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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.ode.nonstiff;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> <a name="line.20"></a> <FONT color="green">021</FONT> /**<a name="line.21"></a> <FONT color="green">022</FONT> * This class implements the 8(5,3) Dormand-Prince integrator for Ordinary<a name="line.22"></a> <FONT color="green">023</FONT> * Differential Equations.<a name="line.23"></a> <FONT color="green">024</FONT> *<a name="line.24"></a> <FONT color="green">025</FONT> * <p>This integrator is an embedded Runge-Kutta integrator<a name="line.25"></a> <FONT color="green">026</FONT> * of order 8(5,3) used in local extrapolation mode (i.e. the solution<a name="line.26"></a> <FONT color="green">027</FONT> * is computed using the high order formula) with stepsize control<a name="line.27"></a> <FONT color="green">028</FONT> * (and automatic step initialization) and continuous output. This<a name="line.28"></a> <FONT color="green">029</FONT> * method uses 12 functions evaluations per step for integration and 4<a name="line.29"></a> <FONT color="green">030</FONT> * evaluations for interpolation. However, since the first<a name="line.30"></a> <FONT color="green">031</FONT> * interpolation evaluation is the same as the first integration<a name="line.31"></a> <FONT color="green">032</FONT> * evaluation of the next step, we have included it in the integrator<a name="line.32"></a> <FONT color="green">033</FONT> * rather than in the interpolator and specified the method was an<a name="line.33"></a> <FONT color="green">034</FONT> * <i>fsal</i>. Hence, despite we have 13 stages here, the cost is<a name="line.34"></a> <FONT color="green">035</FONT> * really 12 evaluations per step even if no interpolation is done,<a name="line.35"></a> <FONT color="green">036</FONT> * and the overcost of interpolation is only 3 evaluations.</p><a name="line.36"></a> <FONT color="green">037</FONT> *<a name="line.37"></a> <FONT color="green">038</FONT> * <p>This method is based on an 8(6) method by Dormand and Prince<a name="line.38"></a> <FONT color="green">039</FONT> * (i.e. order 8 for the integration and order 6 for error estimation)<a name="line.39"></a> <FONT color="green">040</FONT> * modified by Hairer and Wanner to use a 5th order error estimator<a name="line.40"></a> <FONT color="green">041</FONT> * with 3rd order correction. This modification was introduced because<a name="line.41"></a> <FONT color="green">042</FONT> * the original method failed in some cases (wrong steps can be<a name="line.42"></a> <FONT color="green">043</FONT> * accepted when step size is too large, for example in the<a name="line.43"></a> <FONT color="green">044</FONT> * Brusselator problem) and also had <i>severe difficulties when<a name="line.44"></a> <FONT color="green">045</FONT> * applied to problems with discontinuities</i>. This modification is<a name="line.45"></a> <FONT color="green">046</FONT> * explained in the second edition of the first volume (Nonstiff<a name="line.46"></a> <FONT color="green">047</FONT> * Problems) of the reference book by Hairer, Norsett and Wanner:<a name="line.47"></a> <FONT color="green">048</FONT> * <i>Solving Ordinary Differential Equations</i> (Springer-Verlag,<a name="line.48"></a> <FONT color="green">049</FONT> * ISBN 3-540-56670-8).</p><a name="line.49"></a> <FONT color="green">050</FONT> *<a name="line.50"></a> <FONT color="green">051</FONT> * @version $Revision: 810196 $ $Date: 2009-09-01 15:47:46 -0400 (Tue, 01 Sep 2009) $<a name="line.51"></a> <FONT color="green">052</FONT> * @since 1.2<a name="line.52"></a> <FONT color="green">053</FONT> */<a name="line.53"></a> <FONT color="green">054</FONT> <a name="line.54"></a> <FONT color="green">055</FONT> public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {<a name="line.55"></a> <FONT color="green">056</FONT> <a name="line.56"></a> <FONT color="green">057</FONT> /** Integrator