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commons-math-2.1 added
| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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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> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.complex;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import java.io.Serializable;<a name="line.20"></a> <FONT color="green">021</FONT> import java.util.ArrayList;<a name="line.21"></a> <FONT color="green">022</FONT> import java.util.List;<a name="line.22"></a> <FONT color="green">023</FONT> <a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.FieldElement;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.25"></a> <FONT color="green">026</FONT> import org.apache.commons.math.util.MathUtils;<a name="line.26"></a> <FONT color="green">027</FONT> <a name="line.27"></a> <FONT color="green">028</FONT> /**<a name="line.28"></a> <FONT color="green">029</FONT> * Representation of a Complex number - a number which has both a<a name="line.29"></a> <FONT color="green">030</FONT> * real and imaginary part.<a name="line.30"></a> <FONT color="green">031</FONT> * <p><a name="line.31"></a> <FONT color="green">032</FONT> * Implementations of arithmetic operations handle <code>NaN</code> and<a name="line.32"></a> <FONT color="green">033</FONT> * infinite values according to the rules for {@link java.lang.Double}<a name="line.33"></a> <FONT color="green">034</FONT> * arithmetic, applying definitional formulas and returning <code>NaN</code> or<a name="line.34"></a> <FONT color="green">035</FONT> * infinite values in real or imaginary parts as these arise in computation.<a name="line.35"></a> <FONT color="green">036</FONT> * See individual method javadocs for details.</p><a name="line.36"></a> <FONT color="green">037</FONT> * <p><a name="line.37"></a> <FONT color="green">038</FONT> * {@link #equals} identifies all values with <code>NaN</code> in either real<a name="line.38"></a> <FONT color="green">039</FONT> * or imaginary part - e.g., <pre><a name="line.39"></a> <FONT color="green">040</FONT> * <code>1 + NaNi == NaN + i == NaN + NaNi.</code></pre></p><a name="line.40"></a> <FONT color="green">041</FONT> *<a name="line.41"></a> <FONT color="green">042</FONT> * implements Serializable since 2.0<a name="line.42"></a> <FONT color="green">043</FONT> *<a name="line.43"></a> <FONT color="green">044</FONT> * @version $Revision: 922713 $ $Date: 2010-03-13 20:26:13 -0500 (Sat, 13 Mar 2010) $<a name="line.44"></a> <FONT color="green">045</FONT> */<a name="line.45"></a> <FONT color="green">046</FONT> public class Complex implements FieldElement<Complex>, Serializable {<a name="line.46"></a> <FONT color="green">047</FONT> <a name="line.47"></a> <FONT color="green">048</FONT> /** The square root of -1. A number representing "0.0 + 1.0i" */<a name="line.48"></a> <FONT color="green">049</FONT> public static final Complex I = new Complex(0.0, 1.0);<a name="line.49"></a> <FONT color="green">050</FONT> <a name="line.50"></a> <FONT color="green">051</FONT> // CHECKSTYLE: stop ConstantName<a name="line.51"></a> <FONT color="green">052</FONT> /** A complex number representing "NaN + NaNi" */<a name="line.52"></a> <FONT color="green">053</FONT> public static final Complex NaN = new Complex(Double.NaN, Double.NaN);<a name="line.53"></a> <FONT color="green">054</FONT> // CHECKSTYLE: resume ConstantName<a name="line.54"></a> <FONT color="green">055</FONT> <a name="line.55"></a> <FONT color="green">056</FONT> /** A complex number representing "+INF + INFi" */<a name="line.56"></a> <FONT color="green">057</FONT> public static final Complex INF = new Complex(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);<a name="line.57"></a> <FONT color="green">058</FONT> <a name="line.58"></a> <FONT color="green">059</FONT> /** A complex number representing "1.0 + 0.0i" */<a name="line.59"></a> <FONT color="green">060</FONT> public static final Complex ONE = new Complex(1.0, 0.0);<a name="line.60"></a> <FONT color="green">061</FONT> <a name="line.61"></a> <FONT color="green">062</FONT> /** A complex number representing "0.0 + 0.0i" */<a name="line.62"></a> <FONT color="green">063</FONT> public static final Complex ZERO = new Complex(0.0, 0.0);<a name="line.63"></a> <FONT color="green">064</FONT> <a name="line.64"></a> <FONT color="green">065</FONT> /** Serializable version identifier */<a name="line.65"></a> <FONT color="green">066</FONT> private static final long serialVersionUID = -6195664516687396620L;<a name="line.66"></a> <FONT color="green">067</FONT> <a name="line.67"></a> <FONT color="green">068</FONT> /** The imaginary part. */<a name="line.68"></a> <FONT color="green">069</FONT> private final double imaginary;<a name="line.69"></a> <FONT color="green">070</FONT> <a name="line.70"></a> <FONT color="green">071</FONT> /** The real part. */<a name="line.71"></a> <FONT color="green">072</FONT> private final double real;<a name="line.72"></a> <FONT color="green">073</FONT> <a name="line.73"></a> <FONT color="green">074</FONT> /** Record whether this complex number is equal to NaN. */<a name="line.74"></a> <FONT color="green">075</FONT> private final transient boolean isNaN;<a name="line.75"></a> <FONT color="green">076</FONT> <a name="line.76"></a> <FONT color="green">077</FONT> /** Record whether this complex number is infinite. */<a name="line.77"></a> <FONT color="green">078</FONT> private final transient boolean isInfinite;<a name="line.78"></a> <FONT color="green">079</FONT> <a name="line.79"></a> <FONT color="green">080</FONT> /**<a name="line.80"></a> <FONT color="green">081</FONT> * Create a complex number given the real and imaginary parts.<a name="line.81"></a> <FONT color="green">082</FONT> *<a name="line.82"></a> <FONT color="green">083</FONT> * @param real the real part<a name="line.83"></a> <FONT color="green">084</FONT> * @param imaginary the imaginary part<a name="line.84"></a> <FONT color="green">085</FONT> */<a name="line.85"></a> <FONT color="green">086</FONT> public Complex(double real, double imaginary) {<a name="line.86"></a> <FONT color="green">087</FONT> super();<a name="line.87"></a> <FONT color="green">088</FONT> this.real = real;<a name="line.88"></a> <FONT color="green">089</FONT> this.imaginary = imaginary;<a name="line.89"></a> <FONT color="green">090</FONT> <a name="line.90"></a> <FONT color="green">091</FONT> isNaN = Double.isNaN(real) || Double.isNaN(imaginary);<a name="line.91"></a> <FONT color="green">092</FONT> isInfinite = !isNaN &&<a name="line.92"></a> <FONT color="green">093</FONT> (Double.isInfinite(real) || Double.isInfinite(imaginary));<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> /**<a name="line.96"></a> <FONT color="green">097</FONT> * Return the absolute value of this complex number.<a name="line.97"></a> <FONT color="green">098</FONT> * <p><a name="line.98"></a> <FONT color="green">099</FONT> * Returns <code>NaN</code> if either real or imaginary part is<a name="line.99"></a> <FONT color="green">100</FONT> * <code>NaN</code> and <code>Double.POSITIVE_INFINITY</code> if<a name="line.100"></a> <FONT color="green">101</FONT> * neither part is <code>NaN</code>, but at least one part takes an infinite<a name="line.101"></a> <FONT color="green">102</FONT> * value.</p><a name="line.102"></a> <FONT color="green">103</FONT> *<a name="line.103"></a> <FONT color="green">104</FONT> * @return the absolute value<a name="line.104"></a> <FONT color="green">105</FONT> */<a name="line.105"></a> <FONT color="green">106</FONT> public double abs() {<a name="line.106"></a> <FONT color="green">107</FONT> if (isNaN()) {<a name="line.107"></a> <FONT color="green">108</FONT> return Double.NaN;<a name="line.108"></a> <FONT color="green">109</FONT> }<a name="line.109"></a> <FONT color="green">110</FONT> <a name="line.110"></a> <FONT color="green">111</FONT> if (isInfinite()) {<a name="line.111"></a> <FONT color="green">112</FONT> return Double.POSITIVE_INFINITY;<a name="line.112"></a> <FONT color="green">113</FONT> }<a name="line.113"></a> <FONT color="green">114</FONT> <a name="line.114"></a> <FONT color="green">115</FONT> if (Math.abs(real) < Math.abs(imaginary)) {<a name="line.115"></a> <FONT color="green">116</FONT> if (imaginary == 0.0) {<a name="line.116"></a> <FONT color="green">117</FONT> return Math.abs(real);<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> double q = real / imaginary;<a name="line.119"></a> <FONT color="green">120</FONT> return Math.abs(imaginary) * Math.sqrt(1 + q * q);<a name="line.120"></a> <FONT color="green">121</FONT> } else {<a name="line.121"></a> <FONT color="green">122</FONT> if (real == 0.0) {<a name="line.122"></a> <FONT color="green">123</FONT> return Math.abs(imaginary);<a name="line.123"></a> <FONT color="green">124</FONT> }<a name="line.124"></a> <FONT color="green">125</FONT> double q = imaginary / real;<a name="line.125"></a> <FONT color="green">126</FONT> return Math.abs(real) * Math.sqrt(1 + q * q);<a name="line.126"></a> <FONT color="green">127</FONT> }<a name="line.127"></a> <FONT color="green">128</FONT> }<a name="line.128"></a> <FONT color="green">129</FONT> <a name="line.129"></a> <FONT color="green">130</FONT> /**<a name="line.130"></a> <FONT color="green">131</FONT> * Return the sum of this complex number and the given complex number.<a name="line.131"></a> <FONT color="green">132</FONT> * <p><a name="line.132"></a> <FONT color="green">133</FONT> * Uses the definitional formula<a name="line.133"></a> <FONT color="green">134</FONT> * <pre><a name="line.134"></a> <FONT color="green">135</FONT> * (a + bi) + (c + di) = (a+c) + (b+d)i<a name="line.135"></a> <FONT color="green">136</FONT> * </pre></p><a name="line.136"></a> <FONT color="green">137</FONT> * <p><a name="line.137"></a> <FONT color="green">138</FONT> * If either this or <code>rhs</code> has a NaN value in either part,<a name="line.138"></a> <FONT color="green">139</FONT> * {@link #NaN} is returned; otherwise Inifinite and NaN values are<a name="line.139"></a> <FONT color="green">140</FONT> * returned in the parts of the result according to the rules for<a name="line.140"></a> <FONT color="green">141</FONT> * {@link java.lang.Double} arithmetic.