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| <div class="subTitle">org.apache.commons.math3.ode</div> |
| <h2 title="Class MultistepIntegrator" class="title">Class MultistepIntegrator</h2> |
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| <ul class="inheritance"> |
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| <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.MultistepIntegrator</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> |
| </dl> |
| <dl> |
| <dt>Direct Known Subclasses:</dt> |
| <dd><a href="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdamsIntegrator</a></dd> |
| </dl> |
| <hr> |
| <br> |
| <pre>public abstract class <span class="strong">MultistepIntegrator</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 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<sup>(k)</sup><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 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></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>2.0</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: MultistepIntegrator.java 1463684 2013-04-02 19:04:13Z luc $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsBashforthIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>AdamsBashforthIntegrator</code></a>, |
| <a href="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>AdamsMoultonIntegrator</code></a></dd></dl> |
| </li> |
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| <h3>Nested Class Summary</h3> |
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| <caption><span>Nested Classes</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colLast" scope="col">Class and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static interface </code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.NordsieckTransformer.html" title="interface in org.apache.commons.math3.ode">MultistepIntegrator.NordsieckTransformer</a></strong></code> |
| <div class="block">Transformer used to convert the first step to Nordsieck representation.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
| </ul> |
| <!-- =========== FIELD SUMMARY =========== --> |
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| <h3>Field Summary</h3> |
| <table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Field Summary table, listing fields, and an explanation"> |
| <caption><span>Fields</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colLast" scope="col">Field and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>protected <a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#nordsieck">nordsieck</a></strong></code> |
| <div class="block">Nordsieck matrix of the higher scaled derivatives.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>protected double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#scaled">scaled</a></strong></code> |
| <div class="block">First scaled derivative (h y').</div> |
| </td> |
| </tr> |
| </table> |
| <ul class="blockList"> |
| <li class="blockList"><a name="fields_inherited_from_class_org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator"> |
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| </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> |
| <ul class="blockList"> |
| <li class="blockList"><a name="fields_inherited_from_class_org.apache.commons.math3.ode.AbstractIntegrator"> |
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| </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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| <li class="blockList"><a name="constructor_summary"> |
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| </a> |
| <h3>Constructor Summary</h3> |
| <table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Constructor Summary table, listing constructors, and an explanation"> |
| <caption><span>Constructors</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier</th> |
| <th class="colLast" scope="col">Constructor and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>protected </code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#MultistepIntegrator(java.lang.String, int, int, double, double, double[], double[])">MultistepIntegrator</a></strong>(<a href="http://docs.oracle.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> |
| <div class="block">Build a multistep integrator with the given stepsize bounds.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>protected </code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#MultistepIntegrator(java.lang.String, int, int, double, double, double, double)">MultistepIntegrator</a></strong>(<a href="http://docs.oracle.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> |
| <div class="block">Build a multistep integrator with the given stepsize bounds.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
| </ul> |
| <!-- ========== METHOD SUMMARY =========== --> |
| <ul class="blockList"> |
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| </a> |
| <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>protected double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#computeStepGrowShrinkFactor(double)">computeStepGrowShrinkFactor</a></strong>(double error)</code> |
| <div class="block">Compute step grow/shrink factor according to normalized error.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getMaxGrowth()">getMaxGrowth</a></strong>()</code> |
| <div class="block">Get the maximal growth factor for stepsize control.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getMinReduction()">getMinReduction</a></strong>()</code> |
| <div class="block">Get the minimal reduction factor for stepsize control.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getSafety()">getSafety</a></strong>()</code> |
| <div class="block">Get the safety factor for stepsize control.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getStarterIntegrator()">getStarterIntegrator</a></strong>()</code> |
