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8 MultistepIntegrator (Commons Math 2.1 API)
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60 <A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.NordsieckTransformer.html" title="interface in org.apache.commons.math.ode"><B>NEXT CLASS</B></A></FONT></TD>
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90 <H2>
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91 <FONT SIZE="-1">
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92 org.apache.commons.math.ode</FONT>
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93 <BR>
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94 Class MultistepIntegrator</H2>
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95 <PRE>
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96 <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
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97 <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html" title="class in org.apache.commons.math.ode">org.apache.commons.math.ode.AbstractIntegrator</A>
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98 <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math.ode.nonstiff">org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator</A>
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99 <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math.ode.MultistepIntegrator</B>
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100 </PRE>
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101 <DL>
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102 <DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../org/apache/commons/math/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math.ode">FirstOrderIntegrator</A>, <A HREF="../../../../../org/apache/commons/math/ode/ODEIntegrator.html" title="interface in org.apache.commons.math.ode">ODEIntegrator</A></DD>
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103 </DL>
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104 <DL>
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105 <DT><B>Direct Known Subclasses:</B> <DD><A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math.ode.nonstiff">AdamsIntegrator</A></DD>
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106 </DL>
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107 <HR>
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108 <DL>
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109 <DT><PRE>public abstract class <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.59"><B>MultistepIntegrator</B></A><DT>extends <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math.ode.nonstiff">AdaptiveStepsizeIntegrator</A></DL>
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110 </PRE>
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111
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112 <P>
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113 This class is the base class for multistep integrators for Ordinary
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114 Differential Equations.
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115 <p>We define scaled derivatives s<sub>i</sub>(n) at step n as:
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116 <pre>
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117 s<sub>1</sub>(n) = h y'<sub>n</sub> for first derivative
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118 s<sub>2</sub>(n) = h<sup>2</sup>/2 y''<sub>n</sub> for second derivative
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119 s<sub>3</sub>(n) = h<sup>3</sup>/6 y'''<sub>n</sub> for third derivative
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120 ...
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121 s<sub>k</sub>(n) = h<sup>k</sup>/k! y(k)<sub>n</sub> for k<sup>th</sup> derivative
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122 </pre></p>
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123 <p>Rather than storing several previous steps separately, this implementation uses
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124 the Nordsieck vector with higher degrees scaled derivatives all taken at the same
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125 step (y<sub>n</sub>, s<sub>1</sub>(n) and r<sub>n</sub>) where r<sub>n</sub> is defined as:
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126 <pre>
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127 r<sub>n</sub> = [ s<sub>2</sub>(n), s<sub>3</sub>(n) ... s<sub>k</sub>(n) ]<sup>T</sup>
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128 </pre>
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129 (we omit the k index in the notation for clarity)</p>
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130 <p>
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131 Multistep integrators with Nordsieck representation are highly sensitive to
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132 large step changes because when the step is multiplied by a factor a, the
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133 k<sup>th</sup> component of the Nordsieck vector is multiplied by a<sup>k</sup>
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134 and the last components are the least accurate ones. The default max growth
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135 factor is therefore set to a quite low value: 2<sup>1/order</sup>.