method name. */<a name="line.57"></a> <FONT color="green">058</FONT> private static final String METHOD_NAME = "Dormand-Prince 8 (5, 3)";<a name="line.58"></a> <FONT color="green">059</FONT> <a name="line.59"></a> <FONT color="green">060</FONT> /** Time steps Butcher array. */<a name="line.60"></a> <FONT color="green">061</FONT> private static final double[] STATIC_C = {<a name="line.61"></a> <FONT color="green">062</FONT> (12.0 - 2.0 * Math.sqrt(6.0)) / 135.0, (6.0 - Math.sqrt(6.0)) / 45.0, (6.0 - Math.sqrt(6.0)) / 30.0,<a name="line.62"></a> <FONT color="green">063</FONT> (6.0 + Math.sqrt(6.0)) / 30.0, 1.0/3.0, 1.0/4.0, 4.0/13.0, 127.0/195.0, 3.0/5.0,<a name="line.63"></a> <FONT color="green">064</FONT> 6.0/7.0, 1.0, 1.0<a name="line.64"></a> <FONT color="green">065</FONT> };<a name="line.65"></a> <FONT color="green">066</FONT> <a name="line.66"></a> <FONT color="green">067</FONT> /** Internal weights Butcher array. */<a name="line.67"></a> <FONT color="green">068</FONT> private static final double[][] STATIC_A = {<a name="line.68"></a> <FONT color="green">069</FONT> <a name="line.69"></a> <FONT color="green">070</FONT> // k2<a name="line.70"></a> <FONT color="green">071</FONT> {(12.0 - 2.0 * Math.sqrt(6.0)) / 135.0},<a name="line.71"></a> <FONT color="green">072</FONT> <a name="line.72"></a> <FONT color="green">073</FONT> // k3<a name="line.73"></a> <FONT color="green">074</FONT> {(6.0 - Math.sqrt(6.0)) / 180.0, (6.0 - Math.sqrt(6.0)) / 60.0},<a name="line.74"></a> <FONT color="green">075</FONT> <a name="line.75"></a> <FONT color="green">076</FONT> // k4<a name="line.76"></a> <FONT color="green">077</FONT> {(6.0 - Math.sqrt(6.0)) / 120.0, 0.0, (6.0 - Math.sqrt(6.0)) / 40.0},<a name="line.77"></a> <FONT color="green">078</FONT> <a name="line.78"></a> <FONT color="green">079</FONT> // k5<a name="line.79"></a> <FONT color="green">080</FONT> {(462.0 + 107.0 * Math.sqrt(6.0)) / 3000.0, 0.0,<a name="line.80"></a> <FONT color="green">081</FONT> (-402.0 - 197.0 * Math.sqrt(6.0)) / 1000.0, (168.0 + 73.0 * Math.sqrt(6.0)) / 375.0},<a name="line.81"></a> <FONT color="green">082</FONT> <a name="line.82"></a> <FONT color="green">083</FONT> // k6<a name="line.83"></a> <FONT color="green">084</FONT> {1.0 / 27.0, 0.0, 0.0, (16.0 + Math.sqrt(6.0)) / 108.0, (16.0 - Math.sqrt(6.0)) / 108.0},<a name="line.84"></a> <FONT color="green">085</FONT> <a name="line.85"></a> <FONT color="green">086</FONT> // k7<a name="line.86"></a> <FONT color="green">087</FONT> {19.0 / 512.0, 0.0, 0.0, (118.0 + 23.0 * Math.sqrt(6.0)) / 1024.0,<a name="line.87"></a> <FONT color="green">088</FONT> (118.0 - 23.0 * Math.sqrt(6.0)) / 1024.0, -9.0 / 512.0},<a name="line.88"></a> <FONT color="green">089</FONT> <a name="line.89"></a> <FONT color="green">090</FONT> // k8<a name="line.90"></a> <FONT color="green">091</FONT> {13772.0 / 371293.0, 0.0, 0.0, (51544.0 + 4784.0 * Math.sqrt(6.0)) / 371293.0,<a name="line.91"></a> <FONT color="green">092</FONT> (51544.0 - 4784.0 * Math.sqrt(6.0)) / 371293.0, -5688.0 / 371293.0, 3072.0 / 371293.0},<a name="line.92"></a> <FONT color="green">093</FONT> <a name="line.93"></a> <FONT color="green">094</FONT> // k9<a name="line.94"></a> <FONT color="green">095</FONT> {58656157643.0 / 93983540625.0, 0.0, 0.0,<a name="line.95"></a> <FONT color="green">096</FONT> (-1324889724104.0 - 318801444819.0 * Math.sqrt(6.0)) / 626556937500.0,<a name="line.96"></a> <FONT color="green">097</FONT> (-1324889724104.0 + 318801444819.0 * Math.sqrt(6.0)) / 626556937500.0,<a name="line.97"></a> <FONT color="green">098</FONT> 96044563816.0 / 3480871875.0, 5682451879168.0 / 281950621875.0,<a name="line.98"></a> <FONT color="green">099</FONT> -165125654.0 / 3796875.0},<a name="line.99"></a> <FONT color="green">100</FONT> <a name="line.100"></a> <FONT color="green">101</FONT> // k10<a name="line.101"></a> <FONT color="green">102</FONT> {8909899.0 / 18653125.0, 0.0, 0.0,<a name="line.102"></a> <FONT