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Java example source code file (AdaptiveStepsizeIntegrator.java)

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

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Java - Java tags/keywords

abstractintegrator, adaptivestepsizeintegrator, dimensionmismatchexception, expandablestatefulode, maxcountexceededexception, nobracketingexception, numberistoosmallexception, override, string

The AdaptiveStepsizeIntegrator.java Java example 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.math3.ode.nonstiff;

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.AbstractIntegrator;
import org.apache.commons.math3.ode.ExpandableStatefulODE;
import org.apache.commons.math3.util.FastMath;

/**
 * This abstract class holds the common part of all adaptive
 * stepsize integrators for Ordinary Differential Equations.
 *
 * <p>These algorithms perform integration with stepsize control, which
 * means the user does not specify the integration step but rather a
 * tolerance on error. The error threshold is computed as
 * <pre>
 * threshold_i = absTol_i + relTol_i * max (abs (ym), abs (ym+1))
 * </pre>
 * where absTol_i is the absolute tolerance for component i of the
 * state vector and relTol_i is the relative tolerance for the same
 * component. The user can also use only two scalar values absTol and
 * relTol which will be used for all components.
 * </p>
 * <p>
 * If the Ordinary Differential Equations is an {@link ExpandableStatefulODE
 * extended ODE} rather than a {@link
 * org.apache.commons.math3.ode.FirstOrderDifferentialEquations basic ODE}, then
 * <em>only the {@link ExpandableStatefulODE#getPrimaryState() primary part}
 * of the state vector is used for stepsize control, not the complete state vector.
 * </p>
 *
 * <p>If the estimated error for ym+1 is such that
 * <pre>
 * sqrt((sum (errEst_i / threshold_i)^2 ) / n) < 1
 * </pre>
 *
 * (where n is the main set dimension) then the step is accepted,
 * otherwise the step is rejected and a new attempt is made with a new
 * stepsize.</p>
 *
 * @since 1.2
 *
 */

public abstract class AdaptiveStepsizeIntegrator
  extends AbstractIntegrator {

    /** Allowed absolute scalar error. */
    protected double scalAbsoluteTolerance;

    /** Allowed relative scalar error. */
    protected double scalRelativeTolerance;

    /** Allowed absolute vectorial error. */
    protected double[] vecAbsoluteTolerance;

    /** Allowed relative vectorial error. */
    protected double[] vecRelativeTolerance;

    /** Main set dimension. */
    protected int mainSetDimension;

    /** User supplied initial step. */
    private double initialStep;

    /** Minimal step. */
    private double minStep;

    /** Maximal step. */
    private double maxStep;

  /** Build an integrator with the given stepsize bounds.
   * The default step handler does nothing.
   * @param name name of the method
   * @param minStep minimal step (sign is irrelevant, regardless of
   * integration direction, forward or backward), the last step can
   * be smaller than this
   * @param maxStep maximal step (sign is irrelevant, regardless of
   * integration direction, forward or backward), the last step can
   * be smaller than this
   * @param scalAbsoluteTolerance allowed absolute error
   * @param scalRelativeTolerance allowed relative error
   */
  public AdaptiveStepsizeIntegrator(final String name,
                                    final double minStep, final double maxStep,
                                    final double scalAbsoluteTolerance,
                                    final double scalRelativeTolerance) {

    super(name);
    setStepSizeControl(minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
    resetInternalState();

  }

  /** Build an integrator with the given stepsize bounds.
   * The default step handler does nothing.
   * @param name name of the method
   * @param minStep minimal step (sign is irrelevant, regardless of
   * integration direction, forward or backward), the last step can
   * be smaller than this
   * @param maxStep maximal step (sign is irrelevant, regardless of
   * integration direction, forward or backward), the last step can
   * be smaller than this
   * @param vecAbsoluteTolerance allowed absolute error
   * @param vecRelativeTolerance allowed relative error
   */
  public AdaptiveStepsizeIntegrator(final String name,
                                    final double minStep, final double maxStep,
                                    final double[] vecAbsoluteTolerance,
                                    final double[] vecRelativeTolerance) {

    super(name);
    setStepSizeControl(minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
    resetInternalState();