| <div class="block">Get the starter integrator.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>protected abstract <a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#initializeHighOrderDerivatives(double, double[], double[][], double[][])">initializeHighOrderDerivatives</a></strong>(double h, |
| double[] t, |
| double[][] y, |
| double[][] yDot)</code> |
| <div class="block">Initialize the high order scaled derivatives at step start.</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/MultistepIntegrator.html#setMaxGrowth(double)">setMaxGrowth</a></strong>(double maxGrowth)</code> |
| <div class="block">Set the maximal growth factor for stepsize control.</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/MultistepIntegrator.html#setMinReduction(double)">setMinReduction</a></strong>(double minReduction)</code> |
| <div class="block">Set the minimal reduction factor for stepsize control.</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/MultistepIntegrator.html#setSafety(double)">setSafety</a></strong>(double safety)</code> |
| <div class="block">Set the safety factor for stepsize control.</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/MultistepIntegrator.html#setStarterIntegrator(org.apache.commons.math3.ode.FirstOrderIntegrator)">setStarterIntegrator</a></strong>(<a href="../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderIntegrator</a> starterIntegrator)</code> |
| <div class="block">Set the starter integrator.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>protected void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#start(double, double[], double)">start</a></strong>(double t0, |
| double[] y0, |
| double t)</code> |
| <div class="block">Start the integration.</div> |
| </td> |
| </tr> |
| </table> |
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| </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#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">integrate</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> |
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| </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#addEventHandler(org.apache.commons.math3.ode.events.EventHandler, double, double, int, org.apache.commons.math3.analysis.solvers.UnivariateSolver)">addEventHandler</a>, <a href="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addStepHandler(org.apache.commons.math3.ode.sampling.StepHandler)">addStepHandler</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> |
| </ul> |
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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> |
| </li> |
| </ul> |
| </li> |
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| </div> |
| <div class="details"> |
| <ul class="blockList"> |
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| <h3>Field Detail</h3> |
| <a name="scaled"> |
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| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>scaled</h4> |
| <pre>protected double[] scaled</pre> |
| <div class="block">First scaled derivative (h y').</div> |
| </li> |
| </ul> |
| <a name="nordsieck"> |
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| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>nordsieck</h4> |
| <pre>protected <a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</a> nordsieck</pre> |
| <div class="block">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<sup>(k)</sup>)</p></div> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| <!-- ========= CONSTRUCTOR DETAIL ======== --> |
| <ul class="blockList"> |
| <li class="blockList"><a name="constructor_detail"> |
| <!-- --> |
| </a> |
| <h3>Constructor Detail</h3> |
| <a name="MultistepIntegrator(java.lang.String, int, int, double, double, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>MultistepIntegrator</h4> |
| <pre>protected MultistepIntegrator(<a href="http://docs.oracle.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) |
| throws <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></pre> |
| <div class="block">Build a multistep integrator with the given stepsize bounds. |
| <p>The default starter integrator is set to the <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> 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></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>name</code> - name of the method</dd><dd><code>nSteps</code> - number of steps of the multistep method |
| (excluding the one being computed)</dd><dd><code>order</code> - order of the method</dd><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>scalAbsoluteTolerance</code> - allowed absolute error</dd><dd><code>scalRelativeTolerance</code> - allowed relative error</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 number of steps is smaller than 2</dd></dl> |
| </li> |
| </ul> |
| <a name="MultistepIntegrator(java.lang.String, int, int, double, double, double[], double[])"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>MultistepIntegrator</h4> |
| <pre>protected MultistepIntegrator(<a href="http://docs.oracle.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> |
| <div class="block">Build a multistep integrator with the given stepsize bounds. |
| <p>The default starter integrator is set to the <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> 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></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>name</code> - name of the method</dd><dd><code>nSteps</code> - number of steps of the multistep method |
| (excluding the one being computed)</dd><dd><code>order</code> - order of the method</dd><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> |
| <!-- ============ METHOD DETAIL ========== --> |
| <ul class="blockList"> |
| <li class="blockList"><a name="method_detail"> |
| <!-- --> |
| </a> |
| <h3>Method Detail</h3> |
| <a name="getStarterIntegrator()"> |
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| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getStarterIntegrator</h4> |
