> <FONT color="green">205</FONT> /**<a name="line.205"></a> <FONT color="green">206</FONT> * Multiply the instance by a polynomial.<a name="line.206"></a> <FONT color="green">207</FONT> * @param p polynomial to multiply by<a name="line.207"></a> <FONT color="green">208</FONT> * @return a new polynomial<a name="line.208"></a> <FONT color="green">209</FONT> */<a name="line.209"></a> <FONT color="green">210</FONT> public PolynomialFunction multiply(final PolynomialFunction p) {<a name="line.210"></a> <FONT color="green">211</FONT> <a name="line.211"></a> <FONT color="green">212</FONT> double[] newCoefficients = new double[coefficients.length + p.coefficients.length - 1];<a name="line.212"></a> <FONT color="green">213</FONT> <a name="line.213"></a> <FONT color="green">214</FONT> for (int i = 0; i < newCoefficients.length; ++i) {<a name="line.214"></a> <FONT color="green">215</FONT> newCoefficients[i] = 0.0;<a name="line.215"></a> <FONT color="green">216</FONT> for (int j = Math.max(0, i + 1 - p.coefficients.length);<a name="line.216"></a> <FONT color="green">217</FONT> j < Math.min(coefficients.length, i + 1);<a name="line.217"></a> <FONT color="green">218</FONT> ++j) {<a name="line.218"></a> <FONT color="green">219</FONT> newCoefficients[i] += coefficients[j] * p.coefficients[i-j];<a name="line.219"></a> <FONT color="green">220</FONT> }<a name="line.220"></a> <FONT color="green">221</FONT> }<a name="line.221"></a> <FONT color="green">222</FONT> <a name="line.222"></a> <FONT color="green">223</FONT> return new PolynomialFunction(newCoefficients);<a name="line.223"></a> <FONT color="green">224</FONT> <a name="line.224"></a> <FONT color="green">225</FONT> }<a name="line.225"></a> <FONT color="green">226</FONT> <a name="line.226"></a> <FONT color="green">227</FONT> /**<a name="line.227"></a> <FONT color="green">228</FONT> * Returns the coefficients of the derivative of the polynomial with the given coefficients.<a name="line.228"></a> <FONT color="green">229</FONT> *<a name="line.229"></a> <FONT color="green">230</FONT> * @param coefficients the coefficients of the polynomial to differentiate<a name="line.230"></a> <FONT color="green">231</FONT> * @return the coefficients of the derivative or null if coefficients has length 1.<a name="line.231"></a> <FONT color="green">232</FONT> * @throws IllegalArgumentException if coefficients is empty<a name="line.232"></a> <FONT color="green">233</FONT> * @throws NullPointerException if coefficients is null<a name="line.233"></a> <FONT color="green">234</FONT> */<a name="line.234"></a> <FONT color="green">235</FONT> protected static double[] differentiate(double[] coefficients) {<a name="line.235"></a> <FONT color="green">236</FONT> int n = coefficients.length;<a name="line.236"></a> <FONT color="green">237</FONT> if (n < 1) {<a name="line.237"></a> <FONT color="green">238</FONT> throw MathRuntimeException.createIllegalArgumentException(EMPTY_ARRAY_MESSAGE);<a name="line.238"></a> <FONT color="green">239</FONT> }<a name="line.239"></a> <FONT color="green">240</FONT> if (n == 1) {<a name="line.240"></a> <FONT color="green">241</FONT> return new double[]{0};<a name="line.241"></a> <FONT color="green">242</FONT> }<a name="line.242"></a> <FONT color="green">243</FONT> double[] result = new double[n - 1];<a name="line.243"></a> <FONT color="green">244</FONT> for (int i = n - 1; i > 0; i--) {<a name="line.244"></a> <FONT color="green">245</FONT> result[i - 1] = i * coefficients[i];<a name="line.245"></a> <FONT color="green">246</FONT> }<a name="line.246"></a> <FONT color="green">247</FONT> return result;<a name="line.247"></a> <FONT color="green">248</FONT> }<a name="line.248"></a> <FONT color="green">249</FONT> <a name="line.249"></a> <FONT color="green">250</FONT> /**<a name="line.250"></a> <FONT color="green">251</FONT> * Returns the