You are viewing a plain text version of this content. The canonical link for it is here.
Posted to commits@commons.apache.org by lu...@apache.org on 2015/12/09 17:16:55 UTC
[15/50] [abbrv] [math] Added test for field version of classical
Runge-Kutta method.
Added test for field version of classical Runge-Kutta method.
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/e7a0dae4
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/e7a0dae4
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/e7a0dae4
Branch: refs/heads/MATH_3_X
Commit: e7a0dae448cf0268afdb663b643decce65170af8
Parents: e269953
Author: Luc Maisonobe <lu...@apache.org>
Authored: Tue Dec 1 16:45:12 2015 +0100
Committer: Luc Maisonobe <lu...@apache.org>
Committed: Tue Dec 1 16:45:12 2015 +0100
----------------------------------------------------------------------
.../ClassicalRungeKuttaFieldIntegratorTest.java | 428 +++++++++++++++++++
1 file changed, 428 insertions(+)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-math/blob/e7a0dae4/src/test/java/org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaFieldIntegratorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaFieldIntegratorTest.java b/src/test/java/org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaFieldIntegratorTest.java
new file mode 100644
index 0000000..7d93a29
--- /dev/null
+++ b/src/test/java/org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaFieldIntegratorTest.java
@@ -0,0 +1,428 @@
+/*
+ * 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.lang.reflect.Array;
+
+import org.apache.commons.math3.Field;
+import org.apache.commons.math3.RealFieldElement;
+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.FieldExpandableODE;
+import org.apache.commons.math3.ode.FieldFirstOrderDifferentialEquations;
+import org.apache.commons.math3.ode.FieldFirstOrderIntegrator;
+import org.apache.commons.math3.ode.FieldODEState;
+import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
+import org.apache.commons.math3.ode.TestFieldProblem1;
+import org.apache.commons.math3.ode.TestFieldProblem2;
+import org.apache.commons.math3.ode.TestFieldProblem3;
+import org.apache.commons.math3.ode.TestFieldProblem4;
+import org.apache.commons.math3.ode.TestFieldProblem5;
+import org.apache.commons.math3.ode.TestFieldProblem6;
+import org.apache.commons.math3.ode.TestFieldProblemAbstract;
+import org.apache.commons.math3.ode.TestFieldProblemHandler;
+import org.apache.commons.math3.ode.events.Action;
+import org.apache.commons.math3.ode.events.FieldEventHandler;
+import org.apache.commons.math3.ode.sampling.FieldStepHandler;
+import org.apache.commons.math3.ode.sampling.FieldStepInterpolator;
+import org.apache.commons.math3.util.Decimal64Field;
+import org.apache.commons.math3.util.FastMath;
+import org.apache.commons.math3.util.MathArrays;
+import org.junit.Assert;
+import org.junit.Test;
+
+public class ClassicalRungeKuttaFieldIntegratorTest {
+
+ @Test
+ public void testMissedEndEvent()
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ doTestMissedEndEvent(Decimal64Field.getInstance());
+ }
+
+ private <T extends RealFieldElement<T>>void doTestMissedEndEvent(final Field<T> field)
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ final T t0 = field.getZero().add(1878250320.0000029);
+ final T tEvent = field.getZero().add(1878250379.9999986);
+ final T[] k = MathArrays.buildArray(field, 3);
+ k[0] = field.getZero().add(1.0e-4);
+ k[1] = field.getZero().add(1.0e-5);
+ k[2] = field.getZero().add(1.0e-6);
+ FieldFirstOrderDifferentialEquations<T> ode = new FieldFirstOrderDifferentialEquations<T>() {
+
+ public int getDimension() {
+ return k.length;
+ }
+
+ public void init(T t0, T[] y0, T t) {
+ }
+
+ public T[] computeDerivatives(T t, T[] y) {
+ T[] yDot = MathArrays.buildArray(field, k.length);
+ for (int i = 0; i < y.length; ++i) {
+ yDot[i] = k[i].multiply(y[i]);
+ }
+ return yDot;
+ }
+ };
+
+ ClassicalRungeKuttaFieldIntegrator<T> integrator =
