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| <div class="subTitle">org.apache.commons.math3.ode.nonstiff</div> |
| <h2 title="Class GraggBulirschStoerIntegrator" class="title">Class GraggBulirschStoerIntegrator</h2> |
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| <li><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li> |
| <li> |
| <ul class="inheritance"> |
| <li><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">org.apache.commons.math3.ode.AbstractIntegrator</a></li> |
| <li> |
| <ul class="inheritance"> |
| <li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator</a></li> |
| <li> |
| <ul class="inheritance"> |
| <li>org.apache.commons.math3.ode.nonstiff.GraggBulirschStoerIntegrator</li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
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| <div class="description"> |
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| <dl> |
| <dt>All Implemented Interfaces:</dt> |
| <dd><a href="../../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</a></dd> |
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| <hr> |
| <br> |
| <pre>public class <span class="strong">GraggBulirschStoerIntegrator</span> |
| extends <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</a></pre> |
| <div class="block">This class implements a Gragg-Bulirsch-Stoer integrator for |
| Ordinary Differential Equations. |
| |
| <p>The Gragg-Bulirsch-Stoer algorithm is one of the most efficient |
| ones currently available for smooth problems. It uses Richardson |
| extrapolation to estimate what would be the solution if the step |
| size could be decreased down to zero.</p> |
| |
| <p> |
| This method changes both the step size and the order during |
| integration, in order to minimize computation cost. It is |
| particularly well suited when a very high precision is needed. The |
| limit where this method becomes more efficient than high-order |
| embedded Runge-Kutta methods like <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince853Integrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>Dormand-Prince 8(5,3)</code></a> depends on the problem. Results given in the |
| Hairer, Norsett and Wanner book show for example that this limit |
| occurs for accuracy around 1e-6 when integrating Saltzam-Lorenz |
| equations (the authors note this problem is <i>extremely sensitive |
| to the errors in the first integration steps</i>), and around 1e-11 |
| for a two dimensional celestial mechanics problems with seven |
| bodies (pleiades problem, involving quasi-collisions for which |
| <i>automatic step size control is essential</i>). |
| </p> |
| |
| <p> |
| This implementation is basically a reimplementation in Java of the |
| <a |
| href="http://www.unige.ch/math/folks/hairer/prog/nonstiff/odex.f">odex</a> |
| fortran code by E. Hairer and G. Wanner. The redistribution policy |
| for this code is available <a |
| href="http://www.unige.ch/~hairer/prog/licence.txt">here</a>, for |
| convenience, it is reproduced below.</p> |
| </p> |
| |
| <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0"> |
| <tr><td>Copyright (c) 2004, Ernst Hairer</td></tr> |
| |
| <tr><td>Redistribution and use in source and binary forms, with or |
| without modification, are permitted provided that the following |
| conditions are met: |
| <ul> |
| <li>Redistributions of source code must retain the above copyright |
| notice, this list of conditions and the following disclaimer.</li> |
| <li>Redistributions in binary form must reproduce the above copyright |
| notice, this list of conditions and the following disclaimer in the |
| documentation and/or other materials provided with the distribution.</li> |
| </ul></td></tr> |
| |
| <tr><td><strong>THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND |
| CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, |
| BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS |
| FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR |
| CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
| PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
| PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF |
| LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING |
| NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</strong></td></tr> |
| </table></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>1.2</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: GraggBulirschStoerIntegrator.java 1416643 2012-12-03 19:37:14Z tn $</dd></dl> |
| </li> |
| </ul> |
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| <li class="blockList"><a name="fields_inherited_from_class_org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator"> |
| <!-- --> |
| </a> |
| <h3>Fields inherited from class org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#mainSetDimension">mainSetDimension</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalAbsoluteTolerance">scalAbsoluteTolerance</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalRelativeTolerance">scalRelativeTolerance</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecAbsoluteTolerance">vecAbsoluteTolerance</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecRelativeTolerance">vecRelativeTolerance</a></code></li> |
| </ul> |
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| <li class="blockList"><a name="fields_inherited_from_class_org.apache.commons.math3.ode.AbstractIntegrator"> |
