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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.Iterator;
import java.util.List;
import java.util.SortedSet;
import java.util.TreeSet;
import org.apache.commons.math3.analysis.solvers.BracketingNthOrderBrentSolver;
import org.apache.commons.math3.analysis.solvers.UnivariateSolver;
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.exception.util.LocalizedFormats;
import org.apache.commons.math3.ode.events.EventHandler;
import org.apache.commons.math3.ode.events.EventState;
import org.apache.commons.math3.ode.sampling.AbstractStepInterpolator;
import org.apache.commons.math3.ode.sampling.StepHandler;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Incrementor;
import org.apache.commons.math3.util.Precision;
/**
* Base class managing common boilerplate for all integrators.
* @since 2.0
*/
public abstract class AbstractIntegrator implements FirstOrderIntegrator {
/** Step handler. */
protected Collection stepHandlers;
/** Current step start time. */
protected double stepStart;
/** Current stepsize. */
protected double stepSize;
/** Indicator for last step. */
protected boolean isLastStep;
/** Indicator that a state or derivative reset was triggered by some event. */
protected boolean resetOccurred;
/** Events states. */
private Collection eventsStates;
/** Initialization indicator of events states. */
private boolean statesInitialized;
/** Name of the method. */
private final String name;
/** Counter for number of evaluations. */
private Incrementor evaluations;
/** Differential equations to integrate. */
private transient ExpandableStatefulODE expandable;
/** Build an instance.
* @param name name of the method
*/
public AbstractIntegrator(final String name) {
this.name = name;
stepHandlers = new ArrayList();
stepStart = Double.NaN;
stepSize = Double.NaN;
eventsStates = new ArrayList();
statesInitialized = false;
evaluations = new Incrementor();
setMaxEvaluations(-1);
evaluations.resetCount();
}
/** Build an instance with a null name.
*/
protected AbstractIntegrator() {
this(null);
}
/** {@inheritDoc} */
public String getName() {
return name;
}
/** {@inheritDoc} */
public void addStepHandler(final StepHandler handler) {
stepHandlers.add(handler);
}
/** {@inheritDoc} */
public Collection getStepHandlers() {
return Collections.unmodifiableCollection(stepHandlers);
}
/** {@inheritDoc} */
public void clearStepHandlers() {
stepHandlers.clear();
}
/** {@inheritDoc} */
public void addEventHandler(final EventHandler handler,
final double maxCheckInterval,
final double convergence,
final int maxIterationCount) {
addEventHandler(handler, maxCheckInterval, convergence,
maxIterationCount,
new BracketingNthOrderBrentSolver(convergence, 5));
}
/** {@inheritDoc} */
public void addEventHandler(final EventHandler handler,
final double maxCheckInterval,
final double convergence,
final int maxIterationCount,
final UnivariateSolver solver) {
eventsStates.add(new EventState(handler, maxCheckInterval, convergence,
maxIterationCount, solver));
}
/** {@inheritDoc} */
public Collection getEventHandlers() {
final List list = new ArrayList(eventsStates.size());
for (EventState state : eventsStates) {
list.add(state.getEventHandler());
}
return Collections.unmodifiableCollection(list);
}
/** {@inheritDoc} */
public void clearEventHandlers() {
eventsStates.clear();
}
/** {@inheritDoc} */
public double getCurrentStepStart() {
return stepStart;
}
/** {@inheritDoc} */
public double getCurrentSignedStepsize() {
return stepSize;
}
/** {@inheritDoc} */
public void setMaxEvaluations(int maxEvaluations) {
evaluations.setMaximalCount((maxEvaluations < 0) ? Integer.MAX_VALUE : maxEvaluations);
}
/** {@inheritDoc} */
public int getMaxEvaluations() {
return evaluations.getMaximalCount();
}
/** {@inheritDoc} */
public int getEvaluations() {
return evaluations.getCount();
}
/** Prepare the start of an integration.
* @param t0 start value of the independent time variable
* @param y0 array containing the start value of the state vector
* @param t target time for the integration
*/
protected void initIntegration(final double t0, final double[] y0, final double t) {
evaluations.resetCount();
for (final EventState state : eventsStates) {
state.setExpandable(expandable);
state.getEventHandler().init(t0, y0, t);
}
for (StepHandler handler : stepHandlers) {
handler.init(t0, y0, t);
}
setStateInitialized(false);
}
/** Set the equations.
