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1 <HTML>
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2 <BODY BGCOLOR="white">
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3 <PRE>
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4 <FONT color="green">001</FONT> /*<a name="line.1"></a>
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5 <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
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6 <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a>
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7 <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
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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>
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9 <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
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10 <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a>
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11 <FONT color="green">008</FONT> *<a name="line.8"></a>
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12 <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
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13 <FONT color="green">010</FONT> *<a name="line.10"></a>
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14 <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
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15 <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
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16 <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
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17 <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a>
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18 <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a>
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19 <FONT color="green">016</FONT> */<a name="line.16"></a>
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20 <FONT color="green">017</FONT> <a name="line.17"></a>
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21 <FONT color="green">018</FONT> package org.apache.commons.math.ode;<a name="line.18"></a>
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22 <FONT color="green">019</FONT> <a name="line.19"></a>
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23 <FONT color="green">020</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.20"></a>
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24 <FONT color="green">021</FONT> import org.apache.commons.math.linear.Array2DRowRealMatrix;<a name="line.21"></a>
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25 <FONT color="green">022</FONT> import org.apache.commons.math.linear.RealMatrix;<a name="line.22"></a>
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26 <FONT color="green">023</FONT> import org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator;<a name="line.23"></a>
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27 <FONT color="green">024</FONT> import org.apache.commons.math.ode.nonstiff.DormandPrince853Integrator;<a name="line.24"></a>
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28 <FONT color="green">025</FONT> import org.apache.commons.math.ode.sampling.StepHandler;<a name="line.25"></a>
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29 <FONT color="green">026</FONT> import org.apache.commons.math.ode.sampling.StepInterpolator;<a name="line.26"></a>
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30 <FONT color="green">027</FONT> <a name="line.27"></a>
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31 <FONT color="green">028</FONT> /**<a name="line.28"></a>
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32 <FONT color="green">029</FONT> * This class is the base class for multistep integrators for Ordinary<a name="line.29"></a>
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33 <FONT color="green">030</FONT> * Differential Equations.<a name="line.30"></a>
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34 <FONT color="green">031</FONT> * <p>We define scaled derivatives s<sub>i</sub>(n) at step n as:<a name="line.31"></a>
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35 <FONT color="green">032</FONT> * <pre><a name="line.32"></a>
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36 <FONT color="green">033</FONT> * s<sub>1</sub>(n) = h y'<sub>n</sub> for first derivative<a name="line.33"></a>
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37 <FONT color="green">034</FONT> * s<sub>2</sub>(n) = h<sup>2</sup>/2 y''<sub>n</sub> for second derivative<a name="line.34"></a>
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38 <FONT color="green">035</FONT> * s<sub>3</sub>(n) = h<sup>3</sup>/6 y'''<sub>n</sub> for third derivative<a name="line.35"></a>
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39 <FONT color="green">036</FONT> * ...<a name="line.36"></a>
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40 <FONT color="green">037</FONT> * s<sub>k</sub>(n) = h<sup>k</sup>/k! y(k)<sub>n</sub> for k<sup>th</sup> derivative<a name="line.37"></a>
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41 <FONT color="green">038</FONT> * </pre></p><a name="line.38"></a>
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42 <FONT color="green">039</FONT> * <p>Rather than storing several previous steps separately, this implementation uses<a name="line.39"></a>
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43 <FONT color="green">040</FONT> * the Nordsieck vector with higher degrees scaled derivatives all taken at the same<a name="line.40"></a>
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44 <FONT color="green">041</FONT> * step (y<sub>n</sub>, s<sub>1</sub>(n) and r<sub>n</sub>) where r<sub>n</sub> is defined as:<a name="line.41"></a>
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45 <FONT color="green">042</FONT> * <pre><a name="line.42"></a>
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46 <FONT color="green">043</FONT> * r<sub>n</sub> = [ s<sub>2</sub>(n), s<sub>3</sub>(n) ... s<sub>k</sub>(n) ]<sup>T</sup><a name="line.43"></a>
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47 <FONT color="green">044</FONT> * </pre><a name="line.44"></a>
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48 <FONT color="green">045</FONT> * (we omit the k index in the notation for clarity)</p><a name="line.45"></a>
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49 <FONT color="green">046</FONT> * <p><a name="line.46"></a>
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50 <FONT color="green">047</FONT> * Multistep integrators with Nordsieck representation are highly sensitive to<a name="line.47"></a>
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51 <FONT color="green">048</FONT> * large step changes because when the step is multiplied by a factor a, the<a name="line.48"></a>
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52 <FONT color="green">049</FONT> * k<sup>th</sup> component of the Nordsieck vector is multiplied by a<sup>k</sup><a name="line.49"></a>
