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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.ode;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.linear.Array2DRowRealMatrix;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.linear.RealMatrix;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.ode.nonstiff.DormandPrince853Integrator;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.ode.sampling.StepHandler;<a name="line.25"></a> <FONT color="green">026</FONT> import org.apache.commons.math.ode.sampling.StepInterpolator;<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> * This class is the base class for multistep integrators for Ordinary<a name="line.29"></a> <FONT color="green">030</FONT> * Differential Equations.<a name="line.30"></a> <FONT color="green">031</FONT> * <p>We define scaled derivatives s<sub>i</sub>(n) at step n as:<a name="line.31"></a> <FONT color="green">032</FONT> * <pre><a name="line.32"></a> <FONT color="green">033</FONT> * s<sub>1</sub>(n) = h y'<sub>n</sub> for first derivative<a name="line.33"></a> <FONT color="green">034</FONT> * s<sub>2</sub>(n) = h<sup>2</sup>/2 y''<sub>n</sub> for second derivative<a name="line.34"></a> <FONT color="green">035</FONT> * s<sub>3</sub>(n) = h<sup>3</sup>/6 y'''<sub>n</sub> for third derivative<a name="line.35"></a> <FONT color="green">036</FONT> * ...<a name="line.36"></a> <FONT color="green">037</FONT> * s<sub>k</sub>(n) = h<sup>k</sup>/k! y(k)<sub>n</sub> for k<sup>th</sup> derivative<a name="line.37"></a> <FONT color="green">038</FONT> * </pre></p><a name="line.38"></a> <FONT color="green">039</FONT> * <p>Rather than storing several previous steps separately, this implementation uses<a name="line.39"></a> <FONT color="green">040</FONT> * the Nordsieck vector with higher degrees scaled derivatives all taken at the same<a name="line.40"></a> <FONT color="green">041</FONT> * step (y<sub>n</sub>, s<sub>1</sub>(n) and r<sub>n</sub>) where r<sub>n</sub> is defined as:<a name="line.41"></a> <FONT color="green">042</FONT> * <pre><a name="line.42"></a> <FONT color="green">043</FONT> * r<sub>n</sub> = [ s<sub>2</sub>(n), s<sub>3</sub>(n) ... s<sub>k</sub>(n) ]<sup>T</sup><a name="line.43"></a> <FONT color="green">044</FONT> * </pre><a name="line.44"></a> <FONT color="green">045</FONT> * (we omit the k index in the notation for clarity)</p><a name="line.45"></a> <FONT color="green">046</FONT> * <p><a name="line.46"></a> <FONT color="green">047</FONT> * Multistep integrators with Nordsieck representation are highly sensitive to<a name="line.47"></a> <FONT color="green">048</FONT> * large step changes because when the step is multiplied by a factor a, the<a name="line.48"></a> <FONT color="green">049</FONT> * k<sup>th</sup> component of the Nordsieck vector is multiplied by a<sup>k</sup><a name="line.49"></a> <FONT color="green">050</FONT> * and the last components are the least accurate ones. The default max growth<a name="line.50"></a> <FONT color="green">051</FONT> * factor is therefore set to a quite low value: 2<sup>1/order</sup>.<a name="line.51"></a> <FONT color="green">052</FONT> * </p><a name="line.52"></a> <FONT color="green">053</FONT> *<a name="line.53"></a> <FONT color="green">054</FONT> * @see org.apache.commons.math.ode.nonstiff.AdamsBashforthIntegrator<a name="line.54"></a> <FONT color="green">055</FONT> * @see org.apache.commons.math.ode.nonstiff.AdamsMoultonIntegrator<a name="line.55"></a> <FONT color="green">056</FONT> * @version $Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $<a name="line.56"></a> <FONT color="green">057</FONT> * @since 2.0<a name="line.57"></a> <FONT color="green">058</FONT> */<a name="line.58"></a> <FONT color="green">059</FONT> public abstract class MultistepIntegrator extends AdaptiveStepsizeIntegrator {<a name="line.59"></a> <FONT color="green">060</FONT> <a name="line.60"></a> <FONT color="green">061</FONT> /** First scaled derivative (h y'). */<a name="line.61"></a> <FONT color="green">062</FONT> protected double[] scaled;<a name="line.62"></a> <FONT color="green">063</FONT> <a name="line.63"></a> <FONT color="green">064</FONT> /** Nordsieck matrix of the higher scaled derivatives.