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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.sampling;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;
/**
* This class wraps an object implementing {@link FixedStepHandler}
* into a {@link StepHandler}.
* This wrapper allows to use fixed step handlers with general
* integrators which cannot guaranty their integration steps will
* remain constant and therefore only accept general step
* handlers.
*
* The stepsize used is selected at construction time. The {@link
* FixedStepHandler#handleStep handleStep} method of the underlying
* {@link FixedStepHandler} object is called at normalized times. The
* normalized times can be influenced by the {@link StepNormalizerMode} and
* {@link StepNormalizerBounds}.
*
* There is no constraint on the integrator, it can use any time step
* it needs (time steps longer or shorter than the fixed time step and
* non-integer ratios are all allowed).
*
*
*
* Examples (step size = 0.5) Start time End time
* Direction {@link StepNormalizerMode Mode}
* {@link StepNormalizerBounds Bounds} Output 0.3 3.1 forward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#NEITHER NEITHER} 0.8, 1.3, 1.8, 2.3, 2.8 0.3 3.1 forward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#FIRST FIRST} 0.3, 0.8, 1.3, 1.8, 2.3, 2.8 0.3 3.1 forward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#LAST LAST} 0.8, 1.3, 1.8, 2.3, 2.8, 3.1 0.3 3.1 forward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#BOTH BOTH} 0.3, 0.8, 1.3, 1.8, 2.3, 2.8, 3.1 0.3 3.1 forward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#NEITHER NEITHER} 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 0.3 3.1 forward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#FIRST FIRST} 0.3, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 0.3 3.1 forward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#LAST LAST} 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.1 0.3 3.1 forward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#BOTH BOTH} 0.3, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.1 0.0 3.0 forward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#NEITHER NEITHER} 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 0.0 3.0 forward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#FIRST FIRST} 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 0.0 3.0 forward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#LAST LAST} 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 0.0 3.0 forward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#BOTH BOTH} 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 0.0 3.0 forward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#NEITHER NEITHER} 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 0.0 3.0 forward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#FIRST FIRST} 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 0.0 3.0 forward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#LAST LAST} 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 0.0 3.0 forward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#BOTH BOTH} 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 3.1 0.3 backward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#NEITHER NEITHER} 2.6, 2.1, 1.6, 1.1, 0.6 3.1 0.3 backward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#FIRST FIRST} 3.1, 2.6, 2.1, 1.6, 1.1, 0.6 3.1 0.3 backward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#LAST LAST} 2.6, 2.1, 1.6, 1.1, 0.6, 0.3 3.1 0.3 backward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#BOTH BOTH} 3.1, 2.6, 2.1, 1.6, 1.1, 0.6, 0.3 3.1 0.3 backward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#NEITHER NEITHER} 3.0, 2.5, 2.0, 1.5, 1.0, 0.5 3.1 0.3 backward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#FIRST FIRST} 3.1, 3.0, 2.5, 2.0, 1.5, 1.0, 0.5 3.1 0.3 backward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#LAST LAST} 3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.3 3.1 0.3 backward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#BOTH BOTH} 3.1, 3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.3 3.0 0.0 backward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#NEITHER NEITHER} 2.5, 2.0, 1.5, 1.0, 0.5, 0.0 3.0 0.0 backward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#FIRST FIRST} 3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.0 3.0 0.0 backward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#LAST LAST} 2.5, 2.0, 1.5, 1.0, 0.5, 0.0 3.0 0.0 backward {@link StepNormalizerMode#INCREMENT INCREMENT} {@link StepNormalizerBounds#BOTH BOTH} 3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.0 3.0 0.0 backward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#NEITHER NEITHER} 2.5, 2.0, 1.5, 1.0, 0.5, 0.0 3.0 0.0 backward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#FIRST FIRST} 3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.0 3.0 0.0 backward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#LAST LAST} 2.5, 2.0, 1.5, 1.0, 0.5, 0.0 3.0 0.0 backward {@link StepNormalizerMode#MULTIPLES MULTIPLES} {@link StepNormalizerBounds#BOTH BOTH} 3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.0
*
*
* @see StepHandler
* @see FixedStepHandler
* @see StepNormalizerMode
* @see StepNormalizerBounds
* @since 1.2
*/
public class StepNormalizer implements StepHandler {
/** Fixed time step. */
private double h;
/** Underlying step handler. */
private final FixedStepHandler handler;
/** First step time. */
private double firstTime;
/** Last step time. */
private double lastTime;
/** Last state vector. */
private double[] lastState;
/** Last derivatives vector. */
private double[] lastDerivatives;
/** Integration direction indicator. */
private boolean forward;
/** The step normalizer bounds settings to use. */
private final StepNormalizerBounds bounds;
/** The step normalizer mode to use. */
private final StepNormalizerMode mode;
/** Simple constructor. Uses {@link StepNormalizerMode#INCREMENT INCREMENT}
* mode, and {@link StepNormalizerBounds#FIRST FIRST} bounds setting, for
* backwards compatibility.
* @param h fixed time step (sign is not used)
* @param handler fixed time step handler to wrap
*/
public StepNormalizer(final double h, final FixedStepHandler handler) {
this(h, handler, StepNormalizerMode.INCREMENT,
StepNormalizerBounds.FIRST);
}
/** Simple constructor. Uses {@link StepNormalizerBounds#FIRST FIRST}
* bounds setting.