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53 <FONT color="green">050</FONT> * and the last components are the least accurate ones. The default max growth<a name="line.50"></a>
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54 <FONT color="green">051</FONT> * factor is therefore set to a quite low value: 2<sup>1/order</sup>.<a name="line.51"></a>
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55 <FONT color="green">052</FONT> * </p><a name="line.52"></a>
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56 <FONT color="green">053</FONT> *<a name="line.53"></a>
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57 <FONT color="green">054</FONT> * @see org.apache.commons.math.ode.nonstiff.AdamsBashforthIntegrator<a name="line.54"></a>
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58 <FONT color="green">055</FONT> * @see org.apache.commons.math.ode.nonstiff.AdamsMoultonIntegrator<a name="line.55"></a>
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59 <FONT color="green">056</FONT> * @version $Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $<a name="line.56"></a>
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60 <FONT color="green">057</FONT> * @since 2.0<a name="line.57"></a>
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61 <FONT color="green">058</FONT> */<a name="line.58"></a>
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62 <FONT color="green">059</FONT> public abstract class MultistepIntegrator extends AdaptiveStepsizeIntegrator {<a name="line.59"></a>
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63 <FONT color="green">060</FONT> <a name="line.60"></a>
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64 <FONT color="green">061</FONT> /** First scaled derivative (h y'). */<a name="line.61"></a>
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65 <FONT color="green">062</FONT> protected double[] scaled;<a name="line.62"></a>
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66 <FONT color="green">063</FONT> <a name="line.63"></a>
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67 <FONT color="green">064</FONT> /** Nordsieck matrix of the higher scaled derivatives.<a name="line.64"></a>
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68 <FONT color="green">065</FONT> * <p>(h<sup>2</sup>/2 y'', h<sup>3</sup>/6 y''' ..., h<sup>k</sup>/k! y(k))</p><a name="line.65"></a>
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69 <FONT color="green">066</FONT> */<a name="line.66"></a>
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70 <FONT color="green">067</FONT> protected Array2DRowRealMatrix nordsieck;<a name="line.67"></a>
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71 <FONT color="green">068</FONT> <a name="line.68"></a>
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72 <FONT color="green">069</FONT> /** Starter integrator. */<a name="line.69"></a>
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73 <FONT color="green">070</FONT> private FirstOrderIntegrator starter;<a name="line.70"></a>
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74 <FONT color="green">071</FONT> <a name="line.71"></a>
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75 <FONT color="green">072</FONT> /** Number of steps of the multistep method (excluding the one being computed). */<a name="line.72"></a>
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76 <FONT color="green">073</FONT> private final int nSteps;<a name="line.73"></a>
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77 <FONT color="green">074</FONT> <a name="line.74"></a>
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78 <FONT color="green">075</FONT> /** Stepsize control exponent. */<a name="line.75"></a>
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79 <FONT color="green">076</FONT> private double exp;<a name="line.76"></a>
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80 <FONT color="green">077</FONT> <a name="line.77"></a>
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81 <FONT color="green">078</FONT> /** Safety factor for stepsize control. */<a name="line.78"></a>
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82 <FONT color="green">079</FONT> private double safety;<a name="line.79"></a>
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83 <FONT color="green">080</FONT> <a name="line.80"></a>
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84 <FONT color="green">081</FONT> /** Minimal reduction factor for stepsize control. */<a name="line.81"></a>
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85 <FONT color="green">082</FONT> private double minReduction;<a name="line.82"></a>
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86 <FONT color="green">083</FONT> <a name="line.83"></a>
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87 <FONT color="green">084</FONT> /** Maximal growth factor for stepsize control. */<a name="line.84"></a>
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88 <FONT color="green">085</FONT> private double maxGrowth;<a name="line.85"></a>
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89 <FONT color="green">086</FONT> <a name="line.86"></a>
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90 <FONT color="green">087</FONT> /**<a name="line.87"></a>
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91 <FONT color="green">088</FONT> * Build a multistep integrator with the given stepsize bounds.<a name="line.88"></a>
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92 <FONT color="green">089</FONT> * <p>The default starter integrator is set to the {@link<a name="line.89"></a>
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93 <FONT color="green">090</FONT> * DormandPrince853Integrator Dormand-Prince 8(5,3)} integrator with<a name="line.90"></a>
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94 <FONT color="green">091</FONT> * some defaults settings.</p><a name="line.91"></a>
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95 <FONT color="green">092</FONT> * <p><a name="line.92"></a>
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96 <FONT color="green">093</FONT> * The default max growth factor is set to a quite low value: 2<sup>1/order</sup>.<a name="line.93"></a>
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97 <FONT color="green">094</FONT> * </p><a name="line.94"></a>
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98 <FONT color="green">095</FONT> * @param name name of the method<a name="line.95"></a>
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99 <FONT color="green">096</FONT> * @param nSteps number of steps of the multistep method<a name="line.96"></a>
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100 <FONT color="green">097</FONT> * (excluding the one being computed)<a name="line.97"></a>
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101 <FONT color="green">098</FONT> * @param order order of the method<a name="line.98"></a>
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102 <FONT color="green">099</FONT> * @param minStep minimal step (must be positive even for backward<a name="line.99"></a>
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103 <FONT color="green">100</FONT> * integration), the last step can be smaller than this<a name="line.100"></a>