<a name="line.64"></a> <FONT color="green">065</FONT> * <p>(h<sup>2</sup>/2 y'', h<sup>3</sup>/6 y''' ..., h<sup>k</sup>/k! y(k))</p><a name="line.65"></a> <FONT color="green">066</FONT> */<a name="line.66"></a> <FONT color="green">067</FONT> protected Array2DRowRealMatrix nordsieck;<a name="line.67"></a> <FONT color="green">068</FONT> <a name="line.68"></a> <FONT color="green">069</FONT> /** Starter integrator. */<a name="line.69"></a> <FONT color="green">070</FONT> private FirstOrderIntegrator starter;<a name="line.70"></a> <FONT color="green">071</FONT> <a name="line.71"></a> <FONT color="green">072</FONT> /** Number of steps of the multistep method (excluding the one being computed). */<a name="line.72"></a> <FONT color="green">073</FONT> private final int nSteps;<a name="line.73"></a> <FONT color="green">074</FONT> <a name="line.74"></a> <FONT color="green">075</FONT> /** Stepsize control exponent. */<a name="line.75"></a> <FONT color="green">076</FONT> private double exp;<a name="line.76"></a> <FONT color="green">077</FONT> <a name="line.77"></a> <FONT color="green">078</FONT> /** Safety factor for stepsize control. */<a name="line.78"></a> <FONT color="green">079</FONT> private double safety;<a name="line.79"></a> <FONT color="green">080</FONT> <a name="line.80"></a> <FONT color="green">081</FONT> /** Minimal reduction factor for stepsize control. */<a name="line.81"></a> <FONT color="green">082</FONT> private double minReduction;<a name="line.82"></a> <FONT color="green">083</FONT> <a name="line.83"></a> <FONT color="green">084</FONT> /** Maximal growth factor for stepsize control. */<a name="line.84"></a> <FONT color="green">085</FONT> private double maxGrowth;<a name="line.85"></a> <FONT color="green">086</FONT> <a name="line.86"></a> <FONT color="green">087</FONT> /**<a name="line.87"></a> <FONT color="green">088</FONT> * Build a multistep integrator with the given stepsize bounds.<a name="line.88"></a> <FONT color="green">089</FONT> * <p>The default starter integrator is set to the {@link<a name="line.89"></a> <FONT color="green">090</FONT> * DormandPrince853Integrator Dormand-Prince 8(5,3)} integrator with<a name="line.90"></a> <FONT color="green">091</FONT> * some defaults settings.</p><a name="line.91"></a> <FONT color="green">092</FONT> * <p><a name="line.92"></a> <FONT color="green">093</FONT> * The default max growth factor is set to a quite low value: 2<sup>1/order</sup>.<a name="line.93"></a> <FONT color="green">094</FONT> * </p><a name="line.94"></a> <FONT color="green">095</FONT> * @param name name of the method<a name="line.95"></a> <FONT color="green">096</FONT> * @param nSteps number of steps of the multistep method<a name="line.96"></a> <FONT color="green">097</FONT> * (excluding the one being computed)<a name="line.97"></a> <FONT color="green">098</FONT> * @param order order of the method<a name="line.98"></a> <FONT color="green">099</FONT> * @param minStep minimal step (must be positive even for backward<a name="line.99"></a> <FONT color="green">100</FONT> * integration), the last step can be smaller than this<a name="line.100"></a> <FONT color="green">101</FONT> * @param maxStep maximal step (must be positive even for backward<a name="line.101"></a> <FONT color="green">102</FONT> * integration)<a name="line.102"></a> <FONT color="green">103</FONT> * @param scalAbsoluteTolerance allowed absolute error<a name="line.103"></a> <FONT color="green">104</FONT> * @param scalRelativeTolerance allowed relative error<a name="line.104"></a> <FONT color="green">105</FONT> */<a name="line.105"></a> <FONT color="green">106</FONT> protected MultistepIntegrator(final String name, final int nSteps,<a name="line.106"></a> <FONT color="green">107</FONT> final int order,<a name="line.107"></a> <FONT color="green">108</FONT> final double minStep, final double maxStep,<a name="line.108"></a> <FONT