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136 </p>
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137 <P>
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138
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139 <P>
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140 <DL>
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141 <DT><B>Since:</B></DT>
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142 <DD>2.0</DD>
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143 <DT><B>Version:</B></DT>
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144 <DD>$Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $</DD>
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145 <DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdamsBashforthIntegrator.html" title="class in org.apache.commons.math.ode.nonstiff"><CODE>AdamsBashforthIntegrator</CODE></A>,
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146 <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdamsMoultonIntegrator.html" title="class in org.apache.commons.math.ode.nonstiff"><CODE>AdamsMoultonIntegrator</CODE></A></DL>
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147 <HR>
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148
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149 <P>
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150 <!-- ======== NESTED CLASS SUMMARY ======== -->
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151
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152 <A NAME="nested_class_summary"><!-- --></A>
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153 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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154 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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155 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
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156 <B>Nested Class Summary</B></FONT></TH>
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157 </TR>
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158 <TR BGCOLOR="white" CLASS="TableRowColor">
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159 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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160 <CODE>static interface</CODE></FONT></TD>
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161 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.NordsieckTransformer.html" title="interface in org.apache.commons.math.ode">MultistepIntegrator.NordsieckTransformer</A></B></CODE>
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162
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163 <BR>
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164 Transformer used to convert the first step to Nordsieck representation.</TD>
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165 </TR>
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166 </TABLE>
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167 <!-- =========== FIELD SUMMARY =========== -->
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168
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169 <A NAME="field_summary"><!-- --></A>
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170 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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171 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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172 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
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173 <B>Field Summary</B></FONT></TH>
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174 </TR>
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175 <TR BGCOLOR="white" CLASS="TableRowColor">
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176 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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177 <CODE>protected <A HREF="../../../../../org/apache/commons/math/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math.linear">Array2DRowRealMatrix</A></CODE></FONT></TD>
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178 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#nordsieck">nordsieck</A></B></CODE>
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179
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180 <BR>
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181 Nordsieck matrix of the higher scaled derivatives.</TD>
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182 </TR>
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183 <TR BGCOLOR="white" CLASS="TableRowColor">
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184 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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185 <CODE>protected double[]</CODE></FONT></TD>
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186 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#scaled">scaled</A></B></CODE>
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187
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188 <BR>
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189 First scaled derivative (h y').</TD>
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190 </TR>
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191 </TABLE>
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192 <A NAME="fields_inherited_from_class_org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator"><!-- --></A>
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193 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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194 <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
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195 <TH ALIGN="left"><B>Fields inherited from class org.apache.commons.math.ode.nonstiff.<A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math.ode.nonstiff">AdaptiveStepsizeIntegrator</A></B></TH>
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196 </TR>
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197 <TR BGCOLOR="white" CLASS="TableRowColor">
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198 <TD><CODE><A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalAbsoluteTolerance">scalAbsoluteTolerance</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalRelativeTolerance">scalRelativeTolerance</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecAbsoluteTolerance">vecAbsoluteTolerance</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecRelativeTolerance">vecRelativeTolerance</A></CODE></TD>
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199 </TR>
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200 </TABLE>
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201 <A NAME="fields_inherited_from_class_org.apache.commons.math.ode.AbstractIntegrator"><!-- --></A>
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202 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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203 <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
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204 <TH ALIGN="left"><B>Fields inherited from class org.apache.commons.math.ode.<A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html" title="class in org.apache.commons.math.ode">AbstractIntegrator</A></B></TH>
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205 </TR>
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206 <TR BGCOLOR="white" CLASS="TableRowColor">
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207 <TD><CODE><A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#eventsHandlersManager">eventsHandlersManager</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#stepHandlers">stepHandlers</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#stepSize">stepSize</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#stepStart">stepStart</A></CODE></TD>
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208 </TR>
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209 </TABLE>
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210
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211 <!-- ======== CONSTRUCTOR SUMMARY ======== -->
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212
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213 <A NAME="constructor_summary"><!-- --></A>
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214 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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215 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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216 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
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217 <B>Constructor Summary</B></FONT></TH>
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218 </TR>
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219 <TR BGCOLOR="white" CLASS="TableRowColor">
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220 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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221 <CODE>protected </CODE></FONT></TD>
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222 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#MultistepIntegrator(java.lang.String, int, int, double, double, double[], double[])">MultistepIntegrator</A></B>(<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A> name,
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223 int nSteps,
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224 int order,
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225 double minStep,
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226 double maxStep,
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227 double[] vecAbsoluteTolerance,
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228 double[] vecRelativeTolerance)</CODE>
