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Diffstat (limited to 'src/main/java/org/apache/commons/math/ode/sampling')
9 files changed, 1554 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/ode/sampling/AbstractStepInterpolator.java b/src/main/java/org/apache/commons/math/ode/sampling/AbstractStepInterpolator.java new file mode 100644 index 0000000..5cb2979 --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/sampling/AbstractStepInterpolator.java @@ -0,0 +1,519 @@ +/* + * 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.sampling; + +import java.io.IOException; +import java.io.ObjectInput; +import java.io.ObjectOutput; + +import org.apache.commons.math.ode.DerivativeException; + +/** This abstract class represents an interpolator over the last step + * during an ODE integration. + * + * <p>The various ODE integrators provide objects extending this class + * to the step handlers. The handlers can use these objects to + * retrieve the state vector at intermediate times between the + * previous and the current grid points (dense output).</p> + * + * @see org.apache.commons.math.ode.FirstOrderIntegrator + * @see org.apache.commons.math.ode.SecondOrderIntegrator + * @see StepHandler + * + * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ + * @since 1.2 + * + */ + +public abstract class AbstractStepInterpolator + implements StepInterpolator { + + /** current time step */ + protected double h; + + /** current state */ + protected double[] currentState; + + /** interpolated time */ + protected double interpolatedTime; + + /** interpolated state */ + protected double[] interpolatedState; + + /** interpolated derivatives */ + protected double[] interpolatedDerivatives; + + /** global previous time */ + private double globalPreviousTime; + + /** global current time */ + private double globalCurrentTime; + + /** soft previous time */ + private double softPreviousTime; + + /** soft current time */ + private double softCurrentTime; + + /** indicate if the step has been finalized or not. */ + private boolean finalized; + + /** integration direction. */ + private boolean forward; + + /** indicator for dirty state. */ + private boolean dirtyState; + + + /** Simple constructor. + * This constructor builds an instance that is not usable yet, the + * {@link #reinitialize} method should be called before using the + * instance in order to initialize the internal arrays. This + * constructor is used only in order to delay the initialization in + * some cases. As an example, the {@link + * org.apache.commons.math.ode.nonstiff.EmbeddedRungeKuttaIntegrator} + * class uses the prototyping design pattern to create the step + * interpolators by cloning an uninitialized model and latter + * initializing the copy. + */ + protected AbstractStepInterpolator() { + globalPreviousTime = Double.NaN; + globalCurrentTime = Double.NaN; + softPreviousTime = Double.NaN; + softCurrentTime = Double.NaN; + h = Double.NaN; + interpolatedTime = Double.NaN; + currentState = null; + interpolatedState = null; + interpolatedDerivatives = null; + finalized = false; + this.forward = true; + this.dirtyState = true; + } + + /** Simple constructor. + * @param y reference to the integrator array holding the state at + * the end of the step + * @param forward integration direction indicator + */ + protected AbstractStepInterpolator(final double[] y, final boolean forward) { + + globalPreviousTime = Double.NaN; + globalCurrentTime = Double.NaN; + softPreviousTime = Double.NaN; + softCurrentTime = Double.NaN; + h = Double.NaN; + interpolatedTime = Double.NaN; + + currentState = y; + interpolatedState = new double[y.length]; + interpolatedDerivatives = new double[y.length]; + + finalized = false; + this.forward = forward; + this.dirtyState = true; + + } + + /** Copy constructor. + + * <p>The copied interpolator should have been finalized before the + * copy, otherwise the copy will not be able to perform correctly + * any derivative computation and will throw a {@link + * NullPointerException} later. Since we don't want this constructor + * to throw the exceptions finalization may involve and since we + * don't want this method to modify the state of the copied + * interpolator, finalization is <strong>not</strong> done + * automatically, it remains under user control.</p> + * + * <p>The copy is a deep copy: its arrays are separated from the + * original arrays of the instance.</p> + * + * @param interpolator interpolator to copy from. + * + */ + protected AbstractStepInterpolator(final AbstractStepInterpolator interpolator) { + + globalPreviousTime = interpolator.globalPreviousTime; + globalCurrentTime = interpolator.globalCurrentTime; + softPreviousTime = interpolator.softPreviousTime; + softCurrentTime = interpolator.softCurrentTime; + h = interpolator.h; + interpolatedTime = interpolator.interpolatedTime; + + if (interpolator.currentState != null) { + currentState = interpolator.currentState.clone(); + interpolatedState = interpolator.interpolatedState.clone(); + interpolatedDerivatives = interpolator.interpolatedDerivatives.clone(); + } else { + currentState = null; + interpolatedState = null; + interpolatedDerivatives = null; + } + + finalized = interpolator.finalized; + forward = interpolator.forward; + dirtyState = interpolator.dirtyState; + + } + + /** Reinitialize the instance + * @param y reference to the integrator array holding the state at + * the end of the step + * @param isForward integration direction indicator + */ + protected void reinitialize(final double[] y, final boolean isForward) { + + globalPreviousTime = Double.NaN; + globalCurrentTime = Double.NaN; + softPreviousTime = Double.NaN; + softCurrentTime = Double.NaN; + h = Double.NaN; + interpolatedTime = Double.NaN; + + currentState = y; + interpolatedState = new double[y.length]; + interpolatedDerivatives = new double[y.length]; + + finalized = false; + this.forward = isForward; + this.dirtyState = true; + + } + + /** {@inheritDoc} */ + public StepInterpolator copy() throws DerivativeException { + + // finalize the step before performing copy + finalizeStep(); + + // create the new independent instance + return doCopy(); + + } + + /** Really copy the finalized instance. + * <p>This method is called by {@link #copy()} after the + * step has been finalized. It must perform a deep copy + * to have an new instance completely independent for the + * original instance. + * @return a copy of the finalized instance + */ + protected abstract StepInterpolator doCopy(); + + /** Shift one step forward. + * Copy the current time into the previous time, hence preparing the + * interpolator for future calls to {@link #storeTime storeTime} + */ + public void shift() { + globalPreviousTime = globalCurrentTime; + softPreviousTime = globalPreviousTime; + softCurrentTime = globalCurrentTime; + } + + /** Store the current step time. + * @param t current time + */ + public void storeTime(final double t) { + + globalCurrentTime = t; + softCurrentTime = globalCurrentTime; + h = globalCurrentTime - globalPreviousTime; + setInterpolatedTime(t); + + // the step is not finalized anymore + finalized = false; + + } + + /** Restrict step range to a limited part of the global step. + * <p> + * This method can be used to restrict a step and make it appear + * as if the original step was smaller. Calling this method + * <em>only</em> changes the value returned by {@link #getPreviousTime()}, + * it does not change any other property + * </p> + * @param softPreviousTime start of the restricted step + * @since 2.2 + */ + public void setSoftPreviousTime(final double softPreviousTime) { + this.softPreviousTime = softPreviousTime; + } + + /** Restrict step range to a limited part of the global step. + * <p> + * This method can be used to restrict a step and make it appear + * as if the original step was smaller. Calling this method + * <em>only</em> changes the value returned by {@link #getCurrentTime()}, + * it does not change any other property + * </p> + * @param softCurrentTime end of the restricted step + * @since 2.2 + */ + public void setSoftCurrentTime(final double softCurrentTime) { + this.softCurrentTime = softCurrentTime; + } + + /** + * Get the previous global grid point time. + * @return previous global grid point time + * @since 2.2 + */ + public double getGlobalPreviousTime() { + return globalPreviousTime; + } + + /** + * Get the current global grid point time. + * @return current global grid point time + * @since 2.2 + */ + public double getGlobalCurrentTime() { + return globalCurrentTime; + } + + /** + * Get the previous soft grid point time. + * @return previous soft grid point time + * @see #setSoftPreviousTime(double) + */ + public double getPreviousTime() { + return softPreviousTime; + } + + /** + * Get the current soft grid point time. + * @return current soft grid point time + * @see #setSoftCurrentTime(double) + */ + public double getCurrentTime() { + return softCurrentTime; + } + + /** {@inheritDoc} */ + public double getInterpolatedTime() { + return interpolatedTime; + } + + /** {@inheritDoc} */ + public void setInterpolatedTime(final double time) { + interpolatedTime = time; + dirtyState = true; + } + + /** {@inheritDoc} */ + public boolean isForward() { + return forward; + } + + /** Compute the state and derivatives at the interpolated time. + * This is the main processing method that should be implemented by + * the derived classes to perform the interpolation. + * @param theta normalized interpolation abscissa within the step + * (theta is zero at the previous time step and one at the current time step) + * @param oneMinusThetaH time gap between the interpolated time and + * the current time + * @throws DerivativeException this exception is propagated to the caller if the + * underlying user function triggers one + */ + protected abstract void computeInterpolatedStateAndDerivatives(double theta, + double oneMinusThetaH) + throws DerivativeException; + + /** {@inheritDoc} */ + public double[] getInterpolatedState() throws DerivativeException { + + // lazy evaluation of the state + if (dirtyState) { + final double oneMinusThetaH = globalCurrentTime - interpolatedTime; + final double theta = (h == 0) ? 0 : (h - oneMinusThetaH) / h; + computeInterpolatedStateAndDerivatives(theta, oneMinusThetaH); + dirtyState = false; + } + + return interpolatedState; + + } + + /** {@inheritDoc} */ + public double[] getInterpolatedDerivatives() throws DerivativeException { + + // lazy evaluation of the state + if (dirtyState) { + final double oneMinusThetaH = globalCurrentTime - interpolatedTime; + final double theta = (h == 0) ? 