color="green">109</FONT> final double scalAbsoluteTolerance,<a name="line.109"></a> <FONT color="green">110</FONT> final double scalRelativeTolerance) {<a name="line.110"></a> <FONT color="green">111</FONT> <a name="line.111"></a> <FONT color="green">112</FONT> super(name, minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);<a name="line.112"></a> <FONT color="green">113</FONT> <a name="line.113"></a> <FONT color="green">114</FONT> if (nSteps <= 0) {<a name="line.114"></a> <FONT color="green">115</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.115"></a> <FONT color="green">116</FONT> "{0} method needs at least one previous point",<a name="line.116"></a> <FONT color="green">117</FONT> name);<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> <a name="line.119"></a> <FONT color="green">120</FONT> starter = new DormandPrince853Integrator(minStep, maxStep,<a name="line.120"></a> <FONT color="green">121</FONT> scalAbsoluteTolerance,<a name="line.121"></a> <FONT color="green">122</FONT> scalRelativeTolerance);<a name="line.122"></a> <FONT color="green">123</FONT> this.nSteps = nSteps;<a name="line.123"></a> <FONT color="green">124</FONT> <a name="line.124"></a> <FONT color="green">125</FONT> exp = -1.0 / order;<a name="line.125"></a> <FONT color="green">126</FONT> <a name="line.126"></a> <FONT color="green">127</FONT> // set the default values of the algorithm control parameters<a name="line.127"></a> <FONT color="green">128</FONT> setSafety(0.9);<a name="line.128"></a> <FONT color="green">129</FONT> setMinReduction(0.2);<a name="line.129"></a> <FONT color="green">130</FONT> setMaxGrowth(Math.pow(2.0, -exp));<a name="line.130"></a> <FONT color="green">131</FONT> <a name="line.131"></a> <FONT color="green">132</FONT> }<a name="line.132"></a> <FONT color="green">133</FONT> <a name="line.133"></a> <FONT color="green">134</FONT> /**<a name="line.134"></a> <FONT color="green">135</FONT> * Build a multistep integrator with the given stepsize bounds.<a name="line.135"></a> <FONT color="green">136</FONT> * <p>The default starter integrator is set to the {@link<a name="line.136"></a> <FONT color="green">137</FONT> * DormandPrince853Integrator Dormand-Prince 8(5,3)} integrator with<a name="line.137"></a> <FONT color="green">138</FONT> * some defaults settings.</p><a name="line.138"></a> <FONT color="green">139</FONT> * <p><a name="line.139"></a> <FONT color="green">140</FONT> * The default max growth factor is set to a quite low value: 2<sup>1/order</sup>.<a name="line.140"></a> <FONT color="green">141</FONT> * </p><a name="line.141"></a> <FONT color="green">142</FONT> * @param name name of the method<a name="line.142"></a> <FONT color="green">143</FONT> * @param nSteps number of steps of the multistep method<a name="line.143"></a> <FONT color="green">144</FONT> * (excluding the one being computed)<a name="line.144"></a> <FONT color="green">145</FONT> * @param order order of the method<a name="line.145"></a> <FONT color="green">146</FONT> * @param minStep minimal step (must be positive even for backward<a name="line.146"></a> <FONT color="green">147</FONT> * integration), the last step can be smaller than this<a name="line.147"></a> <FONT color="green">148</FONT> * @param maxStep maximal step (must be positive even for backward<a name="line.148"></a> <FONT color="green">149</FONT> * integration)<a name="line.149"></a> <FONT color="green">150</FONT> * @param vecAbsoluteTolerance allowed absolute error<a name="line.150"></a> <FONT color="green">151</FONT> * @param vecRelativeTolerance allowed relative error<a name="line.151"></a> <FONT color="green">152</FONT> */<a name="line.152"></a> <FONT color="green">153</FONT> protected MultistepIntegrator(final String name, final int nSteps,<a name="line.153"></a> <FONT color="green">154</FONT> final int order,<a name="line.154"></a> <FONT color="green">155</FONT> final double minStep, final double maxStep,<a name="line.155"></a> <FONT color="green">156</FONT> final double[] vecAbsoluteTolerance,<a