| <!-- --> |
| </a> |
| <h3>Fields inherited from class org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#isLastStep">isLastStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#resetOccurred">resetOccurred</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepHandlers">stepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepSize">stepSize</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepStart">stepStart</a></code></li> |
| </ul> |
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| </ul> |
| <!-- ======== CONSTRUCTOR SUMMARY ======== --> |
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| <h3>Constructor Summary</h3> |
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| <caption><span>Constructors</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colOne" scope="col">Constructor and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html#GraggBulirschStoerIntegrator(double, double, double[], double[])">GraggBulirschStoerIntegrator</a></strong>(double minStep, |
| double maxStep, |
| double[] vecAbsoluteTolerance, |
| double[] vecRelativeTolerance)</code> |
| <div class="block">Simple constructor.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html#GraggBulirschStoerIntegrator(double, double, double, double)">GraggBulirschStoerIntegrator</a></strong>(double minStep, |
| double maxStep, |
| double scalAbsoluteTolerance, |
| double scalRelativeTolerance)</code> |
| <div class="block">Simple constructor.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
| </ul> |
| <!-- ========== METHOD SUMMARY =========== --> |
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| <h3>Method Summary</h3> |
| <table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation"> |
| <caption><span>Methods</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colLast" scope="col">Method and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.EventHandler, double, double, int, org.apache.commons.math3.analysis.solvers.UnivariateSolver)">addEventHandler</a></strong>(<a href="../../../../../../org/apache/commons/math3/ode/events/EventHandler.html" title="interface in org.apache.commons.math3.ode.events">EventHandler</a> function, |
| double maxCheckInterval, |
| double convergence, |
| int maxIterationCount, |
| <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers">UnivariateSolver</a> solver)</code> |
| <div class="block">Add an event handler to the integrator.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html#addStepHandler(org.apache.commons.math3.ode.sampling.StepHandler)">addStepHandler</a></strong>(<a href="../../../../../../org/apache/commons/math3/ode/sampling/StepHandler.html" title="interface in org.apache.commons.math3.ode.sampling">StepHandler</a> handler)</code> |
| <div class="block">Add a step handler to this integrator.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">integrate</a></strong>(<a href="../../../../../../org/apache/commons/math3/ode/ExpandableStatefulODE.html" title="class in org.apache.commons.math3.ode">ExpandableStatefulODE</a> equations, |
| double t)</code> |
| <div class="block">Integrate a set of differential equations up to the given time.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html#setControlFactors(double, double, double, double)">setControlFactors</a></strong>(double control1, |
| double control2, |
| double control3, |
| double control4)</code> |
| <div class="block">Set the step size control factors.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html#setInterpolationControl(boolean, int)">setInterpolationControl</a></strong>(boolean useInterpolationErrorForControl, |
| int mudifControlParameter)</code> |
| <div class="block">Set the interpolation order control parameter.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html#setOrderControl(int, double, double)">setOrderControl</a></strong>(int maximalOrder, |
| double control1, |
| double control2)</code> |
| <div class="block">Set the order control parameters.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html#setStabilityCheck(boolean, int, int, double)">setStabilityCheck</a></strong>(boolean performStabilityCheck, |
| int maxNumIter, |
| int maxNumChecks, |
| double stepsizeReductionFactor)</code> |
| <div class="block">Set the stability check controls.</div> |
| </td> |
| </tr> |
| </table> |
| <ul class="blockList"> |
| <li class="blockList"><a name="methods_inherited_from_class_org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator"> |
| <!-- --> |
| </a> |
| <h3>Methods inherited from class org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#filterStep(double, boolean, boolean)">filterStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getCurrentStepStart()">getCurrentStepStart</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMaxStep()">getMaxStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMinStep()">getMinStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#initializeStep(boolean, int, double[], double, double[], double[], double[], double[])">initializeStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#resetInternalState()">resetInternalState</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#sanityChecks(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">sanityChecks</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setInitialStepSize(double)">setInitialStepSize</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setStepSizeControl(double, double, double[], double[])">setStepSizeControl</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setStepSizeControl(double, double, double, double)">setStepSizeControl</a></code></li> |
