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Added an order 6 fixed-step ODE integrator. 

The integrator was designed by H. A. Luther in 1968. We have added a
corresponding step interpolator by solving the order conditions provided
by the rkcheck tool.

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1588753 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Luc Maisonobe 2014-04-20 13:25:11 +00:00
parent 4b724bdc2e
commit 7f162008a2
7 changed files with 682 additions and 0 deletions
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3
src/changes/changes.xml
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@ -56,6 +56,9 @@ If the output is not quite correct, check for invisible trailing spaces!
Added new methods for testing floating-point equality between the real
(resp. imaginary) parts of two complex numbers.
</action>
<action dev="luc" type="add" >
Added an order 6 fixed-step ODE integrator designed by H. A. Luther in 1968.
</action>
<action dev="luc" type="update" >
Bracketing utility for univariate root solvers returns a tighter interval than before.
It also allows choosing the search interval expansion rate, supporting both linear

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src/main/java/org/apache/commons/math3/ode/nonstiff/LutherIntegrator.java Normal file
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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.nonstiff;
import org.apache.commons.math3.util.FastMath;
/**
* This class implements the Luther sixth order Runge-Kutta
* integrator for Ordinary Differential Equations.
* <p>
* This method is described in H. A. Luther 1968 paper <a
* href="http://www.ams.org/journals/mcom/1968-22-102/S0025-5718-68-99876-1/S0025-5718-68-99876-1.pdf">
* An explicit Sixth-Order Runge-Kutta Formula</a>.
* </p>
* <p>This method is an explicit Runge-Kutta method, its Butcher-array
* is the following one :
* <pre>
* 0 | 0 0 0 0 0 0
* 1 | 1 0 0 0 0 0
* 1/2 | 3/8 1/8 0 0 0 0
* 2/3 | 8/27 2/27 8/27 0 0 0
* (7-q)/14 | ( -21 + 9q)/392 ( -56 + 8q)/392 ( 336 - 48q)/392 ( -63 + 3q)/392 0 0
* (7+q)/14 | (-1155 - 255q)/1960 ( -280 - 40q)/1960 ( 0 - 320q)/1960 ( 63 + 363q)/1960 ( 2352 + 392q)/1960 0
* 1 | ( 330 + 105q)/180 ( 120 + 0q)/180 ( -200 + 280q)/180 ( 126 - 189q)/180 ( -686 - 126q)/180 ( 490 - 70q)/180
* |--------------------------------------------------------------------------------------------------------------------------------------------------
* | 1/20 0 16/45 0 49/180 49/180 1/20
* </pre>
* where q = &radic;21</p>
*
* @see EulerIntegrator
* @see ClassicalRungeKuttaIntegrator
* @see GillIntegrator
* @see MidpointIntegrator
* @see ThreeEighthesIntegrator
* @version $Id$
* @since 3.3
*/
public class LutherIntegrator extends RungeKuttaIntegrator {
/** Square root. */
private static final double Q = FastMath.sqrt(21);
/** Time steps Butcher array. */
private static final double[] STATIC_C = {
1.0, 1.0 / 2.0, 2.0 / 3.0, (7.0 - Q) / 14.0, (7.0 + Q) / 14.0, 1.0
};
/** Internal weights Butcher array. */
private static final double[][] STATIC_A = {
{ 1.0 },
{ 3.0 / 8.0, 1.0 / 8.0 },
{ 8.0 / 27.0, 2.0 / 27.0, 8.0 / 27.0 },
{ ( -21.0 + 9.0 * Q) / 392.0, ( -56.0 + 8.0 * Q) / 392.0, ( 336.0 - 48.0 * Q) / 392.0, (-63.0 + 3.0 * Q) / 392.0 },
{ (-1155.0 - 255.0 * Q) / 1960.0, (-280.0 - 40.0 * Q) / 1960.0, ( 0.0 - 320.0 * Q) / 1960.0, ( 63.0 + 363.0 * Q) / 1960.0, (2352.0 + 392.0 * Q) / 1960.0 },
{ ( 330.0 + 105.0 * Q) / 180.0, ( 120.0 + 0.0 * Q) / 180.0, (-200.0 + 280.0 * Q) / 180.0, (126.0 - 189.0 * Q) / 180.0, (-686.0 - 126.0 * Q) / 180.0, (490.0 - 70.0 * Q) / 180.0 }
};
/** Propagation weights Butcher array. */
private static final double[] STATIC_B = {
1.0 / 20.0, 0, 16.0 / 45.0, 0, 49.0 / 180.0, 49.0 / 180.0, 1.0 / 20.0
};
/** Simple constructor.
