StepNormalizer.java

  1. /*
  2.  * Licensed to the Apache Software Foundation (ASF) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * The ASF licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *      http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */

  18. package org.apache.commons.math3.ode.sampling;

  20. import org.apache.commons.math3.exception.MaxCountExceededException;
  21. import org.apache.commons.math3.util.FastMath;
  22. import org.apache.commons.math3.util.Precision;

  24. /**
  25.  * This class wraps an object implementing {@link FixedStepHandler}
  26.  * into a {@link StepHandler}.

  28.  * <p>This wrapper allows to use fixed step handlers with general
  29.  * integrators which cannot guaranty their integration steps will
  30.  * remain constant and therefore only accept general step
  31.  * handlers.</p>
  32.  *
  33.  * <p>The stepsize used is selected at construction time. The {@link
  34.  * FixedStepHandler#handleStep handleStep} method of the underlying
  35.  * {@link FixedStepHandler} object is called at normalized times. The
  36.  * normalized times can be influenced by the {@link StepNormalizerMode} and
  37.  * {@link StepNormalizerBounds}.</p>
  38.  *
  39.  * <p>There is no constraint on the integrator, it can use any time step
  40.  * it needs (time steps longer or shorter than the fixed time step and
  41.  * non-integer ratios are all allowed).</p>
  42.  *
  43.  * <p>
  44.  * <table border="1" align="center">
  45.  * <tr BGCOLOR="#CCCCFF"><td colspan=6><font size="+2">Examples (step size = 0.5)</font></td></tr>
  46.  * <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Start time</td><td>End time</td>
  47.  *  <td>Direction</td><td>{@link StepNormalizerMode Mode}</td>
  48.  *  <td>{@link StepNormalizerBounds Bounds}</td><td>Output</td></font></tr>
  49.  * <tr><td>0.3</td><td>3.1</td><td>forward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#NEITHER NEITHER}</td><td>0.8, 1.3, 1.8, 2.3, 2.8</td></tr>
  50.  * <tr><td>0.3</td><td>3.1</td><td>forward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#FIRST FIRST}</td><td>0.3, 0.8, 1.3, 1.8, 2.3, 2.8</td></tr>
  51.  * <tr><td>0.3</td><td>3.1</td><td>forward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#LAST LAST}</td><td>0.8, 1.3, 1.8, 2.3, 2.8, 3.1</td></tr>
  52.  * <tr><td>0.3</td><td>3.1</td><td>forward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#BOTH BOTH}</td><td>0.3, 0.8, 1.3, 1.8, 2.3, 2.8, 3.1</td></tr>
  53.  * <tr><td>0.3</td><td>3.1</td><td>forward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#NEITHER NEITHER}</td><td>0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  54.  * <tr><td>0.3</td><td>3.1</td><td>forward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#FIRST FIRST}</td><td>0.3, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  55.  * <tr><td>0.3</td><td>3.1</td><td>forward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#LAST LAST}</td><td>0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.1</td></tr>
  56.  * <tr><td>0.3</td><td>3.1</td><td>forward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#BOTH BOTH}</td><td>0.3, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.1</td></tr>
  57.  * <tr><td>0.0</td><td>3.0</td><td>forward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#NEITHER NEITHER}</td><td>0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  58.  * <tr><td>0.0</td><td>3.0</td><td>forward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#FIRST FIRST}</td><td>0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  59.  * <tr><td>0.0</td><td>3.0</td><td>forward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#LAST LAST}</td><td>0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  60.  * <tr><td>0.0</td><td>3.0</td><td>forward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#BOTH BOTH}</td><td>0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  61.  * <tr><td>0.0</td><td>3.0</td><td>forward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#NEITHER NEITHER}</td><td>0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  62.  * <tr><td>0.0</td><td>3.0</td><td>forward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#FIRST FIRST}</td><td>0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  63.  * <tr><td>0.0</td><td>3.0</td><td>forward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#LAST LAST}</td><td>0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  64.  * <tr><td>0.0</td><td>3.0</td><td>forward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#BOTH BOTH}</td><td>0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0</td></tr>
