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comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/ode/nonstiff/GraggBulirschStoerIntegrator.html @ 13:cbf34dd4d7e6
commons-math-2.1 added
| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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| 12:970d26a94fb7 | 13:cbf34dd4d7e6 |
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| 1 <HTML> | |
| 2 <BODY BGCOLOR="white"> | |
| 3 <PRE> | |
| 4 <FONT color="green">001</FONT> /*<a name="line.1"></a> | |
| 5 <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> | |
| 6 <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> | |
| 7 <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> | |
| 8 <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> | |
| 9 <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> | |
| 10 <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> | |
| 11 <FONT color="green">008</FONT> *<a name="line.8"></a> | |
| 12 <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> | |
| 13 <FONT color="green">010</FONT> *<a name="line.10"></a> | |
| 14 <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> | |
| 15 <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> | |
| 16 <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> | |
| 17 <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> | |
| 18 <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> | |
| 19 <FONT color="green">016</FONT> */<a name="line.16"></a> | |
| 20 <FONT color="green">017</FONT> <a name="line.17"></a> | |
| 21 <FONT color="green">018</FONT> package org.apache.commons.math.ode.nonstiff;<a name="line.18"></a> | |
| 22 <FONT color="green">019</FONT> <a name="line.19"></a> | |
| 23 <FONT color="green">020</FONT> import org.apache.commons.math.ode.DerivativeException;<a name="line.20"></a> | |
| 24 <FONT color="green">021</FONT> import org.apache.commons.math.ode.FirstOrderDifferentialEquations;<a name="line.21"></a> | |
| 25 <FONT color="green">022</FONT> import org.apache.commons.math.ode.IntegratorException;<a name="line.22"></a> | |
| 26 <FONT color="green">023</FONT> import org.apache.commons.math.ode.events.EventHandler;<a name="line.23"></a> | |
| 27 <FONT color="green">024</FONT> import org.apache.commons.math.ode.sampling.AbstractStepInterpolator;<a name="line.24"></a> | |
| 28 <FONT color="green">025</FONT> import org.apache.commons.math.ode.sampling.DummyStepInterpolator;<a name="line.25"></a> | |
| 29 <FONT color="green">026</FONT> import org.apache.commons.math.ode.sampling.StepHandler;<a name="line.26"></a> | |
| 30 <FONT color="green">027</FONT> <a name="line.27"></a> | |
| 31 <FONT color="green">028</FONT> /**<a name="line.28"></a> | |
| 32 <FONT color="green">029</FONT> * This class implements a Gragg-Bulirsch-Stoer integrator for<a name="line.29"></a> | |
| 33 <FONT color="green">030</FONT> * Ordinary Differential Equations.<a name="line.30"></a> | |
| 34 <FONT color="green">031</FONT> *<a name="line.31"></a> | |
| 35 <FONT color="green">032</FONT> * <p>The Gragg-Bulirsch-Stoer algorithm is one of the most efficient<a name="line.32"></a> | |
| 36 <FONT color="green">033</FONT> * ones currently available for smooth problems. It uses Richardson<a name="line.33"></a> | |
| 37 <FONT color="green">034</FONT> * extrapolation to estimate what would be the solution if the step<a name="line.34"></a> | |
| 38 <FONT color="green">035</FONT> * size could be decreased down to zero.</p><a name="line.35"></a> | |
| 39 <FONT color="green">036</FONT> *<a name="line.36"></a> | |
| 40 <FONT color="green">037</FONT> * <p><a name="line.37"></a> | |
| 41 <FONT color="green">038</FONT> * This method changes both the step size and the order during<a name="line.38"></a> | |
| 42 <FONT color="green">039</FONT> * integration, in order to minimize computation cost. It is<a name="line.39"></a> | |
| 43 <FONT color="green">040</FONT> * particularly well suited when a very high precision is needed. The<a name="line.40"></a> | |
| 44 <FONT color="green">041</FONT> * limit where this method becomes more efficient than high-order<a name="line.41"></a> | |
| 45 <FONT color="green">042</FONT> * embedded Runge-Kutta methods like {@link DormandPrince853Integrator<a name="line.42"></a> | |
| 46 <FONT color="green">043</FONT> * Dormand-Prince 8(5,3)} depends on the problem. Results given in the<a name="line.43"></a> | |
| 47 <FONT color="green">044</FONT> * Hairer, Norsett and Wanner book show for example that this limit<a name="line.44"></a> | |
| 48 <FONT color="green">045</FONT> * occurs for accuracy around 1e-6 when integrating Saltzam-Lorenz<a name="line.45"></a> | |
| 49 <FONT color="green">046</FONT> * equations (the authors note this problem is <i>extremely sensitive<a name="line.46"></a> | |
| 50 <FONT color="green">047</FONT> * to the errors in the first integration steps</i>), and around 1e-11<a name="line.47"></a> | |
| 51 <FONT color="green">048</FONT> * for a two dimensional celestial mechanics problems with seven<a name="line.48"></a> | |
| 52 <FONT color="green">049</FONT> * bodies (pleiades problem, involving quasi-collisions for which<a name="line.49"></a> | |
| 53 <FONT color="green">050</FONT> * <i>automatic step size control is essential</i>).<a name="line.50"></a> | |
| 54 <FONT color="green">051</FONT> * </p><a name="line.51"></a> | |
| 55 <FONT color="green">052</FONT> *<a name="line.52"></a> | |
| 56 <FONT color="green">053</FONT> * <p><a name="line.53"></a> | |
| 57 <FONT color="green">054</FONT> * This implementation is basically a reimplementation in Java of the<a name="line.54"></a> | |
| 58 <FONT color="green">055</FONT> * <a<a name="line.55"></a> | |
| 59 <FONT color="green">056</FONT> * href="http://www.unige.ch/math/folks/hairer/prog/nonstiff/odex.f">odex</a><a name="line.56"></a> | |
| 60 <FONT color="green">057</FONT> * fortran code by E. Hairer and G. Wanner. The redistribution policy<a name="line.57"></a> | |
| 61 <FONT color="green">058</FONT> * for this code is available <a<a name="line.58"></a> | |
| 62 <FONT color="green">059</FONT> * href="http://www.unige.ch/~hairer/prog/licence.txt">here</a>, for<a name="line.59"></a> | |
| 63 <FONT color="green">060</FONT> * convenience, it is reproduced below.</p><a name="line.60"></a> | |
| 64 <FONT color="green">061</FONT> * </p><a name="line.61"></a> | |
| 65 <FONT color="green">062</FONT> *<a name="line.62"></a> | |
| 66 <FONT color="green">063</FONT> * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0"><a name="line.63"></a> | |
| 67 <FONT color="green">064</FONT> * <tr><td>Copyright (c) 2004, Ernst Hairer</td></tr><a name="line.64"></a> | |
| 68 <FONT color="green">065</FONT> *<a name="line.65"></a> | |
| 69 <FONT color="green">066</FONT> * <tr><td>Redistribution and use in source and binary forms, with or<a name="line.66"></a> | |
| 70 <FONT color="green">067</FONT> * without modification, are permitted provided that the following<a name="line.67"></a> | |
| 71 <FONT color="green">068</FONT> * conditions are met:<a name="line.68"></a> | |
| 72 <FONT color="green">069</FONT> * <ul><a name="line.69"></a> | |
| 73 <FONT color="green">070</FONT> * <li>Redistributions of source code must retain the above copyright<a name="line.70"></a> | |
| 74 <FONT color="green">071</FONT> * notice, this list of conditions and the following disclaimer.</li><a name="line.71"></a> | |
| 75 <FONT color="green">072</FONT> * <li>Redistributions in binary form must reproduce the above copyright<a name="line.72"></a> | |
| 76 <FONT color="green">073</FONT> * notice, this list of conditions and the following disclaimer in the<a name="line.73"></a> | |
| 77 <FONT color="green">074</FONT> * documentation and/or other materials provided with the distribution.</li><a name="line.74"></a> | |
| 78 <FONT color="green">075</FONT> * </ul></td></tr><a name="line.75"></a> | |
| 79 <FONT color="green">076</FONT> *<a name="line.76"></a> | |
| 80 <FONT color="green">077</FONT> * <tr><td><strong>THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND<a name="line.77"></a> | |
| 81 <FONT color="green">078</FONT> * CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,<a name="line.78"></a> | |
| 82 <FONT color="green">079</FONT> * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS<a name="line.79"></a> | |
| 83 <FONT color="green">080</FONT> * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR<a name="line.80"></a> | |
| 84 <FONT color="green">081</FONT> * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,<a name="line.81"></a> | |
| 85 <FONT color="green">082</FONT> * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,<a name="line.82"></a> | |
| 86 <FONT color="green">083</FONT> * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR<a name="line.83"></a> | |
| 87 <FONT color="green">084</FONT> * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF<a name="line.84"></a> | |
| 88 <FONT color="green">085</FONT> * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING<a name="line.85"></a> | |
| 89 <FONT color="green">086</FONT> * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS<a name="line.86"></a> | |
| 90 <FONT color="green">087</FONT> * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</strong></td></tr><a name="line.87"></a> | |
| 91 <FONT color="green">088</FONT> * </table><a name="line.88"></a> | |
| 92 <FONT color="green">089</FONT> *<a name="line.89"></a> | |
| 93 <FONT color="green">090</FONT> * @version $Revision: 919479 $ $Date: 2010-03-05 11:35:56 -0500 (Fri, 05 Mar 2010) $<a name="line.90"></a> | |
| 94 <FONT color="green">091</FONT> * @since 1.2<a name="line.91"></a> | |
| 95 <FONT color="green">092</FONT> */<a name="line.92"></a> | |
| 96 <FONT color="green">093</FONT> <a name="line.93"></a> | |
| 97 <FONT color="green">094</FONT> public class GraggBulirschStoerIntegrator extends AdaptiveStepsizeIntegrator {<a name="line.94"></a> | |
| 98 <FONT color="green">095</FONT> <a name="line.95"></a> | |
| 99 <FONT color="green">096</FONT> /** Integrator method name. */<a name="line.96"></a> | |
| 100 <FONT color="green">097</FONT> private static final String METHOD_NAME = "Gragg-Bulirsch-Stoer";<a name="line.97"></a> | |
| 101 <FONT color="green">098</FONT> <a name="line.98"></a> | |
| 102 <FONT color="green">099</FONT> /** maximal order. */<a name="line.99"></a> | |
| 103 <FONT color="green">100</FONT> private int maxOrder;<a name="line.100"></a> | |
| 104 <FONT color="green">101</FONT> <a name="line.101"></a> | |
| 105 <FONT color="green">102</FONT> /** step size sequence. */<a name="line.102"></a> | |
| 106 <FONT color="green">103</FONT> private int[] sequence;<a name="line.103"></a> | |
| 107 <FONT color="green">104</FONT> <a name="line.104"></a> | |
| 108 <FONT color="green">105</FONT> /** overall cost of applying step reduction up to iteration k+1, in number of calls. */<a name="line.105"></a> | |
| 109 <FONT color="green">106</FONT> private int[] costPerStep;<a name="line.106"></a> | |
| 110 <FONT color="green">107</FONT> <a name="line.107"></a> | |
| 111 <FONT color="green">108</FONT> /** cost per unit step. */<a name="line.108"></a> | |
| 112 <FONT color="green">109</FONT> private double[] costPerTimeUnit;<a name="line.109"></a> | |
| 113 <FONT color="green">110</FONT> <a name="line.110"></a> | |
| 114 <FONT color="green">111</FONT> /** optimal steps for each order. */<a name="line.111"></a> | |
| 115 <FONT color="green">112</FONT> private double[] optimalStep;<a name="line.112"></a> | |
| 116 <FONT color="green">113</FONT> <a name="line.113"></a> | |
| 117 <FONT color="green">114</FONT> /** extrapolation coefficients. */<a name="line.114"></a> | |