* Build a fourth-order Luther integrator with the given step.
* @param step integration step
*/
public LutherIntegrator(final double step) {
super("Luther", STATIC_C, STATIC_A, STATIC_B, new LutherStepInterpolator(), step);
}
}

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src/main/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolator.java Normal file
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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.nonstiff;
import org.apache.commons.math3.ode.sampling.StepInterpolator;
import org.apache.commons.math3.util.FastMath;
/**
* This class implements a step interpolator for second order
* Runge-Kutta integrator.
*
* <p>This interpolator computes dense output inside the last
* step computed. The interpolation equation is consistent with the
* integration scheme.</p>
*
* @see LutherIntegrator
* @version $Id$
* @since 3.3
*/
class LutherStepInterpolator extends RungeKuttaStepInterpolator {
/** Serializable version identifier */
private static final long serialVersionUID = 20140416L;
/** Square root. */
private static final double Q = FastMath.sqrt(21);
/** Simple constructor.
* This constructor builds an instance that is not usable yet, the
* {@link
* org.apache.commons.math3.ode.sampling.AbstractStepInterpolator#reinitialize}
* method should be called before using the instance in order to
* initialize the internal arrays. This constructor is used only
* in order to delay the initialization in some cases. The {@link
* RungeKuttaIntegrator} class uses the prototyping design pattern
* to create the step interpolators by cloning an uninitialized model
* and later initializing the copy.
*/
public LutherStepInterpolator() {
}
/** Copy constructor.
* @param interpolator interpolator to copy from. The copy is a deep
* copy: its arrays are separated from the original arrays of the
* instance
*/
public LutherStepInterpolator(final LutherStepInterpolator interpolator) {
super(interpolator);
}
/** {@inheritDoc} */
@Override
protected StepInterpolator doCopy() {
return new LutherStepInterpolator(this);
}
/** {@inheritDoc} */
@Override
protected void computeInterpolatedStateAndDerivatives(final double theta,
final double oneMinusThetaH) {
// the coefficients below have been computed by solving the
// order conditions from a theorem from Butcher (1963), using
// the method explained in Folkmar Bornemann paper "Runge-Kutta
// Methods, Trees, and Maple", Center of Mathematical Sciences, Munich
// University of Technology, February 9, 2001
//<http://wwwzenger.informatik.tu-muenchen.de/selcuk/sjam012101.html>
// the method is implemented in the rkcheck tool
// <https://www.spaceroots.org/software/rkcheck/index.html>.