derivative as a PolynomialRealFunction<a name="line.251"></a> <FONT color="green">252</FONT> *<a name="line.252"></a> <FONT color="green">253</FONT> * @return the derivative polynomial<a name="line.253"></a> <FONT color="green">254</FONT> */<a name="line.254"></a> <FONT color="green">255</FONT> public PolynomialFunction polynomialDerivative() {<a name="line.255"></a> <FONT color="green">256</FONT> return new PolynomialFunction(differentiate(coefficients));<a name="line.256"></a> <FONT color="green">257</FONT> }<a name="line.257"></a> <FONT color="green">258</FONT> <a name="line.258"></a> <FONT color="green">259</FONT> /**<a name="line.259"></a> <FONT color="green">260</FONT> * Returns the derivative as a UnivariateRealFunction<a name="line.260"></a> <FONT color="green">261</FONT> *<a name="line.261"></a> <FONT color="green">262</FONT> * @return the derivative function<a name="line.262"></a> <FONT color="green">263</FONT> */<a name="line.263"></a> <FONT color="green">264</FONT> public UnivariateRealFunction derivative() {<a name="line.264"></a> <FONT color="green">265</FONT> return polynomialDerivative();<a name="line.265"></a> <FONT color="green">266</FONT> }<a name="line.266"></a> <FONT color="green">267</FONT> <a name="line.267"></a> <FONT color="green">268</FONT> /** Returns a string representation of the polynomial.<a name="line.268"></a> <FONT color="green">269</FONT> <a name="line.269"></a> <FONT color="green">270</FONT> * <p>The representation is user oriented. Terms are displayed lowest<a name="line.270"></a> <FONT color="green">271</FONT> * degrees first. The multiplications signs, coefficients equals to<a name="line.271"></a> <FONT color="green">272</FONT> * one and null terms are not displayed (except if the polynomial is 0,<a name="line.272"></a> <FONT color="green">273</FONT> * in which case the 0 constant term is displayed). Addition of terms<a name="line.273"></a> <FONT color="green">274</FONT> * with negative coefficients are replaced by subtraction of terms<a name="line.274"></a> <FONT color="green">275</FONT> * with positive coefficients except for the first displayed term<a name="line.275"></a> <FONT color="green">276</FONT> * (i.e. we display <code>-3</code> for a constant negative polynomial,<a name="line.276"></a> <FONT color="green">277</FONT> * but <code>1 - 3 x + x^2</code> if the negative coefficient is not<a name="line.277"></a> <FONT color="green">278</FONT> * the first one displayed).</p><a name="line.278"></a> <FONT color="green">279</FONT> <a name="line.279"></a> <FONT color="green">280</FONT> * @return a string representation of the polynomial<a name="line.280"></a> <FONT color="green">281</FONT> <a name="line.281"></a> <FONT color="green">282</FONT> */<a name="line.282"></a> <FONT color="green">283</FONT> @Override<a name="line.283"></a> <FONT color="green">284</FONT> public String toString() {<a name="line.284"></a> <FONT color="green">285</FONT> <a name="line.285"></a> <FONT color="green">286</FONT> StringBuffer s = new StringBuffer();<a name="line.286"></a> <FONT color="green">287</FONT> if (coefficients[0] == 0.0) {<a name="line.287"></a> <FONT color="green">288</FONT> if (coefficients.length == 1) {<a name="line.288"></a> <FONT color="green">289</FONT> return "0";<a name="line.289"></a> <FONT color="green">290</FONT> }<a name="line.290"></a> <FONT color="green">291</FONT> } else {<a name="line.291"></a> <FONT color="green">292</FONT> s.append(Double.toString(coefficients[0]));<a name="line.292"></a> <FONT color="green">293</FONT> }<a name="line.293"></a> <FONT color="green">294</FONT> <a name="line.294"></a> <FONT color="green">295</FONT> for (int i = 1; i < coefficients.length; ++i) {<a name="line.295"></a> <FONT color="green">296</FONT> <a name="line.296"></a> <FONT color="green">297</FONT> if (coefficients[i] != 0) {<a