* @param h fixed time step (sign is not used)
* @param handler fixed time step handler to wrap
* @param mode step normalizer mode to use
* @since 3.0
*/
public StepNormalizer(final double h, final FixedStepHandler handler,
final StepNormalizerMode mode) {
this(h, handler, mode, StepNormalizerBounds.FIRST);
}
/** Simple constructor. Uses {@link StepNormalizerMode#INCREMENT INCREMENT}
* mode.
* @param h fixed time step (sign is not used)
* @param handler fixed time step handler to wrap
* @param bounds step normalizer bounds setting to use
* @since 3.0
*/
public StepNormalizer(final double h, final FixedStepHandler handler,
final StepNormalizerBounds bounds) {
this(h, handler, StepNormalizerMode.INCREMENT, bounds);
}
/** Simple constructor.
* @param h fixed time step (sign is not used)
* @param handler fixed time step handler to wrap
* @param mode step normalizer mode to use
* @param bounds step normalizer bounds setting to use
* @since 3.0
*/
public StepNormalizer(final double h, final FixedStepHandler handler,
final StepNormalizerMode mode,
final StepNormalizerBounds bounds) {
this.h = FastMath.abs(h);
this.handler = handler;
this.mode = mode;
this.bounds = bounds;
firstTime = Double.NaN;
lastTime = Double.NaN;
lastState = null;
lastDerivatives = null;
forward = true;
}
/** {@inheritDoc} */
public void init(double t0, double[] y0, double t) {
firstTime = Double.NaN;
lastTime = Double.NaN;
lastState = null;
lastDerivatives = null;
forward = true;
// initialize the underlying handler
handler.init(t0, y0, t);
}
/**
* Handle the last accepted step
* @param interpolator interpolator for the last accepted step. For
* efficiency purposes, the various integrators reuse the same
* object on each call, so if the instance wants to keep it across
* all calls (for example to provide at the end of the integration a
* continuous model valid throughout the integration range), it
* should build a local copy using the clone method and store this
* copy.
* @param isLast true if the step is the last one
* @exception MaxCountExceededException if the interpolator throws one because
* the number of functions evaluations is exceeded
*/
public void handleStep(final StepInterpolator interpolator, final boolean isLast)
throws MaxCountExceededException {
// The first time, update the last state with the start information.
if (lastState == null) {
firstTime = interpolator.getPreviousTime();
lastTime = interpolator.getPreviousTime();
interpolator.setInterpolatedTime(lastTime);
lastState = interpolator.getInterpolatedState().clone();
lastDerivatives = interpolator.getInterpolatedDerivatives().clone();
// Take the integration direction into account.
forward = interpolator.getCurrentTime() >= lastTime;
if (!forward) {
h = -h;
}
}
// Calculate next normalized step time.
double nextTime = (mode == StepNormalizerMode.INCREMENT) ?
lastTime + h :
(FastMath.floor(lastTime / h) + 1) * h;
if (mode == StepNormalizerMode.MULTIPLES &&
Precision.equals(nextTime, lastTime, 1)) {
nextTime += h;
}
// Process normalized steps as long as they are in the current step.
boolean nextInStep = isNextInStep(nextTime, interpolator);
while (nextInStep) {
// Output the stored previous step.
doNormalizedStep(false);
// Store the next step as last step.
storeStep(interpolator, nextTime);
// Move on to the next step.
nextTime += h;
nextInStep = isNextInStep(nextTime, interpolator);
}
if (isLast) {
// There will be no more steps. The stored one should be given to
// the handler. We may have to output one more step. Only the last
// one of those should be flagged as being the last.
boolean addLast = bounds.lastIncluded() &&
lastTime != interpolator.getCurrentTime();
doNormalizedStep(!addLast);
if (addLast) {
storeStep(interpolator, interpolator.getCurrentTime());
doNormalizedStep(true);
}
}
}
/**
* Returns a value indicating whether the next normalized time is in the
* current step.
* @param nextTime the next normalized time
* @param interpolator interpolator for the last accepted step, to use to
* get the end time of the current step
* @return value indicating whether the next normalized time is in the
* current step
*/
private boolean isNextInStep(double nextTime,
StepInterpolator interpolator) {
return forward ?
nextTime <= interpolator.getCurrentTime() :
nextTime >= interpolator.getCurrentTime();
}
/**
* Invokes the underlying step handler for the current normalized step.
* @param isLast true if the step is the last one
*/
private void doNormalizedStep(boolean isLast) {
if (!bounds.firstIncluded() && firstTime == lastTime) {
return;
}
handler.handleStep(lastTime, lastState, lastDerivatives, isLast);
}
/** Stores the interpolated information for the given time in the current
* state.
* @param interpolator interpolator for the last accepted step, to use to
* get the interpolated information
* @param t the time for which to store the interpolated information
* @exception MaxCountExceededException if the interpolator throws one because
* the number of functions evaluations is exceeded
*/
private void storeStep(StepInterpolator interpolator, double t)
throws MaxCountExceededException {
lastTime = t;
interpolator.setInterpolatedTime(lastTime);
System.arraycopy(interpolator.getInterpolatedState(), 0,
lastState, 0, lastState.length);
System.arraycopy(interpolator.getInterpolatedDerivatives(), 0,
lastDerivatives, 0, lastDerivatives.length);
}
}