| 118 <FONT color="green">115</FONT> private double[][] coeff;<a name="line.115"></a> | |
| 119 <FONT color="green">116</FONT> <a name="line.116"></a> | |
| 120 <FONT color="green">117</FONT> /** stability check enabling parameter. */<a name="line.117"></a> | |
| 121 <FONT color="green">118</FONT> private boolean performTest;<a name="line.118"></a> | |
| 122 <FONT color="green">119</FONT> <a name="line.119"></a> | |
| 123 <FONT color="green">120</FONT> /** maximal number of checks for each iteration. */<a name="line.120"></a> | |
| 124 <FONT color="green">121</FONT> private int maxChecks;<a name="line.121"></a> | |
| 125 <FONT color="green">122</FONT> <a name="line.122"></a> | |
| 126 <FONT color="green">123</FONT> /** maximal number of iterations for which checks are performed. */<a name="line.123"></a> | |
| 127 <FONT color="green">124</FONT> private int maxIter;<a name="line.124"></a> | |
| 128 <FONT color="green">125</FONT> <a name="line.125"></a> | |
| 129 <FONT color="green">126</FONT> /** stepsize reduction factor in case of stability check failure. */<a name="line.126"></a> | |
| 130 <FONT color="green">127</FONT> private double stabilityReduction;<a name="line.127"></a> | |
| 131 <FONT color="green">128</FONT> <a name="line.128"></a> | |
| 132 <FONT color="green">129</FONT> /** first stepsize control factor. */<a name="line.129"></a> | |
| 133 <FONT color="green">130</FONT> private double stepControl1;<a name="line.130"></a> | |
| 134 <FONT color="green">131</FONT> <a name="line.131"></a> | |
| 135 <FONT color="green">132</FONT> /** second stepsize control factor. */<a name="line.132"></a> | |
| 136 <FONT color="green">133</FONT> private double stepControl2;<a name="line.133"></a> | |
| 137 <FONT color="green">134</FONT> <a name="line.134"></a> | |
| 138 <FONT color="green">135</FONT> /** third stepsize control factor. */<a name="line.135"></a> | |
| 139 <FONT color="green">136</FONT> private double stepControl3;<a name="line.136"></a> | |
| 140 <FONT color="green">137</FONT> <a name="line.137"></a> | |
| 141 <FONT color="green">138</FONT> /** fourth stepsize control factor. */<a name="line.138"></a> | |
| 142 <FONT color="green">139</FONT> private double stepControl4;<a name="line.139"></a> | |
| 143 <FONT color="green">140</FONT> <a name="line.140"></a> | |
| 144 <FONT color="green">141</FONT> /** first order control factor. */<a name="line.141"></a> | |
| 145 <FONT color="green">142</FONT> private double orderControl1;<a name="line.142"></a> | |
| 146 <FONT color="green">143</FONT> <a name="line.143"></a> | |
| 147 <FONT color="green">144</FONT> /** second order control factor. */<a name="line.144"></a> | |
| 148 <FONT color="green">145</FONT> private double orderControl2;<a name="line.145"></a> | |
| 149 <FONT color="green">146</FONT> <a name="line.146"></a> | |
| 150 <FONT color="green">147</FONT> /** dense outpute required. */<a name="line.147"></a> | |
| 151 <FONT color="green">148</FONT> private boolean denseOutput;<a name="line.148"></a> | |
| 152 <FONT color="green">149</FONT> <a name="line.149"></a> | |
| 153 <FONT color="green">150</FONT> /** use interpolation error in stepsize control. */<a name="line.150"></a> | |
| 154 <FONT color="green">151</FONT> private boolean useInterpolationError;<a name="line.151"></a> | |
| 155 <FONT color="green">152</FONT> <a name="line.152"></a> | |
| 156 <FONT color="green">153</FONT> /** interpolation order control parameter. */<a name="line.153"></a> | |
| 157 <FONT color="green">154</FONT> private int mudif;<a name="line.154"></a> | |
| 158 <FONT color="green">155</FONT> <a name="line.155"></a> | |
| 159 <FONT color="green">156</FONT> /** Simple constructor.<a name="line.156"></a> | |
| 160 <FONT color="green">157</FONT> * Build a Gragg-Bulirsch-Stoer integrator with the given step<a name="line.157"></a> | |
| 161 <FONT color="green">158</FONT> * bounds. All tuning parameters are set to their default<a name="line.158"></a> | |
| 162 <FONT color="green">159</FONT> * values. The default step handler does nothing.<a name="line.159"></a> | |
| 163 <FONT color="green">160</FONT> * @param minStep minimal step (must be positive even for backward<a name="line.160"></a> | |
| 164 <FONT color="green">161</FONT> * integration), the last step can be smaller than this<a name="line.161"></a> | |
| 165 <FONT color="green">162</FONT> * @param maxStep maximal step (must be positive even for backward<a name="line.162"></a> | |
| 166 <FONT color="green">163</FONT> * integration)<a name="line.163"></a> | |
| 167 <FONT color="green">164</FONT> * @param scalAbsoluteTolerance allowed absolute error<a name="line.164"></a> | |
| 168 <FONT color="green">165</FONT> * @param scalRelativeTolerance allowed relative error<a name="line.165"></a> | |
| 169 <FONT color="green">166</FONT> */<a name="line.166"></a> | |
| 170 <FONT color="green">167</FONT> public GraggBulirschStoerIntegrator(final double minStep, final double maxStep,<a name="line.167"></a> | |
| 171 <FONT color="green">168</FONT> final double scalAbsoluteTolerance,<a name="line.168"></a> | |
| 172 <FONT color="green">169</FONT> final double scalRelativeTolerance) {<a name="line.169"></a> | |
| 173 <FONT color="green">170</FONT> super(METHOD_NAME, minStep, maxStep,<a name="line.170"></a> | |
| 174 <FONT color="green">171</FONT> scalAbsoluteTolerance, scalRelativeTolerance);<a name="line.171"></a> | |
| 175 <FONT color="green">172</FONT> denseOutput = requiresDenseOutput() || (! eventsHandlersManager.isEmpty());<a name="line.172"></a> | |
| 176 <FONT color="green">173</FONT> setStabilityCheck(true, -1, -1, -1);<a name="line.173"></a> | |
| 177 <FONT color="green">174</FONT> setStepsizeControl(-1, -1, -1, -1);<a name="line.174"></a> | |
| 178 <FONT color="green">175</FONT> setOrderControl(-1, -1, -1);<a name="line.175"></a> | |
| 179 <FONT color="green">176</FONT> setInterpolationControl(true, -1);<a name="line.176"></a> | |
| 180 <FONT color="green">177</FONT> }<a name="line.177"></a> | |
| 181 <FONT color="green">178</FONT> <a name="line.178"></a> | |
| 182 <FONT color="green">179</FONT> /** Simple constructor.<a name="line.179"></a> | |
| 183 <FONT color="green">180</FONT> * Build a Gragg-Bulirsch-Stoer integrator with the given step<a name="line.180"></a> | |
| 184 <FONT color="green">181</FONT> * bounds. All tuning parameters are set to their default<a name="line.181"></a> | |
| 185 <FONT color="green">182</FONT> * values. The default step handler does nothing.<a name="line.182"></a> | |
| 186 <FONT color="green">183</FONT> * @param minStep minimal step (must be positive even for backward<a name="line.183"></a> | |
| 187 <FONT color="green">184</FONT> * integration), the last step can be smaller than this<a name="line.184"></a> | |
| 188 <FONT color="green">185</FONT> * @param maxStep maximal step (must be positive even for backward<a name="line.185"></a> | |
| 189 <FONT color="green">186</FONT> * integration)<a name="line.186"></a> | |
| 190 <FONT color="green">187</FONT> * @param vecAbsoluteTolerance allowed absolute error<a name="line.187"></a> | |
| 191 <FONT color="green">188</FONT> * @param vecRelativeTolerance allowed relative error<a name="line.188"></a> | |
| 192 <FONT color="green">189</FONT> */<a name="line.189"></a> | |
| 193 <FONT color="green">190</FONT> public GraggBulirschStoerIntegrator(final double minStep, final double maxStep,<a name="line.190"></a> | |
| 194 <FONT color="green">191</FONT> final double[] vecAbsoluteTolerance,<a name="line.191"></a> | |
| 195 <FONT color="green">192</FONT> final double[] vecRelativeTolerance) {<a name="line.192"></a> | |
| 196 <FONT color="green">193</FONT> super(METHOD_NAME, minStep, maxStep,<a name="line.193"></a> | |
| 197 <FONT color="green">194</FONT> vecAbsoluteTolerance, vecRelativeTolerance);<a name="line.194"></a> | |
| 198 <FONT color="green">195</FONT> denseOutput = requiresDenseOutput() || (! eventsHandlersManager.isEmpty());<a name="line.195"></a> | |
| 199 <FONT color="green">196</FONT> setStabilityCheck(true, -1, -1, -1);<a name="line.196"></a> | |
| 200 <FONT color="green">197</FONT> setStepsizeControl(-1, -1, -1, -1);<a name="line.197"></a> | |
| 201 <FONT color="green">198</FONT> setOrderControl(-1, -1, -1);<a name="line.198"></a> | |
| 202 <FONT color="green">199</FONT> setInterpolationControl(true, -1);<a name="line.199"></a> | |
| 203 <FONT color="green">200</FONT> }<a name="line.200"></a> | |
| 204 <FONT color="green">201</FONT> <a name="line.201"></a> | |
| 205 <FONT color="green">202</FONT> /** Set the stability check controls.<a name="line.202"></a> | |
| 206 <FONT color="green">203</FONT> * <p>The stability check is performed on the first few iterations of<a name="line.203"></a> | |
| 207 <FONT color="green">204</FONT> * the extrapolation scheme. If this test fails, the step is rejected<a name="line.204"></a> | |
| 208 <FONT color="green">205</FONT> * and the stepsize is reduced.</p><a name="line.205"></a> | |
| 209 <FONT color="green">206</FONT> * <p>By default, the test is performed, at most during two<a name="line.206"></a> | |
| 210 <FONT color="green">207</FONT> * iterations at each step, and at most once for each of these<a name="line.207"></a> | |
| 211 <FONT color="green">208</FONT> * iterations. The default stepsize reduction factor is 0.5.</p><a name="line.208"></a> | |
| 212 <FONT color="green">209</FONT> * @param performStabilityCheck if true, stability check will be performed,<a name="line.209"></a> | |
| 213 <FONT color="green">210</FONT> if false, the check will be skipped<a name="line.210"></a> | |
| 214 <FONT color="green">211</FONT> * @param maxNumIter maximal number of iterations for which checks are<a name="line.211"></a> | |
| 215 <FONT color="green">212</FONT> * performed (the number of iterations is reset to default if negative<a name="line.212"></a> | |
| 216 <FONT color="green">213</FONT> * or null)<a name="line.213"></a> | |
| 217 <FONT color="green">214</FONT> * @param maxNumChecks maximal number of checks for each iteration<a name="line.214"></a> | |
| 218 <FONT color="green">215</FONT> * (the number of checks is reset to default if negative or null)<a name="line.215"></a> | |
| 219 <FONT color="green">216</FONT> * @param stepsizeReductionFactor stepsize reduction factor in case of<a name="line.216"></a> | |
| 220 <FONT color="green">217</FONT> * failure (the factor is reset to default if lower than 0.0001 or<a name="line.217"></a> | |
| 221 <FONT color="green">218</FONT> * greater than 0.9999)<a name="line.218"></a> | |
| 222 <FONT color="green">219</FONT> */<a name="line.219"></a> | |
| 223 <FONT color="green">220</FONT> public void setStabilityCheck(final boolean performStabilityCheck,<a name="line.220"></a> | |
| 224 <FONT color="green">221</FONT> final int maxNumIter, final int maxNumChecks,<a name="line.221"></a> | |
| 225 <FONT color="green">222</FONT> final double stepsizeReductionFactor) {<a name="line.222"></a> | |
| 226 <FONT color="green">223</FONT> <a name="line.223"></a> | |
| 227 <FONT color="green">224</FONT> this.performTest = performStabilityCheck;<a name="line.224"></a> | |
| 228 <FONT color="green">225</FONT> this.maxIter = (maxNumIter <= 0) ? 2 : maxNumIter;<a name="line.225"></a> | |
| 229 <FONT color="green">226</FONT> this.maxChecks = (maxNumChecks <= 0) ? 1 : maxNumChecks;<a name="line.226"></a> | |
| 230 <FONT color="green">227</FONT> <a name="line.227"></a> | |
| 231 <FONT color="green">228</FONT> if ((stepsizeReductionFactor < 0.0001) || (stepsizeReductionFactor > 0.9999)) {<a name="line.228"></a> | |
| 232 <FONT color="green">229</FONT> this.stabilityReduction = 0.5;<a name="line.229"></a> | |