name="line.156"></a> <FONT color="green">157</FONT> final double[] vecRelativeTolerance) {<a name="line.157"></a> <FONT color="green">158</FONT> super(name, minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);<a name="line.158"></a> <FONT color="green">159</FONT> starter = new DormandPrince853Integrator(minStep, maxStep,<a name="line.159"></a> <FONT color="green">160</FONT> vecAbsoluteTolerance,<a name="line.160"></a> <FONT color="green">161</FONT> vecRelativeTolerance);<a name="line.161"></a> <FONT color="green">162</FONT> this.nSteps = nSteps;<a name="line.162"></a> <FONT color="green">163</FONT> <a name="line.163"></a> <FONT color="green">164</FONT> exp = -1.0 / order;<a name="line.164"></a> <FONT color="green">165</FONT> <a name="line.165"></a> <FONT color="green">166</FONT> // set the default values of the algorithm control parameters<a name="line.166"></a> <FONT color="green">167</FONT> setSafety(0.9);<a name="line.167"></a> <FONT color="green">168</FONT> setMinReduction(0.2);<a name="line.168"></a> <FONT color="green">169</FONT> setMaxGrowth(Math.pow(2.0, -exp));<a name="line.169"></a> <FONT color="green">170</FONT> <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> * Get the starter integrator.<a name="line.174"></a> <FONT color="green">175</FONT> * @return starter integrator<a name="line.175"></a> <FONT color="green">176</FONT> */<a name="line.176"></a> <FONT color="green">177</FONT> public ODEIntegrator getStarterIntegrator() {<a name="line.177"></a> <FONT color="green">178</FONT> return starter;<a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> <a name="line.180"></a> <FONT color="green">181</FONT> /**<a name="line.181"></a> <FONT color="green">182</FONT> * Set the starter integrator.<a name="line.182"></a> <FONT color="green">183</FONT> * <p>The various step and event handlers for this starter integrator<a name="line.183"></a> <FONT color="green">184</FONT> * will be managed automatically by the multi-step integrator. Any<a name="line.184"></a> <FONT color="green">185</FONT> * user configuration for these elements will be cleared before use.</p><a name="line.185"></a> <FONT color="green">186</FONT> * @param starterIntegrator starter integrator<a name="line.186"></a> <FONT color="green">187</FONT> */<a name="line.187"></a> <FONT color="green">188</FONT> public void setStarterIntegrator(FirstOrderIntegrator starterIntegrator) {<a name="line.188"></a> <FONT color="green">189</FONT> this.starter = starterIntegrator;<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> /** Start the integration.<a name="line.192"></a> <FONT color="green">193</FONT> * <p>This method computes one step using the underlying starter integrator,<a name="line.193"></a> <FONT color="green">194</FONT> * and initializes the Nordsieck vector at step start. The starter integrator<a name="line.194"></a> <FONT color="green">195</FONT> * purpose is only to establish initial conditions, it does not really change<a name="line.195"></a> <FONT color="green">196</FONT> * time by itself. The top level multistep integrator remains in charge of<a name="line.196"></a> <FONT color="green">197</FONT> * handling time propagation and events handling as it will starts its own<a name="line.197"></a> <FONT color="green">198</FONT> * computation right from the beginning. In a sense, the starter integrator<a name="line.198"></a> <FONT color="green">199</FONT> * can be seen as a dummy one and so it will never trigger any user event nor<a name="line.199"></a> <FONT color="green">200</FONT> * call any user step handler.