// Running it for order 5 gives the following order conditions
// for an interpolator:
// order 1 conditions
// \sum_{i=1}^{i=s}\left(b_{i} \right) =1
// order 2 conditions
// \sum_{i=1}^{i=s}\left(b_{i} c_{i}\right) = \frac{\theta}{2}
// order 3 conditions
// \sum_{i=2}^{i=s}\left(b_{i} \sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j} \right)}\right) = \frac{\theta^{2}}{6}
// \sum_{i=1}^{i=s}\left(b_{i} c_{i}^{2}\right) = \frac{\theta^{2}}{3}
// order 4 conditions
// \sum_{i=3}^{i=s}\left(b_{i} \sum_{j=2}^{j=i-1}{\left(a_{i,j} \sum_{k=1}^{k=j-1}{\left(a_{j,k} c_{k} \right)} \right)}\right) = \frac{\theta^{3}}{24}
// \sum_{i=2}^{i=s}\left(b_{i} \sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j}^{2} \right)}\right) = \frac{\theta^{3}}{12}
// \sum_{i=2}^{i=s}\left(b_{i} c_{i}\sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j} \right)}\right) = \frac{\theta^{3}}{8}
// \sum_{i=1}^{i=s}\left(b_{i} c_{i}^{3}\right) = \frac{\theta^{3}}{4}
// order 5 conditions
// \sum_{i=4}^{i=s}\left(b_{i} \sum_{j=3}^{j=i-1}{\left(a_{i,j} \sum_{k=2}^{k=j-1}{\left(a_{j,k} \sum_{l=1}^{l=k-1}{\left(a_{k,l} c_{l} \right)} \right)} \right)}\right) = \frac{\theta^{4}}{120}
// \sum_{i=3}^{i=s}\left(b_{i} \sum_{j=2}^{j=i-1}{\left(a_{i,j} \sum_{k=1}^{k=j-1}{\left(a_{j,k} c_{k}^{2} \right)} \right)}\right) = \frac{\theta^{4}}{60}
// \sum_{i=3}^{i=s}\left(b_{i} \sum_{j=2}^{j=i-1}{\left(a_{i,j} c_{j}\sum_{k=1}^{k=j-1}{\left(a_{j,k} c_{k} \right)} \right)}\right) = \frac{\theta^{4}}{40}
// \sum_{i=2}^{i=s}\left(b_{i} \sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j}^{3} \right)}\right) = \frac{\theta^{4}}{20}
// \sum_{i=3}^{i=s}\left(b_{i} c_{i}\sum_{j=2}^{j=i-1}{\left(a_{i,j} \sum_{k=1}^{k=j-1}{\left(a_{j,k} c_{k} \right)} \right)}\right) = \frac{\theta^{4}}{30}
// \sum_{i=2}^{i=s}\left(b_{i} c_{i}\sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j}^{2} \right)}\right) = \frac{\theta^{4}}{15}
// \sum_{i=2}^{i=s}\left(b_{i} \left(\sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j} \right)} \right)^{2}\right) = \frac{\theta^{4}}{20}
// \sum_{i=2}^{i=s}\left(b_{i} c_{i}^{2}\sum_{j=1}^{j=i-1}{\left(a_{i,j} c_{j} \right)}\right) = \frac{\theta^{4}}{10}
// \sum_{i=1}^{i=s}\left(b_{i} c_{i}^{4}\right) = \frac{\theta^{4}}{5}
// The a_{j,k} and c_{k} are given by the integrator Butcher arrays. What remains to solve
// are the b_i for the interpolator. They are found by solving the above equations.
// For a given interpolator, some equations are redundant, so in our case when we select
// all equations from order 1 to 4, we still don't have enough independent equations
// to solve from b_1 to b_7. We need to also select one equation from order 5. Here,
// we selected the last equation. It appears this choice implied at least the last 3 equations
// are fulfilled, but some of the former ones are not, so the resulting interpolator is order 5.
// At the end, we get the b_i as polynomials in theta.