| 233 <FONT color="green">230</FONT> } else {<a name="line.230"></a> | |
| 234 <FONT color="green">231</FONT> this.stabilityReduction = stepsizeReductionFactor;<a name="line.231"></a> | |
| 235 <FONT color="green">232</FONT> }<a name="line.232"></a> | |
| 236 <FONT color="green">233</FONT> <a name="line.233"></a> | |
| 237 <FONT color="green">234</FONT> }<a name="line.234"></a> | |
| 238 <FONT color="green">235</FONT> <a name="line.235"></a> | |
| 239 <FONT color="green">236</FONT> /** Set the step size control factors.<a name="line.236"></a> | |
| 240 <FONT color="green">237</FONT> <a name="line.237"></a> | |
| 241 <FONT color="green">238</FONT> * <p>The new step size hNew is computed from the old one h by:<a name="line.238"></a> | |
| 242 <FONT color="green">239</FONT> * <pre><a name="line.239"></a> | |
| 243 <FONT color="green">240</FONT> * hNew = h * stepControl2 / (err/stepControl1)^(1/(2k+1))<a name="line.240"></a> | |
| 244 <FONT color="green">241</FONT> * </pre><a name="line.241"></a> | |
| 245 <FONT color="green">242</FONT> * where err is the scaled error and k the iteration number of the<a name="line.242"></a> | |
| 246 <FONT color="green">243</FONT> * extrapolation scheme (counting from 0). The default values are<a name="line.243"></a> | |
| 247 <FONT color="green">244</FONT> * 0.65 for stepControl1 and 0.94 for stepControl2.</p><a name="line.244"></a> | |
| 248 <FONT color="green">245</FONT> * <p>The step size is subject to the restriction:<a name="line.245"></a> | |
| 249 <FONT color="green">246</FONT> * <pre><a name="line.246"></a> | |
| 250 <FONT color="green">247</FONT> * stepControl3^(1/(2k+1))/stepControl4 <= hNew/h <= 1/stepControl3^(1/(2k+1))<a name="line.247"></a> | |
| 251 <FONT color="green">248</FONT> * </pre><a name="line.248"></a> | |
| 252 <FONT color="green">249</FONT> * The default values are 0.02 for stepControl3 and 4.0 for<a name="line.249"></a> | |
| 253 <FONT color="green">250</FONT> * stepControl4.</p><a name="line.250"></a> | |
| 254 <FONT color="green">251</FONT> * @param control1 first stepsize control factor (the factor is<a name="line.251"></a> | |
| 255 <FONT color="green">252</FONT> * reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.252"></a> | |
| 256 <FONT color="green">253</FONT> * @param control2 second stepsize control factor (the factor<a name="line.253"></a> | |
| 257 <FONT color="green">254</FONT> * is reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.254"></a> | |
| 258 <FONT color="green">255</FONT> * @param control3 third stepsize control factor (the factor is<a name="line.255"></a> | |
| 259 <FONT color="green">256</FONT> * reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.256"></a> | |
| 260 <FONT color="green">257</FONT> * @param control4 fourth stepsize control factor (the factor<a name="line.257"></a> | |
| 261 <FONT color="green">258</FONT> * is reset to default if lower than 1.0001 or greater than 999.9)<a name="line.258"></a> | |
| 262 <FONT color="green">259</FONT> */<a name="line.259"></a> | |
| 263 <FONT color="green">260</FONT> public void setStepsizeControl(final double control1, final double control2,<a name="line.260"></a> | |
| 264 <FONT color="green">261</FONT> final double control3, final double control4) {<a name="line.261"></a> | |
| 265 <FONT color="green">262</FONT> <a name="line.262"></a> | |
| 266 <FONT color="green">263</FONT> if ((control1 < 0.0001) || (control1 > 0.9999)) {<a name="line.263"></a> | |
| 267 <FONT color="green">264</FONT> this.stepControl1 = 0.65;<a name="line.264"></a> | |
| 268 <FONT color="green">265</FONT> } else {<a name="line.265"></a> | |
| 269 <FONT color="green">266</FONT> this.stepControl1 = control1;<a name="line.266"></a> | |
| 270 <FONT color="green">267</FONT> }<a name="line.267"></a> | |
| 271 <FONT color="green">268</FONT> <a name="line.268"></a> | |
| 272 <FONT color="green">269</FONT> if ((control2 < 0.0001) || (control2 > 0.9999)) {<a name="line.269"></a> | |
| 273 <FONT color="green">270</FONT> this.stepControl2 = 0.94;<a name="line.270"></a> | |
| 274 <FONT color="green">271</FONT> } else {<a name="line.271"></a> | |
| 275 <FONT color="green">272</FONT> this.stepControl2 = control2;<a name="line.272"></a> | |
| 276 <FONT color="green">273</FONT> }<a name="line.273"></a> | |
| 277 <FONT color="green">274</FONT> <a name="line.274"></a> | |
| 278 <FONT color="green">275</FONT> if ((control3 < 0.0001) || (control3 > 0.9999)) {<a name="line.275"></a> | |
| 279 <FONT color="green">276</FONT> this.stepControl3 = 0.02;<a name="line.276"></a> | |
| 280 <FONT color="green">277</FONT> } else {<a name="line.277"></a> | |
| 281 <FONT color="green">278</FONT> this.stepControl3 = control3;<a name="line.278"></a> | |
| 282 <FONT color="green">279</FONT> }<a name="line.279"></a> | |
| 283 <FONT color="green">280</FONT> <a name="line.280"></a> | |
| 284 <FONT color="green">281</FONT> if ((control4 < 1.0001) || (control4 > 999.9)) {<a name="line.281"></a> | |
| 285 <FONT color="green">282</FONT> this.stepControl4 = 4.0;<a name="line.282"></a> | |
| 286 <FONT color="green">283</FONT> } else {<a name="line.283"></a> | |
| 287 <FONT color="green">284</FONT> this.stepControl4 = control4;<a name="line.284"></a> | |
| 288 <FONT color="green">285</FONT> }<a name="line.285"></a> | |
| 289 <FONT color="green">286</FONT> <a name="line.286"></a> | |
| 290 <FONT color="green">287</FONT> }<a name="line.287"></a> | |
| 291 <FONT color="green">288</FONT> <a name="line.288"></a> | |
| 292 <FONT color="green">289</FONT> /** Set the order control parameters.<a name="line.289"></a> | |
| 293 <FONT color="green">290</FONT> * <p>The Gragg-Bulirsch-Stoer method changes both the step size and<a name="line.290"></a> | |
| 294 <FONT color="green">291</FONT> * the order during integration, in order to minimize computation<a name="line.291"></a> | |
| 295 <FONT color="green">292</FONT> * cost. Each extrapolation step increases the order by 2, so the<a name="line.292"></a> | |
| 296 <FONT color="green">293</FONT> * maximal order that will be used is always even, it is twice the<a name="line.293"></a> | |
| 297 <FONT color="green">294</FONT> * maximal number of columns in the extrapolation table.</p><a name="line.294"></a> | |
| 298 <FONT color="green">295</FONT> * <pre><a name="line.295"></a> | |
| 299 <FONT color="green">296</FONT> * order is decreased if w(k-1) <= w(k) * orderControl1<a name="line.296"></a> | |
| 300 <FONT color="green">297</FONT> * order is increased if w(k) <= w(k-1) * orderControl2<a name="line.297"></a> | |
| 301 <FONT color="green">298</FONT> * </pre><a name="line.298"></a> | |
| 302 <FONT color="green">299</FONT> * <p>where w is the table of work per unit step for each order<a name="line.299"></a> | |
| 303 <FONT color="green">300</FONT> * (number of function calls divided by the step length), and k is<a name="line.300"></a> | |
| 304 <FONT color="green">301</FONT> * the current order.</p><a name="line.301"></a> | |
| 305 <FONT color="green">302</FONT> * <p>The default maximal order after construction is 18 (i.e. the<a name="line.302"></a> | |
| 306 <FONT color="green">303</FONT> * maximal number of columns is 9). The default values are 0.8 for<a name="line.303"></a> | |
| 307 <FONT color="green">304</FONT> * orderControl1 and 0.9 for orderControl2.</p><a name="line.304"></a> | |
| 308 <FONT color="green">305</FONT> * @param maximalOrder maximal order in the extrapolation table (the<a name="line.305"></a> | |
| 309 <FONT color="green">306</FONT> * maximal order is reset to default if order <= 6 or odd)<a name="line.306"></a> | |
| 310 <FONT color="green">307</FONT> * @param control1 first order control factor (the factor is<a name="line.307"></a> | |
| 311 <FONT color="green">308</FONT> * reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.308"></a> | |
| 312 <FONT color="green">309</FONT> * @param control2 second order control factor (the factor<a name="line.309"></a> | |
| 313 <FONT color="green">310</FONT> * is reset to default if lower than 0.0001 or greater than 0.9999)<a name="line.310"></a> | |
| 314 <FONT color="green">311</FONT> */<a name="line.311"></a> | |
| 315 <FONT color="green">312</FONT> public void setOrderControl(final int maximalOrder,<a name="line.312"></a> | |
| 316 <FONT color="green">313</FONT> final double control1, final double control2) {<a name="line.313"></a> | |
| 317 <FONT color="green">314</FONT> <a name="line.314"></a> | |
| 318 <FONT color="green">315</FONT> if ((maximalOrder <= 6) || (maximalOrder % 2 != 0)) {<a name="line.315"></a> | |
| 319 <FONT color="green">316</FONT> this.maxOrder = 18;<a name="line.316"></a> | |
| 320 <FONT color="green">317</FONT> }<a name="line.317"></a> | |
| 321 <FONT color="green">318</FONT> <a name="line.318"></a> | |
| 322 <FONT color="green">319</FONT> if ((control1 < 0.0001) || (control1 > 0.9999)) {<a name="line.319"></a> | |
| 323 <FONT color="green">320</FONT> this.orderControl1 = 0.8;<a name="line.320"></a> | |
| 324 <FONT color="green">321</FONT> } else {<a name="line.321"></a> | |
| 325 <FONT color="green">322</FONT> this.orderControl1 = control1;<a name="line.322"></a> | |
| 326 <FONT color="green">323</FONT> }<a name="line.323"></a> | |
| 327 <FONT color="green">324</FONT> <a name="line.324"></a> | |
| 328 <FONT color="green">325</FONT> if ((control2 < 0.0001) || (control2 > 0.9999)) {<a name="line.325"></a> | |
| 329 <FONT color="green">326</FONT> this.orderControl2 = 0.9;<a name="line.326"></a> | |
| 330 <FONT color="green">327</FONT> } else {<a name="line.327"></a> | |
| 331 <FONT color="green">328</FONT> this.orderControl2 = control2;<a name="line.328"></a> | |
| 332 <FONT color="green">329</FONT> }<a name="line.329"></a> | |
| 333 <FONT color="green">330</FONT> <a name="line.330"></a> | |
| 334 <FONT color="green">331</FONT> // reinitialize the arrays<a name="line.331"></a> | |
| 335 <FONT color="green">332</FONT> initializeArrays();<a name="line.332"></a> | |
| 336 <FONT color="green">333</FONT> <a name="line.333"></a> | |
| 337 <FONT color="green">334</FONT> }<a name="line.334"></a> | |
| 338 <FONT color="green">335</FONT> <a name="line.335"></a> | |
| 339 <FONT color="green">336</FONT> /** {@inheritDoc} */<a name="line.336"></a> | |
| 340 <FONT color="green">337</FONT> @Override<a name="line.337"></a> | |
| 341 <FONT color="green">338</FONT> public void addStepHandler (final StepHandler handler) {<a name="line.338"></a> | |
| 342 <FONT color="green">339</FONT> <a name="line.339"></a> | |
| 343 <FONT color="green">340</FONT> super.addStepHandler(handler);<a name="line.340"></a> | |
| 344 <FONT color="green">341</FONT> denseOutput = requiresDenseOutput() || (! eventsHandlersManager.isEmpty());<a name="line.341"></a> | |
| 345 <FONT color="green">342</FONT> <a name="line.342"></a> | |
| 346 <FONT color="green">343</FONT> // reinitialize the arrays<a name="line.343"></a> | |
| 347 <FONT color="green">344</FONT> initializeArrays();<a name="line.344"></a> | |
| 348 <FONT color="green">345</FONT> <a name="line.345"></a> | |
| 349 <FONT color="green">346</FONT> }<a name="line.346"></a> | |
| 350 <FONT color="green">347</FONT> <a name="line.347"></a> | |
| 351 <FONT color="green">348</FONT> /** {@inheritDoc} */<a name="line.348"></a> | |
| 352 <FONT color="green">349</FONT> @Override<a name="line.349"></a> | |
| 353 <FONT color="green">350</FONT> public void addEventHandler(final EventHandler function,<a name="line.350"></a> | |
| 354 <FONT color="green">351</FONT> final double maxCheckInterval,<a name="line.351"></a> | |
| 355 <FONT color="green">352</FONT> final double convergence,<a name="line.352"></a> | |