</p><a name="line.200"></a> <FONT color="green">201</FONT> * @param t0 initial time<a name="line.201"></a> <FONT color="green">202</FONT> * @param y0 initial value of the state vector at t0<a name="line.202"></a> <FONT color="green">203</FONT> * @param t target time for the integration<a name="line.203"></a> <FONT color="green">204</FONT> * (can be set to a value smaller than <code>t0</code> for backward integration)<a name="line.204"></a> <FONT color="green">205</FONT> * @throws IntegratorException if the integrator cannot perform integration<a name="line.205"></a> <FONT color="green">206</FONT> * @throws DerivativeException this exception is propagated to the caller if<a name="line.206"></a> <FONT color="green">207</FONT> * the underlying user function triggers one<a name="line.207"></a> <FONT color="green">208</FONT> */<a name="line.208"></a> <FONT color="green">209</FONT> protected void start(final double t0, final double[] y0, final double t)<a name="line.209"></a> <FONT color="green">210</FONT> throws DerivativeException, IntegratorException {<a name="line.210"></a> <FONT color="green">211</FONT> <a name="line.211"></a> <FONT color="green">212</FONT> // make sure NO user event nor user step handler is triggered,<a name="line.212"></a> <FONT color="green">213</FONT> // this is the task of the top level integrator, not the task<a name="line.213"></a> <FONT color="green">214</FONT> // of the starter integrator<a name="line.214"></a> <FONT color="green">215</FONT> starter.clearEventHandlers();<a name="line.215"></a> <FONT color="green">216</FONT> starter.clearStepHandlers();<a name="line.216"></a> <FONT color="green">217</FONT> <a name="line.217"></a> <FONT color="green">218</FONT> // set up one specific step handler to extract initial Nordsieck vector<a name="line.218"></a> <FONT color="green">219</FONT> starter.addStepHandler(new NordsieckInitializer(y0.length));<a name="line.219"></a> <FONT color="green">220</FONT> <a name="line.220"></a> <FONT color="green">221</FONT> // start integration, expecting a InitializationCompletedMarkerException<a name="line.221"></a> <FONT color="green">222</FONT> try {<a name="line.222"></a> <FONT color="green">223</FONT> starter.integrate(new CountingDifferentialEquations(y0.length),<a name="line.223"></a> <FONT color="green">224</FONT> t0, y0, t, new double[y0.length]);<a name="line.224"></a> <FONT color="green">225</FONT> } catch (DerivativeException de) {<a name="line.225"></a> <FONT color="green">226</FONT> if (!(de instanceof InitializationCompletedMarkerException)) {<a name="line.226"></a> <FONT color="green">227</FONT> // this is not the expected nominal interruption of the start integrator<a name="line.227"></a> <FONT color="green">228</FONT> throw de;<a name="line.228"></a> <FONT color="green">229</FONT> }<a name="line.229"></a> <FONT color="green">230</FONT> }<a name="line.230"></a> <FONT color="green">231</FONT> <a name="line.231"></a> <FONT color="green">232</FONT> // remove the specific step handler<a name="line.232"></a> <FONT color="green">233</FONT> starter.clearStepHandlers();<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> /** Initialize the high order scaled derivatives at step start.<a name="line.237"></a> <FONT color="green">238</FONT> * @param first first scaled derivative at step start<a name="line.238"></a> <FONT color="green">239</FONT> * @param multistep scaled derivatives after step start (hy'1, ..., hy'k-1)<a name="line.239"></a> <FONT color="green">240</FONT> * will be modified<a name="line.240"></a> <FONT color="green">241</FONT> * @return high order scaled derivatives at step start<a name="line.241"></a> <FONT color="green">242</FONT> */<a name="line.242"></a> <FONT color="green">243</FONT> protected abstract Array2DRowRealMatrix initializeHighOrderDerivatives(final double[] first,<a name="line.243"></a> <FONT color="green">244</FONT> final double[][] multistep);<a name="line.244"></a> <FONT color="green">245</FONT> <a name="line.245"></a> <FONT color="green">246</FONT> /** Get the minimal reduction factor for stepsize control.<a name="line.246"></a> <FONT color="green">247</FONT> * @return minimal reduction factor<a name="line.247"></a> <FONT color="green">248</FONT> */<a name="line.248"></a> <FONT color="green">249</FONT> public double getMinReduction() {<a name="line.249"></a> <FONT color="green">250</FONT> return minReduction;<a name="line.250"></a> <FONT color="green">251</FONT> }<a name="line.251"></a> <FONT color="green">252</FONT> <a name="line.252"></a> <FONT color="green">253</FONT> /** Set the minimal reduction factor for stepsize control.