+ new ClassicalRungeKuttaFieldIntegrator<T>(field, field.getZero().add(60.0));
+
+ T[] y0 = MathArrays.buildArray(field, k.length);
+ for (int i = 0; i < y0.length; ++i) {
+ y0[i] = field.getOne().add(i);
+ }
+
+ FieldODEStateAndDerivative<T> result = integrator.integrate(new FieldExpandableODE<T>(ode),
+ new FieldODEState<T>(t0, y0),
+ tEvent);
+ Assert.assertEquals(tEvent.getReal(), result.getTime().getReal(), 5.0e-6);
+ T[] y = result.getState();
+ for (int i = 0; i < y.length; ++i) {
+ Assert.assertEquals(y0[i].multiply(k[i].multiply(result.getTime().subtract(t0)).exp()).getReal(),
+ y[i].getReal(),
+ 1.0e-9);
+ }
+
+ integrator.addEventHandler(new FieldEventHandler<T>() {
+
+ public void init(FieldODEStateAndDerivative<T> state0, T t) {
+ }
+
+ public FieldODEState<T> resetState(FieldODEStateAndDerivative<T> state) {
+ return state;
+ }
+
+ public T g(FieldODEStateAndDerivative<T> state) {
+ return state.getTime().subtract(tEvent);
+ }
+
+ public Action eventOccurred(FieldODEStateAndDerivative<T> state, boolean increasing) {
+ Assert.assertEquals(tEvent.getReal(), state.getTime().getReal(), 5.0e-6);
+ return Action.CONTINUE;
+ }
+ }, Double.POSITIVE_INFINITY, 1.0e-20, 100);
+ result = integrator.integrate(new FieldExpandableODE<T>(ode),
+ new FieldODEState<T>(t0, y0),
+ tEvent.add(120));
+ Assert.assertEquals(tEvent.add(120).getReal(), result.getTime().getReal(), 5.0e-6);
+ y = result.getState();
+ for (int i = 0; i < y.length; ++i) {
+ Assert.assertEquals(y0[i].multiply(k[i].multiply(result.getTime().subtract(t0)).exp()).getReal(),
+ y[i].getReal(),
+ 1.0e-9);
+ }
+
+ }
+
+ @Test
+ public void testSanityChecks()
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ doTestSanityChecks(Decimal64Field.getInstance());
+ }
+
+ private <T extends RealFieldElement<T>>void doTestSanityChecks(Field<T> field)
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ ClassicalRungeKuttaFieldIntegrator<T> integrator =
+ new ClassicalRungeKuttaFieldIntegrator<T>(field, field.getZero().add(0.01));
+ try {
+ TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+ integrator.integrate(new FieldExpandableODE<>(pb),
+ new FieldODEState<T>(field.getZero(), MathArrays.buildArray(field, pb.getDimension() + 10)),
+ field.getOne());
+ Assert.fail("an exception should have been thrown");
+ } catch(DimensionMismatchException ie) {
+ }
+ try {
+ TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+ integrator.integrate(new FieldExpandableODE<>(pb),
+ new FieldODEState<T>(field.getZero(), MathArrays.buildArray(field, pb.getDimension())),
+ field.getZero());
+ Assert.fail("an exception should have been thrown");
+ } catch(NumberIsTooSmallException ie) {
+ }
+ }
+
+ @Test
+ public void testDecreasingSteps()
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ doTestDecreasingSteps(Decimal64Field.getInstance());
+ }
+
+ private <T extends RealFieldElement<T>>void doTestDecreasingSteps(Field<T> field)
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+
+ @SuppressWarnings("unchecked")
+ TestFieldProblemAbstract<T>[] allProblems =
+ (TestFieldProblemAbstract<T>[]) Array.newInstance(TestFieldProblemAbstract.class, 6);
+ allProblems[0] = new TestFieldProblem1<T>(field);
+ allProblems[1] = new TestFieldProblem2<T>(field);
+ allProblems[2] = new TestFieldProblem3<T>(field);
+ allProblems[3] = new TestFieldProblem4<T>(field);
+ allProblems[4] = new TestFieldProblem5<T>(field);
+ allProblems[5] = new TestFieldProblem6<T>(field);
+ for (TestFieldProblemAbstract<T> pb : allProblems) {
+
+ T previousValueError = null;
+ T previousTimeError = null;
+ for (int i = 4; i < 10; ++i) {
+
+ T step = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(FastMath.pow(2.0, -i));
+
+ FieldFirstOrderIntegrator<T> integ = new ClassicalRungeKuttaFieldIntegrator<T>(field, step);
+ TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+ integ.addStepHandler(handler);
+ FieldEventHandler<T>[] functions = pb.getEventsHandlers();