  65.  * <tr><td>3.1</td><td>0.3</td><td>backward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#NEITHER NEITHER}</td><td>2.6, 2.1, 1.6, 1.1, 0.6</td></tr>
  66.  * <tr><td>3.1</td><td>0.3</td><td>backward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#FIRST FIRST}</td><td>3.1, 2.6, 2.1, 1.6, 1.1, 0.6</td></tr>
  67.  * <tr><td>3.1</td><td>0.3</td><td>backward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#LAST LAST}</td><td>2.6, 2.1, 1.6, 1.1, 0.6, 0.3</td></tr>
  68.  * <tr><td>3.1</td><td>0.3</td><td>backward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#BOTH BOTH}</td><td>3.1, 2.6, 2.1, 1.6, 1.1, 0.6, 0.3</td></tr>
  69.  * <tr><td>3.1</td><td>0.3</td><td>backward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#NEITHER NEITHER}</td><td>3.0, 2.5, 2.0, 1.5, 1.0, 0.5</td></tr>
  70.  * <tr><td>3.1</td><td>0.3</td><td>backward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#FIRST FIRST}</td><td>3.1, 3.0, 2.5, 2.0, 1.5, 1.0, 0.5</td></tr>
  71.  * <tr><td>3.1</td><td>0.3</td><td>backward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#LAST LAST}</td><td>3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.3</td></tr>
  72.  * <tr><td>3.1</td><td>0.3</td><td>backward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#BOTH BOTH}</td><td>3.1, 3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.3</td></tr>
  73.  * <tr><td>3.0</td><td>0.0</td><td>backward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#NEITHER NEITHER}</td><td>2.5, 2.0, 1.5, 1.0, 0.5, 0.0</td></tr>
  74.  * <tr><td>3.0</td><td>0.0</td><td>backward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#FIRST FIRST}</td><td>3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.0</td></tr>
  75.  * <tr><td>3.0</td><td>0.0</td><td>backward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#LAST LAST}</td><td>2.5, 2.0, 1.5, 1.0, 0.5, 0.0</td></tr>
  76.  * <tr><td>3.0</td><td>0.0</td><td>backward</td><td>{@link StepNormalizerMode#INCREMENT INCREMENT}</td><td>{@link StepNormalizerBounds#BOTH BOTH}</td><td>3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.0</td></tr>
  77.  * <tr><td>3.0</td><td>0.0</td><td>backward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#NEITHER NEITHER}</td><td>2.5, 2.0, 1.5, 1.0, 0.5, 0.0</td></tr>
  78.  * <tr><td>3.0</td><td>0.0</td><td>backward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#FIRST FIRST}</td><td>3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.0</td></tr>
  79.  * <tr><td>3.0</td><td>0.0</td><td>backward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#LAST LAST}</td><td>2.5, 2.0, 1.5, 1.0, 0.5, 0.0</td></tr>
  80.  * <tr><td>3.0</td><td>0.0</td><td>backward</td><td>{@link StepNormalizerMode#MULTIPLES MULTIPLES}</td><td>{@link StepNormalizerBounds#BOTH BOTH}</td><td>3.0, 2.5, 2.0, 1.5, 1.0, 0.5, 0.0</td></tr>
  81.  * </table>
  82.  * </p>
  83.  *
  84.  * @see StepHandler
  85.  * @see FixedStepHandler
  86.  * @see StepNormalizerMode
  87.  * @see StepNormalizerBounds
  88.  * @since 1.2
  89.  */

  91. public class StepNormalizer implements StepHandler {
  92.     /** Fixed time step. */
  93.     private double h;

  95.     /** Underlying step handler. */
  96.     private final FixedStepHandler handler;

  98.     /** First step time. */
  99.     private double firstTime;

  101.     /** Last step time. */
  102.     private double lastTime;

  104.     /** Last state vector. */
  105.     private double[] lastState;

