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Posted to commits@commons.apache.org by lu...@apache.org on 2014/04/20 15:25:12 UTC
svn commit: r1588753 - in /commons/proper/math/trunk/src: changes/
main/java/org/apache/commons/math3/ode/
main/java/org/apache/commons/math3/ode/nonstiff/ site/xdoc/userguide/
test/java/org/apache/commons/math3/ode/nonstiff/
Author: luc
Date: Sun Apr 20 13:25:11 2014
New Revision: 1588753
URL: http://svn.apache.org/r1588753
Log:
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.
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherIntegrator.java (with props)
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolator.java (with props)
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherIntegratorTest.java (with props)
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolatorTest.java (with props)
Modified:
commons/proper/math/trunk/src/changes/changes.xml
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/package-info.java
commons/proper/math/trunk/src/site/xdoc/userguide/ode.xml
Modified: commons/proper/math/trunk/src/changes/changes.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/changes/changes.xml?rev=1588753&r1=1588752&r2=1588753&view=diff
==============================================================================
--- commons/proper/math/trunk/src/changes/changes.xml (original)
+++ commons/proper/math/trunk/src/changes/changes.xml Sun Apr 20 13:25:11 2014
@@ -56,6 +56,9 @@ If the output is not quite correct, chec
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
Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherIntegrator.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherIntegrator.java?rev=1588753&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherIntegrator.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherIntegrator.java Sun Apr 20 13:25:11 2014
@@ -0,0 +1,90 @@
+/*
+ * 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 = √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);
+ }
+
+}
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherIntegrator.java
------------------------------------------------------------------------------
svn:eol-style = native
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherIntegrator.java
------------------------------------------------------------------------------
svn:keywords = "Author Date Id Revision"
Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolator.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolator.java?rev=1588753&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolator.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolator.java Sun Apr 20 13:25:11 2014
@@ -0,0 +1,180 @@
+/*
+ * 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;
+ }
+ }
+
+ }
+
+}
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolator.java
------------------------------------------------------------------------------
svn:eol-style = native
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolator.java
------------------------------------------------------------------------------
svn:keywords = "Author Date Id Revision"
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/package-info.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/package-info.java?rev=1588753&r1=1588752&r2=1588753&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/package-info.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/ode/package-info.java Sun Apr 20 13:25:11 2014
@@ -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>
*
Modified: commons/proper/math/trunk/src/site/xdoc/userguide/ode.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/site/xdoc/userguide/ode.xml?rev=1588753&r1=1588752&r2=1588753&view=diff
==============================================================================
--- commons/proper/math/trunk/src/site/xdoc/userguide/ode.xml (original)
+++ commons/proper/math/trunk/src/site/xdoc/userguide/ode.xml Sun Apr 20 13:25:11 2014
@@ -265,6 +265,7 @@ public int eventOccurred(double t, doubl
<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>
Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherIntegratorTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherIntegratorTest.java?rev=1588753&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherIntegratorTest.java (added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherIntegratorTest.java Sun Apr 20 13:25:11 2014
@@ -0,0 +1,309 @@
+/*
+ * 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]);
+ }
+
+}
Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherIntegratorTest.java
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Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolatorTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolatorTest.java?rev=1588753&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolatorTest.java (added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolatorTest.java Sun Apr 20 13:25:11 2014
@@ -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);
+
+ }
+
+}
Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/ode/nonstiff/LutherStepInterpolatorTest.java
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