Mercurial > hg > de.mpg.mpiwg.itgroup.digilib.core
view libs/commons-math-2.1/docs/apidocs/org/apache/commons/math/ode/MultistepIntegrator.html @ 32:d7a43156a79b default tip
new tabs
| author | dwinter |
|---|---|
| date | Mon, 10 Oct 2011 17:52:22 +0200 |
| parents | 878723cc40fb |
| children |
line wrap: on
line source
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <!--NewPage--> <HTML> <HEAD> <!-- Generated by javadoc (build 1.6.0_17) on Sat Mar 27 22:46:14 EDT 2010 --> <META http-equiv="Content-Type" content="text/html; charset=UTF-8"> <TITLE> MultistepIntegrator (Commons Math 2.1 API) </TITLE> <META NAME="date" CONTENT="2010-03-27"> <LINK REL ="stylesheet" TYPE="text/css" HREF="../../../../../stylesheet.css" TITLE="Style"> <SCRIPT type="text/javascript"> function windowTitle() { if (location.href.indexOf('is-external=true') == -1) { parent.document.title="MultistepIntegrator (Commons Math 2.1 API)"; } } </SCRIPT> <NOSCRIPT> </NOSCRIPT> </HEAD> <BODY BGCOLOR="white" onload="windowTitle();"> <HR> <!-- ========= START OF TOP NAVBAR ======= --> <A NAME="navbar_top"><!-- --></A> <A HREF="#skip-navbar_top" title="Skip navigation links"></A> <TABLE BORDER="0" WIDTH="100%" CELLPADDING="1" CELLSPACING="0" SUMMARY=""> <TR> <TD COLSPAN=2 BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A NAME="navbar_top_firstrow"><!-- --></A> <TABLE BORDER="0" CELLPADDING="0" CELLSPACING="3" SUMMARY=""> <TR ALIGN="center" VALIGN="top"> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="package-summary.html"><FONT CLASS="NavBarFont1"><B>Package</B></FONT></A> </TD> <TD BGCOLOR="#FFFFFF" CLASS="NavBarCell1Rev"> <FONT CLASS="NavBarFont1Rev"><B>Class</B></FONT> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="class-use/MultistepIntegrator.html"><FONT CLASS="NavBarFont1"><B>Use</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="package-tree.html"><FONT CLASS="NavBarFont1"><B>Tree</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../deprecated-list.html"><FONT CLASS="NavBarFont1"><B>Deprecated</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../index-all.html"><FONT CLASS="NavBarFont1"><B>Index</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../help-doc.html"><FONT CLASS="NavBarFont1"><B>Help</B></FONT></A> </TD> </TR> </TABLE> </TD> <TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM> </EM> </TD> </TR> <TR> <TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2"> <A HREF="../../../../../org/apache/commons/math/ode/IntegratorException.html" title="class in org.apache.commons.math.ode"><B>PREV CLASS</B></A> <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> <TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2"> <A HREF="../../../../../index.html?org/apache/commons/math/ode/MultistepIntegrator.html" target="_top"><B>FRAMES</B></A> <A HREF="MultistepIntegrator.html" target="_top"><B>NO FRAMES</B></A> <SCRIPT type="text/javascript"> <!-- if(window==top) { document.writeln('<A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>'); } //--> </SCRIPT> <NOSCRIPT> <A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A> </NOSCRIPT> </FONT></TD> </TR> <TR> <TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2"> 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> <TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2"> DETAIL: <A HREF="#field_detail">FIELD</A> | <A HREF="#constructor_detail">CONSTR</A> | <A HREF="#method_detail">METHOD</A></FONT></TD> </TR> </TABLE> <A NAME="skip-navbar_top"></A> <!-- ========= END OF TOP NAVBAR ========= --> <HR> <!-- ======== START OF CLASS DATA ======== --> <H2> <FONT SIZE="-1"> org.apache.commons.math.ode</FONT> <BR> Class MultistepIntegrator</H2> <PRE> <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> <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> <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> <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math.ode.MultistepIntegrator</B> </PRE> <DL> <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> </DL> <DL> <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> </DL> <HR> <DL> <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> </PRE> <P> This class is the base class for multistep integrators for Ordinary Differential Equations. <p>We define scaled derivatives s<sub>i</sub>(n) at step n as: <pre> s<sub>1</sub>(n) = h y'<sub>n</sub> for first derivative s<sub>2</sub>(n) = h<sup>2</sup>/2 y''<sub>n</sub> for second derivative s<sub>3</sub>(n) = h<sup>3</sup>/6 y'''<sub>n</sub> for third derivative ... s<sub>k</sub>(n) = h<sup>k</sup>/k! y(k)<sub>n</sub> for k<sup>th</sup> derivative </pre></p> <p>Rather than storing several previous steps separately, this implementation uses the Nordsieck vector with higher degrees scaled derivatives all taken at the same step (y<sub>n</sub>, s<sub>1</sub>(n) and r<sub>n</sub>) where r<sub>n</sub> is defined as: <pre> r<sub>n</sub> = [ s<sub>2</sub>(n), s<sub>3</sub>(n) ... s<sub>k</sub>(n) ]<sup>T</sup> </pre> (we omit the k index in the notation for clarity)</p> <p> Multistep integrators with Nordsieck representation are highly sensitive to large step changes because when the step is multiplied by a factor a, the k<sup>th</sup> component of the Nordsieck vector is multiplied by a<sup>k</sup> and the last components are the least accurate ones. The default max growth factor is therefore set to a quite low value: 2<sup>1/order</sup>. </p> <P> <P> <DL> <DT><B>Since:</B></DT> <DD>2.0</DD> <DT><B>Version:</B></DT> <DD>$Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $</DD> <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>, <A HREF="../../../../../org/apache/commons/math/ode/nonstiff/AdamsMoultonIntegrator.html" title="class in org.apache.commons.math.ode.nonstiff"><CODE>AdamsMoultonIntegrator</CODE></A></DL> <HR> <P> <!-- ======== NESTED CLASS SUMMARY ======== --> <A NAME="nested_class_summary"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2"> <B>Nested Class Summary</B></FONT></TH> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE>static interface</CODE></FONT></TD> <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> <BR> Transformer used to convert the first step to Nordsieck representation.</TD> </TR> </TABLE> <!-- =========== FIELD SUMMARY =========== --> <A NAME="field_summary"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2"> <B>Field Summary</B></FONT></TH> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE>protected <A HREF="../../../../../org/apache/commons/math/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math.linear">Array2DRowRealMatrix</A></CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#nordsieck">nordsieck</A></B></CODE> <BR> Nordsieck matrix of the higher scaled derivatives.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE>protected double[]</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#scaled">scaled</A></B></CODE> <BR> First scaled derivative (h y').</TD> </TR> </TABLE> <A NAME="fields_inherited_from_class_org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor"> <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> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <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> </TR> </TABLE> <A NAME="fields_inherited_from_class_org.apache.commons.math.ode.AbstractIntegrator"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor"> <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> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <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> </TR> </TABLE> <!-- ======== CONSTRUCTOR SUMMARY ======== --> <A NAME="constructor_summary"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2"> <B>Constructor Summary</B></FONT></TH> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE>protected </CODE></FONT></TD> <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, int nSteps, int order, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)</CODE> <BR> Build a multistep integrator with the given stepsize bounds.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE>protected </CODE></FONT></TD> <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, int nSteps, int order, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)</CODE> <BR> Build a multistep integrator with the given stepsize bounds.</TD> </TR> </TABLE> <!-- ========== METHOD SUMMARY =========== --> <A NAME="method_summary"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2"> <B>Method Summary</B></FONT></TH> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE>protected double</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#computeStepGrowShrinkFactor(double)">computeStepGrowShrinkFactor</A></B>(double error)</CODE> <BR> Compute step grow/shrink factor according to normalized error.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> double</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#getMaxGrowth()">getMaxGrowth</A></B>()</CODE> <BR> Get the maximal growth factor for stepsize control.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> double</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#getMinReduction()">getMinReduction</A></B>()</CODE> <BR> Get the minimal reduction factor for stepsize control.