<a name="line.253"></a> <FONT color="green">254</FONT> * @param minReduction minimal reduction factor<a name="line.254"></a> <FONT color="green">255</FONT> */<a name="line.255"></a> <FONT color="green">256</FONT> public void setMinReduction(final double minReduction) {<a name="line.256"></a> <FONT color="green">257</FONT> this.minReduction = minReduction;<a name="line.257"></a> <FONT color="green">258</FONT> }<a name="line.258"></a> <FONT color="green">259</FONT> <a name="line.259"></a> <FONT color="green">260</FONT> /** Get the maximal growth factor for stepsize control.<a name="line.260"></a> <FONT color="green">261</FONT> * @return maximal growth factor<a name="line.261"></a> <FONT color="green">262</FONT> */<a name="line.262"></a> <FONT color="green">263</FONT> public double getMaxGrowth() {<a name="line.263"></a> <FONT color="green">264</FONT> return maxGrowth;<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> /** Set the maximal growth factor for stepsize control.<a name="line.267"></a> <FONT color="green">268</FONT> * @param maxGrowth maximal growth factor<a name="line.268"></a> <FONT color="green">269</FONT> */<a name="line.269"></a> <FONT color="green">270</FONT> public void setMaxGrowth(final double maxGrowth) {<a name="line.270"></a> <FONT color="green">271</FONT> this.maxGrowth = maxGrowth;<a name="line.271"></a> <FONT color="green">272</FONT> }<a name="line.272"></a> <FONT color="green">273</FONT> <a name="line.273"></a> <FONT color="green">274</FONT> /** Get the safety factor for stepsize control.<a name="line.274"></a> <FONT color="green">275</FONT> * @return safety factor<a name="line.275"></a> <FONT color="green">276</FONT> */<a name="line.276"></a> <FONT color="green">277</FONT> public double getSafety() {<a name="line.277"></a> <FONT color="green">278</FONT> return safety;<a name="line.278"></a> <FONT color="green">279</FONT> }<a name="line.279"></a> <FONT color="green">280</FONT> <a name="line.280"></a> <FONT color="green">281</FONT> /** Set the safety factor for stepsize control.<a name="line.281"></a> <FONT color="green">282</FONT> * @param safety safety factor<a name="line.282"></a> <FONT color="green">283</FONT> */<a name="line.283"></a> <FONT color="green">284</FONT> public void setSafety(final double safety) {<a name="line.284"></a> <FONT color="green">285</FONT> this.safety = safety;<a name="line.285"></a> <FONT color="green">286</FONT> }<a name="line.286"></a> <FONT color="green">287</FONT> <a name="line.287"></a> <FONT color="green">288</FONT> /** Compute step grow/shrink factor according to normalized error.<a name="line.288"></a> <FONT color="green">289</FONT> * @param error normalized error of the current step<a name="line.289"></a> <FONT color="green">290</FONT> * @return grow/shrink factor for next step<a name="line.290"></a> <FONT color="green">291</FONT> */<a name="line.291"></a> <FONT color="green">292</FONT> protected double computeStepGrowShrinkFactor(final double error) {<a name="line.292"></a> <FONT color="green">293</FONT> return Math.min(maxGrowth, Math.max(minReduction, safety * Math.pow(error, exp)));<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> /** Transformer used to convert the first step to Nordsieck representation. */<a name="line.296"></a> <FONT color="green">297</FONT> public static interface NordsieckTransformer {<a name="line.297"></a> <FONT color="green">298</FONT> /** Initialize the high order scaled derivatives at step start.