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229
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230 <BR>
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231 Build a multistep integrator with the given stepsize bounds.</TD>
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232 </TR>
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233 <TR BGCOLOR="white" CLASS="TableRowColor">
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234 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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235 <CODE>protected </CODE></FONT></TD>
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236 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#MultistepIntegrator(java.lang.String, int, int, double, double, double, double)">MultistepIntegrator</A></B>(<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A> name,
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237 int nSteps,
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238 int order,
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239 double minStep,
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240 double maxStep,
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241 double scalAbsoluteTolerance,
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242 double scalRelativeTolerance)</CODE>
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243
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244 <BR>
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245 Build a multistep integrator with the given stepsize bounds.</TD>
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246 </TR>
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247 </TABLE>
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248
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249 <!-- ========== METHOD SUMMARY =========== -->
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250
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251 <A NAME="method_summary"><!-- --></A>
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252 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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253 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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254 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
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255 <B>Method Summary</B></FONT></TH>
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256 </TR>
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257 <TR BGCOLOR="white" CLASS="TableRowColor">
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258 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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259 <CODE>protected double</CODE></FONT></TD>
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260 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#computeStepGrowShrinkFactor(double)">computeStepGrowShrinkFactor</A></B>(double error)</CODE>
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261
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262 <BR>
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263 Compute step grow/shrink factor according to normalized error.</TD>
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264 </TR>
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265 <TR BGCOLOR="white" CLASS="TableRowColor">
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266 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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267 <CODE> double</CODE></FONT></TD>
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268 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#getMaxGrowth()">getMaxGrowth</A></B>()</CODE>
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269
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270 <BR>
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271 Get the maximal growth factor for stepsize control.</TD>
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272 </TR>
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273 <TR BGCOLOR="white" CLASS="TableRowColor">
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274 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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275 <CODE> double</CODE></FONT></TD>
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276 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#getMinReduction()">getMinReduction</A></B>()</CODE>
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277
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278 <BR>
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279 Get the minimal reduction factor for stepsize control.</TD>
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280 </TR>
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281 <TR BGCOLOR="white" CLASS="TableRowColor">
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282 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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283 <CODE> double</CODE></FONT></TD>
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284 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#getSafety()">getSafety</A></B>()</CODE>
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285
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286 <BR>
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287 Get the safety factor for stepsize control.</TD>
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288 </TR>
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289 <TR BGCOLOR="white" CLASS="TableRowColor">
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290 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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291 <CODE> <A HREF="../../../../../org/apache/commons/math/ode/ODEIntegrator.html" title="interface in org.apache.commons.math.ode">ODEIntegrator</A></CODE></FONT></TD>
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292 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#getStarterIntegrator()">getStarterIntegrator</A></B>()</CODE>
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293
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294 <BR>
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295 Get the starter integrator.</TD>
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296 </TR>
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297 <TR BGCOLOR="white" CLASS="TableRowColor">
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298 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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299 <CODE>protected abstract <A HREF="../../../../../org/apache/commons/math/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math.linear">Array2DRowRealMatrix</A></CODE></FONT></TD>
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300 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#initializeHighOrderDerivatives(double[], double[][])">initializeHighOrderDerivatives</A></B>(double[] first,
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301 double[][] multistep)</CODE>
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302
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303 <BR>
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304 Initialize the high order scaled derivatives at step start.</TD>
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305 </TR>
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306 <TR BGCOLOR="white" CLASS="TableRowColor">
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307 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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308 <CODE> void</CODE></FONT></TD>
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309 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#setMaxGrowth(double)">setMaxGrowth</A></B>(double maxGrowth)</CODE>
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310
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311 <BR>
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312 Set the maximal growth factor for stepsize control.</TD>
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313 </TR>
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314 <TR BGCOLOR="white" CLASS="TableRowColor">
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315 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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316 <CODE> void</CODE></FONT></TD>
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317 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#setMinReduction(double)">setMinReduction</A></B>(double minReduction)</CODE>
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318
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319 <BR>
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320 Set the minimal reduction factor for stepsize control.</TD>
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321 </TR>
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322 <TR BGCOLOR="white" CLASS="TableRowColor">
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323 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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324 <CODE> void</CODE></FONT></TD>
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325 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#setSafety(double)">setSafety</A></B>(double safety)</CODE>
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326
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327 <BR>
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328 Set the safety factor for stepsize control.</TD>
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329 </TR>
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330 <TR BGCOLOR="white" CLASS="TableRowColor">
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331 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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332 <CODE> void</CODE></FONT></TD>