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> double</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#getSafety()">getSafety</A></B>()</CODE> <BR> Get the safety factor for stepsize control.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> <A HREF="../../../../../org/apache/commons/math/ode/ODEIntegrator.html" title="interface in org.apache.commons.math.ode">ODEIntegrator</A></CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#getStarterIntegrator()">getStarterIntegrator</A></B>()</CODE> <BR> Get the starter integrator.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <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> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#initializeHighOrderDerivatives(double[], double[][])">initializeHighOrderDerivatives</A></B>(double[] first, double[][] multistep)</CODE> <BR> Initialize the high order scaled derivatives at step start.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> void</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#setMaxGrowth(double)">setMaxGrowth</A></B>(double maxGrowth)</CODE> <BR> Set the maximal growth factor for stepsize control.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> void</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#setMinReduction(double)">setMinReduction</A></B>(double minReduction)</CODE> <BR> Set the minimal reduction factor for stepsize control.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> void</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#setSafety(double)">setSafety</A></B>(double safety)</CODE> <BR> Set the safety factor for stepsize control.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> void</CODE></FONT></TD> <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> <BR> Set the starter integrator.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE>protected void</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/ode/MultistepIntegrator.html#start(double, double[], double)">start</A></B>(double t0, double[] y0, double t)</CODE> <BR> Start the integration.</TD> </TR> </TABLE> <A NAME="methods_inherited_from_class_org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor"> <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> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <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> </TR> </TABLE> <A NAME="methods_inherited_from_class_org.apache.commons.math.ode.AbstractIntegrator"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor"> <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> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <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> </TR> </TABLE> <A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor"> <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> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <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> </TR> </TABLE> <P> <!-- ============ FIELD DETAIL =========== --> <A NAME="field_detail"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2"> <B>Field Detail</B></FONT></TH> </TR> </TABLE> <A NAME="scaled"><!-- --></A><H3> scaled</H3> <PRE> protected double[] <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.62"><B>scaled</B></A></PRE> <DL> <DD>First scaled derivative (h y'). <P> <DL> </DL> </DL> <HR> <A NAME="nordsieck"><!-- --></A><H3> nordsieck</H3> <PRE> 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> <DL> <DD>Nordsieck matrix of the higher scaled derivatives. <p>(h<sup>2</sup>/2 y'', h<sup>3</sup>/6 y''' ..., h<sup>k</sup>/k! y(k))</p> <P> <DL> </DL> </DL> <!-- ========= CONSTRUCTOR DETAIL ======== --> <A NAME="constructor_detail"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2"> <B>Constructor Detail</B></FONT></TH> </TR> </TABLE> <A NAME="MultistepIntegrator(java.lang.String, int, int, double, double, double, double)"><!-- --></A><H3> MultistepIntegrator</H3> <PRE> 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, int nSteps, int order, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)</PRE> <DL> <DD>Build a multistep integrator with the given stepsize bounds. <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 some defaults settings.</p> <p> The default max growth factor is set to a quite low value: 2<sup>1/order</sup>. </p> <P> <DL> <DT><B>Parameters:</B><DD><CODE>name</CODE> - name of the method<DD><CODE>nSteps</CODE> - number of steps of the multistep method (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 integration), the last step can be smaller than this<DD><CODE>maxStep</CODE> - maximal step (must be positive even for backward integration)<DD><CODE>scalAbsoluteTolerance</CODE> - allowed absolute error<DD><CODE>scalRelativeTolerance</CODE> - allowed relative error</DL> </DL> <HR> <A NAME="MultistepIntegrator(java.lang.String, int, int, double, double, double[], double[])"><!