Repository: commons-math Updated Branches: refs/heads/MATH_3_X 895e9c1c5 -> c5e6ccb81
http://git-wip-us.apache.org/repos/asf/commons-math/blob/29649959/src/test/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegratorAbstractTest.java ---------------------------------------------------------------------- diff --git a/src/test/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegratorAbstractTest.java b/src/test/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegratorAbstractTest.java new file mode 100644 index 0000000..518690a --- /dev/null +++ b/src/test/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegratorAbstractTest.java @@ -0,0 +1,662 @@ +/* + * 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.analysis.differentiation.DerivativeStructure; +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.FirstOrderFieldDifferentialEquations; +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.ode.sampling.StepInterpolatorTestUtils; +import org.apache.commons.math3.util.FastMath; +import org.apache.commons.math3.util.MathArrays; +import org.junit.Assert; +import org.junit.Test; + +public abstract class RungeKuttaFieldIntegratorAbstractTest { + + protected abstract <T extends RealFieldElement<T>> RungeKuttaFieldIntegrator<T> + createIntegrator(Field<T> field, T step); + + @Test + public abstract void testNonFieldIntegratorConsistency(); + + protected <T extends RealFieldElement<T>> void doTestNonFieldIntegratorConsistency(final Field<T> field) { + try { + + // get the Butcher arrays from the field integrator + RungeKuttaFieldIntegrator<T> fieldIntegrator = createIntegrator(field, field.getZero().add(1)); + T[][] fieldA = fieldIntegrator.getA(); + T[] fieldB = fieldIntegrator.getB(); + T[] fieldC = fieldIntegrator.getC(); + + String fieldName = fieldIntegrator.getClass().getName(); + String regularName = fieldName.replaceAll("Field", ""); + + // get the Butcher arrays from the regular integrator + @SuppressWarnings("unchecked") + Class<RungeKuttaIntegrator> c = (Class<RungeKuttaIntegrator>) Class.forName(regularName); + java.lang.reflect.Field jlrFieldA = c.getDeclaredField("STATIC_A"); + jlrFieldA.setAccessible(true); + double[][] regularA = (double[][]) jlrFieldA.get(null); + java.lang.reflect.Field jlrFieldB = c.getDeclaredField("STATIC_B"); + jlrFieldB.setAccessible(true); + double[] regularB = (double[]) jlrFieldB.get(null); + java.lang.reflect.Field jlrFieldC = c.getDeclaredField("STATIC_C"); + jlrFieldC.setAccessible(true); + double[] regularC = (double[]) jlrFieldC.get(null); + + Assert.assertEquals(regularA.length, fieldA.length); + for (int i = 0; i < regularA.length; ++i) { + checkArray(regularA[i], fieldA[i]); + } + checkArray(regularB, fieldB); + checkArray(regularC, fieldC); + + } catch (ClassNotFoundException cnfe) { + Assert.fail(cnfe.getLocalizedMessage()); + } catch (IllegalAccessException iae) { + Assert.fail(iae.getLocalizedMessage()); + } catch (IllegalArgumentException iae) { + Assert.fail(iae.getLocalizedMessage()); + } catch (SecurityException se) { + Assert.fail(se.getLocalizedMessage()); + } catch (NoSuchFieldException nsfe) { + Assert.fail(nsfe.getLocalizedMessage()); + } + } + + private <T extends RealFieldElement<T>> void checkArray(double[] regularArray, T[] fieldArray) { + Assert.assertEquals(regularArray.length, fieldArray.length); + for (int i = 0; i < regularArray.length; ++i) { + if (regularArray[i] == 0) { + Assert.assertTrue(0.0 == fieldArray[i].getReal()); + } else { + Assert.assertEquals(regularArray[i], fieldArray[i].getReal(), FastMath.ulp(regularArray[i])); + } + } + } + + @Test + public abstract void testMissedEndEvent(); + + protected <T extends RealFieldElement<T>> void doTestMissedEndEvent(final Field<T> field, + final double epsilonT, final double epsilonY) + 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); + FirstOrderFieldDifferentialEquations<T> ode = new