color="green">103</FONT> (-4521408.0 - 1137963.0 * Math.sqrt(6.0)) / 2937500.0,<a name="line.103"></a> <FONT color="green">104</FONT> (-4521408.0 + 1137963.0 * Math.sqrt(6.0)) / 2937500.0,<a name="line.104"></a> <FONT color="green">105</FONT> 96663078.0 / 4553125.0, 2107245056.0 / 137915625.0,<a name="line.105"></a> <FONT color="green">106</FONT> -4913652016.0 / 147609375.0, -78894270.0 / 3880452869.0},<a name="line.106"></a> <FONT color="green">107</FONT> <a name="line.107"></a> <FONT color="green">108</FONT> // k11<a name="line.108"></a> <FONT color="green">109</FONT> {-20401265806.0 / 21769653311.0, 0.0, 0.0,<a name="line.109"></a> <FONT color="green">110</FONT> (354216.0 + 94326.0 * Math.sqrt(6.0)) / 112847.0,<a name="line.110"></a> <FONT color="green">111</FONT> (354216.0 - 94326.0 * Math.sqrt(6.0)) / 112847.0,<a name="line.111"></a> <FONT color="green">112</FONT> -43306765128.0 / 5313852383.0, -20866708358144.0 / 1126708119789.0,<a name="line.112"></a> <FONT color="green">113</FONT> 14886003438020.0 / 654632330667.0, 35290686222309375.0 / 14152473387134411.0,<a name="line.113"></a> <FONT color="green">114</FONT> -1477884375.0 / 485066827.0},<a name="line.114"></a> <FONT color="green">115</FONT> <a name="line.115"></a> <FONT color="green">116</FONT> // k12<a name="line.116"></a> <FONT color="green">117</FONT> {39815761.0 / 17514443.0, 0.0, 0.0,<a name="line.117"></a> <FONT color="green">118</FONT> (-3457480.0 - 960905.0 * Math.sqrt(6.0)) / 551636.0,<a name="line.118"></a> <FONT color="green">119</FONT> (-3457480.0 + 960905.0 * Math.sqrt(6.0)) / 551636.0,<a name="line.119"></a> <FONT color="green">120</FONT> -844554132.0 / 47026969.0, 8444996352.0 / 302158619.0,<a name="line.120"></a> <FONT color="green">121</FONT> -2509602342.0 / 877790785.0, -28388795297996250.0 / 3199510091356783.0,<a name="line.121"></a> <FONT color="green">122</FONT> 226716250.0 / 18341897.0, 1371316744.0 / 2131383595.0},<a name="line.122"></a> <FONT color="green">123</FONT> <a name="line.123"></a> <FONT color="green">124</FONT> // k13 should be for interpolation only, but since it is the same<a name="line.124"></a> <FONT color="green">125</FONT> // stage as the first evaluation of the next step, we perform it<a name="line.125"></a> <FONT color="green">126</FONT> // here at no cost by specifying this is an fsal method<a name="line.126"></a> <FONT color="green">127</FONT> {104257.0/1920240.0, 0.0, 0.0, 0.0, 0.0, 3399327.0/763840.0,<a name="line.127"></a> <FONT color="green">128</FONT> 66578432.0/35198415.0, -1674902723.0/288716400.0,<a name="line.128"></a> <FONT color="green">129</FONT> 54980371265625.0/176692375811392.0, -734375.0/4826304.0,<a name="line.129"></a> <FONT color="green">130</FONT> 171414593.0/851261400.0, 137909.0/3084480.0}<a name="line.130"></a> <FONT color="green">131</FONT> <a name="line.131"></a> <FONT color="green">132</FONT> };<a name="line.132"></a> <FONT color="green">133</FONT> <a name="line.133"></a> <FONT color="green">134</FONT> /** Propagation weights Butcher array. */<a name="line.134"></a> <FONT color="green">135</FONT> private static final double[] STATIC_B = {<a name="line.135"></a> <FONT color="green">136</FONT> 104257.0/1920240.0,<a name="line.136"></a> <FONT color="green">137</FONT> 0.0,<a name="line.137"></a> <FONT color="green">138</FONT> 0.0,<a name="line.138"></a> <FONT color="green">139</FONT> 0.0,<a name="line.139"></a> <FONT color="green">140</FONT> 0.0,<a name="line.140"></a> <FONT color="green">141</FONT> 3399327.0/763840.0,<a name="line.141"></a> <FONT color="green">142</FONT> 66578432.0/35198415.0,<a name="line.142"></a> <FONT color="green">143</FONT> -1674902723.0/288716400.0,<a name="line.143"></a> <FONT color="green">144</FONT> 54980371265625.0/176692375811392.0,<a name="line.144"></a> <FONT color="green">145</FONT> -734375.0/4826304.0,<a name="line.145"></a> <FONT color="green">146</FONT> 171414593.0/851261400.0,<a name="line.146"></a> <FONT color="green">147</FONT> 