| 356 <FONT color="green">353</FONT> final int maxIterationCount) {<a name="line.353"></a> | |
| 357 <FONT color="green">354</FONT> super.addEventHandler(function, maxCheckInterval, convergence, maxIterationCount);<a name="line.354"></a> | |
| 358 <FONT color="green">355</FONT> denseOutput = requiresDenseOutput() || (! eventsHandlersManager.isEmpty());<a name="line.355"></a> | |
| 359 <FONT color="green">356</FONT> <a name="line.356"></a> | |
| 360 <FONT color="green">357</FONT> // reinitialize the arrays<a name="line.357"></a> | |
| 361 <FONT color="green">358</FONT> initializeArrays();<a name="line.358"></a> | |
| 362 <FONT color="green">359</FONT> <a name="line.359"></a> | |
| 363 <FONT color="green">360</FONT> }<a name="line.360"></a> | |
| 364 <FONT color="green">361</FONT> <a name="line.361"></a> | |
| 365 <FONT color="green">362</FONT> /** Initialize the integrator internal arrays. */<a name="line.362"></a> | |
| 366 <FONT color="green">363</FONT> private void initializeArrays() {<a name="line.363"></a> | |
| 367 <FONT color="green">364</FONT> <a name="line.364"></a> | |
| 368 <FONT color="green">365</FONT> final int size = maxOrder / 2;<a name="line.365"></a> | |
| 369 <FONT color="green">366</FONT> <a name="line.366"></a> | |
| 370 <FONT color="green">367</FONT> if ((sequence == null) || (sequence.length != size)) {<a name="line.367"></a> | |
| 371 <FONT color="green">368</FONT> // all arrays should be reallocated with the right size<a name="line.368"></a> | |
| 372 <FONT color="green">369</FONT> sequence = new int[size];<a name="line.369"></a> | |
| 373 <FONT color="green">370</FONT> costPerStep = new int[size];<a name="line.370"></a> | |
| 374 <FONT color="green">371</FONT> coeff = new double[size][];<a name="line.371"></a> | |
| 375 <FONT color="green">372</FONT> costPerTimeUnit = new double[size];<a name="line.372"></a> | |
| 376 <FONT color="green">373</FONT> optimalStep = new double[size];<a name="line.373"></a> | |
| 377 <FONT color="green">374</FONT> }<a name="line.374"></a> | |
| 378 <FONT color="green">375</FONT> <a name="line.375"></a> | |
| 379 <FONT color="green">376</FONT> if (denseOutput) {<a name="line.376"></a> | |
| 380 <FONT color="green">377</FONT> // step size sequence: 2, 6, 10, 14, ...<a name="line.377"></a> | |
| 381 <FONT color="green">378</FONT> for (int k = 0; k < size; ++k) {<a name="line.378"></a> | |
| 382 <FONT color="green">379</FONT> sequence[k] = 4 * k + 2;<a name="line.379"></a> | |
| 383 <FONT color="green">380</FONT> }<a name="line.380"></a> | |
| 384 <FONT color="green">381</FONT> } else {<a name="line.381"></a> | |
| 385 <FONT color="green">382</FONT> // step size sequence: 2, 4, 6, 8, ...<a name="line.382"></a> | |
| 386 <FONT color="green">383</FONT> for (int k = 0; k < size; ++k) {<a name="line.383"></a> | |
| 387 <FONT color="green">384</FONT> sequence[k] = 2 * (k + 1);<a name="line.384"></a> | |
| 388 <FONT color="green">385</FONT> }<a name="line.385"></a> | |
| 389 <FONT color="green">386</FONT> }<a name="line.386"></a> | |
| 390 <FONT color="green">387</FONT> <a name="line.387"></a> | |
| 391 <FONT color="green">388</FONT> // initialize the order selection cost array<a name="line.388"></a> | |
| 392 <FONT color="green">389</FONT> // (number of function calls for each column of the extrapolation table)<a name="line.389"></a> | |
| 393 <FONT color="green">390</FONT> costPerStep[0] = sequence[0] + 1;<a name="line.390"></a> | |
| 394 <FONT color="green">391</FONT> for (int k = 1; k < size; ++k) {<a name="line.391"></a> | |
| 395 <FONT color="green">392</FONT> costPerStep[k] = costPerStep[k-1] + sequence[k];<a name="line.392"></a> | |
| 396 <FONT color="green">393</FONT> }<a name="line.393"></a> | |
| 397 <FONT color="green">394</FONT> <a name="line.394"></a> | |
| 398 <FONT color="green">395</FONT> // initialize the extrapolation tables<a name="line.395"></a> | |
| 399 <FONT color="green">396</FONT> for (int k = 0; k < size; ++k) {<a name="line.396"></a> | |
| 400 <FONT color="green">397</FONT> coeff[k] = (k > 0) ? new double[k] : null;<a name="line.397"></a> | |
| 401 <FONT color="green">398</FONT> for (int l = 0; l < k; ++l) {<a name="line.398"></a> | |
| 402 <FONT color="green">399</FONT> final double ratio = ((double) sequence[k]) / sequence[k-l-1];<a name="line.399"></a> | |
| 403 <FONT color="green">400</FONT> coeff[k][l] = 1.0 / (ratio * ratio - 1.0);<a name="line.400"></a> | |
| 404 <FONT color="green">401</FONT> }<a name="line.401"></a> | |
| 405 <FONT color="green">402</FONT> }<a name="line.402"></a> | |
| 406 <FONT color="green">403</FONT> <a name="line.403"></a> | |
| 407 <FONT color="green">404</FONT> }<a name="line.404"></a> | |
| 408 <FONT color="green">405</FONT> <a name="line.405"></a> | |
| 409 <FONT color="green">406</FONT> /** Set the interpolation order control parameter.<a name="line.406"></a> | |
| 410 <FONT color="green">407</FONT> * The interpolation order for dense output is 2k - mudif + 1. The<a name="line.407"></a> | |
| 411 <FONT color="green">408</FONT> * default value for mudif is 4 and the interpolation error is used<a name="line.408"></a> | |
| 412 <FONT color="green">409</FONT> * in stepsize control by default.<a name="line.409"></a> | |
| 413 <FONT color="green">410</FONT> <a name="line.410"></a> | |
| 414 <FONT color="green">411</FONT> * @param useInterpolationErrorForControl if true, interpolation error is used<a name="line.411"></a> | |
| 415 <FONT color="green">412</FONT> * for stepsize control<a name="line.412"></a> | |
| 416 <FONT color="green">413</FONT> * @param mudifControlParameter interpolation order control parameter (the parameter<a name="line.413"></a> | |
| 417 <FONT color="green">414</FONT> * is reset to default if <= 0 or >= 7)<a name="line.414"></a> | |
| 418 <FONT color="green">415</FONT> */<a name="line.415"></a> | |
| 419 <FONT color="green">416</FONT> public void setInterpolationControl(final boolean useInterpolationErrorForControl,<a name="line.416"></a> | |
| 420 <FONT color="green">417</FONT> final int mudifControlParameter) {<a name="line.417"></a> | |
| 421 <FONT color="green">418</FONT> <a name="line.418"></a> | |
| 422 <FONT color="green">419</FONT> this.useInterpolationError = useInterpolationErrorForControl;<a name="line.419"></a> | |
| 423 <FONT color="green">420</FONT> <a name="line.420"></a> | |
| 424 <FONT color="green">421</FONT> if ((mudifControlParameter <= 0) || (mudifControlParameter >= 7)) {<a name="line.421"></a> | |
| 425 <FONT color="green">422</FONT> this.mudif = 4;<a name="line.422"></a> | |
| 426 <FONT color="green">423</FONT> } else {<a name="line.423"></a> | |
| 427 <FONT color="green">424</FONT> this.mudif = mudifControlParameter;<a name="line.424"></a> | |
| 428 <FONT color="green">425</FONT> }<a name="line.425"></a> | |
| 429 <FONT color="green">426</FONT> <a name="line.426"></a> | |
| 430 <FONT color="green">427</FONT> }<a name="line.427"></a> | |
| 431 <FONT color="green">428</FONT> <a name="line.428"></a> | |
| 432 <FONT color="green">429</FONT> /** Update scaling array.<a name="line.429"></a> | |
| 433 <FONT color="green">430</FONT> * @param y1 first state vector to use for scaling<a name="line.430"></a> | |
| 434 <FONT color="green">431</FONT> * @param y2 second state vector to use for scaling<a name="line.431"></a> | |
| 435 <FONT color="green">432</FONT> * @param scale scaling array to update<a name="line.432"></a> | |
| 436 <FONT color="green">433</FONT> */<a name="line.433"></a> | |
| 437 <FONT color="green">434</FONT> private void rescale(final double[] y1, final double[] y2, final double[] scale) {<a name="line.434"></a> | |
| 438 <FONT color="green">435</FONT> if (vecAbsoluteTolerance == null) {<a name="line.435"></a> | |
| 439 <FONT color="green">436</FONT> for (int i = 0; i < scale.length; ++i) {<a name="line.436"></a> | |
| 440 <FONT color="green">437</FONT> final double yi = Math.max(Math.abs(y1[i]), Math.abs(y2[i]));<a name="line.437"></a> | |
| 441 <FONT color="green">438</FONT> scale[i] = scalAbsoluteTolerance + scalRelativeTolerance * yi;<a name="line.438"></a> | |
| 442 <FONT color="green">439</FONT> }<a name="line.439"></a> | |
| 443 <FONT color="green">440</FONT> } else {<a name="line.440"></a> | |
| 444 <FONT color="green">441</FONT> for (int i = 0; i < scale.length; ++i) {<a name="line.441"></a> | |
| 445 <FONT color="green">442</FONT> final double yi = Math.max(Math.abs(y1[i]), Math.abs(y2[i]));<a name="line.442"></a> | |
| 446 <FONT color="green">443</FONT> scale[i] = vecAbsoluteTolerance[i] + vecRelativeTolerance[i] * yi;<a name="line.443"></a> | |
| 447 <FONT color="green">444</FONT> }<a name="line.444"></a> | |
| 448 <FONT color="green">445</FONT> }<a name="line.445"></a> | |
| 449 <FONT color="green">446</FONT> }<a name="line.446"></a> | |
| 450 <FONT color="green">447</FONT> <a name="line.447"></a> | |
| 451 <FONT color="green">448</FONT> /** Perform integration over one step using substeps of a modified<a name="line.448"></a> | |
| 452 <FONT color="green">449</FONT> * midpoint method.<a name="line.449"></a> | |
| 453 <FONT color="green">450</FONT> * @param t0 initial time<a name="line.450"></a> | |
| 454 <FONT color="green">451</FONT> * @param y0 initial value of the state vector at t0<a name="line.451"></a> | |
| 455 <FONT color="green">452</FONT> * @param step global step<a name="line.452"></a> | |
| 456 <FONT color="green">453</FONT> * @param k iteration number (from 0 to sequence.length - 1)<a name="line.453"></a> | |
| 457 <FONT color="green">454</FONT> * @param scale scaling array<a name="line.454"></a> | |
| 458 <FONT color="green">455</FONT> * @param f placeholder where to put the state vector derivatives at each substep<a name="line.455"></a> | |
| 459 <FONT color="green">456</FONT> * (element 0 already contains initial derivative)<a name="line.456"></a> | |
| 460 <FONT color="green">457</FONT> * @param yMiddle placeholder where to put the state vector at the middle of the step<a name="line.457"></a> | |
| 461 <FONT color="green">458</FONT> * @param yEnd placeholder where to put the state vector at the end<a name="line.458"></a> | |
| 462 <FONT color="green">459</FONT> * @param yTmp placeholder for one state vector<a name="line.459"></a> | |
| 463 <FONT color="green">460</FONT> * @return true if computation was done properly,<a name="line.460"></a> | |
| 464 <FONT color="green">461</FONT> * false if stability check failed before end of computation<a name="line.461"></a> | |
| 465 <FONT color="green">462</FONT> * @throws DerivativeException this exception is propagated to the caller if the<a name="line.462"></a> | |
| 466 <FONT color="green">463</FONT> * underlying user function triggers one<a name="line.463"></a> | |
| 467 <FONT color="green">464</FONT> */<a name="line.464"></a> | |
| 468 <FONT color="green">465</FONT> private boolean tryStep(final double t0, final double[] y0, final double step, final int k,<a name="line.465"></a> | |
| 469 <FONT color="green">466</FONT> final double[] scale, final double[][] f,<a name="line.466"></a> | |
| 470 <FONT color="green">467</FONT> final double[] yMiddle, final double[] yEnd,<a name="line.467"></a> | |
| 471 <FONT color="green">468</FONT> final double[] yTmp)<a name="line.468"></a> | |
| 472 <FONT color="green">469</FONT> throws DerivativeException {<a name="line.469"></a> | |
| 473 <FONT color="green">470</FONT> <a name="line.470"></a> | |
| 474 <FONT color="green">471</FONT> final int n = sequence[k];<a name="line.471"></a> | |
| 475 <FONT color="green">472</FONT> final double subStep = step / n;<a name="line.472"></a> | |
| 476 <FONT color="green">473</FONT> final double subStep2 = 2 * subStep;<a name="line.473"></a> | |