-- --></A><H3> MultistepIntegrator</H3> <PRE> 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, int nSteps, int order, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)</PRE> <DL> <DD>Build a multistep integrator with the given stepsize bounds. <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 some defaults settings.</p> <p> The default max growth factor is set to a quite low value: 2<sup>1/order</sup>. </p> <P> <DL> <DT><B>Parameters:</B><DD><CODE>name</CODE> - name of the method<DD><CODE>nSteps</CODE> - number of steps of the multistep method (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 integration), the last step can be smaller than this<DD><CODE>maxStep</CODE> - maximal step (must be positive even for backward integration)<DD><CODE>vecAbsoluteTolerance</CODE> - allowed absolute error<DD><CODE>vecRelativeTolerance</CODE> - allowed relative error</DL> </DL> <!-- ============ METHOD DETAIL ========== --> <A NAME="method_detail"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2"> <B>Method Detail</B></FONT></TH> </TR> </TABLE> <A NAME="getStarterIntegrator()"><!-- --></A><H3> getStarterIntegrator</H3> <PRE> 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> <DL> <DD>Get the starter integrator. <P> <DD><DL> <DT><B>Returns:</B><DD>starter integrator</DL> </DD> </DL> <HR> <A NAME="setStarterIntegrator(org.apache.commons.math.ode.FirstOrderIntegrator)"><!-- --></A><H3> setStarterIntegrator</H3> <PRE> 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> <DL> <DD>Set the starter integrator. <p>The various step and event handlers for this starter integrator will be managed automatically by the multi-step integrator. Any user configuration for these elements will be cleared before use.</p> <P> <DD><DL> <DT><B>Parameters:</B><DD><CODE>starterIntegrator</CODE> - starter integrator</DL> </DD> </DL> <HR> <A NAME="start(double, double[], double)"><!-- --></A><H3> start</H3> <PRE> protected void <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.209"><B>start</B></A>(double t0, double[] y0, double t) throws <A HREF="../../../../../org/apache/commons/math/ode/DerivativeException.html" title="class in org.apache.commons.math.ode">DerivativeException</A>, <A HREF="../../../../../org/apache/commons/math/ode/IntegratorException.html" title="class in org.apache.commons.math.ode">IntegratorException</A></PRE> <DL> <DD>Start the integration. <p>This method computes one step using the underlying starter integrator, and initializes the Nordsieck vector at step start. The starter integrator purpose is only to establish initial conditions, it does not really change time by itself. The top level multistep integrator remains in charge of handling time propagation and events handling as it will starts its own computation right from the beginning. In a sense, the starter integrator can be seen as a dummy one and so it will never trigger any user event nor call any user step handler.</p> <P> <DD><DL> <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 (can be set to a value smaller than <code>t0</code> for backward integration) <DT><B>Throws:</B> <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 <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 the underlying user function triggers one</DL> </DD> </DL> <HR> <A NAME="initializeHighOrderDerivatives(double[], double[][])"><!-- --></A><H3> initializeHighOrderDerivatives</H3> <PRE> 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, double[][] multistep)</PRE> <DL> <DD>Initialize the high order scaled derivatives at step start. <P> <DD><DL> <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) will be modified <DT><B>Returns:</B><DD>high order scaled derivatives at step start</DL> </DD> </DL> <HR> <A NAME="getMinReduction()"><!-- --></A><H3> getMinReduction</H3> <PRE> public double <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.249"><B>getMinReduction</B></A>()</PRE> <DL> <DD>Get the minimal reduction factor for stepsize control. <P> <DD><DL> <DT><B>Returns:</B><DD>minimal reduction factor</DL> </DD> </DL> <HR> <A NAME="setMinReduction(double)"><!-- --></A><H3> setMinReduction</H3> <PRE> public void <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.256"><B>setMinReduction</B></A>(double minReduction)</PRE> <DL> <DD>Set the minimal reduction factor for stepsize control. <P> <DD><DL> <DT><B>Parameters:</B><DD><CODE>minReduction</CODE> - minimal reduction factor</DL> </DD> </DL> <HR> <A NAME="getMaxGrowth()"><!