FirstOrderFieldDifferentialEquations<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; + } + }; + + RungeKuttaFieldIntegrator<T> integrator = createIntegrator(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(), epsilonT); + 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(), + epsilonY); + } + + 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(), epsilonT); + 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(), epsilonT); + 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(), + epsilonY); + } + + } + + @Test + public abstract void testSanityChecks(); + + protected <T extends RealFieldElement<T>> void doTestSanityChecks(Field<T> field) + throws DimensionMismatchException, NumberIsTooSmallException, + MaxCountExceededException, NoBracketingException { + RungeKuttaFieldIntegrator<T> integrator = createIntegrator(field, field.getZero().add(0.01)); + try { + TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field); + integrator.integrate(new FieldExpandableODE<T>(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<T>(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 abstract void testDecreasingSteps(); + + protected <T extends RealFieldElement<T>> void doTestDecreasingSteps(Field<T> field, + final double safetyValueFactor, + final double safetyTimeFactor, + final double epsilonT) + 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)); + + RungeKuttaFieldIntegrator<T> integ = createIntegrator(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(), epsilonT); + } + + T error = handler.getMaximalValueError(); + if (i > 4) { + Assert.assertTrue(error.subtract(previousValueError.abs().multiply(safetyValueFactor)).getReal() < 0); + } + previousValueError = error; + + T timeError = handler.getMaximalTimeError(); + if (i > 4) { + Assert.assertTrue(timeError.subtract(previousTimeError.abs().multiply(safetyTimeFactor)).getReal() <= 0); + } + previousTimeError = timeError; + + integ.clearEventHandlers(); + Assert.assertEquals(0, integ.getEventHandlers().size()); + } + + } + + } + + @Test + public abstract void testSmallStep(); + + protected <T extends RealFieldElement<T>> void doTestSmallStep(Field<T> field, + final double epsilonLast, + final double epsilonMaxValue, + final double epsilonMaxTime, + final String name) + throws DimensionMismatchException, NumberIsTooSmallException, + MaxCountExceededException, NoBracketingException { + + TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field); + T step = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.001); + + RungeKuttaFieldIntegrator<T> integ = createIntegrator(field, step); + TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ); + integ.addStepHandler(handler); + integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime()); + + Assert.assertEquals(0, handler.getLastError().getReal(), epsilonLast); + Assert.assertEquals(0, handler.getMaximalValueError().getReal(), epsilonMaxValue); + Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), epsilonMaxTime); + Assert.assertEquals(name, integ.getName()); + + } + + @Test + public abstract void testBigStep(); + + protected <T extends RealFieldElement<T>> void doTestBigStep(Field<T> field, + final double belowLast, + final double belowMaxValue, + final double epsilonMaxTime, + final String name) + throws DimensionMismatchException, NumberIsTooSmallException, + MaxCountExceededException, NoBracketingException { + + TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field); + T step = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.2); + + RungeKuttaFieldIntegrator<T> integ = createIntegrator(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() > belowLast); + Assert.assertTrue(handler.getMaximalValueError().getReal() > belowMaxValue); + Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), epsilonMaxTime); + Assert.assertEquals(name, integ.getName()); + + } + + @Test + public abstract void testBackward(); + + protected <T extends RealFieldElement<T>> void doTestBackward(Field<T> field, + final double