  }

  /** Set the adaptive step size control parameters.
   * <p>
   * A side effect of this method is to also reset the initial
   * step so it will be automatically computed by the integrator
   * if {@link #setInitialStepSize(double) setInitialStepSize}
   * is not called by the user.
   * </p>
   * @param minimalStep minimal step (must be positive even for backward
   * integration), the last step can be smaller than this
   * @param maximalStep maximal step (must be positive even for backward
   * integration)
   * @param absoluteTolerance allowed absolute error
   * @param relativeTolerance allowed relative error
   */
  public void setStepSizeControl(final double minimalStep, final double maximalStep,
                                 final double absoluteTolerance,
                                 final double relativeTolerance) {

      minStep     = FastMath.abs(minimalStep);
      maxStep     = FastMath.abs(maximalStep);
      initialStep = -1;

      scalAbsoluteTolerance = absoluteTolerance;
      scalRelativeTolerance = relativeTolerance;
      vecAbsoluteTolerance  = null;
      vecRelativeTolerance  = null;

  }

  /** Set the adaptive step size control parameters.
   * <p>
   * A side effect of this method is to also reset the initial
   * step so it will be automatically computed by the integrator
   * if {@link #setInitialStepSize(double) setInitialStepSize}
   * is not called by the user.
   * </p>
   * @param minimalStep minimal step (must be positive even for backward
   * integration), the last step can be smaller than this
   * @param maximalStep maximal step (must be positive even for backward
   * integration)
   * @param absoluteTolerance allowed absolute error
   * @param relativeTolerance allowed relative error
   */
  public void setStepSizeControl(final double minimalStep, final double maximalStep,
                                 final double[] absoluteTolerance,
                                 final double[] relativeTolerance) {

      minStep     = FastMath.abs(minimalStep);
      maxStep     = FastMath.abs(maximalStep);
      initialStep = -1;

      scalAbsoluteTolerance = 0;
      scalRelativeTolerance = 0;
      vecAbsoluteTolerance  = absoluteTolerance.clone();
      vecRelativeTolerance  = relativeTolerance.clone();

  }

  /** Set the initial step size.
   * <p>This method allows the user to specify an initial positive
   * step size instead of letting the integrator guess it by
   * itself. If this method is not called before integration is
   * started, the initial step size will be estimated by the
   * integrator.</p>
   * @param initialStepSize initial step size to use (must be positive even
   * for backward integration ; providing a negative value or a value
   * outside of the min/max step interval will lead the integrator to
   * ignore the value and compute the initial step size by itself)
   */
  public void setInitialStepSize(final double initialStepSize) {
    if ((initialStepSize < minStep) || (initialStepSize > maxStep)) {
      initialStep = -1.0;
    } else {
      initialStep = initialStepSize;
    }
  }

  /** {@inheritDoc} */
  @Override
  protected void sanityChecks(final ExpandableStatefulODE equations, final double t)
      throws DimensionMismatchException, NumberIsTooSmallException {

      super.sanityChecks(equations, t);

      mainSetDimension = equations.getPrimaryMapper().getDimension();

      if ((vecAbsoluteTolerance != null) && (vecAbsoluteTolerance.length != mainSetDimension)) {
          throw new DimensionMismatchException(mainSetDimension, vecAbsoluteTolerance.length);
      }

      if ((vecRelativeTolerance != null) && (vecRelativeTolerance.length != mainSetDimension)) {
          throw new DimensionMismatchException(mainSetDimension, vecRelativeTolerance.length);
      }

  }

  /** Initialize the integration step.
   * @param forward forward integration indicator
   * @param order order of the method
   * @param scale scaling vector for the state vector (can be shorter than state vector)
   * @param t0 start time
   * @param y0 state vector at t0
   * @param yDot0 first time derivative of y0
   * @param y1 work array for a state vector
   * @param yDot1 work array for the first time derivative of y1
   * @return first integration step
   * @exception MaxCountExceededException if the number of functions evaluations is exceeded
   * @exception DimensionMismatchException if arrays dimensions do not match equations settings
   */
  public double initializeStep(final boolean forward, final int order, final double[] scale,
                               final double t0, final double[] y0, final double[] yDot0,
                               final double[] y1, final double[] yDot1)
      throws MaxCountExceededException, DimensionMismatchException {

    if (initialStep > 0) {
      // use the user provided value
      return forward ? initialStep : -initialStep;
    }