137909.0/3084480.0,<a name="line.147"></a> <FONT color="green">148</FONT> 0.0<a name="line.148"></a> <FONT color="green">149</FONT> };<a name="line.149"></a> <FONT color="green">150</FONT> <a name="line.150"></a> <FONT color="green">151</FONT> /** First error weights array, element 1. */<a name="line.151"></a> <FONT color="green">152</FONT> private static final double E1_01 = 116092271.0 / 8848465920.0;<a name="line.152"></a> <FONT color="green">153</FONT> <a name="line.153"></a> <FONT color="green">154</FONT> // elements 2 to 5 are zero, so they are neither stored nor used<a name="line.154"></a> <FONT color="green">155</FONT> <a name="line.155"></a> <FONT color="green">156</FONT> /** First error weights array, element 6. */<a name="line.156"></a> <FONT color="green">157</FONT> private static final double E1_06 = -1871647.0 / 1527680.0;<a name="line.157"></a> <FONT color="green">158</FONT> <a name="line.158"></a> <FONT color="green">159</FONT> /** First error weights array, element 7. */<a name="line.159"></a> <FONT color="green">160</FONT> private static final double E1_07 = -69799717.0 / 140793660.0;<a name="line.160"></a> <FONT color="green">161</FONT> <a name="line.161"></a> <FONT color="green">162</FONT> /** First error weights array, element 8. */<a name="line.162"></a> <FONT color="green">163</FONT> private static final double E1_08 = 1230164450203.0 / 739113984000.0;<a name="line.163"></a> <FONT color="green">164</FONT> <a name="line.164"></a> <FONT color="green">165</FONT> /** First error weights array, element 9. */<a name="line.165"></a> <FONT color="green">166</FONT> private static final double E1_09 = -1980813971228885.0 / 5654156025964544.0;<a name="line.166"></a> <FONT color="green">167</FONT> <a name="line.167"></a> <FONT color="green">168</FONT> /** First error weights array, element 10. */<a name="line.168"></a> <FONT color="green">169</FONT> private static final double E1_10 = 464500805.0 / 1389975552.0;<a name="line.169"></a> <FONT color="green">170</FONT> <a name="line.170"></a> <FONT color="green">171</FONT> /** First error weights array, element 11. */<a name="line.171"></a> <FONT color="green">172</FONT> private static final double E1_11 = 1606764981773.0 / 19613062656000.0;<a name="line.172"></a> <FONT color="green">173</FONT> <a name="line.173"></a> <FONT color="green">174</FONT> /** First error weights array, element 12. */<a name="line.174"></a> <FONT color="green">175</FONT> private static final double E1_12 = -137909.0 / 6168960.0;<a name="line.175"></a> <FONT color="green">176</FONT> <a name="line.176"></a> <FONT color="green">177</FONT> <a name="line.177"></a> <FONT color="green">178</FONT> /** Second error weights array, element 1. */<a name="line.178"></a> <FONT color="green">179</FONT> private static final double E2_01 = -364463.0 / 1920240.0;<a name="line.179"></a> <FONT color="green">180</FONT> <a name="line.180"></a> <FONT color="green">181</FONT> // elements 2 to 5 are zero, so they are neither stored nor used<a name="line.181"></a> <FONT color="green">182</FONT> <a name="line.182"></a> <FONT color="green">183</FONT> /** Second error weights array, element 6. */<a name="line.183"></a> <FONT color="green">184</FONT> private static final double E2_06 = 3399327.0 / 763840.0;<a name="line.184"></a> <FONT color="green">185</FONT> <a name="line.185"></a> <FONT color="green">186</FONT> /** Second error weights array, element 7. */<a name="line.186"></a> <FONT color="green">187</FONT> private static final double E2_07 = 66578432.0 / 35198415.0;<a name="line.187"></a> <FONT color="green">188</FONT> <a name="line.188"></a> <FONT color="green">189</FONT> /** Second error weights array, element 8. */<a name="line.189"></a> <FONT color="green">190</FONT> private static final double E2_08 = -1674902723.0 / 288716400.0;<a name="line.190"></a> <FONT color="green">191</FONT> <a name="line.191"></a> <FONT color="green">192</FONT> /** Second error weights