<a name="line.298"></a> <FONT color="green">299</FONT> * @param first first scaled derivative at step start<a name="line.299"></a> <FONT color="green">300</FONT> * @param multistep scaled derivatives after step start (hy'1, ..., hy'k-1)<a name="line.300"></a> <FONT color="green">301</FONT> * will be modified<a name="line.301"></a> <FONT color="green">302</FONT> * @return high order derivatives at step start<a name="line.302"></a> <FONT color="green">303</FONT> */<a name="line.303"></a> <FONT color="green">304</FONT> RealMatrix initializeHighOrderDerivatives(double[] first, double[][] multistep);<a name="line.304"></a> <FONT color="green">305</FONT> }<a name="line.305"></a> <FONT color="green">306</FONT> <a name="line.306"></a> <FONT color="green">307</FONT> /** Specialized step handler storing the first step. */<a name="line.307"></a> <FONT color="green">308</FONT> private class NordsieckInitializer implements StepHandler {<a name="line.308"></a> <FONT color="green">309</FONT> <a name="line.309"></a> <FONT color="green">310</FONT> /** Problem dimension. */<a name="line.310"></a> <FONT color="green">311</FONT> private final int n;<a name="line.311"></a> <FONT color="green">312</FONT> <a name="line.312"></a> <FONT color="green">313</FONT> /** Simple constructor.<a name="line.313"></a> <FONT color="green">314</FONT> * @param n problem dimension<a name="line.314"></a> <FONT color="green">315</FONT> */<a name="line.315"></a> <FONT color="green">316</FONT> public NordsieckInitializer(final int n) {<a name="line.316"></a> <FONT color="green">317</FONT> this.n = n;<a name="line.317"></a> <FONT color="green">318</FONT> }<a name="line.318"></a> <FONT color="green">319</FONT> <a name="line.319"></a> <FONT color="green">320</FONT> /** {@inheritDoc} */<a name="line.320"></a> <FONT color="green">321</FONT> public void handleStep(StepInterpolator interpolator, boolean isLast)<a name="line.321"></a> <FONT color="green">322</FONT> throws DerivativeException {<a name="line.322"></a> <FONT color="green">323</FONT> <a name="line.323"></a> <FONT color="green">324</FONT> final double prev = interpolator.getPreviousTime();<a name="line.324"></a> <FONT color="green">325</FONT> final double curr = interpolator.getCurrentTime();<a name="line.325"></a> <FONT color="green">326</FONT> stepStart = prev;<a name="line.326"></a> <FONT color="green">327</FONT> stepSize = (curr - prev) / (nSteps + 1);<a name="line.327"></a> <FONT color="green">328</FONT> <a name="line.328"></a> <FONT color="green">329</FONT> // compute the first scaled derivative<a name="line.329"></a> <FONT color="green">330</FONT> interpolator.setInterpolatedTime(prev);<a name="line.330"></a> <FONT color="green">331</FONT> scaled = interpolator.getInterpolatedDerivatives().clone();<a name="line.331"></a> <FONT color="green">332</FONT> for (int j = 0; j < n; ++j) {<a name="line.332"></a> <FONT color="green">333</FONT> scaled[j] *= stepSize;<a name="line.333"></a> <FONT color="green">334</FONT> }<a name="line.334"></a> <FONT color="green">335</FONT> <a name="line.335"></a> <FONT color="green">336</FONT> // compute the high order scaled derivatives<a name="line.336"></a> <FONT color="green">337</FONT> final double[][] multistep = new double[nSteps][];<a name="line.337"></a> <FONT color="green">338</FONT> for (int i = 1; i <= nSteps; ++i) {<a name="line.338"></a> <FONT color="green">339</FONT> interpolator.setInterpolatedTime(prev + stepSize * i);<a name="line.339"></a> <FONT color="green">340</FONT> final double[] msI = interpolator.getInterpolatedDerivatives().clone();<a name="line.340"></a> <FONT color="green">341</FONT> for (int j = 0; j < n; ++j) {<a name="line.341"></a> <FONT color="green">342</FONT> msI[j] *= stepSize;<a name="line.342"></a> <FONT color="green">343</FONT> }<a name="line.343"></a> <FONT color="green">344</FONT> multistep[i - 1] = msI;<a name="line.344"></a> <FONT color="green">345</FONT> }<a name="line.345"></a> <FONT color="green">346</FONT> nordsieck = initializeHighOrderDerivatives(scaled, multistep);<a name="line.346"></a> <FONT color="green">347</FONT> <a name="line.347"></a> <FONT color="green">348</FONT> // stop the integrator after the first step has been handled<a name="line.348"></a> <FONT color="green">349</FONT> throw new InitializationCompletedMarkerException();<a name="line.349"></a> <FONT color="green">350</FONT> <a name="line.350"></a> <FONT color="green">351</FONT> }<a name="line.351"></a> <FONT color="green">352</FONT> <a