name="line.297"></a> <FONT color="green">298</FONT> <a name="line.298"></a> <FONT color="green">299</FONT> if (s.length() > 0) {<a name="line.299"></a> <FONT color="green">300</FONT> if (coefficients[i] < 0) {<a name="line.300"></a> <FONT color="green">301</FONT> s.append(" - ");<a name="line.301"></a> <FONT color="green">302</FONT> } else {<a name="line.302"></a> <FONT color="green">303</FONT> s.append(" + ");<a name="line.303"></a> <FONT color="green">304</FONT> }<a name="line.304"></a> <FONT color="green">305</FONT> } else {<a name="line.305"></a> <FONT color="green">306</FONT> if (coefficients[i] < 0) {<a name="line.306"></a> <FONT color="green">307</FONT> s.append("-");<a name="line.307"></a> <FONT color="green">308</FONT> }<a name="line.308"></a> <FONT color="green">309</FONT> }<a name="line.309"></a> <FONT color="green">310</FONT> <a name="line.310"></a> <FONT color="green">311</FONT> double absAi = Math.abs(coefficients[i]);<a name="line.311"></a> <FONT color="green">312</FONT> if ((absAi - 1) != 0) {<a name="line.312"></a> <FONT color="green">313</FONT> s.append(Double.toString(absAi));<a name="line.313"></a> <FONT color="green">314</FONT> s.append(' ');<a name="line.314"></a> <FONT color="green">315</FONT> }<a name="line.315"></a> <FONT color="green">316</FONT> <a name="line.316"></a> <FONT color="green">317</FONT> s.append("x");<a name="line.317"></a> <FONT color="green">318</FONT> if (i > 1) {<a name="line.318"></a> <FONT color="green">319</FONT> s.append('^');<a name="line.319"></a> <FONT color="green">320</FONT> s.append(Integer.toString(i));<a name="line.320"></a> <FONT color="green">321</FONT> }<a name="line.321"></a> <FONT color="green">322</FONT> }<a name="line.322"></a> <FONT color="green">323</FONT> <a name="line.323"></a> <FONT color="green">324</FONT> }<a name="line.324"></a> <FONT color="green">325</FONT> <a name="line.325"></a> <FONT color="green">326</FONT> return s.toString();<a name="line.326"></a> <FONT color="green">327</FONT> <a name="line.327"></a> <FONT color="green">328</FONT> }<a name="line.328"></a> <FONT color="green">329</FONT> <a name="line.329"></a> <FONT color="green">330</FONT> /** {@inheritDoc} */<a name="line.330"></a> <FONT color="green">331</FONT> @Override<a name="line.331"></a> <FONT color="green">332</FONT> public int hashCode() {<a name="line.332"></a> <FONT color="green">333</FONT> final int prime = 31;<a name="line.333"></a> <FONT color="green">334</FONT> int result = 1;<a name="line.334"></a> <FONT color="green">335</FONT> result = prime * result + Arrays.hashCode(coefficients);<a name="line.335"></a> <FONT color="green">336</FONT> return result;<a name="line.336"></a> <FONT color="green">337</FONT> }<a name="line.337"></a> <FONT color="green">338</FONT> <a name="line.338"></a> <FONT color="green">339</FONT> /** {@inheritDoc} */<a name="line.339"></a> <FONT color="green">340</FONT> @Override<a name="line.340"></a> <FONT color="green">341</FONT> public boolean equals(Object obj) {<a name="line.341"></a> <FONT color="green">342</FONT> if (this == obj)<a name="line.342"></a> <FONT color="green">343</FONT> return true;<a name="line.343"></a> <FONT color="green">344</FONT> if (!(obj instanceof PolynomialFunction))<a name="line.344"></a> <FONT color="green">345</FONT> return false;<a name="line.345"></a> <FONT color="green">346</FONT> PolynomialFunction other = (PolynomialFunction) obj;<a name="line.346"></a> <FONT color="green">347</FONT> if (!Arrays.equals(coefficients, other.coefficients))<a name="line.347"></a> <FONT color="green">348</FONT> return false;<a name="line.348"></a> <FONT color="green">349</FONT> return true;<a name="line.349"></a> <FONT color="green">350</FONT> }<a name="line.350"></a> <FONT color="green">351</FONT> <a name="line.351"></a> <FONT color="green">352</FONT> }<a name="line.352"></a> </PRE> </BODY> </HTML>