array, element 9. */<a name="line.192"></a> <FONT color="green">193</FONT> private static final double E2_09 = -74684743568175.0 / 176692375811392.0;<a name="line.193"></a> <FONT color="green">194</FONT> <a name="line.194"></a> <FONT color="green">195</FONT> /** Second error weights array, element 10. */<a name="line.195"></a> <FONT color="green">196</FONT> private static final double E2_10 = -734375.0 / 4826304.0;<a name="line.196"></a> <FONT color="green">197</FONT> <a name="line.197"></a> <FONT color="green">198</FONT> /** Second error weights array, element 11. */<a name="line.198"></a> <FONT color="green">199</FONT> private static final double E2_11 = 171414593.0 / 851261400.0;<a name="line.199"></a> <FONT color="green">200</FONT> <a name="line.200"></a> <FONT color="green">201</FONT> /** Second error weights array, element 12. */<a name="line.201"></a> <FONT color="green">202</FONT> private static final double E2_12 = 69869.0 / 3084480.0;<a name="line.202"></a> <FONT color="green">203</FONT> <a name="line.203"></a> <FONT color="green">204</FONT> /** Simple constructor.<a name="line.204"></a> <FONT color="green">205</FONT> * Build an eighth order Dormand-Prince integrator with the given step bounds<a name="line.205"></a> <FONT color="green">206</FONT> * @param minStep minimal step (must be positive even for backward<a name="line.206"></a> <FONT color="green">207</FONT> * integration), the last step can be smaller than this<a name="line.207"></a> <FONT color="green">208</FONT> * @param maxStep maximal step (must be positive even for backward<a name="line.208"></a> <FONT color="green">209</FONT> * integration)<a name="line.209"></a> <FONT color="green">210</FONT> * @param scalAbsoluteTolerance allowed absolute error<a name="line.210"></a> <FONT color="green">211</FONT> * @param scalRelativeTolerance allowed relative error<a name="line.211"></a> <FONT color="green">212</FONT> */<a name="line.212"></a> <FONT color="green">213</FONT> public DormandPrince853Integrator(final double minStep, final double maxStep,<a name="line.213"></a> <FONT color="green">214</FONT> final double scalAbsoluteTolerance,<a name="line.214"></a> <FONT color="green">215</FONT> final double scalRelativeTolerance) {<a name="line.215"></a> <FONT color="green">216</FONT> super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B,<a name="line.216"></a> <FONT color="green">217</FONT> new DormandPrince853StepInterpolator(),<a name="line.217"></a> <FONT color="green">218</FONT> minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);<a name="line.218"></a> <FONT color="green">219</FONT> }<a name="line.219"></a> <FONT color="green">220</FONT> <a name="line.220"></a> <FONT color="green">221</FONT> /** Simple constructor.<a name="line.221"></a> <FONT color="green">222</FONT> * Build an eighth order Dormand-Prince integrator with the given step bounds<a name="line.222"></a> <FONT color="green">223</FONT> * @param minStep minimal step (must be positive even for backward<a name="line.223"></a> <FONT color="green">224</FONT> * integration), the last step can be smaller than this<a name="line.224"></a> <FONT color="green">225</FONT> * @param maxStep maximal step (must be positive even for backward<a name="line.225"></a> <FONT color="green">226</FONT> * integration)<a name="line.226"></a> <FONT color="green">227</FONT> * @param vecAbsoluteTolerance allowed absolute error<a name="line.227"></a> <FONT color="green">228</FONT> * @param vecRelativeTolerance allowed relative error<a name="line.228"></a> <FONT color="green">229</FONT> */<a name="line.229"></a> <FONT color="green">230</FONT> public DormandPrince853Integrator(final double minStep, final double maxStep,<a name="line.230"></a> <FONT color="green">231</FONT> final double[] vecAbsoluteTolerance,<a name="line.231"></a> <FONT color="green">232</FONT> final double[] vecRelativeTolerance) {<a name="line.232"></a> <FONT color="green">233</FONT> super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B,<a