epsilonLast, + final double epsilonMaxValue, + final double epsilonMaxTime, + final String name) + throws DimensionMismatchException, NumberIsTooSmallException, + MaxCountExceededException, NoBracketingException { + + TestFieldProblem5<T> pb = new TestFieldProblem5<T>(field); + T step = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.001).abs(); + + RungeKuttaFieldIntegrator<T> integ = createIntegrator(field, step); + TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ); + integ.addStepHandler(handler); + integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime()); + + Assert.assertEquals(0, handler.getLastError().getReal(), epsilonLast); + Assert.assertEquals(0, handler.getMaximalValueError().getReal(), epsilonMaxValue); + Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), epsilonMaxTime); + Assert.assertEquals(name, integ.getName()); + + } + + @Test + public abstract void testKepler(); + + protected <T extends RealFieldElement<T>> void doTestKepler(Field<T> field, double expectedMaxError, double epsilon) + 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); + + RungeKuttaFieldIntegrator<T> integ = createIntegrator(field, step); + integ.addStepHandler(new KeplerHandler<T>(pb, expectedMaxError, epsilon)); + integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime()); + } + + private static class KeplerHandler<T extends RealFieldElement<T>> implements FieldStepHandler<T> { + private T maxError; + private final TestFieldProblem3<T> pb; + private final double expectedMaxError; + private final double epsilon; + public KeplerHandler(TestFieldProblem3<T> pb, double expectedMaxError, double epsilon) { + this.pb = pb; + this.expectedMaxError = expectedMaxError; + this.epsilon = epsilon; + 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) { + Assert.assertEquals(expectedMaxError, maxError.getReal(), epsilon); + } + } + } + + @Test + public abstract void testStepSize(); + + protected <T extends RealFieldElement<T>> void doTestStepSize(final Field<T> field, final double epsilon) + throws DimensionMismatchException, NumberIsTooSmallException, + MaxCountExceededException, NoBracketingException { + final T step = field.getZero().add(1.23456); + RungeKuttaFieldIntegrator<T> integ = createIntegrator(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(), + epsilon); + } + } + public void init(FieldODEStateAndDerivative<T> s0, T t) { + } + }); + integ.integrate(new FieldExpandableODE<T>(new FirstOrderFieldDifferentialEquations<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 abstract void testSingleStep(); + + protected <T extends RealFieldElement<T>> void doTestSingleStep(final Field<T> field, final double epsilon) { + + final TestFieldProblem3<T> pb = new TestFieldProblem3<T>(field, field.getZero().add(0.9)); + T h = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.0003); + + RungeKuttaFieldIntegrator<T> integ = createIntegrator(field, field.getZero().add(Double.NaN)); + T t = pb.getInitialState().getTime(); + T[] y = pb.getInitialState().getState(); + for (int i = 0; i < 100; ++i) { + y = integ.singleStep(pb, t, y, t.add(h)); + t = t.add(h); + } + T[] yth = pb.computeTheoreticalState(t); + T dx = y[0].subtract(yth[0]); + T dy = y[1].subtract(yth[1]); + T error = dx.multiply(dx).add(dy.multiply(dy)); + Assert.assertEquals(0.0, error.getReal(), epsilon); + } + + @Test + public abstract void testTooLargeFirstStep(); + + protected <T extends RealFieldElement<T>> void doTestTooLargeFirstStep(final Field<T> field) { + + RungeKuttaFieldIntegrator<T> integ = createIntegrator(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); + FirstOrderFieldDifferentialEquations<T> equations = new FirstOrderFieldDifferentialEquations<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<T>(equations), new FieldODEState<T>(t0, y0), t); + + } + + @Test + public abstract void testUnstableDerivative(); + + protected <T extends RealFieldElement<T>> void doTestUnstableDerivative(Field<T> field, double