| </ul> |
| <ul class="blockList"> |
| <li class="blockList"><a name="methods_inherited_from_class_org.apache.commons.math3.ode.AbstractIntegrator"> |
| <!-- --> |
| </a> |
| <h3>Methods inherited from class org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#acceptStep(org.apache.commons.math3.ode.sampling.AbstractStepInterpolator, double[], double[], double)">acceptStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.EventHandler, double, double, int)">addEventHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#clearEventHandlers()">clearEventHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#clearStepHandlers()">clearStepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#computeDerivatives(double, double[], double[])">computeDerivatives</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getCurrentSignedStepsize()">getCurrentSignedStepsize</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getEvaluations()">getEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getEvaluationsCounter()">getEvaluationsCounter</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getEventHandlers()">getEventHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getExpandable()">getExpandable</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getMaxEvaluations()">getMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getName()">getName</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getStepHandlers()">getStepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#initIntegration(double, double[], double)">initIntegration</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#integrate(org.apache.commons.math3.ode.FirstOrderDifferentialEquations, double, double[], double, double[])">integrate</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#setEquations(org.apache.commons.math3.ode.ExpandableStatefulODE)">setEquations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#setMaxEvaluations(int)">setMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#setStateInitialized(boolean)">setStateInitialized</a></code></li> |
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| <h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3> |
| <code><a href="http://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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></li> |
| </ul> |
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| <!-- ========= CONSTRUCTOR DETAIL ======== --> |
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| </a> |
| <h3>Constructor Detail</h3> |
| <a name="GraggBulirschStoerIntegrator(double, double, double, double)"> |
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| </a> |
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| <h4>GraggBulirschStoerIntegrator</h4> |
| <pre>public GraggBulirschStoerIntegrator(double minStep, |
| double maxStep, |
| double scalAbsoluteTolerance, |
| double scalRelativeTolerance)</pre> |
| <div class="block">Simple constructor. |
| Build a Gragg-Bulirsch-Stoer integrator with the given step |
| bounds. All tuning parameters are set to their default |
| values. The default step handler does nothing.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>minStep</code> - minimal step (sign is irrelevant, regardless of |
| integration direction, forward or backward), the last step can |
| be smaller than this</dd><dd><code>maxStep</code> - maximal step (sign is irrelevant, regardless of |
| integration direction, forward or backward), the last step can |
| be smaller than this</dd><dd><code>scalAbsoluteTolerance</code> - allowed absolute error</dd><dd><code>scalRelativeTolerance</code> - allowed relative error</dd></dl> |
| </li> |
| </ul> |
| <a name="GraggBulirschStoerIntegrator(double, double, double[], double[])"> |
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| </a> |
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| <h4>GraggBulirschStoerIntegrator</h4> |
| <pre>public GraggBulirschStoerIntegrator(double minStep, |
| double maxStep, |
| double[] vecAbsoluteTolerance, |
| double[] vecRelativeTolerance)</pre> |
| <div class="block">Simple constructor. |
| Build a Gragg-Bulirsch-Stoer integrator with the given step |
| bounds. All tuning parameters are set to their default |
| values. The default step handler does nothing.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>minStep</code> - minimal step (must be positive even for backward |
| integration), the last step can be smaller than this</dd><dd><code>maxStep</code> - maximal step (must be positive even for backward |
| integration)</dd><dd><code>vecAbsoluteTolerance</code> - allowed absolute error</dd><dd><code>vecRelativeTolerance</code> - allowed relative error</dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
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| <a name="setStabilityCheck(boolean, int, int, double)"> |
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| <h4>setStabilityCheck</h4> |
| <pre>public void setStabilityCheck(boolean performStabilityCheck, |
| int maxNumIter, |
| int maxNumChecks, |
| double stepsizeReductionFactor)</pre> |
| <div class="block">Set the stability check controls. |
