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<div class="subTitle">org.apache.commons.math3.ode.nonstiff</div>
<h2 title="Class EulerFieldIntegrator" class="title">Class EulerFieldIntegrator<T extends <a href="../../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></h2>
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<ul class="inheritance">
<li><a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html" title="class in org.apache.commons.math3.ode">org.apache.commons.math3.ode.AbstractFieldIntegrator</a><T></li>
<li>
<ul class="inheritance">
<li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldIntegrator</a><T></li>
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<li>org.apache.commons.math3.ode.nonstiff.EulerFieldIntegrator<T></li>
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<dl><dt><span class="strong">Type Parameters:</span></dt><dd><code>T</code> - the type of the field elements</dd></dl>
<dl>
<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/ode/FirstOrderFieldIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderFieldIntegrator</a><T>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/FieldButcherArrayProvider.html" title="interface in org.apache.commons.math3.ode.nonstiff">FieldButcherArrayProvider</a><T></dd>
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<pre>public class <span class="strong">EulerFieldIntegrator<T extends <a href="../../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></span>
extends <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">RungeKuttaFieldIntegrator</a><T></pre>
<div class="block">This class implements a simple Euler integrator for Ordinary
Differential Equations.
<p>The Euler algorithm is the simplest one that can be used to
integrate ordinary differential equations. It is a simple inversion
of the forward difference expression :
<code>f'=(f(t+h)-f(t))/h</code> which leads to
<code>f(t+h)=f(t)+hf'</code>. The interpolation scheme used for
dense output is the linear scheme already used for integration.</p>
<p>This algorithm looks cheap because it needs only one function
evaluation per step. However, as it uses linear estimates, it needs
very small steps to achieve high accuracy, and small steps lead to
numerical errors and instabilities.</p>
<p>This algorithm is almost never used and has been included in
this package only as a comparison reference for more useful
integrators.</p></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>3.6</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/MidpointFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>MidpointFieldIntegrator</code></a>,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>ClassicalRungeKuttaFieldIntegrator</code></a>,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/GillFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>GillFieldIntegrator</code></a>,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>ThreeEighthesFieldIntegrator</code></a>,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/LutherFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><code>LutherFieldIntegrator</code></a></dd></dl>
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<caption><span>Constructors</span><span class="tabEnd"> </span></caption>
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<th class="colOne" scope="col">Constructor and Description</th>
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<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html#EulerFieldIntegrator(org.apache.commons.math3.Field,%20T)">EulerFieldIntegrator</a></strong>(<a href="../../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>> field,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a> step)</code>
<div class="block">Simple constructor.</div>
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<h3>Method Summary</h3>
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<caption><span>Methods</span><span class="tabEnd"> </span></caption>
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<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
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<td class="colFirst"><code>protected org.apache.commons.math3.ode.nonstiff.EulerFieldStepInterpolator<<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html#createInterpolator(boolean,%20T[][],%20org.apache.commons.math3.ode.FieldODEStateAndDerivative,%20org.apache.commons.math3.ode.FieldODEStateAndDerivative,%20org.apache.commons.math3.ode.FieldEquationsMapper)">createInterpolator</a></strong>(boolean forward,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>[][] yDotK,
<a href="../../../../../../org/apache/commons/math3/ode/FieldODEStateAndDerivative.html" title="class in org.apache.commons.math3.ode">FieldODEStateAndDerivative</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>> globalPreviousState,
<a href="../../../../../../org/apache/commons/math3/ode/FieldODEStateAndDerivative.html" title="class in org.apache.commons.math3.ode">FieldODEStateAndDerivative</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>> globalCurrentState,
<a href="../../../../../../org/apache/commons/math3/ode/FieldEquationsMapper.html" title="class in org.apache.commons.math3.ode">FieldEquationsMapper</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>> mapper)</code>
<div class="block">Create an interpolator.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>[][]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html#getA()">getA</a></strong>()</code>
<div class="block">Get the internal weights from Butcher array (without the first empty row).</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html#getB()">getB</a></strong>()</code>
<div class="block">Get the external weights for the high order method from Butcher array.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html#getC()">getC</a></strong>()</code>
<div class="block">Get the time steps from Butcher array (without the first zero).</div>
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<h3>Methods inherited from class org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">RungeKuttaFieldIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.html#fraction(int,%20int)">fraction</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.html#integrate(org.apache.commons.math3.ode.FieldExpandableODE,%20org.apache.commons.math3.ode.FieldODEState,%20T)">integrate</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.html#singleStep(org.apache.commons.math3.ode.FirstOrderFieldDifferentialEquations,%20T,%20T[],%20T)">singleStep</a></code></li>