</p><a name="line.141"></a> <FONT color="green">142</FONT> *<a name="line.142"></a> <FONT color="green">143</FONT> * @param rhs the other complex number<a name="line.143"></a> <FONT color="green">144</FONT> * @return the complex number sum<a name="line.144"></a> <FONT color="green">145</FONT> * @throws NullPointerException if <code>rhs</code> is null<a name="line.145"></a> <FONT color="green">146</FONT> */<a name="line.146"></a> <FONT color="green">147</FONT> public Complex add(Complex rhs) {<a name="line.147"></a> <FONT color="green">148</FONT> return createComplex(real + rhs.getReal(),<a name="line.148"></a> <FONT color="green">149</FONT> imaginary + rhs.getImaginary());<a name="line.149"></a> <FONT color="green">150</FONT> }<a name="line.150"></a> <FONT color="green">151</FONT> <a name="line.151"></a> <FONT color="green">152</FONT> /**<a name="line.152"></a> <FONT color="green">153</FONT> * Return the conjugate of this complex number. The conjugate of<a name="line.153"></a> <FONT color="green">154</FONT> * "A + Bi" is "A - Bi".<a name="line.154"></a> <FONT color="green">155</FONT> * <p><a name="line.155"></a> <FONT color="green">156</FONT> * {@link #NaN} is returned if either the real or imaginary<a name="line.156"></a> <FONT color="green">157</FONT> * part of this Complex number equals <code>Double.NaN</code>.</p><a name="line.157"></a> <FONT color="green">158</FONT> * <p><a name="line.158"></a> <FONT color="green">159</FONT> * If the imaginary part is infinite, and the real part is not NaN,<a name="line.159"></a> <FONT color="green">160</FONT> * the returned value has infinite imaginary part of the opposite<a name="line.160"></a> <FONT color="green">161</FONT> * sign - e.g. the conjugate of <code>1 + POSITIVE_INFINITY i</code><a name="line.161"></a> <FONT color="green">162</FONT> * is <code>1 - NEGATIVE_INFINITY i</code></p><a name="line.162"></a> <FONT color="green">163</FONT> *<a name="line.163"></a> <FONT color="green">164</FONT> * @return the conjugate of this Complex object<a name="line.164"></a> <FONT color="green">165</FONT> */<a name="line.165"></a> <FONT color="green">166</FONT> public Complex conjugate() {<a name="line.166"></a> <FONT color="green">167</FONT> if (isNaN()) {<a name="line.167"></a> <FONT color="green">168</FONT> return NaN;<a name="line.168"></a> <FONT color="green">169</FONT> }<a name="line.169"></a> <FONT color="green">170</FONT> return createComplex(real, -imaginary);<a name="line.170"></a> <FONT color="green">171</FONT> }<a name="line.171"></a> <FONT color="green">172</FONT> <a name="line.172"></a> <FONT color="green">173</FONT> /**<a name="line.173"></a> <FONT color="green">174</FONT> * Return the quotient of this complex number and the given complex number.<a name="line.174"></a> <FONT color="green">175</FONT> * <p><a name="line.175"></a> <FONT color="green">176</FONT> * Implements the definitional formula<a name="line.176"></a> <FONT color="green">177</FONT> * <pre><code><a name="line.177"></a> <FONT color="green">178</FONT> * a + bi ac + bd + (bc - ad)i<a name="line.178"></a> <FONT color="green">179</FONT> * ----------- = -------------------------<a name="line.179"></a> <FONT color="green">180</FONT> * c + di c<sup>2</sup> + d<sup>2</sup><a name="line.180"></a> <FONT color="green">181</FONT> * </code></pre><a name="line.181"></a> <FONT color="green">182</FONT> * but uses<a name="line.182"></a> <FONT color="green">183</FONT> * <a href="http://doi.acm.org/10.1145/1039813.1039814"><a name="line.183"></a> <FONT color="green">184</FONT> * prescaling of operands</a> to limit the effects of overflows and<a name="line.184"></a> <FONT color="green">185</FONT> * underflows in the computation.</p><a name="line.185"></a> <FONT color="green">186</FONT> * <p><a name="line.186"></a> <FONT color="green">187</FONT> * Infinite and NaN values are handled / returned according to the<a name="line.187"></a> <FONT color="green">188</FONT> * following rules, applied in the order presented:<a name="line.188"></a> <FONT color="green">189</FONT> * <ul><a name="line.189"></a> <FONT color="green">190</FONT> * <li>If either this or <code>rhs</code> has a NaN value in either part,<a name="line.190"></a> <FONT color="green">191</FONT> * {@link #NaN} is returned.</li><a name="line.191"></a> <FONT color="green">192</FONT> * <li>If <code>rhs</code> equals {@link #ZERO}, {@link #NaN} is returned.<a name="line.192"></a> <FONT color="green">193</FONT> * </li><a name="line.193"></a> <FONT color="green">194</FONT> * <li>If this and <code>rhs</code> are both infinite,<a name="line.194"></a> <FONT color="green">195</FONT> * {@link #NaN} is returned.</li><a name="line.195"></a> <FONT color="green">196</FONT> * <li>If this is finite (i.e., has no infinite or NaN parts) and<a name="line.196"></a> <FONT color="green">197</FONT> * <code>rhs</code> is infinite (one or both parts infinite),<a name="line.197"></a> <FONT color="green">198</FONT> * {@link #ZERO} is returned.</li><a name="line.198"></a> <FONT color="green">199</FONT> * <li>If this is infinite and <code>rhs</code> is finite, NaN values are<a name="line.199"></a> <FONT color="green">200</FONT> * returned in the parts of the result if the {@link java.lang.Double}<a name="line.200"></a> <FONT color="green">201</FONT> * rules applied to the definitional formula force NaN results.</li><a name="line.201"></a> <FONT color="green">202</FONT> * </ul></p><a name="line.202"></a> <FONT color="green">203</FONT> *<a name="line.203"></a> <FONT color="green">204</FONT> * @param rhs the other complex number<a name="line.204"></a> <FONT color="green">205</FONT> * @return the complex number quotient<a name="line.205"></a> <FONT color="green">206</FONT> * @throws NullPointerException if <code>rhs</code> is null<a name="line.206"></a> <FONT color="green">207</FONT> */<a name="line.207"></a> <FONT color="green">208</FONT> public Complex divide(Complex rhs) {<a name="line.208"></a> <FONT color="green">209</FONT> if (isNaN() || rhs.isNaN()) {<a name="line.209"></a> <FONT color="green">210</FONT> return NaN;<a name="line.210"></a> <FONT color="green">211</FONT> }<a name="line.211"></a> <FONT color="green">212</FONT> <a name="line.212"></a> <FONT color="green">213</FONT> double c = rhs.getReal();<a name="line.213"></a> <FONT color="green">214</FONT> double d = rhs.getImaginary();<a name="line.214"></a> <FONT color="green">215</FONT> if (c == 0.0 && d == 0.0) {<a name="line.215"></a> <FONT color="green">216</FONT> return NaN;<a name="line.216"></a> <FONT color="green">217</FONT> }<a name="line.217"></a> <FONT color="green">218</FONT> <a name="line.218"></a> <FONT color="green">219</FONT> if (rhs.isInfinite() && !isInfinite()) {<a name="line.219"></a> <FONT color="green">220</FONT> return ZERO;<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> if (Math.abs(c) < Math.abs(d)) {<a name="line.223"></a> <FONT color="green">224</FONT> double q = c / d;<a name="line.224"></a> <FONT color="green">225</FONT> double denominator = c * q + d;<a name="line.225"></a> <FONT color="green">226</FONT> return createComplex((real * q + imaginary) / denominator,<a name="line.226"></a> <FONT color="green">227</FONT> (imaginary * q - real) / denominator);<a name="line.227"></a> <FONT color="green">228</FONT> } else {<a name="line.228"></a> <FONT color="green">229</FONT> double q = d / c;<a name="line.229"></a> <FONT color="green">230</FONT> double denominator = d * q + c;<a name="line.230"></a> <FONT color="green">231</FONT> return createComplex((imaginary * q + real) / denominator,<a name="line.231"></a> <FONT color="green">232</FONT> (imaginary - real * q) / denominator);<a name="line.232"></a> <FONT color="green">233</FONT> }<a name="line.233"></a> <FONT color="green">234</FONT> }<a name="line.234"></a> <FONT color="green">235</FONT> <a name="line.235"></a> <FONT color="green">236</FONT> /**<a name="line.236"></a> <FONT color="green">237</FONT> * Test for the equality of two Complex objects.<a name="line.237"></a> <FONT color="green">238</FONT> * <p><a name="line.238"></a> <FONT color="green">239</FONT> * If both the real and imaginary parts of two Complex numbers<a name="line.239"></a> <FONT color="green">240</FONT> * are exactly the same, and neither is <code>Double.NaN</code>, the two<a name="line.240"></a> <FONT color="green">241</FONT> * Complex objects are considered to be equal.</p><a name="line.241"></a> <FONT color="green">242</FONT> * <p><a name="line.242"></a> <FONT color="green">243</FONT> * All <code>NaN</code> values are considered to be equal - i.e, if either<a name="line.243"></a> <FONT color="green">244</FONT> * (or both) real and imaginary parts of the complex number are equal<a name="line.244"></a> <FONT color="green">245</FONT> * to <code>Double.NaN</code>, the complex number is equal to<a name="line.245"></a> <FONT color="green">246</FONT> * <code>Complex.NaN</code>.</p><a name="line.246"></a> <FONT color="green">247</FONT> *<a name="line.247"></a> <FONT color="green">248</FONT> * @param other Object to test for equality to this<a name="line.248"></a> <FONT color="green">249</FONT> * @return true if two Complex objects are equal, false if<a name="line.249"></a> <FONT color="green">250</FONT> * object is null, not an instance of Complex, or<a name="line.250"></a> <FONT color="green">251</FONT> * not equal to this Complex instance<a name="line.251"></a> <FONT color="green">252</FONT> *<a name="line.252"></a> <FONT color="green">253</FONT> */<a name="line.253"></a> <FONT color="green">254</FONT> @Override<a name="line.254"></a> <FONT color="green">255</FONT> public boolean equals(Object other) {<a name="line.255"></a> <FONT color="green">256</FONT> if (this == other) {<a name="line.256"></a> <FONT color="green">257</FONT> return true;<a name="line.257"></a> <FONT color="green">258</FONT> }<a name="line.258"></a> <FONT color="green">259</FONT> if (other instanceof Complex){<a name="line.259"></a> <FONT color="green">260</FONT> Complex rhs = (Complex)other;<a name="line.260"></a> <FONT color="green">261</FONT> if (rhs.isNaN()) {<a name="line.261"></a> <FONT color="green">262</FONT> return this.isNaN();<a name="line.262"></a> <FONT color="green">263</FONT> } else {<a name="line.263"></a> <FONT color="green">264</FONT> return (real == rhs.real) && (imaginary == rhs.imaginary);<a name="line.264"></a> <FONT color="green">265</FONT> }<a name="line.265"></a> <FONT color="green">266</FONT> }<a name="line.266"></a> <FONT color="green">267</FONT> return false;<a name="line.267"></a> <FONT color="green">268</FONT> }<a name="line.268"></a> <FONT color="green">269</FONT> <a name="line.269"></a> <FONT color="green">270</FONT> /**<a name="line.270"></a> <FONT color="green">271</FONT> * Get a hashCode for the complex number.