* @param equations equations to set
*/
protected void setEquations(final ExpandableStatefulODE equations) {
this.expandable = equations;
}
/** Get the differential equations to integrate.
* @return differential equations to integrate
* @since 3.2
*/
protected ExpandableStatefulODE getExpandable() {
return expandable;
}
/** Get the evaluations counter.
* @return evaluations counter
* @since 3.2
*/
protected Incrementor getEvaluationsCounter() {
return evaluations;
}
/** {@inheritDoc} */
public double integrate(final FirstOrderDifferentialEquations equations,
final double t0, final double[] y0, final double t, final double[] y)
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
if (y0.length != equations.getDimension()) {
throw new DimensionMismatchException(y0.length, equations.getDimension());
}
if (y.length != equations.getDimension()) {
throw new DimensionMismatchException(y.length, equations.getDimension());
}
// prepare expandable stateful equations
final ExpandableStatefulODE expandableODE = new ExpandableStatefulODE(equations);
expandableODE.setTime(t0);
expandableODE.setPrimaryState(y0);
// perform integration
integrate(expandableODE, t);
// extract results back from the stateful equations
System.arraycopy(expandableODE.getPrimaryState(), 0, y, 0, y.length);
return expandableODE.getTime();
}
/** Integrate a set of differential equations up to the given time.
* This method solves an Initial Value Problem (IVP).
* The set of differential equations is composed of a main set, which
* can be extended by some sets of secondary equations. The set of
* equations must be already set up with initial time and partial states.
* At integration completion, the final time and partial states will be
* available in the same object.
* Since this method stores some internal state variables made
* available in its public interface during integration ({@link
* #getCurrentSignedStepsize()}), it is not thread-safe.
* @param equations complete set of differential equations to integrate
* @param t target time for the integration
* (can be set to a value smaller than t0 for backward integration)
* @exception NumberIsTooSmallException if integration step is too small
* @throws DimensionMismatchException if the dimension of the complete state does not
* match the complete equations sets dimension
* @exception MaxCountExceededException if the number of functions evaluations is exceeded
* @exception NoBracketingException if the location of an event cannot be bracketed
*/
public abstract void integrate(ExpandableStatefulODE equations, double t)
throws NumberIsTooSmallException, DimensionMismatchException,
MaxCountExceededException, NoBracketingException;
/** Compute the derivatives and check the number of evaluations.
* @param t current value of the independent time variable
* @param y array containing the current value of the state vector
* @param yDot placeholder array where to put the time derivative of the state vector
* @exception MaxCountExceededException if the number of functions evaluations is exceeded
* @exception DimensionMismatchException if arrays dimensions do not match equations settings
*/
public void computeDerivatives(final double t, final double[] y, final double[] yDot)
throws MaxCountExceededException, DimensionMismatchException {
evaluations.incrementCount();
expandable.computeDerivatives(t, y, yDot);
}
/** Set the stateInitialized flag.
* This method must be called by integrators with the value
* {@code false} before they start integration, so a proper lazy
* initialization is done automatically on the first step.
* @param stateInitialized new value for the flag
* @since 2.2
*/
protected void setStateInitialized(final boolean stateInitialized) {
this.statesInitialized = stateInitialized;
}
/** Accept a step, triggering events and step handlers.