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<h3>Methods inherited from class org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractFieldIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#acceptStep(org.apache.commons.math3.ode.sampling.AbstractFieldStepInterpolator,%20T)">acceptStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.FieldEventHandler,%20double,%20double,%20int)">addEventHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.FieldEventHandler,%20double,%20double,%20int,%20org.apache.commons.math3.analysis.solvers.BracketedRealFieldUnivariateSolver)">addEventHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#addStepHandler(org.apache.commons.math3.ode.sampling.FieldStepHandler)">addStepHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#clearEventHandlers()">clearEventHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#clearStepHandlers()">clearStepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#computeDerivatives(T,%20T[])">computeDerivatives</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getCurrentSignedStepsize()">getCurrentSignedStepsize</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getCurrentStepStart()">getCurrentStepStart</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getEquations()">getEquations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getEvaluations()">getEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getEvaluationsCounter()">getEvaluationsCounter</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getEventHandlers()">getEventHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getField()">getField</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getMaxEvaluations()">getMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getName()">getName</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getStepHandlers()">getStepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getStepSize()">getStepSize</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#getStepStart()">getStepStart</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#initIntegration(org.apache.commons.math3.ode.FieldExpandableODE,%20T,%20T[],%20T)">initIntegration</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#isLastStep()">isLastStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#resetOccurred()">resetOccurred</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#sanityChecks(org.apache.commons.math3.ode.FieldODEState,%20T)">sanityChecks</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#setIsLastStep(boolean)">setIsLastStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#setMaxEvaluations(int)">setMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#setStateInitialized(boolean)">setStateInitialized</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#setStepSize(T)">setStepSize</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractFieldIntegrator.html#setStepStart(org.apache.commons.math3.ode.FieldODEStateAndDerivative)">setStepStart</a></code></li>
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<h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
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<a name="EulerFieldIntegrator(org.apache.commons.math3.Field,org.apache.commons.math3.RealFieldElement)">
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<h4>EulerFieldIntegrator</h4>
<pre>public EulerFieldIntegrator(<a href="../../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>> field,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a> step)</pre>
<div class="block">Simple constructor.
Build an Euler integrator with the given step.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>field</code> - field to which the time and state vector elements belong</dd><dd><code>step</code> - integration step</dd></dl>
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<h4>getC</h4>
<pre>public <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>[] getC()</pre>
<div class="block">Get the time steps from Butcher array (without the first zero).</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>time steps from Butcher array (without the first zero</dd></dl>
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<h4>getA</h4>
<pre>public <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>[][] getA()</pre>
<div class="block">Get the internal weights from Butcher array (without the first empty row).</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>internal weights from Butcher array (without the first empty row)</dd></dl>
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<h4>getB</h4>
<pre>public <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>[] getB()</pre>
<div class="block">Get the external weights for the high order method from Butcher array.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>external weights for the high order method from Butcher array</dd></dl>
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<a name="createInterpolator(boolean,org.apache.commons.math3.RealFieldElement[][],org.apache.commons.math3.ode.FieldODEStateAndDerivative,org.apache.commons.math3.ode.FieldODEStateAndDerivative,org.apache.commons.math3.ode.FieldEquationsMapper)">
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</a><a name="createInterpolator(boolean, T[][], org.apache.commons.math3.ode.FieldODEStateAndDerivative, org.apache.commons.math3.ode.FieldODEStateAndDerivative, org.apache.commons.math3.ode.FieldEquationsMapper)">
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<h4>createInterpolator</h4>
<pre>protected org.apache.commons.math3.ode.nonstiff.EulerFieldStepInterpolator<<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>> createInterpolator(boolean forward,
<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>[][] yDotK,
<a href="../../../../../../org/apache/commons/math3/ode/FieldODEStateAndDerivative.html" title="class in org.apache.commons.math3.ode">FieldODEStateAndDerivative</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>> globalPreviousState,
<a href="../../../../../../org/apache/commons/math3/ode/FieldODEStateAndDerivative.html" title="class in org.apache.commons.math3.ode">FieldODEStateAndDerivative</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>> globalCurrentState,
<a href="../../../../../../org/apache/commons/math3/ode/FieldEquationsMapper.html" title="class in org.apache.commons.math3.ode">FieldEquationsMapper</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>> mapper)</pre>
<div class="block">Create an interpolator.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.html#createInterpolator(boolean,%20T[][],%20org.apache.commons.math3.ode.FieldODEStateAndDerivative,%20org.apache.commons.math3.ode.FieldODEStateAndDerivative,%20org.apache.commons.math3.ode.FieldEquationsMapper)">createInterpolator</a></code> in class <code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">RungeKuttaFieldIntegrator</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a> extends <a href="../../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/EulerFieldIntegrator.html" title="type parameter in EulerFieldIntegrator">T</a>>></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>forward</code> - integration direction indicator</dd><dd><code>yDotK</code> - slopes at the intermediate points</dd><dd><code>globalPreviousState</code> - start of the global step</dd><dd><code>globalCurrentState</code> - end of the global step</dd><dd><code>mapper</code> - equations mapper for the all equations</dd>
<dt><span class="strong">Returns:</span></dt><dd>external weights for the high order method from Butcher array</dd></dl>
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