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104 <FONT color="green">101</FONT> * @param maxStep maximal step (must be positive even for backward<a name="line.101"></a>
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105 <FONT color="green">102</FONT> * integration)<a name="line.102"></a>
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106 <FONT color="green">103</FONT> * @param scalAbsoluteTolerance allowed absolute error<a name="line.103"></a>
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107 <FONT color="green">104</FONT> * @param scalRelativeTolerance allowed relative error<a name="line.104"></a>
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108 <FONT color="green">105</FONT> */<a name="line.105"></a>
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109 <FONT color="green">106</FONT> protected MultistepIntegrator(final String name, final int nSteps,<a name="line.106"></a>
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110 <FONT color="green">107</FONT> final int order,<a name="line.107"></a>
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111 <FONT color="green">108</FONT> final double minStep, final double maxStep,<a name="line.108"></a>
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112 <FONT color="green">109</FONT> final double scalAbsoluteTolerance,<a name="line.109"></a>
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113 <FONT color="green">110</FONT> final double scalRelativeTolerance) {<a name="line.110"></a>
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114 <FONT color="green">111</FONT> <a name="line.111"></a>
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115 <FONT color="green">112</FONT> super(name, minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);<a name="line.112"></a>
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116 <FONT color="green">113</FONT> <a name="line.113"></a>
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117 <FONT color="green">114</FONT> if (nSteps <= 0) {<a name="line.114"></a>
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118 <FONT color="green">115</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.115"></a>
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119 <FONT color="green">116</FONT> "{0} method needs at least one previous point",<a name="line.116"></a>
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120 <FONT color="green">117</FONT> name);<a name="line.117"></a>
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121 <FONT color="green">118</FONT> }<a name="line.118"></a>
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122 <FONT color="green">119</FONT> <a name="line.119"></a>
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123 <FONT color="green">120</FONT> starter = new DormandPrince853Integrator(minStep, maxStep,<a name="line.120"></a>
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124 <FONT color="green">121</FONT> scalAbsoluteTolerance,<a name="line.121"></a>
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125 <FONT color="green">122</FONT> scalRelativeTolerance);<a name="line.122"></a>
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126 <FONT color="green">123</FONT> this.nSteps = nSteps;<a name="line.123"></a>
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127 <FONT color="green">124</FONT> <a name="line.124"></a>
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128 <FONT color="green">125</FONT> exp = -1.0 / order;<a name="line.125"></a>
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129 <FONT color="green">126</FONT> <a name="line.126"></a>
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130 <FONT color="green">127</FONT> // set the default values of the algorithm control parameters<a name="line.127"></a>
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131 <FONT color="green">128</FONT> setSafety(0.9);<a name="line.128"></a>
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132 <FONT color="green">129</FONT> setMinReduction(0.2);<a name="line.129"></a>
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133 <FONT color="green">130</FONT> setMaxGrowth(Math.pow(2.0, -exp));<a name="line.130"></a>
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134 <FONT color="green">131</FONT> <a name="line.131"></a>
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135 <FONT color="green">132</FONT> }<a name="line.132"></a>
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136 <FONT color="green">133</FONT> <a name="line.133"></a>
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137 <FONT color="green">134</FONT> /**<a name="line.134"></a>
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138 <FONT color="green">135</FONT> * Build a multistep integrator with the given stepsize bounds.<a name="line.135"></a>
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139 <FONT color="green">136</FONT> * <p>The default starter integrator is set to the {@link<a name="line.136"></a>
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140 <FONT color="green">137</FONT> * DormandPrince853Integrator Dormand-Prince 8(5,3)} integrator with<a name="line.137"></a>
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141 <FONT color="green">138</FONT> * some defaults settings.</p><a name="line.138"></a>
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142 <FONT color="green">139</FONT> * <p><a name="line.139"></a>
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143 <FONT color="green">140</FONT> * The default max growth factor is set to a quite low value: 2<sup>1/order</sup>.<a name="line.140"></a>
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144 <FONT color="green">141</FONT> * </p><a name="line.141"></a>
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145 <FONT color="green">142</FONT> * @param name name of the method<a name="line.142"></a>
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146 <FONT color="green">143</FONT> * @param nSteps number of steps of the multistep method<a name="line.143"></a>
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147 <FONT color="green">144</FONT> * (excluding the one being computed)<a name="line.144"></a>
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148 <FONT color="green">145</FONT> * @param order order of the method<a name="line.145"></a>
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149 <FONT color="green">146</FONT> * @param minStep minimal step (must be positive even for backward<a name="line.146"></a>
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150 <FONT color="green">147</FONT> * integration), the last step can be smaller than this<a name="line.147"></a>
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151 <FONT color="green">148</FONT> * @param maxStep maximal step (must be positive even for backward<a name="line.148"></a>
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152 <FONT color="green">149</FONT> * integration)<a name="line.149"></a>
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153 <FONT color="green">150</FONT> * @param vecAbsoluteTolerance allowed absolute error<a name="line.150"></a>
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154 <FONT color="green">151</FONT> * @param vecRelativeTolerance allowed relative error<a name="line.151"></a>