final double coeffDot1 = 1 + theta * ( -54 / 5.0 + theta * ( 36 + theta * ( -47 + theta * 21)));
final double coeffDot2 = 0;
final double coeffDot3 = theta * (-208 / 15.0 + theta * ( 320 / 3.0 + theta * (-608 / 3.0 + theta * 112)));
final double coeffDot4 = theta * ( 324 / 25.0 + theta * ( -486 / 5.0 + theta * ( 972 / 5.0 + theta * -567 / 5.0)));
final double coeffDot5 = theta * ((833 + 343 * Q) / 150.0 + theta * ((-637 - 357 * Q) / 30.0 + theta * ((392 + 287 * Q) / 15.0 + theta * (-49 - 49 * Q) / 5.0)));
final double coeffDot6 = theta * ((833 - 343 * Q) / 150.0 + theta * ((-637 + 357 * Q) / 30.0 + theta * ((392 - 287 * Q) / 15.0 + theta * (-49 + 49 * Q) / 5.0)));
final double coeffDot7 = theta * ( 3 / 5.0 + theta * ( -3 + theta * 3));
if ((previousState != null) && (theta <= 0.5)) {
final double coeff1 = 1 + theta * ( -27 / 5.0 + theta * ( 12 + theta * ( -47 / 4.0 + theta * 21 / 5.0)));
final double coeff2 = 0;
final double coeff3 = theta * (-104 / 15.0 + theta * ( 320 / 9.0 + theta * (-152 / 3.0 + theta * 112 / 5.0)));
final double coeff4 = theta * ( 162 / 25.0 + theta * ( -162 / 5.0 + theta * ( 243 / 5.0 + theta * -567 / 25.0)));
final double coeff5 = theta * ((833 + 343 * Q) / 300.0 + theta * ((-637 - 357 * Q) / 90.0 + theta * ((392 + 287 * Q) / 60.0 + theta * (-49 - 49 * Q) / 25.0)));
final double coeff6 = theta * ((833 - 343 * Q) / 300.0 + theta * ((-637 + 357 * Q) / 90.0 + theta * ((392 - 287 * Q) / 60.0 + theta * (-49 + 49 * Q) / 25.0)));
final double coeff7 = theta * ( 3 / 10.0 + theta * ( -1 + theta * ( 3 / 4.0)));
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot2 = yDotK[1][i];
final double yDot3 = yDotK[2][i];
final double yDot4 = yDotK[3][i];
final double yDot5 = yDotK[4][i];
final double yDot6 = yDotK[5][i];
final double yDot7 = yDotK[6][i];
interpolatedState[i] = previousState[i] +
theta * h * (coeff1 * yDot1 + coeff2 * yDot2 + coeff3 * yDot3 +
coeff4 * yDot4 + coeff5 * yDot5 + coeff6 * yDot6 + coeff7 * yDot7);
interpolatedDerivatives[i] = coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 +
coeffDot4 * yDot4 + coeffDot5 * yDot5 + coeffDot6 * yDot6 + coeffDot7 * yDot7;
}
} else {
final double coeff1 = -1 / 20.0 + theta * ( 19 / 20.0 + theta * ( -89 / 20.0 + theta * ( 151 / 20.0 + theta * -21 / 5.0)));
final double coeff2 = 0;
final double coeff3 = -16 / 45.0 + theta * ( -16 / 45.0 + theta * ( -328 / 45.0 + theta * ( 424 / 15.0 + theta * -112 / 5.0)));
final double coeff4 = theta * ( theta * ( 162 / 25.0 + theta * ( -648 / 25.0 + theta * 567 / 25.0)));
final double coeff5 = -49 / 180.0 + theta * ( -49 / 180.0 + theta * ((2254 + 1029 * Q) / 900.0 + theta * ((-1372 - 847 * Q) / 300.0 + theta * ( 49 + 49 * Q) / 25.0)));
final double coeff6 = -49 / 180.0 + theta * ( -49 / 180.0 + theta * ((2254 - 1029 * Q) / 900.0 + theta * ((-1372 + 847 * Q) / 300.0 + theta * ( 49 - 49 * Q) / 25.0)));
final double coeff7 = -1 / 20.0 + theta * ( -1 / 20.0 + theta * ( 1 / 4.0 + theta * ( -3 / 4.0)));
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot2 = yDotK[1][i];
final double yDot3 = yDotK[2][i];
final double yDot4 = yDotK[3][i];
final double yDot5 = yDotK[4][i];
final double yDot6 = yDotK[5][i];
final double yDot7 = yDotK[6][i];
interpolatedState[i] = currentState[i] +
oneMinusThetaH * (coeff1 * yDot1 + coeff2 * yDot2 + coeff3 * yDot3 +
coeff4 * yDot4 + coeff5 * yDot5 + coeff6 * yDot6 + coeff7 * yDot7);
interpolatedDerivatives[i] = coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 +
coeffDot4 * yDot4 + coeffDot5 * yDot5 + coeffDot6 * yDot6 + coeffDot7 * yDot7;
}
}
}
}

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src/main/java/org/apache/commons/math3/ode/package-info.java
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@ -136,6 +136,7 @@
