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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.ode.nonstiff;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> <a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.ode.AbstractIntegrator;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.ode.DerivativeException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.ode.FirstOrderDifferentialEquations;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.ode.IntegratorException;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.ode.events.CombinedEventsManager;<a name="line.25"></a> <FONT color="green">026</FONT> import org.apache.commons.math.ode.sampling.AbstractStepInterpolator;<a name="line.26"></a> <FONT color="green">027</FONT> import org.apache.commons.math.ode.sampling.DummyStepInterpolator;<a name="line.27"></a> <FONT color="green">028</FONT> import org.apache.commons.math.ode.sampling.StepHandler;<a name="line.28"></a> <FONT color="green">029</FONT> <a name="line.29"></a> <FONT color="green">030</FONT> /**<a name="line.30"></a> <FONT color="green">031</FONT> * This class implements the common part of all fixed step Runge-Kutta<a name="line.31"></a> <FONT color="green">032</FONT> * integrators for Ordinary Differential Equations.<a name="line.32"></a> <FONT color="green">033</FONT> *<a name="line.33"></a> <FONT color="green">034</FONT> * <p>These methods are explicit Runge-Kutta methods, their Butcher<a name="line.34"></a> <FONT color="green">035</FONT> * arrays are as follows :<a name="line.35"></a> <FONT color="green">036</FONT> * <pre><a name="line.36"></a> <FONT color="green">037</FONT> * 0 |<a name="line.37"></a> <FONT color="green">038</FONT> * c2 | a21<a name="line.38"></a> <FONT color="green">039</FONT> * c3 | a31 a32<a name="line.39"></a> <FONT color="green">040</FONT> * ... | ...<a name="line.40"></a> <FONT color="green">041</FONT> * cs | as1 as2 ... ass-1<a name="line.41"></a> <FONT color="green">042</FONT> * |--------------------------<a name="line.42"></a> <FONT color="green">043</FONT> * | b1 b2 ... bs-1 bs<a name="line.43"></a> <FONT color="green">044</FONT> * </pre><a name="line.44"></a> <FONT color="green">045</FONT> * </p><a name="line.45"></a> <FONT color="green">046</FONT> *<a name="line.46"></a> <FONT color="green">047</FONT> * @see EulerIntegrator<a name="line.47"></a> <FONT color="green">048</FONT> * @see ClassicalRungeKuttaIntegrator<a name="line.48"></a> <FONT color="green">049</FONT> * @see GillIntegrator<a name="line.49"></a> <FONT color="green">050</FONT> * @see MidpointIntegrator<a name="line.50"></a> <FONT color="green">051</FONT> * @version $Revision: 927202 $ $Date: 2010-03-24 18:11:51 -0400 (Wed, 24 Mar 2010) $<a name="line.51"></a> <FONT color="green">052</FONT> * @since 1.2<a name="line.52"></a> <FONT color="green">053</FONT> */<a name="line.53"></a> <FONT color="green">054</FONT> <a name="line.54"></a> <FONT color="green">055</FONT> public abstract class RungeKuttaIntegrator extends AbstractIntegrator {<a name="line.55"></a> <FONT color="green">056</FONT> <a name="line.56"></a> <FONT color="green">057</FONT> /** Time steps from Butcher array (without the first zero). */<a name="line.57"></a> <FONT color="green">058</FONT> private final double[] c;<a name="line.58"></a> <FONT color="green">059</FONT> <a name="line.59"></a> <FONT color="green">060</FONT> /** Internal weights from Butcher array (without the first empty row). */<a name="line.60"></a> <FONT color="green">061</FONT> private final double[][] a;<a name="line.61"></a> <FONT color="green">062</FONT> <a name="line.62"></a> <FONT color="green">063</FONT> /** External weights for the high order method from Butcher array. */<a name="line.63"></a> <FONT color="green">064</FONT> private final double[] b;<a name="line.64"></a> <FONT color="green">065</FONT> <a name="line.65"></a> <FONT color="green">066</FONT> /** Prototype of the step interpolator. */<a name="line.66"></a> <FONT color="green">067</FONT> private final RungeKuttaStepInterpolator prototype;<a name="line.67"></a> <FONT color="green">068</FONT> <a name="line.68"></a> <FONT color="green">069</FONT> /** Integration step. */<a name="line.69"></a> <FONT color="green">070</FONT> private final double step;<a name="line.70"></a> <FONT color="green">071</FONT> <a name="line.71"></a> <FONT color="green">072</FONT> /** Simple constructor.