| 477 <FONT color="green">474</FONT> <a name="line.474"></a> | |
| 478 <FONT color="green">475</FONT> // first substep<a name="line.475"></a> | |
| 479 <FONT color="green">476</FONT> double t = t0 + subStep;<a name="line.476"></a> | |
| 480 <FONT color="green">477</FONT> for (int i = 0; i < y0.length; ++i) {<a name="line.477"></a> | |
| 481 <FONT color="green">478</FONT> yTmp[i] = y0[i];<a name="line.478"></a> | |
| 482 <FONT color="green">479</FONT> yEnd[i] = y0[i] + subStep * f[0][i];<a name="line.479"></a> | |
| 483 <FONT color="green">480</FONT> }<a name="line.480"></a> | |
| 484 <FONT color="green">481</FONT> computeDerivatives(t, yEnd, f[1]);<a name="line.481"></a> | |
| 485 <FONT color="green">482</FONT> <a name="line.482"></a> | |
| 486 <FONT color="green">483</FONT> // other substeps<a name="line.483"></a> | |
| 487 <FONT color="green">484</FONT> for (int j = 1; j < n; ++j) {<a name="line.484"></a> | |
| 488 <FONT color="green">485</FONT> <a name="line.485"></a> | |
| 489 <FONT color="green">486</FONT> if (2 * j == n) {<a name="line.486"></a> | |
| 490 <FONT color="green">487</FONT> // save the point at the middle of the step<a name="line.487"></a> | |
| 491 <FONT color="green">488</FONT> System.arraycopy(yEnd, 0, yMiddle, 0, y0.length);<a name="line.488"></a> | |
| 492 <FONT color="green">489</FONT> }<a name="line.489"></a> | |
| 493 <FONT color="green">490</FONT> <a name="line.490"></a> | |
| 494 <FONT color="green">491</FONT> t += subStep;<a name="line.491"></a> | |
| 495 <FONT color="green">492</FONT> for (int i = 0; i < y0.length; ++i) {<a name="line.492"></a> | |
| 496 <FONT color="green">493</FONT> final double middle = yEnd[i];<a name="line.493"></a> | |
| 497 <FONT color="green">494</FONT> yEnd[i] = yTmp[i] + subStep2 * f[j][i];<a name="line.494"></a> | |
| 498 <FONT color="green">495</FONT> yTmp[i] = middle;<a name="line.495"></a> | |
| 499 <FONT color="green">496</FONT> }<a name="line.496"></a> | |
| 500 <FONT color="green">497</FONT> <a name="line.497"></a> | |
| 501 <FONT color="green">498</FONT> computeDerivatives(t, yEnd, f[j+1]);<a name="line.498"></a> | |
| 502 <FONT color="green">499</FONT> <a name="line.499"></a> | |
| 503 <FONT color="green">500</FONT> // stability check<a name="line.500"></a> | |
| 504 <FONT color="green">501</FONT> if (performTest && (j <= maxChecks) && (k < maxIter)) {<a name="line.501"></a> | |
| 505 <FONT color="green">502</FONT> double initialNorm = 0.0;<a name="line.502"></a> | |
| 506 <FONT color="green">503</FONT> for (int l = 0; l < y0.length; ++l) {<a name="line.503"></a> | |
| 507 <FONT color="green">504</FONT> final double ratio = f[0][l] / scale[l];<a name="line.504"></a> | |
| 508 <FONT color="green">505</FONT> initialNorm += ratio * ratio;<a name="line.505"></a> | |
| 509 <FONT color="green">506</FONT> }<a name="line.506"></a> | |
| 510 <FONT color="green">507</FONT> double deltaNorm = 0.0;<a name="line.507"></a> | |
| 511 <FONT color="green">508</FONT> for (int l = 0; l < y0.length; ++l) {<a name="line.508"></a> | |
| 512 <FONT color="green">509</FONT> final double ratio = (f[j+1][l] - f[0][l]) / scale[l];<a name="line.509"></a> | |
| 513 <FONT color="green">510</FONT> deltaNorm += ratio * ratio;<a name="line.510"></a> | |
| 514 <FONT color="green">511</FONT> }<a name="line.511"></a> | |
| 515 <FONT color="green">512</FONT> if (deltaNorm > 4 * Math.max(1.0e-15, initialNorm)) {<a name="line.512"></a> | |
| 516 <FONT color="green">513</FONT> return false;<a name="line.513"></a> | |
| 517 <FONT color="green">514</FONT> }<a name="line.514"></a> | |
| 518 <FONT color="green">515</FONT> }<a name="line.515"></a> | |
| 519 <FONT color="green">516</FONT> <a name="line.516"></a> | |
| 520 <FONT color="green">517</FONT> }<a name="line.517"></a> | |
| 521 <FONT color="green">518</FONT> <a name="line.518"></a> | |
| 522 <FONT color="green">519</FONT> // correction of the last substep (at t0 + step)<a name="line.519"></a> | |
| 523 <FONT color="green">520</FONT> for (int i = 0; i < y0.length; ++i) {<a name="line.520"></a> | |
| 524 <FONT color="green">521</FONT> yEnd[i] = 0.5 * (yTmp[i] + yEnd[i] + subStep * f[n][i]);<a name="line.521"></a> | |
| 525 <FONT color="green">522</FONT> }<a name="line.522"></a> | |
| 526 <FONT color="green">523</FONT> <a name="line.523"></a> | |
| 527 <FONT color="green">524</FONT> return true;<a name="line.524"></a> | |
| 528 <FONT color="green">525</FONT> <a name="line.525"></a> | |
| 529 <FONT color="green">526</FONT> }<a name="line.526"></a> | |
| 530 <FONT color="green">527</FONT> <a name="line.527"></a> | |
| 531 <FONT color="green">528</FONT> /** Extrapolate a vector.<a name="line.528"></a> | |
| 532 <FONT color="green">529</FONT> * @param offset offset to use in the coefficients table<a name="line.529"></a> | |
| 533 <FONT color="green">530</FONT> * @param k index of the last updated point<a name="line.530"></a> | |
| 534 <FONT color="green">531</FONT> * @param diag working diagonal of the Aitken-Neville's<a name="line.531"></a> | |
| 535 <FONT color="green">532</FONT> * triangle, without the last element<a name="line.532"></a> | |
| 536 <FONT color="green">533</FONT> * @param last last element<a name="line.533"></a> | |
| 537 <FONT color="green">534</FONT> */<a name="line.534"></a> | |
| 538 <FONT color="green">535</FONT> private void extrapolate(final int offset, final int k,<a name="line.535"></a> | |
| 539 <FONT color="green">536</FONT> final double[][] diag, final double[] last) {<a name="line.536"></a> | |
| 540 <FONT color="green">537</FONT> <a name="line.537"></a> | |
| 541 <FONT color="green">538</FONT> // update the diagonal<a name="line.538"></a> | |
| 542 <FONT color="green">539</FONT> for (int j = 1; j < k; ++j) {<a name="line.539"></a> | |
| 543 <FONT color="green">540</FONT> for (int i = 0; i < last.length; ++i) {<a name="line.540"></a> | |
| 544 <FONT color="green">541</FONT> // Aitken-Neville's recursive formula<a name="line.541"></a> | |
| 545 <FONT color="green">542</FONT> diag[k-j-1][i] = diag[k-j][i] +<a name="line.542"></a> | |
| 546 <FONT color="green">543</FONT> coeff[k+offset][j-1] * (diag[k-j][i] - diag[k-j-1][i]);<a name="line.543"></a> | |
| 547 <FONT color="green">544</FONT> }<a name="line.544"></a> | |
| 548 <FONT color="green">545</FONT> }<a name="line.545"></a> | |
| 549 <FONT color="green">546</FONT> <a name="line.546"></a> | |
| 550 <FONT color="green">547</FONT> // update the last element<a name="line.547"></a> | |
| 551 <FONT color="green">548</FONT> for (int i = 0; i < last.length; ++i) {<a name="line.548"></a> | |
| 552 <FONT color="green">549</FONT> // Aitken-Neville's recursive formula<a name="line.549"></a> | |
| 553 <FONT color="green">550</FONT> last[i] = diag[0][i] + coeff[k+offset][k-1] * (diag[0][i] - last[i]);<a name="line.550"></a> | |
| 554 <FONT color="green">551</FONT> }<a name="line.551"></a> | |
| 555 <FONT color="green">552</FONT> }<a name="line.552"></a> | |
| 556 <FONT color="green">553</FONT> <a name="line.553"></a> | |
| 557 <FONT color="green">554</FONT> /** {@inheritDoc} */<a name="line.554"></a> | |
| 558 <FONT color="green">555</FONT> @Override<a name="line.555"></a> | |
| 559 <FONT color="green">556</FONT> public double integrate(final FirstOrderDifferentialEquations equations,<a name="line.556"></a> | |
| 560 <FONT color="green">557</FONT> final double t0, final double[] y0, final double t, final double[] y)<a name="line.557"></a> | |
| 561 <FONT color="green">558</FONT> throws DerivativeException, IntegratorException {<a name="line.558"></a> | |
| 562 <FONT color="green">559</FONT> <a name="line.559"></a> | |
| 563 <FONT color="green">560</FONT> sanityChecks(equations, t0, y0, t, y);<a name="line.560"></a> | |
| 564 <FONT color="green">561</FONT> setEquations(equations);<a name="line.561"></a> | |
| 565 <FONT color="green">562</FONT> resetEvaluations();<a name="line.562"></a> | |
| 566 <FONT color="green">563</FONT> final boolean forward = t > t0;<a name="line.563"></a> | |
| 567 <FONT color="green">564</FONT> <a name="line.564"></a> | |
| 568 <FONT color="green">565</FONT> // create some internal working arrays<a name="line.565"></a> | |
| 569 <FONT color="green">566</FONT> final double[] yDot0 = new double[y0.length];<a name="line.566"></a> | |
| 570 <FONT color="green">567</FONT> final double[] y1 = new double[y0.length];<a name="line.567"></a> | |
| 571 <FONT color="green">568</FONT> final double[] yTmp = new double[y0.length];<a name="line.568"></a> | |
| 572 <FONT color="green">569</FONT> final double[] yTmpDot = new double[y0.length];<a name="line.569"></a> | |
| 573 <FONT color="green">570</FONT> <a name="line.570"></a> | |
| 574 <FONT color="green">571</FONT> final double[][] diagonal = new double[sequence.length-1][];<a name="line.571"></a> | |
| 575 <FONT color="green">572</FONT> final double[][] y1Diag = new double[sequence.length-1][];<a name="line.572"></a> | |
| 576 <FONT color="green">573</FONT> for (int k = 0; k < sequence.length-1; ++k) {<a name="line.573"></a> | |
| 577 <FONT color="green">574</FONT> diagonal[k] = new double[y0.length];<a name="line.574"></a> | |
| 578 <FONT color="green">575</FONT> y1Diag[k] = new double[y0.length];<a name="line.575"></a> | |
| 579 <FONT color="green">576</FONT> }<a name="line.576"></a> | |
| 580 <FONT color="green">577</FONT> <a name="line.577"></a> | |
| 581 <FONT color="green">578</FONT> final double[][][] fk = new double[sequence.length][][];<a name="line.578"></a> | |
| 582 <FONT color="green">579</FONT> for (int k = 0; k < sequence.length; ++k) {<a name="line.579"></a> | |
| 583 <FONT color="green">580</FONT> <a name="line.580"></a> | |
| 584 <FONT color="green">581</FONT> fk[k] = new double[sequence[k] + 1][];<a name="line.581"></a> | |
| 585 <FONT color="green">582</FONT> <a name="line.582"></a> | |
| 586 <FONT color="green">583</FONT> // all substeps start at the same point, so share the first array<a name="line.583"></a> | |
| 587 <FONT color="green">584</FONT> fk[k][0] = yDot0;<a name="line.584"></a> | |
| 588 <FONT color="green">585</FONT> <a name="line.585"></a> | |
| 589 <FONT color="green">586</FONT> for (int l = 0; l < sequence[k]; ++l) {<a name="line.586"></a> | |
| 590 <FONT color="green">587</FONT> fk[k][l+1] = new double[y0.length];<a name="line.587"></a> | |
| 591 <FONT color="green">588</FONT> }<a name="line.588"></a> | |
| 592 <FONT color="green">589</FONT> <a name="line.589"></a> | |
| 593 <FONT color="green">590</FONT> }<a name="line.590"></a> | |
| 594 <FONT color="green">591</FONT> <a name="line.591"></a> | |
| 595 <FONT color="green">592</FONT> if (y != y0) {<a name="line.592"></a> | |
| 596 <FONT color="green">593</FONT> System.arraycopy(y0, 0, y, 0, y0.length);<a name="line.593"></a> | |
| 597 <FONT color="green">594</FONT> }<a name="line.594"></a> | |
| 598 <FONT color="green">595</FONT> <a name="line.595"></a> | |
| 599 <FONT color="green">596</FONT> double[] yDot1 = null;<a name="line.596"></a> | |
| 600 <FONT color="green">597</FONT> double[][] yMidDots = null;<a name="line.597"></a> | |
| 601 <FONT color="green">598</FONT> if (denseOutput) {<a name="line.598"></a> | |
| 602 <FONT color="green">599</FONT> yDot1 = new double[y0.length];<a name="line.599"></a> | |
| 603 <FONT color="green">600</FONT> yMidDots = new double[1 + 2 * sequence.length][];<a name="line.600"></a> | |
| 604 <FONT color="green">601</FONT> for (int j = 0; j < yMidDots.length; ++j) {<a name="line.601"></a> | |
| 605 <FONT color="green">602</FONT> yMidDots[j] = new double[y0.length];<a name="line.602"></a> | |
| 606 <FONT color="green">603</FONT> }<a name="line.603"></a> | |