* <tr><td>{@link org.apache.commons.math3.ode.nonstiff.ClassicalRungeKuttaIntegrator Classical Runge-Kutta}</td><td>4</td></tr>
* <tr><td>{@link org.apache.commons.math3.ode.nonstiff.GillIntegrator Gill}</td><td>4</td></tr>
* <tr><td>{@link org.apache.commons.math3.ode.nonstiff.ThreeEighthesIntegrator 3/8}</td><td>4</td></tr>
* <tr><td>{@link org.apache.commons.math3.ode.nonstiff.LutherIntegrator Luther}</td><td>6</td></tr>
* </table>
* </p>
*

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src/site/xdoc/userguide/ode.xml
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@ -265,6 +265,7 @@ public int eventOccurred(double t, double[] y, boolean increasing) {
<tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaIntegrator.html">Classical Runge-Kutta</a></td><td>4</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/GillIntegrator.html">Gill</a></td><td>4</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/ThreeEighthesIntegrator.html">3/8</a></td><td>4</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/LutherIntegrator.html">Luther</a></td><td>6</td></tr>
</table>
</p>
<p>

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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.nonstiff;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.ode.FirstOrderDifferentialEquations;
import org.apache.commons.math3.ode.FirstOrderIntegrator;
import org.apache.commons.math3.ode.TestProblem1;
import org.apache.commons.math3.ode.TestProblem3;
import org.apache.commons.math3.ode.TestProblem5;
import org.apache.commons.math3.ode.TestProblemAbstract;
import org.apache.commons.math3.ode.TestProblemFactory;
import org.apache.commons.math3.ode.TestProblemHandler;
import org.apache.commons.math3.ode.events.EventHandler;
import org.apache.commons.math3.ode.sampling.StepHandler;
import org.apache.commons.math3.ode.sampling.StepInterpolator;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class LutherIntegratorTest {
@Test
public void testMissedEndEvent()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
final double t0 = 1878250320.0000029;
final double tEvent = 1878250379.9999986;
final double[] k = { 1.0e-4, 1.0e-5, 1.0e-6 };
FirstOrderDifferentialEquations ode = new FirstOrderDifferentialEquations() {
public int getDimension() {
return k.length;
}
public void computeDerivatives(double t, double[] y, double[] yDot) {
for (int i = 0; i < y.length; ++i) {
yDot[i] = k[i] * y[i];
}
}
};
LutherIntegrator integrator = new LutherIntegrator(60.0);
double[] y0 = new double[k.length];
for (int i = 0; i < y0.length; ++i) {
y0[i] = i + 1;
}
double[] y = new double[k.length];
double finalT = integrator.integrate(ode, t0, y0, tEvent, y);
Assert.assertEquals(tEvent, finalT, 1.0e-15);
for (int i = 0; i < y.length; ++i) {
Assert.assertEquals(y0[i] * FastMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-15);
}
integrator.addEventHandler(new EventHandler() {
public void init(double t0, double[] y0, double t) {
}
public void resetState(double t, double[] y) {
}
public double g(double t, double[] y) {
return t - tEvent;
}
public Action eventOccurred(double t, double[] y, boolean increasing) {
Assert.assertEquals(tEvent, t, 1.0e-15);
return Action.CONTINUE;
}
}, Double.POSITIVE_INFINITY, 1.0e-20, 100);
finalT = integrator.integrate(ode, t0, y0, tEvent + 120, y);
Assert.assertEquals(tEvent + 120, finalT, 1.0e-15);
for (int i = 0; i < y.length; ++i) {
Assert.assertEquals(y0[i] * FastMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-15);
}
}
@Test
public void testSanityChecks()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
try {
TestProblem1 pb = new TestProblem1();
new LutherIntegrator(0.01).integrate(pb,