  107.     /** Last derivatives vector. */
  108.     private double[] lastDerivatives;

  110.     /** Integration direction indicator. */
  111.     private boolean forward;

  113.     /** The step normalizer bounds settings to use. */
  114.     private final StepNormalizerBounds bounds;

  116.     /** The step normalizer mode to use. */
  117.     private final StepNormalizerMode mode;

  119.     /** Simple constructor. Uses {@link StepNormalizerMode#INCREMENT INCREMENT}
  120.      * mode, and {@link StepNormalizerBounds#FIRST FIRST} bounds setting, for
  121.      * backwards compatibility.
  122.      * @param h fixed time step (sign is not used)
  123.      * @param handler fixed time step handler to wrap
  124.      */
  125.     public StepNormalizer(final double h, final FixedStepHandler handler) {
  126.         this(h, handler, StepNormalizerMode.INCREMENT,
  127.              StepNormalizerBounds.FIRST);
  128.     }

  130.     /** Simple constructor. Uses {@link StepNormalizerBounds#FIRST FIRST}
  131.      * bounds setting.
  132.      * @param h fixed time step (sign is not used)
  133.      * @param handler fixed time step handler to wrap
  134.      * @param mode step normalizer mode to use
  135.      * @since 3.0
  136.      */
  137.     public StepNormalizer(final double h, final FixedStepHandler handler,
  138.                           final StepNormalizerMode mode) {
  139.         this(h, handler, mode, StepNormalizerBounds.FIRST);
  140.     }

  142.     /** Simple constructor. Uses {@link StepNormalizerMode#INCREMENT INCREMENT}
  143.      * mode.
  144.      * @param h fixed time step (sign is not used)
  145.      * @param handler fixed time step handler to wrap
  146.      * @param bounds step normalizer bounds setting to use
  147.      * @since 3.0
  148.      */
  149.     public StepNormalizer(final double h, final FixedStepHandler handler,
  150.                           final StepNormalizerBounds bounds) {
  151.         this(h, handler, StepNormalizerMode.INCREMENT, bounds);
  152.     }

  154.     /** Simple constructor.
  155.      * @param h fixed time step (sign is not used)
  156.      * @param handler fixed time step handler to wrap
  157.      * @param mode step normalizer mode to use
  158.      * @param bounds step normalizer bounds setting to use
  159.      * @since 3.0
  160.      */
  161.     public StepNormalizer(final double h, final FixedStepHandler handler,
  162.                           final StepNormalizerMode mode,
  163.                           final StepNormalizerBounds bounds) {
  164.         this.h          = FastMath.abs(h);
  165.         this.handler    = handler;
  166.         this.mode       = mode;
  167.         this.bounds     = bounds;
  168.         firstTime       = Double.NaN;
  169.         lastTime        = Double.NaN;
  170.         lastState       = null;
  171.         lastDerivatives = null;
  172.         forward         = true;
  173.     }

  175.     /** {@inheritDoc} */
  176.     public void init(double t0, double[] y0, double t) {

  178.         firstTime       = Double.NaN;
  179.         lastTime        = Double.NaN;
  180.         lastState       = null;
  181.         lastDerivatives = null;
  182.         forward         = true;

  184.         // initialize the underlying handler
  185.         handler.init(t0, y0, t);

  187.     }

  189.     /**
  190.      * Handle the last accepted step
  191.      * @param interpolator interpolator for the last accepted step. For
  192.      * efficiency purposes, the various integrators reuse the same
  193.      * object on each call, so if the instance wants to keep it across
  194.      * all calls (for example to provide at the end of the integration a
  195.      * continuous model valid throughout the integration range), it
  196.      * should build a local copy using the clone method and store this
  197.      * copy.
  198.      * @param isLast true if the step is the last one
  199.      * @exception MaxCountExceededException if the interpolator throws one because
  200.      * the number of functions evaluations is exceeded
  201.      */
  202.     public void handleStep(final StepInterpolator interpolator, final boolean isLast)
  203.         throws MaxCountExceededException {
  204.         // The first time, update the last state with the start information.
  205.         if (lastState == null) {
  206.             firstTime = interpolator.getPreviousTime();
  207.             lastTime = interpolator.getPreviousTime();
  208.             interpolator.setInterpolatedTime(lastTime);
  209.             lastState = interpolator.getInterpolatedState().clone();
  210.             lastDerivatives = interpolator.getInterpolatedDerivatives().clone();