<a name="line.271"></a> <FONT color="green">272</FONT> * <p><a name="line.272"></a> <FONT color="green">273</FONT> * All NaN values have the same hash code.</p><a name="line.273"></a> <FONT color="green">274</FONT> *<a name="line.274"></a> <FONT color="green">275</FONT> * @return a hash code value for this object<a name="line.275"></a> <FONT color="green">276</FONT> */<a name="line.276"></a> <FONT color="green">277</FONT> @Override<a name="line.277"></a> <FONT color="green">278</FONT> public int hashCode() {<a name="line.278"></a> <FONT color="green">279</FONT> if (isNaN()) {<a name="line.279"></a> <FONT color="green">280</FONT> return 7;<a name="line.280"></a> <FONT color="green">281</FONT> }<a name="line.281"></a> <FONT color="green">282</FONT> return 37 * (17 * MathUtils.hash(imaginary) +<a name="line.282"></a> <FONT color="green">283</FONT> MathUtils.hash(real));<a name="line.283"></a> <FONT color="green">284</FONT> }<a name="line.284"></a> <FONT color="green">285</FONT> <a name="line.285"></a> <FONT color="green">286</FONT> /**<a name="line.286"></a> <FONT color="green">287</FONT> * Access the imaginary part.<a name="line.287"></a> <FONT color="green">288</FONT> *<a name="line.288"></a> <FONT color="green">289</FONT> * @return the imaginary part<a name="line.289"></a> <FONT color="green">290</FONT> */<a name="line.290"></a> <FONT color="green">291</FONT> public double getImaginary() {<a name="line.291"></a> <FONT color="green">292</FONT> return imaginary;<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> /**<a name="line.295"></a> <FONT color="green">296</FONT> * Access the real part.<a name="line.296"></a> <FONT color="green">297</FONT> *<a name="line.297"></a> <FONT color="green">298</FONT> * @return the real part<a name="line.298"></a> <FONT color="green">299</FONT> */<a name="line.299"></a> <FONT color="green">300</FONT> public double getReal() {<a name="line.300"></a> <FONT color="green">301</FONT> return real;<a name="line.301"></a> <FONT color="green">302</FONT> }<a name="line.302"></a> <FONT color="green">303</FONT> <a name="line.303"></a> <FONT color="green">304</FONT> /**<a name="line.304"></a> <FONT color="green">305</FONT> * Returns true if either or both parts of this complex number is NaN;<a name="line.305"></a> <FONT color="green">306</FONT> * false otherwise<a name="line.306"></a> <FONT color="green">307</FONT> *<a name="line.307"></a> <FONT color="green">308</FONT> * @return true if either or both parts of this complex number is NaN;<a name="line.308"></a> <FONT color="green">309</FONT> * false otherwise<a name="line.309"></a> <FONT color="green">310</FONT> */<a name="line.310"></a> <FONT color="green">311</FONT> public boolean isNaN() {<a name="line.311"></a> <FONT color="green">312</FONT> return isNaN;<a name="line.312"></a> <FONT color="green">313</FONT> }<a name="line.313"></a> <FONT color="green">314</FONT> <a name="line.314"></a> <FONT color="green">315</FONT> /**<a name="line.315"></a> <FONT color="green">316</FONT> * Returns true if either the real or imaginary part of this complex number<a name="line.316"></a> <FONT color="green">317</FONT> * takes an infinite value (either <code>Double.POSITIVE_INFINITY</code> or<a name="line.317"></a> <FONT color="green">318</FONT> * <code>Double.NEGATIVE_INFINITY</code>) and neither part<a name="line.318"></a> <FONT color="green">319</FONT> * is <code>NaN</code>.<a name="line.319"></a> <FONT color="green">320</FONT> *<a name="line.320"></a> <FONT color="green">321</FONT> * @return true if one or both parts of this complex number are infinite<a name="line.321"></a> <FONT color="green">322</FONT> * and neither part is <code>NaN</code><a name="line.322"></a> <FONT color="green">323</FONT> */<a name="line.323"></a> <FONT color="green">324</FONT> public boolean isInfinite() {<a name="line.324"></a> <FONT color="green">325</FONT> return isInfinite;<a name="line.325"></a> <FONT color="green">326</FONT> }<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> * Return the product of this complex number and the given complex number.<a name="line.329"></a> <FONT color="green">330</FONT> * <p><a name="line.330"></a> <FONT color="green">331</FONT> * Implements preliminary checks for NaN and infinity followed by<a name="line.331"></a> <FONT color="green">332</FONT> * the definitional formula:<a name="line.332"></a> <FONT color="green">333</FONT> * <pre><code><a name="line.333"></a> <FONT color="green">334</FONT> * (a + bi)(c + di) = (ac - bd) + (ad + bc)i<a name="line.334"></a> <FONT color="green">335</FONT> * </code></pre><a name="line.335"></a> <FONT color="green">336</FONT> * </p><a name="line.336"></a> <FONT color="green">337</FONT> * <p><a name="line.337"></a> <FONT color="green">338</FONT> * Returns {@link #NaN} if either this or <code>rhs</code> has one or more<a name="line.338"></a> <FONT color="green">339</FONT> * NaN parts.<a name="line.339"></a> <FONT color="green">340</FONT> * </p><a name="line.340"></a> <FONT color="green">341</FONT> * Returns {@link #INF} if neither this nor <code>rhs</code> has one or more<a name="line.341"></a> <FONT color="green">342</FONT> * NaN parts and if either this or <code>rhs</code> has one or more<a name="line.342"></a> <FONT color="green">343</FONT> * infinite parts (same result is returned regardless of the sign of the<a name="line.343"></a> <FONT color="green">344</FONT> * components).<a name="line.344"></a> <FONT color="green">345</FONT> * </p><a name="line.345"></a> <FONT color="green">346</FONT> * <p><a name="line.346"></a> <FONT color="green">347</FONT> * Returns finite values in components of the result per the<a name="line.347"></a> <FONT color="green">348</FONT> * definitional formula in all remaining cases.<a name="line.348"></a> <FONT color="green">349</FONT> * </p><a name="line.349"></a> <FONT color="green">350</FONT> *<a name="line.350"></a> <FONT color="green">351</FONT> * @param rhs the other complex number<a name="line.351"></a> <FONT color="green">352</FONT> * @return the complex number product<a name="line.352"></a> <FONT color="green">353</FONT> * @throws NullPointerException if <code>rhs</code> is null<a name="line.353"></a> <FONT color="green">354</FONT> */<a name="line.354"></a> <FONT color="green">355</FONT> public Complex multiply(Complex rhs) {<a name="line.355"></a> <FONT color="green">356</FONT> if (isNaN() || rhs.isNaN()) {<a name="line.356"></a> <FONT color="green">357</FONT> return NaN;<a name="line.357"></a> <FONT color="green">358</FONT> }<a name="line.358"></a> <FONT color="green">359</FONT> if (Double.isInfinite(real) || Double.isInfinite(imaginary) ||<a name="line.359"></a> <FONT color="green">360</FONT> Double.isInfinite(rhs.real)|| Double.isInfinite(rhs.imaginary)) {<a name="line.360"></a> <FONT color="green">361</FONT> // we don't use Complex.isInfinite() to avoid testing for NaN again<a name="line.361"></a> <FONT color="green">362</FONT> return INF;<a name="line.362"></a> <FONT color="green">363</FONT> }<a name="line.363"></a> <FONT color="green">364</FONT> return createComplex(real * rhs.real - imaginary * rhs.imaginary,<a name="line.364"></a> <FONT color="green">365</FONT> real * rhs.imaginary + imaginary * rhs.real);<a name="line.365"></a> <FONT color="green">366</FONT> }<a name="line.366"></a> <FONT color="green">367</FONT> <a name="line.367"></a> <FONT color="green">368</FONT> /**<a name="line.368"></a> <FONT color="green">369</FONT> * Return the product of this complex number and the given scalar number.<a name="line.369"></a> <FONT color="green">370</FONT> * <p><a name="line.370"></a> <FONT color="green">371</FONT> * Implements preliminary checks for NaN and infinity followed by<a name="line.371"></a> <FONT color="green">372</FONT> * the definitional formula:<a name="line.372"></a> <FONT color="green">373</FONT> * <pre><code><a name="line.373"></a> <FONT color="green">374</FONT> * c(a + bi) = (ca) + (cb)i<a name="line.374"></a> <FONT color="green">375</FONT> * </code></pre><a name="line.375"></a> <FONT color="green">376</FONT> * </p><a name="line.376"></a> <FONT color="green">377</FONT> * <p><a name="line.377"></a> <FONT color="green">378</FONT> * Returns {@link #NaN} if either this or <code>rhs</code> has one or more<a name="line.378"></a> <FONT color="green">379</FONT> * NaN parts.<a name="line.379"></a> <FONT color="green">380</FONT> * </p><a name="line.380"></a> <FONT color="green">381</FONT> * Returns {@link #INF} if neither this nor <code>rhs</code> has one or more<a name="line.381"></a> <FONT color="green">382</FONT> * NaN parts and if either this or <code>rhs</code> has one or more<a name="line.382"></a> <FONT color="green">383</FONT> * infinite parts (same result is returned regardless of the sign of the<a name="line.383"></a> <FONT color="green">384</FONT> * components).<a name="line.384"></a> <FONT color="green">385</FONT> * </p><a name="line.385"></a> <FONT color="green">386</FONT> * <p><a name="line.386"></a> <FONT color="green">387</FONT> * Returns finite values in components of the result per the<a name="line.387"></a> <FONT color="green">388</FONT> * definitional formula in all remaining cases.