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333 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#setStarterIntegrator(org.apache.commons.math.ode.FirstOrderIntegrator)">setStarterIntegrator</A></B>(<A HREF="../../../../../org/apache/commons/math/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math.ode">FirstOrderIntegrator</A> starterIntegrator)</CODE>
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334
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335 <BR>
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336 Set the starter integrator.</TD>
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337 </TR>
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338 <TR BGCOLOR="white" CLASS="TableRowColor">
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339 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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340 <CODE>protected void</CODE></FONT></TD>
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341 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#start(double, double[], double)">start</A></B>(double t0,
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342 double[] y0,
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343 double t)</CODE>
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344
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345 <BR>
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346 Start the integration.</TD>
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347 </TR>
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348 </TABLE>
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349 <A NAME="methods_inherited_from_class_org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator"><!-- --></A>
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350 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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351 <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
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352 <TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math.ode.nonstiff.<A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math.ode.nonstiff">AdaptiveStepsizeIntegrator</A></B></TH>
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353 </TR>
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354 <TR BGCOLOR="white" CLASS="TableRowColor">
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355 <TD><CODE><A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#filterStep(double, boolean, boolean)">filterStep</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getCurrentStepStart()">getCurrentStepStart</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMaxStep()">getMaxStep</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMinStep()">getMinStep</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#initializeStep(org.apache.commons.math.ode.FirstOrderDifferentialEquations, boolean, int, double[], double, double[], double[], double[], double[])">initializeStep</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#integrate(org.apache.commons.math.ode.FirstOrderDifferentialEquations, double, double[], double, double[])">integrate</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#resetInternalState()">resetInternalState</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#sanityChecks(org.apache.commons.math.ode.FirstOrderDifferentialEquations, double, double[], double, double[])">sanityChecks</A>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setInitialStepSize(double)">setInitialStepSize</A></CODE></TD>
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356 </TR>
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357 </TABLE>
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358 <A NAME="methods_inherited_from_class_org.apache.commons.math.ode.AbstractIntegrator"><!-- --></A>
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359 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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360 <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
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361 <TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math.ode.<A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html" title="class in org.apache.commons.math.ode">AbstractIntegrator</A></B></TH>
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362 </TR>
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363 <TR BGCOLOR="white" CLASS="TableRowColor">
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364 <TD><CODE><A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#addEndTimeChecker(double, double, org.apache.commons.math.ode.events.CombinedEventsManager)">addEndTimeChecker</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#addEventHandler(org.apache.commons.math.ode.events.EventHandler, double, double, int)">addEventHandler</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#addStepHandler(org.apache.commons.math.ode.sampling.StepHandler)">addStepHandler</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#clearEventHandlers()">clearEventHandlers</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#clearStepHandlers()">clearStepHandlers</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#computeDerivatives(double, double[], double[])">computeDerivatives</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#getCurrentSignedStepsize()">getCurrentSignedStepsize</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#getEvaluations()">getEvaluations</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#getEventHandlers()">getEventHandlers</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#getMaxEvaluations()">getMaxEvaluations</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#getName()">getName</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#getStepHandlers()">getStepHandlers</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#requiresDenseOutput()">requiresDenseOutput</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#resetEvaluations()">resetEvaluations</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#setEquations(org.apache.commons.math.ode.FirstOrderDifferentialEquations)">setEquations</A>, <A HREF="../../../../../org/apache/commons/math/ode/AbstractIntegrator.html#setMaxEvaluations(int)">setMaxEvaluations</A></CODE></TD>
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365 </TR>
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366 </TABLE>
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367 <A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
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368 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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369 <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
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370 <TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
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371 </TR>
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372 <TR BGCOLOR="white" CLASS="TableRowColor">
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373 <TD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
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374 </TR>
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375 </TABLE>
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376
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377 <P>
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378
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379 <!-- ============ FIELD DETAIL =========== -->
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380
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381 <A NAME="field_detail"><!-- --></A>
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382 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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383 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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384 <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
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385 <B>Field Detail</B></FONT></TH>
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386 </TR>
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387 </TABLE>
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388
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389 <A NAME="scaled"><!-- --></A><H3>
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390 scaled</H3>
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391 <PRE>
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392 protected double[] <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.62"><B>scaled</B></A></PRE>
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393 <DL>
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394 <DD>First scaled derivative (h y').
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395 <P>
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396 <DL>
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397 </DL>
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398 </DL>
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399 <HR>
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400
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401 <A NAME="nordsieck"><!-- --></A><H3>
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402 nordsieck</H3>
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403 <PRE>
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404 protected <A HREF="../../../../../org/apache/commons/math/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math.linear">Array2DRowRealMatrix</A> <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.67"><B>nordsieck</B></A></PRE>
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405 <DL>
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406 <DD>Nordsieck matrix of the higher scaled derivatives.