| 607 <FONT color="green">604</FONT> } else {<a name="line.604"></a> | |
| 608 <FONT color="green">605</FONT> yMidDots = new double[1][];<a name="line.605"></a> | |
| 609 <FONT color="green">606</FONT> yMidDots[0] = new double[y0.length];<a name="line.606"></a> | |
| 610 <FONT color="green">607</FONT> }<a name="line.607"></a> | |
| 611 <FONT color="green">608</FONT> <a name="line.608"></a> | |
| 612 <FONT color="green">609</FONT> // initial scaling<a name="line.609"></a> | |
| 613 <FONT color="green">610</FONT> final double[] scale = new double[y0.length];<a name="line.610"></a> | |
| 614 <FONT color="green">611</FONT> rescale(y, y, scale);<a name="line.611"></a> | |
| 615 <FONT color="green">612</FONT> <a name="line.612"></a> | |
| 616 <FONT color="green">613</FONT> // initial order selection<a name="line.613"></a> | |
| 617 <FONT color="green">614</FONT> final double tol =<a name="line.614"></a> | |
| 618 <FONT color="green">615</FONT> (vecRelativeTolerance == null) ? scalRelativeTolerance : vecRelativeTolerance[0];<a name="line.615"></a> | |
| 619 <FONT color="green">616</FONT> final double log10R = Math.log(Math.max(1.0e-10, tol)) / Math.log(10.0);<a name="line.616"></a> | |
| 620 <FONT color="green">617</FONT> int targetIter = Math.max(1,<a name="line.617"></a> | |
| 621 <FONT color="green">618</FONT> Math.min(sequence.length - 2,<a name="line.618"></a> | |
| 622 <FONT color="green">619</FONT> (int) Math.floor(0.5 - 0.6 * log10R)));<a name="line.619"></a> | |
| 623 <FONT color="green">620</FONT> // set up an interpolator sharing the integrator arrays<a name="line.620"></a> | |
| 624 <FONT color="green">621</FONT> AbstractStepInterpolator interpolator = null;<a name="line.621"></a> | |
| 625 <FONT color="green">622</FONT> if (denseOutput || (! eventsHandlersManager.isEmpty())) {<a name="line.622"></a> | |
| 626 <FONT color="green">623</FONT> interpolator = new GraggBulirschStoerStepInterpolator(y, yDot0,<a name="line.623"></a> | |
| 627 <FONT color="green">624</FONT> y1, yDot1,<a name="line.624"></a> | |
| 628 <FONT color="green">625</FONT> yMidDots, forward);<a name="line.625"></a> | |
| 629 <FONT color="green">626</FONT> } else {<a name="line.626"></a> | |
| 630 <FONT color="green">627</FONT> interpolator = new DummyStepInterpolator(y, yDot1, forward);<a name="line.627"></a> | |
| 631 <FONT color="green">628</FONT> }<a name="line.628"></a> | |
| 632 <FONT color="green">629</FONT> interpolator.storeTime(t0);<a name="line.629"></a> | |
| 633 <FONT color="green">630</FONT> <a name="line.630"></a> | |
| 634 <FONT color="green">631</FONT> stepStart = t0;<a name="line.631"></a> | |
| 635 <FONT color="green">632</FONT> double hNew = 0;<a name="line.632"></a> | |
| 636 <FONT color="green">633</FONT> double maxError = Double.MAX_VALUE;<a name="line.633"></a> | |
| 637 <FONT color="green">634</FONT> boolean previousRejected = false;<a name="line.634"></a> | |
| 638 <FONT color="green">635</FONT> boolean firstTime = true;<a name="line.635"></a> | |
| 639 <FONT color="green">636</FONT> boolean newStep = true;<a name="line.636"></a> | |
| 640 <FONT color="green">637</FONT> boolean lastStep = false;<a name="line.637"></a> | |
| 641 <FONT color="green">638</FONT> boolean firstStepAlreadyComputed = false;<a name="line.638"></a> | |
| 642 <FONT color="green">639</FONT> for (StepHandler handler : stepHandlers) {<a name="line.639"></a> | |
| 643 <FONT color="green">640</FONT> handler.reset();<a name="line.640"></a> | |
| 644 <FONT color="green">641</FONT> }<a name="line.641"></a> | |
| 645 <FONT color="green">642</FONT> costPerTimeUnit[0] = 0;<a name="line.642"></a> | |
| 646 <FONT color="green">643</FONT> while (! lastStep) {<a name="line.643"></a> | |
| 647 <FONT color="green">644</FONT> <a name="line.644"></a> | |
| 648 <FONT color="green">645</FONT> double error;<a name="line.645"></a> | |
| 649 <FONT color="green">646</FONT> boolean reject = false;<a name="line.646"></a> | |
| 650 <FONT color="green">647</FONT> <a name="line.647"></a> | |
| 651 <FONT color="green">648</FONT> if (newStep) {<a name="line.648"></a> | |
| 652 <FONT color="green">649</FONT> <a name="line.649"></a> | |
| 653 <FONT color="green">650</FONT> interpolator.shift();<a name="line.650"></a> | |
| 654 <FONT color="green">651</FONT> <a name="line.651"></a> | |
| 655 <FONT color="green">652</FONT> // first evaluation, at the beginning of the step<a name="line.652"></a> | |
| 656 <FONT color="green">653</FONT> if (! firstStepAlreadyComputed) {<a name="line.653"></a> | |
| 657 <FONT color="green">654</FONT> computeDerivatives(stepStart, y, yDot0);<a name="line.654"></a> | |
| 658 <FONT color="green">655</FONT> }<a name="line.655"></a> | |
| 659 <FONT color="green">656</FONT> <a name="line.656"></a> | |
| 660 <FONT color="green">657</FONT> if (firstTime) {<a name="line.657"></a> | |
| 661 <FONT color="green">658</FONT> <a name="line.658"></a> | |
| 662 <FONT color="green">659</FONT> hNew = initializeStep(equations, forward,<a name="line.659"></a> | |
| 663 <FONT color="green">660</FONT> 2 * targetIter + 1, scale,<a name="line.660"></a> | |
| 664 <FONT color="green">661</FONT> stepStart, y, yDot0, yTmp, yTmpDot);<a name="line.661"></a> | |
| 665 <FONT color="green">662</FONT> <a name="line.662"></a> | |
| 666 <FONT color="green">663</FONT> if (! forward) {<a name="line.663"></a> | |
| 667 <FONT color="green">664</FONT> hNew = -hNew;<a name="line.664"></a> | |
| 668 <FONT color="green">665</FONT> }<a name="line.665"></a> | |
| 669 <FONT color="green">666</FONT> <a name="line.666"></a> | |
| 670 <FONT color="green">667</FONT> }<a name="line.667"></a> | |
| 671 <FONT color="green">668</FONT> <a name="line.668"></a> | |
| 672 <FONT color="green">669</FONT> newStep = false;<a name="line.669"></a> | |
| 673 <FONT color="green">670</FONT> <a name="line.670"></a> | |
| 674 <FONT color="green">671</FONT> }<a name="line.671"></a> | |
| 675 <FONT color="green">672</FONT> <a name="line.672"></a> | |
| 676 <FONT color="green">673</FONT> stepSize = hNew;<a name="line.673"></a> | |
| 677 <FONT color="green">674</FONT> <a name="line.674"></a> | |
| 678 <FONT color="green">675</FONT> // step adjustment near bounds<a name="line.675"></a> | |
| 679 <FONT color="green">676</FONT> if ((forward && (stepStart + stepSize > t)) ||<a name="line.676"></a> | |
| 680 <FONT color="green">677</FONT> ((! forward) && (stepStart + stepSize < t))) {<a name="line.677"></a> | |
| 681 <FONT color="green">678</FONT> stepSize = t - stepStart;<a name="line.678"></a> | |
| 682 <FONT color="green">679</FONT> }<a name="line.679"></a> | |
| 683 <FONT color="green">680</FONT> final double nextT = stepStart + stepSize;<a name="line.680"></a> | |
| 684 <FONT color="green">681</FONT> lastStep = forward ? (nextT >= t) : (nextT <= t);<a name="line.681"></a> | |
| 685 <FONT color="green">682</FONT> <a name="line.682"></a> | |
| 686 <FONT color="green">683</FONT> // iterate over several substep sizes<a name="line.683"></a> | |
| 687 <FONT color="green">684</FONT> int k = -1;<a name="line.684"></a> | |
| 688 <FONT color="green">685</FONT> for (boolean loop = true; loop; ) {<a name="line.685"></a> | |
| 689 <FONT color="green">686</FONT> <a name="line.686"></a> | |
| 690 <FONT color="green">687</FONT> ++k;<a name="line.687"></a> | |
| 691 <FONT color="green">688</FONT> <a name="line.688"></a> | |
| 692 <FONT color="green">689</FONT> // modified midpoint integration with the current substep<a name="line.689"></a> | |
| 693 <FONT color="green">690</FONT> if ( ! tryStep(stepStart, y, stepSize, k, scale, fk[k],<a name="line.690"></a> | |
| 694 <FONT color="green">691</FONT> (k == 0) ? yMidDots[0] : diagonal[k-1],<a name="line.691"></a> | |
| 695 <FONT color="green">692</FONT> (k == 0) ? y1 : y1Diag[k-1],<a name="line.692"></a> | |
| 696 <FONT color="green">693</FONT> yTmp)) {<a name="line.693"></a> | |
| 697 <FONT color="green">694</FONT> <a name="line.694"></a> | |
| 698 <FONT color="green">695</FONT> // the stability check failed, we reduce the global step<a name="line.695"></a> | |
| 699 <FONT color="green">696</FONT> hNew = Math.abs(filterStep(stepSize * stabilityReduction, forward, false));<a name="line.696"></a> | |
| 700 <FONT color="green">697</FONT> reject = true;<a name="line.697"></a> | |
| 701 <FONT color="green">698</FONT> loop = false;<a name="line.698"></a> | |
| 702 <FONT color="green">699</FONT> <a name="line.699"></a> | |
| 703 <FONT color="green">700</FONT> } else {<a name="line.700"></a> | |
| 704 <FONT color="green">701</FONT> <a name="line.701"></a> | |
| 705 <FONT color="green">702</FONT> // the substep was computed successfully<a name="line.702"></a> | |
| 706 <FONT color="green">703</FONT> if (k > 0) {<a name="line.703"></a> | |
| 707 <FONT color="green">704</FONT> <a name="line.704"></a> | |
| 708 <FONT color="green">705</FONT> // extrapolate the state at the end of the step<a name="line.705"></a> | |
| 709 <FONT color="green">706</FONT> // using last iteration data<a name="line.706"></a> | |
| 710 <FONT color="green">707</FONT> extrapolate(0, k, y1Diag, y1);<a name="line.707"></a> | |
| 711 <FONT color="green">708</FONT> rescale(y, y1, scale);<a name="line.708"></a> | |
| 712 <FONT color="green">709</FONT> <a name="line.709"></a> | |
| 713 <FONT color="green">710</FONT> // estimate the error at the end of the step.<a name="line.710"></a> | |
| 714 <FONT color="green">711</FONT> error = 0;<a name="line.711"></a> | |
| 715 <FONT color="green">712</FONT> for (int j = 0; j < y0.length; ++j) {<a name="line.712"></a> | |
| 716 <FONT color="green">713</FONT> final double e = Math.abs(y1[j] - y1Diag[0][j]) / scale[j];<a name="line.713"></a> | |
| 717 <FONT color="green">714</FONT> error += e * e;<a name="line.714"></a> | |
| 718 <FONT color="green">715</FONT> }<a name="line.715"></a> | |
| 719 <FONT color="green">716</FONT> error = Math.sqrt(error / y0.length);<a name="line.716"></a> | |
| 720 <FONT color="green">717</FONT> <a name="line.717"></a> | |
| 721 <FONT color="green">718</FONT> if ((error > 1.0e15) || ((k > 1) && (error > maxError))) {<a name="line.718"></a> | |
| 722 <FONT color="green">719</FONT> // error is too big, we reduce the global step<a name="line.719"></a> | |
| 723 <FONT color="green">720</FONT> hNew = Math.abs(filterStep(stepSize * stabilityReduction, forward, false));<a name="line.720"></a> | |
| 724 <FONT color="green">721</FONT> reject = true;<a name="line.721"></a> | |
| 725 <FONT color="green">722</FONT> loop = false;<a name="line.722"></a> | |
| 726 <FONT color="green">723</FONT> } else {<a name="line.723"></a> | |
| 727 <FONT color="green">724</FONT> <a name="line.724"></a> | |
| 728 <FONT color="green">725</FONT> maxError = Math.max(4 * error, 1.0);<a name="line.725"></a> | |
| 729 <FONT color="green">726</FONT> <a name="line.726"></a> | |
| 730 <FONT color="green">727</FONT> // compute optimal stepsize for this order<a name="line.727"></a> | |
| 731 <FONT color="green">728</FONT> final double exp = 1.0 / (2 * k + 1);<a name="line.728"></a> | |
| 732 <FONT color="green">729</FONT> double fac = stepControl2 / Math.pow(error / stepControl1, exp);<a name="line.729"></a> | |
| 733 <FONT color="green">730</FONT> final double pow = Math.pow(stepControl3, exp);<a name="line.730"></a> | |
| 734 <FONT color="green">731</FONT> fac = Math.max(pow / stepControl4, Math.min(1 / pow, fac));<a name="line.731"></a> | |
| 735 <FONT color="green">732</FONT> optimalStep[k] = Math.abs(filterStep(stepSize * fac, forward, true));<a name="line.732"></a> | |
| 736 <FONT color="green">733</FONT> costPerTimeUnit[k] = costPerStep[k] / optimalStep[k];<a name="line.733"></a> | |