0.0, new double[pb.getDimension()+10],
1.0, new double[pb.getDimension()]);
Assert.fail("an exception should have been thrown");
} catch(DimensionMismatchException ie) {
}
try {
TestProblem1 pb = new TestProblem1();
new LutherIntegrator(0.01).integrate(pb,
0.0, new double[pb.getDimension()],
1.0, new double[pb.getDimension()+10]);
Assert.fail("an exception should have been thrown");
} catch(DimensionMismatchException ie) {
}
try {
TestProblem1 pb = new TestProblem1();
new LutherIntegrator(0.01).integrate(pb,
0.0, new double[pb.getDimension()],
0.0, new double[pb.getDimension()]);
Assert.fail("an exception should have been thrown");
} catch(NumberIsTooSmallException ie) {
}
}
@Test
public void testDecreasingSteps()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblemAbstract[] problems = TestProblemFactory.getProblems();
for (int k = 0; k < problems.length; ++k) {
double previousValueError = Double.NaN;
double previousTimeError = Double.NaN;
for (int i = 4; i < 10; ++i) {
TestProblemAbstract pb = problems[k].copy();
double step = (pb.getFinalTime() - pb.getInitialTime()) * FastMath.pow(2.0, -i);
FirstOrderIntegrator integ = new LutherIntegrator(step);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
EventHandler[] functions = pb.getEventsHandlers();
for (int l = 0; l < functions.length; ++l) {
integ.addEventHandler(functions[l],
Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000);
}
Assert.assertEquals(functions.length, integ.getEventHandlers().size());
double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
if (functions.length == 0) {
Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
}
double error = handler.getMaximalValueError();
if (i > 4) {
Assert.assertTrue(error < 1.01 * FastMath.abs(previousValueError));
}
previousValueError = error;
double timeError = handler.getMaximalTimeError();
if (i > 4) {
Assert.assertTrue(timeError <= FastMath.abs(previousTimeError));
}
previousTimeError = timeError;
integ.clearEventHandlers();
Assert.assertEquals(0, integ.getEventHandlers().size());
}
}
}
@Test
public void testSmallStep()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
FirstOrderIntegrator integ = new LutherIntegrator(step);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertTrue(handler.getLastError() < 9.0e-17);
Assert.assertTrue(handler.getMaximalValueError() < 4.0e-15);
Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
Assert.assertEquals("Luther", integ.getName());
}
@Test
public void testBigStep()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;
FirstOrderIntegrator integ = new LutherIntegrator(step);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertTrue(handler.getLastError() > 0.00002);
Assert.assertTrue(handler.getMaximalValueError() > 0.001);
Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
}
@Test
public void testBackward()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem5 pb = new TestProblem5();
double step = FastMath.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;
FirstOrderIntegrator integ = new LutherIntegrator(step);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertTrue(handler.getLastError() < 3.0e-13);
Assert.assertTrue(handler.getMaximalValueError() < 5.0e-13);
Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
Assert.assertEquals("Luther", integ.getName());
}
@Test
public void testKepler()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
final TestProblem3 pb = new TestProblem3(0.9);
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
FirstOrderIntegrator integ = new LutherIntegrator(step);
integ.addStepHandler(new KeplerHandler(pb));
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
}
private static class KeplerHandler implements StepHandler {