<a name="line.388"></a> <FONT color="green">389</FONT> * </p><a name="line.389"></a> <FONT color="green">390</FONT> *<a name="line.390"></a> <FONT color="green">391</FONT> * @param rhs the scalar number<a name="line.391"></a> <FONT color="green">392</FONT> * @return the complex number product<a name="line.392"></a> <FONT color="green">393</FONT> */<a name="line.393"></a> <FONT color="green">394</FONT> public Complex multiply(double rhs) {<a name="line.394"></a> <FONT color="green">395</FONT> if (isNaN() || Double.isNaN(rhs)) {<a name="line.395"></a> <FONT color="green">396</FONT> return NaN;<a name="line.396"></a> <FONT color="green">397</FONT> }<a name="line.397"></a> <FONT color="green">398</FONT> if (Double.isInfinite(real) || Double.isInfinite(imaginary) ||<a name="line.398"></a> <FONT color="green">399</FONT> Double.isInfinite(rhs)) {<a name="line.399"></a> <FONT color="green">400</FONT> // we don't use Complex.isInfinite() to avoid testing for NaN again<a name="line.400"></a> <FONT color="green">401</FONT> return INF;<a name="line.401"></a> <FONT color="green">402</FONT> }<a name="line.402"></a> <FONT color="green">403</FONT> return createComplex(real * rhs, imaginary * rhs);<a name="line.403"></a> <FONT color="green">404</FONT> }<a name="line.404"></a> <FONT color="green">405</FONT> <a name="line.405"></a> <FONT color="green">406</FONT> /**<a name="line.406"></a> <FONT color="green">407</FONT> * Return the additive inverse of this complex number.<a name="line.407"></a> <FONT color="green">408</FONT> * <p><a name="line.408"></a> <FONT color="green">409</FONT> * Returns <code>Complex.NaN</code> if either real or imaginary<a name="line.409"></a> <FONT color="green">410</FONT> * part of this Complex number equals <code>Double.NaN</code>.</p><a name="line.410"></a> <FONT color="green">411</FONT> *<a name="line.411"></a> <FONT color="green">412</FONT> * @return the negation of this complex number<a name="line.412"></a> <FONT color="green">413</FONT> */<a name="line.413"></a> <FONT color="green">414</FONT> public Complex negate() {<a name="line.414"></a> <FONT color="green">415</FONT> if (isNaN()) {<a name="line.415"></a> <FONT color="green">416</FONT> return NaN;<a name="line.416"></a> <FONT color="green">417</FONT> }<a name="line.417"></a> <FONT color="green">418</FONT> <a name="line.418"></a> <FONT color="green">419</FONT> return createComplex(-real, -imaginary);<a name="line.419"></a> <FONT color="green">420</FONT> }<a name="line.420"></a> <FONT color="green">421</FONT> <a name="line.421"></a> <FONT color="green">422</FONT> /**<a name="line.422"></a> <FONT color="green">423</FONT> * Return the difference between this complex number and the given complex<a name="line.423"></a> <FONT color="green">424</FONT> * number.<a name="line.424"></a> <FONT color="green">425</FONT> * <p><a name="line.425"></a> <FONT color="green">426</FONT> * Uses the definitional formula<a name="line.426"></a> <FONT color="green">427</FONT> * <pre><a name="line.427"></a> <FONT color="green">428</FONT> * (a + bi) - (c + di) = (a-c) + (b-d)i<a name="line.428"></a> <FONT color="green">429</FONT> * </pre></p><a name="line.429"></a> <FONT color="green">430</FONT> * <p><a name="line.430"></a> <FONT color="green">431</FONT> * If either this or <code>rhs</code> has a NaN value in either part,<a name="line.431"></a> <FONT color="green">432</FONT> * {@link #NaN} is returned; otherwise inifinite and NaN values are<a name="line.432"></a> <FONT color="green">433</FONT> * returned in the parts of the result according to the rules for<a name="line.433"></a> <FONT color="green">434</FONT> * {@link java.lang.Double} arithmetic. </p><a name="line.434"></a> <FONT color="green">435</FONT> *<a name="line.435"></a> <FONT color="green">436</FONT> * @param rhs the other complex number<a name="line.436"></a> <FONT color="green">437</FONT> * @return the complex number difference<a name="line.437"></a> <FONT color="green">438</FONT> * @throws NullPointerException if <code>rhs</code> is null<a name="line.438"></a> <FONT color="green">439</FONT> */<a name="line.439"></a> <FONT color="green">440</FONT> public Complex subtract(Complex rhs) {<a name="line.440"></a> <FONT color="green">441</FONT> if (isNaN() || rhs.isNaN()) {<a name="line.441"></a> <FONT color="green">442</FONT> return NaN;<a name="line.442"></a> <FONT color="green">443</FONT> }<a name="line.443"></a> <FONT color="green">444</FONT> <a name="line.444"></a> <FONT color="green">445</FONT> return createComplex(real - rhs.getReal(),<a name="line.445"></a> <FONT color="green">446</FONT> imaginary - rhs.getImaginary());<a name="line.446"></a> <FONT color="green">447</FONT> }<a name="line.447"></a> <FONT color="green">448</FONT> <a name="line.448"></a> <FONT color="green">449</FONT> /**<a name="line.449"></a> <FONT color="green">450</FONT> * Compute the<a name="line.450"></a> <FONT color="green">451</FONT> * <a href="http://mathworld.wolfram.com/InverseCosine.html" TARGET="_top"><a name="line.451"></a> <FONT color="green">452</FONT> * inverse cosine</a> of this complex number.<a name="line.452"></a> <FONT color="green">453</FONT> * <p><a name="line.453"></a> <FONT color="green">454</FONT> * Implements the formula: <pre><a name="line.454"></a> <FONT color="green">455</FONT> * <code> acos(z) = -i (log(z + i (sqrt(1 - z<sup>2</sup>))))</code></pre></p><a name="line.455"></a> <FONT color="green">456</FONT> * <p><a name="line.456"></a> <FONT color="green">457</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.457"></a> <FONT color="green">458</FONT> * input argument is <code>NaN</code> or infinite.</p><a name="line.458"></a> <FONT color="green">459</FONT> *<a name="line.459"></a> <FONT color="green">460</FONT> * @return the inverse cosine of this complex number<a name="line.460"></a> <FONT color="green">461</FONT> * @since 1.2<a name="line.461"></a> <FONT color="green">462</FONT> */<a name="line.462"></a> <FONT color="green">463</FONT> public Complex acos() {<a name="line.463"></a> <FONT color="green">464</FONT> if (isNaN()) {<a name="line.464"></a> <FONT color="green">465</FONT> return Complex.NaN;<a name="line.465"></a> <FONT color="green">466</FONT> }<a name="line.466"></a> <FONT color="green">467</FONT> <a name="line.467"></a> <FONT color="green">468</FONT> return this.add(this.sqrt1z().multiply(Complex.I)).log()<a name="line.468"></a> <FONT color="green">469</FONT> .multiply(Complex.I.negate());<a name="line.469"></a> <FONT color="green">470</FONT> }<a name="line.470"></a> <FONT color="green">471</FONT> <a name="line.471"></a> <FONT color="green">472</FONT> /**<a name="line.472"></a> <FONT color="green">473</FONT> * Compute the<a name="line.473"></a> <FONT color="green">474</FONT> * <a href="http://mathworld.wolfram.com/InverseSine.html" TARGET="_top"><a name="line.474"></a> <FONT color="green">475</FONT> * inverse sine</a> of this complex number.<a name="line.475"></a> <FONT color="green">476</FONT> * <p><a name="line.476"></a> <FONT color="green">477</FONT> * Implements the formula: <pre><a name="line.477"></a> <FONT color="green">478</FONT> * <code> asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz)) </code></pre></p><a name="line.478"></a> <FONT color="green">479</FONT> * <p><a name="line.479"></a> <FONT color="green">480</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.480"></a> <FONT color="green">481</FONT> * input argument is <code>NaN</code> or infinite.</p><a name="line.481"></a> <FONT color="green">482</FONT> *<a name="line.482"></a> <FONT color="green">483</FONT> * @return the inverse sine of this complex number.<a name="line.483"></a> <FONT color="green">484</FONT> * @since 1.2<a name="line.484"></a> <FONT color="green">485</FONT> */<a name="line.485"></a> <FONT color="green">486</FONT> public Complex asin() {<a name="line.486"></a> <FONT color="green">487</FONT> if (isNaN()) {<a name="line.487"></a> <FONT color="green">488</FONT> return Complex.NaN;<a name="line.488"></a> <FONT color="green">489</FONT> }<a name="line.489"></a> <FONT color="green">490</FONT> <a name="line.490"></a> <FONT color="green">491</FONT> return sqrt1z().add(this.multiply(Complex.I)).log()<a name="line.491"></a> <FONT color="green">492</FONT> .multiply(Complex.I.negate());<a name="line.492"></a> <FONT color="green">493</FONT> }<a name="line.493"></a> <FONT color="green">494</FONT> <a name="line.494"></a> <FONT color="green">495</FONT> /**<a name="line.495"></a> <FONT color="green">496</FONT> * Compute the<a name="line.496"></a> <FONT color="green">497</FONT> * <a href="http://mathworld.wolfram.com/InverseTangent.html" TARGET="_top"><a name="line.497"></a> <FONT color="green">498</FONT> * inverse tangent</a> of this complex number.<a name="line.498"></a> <FONT color="green">499</FONT> * <p><a name="line.499"></a> <FONT color="green">500</FONT> * Implements the formula: <pre><a name="line.500"></a> <FONT color="green">501</FONT> * <code> atan(z) = (i/2) log((i + z)/(i - z)) </code></pre></p><a name="line.501"></a> <FONT color="green">502</FONT> * <p><a name="line.502"></a> <FONT color="green">503</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.503"></a> <FONT color="green">504</FONT> * input argument is <code>NaN</code> or infinite.</p><a name="line.504"></a> <FONT color="green">505</FONT> *<a name="line.505"></a> <FONT color="green">506</FONT> * @return the inverse tangent of this complex number<a name="line.506"></a> <FONT color="green">507</FONT> * @since 1.2<a name="line.507"></a> <FONT color="green">508</FONT> */<a name="line.508"></a> <FONT color="green">509</FONT> public Complex atan() {<a name="line.509"></a> <FONT color="green">510</FONT> if (isNaN()) {<a name="line.510"></a> <FONT color="green">511</FONT> return Complex.NaN;<a name="line.511"></a> <FONT color="green">512</FONT> }<a name="line.512"></a> <FONT color="green">513</FONT> <a name="line.513"></a> <FONT color="green">514</FONT> return this.add(Complex.I).divide(Complex.I.subtract(this)).log()<a name="line.514"></a> <FONT color="green">515</FONT> .multiply(Complex.I.divide(createComplex(2.0, 0.0)));<a name="line.515"></a> <FONT color="green">516</FONT> }<a name="line.516"></a> <FONT color="green">517</FONT> <a name="line.517"></a> <FONT color="green">518</FONT> /**<a name="line.518"></a> <FONT color="green">519</FONT> * Compute the<a name="line.519"></a> <FONT color="green">520</FONT> * <a href="http://mathworld.wolfram.com/Cosine.html" TARGET="_top"><a name="line.520"></a> <FONT color="green">521</FONT> * cosine</a><a name="line.521"></a> <FONT color="green">522</FONT> * of this complex number.<a name="line.522"></a> <FONT color="green">523</FONT> * <p><a name="line.523"></a> <FONT color="green">524</FONT> * Implements the formula: <pre><a name="line.524"></a> <FONT color="green">525</FONT> * <code> cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i</code></pre><a name="line.525"></a> <FONT color="green">526</FONT> * where the (real) functions on the right-hand side are<a name="line.526"></a> <FONT color="green">527</FONT> * {@link java.lang.Math#sin}, {@link java.lang.Math#cos},<a name="line.527"></a> <FONT color="green">528</FONT> * {@link MathUtils#cosh} and {@link MathUtils#sinh}.