Commons Math example source code file (ContinuousOutputModel.java)

This example Commons Math source code file (ContinuousOutputModel.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" ^TM.

Java - Commons Math tags/keywords

arraylist, continuousoutputmodel, continuousoutputmodel, derivativeexception, derivativeexception, io, list, serializable, serializable, stephandler, stepinterpolator, stepinterpolator, util

The Commons Math ContinuousOutputModel.java source code

/*
 * 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.math.ode;

import java.util.ArrayList;
import java.util.List;
import java.io.Serializable;

import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.ode.sampling.StepHandler;
import org.apache.commons.math.ode.sampling.StepInterpolator;

/**
 * This class stores all information provided by an ODE integrator
 * during the integration process and build a continuous model of the
 * solution from this.
 *
 * <p>This class act as a step handler from the integrator point of
 * view. It is called iteratively during the integration process and
 * stores a copy of all steps information in a sorted collection for
 * later use. Once the integration process is over, the user can use
 * the {@link #setInterpolatedTime setInterpolatedTime} and {@link
 * #getInterpolatedState getInterpolatedState} to retrieve this
 * information at any time. It is important to wait for the
 * integration to be over before attempting to call {@link
 * #setInterpolatedTime setInterpolatedTime} because some internal
 * variables are set only once the last step has been handled.</p>
 *
 * <p>This is useful for example if the main loop of the user
 * application should remain independent from the integration process
 * or if one needs to mimic the behaviour of an analytical model
 * despite a numerical model is used (i.e. one needs the ability to
 * get the model value at any time or to navigate through the
 * data).</p>
 *
 * <p>If problem modeling is done with several separate
 * integration phases for contiguous intervals, the same
 * ContinuousOutputModel can be used as step handler for all
 * integration phases as long as they are performed in order and in
 * the same direction. As an example, one can extrapolate the
 * trajectory of a satellite with one model (i.e. one set of
 * differential equations) up to the beginning of a maneuver, use
 * another more complex model including thrusters modeling and
 * accurate attitude control during the maneuver, and revert to the
 * first model after the end of the maneuver. If the same continuous
 * output model handles the steps of all integration phases, the user
 * do not need to bother when the maneuver begins or ends, he has all
 * the data available in a transparent manner.</p>
 *
 * <p>An important feature of this class is that it implements the
 * <code>Serializable interface. This means that the result of
 * an integration can be serialized and reused later (if stored into a
 * persistent medium like a filesystem or a database) or elsewhere (if
 * sent to another application). Only the result of the integration is
 * stored, there is no reference to the integrated problem by
 * itself.</p>
 *
 * <p>One should be aware that the amount of data stored in a
 * ContinuousOutputModel instance can be important if the state vector
 * is large, if the integration interval is long or if the steps are
 * small (which can result from small tolerance settings in {@link
 * org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator adaptive
 * step size integrators}).</p>
 *
 * @see StepHandler
 * @see StepInterpolator
 * @version $Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $
 * @since 1.2
 */

public class ContinuousOutputModel
  implements StepHandler, Serializable {

    /** Serializable version identifier */
    private static final long serialVersionUID = -1417964919405031606L;

    /** Initial integration time. */
    private double initialTime;

    /** Final integration time. */
    private double finalTime;

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

    /** Current interpolator index. */
    private int index;

    /** Steps table. */
    private List<StepInterpolator> steps;

  /** Simple constructor.
   * Build an empty continuous output model.
   */
  public ContinuousOutputModel() {
    steps = new ArrayList<StepInterpolator>();
    reset();
  }

  /** Append another model at the end of the instance.
   * @param model model to add at the end of the instance
   * @exception DerivativeException if some step interpolators from
   * the appended model cannot be copied
   * @exception IllegalArgumentException if the model to append is not
   * compatible with the instance (dimension of the state vector,
   * propagation direction, hole between the dates)
   */
  public void append(final ContinuousOutputModel model)
    throws DerivativeException {

    if (model.steps.size() == 0) {
      return;
    }

    if (steps.size() == 0) {
      initialTime = model.initialTime;
      forward     = model.forward;
    } else {

      if (getInterpolatedState().length != model.getInterpolatedState().length) {
          throw MathRuntimeException.createIllegalArgumentException(
                "dimension mismatch {0} != {1}",
                getInterpolatedState().length, model.getInterpolatedState().length);
      }

      if (forward ^ model.forward) {
          throw MathRuntimeException.createIllegalArgumentException(
                "propagation direction mismatch");
      }

      final StepInterpolator lastInterpolator = steps.get(index);
      final double current  = lastInterpolator.getCurrentTime();
      final double previous = lastInterpolator.getPreviousTime();
      final double step = current - previous;
      final double gap = model.getInitialTime() - current;
      if (Math.abs(gap) > 1.0e-3 * Math.abs(step)) {
        throw MathRuntimeException.createIllegalArgumentException(
              "{0} wide hole between models time ranges", Math.abs(gap));
      }

    }

    for (StepInterpolator interpolator : model.steps) {
      steps.add(interpolator.copy());
    }

    index = steps.size() - 1;
    finalTime = (steps.get(index)).getCurrentTime();

  }

  /** Determines whether this handler needs dense output.
   * <p>The essence of this class is to provide dense output over all
   * steps, hence it requires the internal steps to provide themselves
   * dense output. The method therefore returns always true.</p>
   * @return always true
   */
  public boolean requiresDenseOutput() {
    return true;
  }

  /** Reset the step handler.
   * Initialize the internal data as required before the first step is
   * handled.
   */
  public void reset() {
    initialTime = Double.NaN;
    finalTime   = Double.NaN;
    forward     = true;
    index       = 0;
    steps.clear();
   }