<a name="line.72"></a> <FONT color="green">073</FONT> * Build a Runge-Kutta integrator with the given<a name="line.73"></a> <FONT color="green">074</FONT> * step. The default step handler does nothing.<a name="line.74"></a> <FONT color="green">075</FONT> * @param name name of the method<a name="line.75"></a> <FONT color="green">076</FONT> * @param c time steps from Butcher array (without the first zero)<a name="line.76"></a> <FONT color="green">077</FONT> * @param a internal weights from Butcher array (without the first empty row)<a name="line.77"></a> <FONT color="green">078</FONT> * @param b propagation weights for the high order method from Butcher array<a name="line.78"></a> <FONT color="green">079</FONT> * @param prototype prototype of the step interpolator to use<a name="line.79"></a> <FONT color="green">080</FONT> * @param step integration step<a name="line.80"></a> <FONT color="green">081</FONT> */<a name="line.81"></a> <FONT color="green">082</FONT> protected RungeKuttaIntegrator(final String name,<a name="line.82"></a> <FONT color="green">083</FONT> final double[] c, final double[][] a, final double[] b,<a name="line.83"></a> <FONT color="green">084</FONT> final RungeKuttaStepInterpolator prototype,<a name="line.84"></a> <FONT color="green">085</FONT> final double step) {<a name="line.85"></a> <FONT color="green">086</FONT> super(name);<a name="line.86"></a> <FONT color="green">087</FONT> this.c = c;<a name="line.87"></a> <FONT color="green">088</FONT> this.a = a;<a name="line.88"></a> <FONT color="green">089</FONT> this.b = b;<a name="line.89"></a> <FONT color="green">090</FONT> this.prototype = prototype;<a name="line.90"></a> <FONT color="green">091</FONT> this.step = Math.abs(step);<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> /** {@inheritDoc} */<a name="line.94"></a> <FONT color="green">095</FONT> public double integrate(final FirstOrderDifferentialEquations equations,<a name="line.95"></a> <FONT color="green">096</FONT> final double t0, final double[] y0,<a name="line.96"></a> <FONT color="green">097</FONT> final double t, final double[] y)<a name="line.97"></a> <FONT color="green">098</FONT> throws DerivativeException, IntegratorException {<a name="line.98"></a> <FONT color="green">099</FONT> <a name="line.99"></a> <FONT color="green">100</FONT> sanityChecks(equations, t0, y0, t, y);<a name="line.100"></a> <FONT color="green">101</FONT> setEquations(equations);<a name="line.101"></a> <FONT color="green">102</FONT> resetEvaluations();<a name="line.102"></a> <FONT color="green">103</FONT> final boolean forward = t > t0;<a name="line.103"></a> <FONT color="green">104</FONT> <a name="line.104"></a> <FONT color="green">105</FONT> // create some internal working arrays<a name="line.105"></a> <FONT color="green">106</FONT> final int stages = c.length + 1;<a name="line.106"></a> <FONT color="green">107</FONT> if (y != y0) {<a name="line.107"></a> <FONT color="green">108</FONT> System.arraycopy(y0, 0, y, 0, y0.length);<a name="line.108"></a> <FONT color="green">109</FONT> }<a name="line.109"></a> <FONT color="green">110</FONT> final double[][] yDotK = new double[stages][];<a name="line.110"></a> <FONT color="green">111</FONT> for (int i = 0; i < stages; ++i) {<a name="line.111"></a> <FONT color="green">112</FONT> yDotK [i] = new double[y0.length];<a name="line.112"></a> <FONT color="green">113</FONT> }<a name="line.113"></a> <FONT color="green">114</FONT> final double[] yTmp = new double[y0.length];<a name="line.114"></a> <FONT color="green">115</FONT> <a name="line.115"></a> <FONT color="green">116</FONT> // set up an interpolator sharing the integrator arrays<a name="line.116"></a> <FONT color="green">117</FONT> AbstractStepInterpolator interpolator;<a name="line.117"></a> <FONT color="green">118</FONT> if (requiresDenseOutput() || (! eventsHandlersManager.isEmpty())) {<a name="line.118"></a> <FONT color="green">119</FONT> final RungeKuttaStepInterpolator rki = (RungeKuttaStepInterpolator) prototype.copy();<a name="line.119"></a> <FONT color="green">120</FONT> rki.reinitialize(this, yTmp, yDotK, forward);<a name="line.120"></a> <FONT color="green">121</FONT> interpolator = rki;<a name="line.121"></a> <FONT color="green">122</FONT> } else {<a name="line.122"></a> <FONT color="green">123</FONT> interpolator = new DummyStepInterpolator(yTmp, yDotK[stages - 1], forward);<a name="line.123"></a> <FONT color="green">124</FONT> }<a name="line.124"></a> <FONT color="green">125</FONT> interpolator.storeTime(t0);<a name="line.125"></a> <FONT color="green">126</FONT> <a name="line.126"></a> <FONT color="green">127</FONT> // set up integration control objects<a name="line.127"></a> <FONT color="green">128</FONT> stepStart = t0;<a name="line.128"></a> <FONT color="green">129</FONT> stepSize = forward ? step : -step;<a name="line.129"></a> <FONT color="green">130</FONT> for (StepHandler handler : stepHandlers) {<a name="line.130"></a> <FONT color="green">131</FONT> handler.reset();<a name="line.131"></a> <FONT color="green">132</FONT> }<a name="line.132"></a> <FONT color="green">133</FONT> CombinedEventsManager manager = addEndTimeChecker(t0, t, eventsHandlersManager);<a name="line.133"></a> <FONT color="green">134</FONT> boolean lastStep = false;<a name="line.134"></a> <FONT color="green">135</FONT> <a name="line.135"></a> <FONT color="green">136</FONT> // main integration loop<a name="line.136"></a> <FONT color="green">137</FONT> while (!lastStep) {<a name="line.137"></a> <FONT color="green">138</FONT> <a name="line.138"></a> <FONT color="green">139</FONT> interpolator.shift();<a name="line.139"></a> <FONT color="green">140</FONT> <a name="line.140"></a> <FONT color="green">141</FONT> for (boolean loop = true; loop;) {<a name="line.141"></a> <FONT color="green">142</FONT> <a name="line.142"></a> <FONT color="green">143</FONT> // first stage<a name="line.143"></a> <FONT color="green">144</FONT> computeDerivatives(stepStart, y, yDotK[0]);<a name="line.144"></a> <FONT color="green">145</FONT> <a name="line.145"></a> <FONT color="green">146</FONT> // next stages<a name="line.146"></a> <FONT color="green">147</FONT> for (int k = 1; k < stages; ++k) {<a name="line.147"></a> <FONT color="green">148</FONT> <a name="line.148"></a> <FONT color="green">149</FONT> for (int j = 0; j < y0.length; ++j) {<a name="line.149"></a> <FONT color="green">150</FONT> double sum = a[k-1][0] * yDotK[0][j];<a name="line.150"></a> <FONT color="green">151</FONT> for (int l = 1; l < k; ++l) {<a name="line.151"></a> <FONT color="green">152</FONT> sum += a[k-1][l] * yDotK[l][j];<a name="line.152"></a> <FONT color="green">153</FONT> }<a name="line.153"></a> <FONT color="green">154</FONT> yTmp[j] = y[j] + stepSize * sum;<a name="line.154"></a> <FONT color="green">155</FONT> }<a name="line.155"></a> <FONT color="green">156</FONT> <a name="line.156"></a> <FONT color="green">157</FONT> computeDerivatives(stepStart + c[k-1] * stepSize, yTmp, yDotK[k]);<a name="line.157"></a> <FONT color="green">158</FONT> <a name="line.158"></a> <FONT color="green">159</FONT> }<a name="line.159"></a> <FONT color="green">160</FONT> <a name="line.160"></a> <FONT color="green">161</FONT> // estimate the state at the end of the step<a name="line.161"></a> <FONT color="green">162</FONT> for (int j = 0; j < y0.length; ++j) {<a name="line.162"></a> <FONT color="green">163</FONT> double sum = b[0] * yDotK[0][j];<a name="line.163"></a> <FONT color="green">164</FONT> for (int l = 1; l < stages; ++l) {<a name="line.164"></a> <FONT color="green">165</FONT> sum += b[l] * yDotK[l][j];<a name="line.165"></a> <FONT color="green">166</FONT> }<a name="line.166"></a> <FONT color="green">167</FONT> yTmp[j] = y[j] + stepSize * sum;<a name="line.167"></a> <FONT color="green">168</FONT> }<a name="line.168"></a> <FONT color="green">169</FONT> <a name="line.169"></a> <FONT color="green">170</FONT> // discrete events handling<a