</p><a name="line.528"></a> <FONT color="green">529</FONT> * <p><a name="line.529"></a> <FONT color="green">530</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.530"></a> <FONT color="green">531</FONT> * input argument is <code>NaN</code>.</p><a name="line.531"></a> <FONT color="green">532</FONT> * <p><a name="line.532"></a> <FONT color="green">533</FONT> * Infinite values in real or imaginary parts of the input may result in<a name="line.533"></a> <FONT color="green">534</FONT> * infinite or NaN values returned in parts of the result.<pre><a name="line.534"></a> <FONT color="green">535</FONT> * Examples:<a name="line.535"></a> <FONT color="green">536</FONT> * <code><a name="line.536"></a> <FONT color="green">537</FONT> * cos(1 &plusmn; INFINITY i) = 1 &#x2213; INFINITY i<a name="line.537"></a> <FONT color="green">538</FONT> * cos(&plusmn;INFINITY + i) = NaN + NaN i<a name="line.538"></a> <FONT color="green">539</FONT> * cos(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i</code></pre></p><a name="line.539"></a> <FONT color="green">540</FONT> *<a name="line.540"></a> <FONT color="green">541</FONT> * @return the cosine of this complex number<a name="line.541"></a> <FONT color="green">542</FONT> * @since 1.2<a name="line.542"></a> <FONT color="green">543</FONT> */<a name="line.543"></a> <FONT color="green">544</FONT> public Complex cos() {<a name="line.544"></a> <FONT color="green">545</FONT> if (isNaN()) {<a name="line.545"></a> <FONT color="green">546</FONT> return Complex.NaN;<a name="line.546"></a> <FONT color="green">547</FONT> }<a name="line.547"></a> <FONT color="green">548</FONT> <a name="line.548"></a> <FONT color="green">549</FONT> return createComplex(Math.cos(real) * MathUtils.cosh(imaginary),<a name="line.549"></a> <FONT color="green">550</FONT> -Math.sin(real) * MathUtils.sinh(imaginary));<a name="line.550"></a> <FONT color="green">551</FONT> }<a name="line.551"></a> <FONT color="green">552</FONT> <a name="line.552"></a> <FONT color="green">553</FONT> /**<a name="line.553"></a> <FONT color="green">554</FONT> * Compute the<a name="line.554"></a> <FONT color="green">555</FONT> * <a href="http://mathworld.wolfram.com/HyperbolicCosine.html" TARGET="_top"><a name="line.555"></a> <FONT color="green">556</FONT> * hyperbolic cosine</a> of this complex number.<a name="line.556"></a> <FONT color="green">557</FONT> * <p><a name="line.557"></a> <FONT color="green">558</FONT> * Implements the formula: <pre><a name="line.558"></a> <FONT color="green">559</FONT> * <code> cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i</code></pre><a name="line.559"></a> <FONT color="green">560</FONT> * where the (real) functions on the right-hand side are<a name="line.560"></a> <FONT color="green">561</FONT> * {@link java.lang.Math#sin}, {@link java.lang.Math#cos},<a name="line.561"></a> <FONT color="green">562</FONT> * {@link MathUtils#cosh} and {@link MathUtils#sinh}.</p><a name="line.562"></a> <FONT color="green">563</FONT> * <p><a name="line.563"></a> <FONT color="green">564</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.564"></a> <FONT color="green">565</FONT> * input argument is <code>NaN</code>.</p><a name="line.565"></a> <FONT color="green">566</FONT> * <p><a name="line.566"></a> <FONT color="green">567</FONT> * Infinite values in real or imaginary parts of the input may result in<a name="line.567"></a> <FONT color="green">568</FONT> * infinite or NaN values returned in parts of the result.<pre><a name="line.568"></a> <FONT color="green">569</FONT> * Examples:<a name="line.569"></a> <FONT color="green">570</FONT> * <code><a name="line.570"></a> <FONT color="green">571</FONT> * cosh(1 &plusmn; INFINITY i) = NaN + NaN i<a name="line.571"></a> <FONT color="green">572</FONT> * cosh(&plusmn;INFINITY + i) = INFINITY &plusmn; INFINITY i<a name="line.572"></a> <FONT color="green">573</FONT> * cosh(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i</code></pre></p><a name="line.573"></a> <FONT color="green">574</FONT> *<a name="line.574"></a> <FONT color="green">575</FONT> * @return the hyperbolic cosine of this complex number.<a name="line.575"></a> <FONT color="green">576</FONT> * @since 1.2<a name="line.576"></a> <FONT color="green">577</FONT> */<a name="line.577"></a> <FONT color="green">578</FONT> public Complex cosh() {<a name="line.578"></a> <FONT color="green">579</FONT> if (isNaN()) {<a name="line.579"></a> <FONT color="green">580</FONT> return Complex.NaN;<a name="line.580"></a> <FONT color="green">581</FONT> }<a name="line.581"></a> <FONT color="green">582</FONT> <a name="line.582"></a> <FONT color="green">583</FONT> return createComplex(MathUtils.cosh(real) * Math.cos(imaginary),<a name="line.583"></a> <FONT color="green">584</FONT> MathUtils.sinh(real) * Math.sin(imaginary));<a name="line.584"></a> <FONT color="green">585</FONT> }<a name="line.585"></a> <FONT color="green">586</FONT> <a name="line.586"></a> <FONT color="green">587</FONT> /**<a name="line.587"></a> <FONT color="green">588</FONT> * Compute the<a name="line.588"></a> <FONT color="green">589</FONT> * <a href="http://mathworld.wolfram.com/ExponentialFunction.html" TARGET="_top"><a name="line.589"></a> <FONT color="green">590</FONT> * exponential function</a> of this complex number.<a name="line.590"></a> <FONT color="green">591</FONT> * <p><a name="line.591"></a> <FONT color="green">592</FONT> * Implements the formula: <pre><a name="line.592"></a> <FONT color="green">593</FONT> * <code> exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i</code></pre><a name="line.593"></a> <FONT color="green">594</FONT> * where the (real) functions on the right-hand side are<a name="line.594"></a> <FONT color="green">595</FONT> * {@link java.lang.Math#exp}, {@link java.lang.Math#cos}, and<a name="line.595"></a> <FONT color="green">596</FONT> * {@link java.lang.Math#sin}.</p><a name="line.596"></a> <FONT color="green">597</FONT> * <p><a name="line.597"></a> <FONT color="green">598</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.598"></a> <FONT color="green">599</FONT> * input argument is <code>NaN</code>.</p><a name="line.599"></a> <FONT color="green">600</FONT> * <p><a name="line.600"></a> <FONT color="green">601</FONT> * Infinite values in real or imaginary parts of the input may result in<a name="line.601"></a> <FONT color="green">602</FONT> * infinite or NaN values returned in parts of the result.<pre><a name="line.602"></a> <FONT color="green">603</FONT> * Examples:<a name="line.603"></a> <FONT color="green">604</FONT> * <code><a name="line.604"></a> <FONT color="green">605</FONT> * exp(1 &plusmn; INFINITY i) = NaN + NaN i<a name="line.605"></a> <FONT color="green">606</FONT> * exp(INFINITY + i) = INFINITY + INFINITY i<a name="line.606"></a> <FONT color="green">607</FONT> * exp(-INFINITY + i) = 0 + 0i<a name="line.607"></a> <FONT color="green">608</FONT> * exp(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i</code></pre></p><a name="line.608"></a> <FONT color="green">609</FONT> *<a name="line.609"></a> <FONT color="green">610</FONT> * @return <i>e</i><sup><code>this</code></sup><a name="line.610"></a> <FONT color="green">611</FONT> * @since 1.2<a name="line.611"></a> <FONT color="green">612</FONT> */<a name="line.612"></a> <FONT color="green">613</FONT> public Complex exp() {<a name="line.613"></a> <FONT color="green">614</FONT> if (isNaN()) {<a name="line.614"></a> <FONT color="green">615</FONT> return Complex.NaN;<a name="line.615"></a> <FONT color="green">616</FONT> }<a name="line.616"></a> <FONT color="green">617</FONT> <a name="line.617"></a> <FONT color="green">618</FONT> double expReal = Math.exp(real);<a name="line.618"></a> <FONT color="green">619</FONT> return createComplex(expReal * Math.cos(imaginary), expReal * Math.sin(imaginary));<a name="line.619"></a> <FONT color="green">620</FONT> }<a name="line.620"></a> <FONT color="green">621</FONT> <a name="line.621"></a> <FONT color="green">622</FONT> /**<a name="line.622"></a> <FONT color="green">623</FONT> * Compute the<a name="line.623"></a> <FONT color="green">624</FONT> * <a href="http://mathworld.wolfram.com/NaturalLogarithm.html" TARGET="_top"><a name="line.624"></a> <FONT color="green">625</FONT> * natural logarithm</a> of this complex number.<a name="line.625"></a> <FONT color="green">626</FONT> * <p><a name="line.626"></a> <FONT color="green">627</FONT> * Implements the formula: <pre><a name="line.627"></a> <FONT color="green">628</FONT> * <code> log(a + bi) = ln(|a + bi|) + arg(a + bi)i</code></pre><a name="line.628"></a> <FONT color="green">629</FONT> * where ln on the right hand side is {@link java.lang.Math#log},<a name="line.629"></a> <FONT color="green">630</FONT> * <code>|a + bi|</code> is the modulus, {@link Complex#abs}, and<a name="line.630"></a> <FONT color="green">631</FONT> * <code>arg(a + bi) = {@link java.lang.Math#atan2}(b, a)</code></p><a name="line.631"></a> <FONT color="green">632</FONT> * <p><a name="line.632"></a> <FONT color="green">633</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.633"></a> <FONT color="green">634</FONT> * input argument is <code>NaN</code>.</p><a name="line.634"></a> <FONT color="green">635</FONT> * <p><a name="line.635"></a> <FONT color="green">636</FONT> * Infinite (or critical) values in real or imaginary parts of the input may<a name="line.636"></a> <FONT color="green">637</FONT> * result in infinite or NaN values returned in parts of the result.<pre><a name="line.637"></a> <FONT color="green">638</FONT> * Examples:<a name="line.638"></a> <FONT color="green">639</FONT> * <code><a name="line.639"></a> <FONT color="green">640</FONT> * log(1 &plusmn; INFINITY i) = INFINITY &plusmn; (&pi;/2)i<a name="line.640"></a> <FONT color="green">641</FONT> * log(INFINITY + i) = INFINITY + 0i<a name="line.641"></a> <FONT color="green">642</FONT> * log(-INFINITY + i) = INFINITY + &pi;i<a name="line.642"></a> <FONT color="green">643</FONT> * log(INFINITY &plusmn; INFINITY i) = INFINITY &plusmn; (&pi;/4)i<a name="line.643"></a> <FONT color="green">644</FONT> * log(-INFINITY &plusmn; INFINITY i) = INFINITY &plusmn; (3&pi;/4)i<a name="line.644"></a> <FONT color="green">645</FONT> * log(0 + 0i) = -INFINITY + 0i<a name="line.645"></a> <FONT color="green">646</FONT> * </code></pre></p><a name="line.646"></a> <FONT color="green">647</FONT> *<a name="line.647"></a> <FONT color="green">648</FONT> * @return ln of this complex number.