+ for (int l = 0; l < functions.length; ++l) {
+ integ.addEventHandler(functions[l],
+ Double.POSITIVE_INFINITY, 1.0e-6 * step.getReal(), 1000);
+ }
+ Assert.assertEquals(functions.length, integ.getEventHandlers().size());
+ FieldODEStateAndDerivative<T> stop = integ.integrate(new FieldExpandableODE<T>(pb),
+ pb.getInitialState(),
+ pb.getFinalTime());
+ if (functions.length == 0) {
+ Assert.assertEquals(pb.getFinalTime().getReal(), stop.getTime().getReal(), 1.0e-10);
+ }
+
+ T error = handler.getMaximalValueError();
+ if (i > 4) {
+ Assert.assertTrue(error.subtract(previousValueError.abs().multiply(1.01)).getReal() < 0);
+ }
+ previousValueError = error;
+
+ T timeError = handler.getMaximalTimeError();
+ if (i > 4) {
+ Assert.assertTrue(timeError.subtract(previousTimeError.abs()).getReal() <= 0);
+ }
+ previousTimeError = timeError;
+
+ integ.clearEventHandlers();
+ Assert.assertEquals(0, integ.getEventHandlers().size());
+ }
+
+ }
+
+ }
+
+ @Test
+ public void testSmallStep()
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ doTestSmallStep(Decimal64Field.getInstance());
+ }
+
+ private <T extends RealFieldElement<T>>void doTestSmallStep(Field<T> field)
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+
+ TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+ T step = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.001);
+
+ FieldFirstOrderIntegrator<T> integ = new ClassicalRungeKuttaFieldIntegrator<T>(field, step);
+ TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+ integ.addStepHandler(handler);
+ integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+ Assert.assertTrue(handler.getLastError().getReal() < 2.0e-13);
+ Assert.assertTrue(handler.getMaximalValueError().getReal() < 4.0e-12);
+ Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), 1.0e-12);
+ Assert.assertEquals("classical Runge-Kutta", integ.getName());
+ }
+
+ @Test
+ public void testBigStep()
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ doTestBigStep(Decimal64Field.getInstance());
+ }
+
+ private <T extends RealFieldElement<T>>void doTestBigStep(Field<T> field)
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+
+ TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+ T step = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.2);
+
+ FieldFirstOrderIntegrator<T> integ = new ClassicalRungeKuttaFieldIntegrator<T>(field, step);
+ TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+ integ.addStepHandler(handler);
+ integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+ Assert.assertTrue(handler.getLastError().getReal() > 0.0004);
+ Assert.assertTrue(handler.getMaximalValueError().getReal() > 0.005);
+ Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), 1.0e-12);
+
+ }
+
+ @Test
+ public void testBackward()
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ doTestBackward(Decimal64Field.getInstance());
+ }
+
+ private <T extends RealFieldElement<T>>void doTestBackward(Field<T> field)
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+
+ TestFieldProblem5<T> pb = new TestFieldProblem5<T>(field);
+ T step = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.001).abs();
+
+ FieldFirstOrderIntegrator<T> integ = new ClassicalRungeKuttaFieldIntegrator<T>(field, step);
+ TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+ integ.addStepHandler(handler);
+ integ.integrate(new FieldExpandableODE<>(pb), pb.getInitialState(), pb.getFinalTime());
+
+ Assert.assertTrue(handler.getLastError().getReal() < 5.0e-10);
+ Assert.assertTrue(handler.getMaximalValueError().getReal() < 7.0e-10);
+ Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), 1.0e-12);
+ Assert.assertEquals("classical Runge-Kutta", integ.getName());
+ }
+
+ @Test
+ public void testKepler()
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ doTestKepler(Decimal64Field.getInstance());
+ }
+
+ private <T extends RealFieldElement<T>>void doTestKepler(Field<T> field)