* @param interpolator step interpolator
* @param y state vector at step end time, must be reset if an event
* asks for resetting or if an events stops integration during the step
* @param yDot placeholder array where to put the time derivative of the state vector
* @param tEnd final integration time
* @return time at end of step
* @exception MaxCountExceededException if the interpolator throws one because
* the number of functions evaluations is exceeded
* @exception NoBracketingException if the location of an event cannot be bracketed
* @exception DimensionMismatchException if arrays dimensions do not match equations settings
* @since 2.2
*/
protected double acceptStep(final AbstractStepInterpolator interpolator,
final double[] y, final double[] yDot, final double tEnd)
throws MaxCountExceededException, DimensionMismatchException, NoBracketingException {
double previousT = interpolator.getGlobalPreviousTime();
final double currentT = interpolator.getGlobalCurrentTime();
// initialize the events states if needed
if (! statesInitialized) {
for (EventState state : eventsStates) {
state.reinitializeBegin(interpolator);
}
statesInitialized = true;
}
// search for next events that may occur during the step
final int orderingSign = interpolator.isForward() ? +1 : -1;
SortedSet occurringEvents = new TreeSet(new Comparator() {
/** {@inheritDoc} */
public int compare(EventState es0, EventState es1) {
return orderingSign * Double.compare(es0.getEventTime(), es1.getEventTime());
}
});
for (final EventState state : eventsStates) {
if (state.evaluateStep(interpolator)) {
// the event occurs during the current step
occurringEvents.add(state);
}
}
while (!occurringEvents.isEmpty()) {
// handle the chronologically first event
final Iterator iterator = occurringEvents.iterator();
final EventState currentEvent = iterator.next();
iterator.remove();
// restrict the interpolator to the first part of the step, up to the event
final double eventT = currentEvent.getEventTime();
interpolator.setSoftPreviousTime(previousT);
interpolator.setSoftCurrentTime(eventT);
// get state at event time
interpolator.setInterpolatedTime(eventT);
final double[] eventYComplete = new double[y.length];
expandable.getPrimaryMapper().insertEquationData(interpolator.getInterpolatedState(),
eventYComplete);
int index = 0;
for (EquationsMapper secondary : expandable.getSecondaryMappers()) {
secondary.insertEquationData(interpolator.getInterpolatedSecondaryState(index++),
eventYComplete);
}
// advance all event states to current time
for (final EventState state : eventsStates) {
state.stepAccepted(eventT, eventYComplete);
isLastStep = isLastStep || state.stop();
}
// handle the first part of the step, up to the event
for (final StepHandler handler : stepHandlers) {
handler.handleStep(interpolator, isLastStep);
}
if (isLastStep) {
// the event asked to stop integration
System.arraycopy(eventYComplete, 0, y, 0, y.length);
return eventT;
}
boolean needReset = false;
for (final EventState state : eventsStates) {
needReset = needReset || state.reset(eventT, eventYComplete);
}
if (needReset) {
// some event handler has triggered changes that
// invalidate the derivatives, we need to recompute them
interpolator.setInterpolatedTime(eventT);
System.arraycopy(eventYComplete, 0, y, 0, y.length);
computeDerivatives(eventT, y, yDot);
resetOccurred = true;
return eventT;
}
// prepare handling of the remaining part of the step
previousT = eventT;
interpolator.setSoftPreviousTime(eventT);
interpolator.setSoftCurrentTime(currentT);
// check if the same event occurs again in the remaining part of the step
if (currentEvent.evaluateStep(interpolator)) {
// the event occurs during the current step
occurringEvents.add(currentEvent);
}
}
// last part of the step, after the last event
interpolator.setInterpolatedTime(currentT);
final double[] currentY = new double[y.length];
expandable.getPrimaryMapper().insertEquationData(interpolator.getInterpolatedState(),
currentY);
int index = 0;
for (EquationsMapper secondary : expandable.getSecondaryMappers()) {
secondary.insertEquationData(interpolator.getInterpolatedSecondaryState(index++),
currentY);
}
for (final EventState state : eventsStates) {
state.stepAccepted(currentT, currentY);
isLastStep = isLastStep || state.stop();
}
isLastStep = isLastStep || Precision.equals(currentT, tEnd, 1);
// handle the remaining part of the step, after all events if any
for (StepHandler handler : stepHandlers) {
handler.handleStep(interpolator, isLastStep);
}
return currentT;
}
/** Check the integration span.
* @param equations set of differential equations
* @param t target time for the integration
* @exception NumberIsTooSmallException if integration span is too small
* @exception DimensionMismatchException if adaptive step size integrators
* tolerance arrays dimensions are not compatible with equations settings
*/
protected void sanityChecks(final ExpandableStatefulODE equations, final double t)
throws NumberIsTooSmallException, DimensionMismatchException {
final double threshold = 1000 * FastMath.ulp(FastMath.max(FastMath.abs(equations.getTime()),
FastMath.abs(t)));
final double dt = FastMath.abs(equations.getTime() - t);
if (dt <= threshold) {
throw new NumberIsTooSmallException(LocalizedFormats.TOO_SMALL_INTEGRATION_INTERVAL,
dt, threshold, false);
}
}
}