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407 <p>(h<sup>2</sup>/2 y'', h<sup>3</sup>/6 y''' ..., h<sup>k</sup>/k! y(k))</p>
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408 <P>
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409 <DL>
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410 </DL>
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411 </DL>
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412
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413 <!-- ========= CONSTRUCTOR DETAIL ======== -->
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414
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415 <A NAME="constructor_detail"><!-- --></A>
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416 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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417 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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418 <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
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419 <B>Constructor Detail</B></FONT></TH>
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420 </TR>
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421 </TABLE>
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422
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423 <A NAME="MultistepIntegrator(java.lang.String, int, int, double, double, double, double)"><!-- --></A><H3>
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424 MultistepIntegrator</H3>
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425 <PRE>
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426 protected <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.106"><B>MultistepIntegrator</B></A>(<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A> name,
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427 int nSteps,
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428 int order,
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429 double minStep,
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430 double maxStep,
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431 double scalAbsoluteTolerance,
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432 double scalRelativeTolerance)</PRE>
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433 <DL>
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434 <DD>Build a multistep integrator with the given stepsize bounds.
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435 <p>The default starter integrator is set to the <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.html" title="class in org.apache.commons.math.ode.nonstiff"><CODE>Dormand-Prince 8(5,3)</CODE></A> integrator with
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436 some defaults settings.</p>
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437 <p>
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438 The default max growth factor is set to a quite low value: 2<sup>1/order</sup>.
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439 </p>
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440 <P>
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441 <DL>
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442 <DT><B>Parameters:</B><DD><CODE>name</CODE> - name of the method<DD><CODE>nSteps</CODE> - number of steps of the multistep method
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443 (excluding the one being computed)<DD><CODE>order</CODE> - order of the method<DD><CODE>minStep</CODE> - minimal step (must be positive even for backward
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444 integration), the last step can be smaller than this<DD><CODE>maxStep</CODE> - maximal step (must be positive even for backward
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445 integration)<DD><CODE>scalAbsoluteTolerance</CODE> - allowed absolute error<DD><CODE>scalRelativeTolerance</CODE> - allowed relative error</DL>
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446 </DL>
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447 <HR>
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448
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449 <A NAME="MultistepIntegrator(java.lang.String, int, int, double, double, double[], double[])"><!-- --></A><H3>
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450 MultistepIntegrator</H3>
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451 <PRE>
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452 protected <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.153"><B>MultistepIntegrator</B></A>(<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A> name,
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453 int nSteps,
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454 int order,
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455 double minStep,
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456 double maxStep,
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457 double[] vecAbsoluteTolerance,
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458 double[] vecRelativeTolerance)</PRE>
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459 <DL>
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460 <DD>Build a multistep integrator with the given stepsize bounds.
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461 <p>The default starter integrator is set to the <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.html" title="class in org.apache.commons.math.ode.nonstiff"><CODE>Dormand-Prince 8(5,3)</CODE></A> integrator with
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462 some defaults settings.</p>
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463 <p>
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464 The default max growth factor is set to a quite low value: 2<sup>1/order</sup>.
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465 </p>
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466 <P>
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467 <DL>
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468 <DT><B>Parameters:</B><DD><CODE>name</CODE> - name of the method<DD><CODE>nSteps</CODE> - number of steps of the multistep method
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469 (excluding the one being computed)<DD><CODE>order</CODE> - order of the method<DD><CODE>minStep</CODE> - minimal step (must be positive even for backward
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470 integration), the last step can be smaller than this<DD><CODE>maxStep</CODE> - maximal step (must be positive even for backward
|
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471 integration)<DD><CODE>vecAbsoluteTolerance</CODE> - allowed absolute error<DD><CODE>vecRelativeTolerance</CODE> - allowed relative error</DL>
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472 </DL>
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473
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474 <!-- ============ METHOD DETAIL ========== -->
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475
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476 <A NAME="method_detail"><!-- --></A>
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477 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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478 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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479 <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
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480 <B>Method Detail</B></FONT></TH>
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481 </TR>
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482 </TABLE>
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483
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484 <A NAME="getStarterIntegrator()"><!-- --></A><H3>
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485 getStarterIntegrator</H3>
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486 <PRE>
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487 public <A HREF="../../../../../org/apache/commons/math/ode/ODEIntegrator.html" title="interface in org.apache.commons.math.ode">ODEIntegrator</A> <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.177"><B>getStarterIntegrator</B></A>()</PRE>
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488 <DL>
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489 <DD>Get the starter integrator.