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155 <FONT color="green">152</FONT> */<a name="line.152"></a>
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156 <FONT color="green">153</FONT> protected MultistepIntegrator(final String name, final int nSteps,<a name="line.153"></a>
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157 <FONT color="green">154</FONT> final int order,<a name="line.154"></a>
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158 <FONT color="green">155</FONT> final double minStep, final double maxStep,<a name="line.155"></a>
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159 <FONT color="green">156</FONT> final double[] vecAbsoluteTolerance,<a name="line.156"></a>
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160 <FONT color="green">157</FONT> final double[] vecRelativeTolerance) {<a name="line.157"></a>
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161 <FONT color="green">158</FONT> super(name, minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);<a name="line.158"></a>
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162 <FONT color="green">159</FONT> starter = new DormandPrince853Integrator(minStep, maxStep,<a name="line.159"></a>
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163 <FONT color="green">160</FONT> vecAbsoluteTolerance,<a name="line.160"></a>
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164 <FONT color="green">161</FONT> vecRelativeTolerance);<a name="line.161"></a>
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165 <FONT color="green">162</FONT> this.nSteps = nSteps;<a name="line.162"></a>
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166 <FONT color="green">163</FONT> <a name="line.163"></a>
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167 <FONT color="green">164</FONT> exp = -1.0 / order;<a name="line.164"></a>
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168 <FONT color="green">165</FONT> <a name="line.165"></a>
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169 <FONT color="green">166</FONT> // set the default values of the algorithm control parameters<a name="line.166"></a>
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170 <FONT color="green">167</FONT> setSafety(0.9);<a name="line.167"></a>
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171 <FONT color="green">168</FONT> setMinReduction(0.2);<a name="line.168"></a>
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172 <FONT color="green">169</FONT> setMaxGrowth(Math.pow(2.0, -exp));<a name="line.169"></a>
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173 <FONT color="green">170</FONT> <a name="line.170"></a>
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174 <FONT color="green">171</FONT> }<a name="line.171"></a>
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175 <FONT color="green">172</FONT> <a name="line.172"></a>
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176 <FONT color="green">173</FONT> /**<a name="line.173"></a>
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177 <FONT color="green">174</FONT> * Get the starter integrator.<a name="line.174"></a>
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178 <FONT color="green">175</FONT> * @return starter integrator<a name="line.175"></a>
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179 <FONT color="green">176</FONT> */<a name="line.176"></a>
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180 <FONT color="green">177</FONT> public ODEIntegrator getStarterIntegrator() {<a name="line.177"></a>
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181 <FONT color="green">178</FONT> return starter;<a name="line.178"></a>
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182 <FONT color="green">179</FONT> }<a name="line.179"></a>
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183 <FONT color="green">180</FONT> <a name="line.180"></a>
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184 <FONT color="green">181</FONT> /**<a name="line.181"></a>
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185 <FONT color="green">182</FONT> * Set the starter integrator.<a name="line.182"></a>
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186 <FONT color="green">183</FONT> * <p>The various step and event handlers for this starter integrator<a name="line.183"></a>
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187 <FONT color="green">184</FONT> * will be managed automatically by the multi-step integrator. Any<a name="line.184"></a>
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188 <FONT color="green">185</FONT> * user configuration for these elements will be cleared before use.</p><a name="line.185"></a>
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189 <FONT color="green">186</FONT> * @param starterIntegrator starter integrator<a name="line.186"></a>
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190 <FONT color="green">187</FONT> */<a name="line.187"></a>
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191 <FONT color="green">188</FONT> public void setStarterIntegrator(FirstOrderIntegrator starterIntegrator) {<a name="line.188"></a>
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192 <FONT color="green">189</FONT> this.starter = starterIntegrator;<a name="line.189"></a>
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193 <FONT color="green">190</FONT> }<a name="line.190"></a>
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194 <FONT color="green">191</FONT> <a name="line.191"></a>
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195 <FONT color="green">192</FONT> /** Start the integration.<a name="line.192"></a>
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196 <FONT color="green">193</FONT> * <p>This method computes one step using the underlying starter integrator,<a name="line.193"></a>
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197 <FONT color="green">194</FONT> * and initializes the Nordsieck vector at step start. The starter integrator<a name="line.194"></a>
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198 <FONT color="green">195</FONT> * purpose is only to establish initial conditions, it does not really change<a name="line.195"></a>
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199 <FONT color="green">196</FONT> * time by itself. The top level multistep integrator remains in charge of<a name="line.196"></a>
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200 <FONT color="green">197</FONT> * handling time propagation and events handling as it will starts its own<a name="line.197"></a>
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201 <FONT color="green">198</FONT> * computation right from the beginning. In a sense, the starter integrator<a name="line.198"></a>
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202 <FONT color="green">199</FONT> * can be seen as a dummy one and so it will never trigger any user event nor<a name="line.199"></a>
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203 <FONT color="green">200</FONT> * call any user step handler.</p><a name="line.200"></a>
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204 <FONT color="green">201</FONT> * @param t0 initial time<a name="line.201"></a>