-- --></A><H3> getMaxGrowth</H3> <PRE> public double <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.263"><B>getMaxGrowth</B></A>()</PRE> <DL> <DD>Get the maximal growth factor for stepsize control. <P> <DD><DL> <DT><B>Returns:</B><DD>maximal growth factor</DL> </DD> </DL> <HR> <A NAME="setMaxGrowth(double)"><!-- --></A><H3> setMaxGrowth</H3> <PRE> public void <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.270"><B>setMaxGrowth</B></A>(double maxGrowth)</PRE> <DL> <DD>Set the maximal growth factor for stepsize control. <P> <DD><DL> <DT><B>Parameters:</B><DD><CODE>maxGrowth</CODE> - maximal growth factor</DL> </DD> </DL> <HR> <A NAME="getSafety()"><!-- --></A><H3> getSafety</H3> <PRE> public double <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.277"><B>getSafety</B></A>()</PRE> <DL> <DD>Get the safety factor for stepsize control. <P> <DD><DL> <DT><B>Returns:</B><DD>safety factor</DL> </DD> </DL> <HR> <A NAME="setSafety(double)"><!-- --></A><H3> setSafety</H3> <PRE> public void <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.284"><B>setSafety</B></A>(double safety)</PRE> <DL> <DD>Set the safety factor for stepsize control. <P> <DD><DL> <DT><B>Parameters:</B><DD><CODE>safety</CODE> - safety factor</DL> </DD> </DL> <HR> <A NAME="computeStepGrowShrinkFactor(double)"><!-- --></A><H3> computeStepGrowShrinkFactor</H3> <PRE> protected double <A HREF="../../../../../src-html/org/apache/commons/math/ode/MultistepIntegrator.html#line.292"><B>computeStepGrowShrinkFactor</B></A>(double error)</PRE> <DL> <DD>Compute step grow/shrink factor according to normalized error. <P> <DD><DL> <DT><B>Parameters:</B><DD><CODE>error</CODE> - normalized error of the current step <DT><B>Returns:</B><DD>grow/shrink factor for next step</DL> </DD> </DL> <!-- ========= END OF CLASS DATA ========= --> <HR> <!-- ======= START OF BOTTOM NAVBAR ====== --> <A NAME="navbar_bottom"><!-- --></A> <A HREF="#skip-navbar_bottom" title="Skip navigation links"></A> <TABLE BORDER="0" WIDTH="100%" CELLPADDING="1" CELLSPACING="0" SUMMARY=""> <TR> <TD COLSPAN=2 BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A NAME="navbar_bottom_firstrow"><!-- --></A> <TABLE BORDER="0" CELLPADDING="0" CELLSPACING="3" SUMMARY=""> <TR ALIGN="center" VALIGN="top"> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="package-summary.html"><FONT CLASS="NavBarFont1"><B>Package</B></FONT></A> </TD> <TD BGCOLOR="#FFFFFF" CLASS="NavBarCell1Rev"> <FONT CLASS="NavBarFont1Rev"><B>Class</B></FONT> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="class-use/MultistepIntegrator.html"><FONT CLASS="NavBarFont1"><B>Use</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="package-tree.html"><FONT CLASS="NavBarFont1"><B>Tree</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../deprecated-list.html"><FONT CLASS="NavBarFont1"><B>Deprecated</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../index-all.html"><FONT CLASS="NavBarFont1"><B>Index</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../help-doc.html"><FONT CLASS="NavBarFont1"><B>Help</B></FONT></A> </TD> </TR> </TABLE> </TD> <TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM> </EM> </TD> </TR> <TR> <TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2"> <A HREF="../../../../../org/apache/commons/math/ode/IntegratorException.html" title="class in org.apache.commons.math.ode"><B>PREV CLASS</B></A> <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> <TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2"> <A HREF="../../../../../index.html?org/apache/commons/math/ode/MultistepIntegrator.html" target="_top"><B>FRAMES</B></A> <A HREF="MultistepIntegrator.html" target="_top"><B>NO FRAMES</B></A> <SCRIPT type="text/javascript"> <!-- if(window==top) { document.writeln('<A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>'); } //--> </SCRIPT> <NOSCRIPT> <A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A> </NOSCRIPT> </FONT></TD> </TR> <TR> <TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2"> 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> <TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2"> DETAIL: <A HREF="#field_detail">FIELD</A> | <A HREF="#constructor_detail">CONSTR</A> | <A HREF="#method_detail">METHOD</A></FONT></TD> </TR> </TABLE> <A NAME="skip-navbar_bottom"></A> <!-- ======== END OF BOTTOM NAVBAR ======= --> <HR> Copyright © 2003-2010 <a href="http://www.apache.org/">The Apache Software Foundation</a>. All Rights Reserved. </BODY> </HTML>