name="line.352"></a> <FONT color="green">353</FONT> /** {@inheritDoc} */<a name="line.353"></a> <FONT color="green">354</FONT> public boolean requiresDenseOutput() {<a name="line.354"></a> <FONT color="green">355</FONT> return true;<a name="line.355"></a> <FONT color="green">356</FONT> }<a name="line.356"></a> <FONT color="green">357</FONT> <a name="line.357"></a> <FONT color="green">358</FONT> /** {@inheritDoc} */<a name="line.358"></a> <FONT color="green">359</FONT> public void reset() {<a name="line.359"></a> <FONT color="green">360</FONT> // nothing to do<a name="line.360"></a> <FONT color="green">361</FONT> }<a name="line.361"></a> <FONT color="green">362</FONT> <a name="line.362"></a> <FONT color="green">363</FONT> }<a name="line.363"></a> <FONT color="green">364</FONT> <a name="line.364"></a> <FONT color="green">365</FONT> /** Marker exception used ONLY to stop the starter integrator after first step. */<a name="line.365"></a> <FONT color="green">366</FONT> private static class InitializationCompletedMarkerException<a name="line.366"></a> <FONT color="green">367</FONT> extends DerivativeException {<a name="line.367"></a> <FONT color="green">368</FONT> <a name="line.368"></a> <FONT color="green">369</FONT> /** Serializable version identifier. */<a name="line.369"></a> <FONT color="green">370</FONT> private static final long serialVersionUID = -4105805787353488365L;<a name="line.370"></a> <FONT color="green">371</FONT> <a name="line.371"></a> <FONT color="green">372</FONT> /** Simple constructor. */<a name="line.372"></a> <FONT color="green">373</FONT> public InitializationCompletedMarkerException() {<a name="line.373"></a> <FONT color="green">374</FONT> super((Throwable) null);<a name="line.374"></a> <FONT color="green">375</FONT> }<a name="line.375"></a> <FONT color="green">376</FONT> <a name="line.376"></a> <FONT color="green">377</FONT> }<a name="line.377"></a> <FONT color="green">378</FONT> <a name="line.378"></a> <FONT color="green">379</FONT> /** Wrapper for differential equations, ensuring start evaluations are counted. */<a name="line.379"></a> <FONT color="green">380</FONT> private class CountingDifferentialEquations implements FirstOrderDifferentialEquations {<a name="line.380"></a> <FONT color="green">381</FONT> <a name="line.381"></a> <FONT color="green">382</FONT> /** Dimension of the problem. */<a name="line.382"></a> <FONT color="green">383</FONT> private final int dimension;<a name="line.383"></a> <FONT color="green">384</FONT> <a name="line.384"></a> <FONT color="green">385</FONT> /** Simple constructor.<a name="line.385"></a> <FONT color="green">386</FONT> * @param dimension dimension of the problem<a name="line.386"></a> <FONT color="green">387</FONT> */<a name="line.387"></a> <FONT color="green">388</FONT> public CountingDifferentialEquations(final int dimension) {<a name="line.388"></a> <FONT color="green">389</FONT> this.dimension = dimension;<a name="line.389"></a> <FONT color="green">390</FONT> }<a name="line.390"></a> <FONT color="green">391</FONT> <a name="line.391"></a> <FONT color="green">392</FONT> /** {@inheritDoc} */<a name="line.392"></a> <FONT color="green">393</FONT> public void computeDerivatives(double t, double[] y, double[] dot)<a name="line.393"></a> <FONT color="green">394</FONT> throws DerivativeException {<a name="line.394"></a> <FONT color="green">395</FONT> MultistepIntegrator.this.computeDerivatives(t, y, dot);<a name="line.395"></a> <FONT color="green">396</FONT> }<a name="line.396"></a> <FONT color="green">397</FONT> <a name="line.397"></a> <FONT color="green">398</FONT> /** {@inheritDoc} */<a name="line.398"></a> <FONT color="green">399</FONT> public int getDimension() {<a name="line.399"></a> <FONT color="green">400</FONT> return dimension;<a name="line.400"></a> <FONT color="green">401</FONT> }<a name="line.401"></a> <FONT color="green">402</FONT> }<a name="line.402"></a> <FONT color="green">403</FONT> <a name="line.403"></a> <FONT color="green">404</FONT> }<a name="line.404"></a> </PRE> </BODY> </HTML>