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490 <P>
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491 <DD><DL>
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492
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493 <DT><B>Returns:</B><DD>starter integrator</DL>
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494 </DD>
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495 </DL>
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496 <HR>
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497
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498 <A NAME="setStarterIntegrator(org.apache.commons.math.ode.FirstOrderIntegrator)"><!-- --></A><H3>
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499 setStarterIntegrator</H3>
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500 <PRE>
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501 public void <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.188"><B>setStarterIntegrator</B></A>(<A HREF="../../../../../org/apache/commons/math/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math.ode">FirstOrderIntegrator</A> starterIntegrator)</PRE>
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502 <DL>
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503 <DD>Set the starter integrator.
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504 <p>The various step and event handlers for this starter integrator
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505 will be managed automatically by the multi-step integrator. Any
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506 user configuration for these elements will be cleared before use.</p>
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507 <P>
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508 <DD><DL>
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509 <DT><B>Parameters:</B><DD><CODE>starterIntegrator</CODE> - starter integrator</DL>
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510 </DD>
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511 </DL>
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512 <HR>
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513
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514 <A NAME="start(double, double[], double)"><!-- --></A><H3>
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515 start</H3>
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516 <PRE>
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517 protected void <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.209"><B>start</B></A>(double t0,
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518 double[] y0,
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519 double t)
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520 throws <A HREF="../../../../../org/apache/commons/math/ode/DerivativeException.html" title="class in org.apache.commons.math.ode">DerivativeException</A>,
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521 <A HREF="../../../../../org/apache/commons/math/ode/IntegratorException.html" title="class in org.apache.commons.math.ode">IntegratorException</A></PRE>
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522 <DL>
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523 <DD>Start the integration.
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524 <p>This method computes one step using the underlying starter integrator,
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525 and initializes the Nordsieck vector at step start. The starter integrator
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526 purpose is only to establish initial conditions, it does not really change
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527 time by itself. The top level multistep integrator remains in charge of
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528 handling time propagation and events handling as it will starts its own
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529 computation right from the beginning. In a sense, the starter integrator
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530 can be seen as a dummy one and so it will never trigger any user event nor
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531 call any user step handler.</p>
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532 <P>
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533 <DD><DL>
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534 <DT><B>Parameters:</B><DD><CODE>t0</CODE> - initial time<DD><CODE>y0</CODE> - initial value of the state vector at t0<DD><CODE>t</CODE> - target time for the integration
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535 (can be set to a value smaller than <code>t0</code> for backward integration)
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536 <DT><B>Throws:</B>
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537 <DD><CODE><A HREF="../../../../../org/apache/commons/math/ode/IntegratorException.html" title="class in org.apache.commons.math.ode">IntegratorException</A></CODE> - if the integrator cannot perform integration
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538 <DD><CODE><A HREF="../../../../../org/apache/commons/math/ode/DerivativeException.html" title="class in org.apache.commons.math.ode">DerivativeException</A></CODE> - this exception is propagated to the caller if
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539 the underlying user function triggers one</DL>
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540 </DD>
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541 </DL>
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542 <HR>
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543
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544 <A NAME="initializeHighOrderDerivatives(double[], double[][])"><!-- --></A><H3>
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545 initializeHighOrderDerivatives</H3>
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546 <PRE>
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547 protected abstract <A HREF="../../../../../org/apache/commons/math/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math.linear">Array2DRowRealMatrix</A> <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.243"><B>initializeHighOrderDerivatives</B></A>(double[] first,
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548 double[][] multistep)</PRE>
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549 <DL>
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550 <DD>Initialize the high order scaled derivatives at step start.
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551 <P>
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552 <DD><DL>
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553 <DT><B>Parameters:</B><DD><CODE>first</CODE> - first scaled derivative at step start<DD><CODE>multistep</CODE> - scaled derivatives after step start (hy'1, ..., hy'k-1)
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554 will be modified
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555 <DT><B>Returns:</B><DD>high order scaled derivatives at step start</DL>
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556 </DD>
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557 </DL>
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558 <HR>
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559
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560 <A NAME="getMinReduction()"><!-- --></A><H3>
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561 getMinReduction</H3>
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562 <PRE>
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563 public double <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.249"><B>getMinReduction</B></A>()</PRE>
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564 <DL>
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565 <DD>Get the minimal reduction factor for stepsize control.