| <p>The stability check is performed on the first few iterations of |
| the extrapolation scheme. If this test fails, the step is rejected |
| and the stepsize is reduced.</p> |
| <p>By default, the test is performed, at most during two |
| iterations at each step, and at most once for each of these |
| iterations. The default stepsize reduction factor is 0.5.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>performStabilityCheck</code> - if true, stability check will be performed, |
| if false, the check will be skipped</dd><dd><code>maxNumIter</code> - maximal number of iterations for which checks are |
| performed (the number of iterations is reset to default if negative |
| or null)</dd><dd><code>maxNumChecks</code> - maximal number of checks for each iteration |
| (the number of checks is reset to default if negative or null)</dd><dd><code>stepsizeReductionFactor</code> - stepsize reduction factor in case of |
| failure (the factor is reset to default if lower than 0.0001 or |
| greater than 0.9999)</dd></dl> |
| </li> |
| </ul> |
| <a name="setControlFactors(double, double, double, double)"> |
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| <h4>setControlFactors</h4> |
| <pre>public void setControlFactors(double control1, |
| double control2, |
| double control3, |
| double control4)</pre> |
| <div class="block">Set the step size control factors. |
| |
| <p>The new step size hNew is computed from the old one h by: |
| <pre> |
| hNew = h * stepControl2 / (err/stepControl1)^(1/(2k+1)) |
| </pre> |
| where err is the scaled error and k the iteration number of the |
| extrapolation scheme (counting from 0). The default values are |
| 0.65 for stepControl1 and 0.94 for stepControl2.</p> |
| <p>The step size is subject to the restriction: |
| <pre> |
| stepControl3^(1/(2k+1))/stepControl4 <= hNew/h <= 1/stepControl3^(1/(2k+1)) |
| </pre> |
| The default values are 0.02 for stepControl3 and 4.0 for |
| stepControl4.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>control1</code> - first stepsize control factor (the factor is |
| reset to default if lower than 0.0001 or greater than 0.9999)</dd><dd><code>control2</code> - second stepsize control factor (the factor |
| is reset to default if lower than 0.0001 or greater than 0.9999)</dd><dd><code>control3</code> - third stepsize control factor (the factor is |
| reset to default if lower than 0.0001 or greater than 0.9999)</dd><dd><code>control4</code> - fourth stepsize control factor (the factor |
| is reset to default if lower than 1.0001 or greater than 999.9)</dd></dl> |
| </li> |
| </ul> |
| <a name="setOrderControl(int, double, double)"> |
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| </a> |
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| <h4>setOrderControl</h4> |
| <pre>public void setOrderControl(int maximalOrder, |
| double control1, |
| double control2)</pre> |
| <div class="block">Set the order control parameters. |
| <p>The Gragg-Bulirsch-Stoer method changes both the step size and |
| the order during integration, in order to minimize computation |
| cost. Each extrapolation step increases the order by 2, so the |
| maximal order that will be used is always even, it is twice the |
| maximal number of columns in the extrapolation table.</p> |
| <pre> |
| order is decreased if w(k-1) <= w(k) * orderControl1 |
| order is increased if w(k) <= w(k-1) * orderControl2 |
| </pre> |
| <p>where w is the table of work per unit step for each order |
| (number of function calls divided by the step length), and k is |
| the current order.</p> |
| <p>The default maximal order after construction is 18 (i.e. the |
| maximal number of columns is 9). The default values are 0.8 for |
| orderControl1 and 0.9 for orderControl2.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>maximalOrder</code> - maximal order in the extrapolation table (the |
| maximal order is reset to default if order <= 6 or odd)</dd><dd><code>control1</code> - first order control factor (the factor is |
| reset to default if lower than 0.0001 or greater than 0.9999)</dd><dd><code>control2</code> - second order control factor (the factor |
| is reset to default if lower than 0.0001 or greater than 0.9999)</dd></dl> |
| </li> |
| </ul> |
| <a name="addStepHandler(org.apache.commons.math3.ode.sampling.StepHandler)"> |
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| </a> |
| <ul class="blockList"> |
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| <h4>addStepHandler</h4> |
| <pre>public void addStepHandler(<a href="../../../../../../org/apache/commons/math3/ode/sampling/StepHandler.html" title="interface in org.apache.commons.math3.ode.sampling">StepHandler</a> handler)</pre> |
| <div class="block">Add a step handler to this integrator. |
| <p>The handler will be called by the integrator for each accepted |
| step.</p></div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html#addStepHandler(org.apache.commons.math3.ode.sampling.StepHandler)">addStepHandler</a></code> in interface <code><a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</a></code></dd> |
| <dt><strong>Overrides:</strong></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addStepHandler(org.apache.commons.math3.ode.sampling.StepHandler)">addStepHandler</a></code> in class <code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>handler</code> - handler for the accepted steps</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html#getStepHandlers()"><code>ODEIntegrator.getStepHandlers()</code></a>, |