<a name="line.648"></a> <FONT color="green">649</FONT> * @since 1.2<a name="line.649"></a> <FONT color="green">650</FONT> */<a name="line.650"></a> <FONT color="green">651</FONT> public Complex log() {<a name="line.651"></a> <FONT color="green">652</FONT> if (isNaN()) {<a name="line.652"></a> <FONT color="green">653</FONT> return Complex.NaN;<a name="line.653"></a> <FONT color="green">654</FONT> }<a name="line.654"></a> <FONT color="green">655</FONT> <a name="line.655"></a> <FONT color="green">656</FONT> return createComplex(Math.log(abs()),<a name="line.656"></a> <FONT color="green">657</FONT> Math.atan2(imaginary, real));<a name="line.657"></a> <FONT color="green">658</FONT> }<a name="line.658"></a> <FONT color="green">659</FONT> <a name="line.659"></a> <FONT color="green">660</FONT> /**<a name="line.660"></a> <FONT color="green">661</FONT> * Returns of value of this complex number raised to the power of <code>x</code>.<a name="line.661"></a> <FONT color="green">662</FONT> * <p><a name="line.662"></a> <FONT color="green">663</FONT> * Implements the formula: <pre><a name="line.663"></a> <FONT color="green">664</FONT> * <code> y<sup>x</sup> = exp(x&middot;log(y))</code></pre><a name="line.664"></a> <FONT color="green">665</FONT> * where <code>exp</code> and <code>log</code> are {@link #exp} and<a name="line.665"></a> <FONT color="green">666</FONT> * {@link #log}, respectively.</p><a name="line.666"></a> <FONT color="green">667</FONT> * <p><a name="line.667"></a> <FONT color="green">668</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.668"></a> <FONT color="green">669</FONT> * input argument is <code>NaN</code> or infinite, or if <code>y</code><a name="line.669"></a> <FONT color="green">670</FONT> * equals {@link Complex#ZERO}.</p><a name="line.670"></a> <FONT color="green">671</FONT> *<a name="line.671"></a> <FONT color="green">672</FONT> * @param x the exponent.<a name="line.672"></a> <FONT color="green">673</FONT> * @return <code>this</code><sup><code>x</code></sup><a name="line.673"></a> <FONT color="green">674</FONT> * @throws NullPointerException if x is null<a name="line.674"></a> <FONT color="green">675</FONT> * @since 1.2<a name="line.675"></a> <FONT color="green">676</FONT> */<a name="line.676"></a> <FONT color="green">677</FONT> public Complex pow(Complex x) {<a name="line.677"></a> <FONT color="green">678</FONT> if (x == null) {<a name="line.678"></a> <FONT color="green">679</FONT> throw new NullPointerException();<a name="line.679"></a> <FONT color="green">680</FONT> }<a name="line.680"></a> <FONT color="green">681</FONT> return this.log().multiply(x).exp();<a name="line.681"></a> <FONT color="green">682</FONT> }<a name="line.682"></a> <FONT color="green">683</FONT> <a name="line.683"></a> <FONT color="green">684</FONT> /**<a name="line.684"></a> <FONT color="green">685</FONT> * Compute the<a name="line.685"></a> <FONT color="green">686</FONT> * <a href="http://mathworld.wolfram.com/Sine.html" TARGET="_top"><a name="line.686"></a> <FONT color="green">687</FONT> * sine</a><a name="line.687"></a> <FONT color="green">688</FONT> * of this complex number.<a name="line.688"></a> <FONT color="green">689</FONT> * <p><a name="line.689"></a> <FONT color="green">690</FONT> * Implements the formula: <pre><a name="line.690"></a> <FONT color="green">691</FONT> * <code> sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i</code></pre><a name="line.691"></a> <FONT color="green">692</FONT> * where the (real) functions on the right-hand side are<a name="line.692"></a> <FONT color="green">693</FONT> * {@link java.lang.Math#sin}, {@link java.lang.Math#cos},<a name="line.693"></a> <FONT color="green">694</FONT> * {@link MathUtils#cosh} and {@link MathUtils#sinh}.</p><a name="line.694"></a> <FONT color="green">695</FONT> * <p><a name="line.695"></a> <FONT color="green">696</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.696"></a> <FONT color="green">697</FONT> * input argument is <code>NaN</code>.</p><a name="line.697"></a> <FONT color="green">698</FONT> * <p><a name="line.698"></a> <FONT color="green">699</FONT> * Infinite values in real or imaginary parts of the input may result in<a name="line.699"></a> <FONT color="green">700</FONT> * infinite or NaN values returned in parts of the result.<pre><a name="line.700"></a> <FONT color="green">701</FONT> * Examples:<a name="line.701"></a> <FONT color="green">702</FONT> * <code><a name="line.702"></a> <FONT color="green">703</FONT> * sin(1 &plusmn; INFINITY i) = 1 &plusmn; INFINITY i<a name="line.703"></a> <FONT color="green">704</FONT> * sin(&plusmn;INFINITY + i) = NaN + NaN i<a name="line.704"></a> <FONT color="green">705</FONT> * sin(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i</code></pre></p><a name="line.705"></a> <FONT color="green">706</FONT> *<a name="line.706"></a> <FONT color="green">707</FONT> * @return the sine of this complex number.<a name="line.707"></a> <FONT color="green">708</FONT> * @since 1.2<a name="line.708"></a> <FONT color="green">709</FONT> */<a name="line.709"></a> <FONT color="green">710</FONT> public Complex sin() {<a name="line.710"></a> <FONT color="green">711</FONT> if (isNaN()) {<a name="line.711"></a> <FONT color="green">712</FONT> return Complex.NaN;<a name="line.712"></a> <FONT color="green">713</FONT> }<a name="line.713"></a> <FONT color="green">714</FONT> <a name="line.714"></a> <FONT color="green">715</FONT> return createComplex(Math.sin(real) * MathUtils.cosh(imaginary),<a name="line.715"></a> <FONT color="green">716</FONT> Math.cos(real) * MathUtils.sinh(imaginary));<a name="line.716"></a> <FONT color="green">717</FONT> }<a name="line.717"></a> <FONT color="green">718</FONT> <a name="line.718"></a> <FONT color="green">719</FONT> /**<a name="line.719"></a> <FONT color="green">720</FONT> * Compute the<a name="line.720"></a> <FONT color="green">721</FONT> * <a href="http://mathworld.wolfram.com/HyperbolicSine.html" TARGET="_top"><a name="line.721"></a> <FONT color="green">722</FONT> * hyperbolic sine</a> of this complex number.<a name="line.722"></a> <FONT color="green">723</FONT> * <p><a name="line.723"></a> <FONT color="green">724</FONT> * Implements the formula: <pre><a name="line.724"></a> <FONT color="green">725</FONT> * <code> sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i</code></pre><a name="line.725"></a> <FONT color="green">726</FONT> * where the (real) functions on the right-hand side are<a name="line.726"></a> <FONT color="green">727</FONT> * {@link java.lang.Math#sin}, {@link java.lang.Math#cos},<a name="line.727"></a> <FONT color="green">728</FONT> * {@link MathUtils#cosh} and {@link MathUtils#sinh}.</p><a name="line.728"></a> <FONT color="green">729</FONT> * <p><a name="line.729"></a> <FONT color="green">730</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.730"></a> <FONT color="green">731</FONT> * input argument is <code>NaN</code>.</p><a name="line.731"></a> <FONT color="green">732</FONT> * <p><a name="line.732"></a> <FONT color="green">733</FONT> * Infinite values in real or imaginary parts of the input may result in<a name="line.733"></a> <FONT color="green">734</FONT> * infinite or NaN values returned in parts of the result.<pre><a name="line.734"></a> <FONT color="green">735</FONT> * Examples:<a name="line.735"></a> <FONT color="green">736</FONT> * <code><a name="line.736"></a> <FONT color="green">737</FONT> * sinh(1 &plusmn; INFINITY i) = NaN + NaN i<a name="line.737"></a> <FONT color="green">738</FONT> * sinh(&plusmn;INFINITY + i) = &plusmn; INFINITY + INFINITY i<a name="line.738"></a> <FONT color="green">739</FONT> * sinh(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i</code></pre></p><a name="line.739"></a> <FONT color="green">740</FONT> *<a name="line.740"></a> <FONT color="green">741</FONT> * @return the hyperbolic sine of this complex number<a name="line.741"></a> <FONT color="green">742</FONT> * @since 1.2<a name="line.742"></a> <FONT color="green">743</FONT> */<a name="line.743"></a> <FONT color="green">744</FONT> public Complex sinh() {<a name="line.744"></a> <FONT color="green">745</FONT> if (isNaN()) {<a name="line.745"></a> <FONT color="green">746</FONT> return Complex.NaN;<a name="line.746"></a> <FONT color="green">747</FONT> }<a name="line.747"></a> <FONT color="green">748</FONT> <a name="line.748"></a> <FONT color="green">749</FONT> return createComplex(MathUtils.sinh(real) * Math.cos(imaginary),<a name="line.749"></a> <FONT color="green">750</FONT> MathUtils.cosh(real) * Math.sin(imaginary));<a name="line.750"></a> <FONT color="green">751</FONT> }<a name="line.751"></a> <FONT color="green">752</FONT> <a name="line.752"></a> <FONT color="green">753</FONT> /**<a name="line.753"></a> <FONT color="green">754</FONT> * Compute the<a name="line.754"></a> <FONT color="green">755</FONT> * <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top"><a name="line.755"></a> <FONT color="green">756</FONT> * square root</a> of this complex number.<a name="line.756"></a> <FONT color="green">757</FONT> * <p><a name="line.757"></a> <FONT color="green">758</FONT> * Implements the following algorithm to compute <code>sqrt(a + bi)</code>:<a name="line.758"></a> <FONT color="green">759</FONT> * <ol><li>Let <code>t = sqrt((|a| + |a + bi|) / 2)</code></li><a name="line.759"></a> <FONT color="green">760</FONT> * <li><pre>if <code> a &#8805; 0</code> return <code>t + (b/2t)i</code><a name="line.760"></a> <FONT color="green">761</FONT> * else return <code>|b|/2t + sign(b)t i </code></pre></li><a name="line.761"></a> <FONT color="green">762</FONT> * </ol><a name="line.762"></a> <FONT color="green">763</FONT> * where <ul><a name="line.763"></a> <FONT color="green">764</FONT> * <li><code>|a| = {@link Math#abs}(a)</code></li><a name="line.764"></a> <FONT color="green">765</FONT> * <li><code>|a + bi| = {@link Complex#abs}(a + bi) </code></li><a name="line.765"></a> <FONT color="green">766</FONT> * <li><code>sign(b) = {@link MathUtils#indicator}(b) </code><a name="line.766"></a> <FONT color="green">767</FONT> * </ul></p><a name="line.767"></a> <FONT color="green">768</FONT> * <p><a name="line.768"></a> <FONT color="green">769</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.769"></a> <FONT color="green">770</FONT> * input argument is <code>NaN</code>.