| 737 <FONT color="green">734</FONT> <a name="line.734"></a> | |
| 738 <FONT color="green">735</FONT> // check convergence<a name="line.735"></a> | |
| 739 <FONT color="green">736</FONT> switch (k - targetIter) {<a name="line.736"></a> | |
| 740 <FONT color="green">737</FONT> <a name="line.737"></a> | |
| 741 <FONT color="green">738</FONT> case -1 :<a name="line.738"></a> | |
| 742 <FONT color="green">739</FONT> if ((targetIter > 1) && ! previousRejected) {<a name="line.739"></a> | |
| 743 <FONT color="green">740</FONT> <a name="line.740"></a> | |
| 744 <FONT color="green">741</FONT> // check if we can stop iterations now<a name="line.741"></a> | |
| 745 <FONT color="green">742</FONT> if (error <= 1.0) {<a name="line.742"></a> | |
| 746 <FONT color="green">743</FONT> // convergence have been reached just before targetIter<a name="line.743"></a> | |
| 747 <FONT color="green">744</FONT> loop = false;<a name="line.744"></a> | |
| 748 <FONT color="green">745</FONT> } else {<a name="line.745"></a> | |
| 749 <FONT color="green">746</FONT> // estimate if there is a chance convergence will<a name="line.746"></a> | |
| 750 <FONT color="green">747</FONT> // be reached on next iteration, using the<a name="line.747"></a> | |
| 751 <FONT color="green">748</FONT> // asymptotic evolution of error<a name="line.748"></a> | |
| 752 <FONT color="green">749</FONT> final double ratio = ((double) sequence [targetIter] * sequence[targetIter + 1]) /<a name="line.749"></a> | |
| 753 <FONT color="green">750</FONT> (sequence[0] * sequence[0]);<a name="line.750"></a> | |
| 754 <FONT color="green">751</FONT> if (error > ratio * ratio) {<a name="line.751"></a> | |
| 755 <FONT color="green">752</FONT> // we don't expect to converge on next iteration<a name="line.752"></a> | |
| 756 <FONT color="green">753</FONT> // we reject the step immediately and reduce order<a name="line.753"></a> | |
| 757 <FONT color="green">754</FONT> reject = true;<a name="line.754"></a> | |
| 758 <FONT color="green">755</FONT> loop = false;<a name="line.755"></a> | |
| 759 <FONT color="green">756</FONT> targetIter = k;<a name="line.756"></a> | |
| 760 <FONT color="green">757</FONT> if ((targetIter > 1) &&<a name="line.757"></a> | |
| 761 <FONT color="green">758</FONT> (costPerTimeUnit[targetIter-1] <<a name="line.758"></a> | |
| 762 <FONT color="green">759</FONT> orderControl1 * costPerTimeUnit[targetIter])) {<a name="line.759"></a> | |
| 763 <FONT color="green">760</FONT> --targetIter;<a name="line.760"></a> | |
| 764 <FONT color="green">761</FONT> }<a name="line.761"></a> | |
| 765 <FONT color="green">762</FONT> hNew = optimalStep[targetIter];<a name="line.762"></a> | |
| 766 <FONT color="green">763</FONT> }<a name="line.763"></a> | |
| 767 <FONT color="green">764</FONT> }<a name="line.764"></a> | |
| 768 <FONT color="green">765</FONT> }<a name="line.765"></a> | |
| 769 <FONT color="green">766</FONT> break;<a name="line.766"></a> | |
| 770 <FONT color="green">767</FONT> <a name="line.767"></a> | |
| 771 <FONT color="green">768</FONT> case 0:<a name="line.768"></a> | |
| 772 <FONT color="green">769</FONT> if (error <= 1.0) {<a name="line.769"></a> | |
| 773 <FONT color="green">770</FONT> // convergence has been reached exactly at targetIter<a name="line.770"></a> | |
| 774 <FONT color="green">771</FONT> loop = false;<a name="line.771"></a> | |
| 775 <FONT color="green">772</FONT> } else {<a name="line.772"></a> | |
| 776 <FONT color="green">773</FONT> // estimate if there is a chance convergence will<a name="line.773"></a> | |
| 777 <FONT color="green">774</FONT> // be reached on next iteration, using the<a name="line.774"></a> | |
| 778 <FONT color="green">775</FONT> // asymptotic evolution of error<a name="line.775"></a> | |
| 779 <FONT color="green">776</FONT> final double ratio = ((double) sequence[k+1]) / sequence[0];<a name="line.776"></a> | |
| 780 <FONT color="green">777</FONT> if (error > ratio * ratio) {<a name="line.777"></a> | |
| 781 <FONT color="green">778</FONT> // we don't expect to converge on next iteration<a name="line.778"></a> | |
| 782 <FONT color="green">779</FONT> // we reject the step immediately<a name="line.779"></a> | |
| 783 <FONT color="green">780</FONT> reject = true;<a name="line.780"></a> | |
| 784 <FONT color="green">781</FONT> loop = false;<a name="line.781"></a> | |
| 785 <FONT color="green">782</FONT> if ((targetIter > 1) &&<a name="line.782"></a> | |
| 786 <FONT color="green">783</FONT> (costPerTimeUnit[targetIter-1] <<a name="line.783"></a> | |
| 787 <FONT color="green">784</FONT> orderControl1 * costPerTimeUnit[targetIter])) {<a name="line.784"></a> | |
| 788 <FONT color="green">785</FONT> --targetIter;<a name="line.785"></a> | |
| 789 <FONT color="green">786</FONT> }<a name="line.786"></a> | |
| 790 <FONT color="green">787</FONT> hNew = optimalStep[targetIter];<a name="line.787"></a> | |
| 791 <FONT color="green">788</FONT> }<a name="line.788"></a> | |
| 792 <FONT color="green">789</FONT> }<a name="line.789"></a> | |
| 793 <FONT color="green">790</FONT> break;<a name="line.790"></a> | |
| 794 <FONT color="green">791</FONT> <a name="line.791"></a> | |
| 795 <FONT color="green">792</FONT> case 1 :<a name="line.792"></a> | |
| 796 <FONT color="green">793</FONT> if (error > 1.0) {<a name="line.793"></a> | |
| 797 <FONT color="green">794</FONT> reject = true;<a name="line.794"></a> | |
| 798 <FONT color="green">795</FONT> if ((targetIter > 1) &&<a name="line.795"></a> | |
| 799 <FONT color="green">796</FONT> (costPerTimeUnit[targetIter-1] <<a name="line.796"></a> | |
| 800 <FONT color="green">797</FONT> orderControl1 * costPerTimeUnit[targetIter])) {<a name="line.797"></a> | |
| 801 <FONT color="green">798</FONT> --targetIter;<a name="line.798"></a> | |
| 802 <FONT color="green">799</FONT> }<a name="line.799"></a> | |
| 803 <FONT color="green">800</FONT> hNew = optimalStep[targetIter];<a name="line.800"></a> | |
| 804 <FONT color="green">801</FONT> }<a name="line.801"></a> | |
| 805 <FONT color="green">802</FONT> loop = false;<a name="line.802"></a> | |
| 806 <FONT color="green">803</FONT> break;<a name="line.803"></a> | |
| 807 <FONT color="green">804</FONT> <a name="line.804"></a> | |
| 808 <FONT color="green">805</FONT> default :<a name="line.805"></a> | |
| 809 <FONT color="green">806</FONT> if ((firstTime || lastStep) && (error <= 1.0)) {<a name="line.806"></a> | |
| 810 <FONT color="green">807</FONT> loop = false;<a name="line.807"></a> | |
| 811 <FONT color="green">808</FONT> }<a name="line.808"></a> | |
| 812 <FONT color="green">809</FONT> break;<a name="line.809"></a> | |
| 813 <FONT color="green">810</FONT> <a name="line.810"></a> | |
| 814 <FONT color="green">811</FONT> }<a name="line.811"></a> | |
| 815 <FONT color="green">812</FONT> <a name="line.812"></a> | |
| 816 <FONT color="green">813</FONT> }<a name="line.813"></a> | |
| 817 <FONT color="green">814</FONT> }<a name="line.814"></a> | |
| 818 <FONT color="green">815</FONT> }<a name="line.815"></a> | |
| 819 <FONT color="green">816</FONT> }<a name="line.816"></a> | |
| 820 <FONT color="green">817</FONT> <a name="line.817"></a> | |
| 821 <FONT color="green">818</FONT> // dense output handling<a name="line.818"></a> | |
| 822 <FONT color="green">819</FONT> double hInt = getMaxStep();<a name="line.819"></a> | |
| 823 <FONT color="green">820</FONT> if (denseOutput && ! reject) {<a name="line.820"></a> | |
| 824 <FONT color="green">821</FONT> <a name="line.821"></a> | |
| 825 <FONT color="green">822</FONT> // extrapolate state at middle point of the step<a name="line.822"></a> | |
| 826 <FONT color="green">823</FONT> for (int j = 1; j <= k; ++j) {<a name="line.823"></a> | |
| 827 <FONT color="green">824</FONT> extrapolate(0, j, diagonal, yMidDots[0]);<a name="line.824"></a> | |
| 828 <FONT color="green">825</FONT> }<a name="line.825"></a> | |
| 829 <FONT color="green">826</FONT> <a name="line.826"></a> | |
| 830 <FONT color="green">827</FONT> // derivative at end of step<a name="line.827"></a> | |
| 831 <FONT color="green">828</FONT> computeDerivatives(stepStart + stepSize, y1, yDot1);<a name="line.828"></a> | |
| 832 <FONT color="green">829</FONT> <a name="line.829"></a> | |
| 833 <FONT color="green">830</FONT> final int mu = 2 * k - mudif + 3;<a name="line.830"></a> | |
| 834 <FONT color="green">831</FONT> <a name="line.831"></a> | |
| 835 <FONT color="green">832</FONT> for (int l = 0; l < mu; ++l) {<a name="line.832"></a> | |
| 836 <FONT color="green">833</FONT> <a name="line.833"></a> | |
| 837 <FONT color="green">834</FONT> // derivative at middle point of the step<a name="line.834"></a> | |
| 838 <FONT color="green">835</FONT> final int l2 = l / 2;<a name="line.835"></a> | |
| 839 <FONT color="green">836</FONT> double factor = Math.pow(0.5 * sequence[l2], l);<a name="line.836"></a> | |
| 840 <FONT color="green">837</FONT> int middleIndex = fk[l2].length / 2;<a name="line.837"></a> | |
| 841 <FONT color="green">838</FONT> for (int i = 0; i < y0.length; ++i) {<a name="line.838"></a> | |
| 842 <FONT color="green">839</FONT> yMidDots[l+1][i] = factor * fk[l2][middleIndex + l][i];<a name="line.839"></a> | |
| 843 <FONT color="green">840</FONT> }<a name="line.840"></a> | |
| 844 <FONT color="green">841</FONT> for (int j = 1; j <= k - l2; ++j) {<a name="line.841"></a> | |
| 845 <FONT color="green">842</FONT> factor = Math.pow(0.5 * sequence[j + l2], l);<a name="line.842"></a> | |
| 846 <FONT color="green">843</FONT> middleIndex = fk[l2+j].length / 2;<a name="line.843"></a> | |
| 847 <FONT color="green">844</FONT> for (int i = 0; i < y0.length; ++i) {<a name="line.844"></a> | |
| 848 <FONT color="green">845</FONT> diagonal[j-1][i] = factor * fk[l2+j][middleIndex+l][i];<a name="line.845"></a> | |
| 849 <FONT color="green">846</FONT> }<a name="line.846"></a> | |
| 850 <FONT color="green">847</FONT> extrapolate(l2, j, diagonal, yMidDots[l+1]);<a name="line.847"></a> | |
| 851 <FONT color="green">848</FONT> }<a name="line.848"></a> | |
| 852 <FONT color="green">849</FONT> for (int i = 0; i < y0.length; ++i) {<a name="line.849"></a> | |
| 853 <FONT color="green">850</FONT> yMidDots[l+1][i] *= stepSize;<a name="line.850"></a> | |
| 854 <FONT color="green">851</FONT> }<a name="line.851"></a> | |
| 855 <FONT color="green">852</FONT> <a name="line.852"></a> | |
| 856 <FONT color="green">853</FONT> // compute centered differences to evaluate next derivatives<a name="line.853"></a> | |
| 857 <FONT color="green">854</FONT> for (int j = (l + 1) / 2; j <= k; ++j) {<a name="line.854"></a> | |
| 858 <FONT color="green">855</FONT> for (int m = fk[j].length - 1; m >= 2 * (l + 1); --m) {<a name="line.855"></a> | |
| 859 <FONT color="green">856</FONT> for (int i = 0; i < y0.length; ++i) {<a name="line.856"></a> | |
| 860 <FONT color="green">857</FONT> fk[j][m][i] -= fk[j][m-2][i];<a name="line.857"></a> | |
| 861 <FONT color="green">858</FONT> }<a name="line.858"></a> | |
| 862 <FONT color="green">859</FONT> }<a name="line.859"></a> | |
| 863 <FONT color="green">860</FONT> }<a name="line.860"></a> | |
| 864 <FONT color="green">861</FONT> <a name="line.861"></a> | |
| 865 <FONT color="green">862</FONT> }<a name="line.862"></a> | |
| 866 <FONT color="green">863</FONT> <a name="line.863"></a> | |
| 867 <FONT color="green">864</FONT> if (mu >= 0) {<a name="line.864"></a> | |
| 868 <FONT color="green">865</FONT> <a name="line.865"></a> | |
| 869 <FONT color="green">866</FONT> // estimate the dense output coefficients<a name="line.866"></a> | |
| 870 <FONT color="green">867</FONT> final GraggBulirschStoerStepInterpolator gbsInterpolator<a name="line.867"></a> | |