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205 <FONT color="green">202</FONT> * @param y0 initial value of the state vector at t0<a name="line.202"></a>
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206 <FONT color="green">203</FONT> * @param t target time for the integration<a name="line.203"></a>
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207 <FONT color="green">204</FONT> * (can be set to a value smaller than <code>t0</code> for backward integration)<a name="line.204"></a>
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208 <FONT color="green">205</FONT> * @throws IntegratorException if the integrator cannot perform integration<a name="line.205"></a>
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209 <FONT color="green">206</FONT> * @throws DerivativeException this exception is propagated to the caller if<a name="line.206"></a>
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210 <FONT color="green">207</FONT> * the underlying user function triggers one<a name="line.207"></a>
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211 <FONT color="green">208</FONT> */<a name="line.208"></a>
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212 <FONT color="green">209</FONT> protected void start(final double t0, final double[] y0, final double t)<a name="line.209"></a>
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213 <FONT color="green">210</FONT> throws DerivativeException, IntegratorException {<a name="line.210"></a>
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214 <FONT color="green">211</FONT> <a name="line.211"></a>
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215 <FONT color="green">212</FONT> // make sure NO user event nor user step handler is triggered,<a name="line.212"></a>
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216 <FONT color="green">213</FONT> // this is the task of the top level integrator, not the task<a name="line.213"></a>
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217 <FONT color="green">214</FONT> // of the starter integrator<a name="line.214"></a>
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218 <FONT color="green">215</FONT> starter.clearEventHandlers();<a name="line.215"></a>
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219 <FONT color="green">216</FONT> starter.clearStepHandlers();<a name="line.216"></a>
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220 <FONT color="green">217</FONT> <a name="line.217"></a>
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221 <FONT color="green">218</FONT> // set up one specific step handler to extract initial Nordsieck vector<a name="line.218"></a>
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222 <FONT color="green">219</FONT> starter.addStepHandler(new NordsieckInitializer(y0.length));<a name="line.219"></a>
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223 <FONT color="green">220</FONT> <a name="line.220"></a>
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224 <FONT color="green">221</FONT> // start integration, expecting a InitializationCompletedMarkerException<a name="line.221"></a>
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225 <FONT color="green">222</FONT> try {<a name="line.222"></a>
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226 <FONT color="green">223</FONT> starter.integrate(new CountingDifferentialEquations(y0.length),<a name="line.223"></a>
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227 <FONT color="green">224</FONT> t0, y0, t, new double[y0.length]);<a name="line.224"></a>
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228 <FONT color="green">225</FONT> } catch (DerivativeException de) {<a name="line.225"></a>
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229 <FONT color="green">226</FONT> if (!(de instanceof InitializationCompletedMarkerException)) {<a name="line.226"></a>
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230 <FONT color="green">227</FONT> // this is not the expected nominal interruption of the start integrator<a name="line.227"></a>
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231 <FONT color="green">228</FONT> throw de;<a name="line.228"></a>
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232 <FONT color="green">229</FONT> }<a name="line.229"></a>
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233 <FONT color="green">230</FONT> }<a name="line.230"></a>
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234 <FONT color="green">231</FONT> <a name="line.231"></a>
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235 <FONT color="green">232</FONT> // remove the specific step handler<a name="line.232"></a>
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236 <FONT color="green">233</FONT> starter.clearStepHandlers();<a name="line.233"></a>
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237 <FONT color="green">234</FONT> <a name="line.234"></a>
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238 <FONT color="green">235</FONT> }<a name="line.235"></a>
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239 <FONT color="green">236</FONT> <a name="line.236"></a>
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240 <FONT color="green">237</FONT> /** Initialize the high order scaled derivatives at step start.<a name="line.237"></a>
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241 <FONT color="green">238</FONT> * @param first first scaled derivative at step start<a name="line.238"></a>
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242 <FONT color="green">239</FONT> * @param multistep scaled derivatives after step start (hy'1, ..., hy'k-1)<a name="line.239"></a>
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243 <FONT color="green">240</FONT> * will be modified<a name="line.240"></a>
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244 <FONT color="green">241</FONT> * @return high order scaled derivatives at step start<a name="line.241"></a>
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245 <FONT color="green">242</FONT> */<a name="line.242"></a>
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246 <FONT color="green">243</FONT> protected abstract Array2DRowRealMatrix initializeHighOrderDerivatives(final double[] first,<a name="line.243"></a>
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247 <FONT color="green">244</FONT> final double[][] multistep);<a name="line.244"></a>
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248 <FONT color="green">245</FONT> <a name="line.245"></a>
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249 <FONT color="green">246</FONT> /** Get the minimal reduction factor for stepsize control.<a name="line.246"></a>
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250 <FONT color="green">247</FONT> * @return minimal reduction factor<a name="line.247"></a>
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251 <FONT color="green">248</FONT> */<a name="line.248"></a>
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252 <FONT color="green">249</FONT> public double getMinReduction() {<a name="line.249"></a>
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253 <FONT color="green">250</FONT> return minReduction;<a name="line.250"></a>