</p><a name="line.770"></a> <FONT color="green">771</FONT> * <p><a name="line.771"></a> <FONT color="green">772</FONT> * Infinite values in real or imaginary parts of the input may result in<a name="line.772"></a> <FONT color="green">773</FONT> * infinite or NaN values returned in parts of the result.<pre><a name="line.773"></a> <FONT color="green">774</FONT> * Examples:<a name="line.774"></a> <FONT color="green">775</FONT> * <code><a name="line.775"></a> <FONT color="green">776</FONT> * sqrt(1 &plusmn; INFINITY i) = INFINITY + NaN i<a name="line.776"></a> <FONT color="green">777</FONT> * sqrt(INFINITY + i) = INFINITY + 0i<a name="line.777"></a> <FONT color="green">778</FONT> * sqrt(-INFINITY + i) = 0 + INFINITY i<a name="line.778"></a> <FONT color="green">779</FONT> * sqrt(INFINITY &plusmn; INFINITY i) = INFINITY + NaN i<a name="line.779"></a> <FONT color="green">780</FONT> * sqrt(-INFINITY &plusmn; INFINITY i) = NaN &plusmn; INFINITY i<a name="line.780"></a> <FONT color="green">781</FONT> * </code></pre></p><a name="line.781"></a> <FONT color="green">782</FONT> *<a name="line.782"></a> <FONT color="green">783</FONT> * @return the square root of this complex number<a name="line.783"></a> <FONT color="green">784</FONT> * @since 1.2<a name="line.784"></a> <FONT color="green">785</FONT> */<a name="line.785"></a> <FONT color="green">786</FONT> public Complex sqrt() {<a name="line.786"></a> <FONT color="green">787</FONT> if (isNaN()) {<a name="line.787"></a> <FONT color="green">788</FONT> return Complex.NaN;<a name="line.788"></a> <FONT color="green">789</FONT> }<a name="line.789"></a> <FONT color="green">790</FONT> <a name="line.790"></a> <FONT color="green">791</FONT> if (real == 0.0 && imaginary == 0.0) {<a name="line.791"></a> <FONT color="green">792</FONT> return createComplex(0.0, 0.0);<a name="line.792"></a> <FONT color="green">793</FONT> }<a name="line.793"></a> <FONT color="green">794</FONT> <a name="line.794"></a> <FONT color="green">795</FONT> double t = Math.sqrt((Math.abs(real) + abs()) / 2.0);<a name="line.795"></a> <FONT color="green">796</FONT> if (real >= 0.0) {<a name="line.796"></a> <FONT color="green">797</FONT> return createComplex(t, imaginary / (2.0 * t));<a name="line.797"></a> <FONT color="green">798</FONT> } else {<a name="line.798"></a> <FONT color="green">799</FONT> return createComplex(Math.abs(imaginary) / (2.0 * t),<a name="line.799"></a> <FONT color="green">800</FONT> MathUtils.indicator(imaginary) * t);<a name="line.800"></a> <FONT color="green">801</FONT> }<a name="line.801"></a> <FONT color="green">802</FONT> }<a name="line.802"></a> <FONT color="green">803</FONT> <a name="line.803"></a> <FONT color="green">804</FONT> /**<a name="line.804"></a> <FONT color="green">805</FONT> * Compute the<a name="line.805"></a> <FONT color="green">806</FONT> * <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top"><a name="line.806"></a> <FONT color="green">807</FONT> * square root</a> of 1 - <code>this</code><sup>2</sup> for this complex<a name="line.807"></a> <FONT color="green">808</FONT> * number.<a name="line.808"></a> <FONT color="green">809</FONT> * <p><a name="line.809"></a> <FONT color="green">810</FONT> * Computes the result directly as<a name="line.810"></a> <FONT color="green">811</FONT> * <code>sqrt(Complex.ONE.subtract(z.multiply(z)))</code>.</p><a name="line.811"></a> <FONT color="green">812</FONT> * <p><a name="line.812"></a> <FONT color="green">813</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.813"></a> <FONT color="green">814</FONT> * input argument is <code>NaN</code>.</p><a name="line.814"></a> <FONT color="green">815</FONT> * <p><a name="line.815"></a> <FONT color="green">816</FONT> * Infinite values in real or imaginary parts of the input may result in<a name="line.816"></a> <FONT color="green">817</FONT> * infinite or NaN values returned in parts of the result.</p><a name="line.817"></a> <FONT color="green">818</FONT> *<a name="line.818"></a> <FONT color="green">819</FONT> * @return the square root of 1 - <code>this</code><sup>2</sup><a name="line.819"></a> <FONT color="green">820</FONT> * @since 1.2<a name="line.820"></a> <FONT color="green">821</FONT> */<a name="line.821"></a> <FONT color="green">822</FONT> public Complex sqrt1z() {<a name="line.822"></a> <FONT color="green">823</FONT> return createComplex(1.0, 0.0).subtract(this.multiply(this)).sqrt();<a name="line.823"></a> <FONT color="green">824</FONT> }<a name="line.824"></a> <FONT color="green">825</FONT> <a name="line.825"></a> <FONT color="green">826</FONT> /**<a name="line.826"></a> <FONT color="green">827</FONT> * Compute the<a name="line.827"></a> <FONT color="green">828</FONT> * <a href="http://mathworld.wolfram.com/Tangent.html" TARGET="_top"><a name="line.828"></a> <FONT color="green">829</FONT> * tangent</a> of this complex number.<a name="line.829"></a> <FONT color="green">830</FONT> * <p><a name="line.830"></a> <FONT color="green">831</FONT> * Implements the formula: <pre><a name="line.831"></a> <FONT color="green">832</FONT> * <code>tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i</code></pre><a name="line.832"></a> <FONT color="green">833</FONT> * where the (real) functions on the right-hand side are<a name="line.833"></a> <FONT color="green">834</FONT> * {@link java.lang.Math#sin}, {@link java.lang.Math#cos},<a name="line.834"></a> <FONT color="green">835</FONT> * {@link MathUtils#cosh} and {@link MathUtils#sinh}.</p><a name="line.835"></a> <FONT color="green">836</FONT> * <p><a name="line.836"></a> <FONT color="green">837</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.837"></a> <FONT color="green">838</FONT> * input argument is <code>NaN</code>.</p><a name="line.838"></a> <FONT color="green">839</FONT> * <p><a name="line.839"></a> <FONT color="green">840</FONT> * Infinite (or critical) values in real or imaginary parts of the input may<a name="line.840"></a> <FONT color="green">841</FONT> * result in infinite or NaN values returned in parts of the result.<pre><a name="line.841"></a> <FONT color="green">842</FONT> * Examples:<a name="line.842"></a> <FONT color="green">843</FONT> * <code><a name="line.843"></a> <FONT color="green">844</FONT> * tan(1 &plusmn; INFINITY i) = 0 + NaN i<a name="line.844"></a> <FONT color="green">845</FONT> * tan(&plusmn;INFINITY + i) = NaN + NaN i<a name="line.845"></a> <FONT color="green">846</FONT> * tan(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i<a name="line.846"></a> <FONT color="green">847</FONT> * tan(&plusmn;&pi;/2 + 0 i) = &plusmn;INFINITY + NaN i</code></pre></p><a name="line.847"></a> <FONT color="green">848</FONT> *<a name="line.848"></a> <FONT color="green">849</FONT> * @return the tangent of this complex number<a name="line.849"></a> <FONT color="green">850</FONT> * @since 1.2<a name="line.850"></a> <FONT color="green">851</FONT> */<a name="line.851"></a> <FONT color="green">852</FONT> public Complex tan() {<a name="line.852"></a> <FONT color="green">853</FONT> if (isNaN()) {<a name="line.853"></a> <FONT color="green">854</FONT> return Complex.NaN;<a name="line.854"></a> <FONT color="green">855</FONT> }<a name="line.855"></a> <FONT color="green">856</FONT> <a name="line.856"></a> <FONT color="green">857</FONT> double real2 = 2.0 * real;<a name="line.857"></a> <FONT color="green">858</FONT> double imaginary2 = 2.0 * imaginary;<a name="line.858"></a> <FONT color="green">859</FONT> double d = Math.cos(real2) + MathUtils.cosh(imaginary2);<a name="line.859"></a> <FONT color="green">860</FONT> <a name="line.860"></a> <FONT color="green">861</FONT> return createComplex(Math.sin(real2) / d, MathUtils.sinh(imaginary2) / d);<a name="line.861"></a> <FONT color="green">862</FONT> }<a name="line.862"></a> <FONT color="green">863</FONT> <a name="line.863"></a> <FONT color="green">864</FONT> /**<a name="line.864"></a> <FONT color="green">865</FONT> * Compute the<a name="line.865"></a> <FONT color="green">866</FONT> * <a href="http://mathworld.wolfram.com/HyperbolicTangent.html" TARGET="_top"><a name="line.866"></a> <FONT color="green">867</FONT> * hyperbolic tangent</a> of this complex number.<a name="line.867"></a> <FONT color="green">868</FONT> * <p><a name="line.868"></a> <FONT color="green">869</FONT> * Implements the formula: <pre><a name="line.869"></a> <FONT color="green">870</FONT> * <code>tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i</code></pre><a name="line.870"></a> <FONT color="green">871</FONT> * where the (real) functions on the right-hand side are<a name="line.871"></a> <FONT color="green">872</FONT> * {@link java.lang.Math#sin}, {@link java.lang.Math#cos},<a name="line.872"></a> <FONT color="green">873</FONT> * {@link MathUtils#cosh} and {@link MathUtils#sinh}.</p><a name="line.873"></a> <FONT color="green">874</FONT> * <p><a name="line.874"></a> <FONT color="green">875</FONT> * Returns {@link Complex#NaN} if either real or imaginary part of the<a name="line.875"></a> <FONT color="green">876</FONT> * input argument is <code>NaN</code>.</p><a name="line.876"></a> <FONT color="green">877</FONT> * <p><a name="line.877"></a> <FONT color="green">878</FONT> * Infinite values in real or imaginary parts of the input may result in<a name="line.878"></a> <FONT color="green">879</FONT> * infinite or NaN values returned in parts of the result.