epsilon) { + final StepFieldProblem<T> stepProblem = new StepFieldProblem<T>(field, + field.getZero().add(0.0), + field.getZero().add(1.0), + field.getZero().add(2.0)); + RungeKuttaFieldIntegrator<T> integ = createIntegrator(field, field.getZero().add(0.3)); + integ.addEventHandler(stepProblem, 1.0, 1.0e-12, 1000); + FieldODEStateAndDerivative<T> result = integ.integrate(new FieldExpandableODE<T>(stepProblem), + new FieldODEState<T>(field.getZero(), MathArrays.buildArray(field, 1)), + field.getZero().add(10.0)); + Assert.assertEquals(8.0, result.getState()[0].getReal(), epsilon); + } + + @Test + public abstract void testDerivativesConsistency(); + + protected <T extends RealFieldElement<T>> void doTestDerivativesConsistency(final Field<T> field, double epsilon) { + TestFieldProblem3<T> pb = new TestFieldProblem3<T>(field); + T step = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.001); + RungeKuttaFieldIntegrator<T> integ = createIntegrator(field, step); + StepInterpolatorTestUtils.checkDerivativesConsistency(integ, pb, 1.0e-10); + } + + @Test + public abstract void testPartialDerivatives(); + + protected void doTestPartialDerivatives(final double epsilonY, + final double[] epsilonPartials) { + + // parameters indices + final int parameters = 5; + final int order = 1; + final int parOmega = 0; + final int parTO = 1; + final int parY00 = 2; + final int parY01 = 3; + final int parT = 4; + + DerivativeStructure omega = new DerivativeStructure(parameters, order, parOmega, 1.3); + DerivativeStructure t0 = new DerivativeStructure(parameters, order, parTO, 1.3); + DerivativeStructure[] y0 = new DerivativeStructure[] { + new DerivativeStructure(parameters, order, parY00, 3.0), + new DerivativeStructure(parameters, order, parY01, 4.0) + }; + DerivativeStructure t = new DerivativeStructure(parameters, order, parT, 6.0); + SinCos sinCos = new SinCos(omega); + + RungeKuttaFieldIntegrator<DerivativeStructure> integrator = + createIntegrator(omega.getField(), t.subtract(t0).multiply(0.001)); + FieldODEStateAndDerivative<DerivativeStructure> result = + integrator.integrate(new FieldExpandableODE<DerivativeStructure>(sinCos), + new FieldODEState<DerivativeStructure>(t0, y0), + t); + + // check values + for (int i = 0; i < sinCos.getDimension(); ++i) { + Assert.assertEquals(sinCos.theoreticalY(t.getReal())[i], result.getState()[i].getValue(), epsilonY); + } + + // check derivatives + final double[][] derivatives = sinCos.getDerivatives(t.getReal()); + for (int i = 0; i < sinCos.getDimension(); ++i) { + for (int parameter = 0; parameter < parameters; ++parameter) { + Assert.assertEquals(derivatives[i][parameter], + dYdP(result.getState()[i], parameter), + epsilonPartials[parameter]); + } + } + + } + + private double dYdP(final DerivativeStructure y, final int parameter) { + int[] orders = new int[y.getFreeParameters()]; + orders[parameter] = 1; + return y.getPartialDerivative(orders); + } + + private static class SinCos implements FirstOrderFieldDifferentialEquations<DerivativeStructure> { + + private final DerivativeStructure omega; + private DerivativeStructure r; + private DerivativeStructure alpha; + + private double dRdY00; + private double dRdY01; + private double dAlphadOmega; + private double dAlphadT0; + private double dAlphadY00; + private double dAlphadY01; + + protected SinCos(final DerivativeStructure omega) { + this.omega = omega; + } + + public int getDimension() { + return 2; + } + + public void init(final DerivativeStructure t0, final DerivativeStructure[] y0, + final DerivativeStructure finalTime) { + + // theoretical solution is y(t) = { r * sin(omega * t + alpha), r * cos(omega * t + alpha) } + // so we retrieve alpha by identification from the initial state + final DerivativeStructure r2 = y0[0].multiply(y0[0]).add(y0[1].multiply(y0[1])); + + this.r = r2.sqrt(); + this.dRdY00 = y0[0].divide(r).getReal(); + this.dRdY01 = y0[1].divide(r).getReal(); + + this.alpha = y0[0].atan2(y0[1]).subtract(t0.multiply(omega)); + this.dAlphadOmega = -t0.getReal(); + this.dAlphadT0 = -omega.getReal(); + this.dAlphadY00 = y0[1].divide(r2).getReal(); + this.dAlphadY01 = y0[0].negate().divide(r2).getReal(); + + } + + public DerivativeStructure[] computeDerivatives(final DerivativeStructure t, final DerivativeStructure[] y) { + return new DerivativeStructure[] { + omega.multiply(y[1]), + omega.multiply(y[0]).negate() + }; + } + + public double[] theoreticalY(final double t) { + final double theta = omega.getReal() * t + alpha.getReal(); + return new double[] { + r.getReal() * FastMath.sin(theta), r.getReal() * FastMath.cos(theta) + }; + } + + public double[][] getDerivatives(final double t) { + + // intermediate angle and state + final double theta = omega.getReal() * t + alpha.getReal(); + final double sin = FastMath.sin(theta); + final double cos = FastMath.cos(theta); + final double y0 = r.getReal() * sin; + final double y1 = r.getReal() * cos; + + // partial derivatives of the state first component + final double dY0dOmega = y1 * (t + dAlphadOmega); + final double dY0dT0 = y1 * dAlphadT0; + final double dY0dY00 = dRdY00 * sin + y1 * dAlphadY00; + final double dY0dY01 = dRdY01 * sin + y1 * dAlphadY01; + final double dY0dT = y1 * omega.getReal(); + + // partial derivatives of the state second component + final double dY1dOmega = - y0 * (t + dAlphadOmega); + final double dY1dT0 = - y0 * dAlphadT0; + final double dY1dY00 = dRdY00 * cos - y0 * dAlphadY00; + final double dY1dY01 = dRdY01 * cos - y0 * dAlphadY01; + final double dY1dT = - y0 * omega.getReal(); + + return new double[][] { + { dY0dOmega, dY0dT0, dY0dY00, dY0dY01, dY0dT }, + { dY1dOmega, dY1dT0, dY1dY00, dY1dY01, dY1dT } + }; + + } + + } + +} http://git-wip-us.apache.org/repos/asf/commons-math/blob/29649959/src/test/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldStepInterpolatorAbstractTest.java ---------------------------------------------------------------------- diff --git a/src/test/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldStepInterpolatorAbstractTest.java b/src/test/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldStepInterpolatorAbstractTest.java new file mode 100644 index 0000000..601e7b0 --- /dev/null +++ b/src/test/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldStepInterpolatorAbstractTest.java @@ -0,0 +1,305 @@ +/* + * 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.Field; +import org.apache.commons.math3.RealFieldElement; +import org.apache.commons.math3.ode.AbstractIntegrator; +import org.apache.commons.math3.ode.EquationsMapper; +import org.apache.commons.math3.ode.ExpandableStatefulODE; +import org.apache.commons.math3.ode.FieldEquationsMapper; +import org.apache.commons.math3.ode.FieldExpandableODE; +import org.apache.commons.math3.ode.FirstOrderFieldDifferentialEquations; +import org.apache.commons.math3.ode.FieldODEStateAndDerivative; +import org.apache.commons.math3.ode.sampling.AbstractFieldStepInterpolator; +import org.apache.commons.math3.util.FastMath; +import org.apache.commons.math3.util.MathArrays; +import org.junit.Assert; +import org.junit.Test; + +public abstract class RungeKuttaFieldStepInterpolatorAbstractTest { + + protected abstract <T extends RealFieldElement<T>> RungeKuttaFieldStepInterpolator<T> + createInterpolator(Field<T> field, boolean forward, T[][] yDotK, + FieldODEStateAndDerivative<T> globalPreviousState, + FieldODEStateAndDerivative<T> globalCurrentState, + FieldODEStateAndDerivative<T> softPreviousState, + FieldODEStateAndDerivative<T> softCurrentState, + FieldEquationsMapper<T> mapper); + + protected abstract <T extends RealFieldElement<T>> FieldButcherArrayProvider<T> + createButcherArrayProvider(final Field<T> field); + + @Test + public abstract void interpolationAtBounds(); + + protected <T extends RealFieldElement<T>> void doInterpolationAtBounds(final Field<T> field, double epsilon) { + + RungeKuttaFieldStepInterpolator<T> interpolator = setUpInterpolator(field, + new SinCos<T>(field), + 0.0, new double[] { 0.0, 1.0 }, 0.125); + + Assert.assertEquals(0.0, interpolator.getPreviousState().getTime().getReal(), 1.0e-15); + for (int i = 0; i < 2; ++i) { + Assert.assertEquals(interpolator.getPreviousState().getState()[i].getReal(), + interpolator.getInterpolatedState(interpolator.getPreviousState().getTime()).getState()[i].getReal(), + epsilon); + } + Assert.assertEquals(0.125, interpolator.getCurrentState().getTime().getReal(), 1.0e-15); + for (int i = 0; i < 2; ++i) { + Assert.assertEquals(interpolator.getCurrentState().getState()[i].getReal(), + interpolator.getInterpolatedState(interpolator.getCurrentState().getTime()).getState()[i].getReal(), + epsilon); + } + + } + + @Test + public abstract void interpolationInside(); + + protected <T extends RealFieldElement<T>> void doInterpolationInside(final Field<T> field, + double epsilonSin, double epsilonCos) { + + RungeKuttaFieldStepInterpolator<T> interpolator = setUpInterpolator(field, + new SinCos<T>(field), + 0.0, new double[] { 0.0, 1.0 }, 0.0125); + + int n = 100; + double maxErrorSin = 0; + double maxErrorCos = 0; + for (int i = 0; i <= n; ++i) { + T t = interpolator.getPreviousState().getTime().multiply(n - i). + add(interpolator.getCurrentState().getTime().multiply(i)). + divide(n); + FieldODEStateAndDerivative<T> state = interpolator.getInterpolatedState(t); + maxErrorSin = FastMath.max(maxErrorSin, state.getState()[0].subtract(t.sin()).abs().getReal()); + maxErrorCos = FastMath.max(maxErrorCos, state.getState()[1].subtract(t.cos()).abs().getReal()); + } + Assert.assertEquals(0.0, maxErrorSin, epsilonSin); + Assert.assertEquals(0.0, maxErrorCos, epsilonCos); + + } + + @Test + public abstract void nonFieldInterpolatorConsistency(); + + protected <T extends RealFieldElement<T>> void doNonFieldInterpolatorConsistency(final Field<T> field, + double epsilonSin, double epsilonCos, + double epsilonSinDot, double epsilonCosDot) { + + FirstOrderFieldDifferentialEquations<T> eqn = new SinCos<T>(field); + RungeKuttaFieldStepInterpolator<T> fieldInterpolator = + setUpInterpolator(field, eqn, 0.0, new double[] { 0.0, 1.0 }, 0.125); + RungeKuttaStepInterpolator regularInterpolator = convertInterpolator(fieldInterpolator, eqn); + + int n = 100; + double maxErrorSin = 0; + double maxErrorCos = 0; + double maxErrorSinDot = 0; + double maxErrorCosDot = 0; + for (int i = 0; i <= n; ++i) { + + T t = fieldInterpolator.getPreviousState().getTime().multiply(n - i). + add(fieldInterpolator.getCurrentState().getTime().multiply(i)). + divide(n); + + FieldODEStateAndDerivative<T> state = fieldInterpolator.getInterpolatedState(t); + T[] fieldY = state.getState(); + T[] fieldYDot = state.getDerivative(); + + regularInterpolator.setInterpolatedTime(t.getReal()); + double[] regularY = regularInterpolator.getInterpolatedState(); + double[] regularYDot = regularInterpolator.getInterpolatedDerivatives(); + + maxErrorSin = FastMath.max(maxErrorSin, fieldY[0].subtract(regularY[0]).abs().getReal()); + maxErrorCos = FastMath.max(maxErrorCos, fieldY[1].subtract(regularY[1]).abs().getReal()); + maxErrorSinDot = FastMath.max(maxErrorSinDot, fieldYDot[0].subtract(regularYDot[0]).abs().getReal()); + maxErrorCosDot = FastMath.max(maxErrorCosDot, fieldYDot[1].subtract(regularYDot[1]).abs().getReal()); + + } + Assert.assertEquals(0.0, maxErrorSin, epsilonSin); + Assert.assertEquals(0.0, maxErrorCos, epsilonCos); + Assert.assertEquals(0.0, maxErrorSinDot, epsilonSinDot); + Assert.assertEquals(0.0, maxErrorCosDot, epsilonCosDot); + + } + + private <T extends RealFieldElement<T>> + RungeKuttaFieldStepInterpolator<T> setUpInterpolator(final Field<T> field, + final FirstOrderFieldDifferentialEquations<T> eqn, + final double t0, final double[] y0, + final double t1) { + + // get the Butcher arrays from the field integrator + FieldButcherArrayProvider<T> provider = createButcherArrayProvider(field); + T[][] a = provider.getA(); + T[] b = provider.getB(); + T[] c = provider.getC(); + + // store initial state + T t = field.getZero().add(t0); + T[] fieldY = MathArrays.buildArray(field, eqn.getDimension()); + T[][] fieldYDotK = MathArrays.buildArray(field, b.length, -1); + for (int i = 0; i < y0.length; ++i) { + fieldY[i] = field.getZero().add(y0[i]); + } + fieldYDotK[0] = eqn.computeDerivatives(t, fieldY); + FieldODEStateAndDerivative<T> s0 = new FieldODEStateAndDerivative<T>(t, fieldY, fieldYDotK[0]); + + // perform one integration step, in order to get consistent derivatives + T h = field.getZero().add(t1 - t0); + for (int k = 0; k < a.length; ++k) { + for (int i = 0; i < y0.length; ++i) { + fieldY[i] = field.getZero().add(y0[i]); + for (int s = 0; s <= k; ++s) { + fieldY[i] = fieldY[i].add(h.multiply(a[k][s].multiply(fieldYDotK[s][i]))); + } + } + fieldYDotK[k + 1] = eqn.computeDerivatives(h.multiply(c[k]).add(t0), fieldY); + } + + // store state at step end + t = field.getZero().add(t1); + for (int i = 0; i < y0.length; ++i) { + fieldY[i] = field.getZero().add(y0[i]); + for (int s = 0; s < b.length; ++s) { + fieldY[i] = fieldY[i].add(h.multiply(b[s].multiply(fieldYDotK[s][i]))); + } + } + FieldODEStateAndDerivative<T> s1 = new FieldODEStateAndDerivative<T>(t, fieldY, + eqn.computeDerivatives(t, fieldY)); + + return createInterpolator(field, t1 > t0, fieldYDotK, s0, s1, s0, s1, + new FieldExpandableODE<T>(eqn).getMapper()); + + } + + private <T extends RealFieldElement<T>> + RungeKuttaStepInterpolator convertInterpolator(final RungeKuttaFieldStepInterpolator<T> fieldInterpolator, + final FirstOrderFieldDifferentialEquations<T> eqn) { + + RungeKuttaStepInterpolator regularInterpolator = null; + try { + + String interpolatorName = fieldInterpolator.getClass().getName(); + String integratorName = interpolatorName.replaceAll("Field", ""); + @SuppressWarnings("unchecked") + Class<RungeKuttaStepInterpolator> clz = (Class<RungeKuttaStepInterpolator>) Class.forName(integratorName); + regularInterpolator = clz.newInstance(); + + double[][] yDotArray = null; + java.lang.reflect.Field fYD = RungeKuttaFieldStepInterpolator.class.getDeclaredField("yDotK"); + fYD.setAccessible(true); + @SuppressWarnings("unchecked") + T[][] fieldYDotk = (T[][]) fYD.get(fieldInterpolator); + yDotArray = new double[fieldYDotk.length][]; + for (int i = 0; i < yDotArray.length; ++i) { + yDotArray[i] = new double[fieldYDotk[i].length]; + for (int j = 0; j < yDotArray[i].length; ++j) { + yDotArray[i][j] = fieldYDotk[i][j].getReal(); + } + } + double[] y = new double[yDotArray[0].length]; + + EquationsMapper primaryMapper = null; + EquationsMapper[] secondaryMappers = null; + java.lang.reflect.Field fMapper = AbstractFieldStepInterpolator.class.getDeclaredField("mapper"); + fMapper.setAccessible(true); + @SuppressWarnings("unchecked") + FieldEquationsMapper<T> mapper = (FieldEquationsMapper<T>) fMapper.get(fieldInterpolator); + java.lang.reflect.Field fStart = FieldEquationsMapper.class.getDeclaredField("start"); + fStart.setAccessible(true); + int[] start = (int[]) fStart.get(mapper); + primaryMapper = new EquationsMapper(start[0], start[1]); + secondaryMappers = new EquationsMapper[mapper.getNumberOfEquations() - 1]; + for (int i = 0; i < secondaryMappers.length; ++i) { + secondaryMappers[i] = new EquationsMapper(start[i + 1], start[i + 2]); + } + + AbstractIntegrator dummyIntegrator = new AbstractIntegrator("dummy") { + @Override + public void integrate(ExpandableStatefulODE equations, double t) { + Assert.fail("this method should not be called"); + } + @Override + public void computeDerivatives(final double t, final double[] y, final double[] yDot) { + T fieldT = fieldInterpolator.getCurrentState().getTime().getField().getZero().add(t); + T[] fieldY = MathArrays.buildArray(fieldInterpolator.getCurrentState().getTime().getField(), y.length); + for (int i = 0; i < y.length; ++i) { + fieldY[i] = fieldInterpolator.getCurrentState().getTime().getField().getZero().add(y[i]); + } + T[] fieldYDot = eqn.computeDerivatives(fieldT, fieldY); + for (int i = 0; i < yDot.length; ++i) { + yDot[i] = fieldYDot[i].getReal(); + } + } + }; + regularInterpolator.reinitialize(dummyIntegrator, y, yDotArray, + fieldInterpolator.isForward(), + primaryMapper, secondaryMappers); + + T[] fieldPreviousY = fieldInterpolator.getPreviousState().getState(); + for (int i = 0; i < y.length; ++i) { + y[i] = fieldPreviousY[i].getReal(); + } + regularInterpolator.storeTime(fieldInterpolator.getPreviousState().getTime().getReal()); + + regularInterpolator.shift(); + + T[] fieldCurrentY = fieldInterpolator.getCurrentState().getState(); + for (int i = 0; i < y.length; ++i) { + y[i] = fieldCurrentY[i].getReal(); + } + regularInterpolator.storeTime(fieldInterpolator.getCurrentState().getTime().getReal()); + + } catch (ClassNotFoundException cnfe) { + Assert.fail(cnfe.getLocalizedMessage()); + } catch (InstantiationException ie) { + Assert.fail(ie.getLocalizedMessage()); + } catch (IllegalAccessException iae) { + Assert.fail(iae.getLocalizedMessage()); + } catch (NoSuchFieldException nsfe) { + Assert.fail(nsfe.getLocalizedMessage()); + } catch (IllegalArgumentException iae) { + Assert.fail(iae.getLocalizedMessage()); + } + + return regularInterpolator; + + } + + private static class SinCos<T extends RealFieldElement<T>> implements FirstOrderFieldDifferentialEquations<T> { + private final Field<T> field; + protected SinCos(final Field<T> field) { + this.field = field; + } + public int getDimension() { + return 2; + } + public void init(final T t0, final T[] y0, final T finalTime) { + } + public T[] computeDerivatives(final T t, final T[] y) { + T[] yDot = MathArrays.buildArray(field, 2); + yDot[0] = y[1]; + yDot[1] = y[0].negate(); + return yDot; + } + } + +} http://git-wip-us.apache.org/repos/asf/commons-math/blob/29649959/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldIntegratorTest.java ---------------------------------------------------------------------- diff --git a/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldIntegratorTest.java b/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldIntegratorTest.java index 700661d..971dac8 100644 --- a/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldIntegratorTest.java +++ b/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldIntegratorTest.java @@ -22,7 +22,7 @@ import org.apache.commons.math3.Field; import org.apache.commons.math3.RealFieldElement; import org.apache.commons.math3.util.Decimal64Field; -public class ThreeEighthesFieldIntegratorTest extends AbstractRungeKuttaFieldIntegratorTest { +public class ThreeEighthesFieldIntegratorTest extends RungeKuttaFieldIntegratorAbstractTest { protected <T extends RealFieldElement<T>> RungeKuttaFieldIntegrator<T> createIntegrator(Field<T> field, T step) { http://git-wip-us.apache.org/repos/asf/commons-math/blob/29649959/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldStepInterpolatorTest.java ---------------------------------------------------------------------- diff --git a/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldStepInterpolatorTest.java b/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldStepInterpolatorTest.java index f1a2d28..f326a2b 100644 --- a/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldStepInterpolatorTest.java +++ b/src/test/java/org/apache/commons/math3/ode/nonstiff/ThreeEighthesFieldStepInterpolatorTest.java @@ -25,7 +25,7 @@ import org.apache.commons.math3.ode.FieldODEStateAndDerivative; import org.apache.commons.math3.util.Decimal64Field; import org.junit.Test; -public class ThreeEighthesFieldStepInterpolatorTest extends AbstractRungeKuttaFieldStepInterpolatorTest { +public class ThreeEighthesFieldStepInterpolatorTest extends RungeKuttaFieldStepInterpolatorAbstractTest { protected <T extends RealFieldElement<T>> RungeKuttaFieldStepInterpolator<T> createInterpolator(Field<T> field, boolean forward, T[][] yDotK,