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254 <FONT color="green">251</FONT> }<a name="line.251"></a>
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255 <FONT color="green">252</FONT> <a name="line.252"></a>
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256 <FONT color="green">253</FONT> /** Set the minimal reduction factor for stepsize control.<a name="line.253"></a>
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257 <FONT color="green">254</FONT> * @param minReduction minimal reduction factor<a name="line.254"></a>
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258 <FONT color="green">255</FONT> */<a name="line.255"></a>
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259 <FONT color="green">256</FONT> public void setMinReduction(final double minReduction) {<a name="line.256"></a>
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260 <FONT color="green">257</FONT> this.minReduction = minReduction;<a name="line.257"></a>
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261 <FONT color="green">258</FONT> }<a name="line.258"></a>
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262 <FONT color="green">259</FONT> <a name="line.259"></a>
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263 <FONT color="green">260</FONT> /** Get the maximal growth factor for stepsize control.<a name="line.260"></a>
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264 <FONT color="green">261</FONT> * @return maximal growth factor<a name="line.261"></a>
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265 <FONT color="green">262</FONT> */<a name="line.262"></a>
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266 <FONT color="green">263</FONT> public double getMaxGrowth() {<a name="line.263"></a>
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267 <FONT color="green">264</FONT> return maxGrowth;<a name="line.264"></a>
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268 <FONT color="green">265</FONT> }<a name="line.265"></a>
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269 <FONT color="green">266</FONT> <a name="line.266"></a>
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270 <FONT color="green">267</FONT> /** Set the maximal growth factor for stepsize control.<a name="line.267"></a>
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271 <FONT color="green">268</FONT> * @param maxGrowth maximal growth factor<a name="line.268"></a>
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272 <FONT color="green">269</FONT> */<a name="line.269"></a>
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273 <FONT color="green">270</FONT> public void setMaxGrowth(final double maxGrowth) {<a name="line.270"></a>
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274 <FONT color="green">271</FONT> this.maxGrowth = maxGrowth;<a name="line.271"></a>
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275 <FONT color="green">272</FONT> }<a name="line.272"></a>
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276 <FONT color="green">273</FONT> <a name="line.273"></a>
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277 <FONT color="green">274</FONT> /** Get the safety factor for stepsize control.<a name="line.274"></a>
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278 <FONT color="green">275</FONT> * @return safety factor<a name="line.275"></a>
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279 <FONT color="green">276</FONT> */<a name="line.276"></a>
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280 <FONT color="green">277</FONT> public double getSafety() {<a name="line.277"></a>
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281 <FONT color="green">278</FONT> return safety;<a name="line.278"></a>
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282 <FONT color="green">279</FONT> }<a name="line.279"></a>
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283 <FONT color="green">280</FONT> <a name="line.280"></a>
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284 <FONT color="green">281</FONT> /** Set the safety factor for stepsize control.<a name="line.281"></a>
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285 <FONT color="green">282</FONT> * @param safety safety factor<a name="line.282"></a>
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286 <FONT color="green">283</FONT> */<a name="line.283"></a>
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287 <FONT color="green">284</FONT> public void setSafety(final double safety) {<a name="line.284"></a>
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288 <FONT color="green">285</FONT> this.safety = safety;<a name="line.285"></a>
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289 <FONT color="green">286</FONT> }<a name="line.286"></a>
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290 <FONT color="green">287</FONT> <a name="line.287"></a>
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291 <FONT color="green">288</FONT> /** Compute step grow/shrink factor according to normalized error.<a name="line.288"></a>
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292 <FONT color="green">289</FONT> * @param error normalized error of the current step<a name="line.289"></a>
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293 <FONT color="green">290</FONT> * @return grow/shrink factor for next step<a name="line.290"></a>
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294 <FONT color="green">291</FONT> */<a name="line.291"></a>
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295 <FONT color="green">292</FONT> protected double computeStepGrowShrinkFactor(final double error) {<a name="line.292"></a>
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296 <FONT color="green">293</FONT> return Math.min(maxGrowth, Math.max(minReduction, safety * Math.pow(error, exp)));<a name="line.293"></a>
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297 <FONT color="green">294</FONT> }<a name="line.294"></a>
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298 <FONT color="green">295</FONT> <a name="line.295"></a>
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299 <FONT color="green">296</FONT> /** Transformer used to convert the first step to Nordsieck representation. */<a name="line.296"></a>
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300 <FONT color="green">297</FONT> public static interface NordsieckTransformer {<a name="line.297"></a>
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301 <FONT color="green">298</FONT> /** Initialize the high order scaled derivatives at step start.<a name="line.298"></a>
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302 <FONT color="green">299</FONT> * @param first first scaled derivative at step start<a name="line.299"></a>
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|
303 <FONT color="green">300</FONT> * @param multistep scaled derivatives after step start (hy'1, ..., hy'k-1)<a name="line.300"></a>
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304 <FONT color="green">301</FONT> * will be modified<a name="line.301"></a>
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305 <FONT color="green">302</FONT> * @return high order derivatives at step start<a name="line.302"></a>