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+
+ final TestFieldProblem3<T> pb = new TestFieldProblem3<T>(field, field.getZero().add(0.9));
+ T step = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.0003);
+
+ FieldFirstOrderIntegrator<T> integ = new ClassicalRungeKuttaFieldIntegrator<T>(field, step);
+ integ.addStepHandler(new KeplerHandler<T>(pb));
+ integ.integrate(new FieldExpandableODE<>(pb), pb.getInitialState(), pb.getFinalTime());
+ }
+
+ private static class KeplerHandler<T extends RealFieldElement<T>> implements FieldStepHandler<T> {
+ public KeplerHandler(TestFieldProblem3<T> pb) {
+ this.pb = pb;
+ maxError = pb.getField().getZero();
+ }
+ public void init(FieldODEStateAndDerivative<T> state0, T t) {
+ maxError = pb.getField().getZero();
+ }
+ public void handleStep(FieldStepInterpolator<T> interpolator, boolean isLast)
+ throws MaxCountExceededException {
+
+ FieldODEStateAndDerivative<T> current = interpolator.getCurrentState();
+ T[] theoreticalY = pb.computeTheoreticalState(current.getTime());
+ T dx = current.getState()[0].subtract(theoreticalY[0]);
+ T dy = current.getState()[1].subtract(theoreticalY[1]);
+ T error = dx.multiply(dx).add(dy.multiply(dy));
+ if (error.subtract(maxError).getReal() > 0) {
+ maxError = error;
+ }
+ if (isLast) {
+ // even with more than 1000 evaluations per period,
+ // RK4 is not able to integrate such an eccentric
+ // orbit with a good accuracy
+ Assert.assertTrue(maxError.getReal() > 0.005);
+ }
+ }
+ private T maxError;
+ private TestFieldProblem3<T> pb;
+ }
+
+ @Test
+ public void testStepSize()
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ doTestStepSize(Decimal64Field.getInstance());
+ }
+
+ private <T extends RealFieldElement<T>>void doTestStepSize(Field<T> field)
+ throws DimensionMismatchException, NumberIsTooSmallException,
+ MaxCountExceededException, NoBracketingException {
+ final T step = field.getZero().add(1.23456);
+ FieldFirstOrderIntegrator<T> integ = new ClassicalRungeKuttaFieldIntegrator<T>(field, step);
+ integ.addStepHandler(new FieldStepHandler<T>() {
+ public void handleStep(FieldStepInterpolator<T> interpolator, boolean isLast) {
+ if (! isLast) {
+ Assert.assertEquals(step.getReal(),
+ interpolator.getCurrentState().getTime().subtract(interpolator.getPreviousState().getTime()).getReal(),
+ 1.0e-12);
+ }
+ }
+ public void init(FieldODEStateAndDerivative<T> s0, T t) {
+ }
+ });
+ integ.integrate(new FieldExpandableODE<T>(new FieldFirstOrderDifferentialEquations<T>() {
+ public void init(T t0, T[] y0, T t) {
+ }
+ public T[] computeDerivatives(T t, T[] y) {
+ T[] dot = MathArrays.buildArray(t.getField(), 1);
+ dot[0] = t.getField().getOne();
+ return dot;
+ }
+ public int getDimension() {
+ return 1;
+ }
+ }), new FieldODEState<T>(field.getZero(), MathArrays.buildArray(field, 1)), field.getZero().add(5.0));
+ }
+
+ @Test
+ public void testTooLargeFirstStep() {
+ doTestTooLargeFirstStep(Decimal64Field.getInstance());
+ }
+
+ private <T extends RealFieldElement<T>>void doTestTooLargeFirstStep(final Field<T> field) {
+
+ RungeKuttaFieldIntegrator<T> integ = new ClassicalRungeKuttaFieldIntegrator<T>(field, field.getZero().add(0.5));
+ final T t0 = field.getZero();
+ final T[] y0 = MathArrays.buildArray(field, 1);
+ y0[0] = field.getOne();
+ final T t = field.getZero().add(0.001);
+ FieldFirstOrderDifferentialEquations<T> equations = new FieldFirstOrderDifferentialEquations<T>() {
+
+ public int getDimension() {
+ return 1;
+ }
+
+ public void init(T t0, T[] y0, T t) {
+ }
+
+ public T[] computeDerivatives(T t, T[] y) {
+ Assert.assertTrue(t.getReal() >= FastMath.nextAfter(t0.getReal(), Double.NEGATIVE_INFINITY));
+ Assert.assertTrue(t.getReal() <= FastMath.nextAfter(t.getReal(), Double.POSITIVE_INFINITY));
+ T[] yDot = MathArrays.buildArray(field, 1);
+ yDot[0] = y[0].multiply(-100.0);
+ return yDot;
+ }
+
+ };
+
+ integ.integrate(new FieldExpandableODE<>(equations), new FieldODEState<T>(t0, y0), t);
+
+ }
+
+}