| <pre>public <a href="../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</a> getStarterIntegrator()</pre> |
| <div class="block">Get the starter integrator.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>starter integrator</dd></dl> |
| </li> |
| </ul> |
| <a name="setStarterIntegrator(org.apache.commons.math3.ode.FirstOrderIntegrator)"> |
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| </a> |
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| <h4>setStarterIntegrator</h4> |
| <pre>public void setStarterIntegrator(<a href="../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderIntegrator</a> starterIntegrator)</pre> |
| <div class="block">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></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>starterIntegrator</code> - starter integrator</dd></dl> |
| </li> |
| </ul> |
| <a name="start(double, double[], double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>start</h4> |
| <pre>protected void start(double t0, |
| double[] y0, |
| double t) |
| throws <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/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</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">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></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>t0</code> - initial time</dd><dd><code>y0</code> - initial value of the state vector at t0</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/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if arrays dimension do not match equations settings</dd> |
| <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/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> |
| </li> |
| </ul> |
| <a name="initializeHighOrderDerivatives(double, double[], double[][], double[][])"> |
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| </a> |
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| <li class="blockList"> |
| <h4>initializeHighOrderDerivatives</h4> |
| <pre>protected abstract <a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</a> initializeHighOrderDerivatives(double h, |
| double[] t, |
| double[][] y, |
| double[][] yDot)</pre> |
| <div class="block">Initialize the high order scaled derivatives at step start.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>h</code> - step size to use for scaling</dd><dd><code>t</code> - first steps times</dd><dd><code>y</code> - first steps states</dd><dd><code>yDot</code> - first steps derivatives</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>Nordieck vector at first step (h<sup>2</sup>/2 y''<sub>n</sub>, |
| h<sup>3</sup>/6 y'''<sub>n</sub> ... h<sup>k</sup>/k! y<sup>(k)</sup><sub>n</sub>)</dd></dl> |
| </li> |
| </ul> |
| <a name="getMinReduction()"> |
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| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getMinReduction</h4> |
| <pre>public double getMinReduction()</pre> |
| <div class="block">Get the minimal reduction factor for stepsize control.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>minimal reduction factor</dd></dl> |
| </li> |
| </ul> |
| <a name="setMinReduction(double)"> |
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| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>setMinReduction</h4> |
| <pre>public void setMinReduction(double minReduction)</pre> |
| <div class="block">Set the minimal reduction factor for stepsize control.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>minReduction</code> - minimal reduction factor</dd></dl> |
| </li> |
| </ul> |
| <a name="getMaxGrowth()"> |
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| </a> |
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| <li class="blockList"> |
| <h4>getMaxGrowth</h4> |
| <pre>public double getMaxGrowth()</pre> |
| <div class="block">Get the maximal growth factor for stepsize control.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>maximal growth factor</dd></dl> |
| </li> |
| </ul> |
| <a name="setMaxGrowth(double)"> |
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| </a> |
| <ul class="blockList"> |
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| <h4>setMaxGrowth</h4> |
| <pre>public void setMaxGrowth(double maxGrowth)</pre> |
| <div class="block">Set the maximal growth factor for stepsize control.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>maxGrowth</code> - maximal growth factor</dd></dl> |
| </li> |
| </ul> |
| <a name="getSafety()"> |
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| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getSafety</h4> |
| <pre>public double getSafety()</pre> |
| <div class="block">Get the safety factor for stepsize control.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>safety factor</dd></dl> |
| </li> |
| </ul> |
| <a name="setSafety(double)"> |
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| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>setSafety</h4> |
| <pre>public void setSafety(double safety)</pre> |
| <div class="block">Set the safety factor for stepsize control.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>safety</code> - safety factor</dd></dl> |
| </li> |
| </ul> |
| <a name="computeStepGrowShrinkFactor(double)"> |
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| </a> |
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| <li class="blockList"> |
| <h4>computeStepGrowShrinkFactor</h4> |
| <pre>protected double computeStepGrowShrinkFactor(double error)</pre> |
| <div class="block">Compute step grow/shrink factor according to normalized error.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>error</code> - normalized error of the current step</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>grow/shrink factor for next step</dd></dl> |
| </li> |
| </ul> |
| </li> |
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