name="line.170"></a> <FONT color="green">171</FONT> interpolator.storeTime(stepStart + stepSize);<a name="line.171"></a> <FONT color="green">172</FONT> if (manager.evaluateStep(interpolator)) {<a name="line.172"></a> <FONT color="green">173</FONT> final double dt = manager.getEventTime() - stepStart;<a name="line.173"></a> <FONT color="green">174</FONT> if (Math.abs(dt) <= Math.ulp(stepStart)) {<a name="line.174"></a> <FONT color="green">175</FONT> // we cannot simply truncate the step, reject the current computation<a name="line.175"></a> <FONT color="green">176</FONT> // and let the loop compute another state with the truncated step.<a name="line.176"></a> <FONT color="green">177</FONT> // it is so small (much probably exactly 0 due to limited accuracy)<a name="line.177"></a> <FONT color="green">178</FONT> // that the code above would fail handling it.<a name="line.178"></a> <FONT color="green">179</FONT> // So we set up an artificial 0 size step by copying states<a name="line.179"></a> <FONT color="green">180</FONT> interpolator.storeTime(stepStart);<a name="line.180"></a> <FONT color="green">181</FONT> System.arraycopy(y, 0, yTmp, 0, y0.length);<a name="line.181"></a> <FONT color="green">182</FONT> stepSize = 0;<a name="line.182"></a> <FONT color="green">183</FONT> loop = false;<a name="line.183"></a> <FONT color="green">184</FONT> } else {<a name="line.184"></a> <FONT color="green">185</FONT> // reject the step to match exactly the next switch time<a name="line.185"></a> <FONT color="green">186</FONT> stepSize = dt;<a name="line.186"></a> <FONT color="green">187</FONT> }<a name="line.187"></a> <FONT color="green">188</FONT> } else {<a name="line.188"></a> <FONT color="green">189</FONT> loop = false;<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> // the step has been accepted<a name="line.194"></a> <FONT color="green">195</FONT> final double nextStep = stepStart + stepSize;<a name="line.195"></a> <FONT color="green">196</FONT> System.arraycopy(yTmp, 0, y, 0, y0.length);<a name="line.196"></a> <FONT color="green">197</FONT> manager.stepAccepted(nextStep, y);<a name="line.197"></a> <FONT color="green">198</FONT> lastStep = manager.stop();<a name="line.198"></a> <FONT color="green">199</FONT> <a name="line.199"></a> <FONT color="green">200</FONT> // provide the step data to the step handler<a name="line.200"></a> <FONT color="green">201</FONT> interpolator.storeTime(nextStep);<a name="line.201"></a> <FONT color="green">202</FONT> for (StepHandler handler : stepHandlers) {<a name="line.202"></a> <FONT color="green">203</FONT> handler.handleStep(interpolator, lastStep);<a name="line.203"></a> <FONT color="green">204</FONT> }<a name="line.204"></a> <FONT color="green">205</FONT> stepStart = nextStep;<a name="line.205"></a> <FONT color="green">206</FONT> <a name="line.206"></a> <FONT color="green">207</FONT> if (manager.reset(stepStart, y) && ! lastStep) {<a name="line.207"></a> <FONT color="green">208</FONT> // some events handler has triggered changes that<a name="line.208"></a> <FONT color="green">209</FONT> // invalidate the derivatives, we need to recompute them<a name="line.209"></a> <FONT color="green">210</FONT> computeDerivatives(stepStart, y, yDotK[0]);<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> // make sure step size is set to default before next step<a name="line.213"></a> <FONT color="green">214</FONT> stepSize = forward ? step : -step;<a name="line.214"></a> <FONT color="green">215</FONT> <a name="line.215"></a> <FONT color="green">216</FONT> }<a name="line.216"></a> <FONT color="green">217</FONT> <a name="line.217"></a> <FONT color="green">218</FONT> final double stopTime = stepStart;<a name="line.218"></a> <FONT color="green">219</FONT> stepStart = Double.NaN;<a name="line.219"></a> <FONT color="green">220</FONT> stepSize = Double.NaN;<a name="line.220"></a> <FONT color="green">221</FONT> return stopTime;<a name="line.221"></a> <FONT color="green">222</FONT> <a name="line.222"></a> <FONT color="green">223</FONT> }<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> </PRE> </BODY> </HTML>