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|
306 <FONT color="green">303</FONT> */<a name="line.303"></a>
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|
307 <FONT color="green">304</FONT> RealMatrix initializeHighOrderDerivatives(double[] first, double[][] multistep);<a name="line.304"></a>
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308 <FONT color="green">305</FONT> }<a name="line.305"></a>
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309 <FONT color="green">306</FONT> <a name="line.306"></a>
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310 <FONT color="green">307</FONT> /** Specialized step handler storing the first step. */<a name="line.307"></a>
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|
311 <FONT color="green">308</FONT> private class NordsieckInitializer implements StepHandler {<a name="line.308"></a>
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312 <FONT color="green">309</FONT> <a name="line.309"></a>
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|
313 <FONT color="green">310</FONT> /** Problem dimension. */<a name="line.310"></a>
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|
314 <FONT color="green">311</FONT> private final int n;<a name="line.311"></a>
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|
315 <FONT color="green">312</FONT> <a name="line.312"></a>
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316 <FONT color="green">313</FONT> /** Simple constructor.<a name="line.313"></a>
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317 <FONT color="green">314</FONT> * @param n problem dimension<a name="line.314"></a>
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318 <FONT color="green">315</FONT> */<a name="line.315"></a>
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319 <FONT color="green">316</FONT> public NordsieckInitializer(final int n) {<a name="line.316"></a>
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320 <FONT color="green">317</FONT> this.n = n;<a name="line.317"></a>
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321 <FONT color="green">318</FONT> }<a name="line.318"></a>
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|
322 <FONT color="green">319</FONT> <a name="line.319"></a>
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|
323 <FONT color="green">320</FONT> /** {@inheritDoc} */<a name="line.320"></a>
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|
324 <FONT color="green">321</FONT> public void handleStep(StepInterpolator interpolator, boolean isLast)<a name="line.321"></a>
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|
325 <FONT color="green">322</FONT> throws DerivativeException {<a name="line.322"></a>
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326 <FONT color="green">323</FONT> <a name="line.323"></a>
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327 <FONT color="green">324</FONT> final double prev = interpolator.getPreviousTime();<a name="line.324"></a>
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|
328 <FONT color="green">325</FONT> final double curr = interpolator.getCurrentTime();<a name="line.325"></a>
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329 <FONT color="green">326</FONT> stepStart = prev;<a name="line.326"></a>
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330 <FONT color="green">327</FONT> stepSize = (curr - prev) / (nSteps + 1);<a name="line.327"></a>
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331 <FONT color="green">328</FONT> <a name="line.328"></a>
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332 <FONT color="green">329</FONT> // compute the first scaled derivative<a name="line.329"></a>
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|
333 <FONT color="green">330</FONT> interpolator.setInterpolatedTime(prev);<a name="line.330"></a>
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|
334 <FONT color="green">331</FONT> scaled = interpolator.getInterpolatedDerivatives().clone();<a name="line.331"></a>
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|
335 <FONT color="green">332</FONT> for (int j = 0; j < n; ++j) {<a name="line.332"></a>
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336 <FONT color="green">333</FONT> scaled[j] *= stepSize;<a name="line.333"></a>
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337 <FONT color="green">334</FONT> }<a name="line.334"></a>
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338 <FONT color="green">335</FONT> <a name="line.335"></a>
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339 <FONT color="green">336</FONT> // compute the high order scaled derivatives<a name="line.336"></a>
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|
340 <FONT color="green">337</FONT> final double[][] multistep = new double[nSteps][];<a name="line.337"></a>
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|
341 <FONT color="green">338</FONT> for (int i = 1; i <= nSteps; ++i) {<a name="line.338"></a>
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342 <FONT color="green">339</FONT> interpolator.setInterpolatedTime(prev + stepSize * i);<a name="line.339"></a>
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|
343 <FONT color="green">340</FONT> final double[] msI = interpolator.getInterpolatedDerivatives().clone();<a name="line.340"></a>
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|
344 <FONT color="green">341</FONT> for (int j = 0; j < n; ++j) {<a name="line.341"></a>
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345 <FONT color="green">342</FONT> msI[j] *= stepSize;<a name="line.342"></a>
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346 <FONT color="green">343</FONT> }<a name="line.343"></a>
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347 <FONT color="green">344</FONT> multistep[i - 1] = msI;<a name="line.344"></a>
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348 <FONT color="green">345</FONT> }<a name="line.345"></a>
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|
349 <FONT color="green">346</FONT> nordsieck = initializeHighOrderDerivatives(scaled, multistep);<a name="line.346"></a>
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350 <FONT color="green">347</FONT> <a name="line.347"></a>
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|
351 <FONT color="green">348</FONT> // stop the integrator after the first step has been handled<a name="line.348"></a>
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|
352 <FONT color="green">349</FONT> throw new InitializationCompletedMarkerException();<a name="line.349"></a>
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|
353 <FONT color="green">350</FONT> <a name="line.350"></a>
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354 <FONT color="green">351</FONT> }<a name="line.351"></a>
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355 <FONT color="green">352</FONT> <a name="line.352"></a>
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|
356 <FONT color="green">353</FONT> /** {@inheritDoc} */<a name="line.353"></a>
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|