  /** Handle the last accepted step.
   * A copy of the information provided by the last step is stored in
   * the instance for later use.
   * @param interpolator interpolator for the last accepted step.
   * @param isLast true if the step is the last one
   * @throws DerivativeException this exception is propagated to the
   * caller if the underlying user function triggers one
   */
  public void handleStep(final StepInterpolator interpolator, final boolean isLast)
    throws DerivativeException {

    if (steps.size() == 0) {
      initialTime = interpolator.getPreviousTime();
      forward     = interpolator.isForward();
    }

    steps.add(interpolator.copy());

    if (isLast) {
      finalTime = interpolator.getCurrentTime();
      index     = steps.size() - 1;
    }

  }

  /**
   * Get the initial integration time.
   * @return initial integration time
   */
  public double getInitialTime() {
    return initialTime;
  }

  /**
   * Get the final integration time.
   * @return final integration time
   */
  public double getFinalTime() {
    return finalTime;
  }

  /**
   * Get the time of the interpolated point.
   * If {@link #setInterpolatedTime} has not been called, it returns
   * the final integration time.
   * @return interpolation point time
   */
  public double getInterpolatedTime() {
    return steps.get(index).getInterpolatedTime();
  }

  /** Set the time of the interpolated point.
   * <p>This method should not be called before the
   * integration is over because some internal variables are set only
   * once the last step has been handled.</p>
   * <p>Setting the time outside of the integration interval is now
   * allowed (it was not allowed up to version 5.9 of Mantissa), but
   * should be used with care since the accuracy of the interpolator
   * will probably be very poor far from this interval. This allowance
   * has been added to simplify implementation of search algorithms
   * near the interval endpoints.</p>
   * @param time time of the interpolated point
   */
  public void setInterpolatedTime(final double time) {

      // initialize the search with the complete steps table
      int iMin = 0;
      final StepInterpolator sMin = steps.get(iMin);
      double tMin = 0.5 * (sMin.getPreviousTime() + sMin.getCurrentTime());

      int iMax = steps.size() - 1;
      final StepInterpolator sMax = steps.get(iMax);
      double tMax = 0.5 * (sMax.getPreviousTime() + sMax.getCurrentTime());

      // handle points outside of the integration interval
      // or in the first and last step
      if (locatePoint(time, sMin) <= 0) {
        index = iMin;
        sMin.setInterpolatedTime(time);
        return;
      }
      if (locatePoint(time, sMax) >= 0) {
        index = iMax;
        sMax.setInterpolatedTime(time);
        return;
      }

      // reduction of the table slice size
      while (iMax - iMin > 5) {

        // use the last estimated index as the splitting index
        final StepInterpolator si = steps.get(index);
        final int location = locatePoint(time, si);
        if (location < 0) {
          iMax = index;
          tMax = 0.5 * (si.getPreviousTime() + si.getCurrentTime());
        } else if (location > 0) {
          iMin = index;
          tMin = 0.5 * (si.getPreviousTime() + si.getCurrentTime());
        } else {
          // we have found the target step, no need to continue searching
          si.setInterpolatedTime(time);
          return;
        }

        // compute a new estimate of the index in the reduced table slice
        final int iMed = (iMin + iMax) / 2;
        final StepInterpolator sMed = steps.get(iMed);
        final double tMed = 0.5 * (sMed.getPreviousTime() + sMed.getCurrentTime());

        if ((Math.abs(tMed - tMin) < 1e-6) || (Math.abs(tMax - tMed) < 1e-6)) {
          // too close to the bounds, we estimate using a simple dichotomy
          index = iMed;
        } else {
          // estimate the index using a reverse quadratic polynom
          // (reverse means we have i = P(t), thus allowing to simply
          // compute index = P(time) rather than solving a quadratic equation)
          final double d12 = tMax - tMed;
          final double d23 = tMed - tMin;
          final double d13 = tMax - tMin;
          final double dt1 = time - tMax;
          final double dt2 = time - tMed;
          final double dt3 = time - tMin;
          final double iLagrange = ((dt2 * dt3 * d23) * iMax -
                                    (dt1 * dt3 * d13) * iMed +
                                    (dt1 * dt2 * d12) * iMin) /
                                   (d12 * d23 * d13);
          index = (int) Math.rint(iLagrange);
        }

        // force the next size reduction to be at least one tenth
        final int low  = Math.max(iMin + 1, (9 * iMin + iMax) / 10);
        final int high = Math.min(iMax - 1, (iMin + 9 * iMax) / 10);
        if (index < low) {
          index = low;
        } else if (index > high) {
          index = high;
        }

      }

      // now the table slice is very small, we perform an iterative search
      index = iMin;
      while ((index <= iMax) && (locatePoint(time, steps.get(index)) > 0)) {
        ++index;
      }

      steps.get(index).setInterpolatedTime(time);

  }

  /**
   * Get the state vector of the interpolated point.
   * @return state vector at time {@link #getInterpolatedTime}
   * @throws DerivativeException if this call induces an automatic
   * step finalization that throws one
   */
  public double[] getInterpolatedState() throws DerivativeException {
    return steps.get(index).getInterpolatedState();
  }

  /** Compare a step interval and a double.
   * @param time point to locate
   * @param interval step interval
   * @return -1 if the double is before the interval, 0 if it is in
   * the interval, and +1 if it is after the interval, according to
   * the interval direction
   */
  private int locatePoint(final double time, final StepInterpolator interval) {
    if (forward) {
      if (time < interval.getPreviousTime()) {
        return -1;
      } else if (time > interval.getCurrentTime()) {
        return +1;
      } else {
        return 0;
      }
    }
    if (time > interval.getPreviousTime()) {
      return -1;
    } else if (time < interval.getCurrentTime()) {
      return +1;
    } else {
      return 0;
    }
  }

}