public KeplerHandler(TestProblem3 pb) {
this.pb = pb;
maxError = 0;
}
public void init(double t0, double[] y0, double t) {
maxError = 0;
}
public void handleStep(StepInterpolator interpolator, boolean isLast) {
double[] interpolatedY = interpolator.getInterpolatedState ();
double[] theoreticalY = pb.computeTheoreticalState(interpolator.getCurrentTime());
double dx = interpolatedY[0] - theoreticalY[0];
double dy = interpolatedY[1] - theoreticalY[1];
double error = dx * dx + dy * dy;
if (error > maxError) {
maxError = error;
}
if (isLast) {
Assert.assertTrue(maxError < 2.2e-7);
}
}
private double maxError = 0;
private TestProblem3 pb;
}
@Test
public void testStepSize()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
final double step = 1.23456;
FirstOrderIntegrator integ = new LutherIntegrator(step);
integ.addStepHandler(new StepHandler() {
public void handleStep(StepInterpolator interpolator, boolean isLast) {
if (! isLast) {
Assert.assertEquals(step,
interpolator.getCurrentTime() - interpolator.getPreviousTime(),
1.0e-12);
}
}
public void init(double t0, double[] y0, double t) {
}
});
integ.integrate(new FirstOrderDifferentialEquations() {
public void computeDerivatives(double t, double[] y, double[] dot) {
dot[0] = 1.0;
}
public int getDimension() {
return 1;
}
}, 0.0, new double[] { 0.0 }, 5.0, new double[1]);
}
}

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@ -0,0 +1,98 @@
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.nonstiff;
import java.io.ByteArrayInputStream;
import java.io.ByteArrayOutputStream;
import java.io.IOException;
import java.io.ObjectInputStream;
import java.io.ObjectOutputStream;
import java.util.Random;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.ode.ContinuousOutputModel;
import org.apache.commons.math3.ode.TestProblem3;
import org.apache.commons.math3.ode.sampling.StepHandler;
import org.apache.commons.math3.ode.sampling.StepInterpolatorTestUtils;
import org.junit.Assert;
import org.junit.Test;
public class LutherStepInterpolatorTest {
@Test
public void derivativesConsistency()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem3 pb = new TestProblem3();
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
LutherIntegrator integ = new LutherIntegrator(step);
StepInterpolatorTestUtils.checkDerivativesConsistency(integ, pb, 1.0e-10);
}
@Test
public void serialization()
throws IOException, ClassNotFoundException,
DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem3 pb = new TestProblem3(0.9);
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
LutherIntegrator integ = new LutherIntegrator(step);
integ.addStepHandler(new ContinuousOutputModel());
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
ByteArrayOutputStream bos = new ByteArrayOutputStream();
ObjectOutputStream oos = new ObjectOutputStream(bos);
for (StepHandler handler : integ.getStepHandlers()) {
oos.writeObject(handler);
}
Assert.assertTrue(bos.size() > 1200000);
Assert.assertTrue(bos.size() < 1250000);
ByteArrayInputStream bis = new ByteArrayInputStream(bos.toByteArray());
ObjectInputStream ois = new ObjectInputStream(bis);
ContinuousOutputModel cm = (ContinuousOutputModel) ois.readObject();
Random random = new Random(347588535632l);
double maxError = 0.0;
for (int i = 0; i < 1000; ++i) {
double r = random.nextDouble();
double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
cm.setInterpolatedTime(time);
double[] interpolatedY = cm.getInterpolatedState ();
double[] theoreticalY = pb.computeTheoreticalState(time);
double dx = interpolatedY[0] - theoreticalY[0];
double dy = interpolatedY[1] - theoreticalY[1];
double error = dx * dx + dy * dy;
if (error > maxError) {
maxError = error;
}
}
Assert.assertTrue(maxError < 2.2e-7);
}
}