<pre><a name="line.879"></a> <FONT color="green">880</FONT> * Examples:<a name="line.880"></a> <FONT color="green">881</FONT> * <code><a name="line.881"></a> <FONT color="green">882</FONT> * tanh(1 &plusmn; INFINITY i) = NaN + NaN i<a name="line.882"></a> <FONT color="green">883</FONT> * tanh(&plusmn;INFINITY + i) = NaN + 0 i<a name="line.883"></a> <FONT color="green">884</FONT> * tanh(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i<a name="line.884"></a> <FONT color="green">885</FONT> * tanh(0 + (&pi;/2)i) = NaN + INFINITY i</code></pre></p><a name="line.885"></a> <FONT color="green">886</FONT> *<a name="line.886"></a> <FONT color="green">887</FONT> * @return the hyperbolic tangent of this complex number<a name="line.887"></a> <FONT color="green">888</FONT> * @since 1.2<a name="line.888"></a> <FONT color="green">889</FONT> */<a name="line.889"></a> <FONT color="green">890</FONT> public Complex tanh() {<a name="line.890"></a> <FONT color="green">891</FONT> if (isNaN()) {<a name="line.891"></a> <FONT color="green">892</FONT> return Complex.NaN;<a name="line.892"></a> <FONT color="green">893</FONT> }<a name="line.893"></a> <FONT color="green">894</FONT> <a name="line.894"></a> <FONT color="green">895</FONT> double real2 = 2.0 * real;<a name="line.895"></a> <FONT color="green">896</FONT> double imaginary2 = 2.0 * imaginary;<a name="line.896"></a> <FONT color="green">897</FONT> double d = MathUtils.cosh(real2) + Math.cos(imaginary2);<a name="line.897"></a> <FONT color="green">898</FONT> <a name="line.898"></a> <FONT color="green">899</FONT> return createComplex(MathUtils.sinh(real2) / d, Math.sin(imaginary2) / d);<a name="line.899"></a> <FONT color="green">900</FONT> }<a name="line.900"></a> <FONT color="green">901</FONT> <a name="line.901"></a> <FONT color="green">902</FONT> <a name="line.902"></a> <FONT color="green">903</FONT> <a name="line.903"></a> <FONT color="green">904</FONT> /**<a name="line.904"></a> <FONT color="green">905</FONT> * <p>Compute the argument of this complex number.<a name="line.905"></a> <FONT color="green">906</FONT> * </p><a name="line.906"></a> <FONT color="green">907</FONT> * <p>The argument is the angle phi between the positive real axis and the point<a name="line.907"></a> <FONT color="green">908</FONT> * representing this number in the complex plane. The value returned is between -PI (not inclusive)<a name="line.908"></a> <FONT color="green">909</FONT> * and PI (inclusive), with negative values returned for numbers with negative imaginary parts.<a name="line.909"></a> <FONT color="green">910</FONT> * </p><a name="line.910"></a> <FONT color="green">911</FONT> * <p>If either real or imaginary part (or both) is NaN, NaN is returned. Infinite parts are handled<a name="line.911"></a> <FONT color="green">912</FONT> * as java.Math.atan2 handles them, essentially treating finite parts as zero in the presence of<a name="line.912"></a> <FONT color="green">913</FONT> * an infinite coordinate and returning a multiple of pi/4 depending on the signs of the infinite<a name="line.913"></a> <FONT color="green">914</FONT> * parts. See the javadoc for java.Math.atan2 for full details.</p><a name="line.914"></a> <FONT color="green">915</FONT> *<a name="line.915"></a> <FONT color="green">916</FONT> * @return the argument of this complex number<a name="line.916"></a> <FONT color="green">917</FONT> */<a name="line.917"></a> <FONT color="green">918</FONT> public double getArgument() {<a name="line.918"></a> <FONT color="green">919</FONT> return Math.atan2(getImaginary(), getReal());<a name="line.919"></a> <FONT color="green">920</FONT> }<a name="line.920"></a> <FONT color="green">921</FONT> <a name="line.921"></a> <FONT color="green">922</FONT> /**<a name="line.922"></a> <FONT color="green">923</FONT> * <p>Computes the n-th roots of this complex number.<a name="line.923"></a> <FONT color="green">924</FONT> * </p><a name="line.924"></a> <FONT color="green">925</FONT> * <p>The nth roots are defined by the formula: <pre><a name="line.925"></a> <FONT color="green">926</FONT> * <code> z<sub>k</sub> = abs<sup> 1/n</sup> (cos(phi + 2&pi;k/n) + i (sin(phi + 2&pi;k/n))</code></pre><a name="line.926"></a> <FONT color="green">927</FONT> * for <i><code>k=0, 1, ..., n-1</code></i>, where <code>abs</code> and <code>phi</code> are<a name="line.927"></a> <FONT color="green">928</FONT> * respectively the {@link #abs() modulus} and {@link #getArgument() argument} of this complex number.<a name="line.928"></a> <FONT color="green">929</FONT> * </p><a name="line.929"></a> <FONT color="green">930</FONT> * <p>If one or both parts of this complex number is NaN, a list with just one element,<a name="line.930"></a> <FONT color="green">931</FONT> * {@link #NaN} is returned.</p><a name="line.931"></a> <FONT color="green">932</FONT> * <p>if neither part is NaN, but at least one part is infinite, the result is a one-element<a name="line.932"></a> <FONT color="green">933</FONT> * list containing {@link #INF}.</p><a name="line.933"></a> <FONT color="green">934</FONT> *<a name="line.934"></a> <FONT color="green">935</FONT> * @param n degree of root<a name="line.935"></a> <FONT color="green">936</FONT> * @return List<Complex> all nth roots of this complex number<a name="line.936"></a> <FONT color="green">937</FONT> * @throws IllegalArgumentException if parameter n is less than or equal to 0<a name="line.937"></a> <FONT color="green">938</FONT> * @since 2.0<a name="line.938"></a> <FONT color="green">939</FONT> */<a name="line.939"></a> <FONT color="green">940</FONT> public List<Complex> nthRoot(int n) throws IllegalArgumentException {<a name="line.940"></a> <FONT color="green">941</FONT> <a name="line.941"></a> <FONT color="green">942</FONT> if (n <= 0) {<a name="line.942"></a> <FONT color="green">943</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.943"></a> <FONT color="green">944</FONT> "cannot compute nth root for null or negative n: {0}",<a name="line.944"></a> <FONT color="green">945</FONT> n);<a name="line.945"></a> <FONT color="green">946</FONT> }<a name="line.946"></a> <FONT color="green">947</FONT> <a name="line.947"></a> <FONT color="green">948</FONT> List<Complex> result = new ArrayList<Complex>();<a name="line.948"></a> <FONT color="green">949</FONT> <a name="line.949"></a> <FONT color="green">950</FONT> if (isNaN()) {<a name="line.950"></a> <FONT color="green">951</FONT> result.add(Complex.NaN);<a name="line.951"></a> <FONT color="green">952</FONT> return result;<a name="line.952"></a> <FONT color="green">953</FONT> }<a name="line.953"></a> <FONT color="green">954</FONT> <a name="line.954"></a> <FONT color="green">955</FONT> if (isInfinite()) {<a name="line.955"></a> <FONT color="green">956</FONT> result.add(Complex.INF);<a name="line.956"></a> <FONT color="green">957</FONT> return result;<a name="line.957"></a> <FONT color="green">958</FONT> }<a name="line.958"></a> <FONT color="green">959</FONT> <a name="line.959"></a> <FONT color="green">960</FONT> // nth root of abs -- faster / more accurate to use a solver here?<a name="line.960"></a> <FONT color="green">961</FONT> final double nthRootOfAbs = Math.pow(abs(), 1.0 / n);<a name="line.961"></a> <FONT color="green">962</FONT> <a name="line.962"></a> <FONT color="green">963</FONT> // Compute nth roots of complex number with k = 0, 1, ... n-1<a name="line.963"></a> <FONT color="green">964</FONT> final double nthPhi = getArgument()/n;<a name="line.964"></a> <FONT color="green">965</FONT> final double slice = 2 * Math.PI / n;<a name="line.965"></a> <FONT color="green">966</FONT> double innerPart = nthPhi;<a name="line.966"></a> <FONT color="green">967</FONT> for (int k = 0; k < n ; k++) {<a name="line.967"></a> <FONT color="green">968</FONT> // inner part<a name="line.968"></a> <FONT color="green">969</FONT> final double realPart = nthRootOfAbs * Math.cos(innerPart);<a name="line.969"></a> <FONT color="green">970</FONT> final double imaginaryPart = nthRootOfAbs * Math.sin(innerPart);<a name="line.970"></a> <FONT color="green">971</FONT> result.add(createComplex(realPart, imaginaryPart));<a name="line.971"></a> <FONT color="green">972</FONT> innerPart += slice;<a name="line.972"></a> <FONT color="green">973</FONT> }<a name="line.973"></a> <FONT color="green">974</FONT> <a name="line.974"></a> <FONT color="green">975</FONT> return result;<a name="line.975"></a> <FONT color="green">976</FONT> }<a name="line.976"></a> <FONT color="green">977</FONT> <a name="line.977"></a> <FONT color="green">978</FONT> /**<a name="line.978"></a> <FONT color="green">979</FONT> * Create a complex number given the real and imaginary parts.<a name="line.979"></a> <FONT color="green">980</FONT> *<a name="line.980"></a> <FONT color="green">981</FONT> * @param realPart the real part<a name="line.981"></a> <FONT color="green">982</FONT> * @param imaginaryPart the imaginary part<a name="line.982"></a> <FONT color="green">983</FONT> * @return a new complex number instance<a name="line.983"></a> <FONT color="green">984</FONT> * @since 1.2<a name="line.984"></a> <FONT color="green">985</FONT> */<a name="line.985"></a> <FONT color="green">986</FONT> protected Complex createComplex(double realPart, double imaginaryPart) {<a name="line.986"></a> <FONT color="green">987</FONT> return new Complex(realPart, imaginaryPart);<a name="line.987"></a> <FONT color="green">988</FONT> }<a name="line.988"></a> <FONT color="green">989</FONT> <a name="line.989"></a> <FONT color="green">990</FONT> /**<a name="line.990"></a> <FONT color="green">991</FONT> * <p>Resolve the transient fields in a deserialized Complex Object.</p><a name="line.991"></a> <FONT color="green">992</FONT> * <p>Subclasses will need to override {@link #createComplex} to deserialize properly</p><a name="line.992"></a> <FONT color="green">993</FONT> * @return A Complex instance with all fields resolved.<a name="line.993"></a> <FONT color="green">994</FONT> * @since 2.0<a name="line.994"></a> <FONT color="green">995</FONT> */<a name="line.995"></a> <FONT color="green">996</FONT> protected final Object readResolve() {<a name="line.996"></a> <FONT color="green">997</FONT> return createComplex(real, imaginary);<a name="line.997"></a> <FONT color="green">998</FONT> }<a name="line.998"></a> <FONT color="green">999</FONT> <a name="line.999"></a> <FONT color="green">1000</FONT> /** {@inheritDoc} */<a name="line.1000"></a> <FONT color="green">1001</FONT> public ComplexField getField() {<a name="line.1001"></a> <FONT color="green">1002</FONT> return ComplexField.getInstance();<a name="line.1002"></a> <FONT color="green">1003</FONT> }<a name="line.1003"></a> <FONT color="green">1004</FONT> <a name="line.1004"></a> <FONT color="green">1005</FONT> }<a name="line.1005"></a> </PRE> </BODY> </HTML>