  212.             // Take the integration direction into account.
  213.             forward = interpolator.getCurrentTime() >= lastTime;
  214.             if (!forward) {
  215.                 h = -h;
  216.             }
  217.         }

  219.         // Calculate next normalized step time.
  220.         double nextTime = (mode == StepNormalizerMode.INCREMENT) ?
  221.                           lastTime + h :
  222.                           (FastMath.floor(lastTime / h) + 1) * h;
  223.         if (mode == StepNormalizerMode.MULTIPLES &&
  224.             Precision.equals(nextTime, lastTime, 1)) {
  225.             nextTime += h;
  226.         }

  228.         // Process normalized steps as long as they are in the current step.
  229.         boolean nextInStep = isNextInStep(nextTime, interpolator);
  230.         while (nextInStep) {
  231.             // Output the stored previous step.
  232.             doNormalizedStep(false);

  234.             // Store the next step as last step.
  235.             storeStep(interpolator, nextTime);

  237.             // Move on to the next step.
  238.             nextTime += h;
  239.             nextInStep = isNextInStep(nextTime, interpolator);
  240.         }

  242.         if (isLast) {
  243.             // There will be no more steps. The stored one should be given to
  244.             // the handler. We may have to output one more step. Only the last
  245.             // one of those should be flagged as being the last.
  246.             boolean addLast = bounds.lastIncluded() &&
  247.                               lastTime != interpolator.getCurrentTime();
  248.             doNormalizedStep(!addLast);
  249.             if (addLast) {
  250.                 storeStep(interpolator, interpolator.getCurrentTime());
  251.                 doNormalizedStep(true);
  252.             }
  253.         }
  254.     }

  256.     /**
  257.      * Returns a value indicating whether the next normalized time is in the
  258.      * current step.
  259.      * @param nextTime the next normalized time
  260.      * @param interpolator interpolator for the last accepted step, to use to
  261.      * get the end time of the current step
  262.      * @return value indicating whether the next normalized time is in the
  263.      * current step
  264.      */
  265.     private boolean isNextInStep(double nextTime,
  266.                                  StepInterpolator interpolator) {
  267.         return forward ?
  268.                nextTime <= interpolator.getCurrentTime() :
  269.                nextTime >= interpolator.getCurrentTime();
  270.     }

  272.     /**
  273.      * Invokes the underlying step handler for the current normalized step.
  274.      * @param isLast true if the step is the last one
  275.      */
  276.     private void doNormalizedStep(boolean isLast) {
  277.         if (!bounds.firstIncluded() && firstTime == lastTime) {
  278.             return;
  279.         }
  280.         handler.handleStep(lastTime, lastState, lastDerivatives, isLast);
  281.     }

  283.     /** Stores the interpolated information for the given time in the current
  284.      * state.
  285.      * @param interpolator interpolator for the last accepted step, to use to
  286.      * get the interpolated information
  287.      * @param t the time for which to store the interpolated information
  288.      * @exception MaxCountExceededException if the interpolator throws one because
  289.      * the number of functions evaluations is exceeded
  290.      */
  291.     private void storeStep(StepInterpolator interpolator, double t)
  292.         throws MaxCountExceededException {
  293.         lastTime = t;
  294.         interpolator.setInterpolatedTime(lastTime);
  295.         System.arraycopy(interpolator.getInterpolatedState(), 0,
  296.                          lastState, 0, lastState.length);
  297.         System.arraycopy(interpolator.getInterpolatedDerivatives(), 0,
  298.                          lastDerivatives, 0, lastDerivatives.length);
  299.     }
  300. }
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