name="line.233"></a> <FONT color="green">234</FONT> new DormandPrince853StepInterpolator(),<a name="line.234"></a> <FONT color="green">235</FONT> minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);<a name="line.235"></a> <FONT color="green">236</FONT> }<a name="line.236"></a> <FONT color="green">237</FONT> <a name="line.237"></a> <FONT color="green">238</FONT> /** {@inheritDoc} */<a name="line.238"></a> <FONT color="green">239</FONT> @Override<a name="line.239"></a> <FONT color="green">240</FONT> public int getOrder() {<a name="line.240"></a> <FONT color="green">241</FONT> return 8;<a name="line.241"></a> <FONT color="green">242</FONT> }<a name="line.242"></a> <FONT color="green">243</FONT> <a name="line.243"></a> <FONT color="green">244</FONT> /** {@inheritDoc} */<a name="line.244"></a> <FONT color="green">245</FONT> @Override<a name="line.245"></a> <FONT color="green">246</FONT> protected double estimateError(final double[][] yDotK,<a name="line.246"></a> <FONT color="green">247</FONT> final double[] y0, final double[] y1,<a name="line.247"></a> <FONT color="green">248</FONT> final double h) {<a name="line.248"></a> <FONT color="green">249</FONT> double error1 = 0;<a name="line.249"></a> <FONT color="green">250</FONT> double error2 = 0;<a name="line.250"></a> <FONT color="green">251</FONT> <a name="line.251"></a> <FONT color="green">252</FONT> for (int j = 0; j < y0.length; ++j) {<a name="line.252"></a> <FONT color="green">253</FONT> final double errSum1 = E1_01 * yDotK[0][j] + E1_06 * yDotK[5][j] +<a name="line.253"></a> <FONT color="green">254</FONT> E1_07 * yDotK[6][j] + E1_08 * yDotK[7][j] +<a name="line.254"></a> <FONT color="green">255</FONT> E1_09 * yDotK[8][j] + E1_10 * yDotK[9][j] +<a name="line.255"></a> <FONT color="green">256</FONT> E1_11 * yDotK[10][j] + E1_12 * yDotK[11][j];<a name="line.256"></a> <FONT color="green">257</FONT> final double errSum2 = E2_01 * yDotK[0][j] + E2_06 * yDotK[5][j] +<a name="line.257"></a> <FONT color="green">258</FONT> E2_07 * yDotK[6][j] + E2_08 * yDotK[7][j] +<a name="line.258"></a> <FONT color="green">259</FONT> E2_09 * yDotK[8][j] + E2_10 * yDotK[9][j] +<a name="line.259"></a> <FONT color="green">260</FONT> E2_11 * yDotK[10][j] + E2_12 * yDotK[11][j];<a name="line.260"></a> <FONT color="green">261</FONT> <a name="line.261"></a> <FONT color="green">262</FONT> final double yScale = Math.max(Math.abs(y0[j]), Math.abs(y1[j]));<a name="line.262"></a> <FONT color="green">263</FONT> final double tol = (vecAbsoluteTolerance == null) ?<a name="line.263"></a> <FONT color="green">264</FONT> (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :<a name="line.264"></a> <FONT color="green">265</FONT> (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);<a name="line.265"></a> <FONT color="green">266</FONT> final double ratio1 = errSum1 / tol;<a name="line.266"></a> <FONT color="green">267</FONT> error1 += ratio1 * ratio1;<a name="line.267"></a> <FONT color="green">268</FONT> final double ratio2 = errSum2 / tol;<a name="line.268"></a> <FONT color="green">269</FONT> error2 += ratio2 * ratio2;<a name="line.269"></a> <FONT color="green">270</FONT> }<a name="line.270"></a> <FONT color="green">271</FONT> <a name="line.271"></a> <FONT color="green">272</FONT> double den = error1 + 0.01 * error2;<a name="line.272"></a> <FONT color="green">273</FONT> if (den <= 0.0) {<a name="line.273"></a> <FONT color="green">274</FONT> den = 1.0;<a name="line.274"></a> <FONT color="green">275</FONT> }<a name="line.275"></a> <FONT color="green">276</FONT> <a name="line.276"></a> <FONT color="green">277</FONT> return Math.abs(h) * error1 / Math.sqrt(y0.length * den);<a name="line.277"></a> <FONT color="green">278</FONT> <a name="line.278"></a> <FONT color="green">279</FONT> }<a name="line.279"></a> <FONT color="green">280</FONT> <a name="line.280"></a> <FONT color="green">281</FONT> }<a name="line.281"></a> </PRE> </BODY> </HTML>