| <a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html#clearStepHandlers()"><code>ODEIntegrator.clearStepHandlers()</code></a></dd></dl> |
| </li> |
| </ul> |
| <a name="addEventHandler(org.apache.commons.math3.ode.events.EventHandler, double, double, int, org.apache.commons.math3.analysis.solvers.UnivariateSolver)"> |
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| </a> |
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| <h4>addEventHandler</h4> |
| <pre>public void addEventHandler(<a href="../../../../../../org/apache/commons/math3/ode/events/EventHandler.html" title="interface in org.apache.commons.math3.ode.events">EventHandler</a> function, |
| double maxCheckInterval, |
| double convergence, |
| int maxIterationCount, |
| <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers">UnivariateSolver</a> solver)</pre> |
| <div class="block">Add an event handler to the integrator.</div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.EventHandler, double, double, int, org.apache.commons.math3.analysis.solvers.UnivariateSolver)">addEventHandler</a></code> in interface <code><a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</a></code></dd> |
| <dt><strong>Overrides:</strong></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.EventHandler, double, double, int, org.apache.commons.math3.analysis.solvers.UnivariateSolver)">addEventHandler</a></code> in class <code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - event handler</dd><dd><code>maxCheckInterval</code> - maximal time interval between switching |
| function checks (this interval prevents missing sign changes in |
| case the integration steps becomes very large)</dd><dd><code>convergence</code> - convergence threshold in the event time search</dd><dd><code>maxIterationCount</code> - upper limit of the iteration count in |
| the event time search</dd><dd><code>solver</code> - The root-finding algorithm to use to detect the state |
| events.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html#getEventHandlers()"><code>ODEIntegrator.getEventHandlers()</code></a>, |
| <a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html#clearEventHandlers()"><code>ODEIntegrator.clearEventHandlers()</code></a></dd></dl> |
| </li> |
| </ul> |
| <a name="setInterpolationControl(boolean, int)"> |
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| </a> |
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| <li class="blockList"> |
| <h4>setInterpolationControl</h4> |
| <pre>public void setInterpolationControl(boolean useInterpolationErrorForControl, |
| int mudifControlParameter)</pre> |
| <div class="block">Set the interpolation order control parameter. |
| The interpolation order for dense output is 2k - mudif + 1. The |
| default value for mudif is 4 and the interpolation error is used |
| in stepsize control by default.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>useInterpolationErrorForControl</code> - if true, interpolation error is used |
| for stepsize control</dd><dd><code>mudifControlParameter</code> - interpolation order control parameter (the parameter |
| is reset to default if <= 0 or >= 7)</dd></dl> |
| </li> |
| </ul> |
| <a name="integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)"> |
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| <h4>integrate</h4> |
| <pre>public void integrate(<a href="../../../../../../org/apache/commons/math3/ode/ExpandableStatefulODE.html" title="class in org.apache.commons.math3.ode">ExpandableStatefulODE</a> equations, |
| double t) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre> |
| <div class="block">Integrate a set of differential equations up to the given time. |
| <p>This method solves an Initial Value Problem (IVP).</p> |
| <p>The set of differential equations is composed of a main set, which |
| can be extended by some sets of secondary equations. The set of |
| equations must be already set up with initial time and partial states. |
| At integration completion, the final time and partial states will be |
| available in the same object.</p> |
| <p>Since this method stores some internal state variables made |
| available in its public interface during integration (<a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getCurrentSignedStepsize()"><code>AbstractIntegrator.getCurrentSignedStepsize()</code></a>), it is <em>not</em> thread-safe.</p></div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">integrate</a></code> in class <code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>equations</code> - complete set of differential equations to integrate</dd><dd><code>t</code> - target time for the integration |
| (can be set to a value smaller than <code>t0</code> for backward integration)</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if integration step is too small</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the dimension of the complete state does not |
| match the complete equations sets dimension</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if the number of functions evaluations is exceeded</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if the location of an event cannot be bracketed</dd></dl> |
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