357 <FONT color="green">354</FONT> public boolean requiresDenseOutput() {<a name="line.354"></a>
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|
358 <FONT color="green">355</FONT> return true;<a name="line.355"></a>
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|
359 <FONT color="green">356</FONT> }<a name="line.356"></a>
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|
360 <FONT color="green">357</FONT> <a name="line.357"></a>
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|
361 <FONT color="green">358</FONT> /** {@inheritDoc} */<a name="line.358"></a>
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|
362 <FONT color="green">359</FONT> public void reset() {<a name="line.359"></a>
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|
363 <FONT color="green">360</FONT> // nothing to do<a name="line.360"></a>
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|
364 <FONT color="green">361</FONT> }<a name="line.361"></a>
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|
365 <FONT color="green">362</FONT> <a name="line.362"></a>
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366 <FONT color="green">363</FONT> }<a name="line.363"></a>
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|
367 <FONT color="green">364</FONT> <a name="line.364"></a>
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|
368 <FONT color="green">365</FONT> /** Marker exception used ONLY to stop the starter integrator after first step. */<a name="line.365"></a>
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|
369 <FONT color="green">366</FONT> private static class InitializationCompletedMarkerException<a name="line.366"></a>
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|
370 <FONT color="green">367</FONT> extends DerivativeException {<a name="line.367"></a>
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|
371 <FONT color="green">368</FONT> <a name="line.368"></a>
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|
372 <FONT color="green">369</FONT> /** Serializable version identifier. */<a name="line.369"></a>
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|
373 <FONT color="green">370</FONT> private static final long serialVersionUID = -4105805787353488365L;<a name="line.370"></a>
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374 <FONT color="green">371</FONT> <a name="line.371"></a>
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|
375 <FONT color="green">372</FONT> /** Simple constructor. */<a name="line.372"></a>
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|
376 <FONT color="green">373</FONT> public InitializationCompletedMarkerException() {<a name="line.373"></a>
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|
377 <FONT color="green">374</FONT> super((Throwable) null);<a name="line.374"></a>
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378 <FONT color="green">375</FONT> }<a name="line.375"></a>
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379 <FONT color="green">376</FONT> <a name="line.376"></a>
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380 <FONT color="green">377</FONT> }<a name="line.377"></a>
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381 <FONT color="green">378</FONT> <a name="line.378"></a>
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382 <FONT color="green">379</FONT> /** Wrapper for differential equations, ensuring start evaluations are counted. */<a name="line.379"></a>
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|
383 <FONT color="green">380</FONT> private class CountingDifferentialEquations implements FirstOrderDifferentialEquations {<a name="line.380"></a>
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|
384 <FONT color="green">381</FONT> <a name="line.381"></a>
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|
385 <FONT color="green">382</FONT> /** Dimension of the problem. */<a name="line.382"></a>
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|
386 <FONT color="green">383</FONT> private final int dimension;<a name="line.383"></a>
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|
387 <FONT color="green">384</FONT> <a name="line.384"></a>
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|
388 <FONT color="green">385</FONT> /** Simple constructor.<a name="line.385"></a>
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|
389 <FONT color="green">386</FONT> * @param dimension dimension of the problem<a name="line.386"></a>
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|
390 <FONT color="green">387</FONT> */<a name="line.387"></a>
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|
391 <FONT color="green">388</FONT> public CountingDifferentialEquations(final int dimension) {<a name="line.388"></a>
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|
392 <FONT color="green">389</FONT> this.dimension = dimension;<a name="line.389"></a>
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|
393 <FONT color="green">390</FONT> }<a name="line.390"></a>
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|
394 <FONT color="green">391</FONT> <a name="line.391"></a>
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|
395 <FONT color="green">392</FONT> /** {@inheritDoc} */<a name="line.392"></a>
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|
396 <FONT color="green">393</FONT> public void computeDerivatives(double t, double[] y, double[] dot)<a name="line.393"></a>
|
|
|
397 <FONT color="green">394</FONT> throws DerivativeException {<a name="line.394"></a>
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|
398 <FONT color="green">395</FONT> MultistepIntegrator.this.computeDerivatives(t, y, dot);<a name="line.395"></a>
|
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|
399 <FONT color="green">396</FONT> }<a name="line.396"></a>
|
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|
400 <FONT color="green">397</FONT> <a name="line.397"></a>
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|
401 <FONT color="green">398</FONT> /** {@inheritDoc} */<a name="line.398"></a>
|
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|
402 <FONT color="green">399</FONT> public int getDimension() {<a name="line.399"></a>
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|
|
403 <FONT color="green">400</FONT> return dimension;<a name="line.400"></a>
|
|
|
404 <FONT color="green">401</FONT> }<a name="line.401"></a>
|
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|
405 <FONT color="green">402</FONT> }<a name="line.402"></a>
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|
406 <FONT color="green">403</FONT> <a name="line.403"></a>
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|
407 <FONT color="green">404</FONT> }<a name="line.404"></a>
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408
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409
|
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410
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411
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412
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468 </PRE>
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469 </BODY>
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470 </HTML>
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