| 871 <FONT color="green">868</FONT> = (GraggBulirschStoerStepInterpolator) interpolator;<a name="line.868"></a> | |
| 872 <FONT color="green">869</FONT> gbsInterpolator.computeCoefficients(mu, stepSize);<a name="line.869"></a> | |
| 873 <FONT color="green">870</FONT> <a name="line.870"></a> | |
| 874 <FONT color="green">871</FONT> if (useInterpolationError) {<a name="line.871"></a> | |
| 875 <FONT color="green">872</FONT> // use the interpolation error to limit stepsize<a name="line.872"></a> | |
| 876 <FONT color="green">873</FONT> final double interpError = gbsInterpolator.estimateError(scale);<a name="line.873"></a> | |
| 877 <FONT color="green">874</FONT> hInt = Math.abs(stepSize / Math.max(Math.pow(interpError, 1.0 / (mu+4)),<a name="line.874"></a> | |
| 878 <FONT color="green">875</FONT> 0.01));<a name="line.875"></a> | |
| 879 <FONT color="green">876</FONT> if (interpError > 10.0) {<a name="line.876"></a> | |
| 880 <FONT color="green">877</FONT> hNew = hInt;<a name="line.877"></a> | |
| 881 <FONT color="green">878</FONT> reject = true;<a name="line.878"></a> | |
| 882 <FONT color="green">879</FONT> }<a name="line.879"></a> | |
| 883 <FONT color="green">880</FONT> }<a name="line.880"></a> | |
| 884 <FONT color="green">881</FONT> <a name="line.881"></a> | |
| 885 <FONT color="green">882</FONT> // Discrete events handling<a name="line.882"></a> | |
| 886 <FONT color="green">883</FONT> if (!reject) {<a name="line.883"></a> | |
| 887 <FONT color="green">884</FONT> interpolator.storeTime(stepStart + stepSize);<a name="line.884"></a> | |
| 888 <FONT color="green">885</FONT> if (eventsHandlersManager.evaluateStep(interpolator)) {<a name="line.885"></a> | |
| 889 <FONT color="green">886</FONT> final double dt = eventsHandlersManager.getEventTime() - stepStart;<a name="line.886"></a> | |
| 890 <FONT color="green">887</FONT> if (Math.abs(dt) > Math.ulp(stepStart)) {<a name="line.887"></a> | |
| 891 <FONT color="green">888</FONT> // reject the step to match exactly the next switch time<a name="line.888"></a> | |
| 892 <FONT color="green">889</FONT> hNew = Math.abs(dt);<a name="line.889"></a> | |
| 893 <FONT color="green">890</FONT> reject = true;<a name="line.890"></a> | |
| 894 <FONT color="green">891</FONT> }<a name="line.891"></a> | |
| 895 <FONT color="green">892</FONT> }<a name="line.892"></a> | |
| 896 <FONT color="green">893</FONT> }<a name="line.893"></a> | |
| 897 <FONT color="green">894</FONT> <a name="line.894"></a> | |
| 898 <FONT color="green">895</FONT> }<a name="line.895"></a> | |
| 899 <FONT color="green">896</FONT> <a name="line.896"></a> | |
| 900 <FONT color="green">897</FONT> if (!reject) {<a name="line.897"></a> | |
| 901 <FONT color="green">898</FONT> // we will reuse the slope for the beginning of next step<a name="line.898"></a> | |
| 902 <FONT color="green">899</FONT> firstStepAlreadyComputed = true;<a name="line.899"></a> | |
| 903 <FONT color="green">900</FONT> System.arraycopy(yDot1, 0, yDot0, 0, y0.length);<a name="line.900"></a> | |
| 904 <FONT color="green">901</FONT> }<a name="line.901"></a> | |
| 905 <FONT color="green">902</FONT> <a name="line.902"></a> | |
| 906 <FONT color="green">903</FONT> }<a name="line.903"></a> | |
| 907 <FONT color="green">904</FONT> <a name="line.904"></a> | |
| 908 <FONT color="green">905</FONT> if (! reject) {<a name="line.905"></a> | |
| 909 <FONT color="green">906</FONT> <a name="line.906"></a> | |
| 910 <FONT color="green">907</FONT> // store end of step state<a name="line.907"></a> | |
| 911 <FONT color="green">908</FONT> final double nextStep = stepStart + stepSize;<a name="line.908"></a> | |
| 912 <FONT color="green">909</FONT> System.arraycopy(y1, 0, y, 0, y0.length);<a name="line.909"></a> | |
| 913 <FONT color="green">910</FONT> <a name="line.910"></a> | |
| 914 <FONT color="green">911</FONT> eventsHandlersManager.stepAccepted(nextStep, y);<a name="line.911"></a> | |
| 915 <FONT color="green">912</FONT> if (eventsHandlersManager.stop()) {<a name="line.912"></a> | |
| 916 <FONT color="green">913</FONT> lastStep = true;<a name="line.913"></a> | |
| 917 <FONT color="green">914</FONT> }<a name="line.914"></a> | |
| 918 <FONT color="green">915</FONT> <a name="line.915"></a> | |
| 919 <FONT color="green">916</FONT> // provide the step data to the step handler<a name="line.916"></a> | |
| 920 <FONT color="green">917</FONT> interpolator.storeTime(nextStep);<a name="line.917"></a> | |
| 921 <FONT color="green">918</FONT> for (StepHandler handler : stepHandlers) {<a name="line.918"></a> | |
| 922 <FONT color="green">919</FONT> handler.handleStep(interpolator, lastStep);<a name="line.919"></a> | |
| 923 <FONT color="green">920</FONT> }<a name="line.920"></a> | |
| 924 <FONT color="green">921</FONT> stepStart = nextStep;<a name="line.921"></a> | |
| 925 <FONT color="green">922</FONT> <a name="line.922"></a> | |
| 926 <FONT color="green">923</FONT> if (eventsHandlersManager.reset(stepStart, y) && ! lastStep) {<a name="line.923"></a> | |
| 927 <FONT color="green">924</FONT> // some switching function has triggered changes that<a name="line.924"></a> | |
| 928 <FONT color="green">925</FONT> // invalidate the derivatives, we need to recompute them<a name="line.925"></a> | |
| 929 <FONT color="green">926</FONT> firstStepAlreadyComputed = false;<a name="line.926"></a> | |
| 930 <FONT color="green">927</FONT> }<a name="line.927"></a> | |
| 931 <FONT color="green">928</FONT> <a name="line.928"></a> | |
| 932 <FONT color="green">929</FONT> int optimalIter;<a name="line.929"></a> | |
| 933 <FONT color="green">930</FONT> if (k == 1) {<a name="line.930"></a> | |
| 934 <FONT color="green">931</FONT> optimalIter = 2;<a name="line.931"></a> | |
| 935 <FONT color="green">932</FONT> if (previousRejected) {<a name="line.932"></a> | |
| 936 <FONT color="green">933</FONT> optimalIter = 1;<a name="line.933"></a> | |
| 937 <FONT color="green">934</FONT> }<a name="line.934"></a> | |
| 938 <FONT color="green">935</FONT> } else if (k <= targetIter) {<a name="line.935"></a> | |
| 939 <FONT color="green">936</FONT> optimalIter = k;<a name="line.936"></a> | |
| 940 <FONT color="green">937</FONT> if (costPerTimeUnit[k-1] < orderControl1 * costPerTimeUnit[k]) {<a name="line.937"></a> | |
| 941 <FONT color="green">938</FONT> optimalIter = k-1;<a name="line.938"></a> | |
| 942 <FONT color="green">939</FONT> } else if (costPerTimeUnit[k] < orderControl2 * costPerTimeUnit[k-1]) {<a name="line.939"></a> | |
| 943 <FONT color="green">940</FONT> optimalIter = Math.min(k+1, sequence.length - 2);<a name="line.940"></a> | |
| 944 <FONT color="green">941</FONT> }<a name="line.941"></a> | |
| 945 <FONT color="green">942</FONT> } else {<a name="line.942"></a> | |
| 946 <FONT color="green">943</FONT> optimalIter = k - 1;<a name="line.943"></a> | |
| 947 <FONT color="green">944</FONT> if ((k > 2) &&<a name="line.944"></a> | |
| 948 <FONT color="green">945</FONT> (costPerTimeUnit[k-2] < orderControl1 * costPerTimeUnit[k-1])) {<a name="line.945"></a> | |
| 949 <FONT color="green">946</FONT> optimalIter = k - 2;<a name="line.946"></a> | |
| 950 <FONT color="green">947</FONT> }<a name="line.947"></a> | |
| 951 <FONT color="green">948</FONT> if (costPerTimeUnit[k] < orderControl2 * costPerTimeUnit[optimalIter]) {<a name="line.948"></a> | |
| 952 <FONT color="green">949</FONT> optimalIter = Math.min(k, sequence.length - 2);<a name="line.949"></a> | |
| 953 <FONT color="green">950</FONT> }<a name="line.950"></a> | |
| 954 <FONT color="green">951</FONT> }<a name="line.951"></a> | |
| 955 <FONT color="green">952</FONT> <a name="line.952"></a> | |
| 956 <FONT color="green">953</FONT> if (previousRejected) {<a name="line.953"></a> | |
| 957 <FONT color="green">954</FONT> // after a rejected step neither order nor stepsize<a name="line.954"></a> | |
| 958 <FONT color="green">955</FONT> // should increase<a name="line.955"></a> | |
| 959 <FONT color="green">956</FONT> targetIter = Math.min(optimalIter, k);<a name="line.956"></a> | |
| 960 <FONT color="green">957</FONT> hNew = Math.min(Math.abs(stepSize), optimalStep[targetIter]);<a name="line.957"></a> | |
| 961 <FONT color="green">958</FONT> } else {<a name="line.958"></a> | |
| 962 <FONT color="green">959</FONT> // stepsize control<a name="line.959"></a> | |
| 963 <FONT color="green">960</FONT> if (optimalIter <= k) {<a name="line.960"></a> | |
| 964 <FONT color="green">961</FONT> hNew = optimalStep[optimalIter];<a name="line.961"></a> | |
| 965 <FONT color="green">962</FONT> } else {<a name="line.962"></a> | |
| 966 <FONT color="green">963</FONT> if ((k < targetIter) &&<a name="line.963"></a> | |
| 967 <FONT color="green">964</FONT> (costPerTimeUnit[k] < orderControl2 * costPerTimeUnit[k-1])) {<a name="line.964"></a> | |
| 968 <FONT color="green">965</FONT> hNew = filterStep(optimalStep[k] * costPerStep[optimalIter+1] / costPerStep[k],<a name="line.965"></a> | |
| 969 <FONT color="green">966</FONT> forward, false);<a name="line.966"></a> | |
| 970 <FONT color="green">967</FONT> } else {<a name="line.967"></a> | |
| 971 <FONT color="green">968</FONT> hNew = filterStep(optimalStep[k] * costPerStep[optimalIter] / costPerStep[k],<a name="line.968"></a> | |
| 972 <FONT color="green">969</FONT> forward, false);<a name="line.969"></a> | |
| 973 <FONT color="green">970</FONT> }<a name="line.970"></a> | |
| 974 <FONT color="green">971</FONT> }<a name="line.971"></a> | |
| 975 <FONT color="green">972</FONT> <a name="line.972"></a> | |
| 976 <FONT color="green">973</FONT> targetIter = optimalIter;<a name="line.973"></a> | |
| 977 <FONT color="green">974</FONT> <a name="line.974"></a> | |
| 978 <FONT color="green">975</FONT> }<a name="line.975"></a> | |
| 979 <FONT color="green">976</FONT> <a name="line.976"></a> | |
| 980 <FONT color="green">977</FONT> newStep = true;<a name="line.977"></a> | |
| 981 <FONT color="green">978</FONT> <a name="line.978"></a> | |
| 982 <FONT color="green">979</FONT> }<a name="line.979"></a> | |
| 983 <FONT color="green">980</FONT> <a name="line.980"></a> | |
| 984 <FONT color="green">981</FONT> hNew = Math.min(hNew, hInt);<a name="line.981"></a> | |
| 985 <FONT color="green">982</FONT> if (! forward) {<a name="line.982"></a> | |
| 986 <FONT color="green">983</FONT> hNew = -hNew;<a name="line.983"></a> | |
| 987 <FONT color="green">984</FONT> }<a name="line.984"></a> | |
| 988 <FONT color="green">985</FONT> <a name="line.985"></a> | |
| 989 <FONT color="green">986</FONT> firstTime = false;<a name="line.986"></a> | |
| 990 <FONT color="green">987</FONT> <a name="line.987"></a> | |
| 991 <FONT color="green">988</FONT> if (reject) {<a name="line.988"></a> | |
| 992 <FONT color="green">989</FONT> lastStep = false;<a name="line.989"></a> | |
| 993 <FONT color="green">990</FONT> previousRejected = true;<a name="line.990"></a> | |
| 994 <FONT color="green">991</FONT> } else {<a name="line.991"></a> | |
| 995 <FONT color="green">992</FONT> previousRejected = false;<a name="line.992"></a> | |
| 996 <FONT color="green">993</FONT> }<a name="line.993"></a> | |
| 997 <FONT color="green">994</FONT> <a name="line.994"></a> | |
| 998 <FONT color="green">995</FONT> }<a name="line.995"></a> | |
| 999 <FONT color="green">996</FONT> <a name="line.996"></a> | |
| 1000 <FONT color="green">997</FONT> return stepStart;<a name="line.997"></a> | |
| 1001 <FONT color="green">998</FONT> <a name="line.998"></a> | |
| 1002 <FONT color="green">999</FONT> }<a name="line.999"></a> | |
| 1003 <FONT color="green">1000</FONT> <a name="line.1000"></a> | |
| 1004 <FONT color="green">1001</FONT> }<a name="line.1001"></a> | |
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| 1065 </PRE> | |
| 1066 </BODY> | |
| 1067 </HTML> |