    // very rough first guess : h = 0.01 * ||y/scale|| / ||y'/scale||
    // this guess will be used to perform an Euler step
    double ratio;
    double yOnScale2 = 0;
    double yDotOnScale2 = 0;
    for (int j = 0; j < scale.length; ++j) {
      ratio         = y0[j] / scale[j];
      yOnScale2    += ratio * ratio;
      ratio         = yDot0[j] / scale[j];
      yDotOnScale2 += ratio * ratio;
    }

    double h = ((yOnScale2 < 1.0e-10) || (yDotOnScale2 < 1.0e-10)) ?
               1.0e-6 : (0.01 * FastMath.sqrt(yOnScale2 / yDotOnScale2));
    if (! forward) {
      h = -h;
    }

    // perform an Euler step using the preceding rough guess
    for (int j = 0; j < y0.length; ++j) {
      y1[j] = y0[j] + h * yDot0[j];
    }
    computeDerivatives(t0 + h, y1, yDot1);

    // estimate the second derivative of the solution
    double yDDotOnScale = 0;
    for (int j = 0; j < scale.length; ++j) {
      ratio         = (yDot1[j] - yDot0[j]) / scale[j];
      yDDotOnScale += ratio * ratio;
    }
    yDDotOnScale = FastMath.sqrt(yDDotOnScale) / h;

    // step size is computed such that
    // h^order * max (||y'/tol||, ||y''/tol||) = 0.01
    final double maxInv2 = FastMath.max(FastMath.sqrt(yDotOnScale2), yDDotOnScale);
    final double h1 = (maxInv2 < 1.0e-15) ?
                      FastMath.max(1.0e-6, 0.001 * FastMath.abs(h)) :
                      FastMath.pow(0.01 / maxInv2, 1.0 / order);
    h = FastMath.min(100.0 * FastMath.abs(h), h1);
    h = FastMath.max(h, 1.0e-12 * FastMath.abs(t0));  // avoids cancellation when computing t1 - t0
    if (h < getMinStep()) {
      h = getMinStep();
    }
    if (h > getMaxStep()) {
      h = getMaxStep();
    }
    if (! forward) {
      h = -h;
    }

    return h;

  }

  /** Filter the integration step.
   * @param h signed step
   * @param forward forward integration indicator
   * @param acceptSmall if true, steps smaller than the minimal value
   * are silently increased up to this value, if false such small
   * steps generate an exception
   * @return a bounded integration step (h if no bound is reach, or a bounded value)
   * @exception NumberIsTooSmallException if the step is too small and acceptSmall is false
   */
  protected double filterStep(final double h, final boolean forward, final boolean acceptSmall)
    throws NumberIsTooSmallException {

      double filteredH = h;
      if (FastMath.abs(h) < minStep) {
          if (acceptSmall) {
              filteredH = forward ? minStep : -minStep;
          } else {
              throw new NumberIsTooSmallException(LocalizedFormats.MINIMAL_STEPSIZE_REACHED_DURING_INTEGRATION,
                                                  FastMath.abs(h), minStep, true);
          }
      }

      if (filteredH > maxStep) {
          filteredH = maxStep;
      } else if (filteredH < -maxStep) {
          filteredH = -maxStep;
      }

      return filteredH;

  }

  /** {@inheritDoc} */
  @Override
  public abstract void integrate (ExpandableStatefulODE equations, double t)
      throws NumberIsTooSmallException, DimensionMismatchException,
             MaxCountExceededException, NoBracketingException;

  /** {@inheritDoc} */
  @Override
  public double getCurrentStepStart() {
    return stepStart;
  }

  /** Reset internal state to dummy values. */
  protected void resetInternalState() {
    stepStart = Double.NaN;
    stepSize  = FastMath.sqrt(minStep * maxStep);
  }

  /** Get the minimal step.
   * @return minimal step
   */
  public double getMinStep() {
    return minStep;
  }

  /** Get the maximal step.
   * @return maximal step
   */
  public double getMaxStep() {
    return maxStep;
  }

}

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