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566 <P>
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567 <DD><DL>
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568
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569 <DT><B>Returns:</B><DD>minimal reduction factor</DL>
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570 </DD>
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571 </DL>
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572 <HR>
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573
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574 <A NAME="setMinReduction(double)"><!-- --></A><H3>
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575 setMinReduction</H3>
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576 <PRE>
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577 public void <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.256"><B>setMinReduction</B></A>(double minReduction)</PRE>
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578 <DL>
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579 <DD>Set the minimal reduction factor for stepsize control.
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580 <P>
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581 <DD><DL>
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582 <DT><B>Parameters:</B><DD><CODE>minReduction</CODE> - minimal reduction factor</DL>
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583 </DD>
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584 </DL>
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585 <HR>
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586
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587 <A NAME="getMaxGrowth()"><!-- --></A><H3>
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588 getMaxGrowth</H3>
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589 <PRE>
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590 public double <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.263"><B>getMaxGrowth</B></A>()</PRE>
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591 <DL>
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592 <DD>Get the maximal growth factor for stepsize control.
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593 <P>
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594 <DD><DL>
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595
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596 <DT><B>Returns:</B><DD>maximal growth factor</DL>
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597 </DD>
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598 </DL>
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599 <HR>
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600
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601 <A NAME="setMaxGrowth(double)"><!-- --></A><H3>
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602 setMaxGrowth</H3>
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603 <PRE>
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604 public void <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.270"><B>setMaxGrowth</B></A>(double maxGrowth)</PRE>
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605 <DL>
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606 <DD>Set the maximal growth factor for stepsize control.
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607 <P>
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|
608 <DD><DL>
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609 <DT><B>Parameters:</B><DD><CODE>maxGrowth</CODE> - maximal growth factor</DL>
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|
610 </DD>
|
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|
611 </DL>
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612 <HR>
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613
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614 <A NAME="getSafety()"><!-- --></A><H3>
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615 getSafety</H3>
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616 <PRE>
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617 public double <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.277"><B>getSafety</B></A>()</PRE>
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618 <DL>
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619 <DD>Get the safety factor for stepsize control.
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|
620 <P>
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|
621 <DD><DL>
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|
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622
|
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|
623 <DT><B>Returns:</B><DD>safety factor</DL>
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|
624 </DD>
|
|
|
625 </DL>
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|
626 <HR>
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627
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628 <A NAME="setSafety(double)"><!-- --></A><H3>
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629 setSafety</H3>
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|
630 <PRE>
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|
|
631 public void <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.284"><B>setSafety</B></A>(double safety)</PRE>
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|
632 <DL>
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633 <DD>Set the safety factor for stepsize control.
|
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|
634 <P>
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|
|
635 <DD><DL>
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|
|
636 <DT><B>Parameters:</B><DD><CODE>safety</CODE> - safety factor</DL>
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|
637 </DD>
|
|
|
638 </DL>
|
|
|
639 <HR>
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640
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|
641 <A NAME="computeStepGrowShrinkFactor(double)"><!-- --></A><H3>
|
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|
642 computeStepGrowShrinkFactor</H3>
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643 <PRE>
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|
644 protected double <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.292"><B>computeStepGrowShrinkFactor</B></A>(double error)</PRE>
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|
|
645 <DL>
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|
646 <DD>Compute step grow/shrink factor according to normalized error.
|
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|
647 <P>
|
|
|
648 <DD><DL>
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|
|
649 <DT><B>Parameters:</B><DD><CODE>error</CODE> - normalized error of the current step
|
|
|
650 <DT><B>Returns:</B><DD>grow/shrink factor for next step</DL>
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651 </DD>
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652 </DL>
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653 <!-- ========= END OF CLASS DATA ========= -->
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654 <HR>
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655
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656
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657 <!-- ======= START OF BOTTOM NAVBAR ====== -->
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658 <A NAME="navbar_bottom"><!-- --></A>
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666 <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A> </TD>
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677 <TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM>
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685 <A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.NordsieckTransformer.html" title="interface in org.apache.commons.math.ode"><B>NEXT CLASS</B></A></FONT></TD>
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705 SUMMARY: <A HREF="#nested_class_summary">NESTED</A> | <A HREF="#field_summary">FIELD</A> | <A HREF="#constructor_summary">CONSTR</A> | <A HREF="#method_summary">METHOD</A></FONT></TD>
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