0 : (h - oneMinusThetaH) / h; + computeInterpolatedStateAndDerivatives(theta, oneMinusThetaH); + dirtyState = false; + } + + return interpolatedDerivatives; + + } + + /** + * Finalize the step. + * + * <p>Some embedded Runge-Kutta integrators need fewer functions + * evaluations than their counterpart step interpolators. These + * interpolators should perform the last evaluations they need by + * themselves only if they need them. This method triggers these + * extra evaluations. It can be called directly by the user step + * handler and it is called automatically if {@link + * #setInterpolatedTime} is called.</p> + * + * <p>Once this method has been called, <strong>no</strong> other + * evaluation will be performed on this step. If there is a need to + * have some side effects between the step handler and the + * differential equations (for example update some data in the + * equations once the step has been done), it is advised to call + * this method explicitly from the step handler before these side + * effects are set up. If the step handler induces no side effect, + * then this method can safely be ignored, it will be called + * transparently as needed.</p> + * + * <p><strong>Warning</strong>: since the step interpolator provided + * to the step handler as a parameter of the {@link + * StepHandler#handleStep handleStep} is valid only for the duration + * of the {@link StepHandler#handleStep handleStep} call, one cannot + * simply store a reference and reuse it later. One should first + * finalize the instance, then copy this finalized instance into a + * new object that can be kept.</p> + * + * <p>This method calls the protected <code>doFinalize</code> method + * if it has never been called during this step and set a flag + * indicating that it has been called once. It is the <code> + * doFinalize</code> method which should perform the evaluations. + * This wrapping prevents from calling <code>doFinalize</code> several + * times and hence evaluating the differential equations too often. + * Therefore, subclasses are not allowed not reimplement it, they + * should rather reimplement <code>doFinalize</code>.</p> + * + * @throws DerivativeException this exception is propagated to the + * caller if the underlying user function triggers one + */ + public final void finalizeStep() + throws DerivativeException { + if (! finalized) { + doFinalize(); + finalized = true; + } + } + + /** + * Really finalize the step. + * The default implementation of this method does nothing. + * @throws DerivativeException this exception is propagated to the + * caller if the underlying user function triggers one + */ + protected void doFinalize() + throws DerivativeException { + } + + /** {@inheritDoc} */ + public abstract void writeExternal(ObjectOutput out) + throws IOException; + + /** {@inheritDoc} */ + public abstract void readExternal(ObjectInput in) + throws IOException, ClassNotFoundException; + + /** Save the base state of the instance. + * This method performs step finalization if it has not been done + * before. + * @param out stream where to save the state + * @exception IOException in case of write error + */ + protected void writeBaseExternal(final ObjectOutput out) + throws IOException { + + if (currentState == null) { + out.writeInt(-1); + } else { + out.writeInt(currentState.length); + } + out.writeDouble(globalPreviousTime); + out.writeDouble(globalCurrentTime); + out.writeDouble(softPreviousTime); + out.writeDouble(softCurrentTime); + out.writeDouble(h); + out.writeBoolean(forward); + + if (currentState != null) { + for (int i = 0; i < currentState.length; ++i) { + out.writeDouble(currentState[i]); + } + } + + out.writeDouble(interpolatedTime); + + // we do not store the interpolated state, + // it will be recomputed as needed after reading + + // finalize the step (and don't bother saving the now true flag) + try { + finalizeStep(); + } catch (DerivativeException e) { + IOException ioe = new IOException(e.getLocalizedMessage()); + ioe.initCause(e); + throw ioe; + } + + } + + /** Read the base state of the instance. + * This method does <strong>neither</strong> set the interpolated + * time nor state. It is up to the derived class to reset it + * properly calling the {@link #setInterpolatedTime} method later, + * once all rest of the object state has been set up properly. + * @param in stream where to read the state from + * @return interpolated time be set later by the caller + * @exception IOException in case of read error + */ + protected double readBaseExternal(final ObjectInput in) + throws IOException { + + final int dimension = in.readInt(); + globalPreviousTime = in.readDouble(); + globalCurrentTime = in.readDouble(); + softPreviousTime = in.readDouble(); + softCurrentTime = in.readDouble(); + h = in.readDouble(); + forward = in.readBoolean(); + dirtyState = true; + + if (dimension < 0) { + currentState = null; + } else { + currentState = new double[dimension]; + for (int i = 0; i < currentState.length; ++i) { + currentState[i] = in.readDouble(); + } + } + + // we do NOT handle the interpolated time and state here + interpolatedTime = Double.NaN; + interpolatedState = (dimension < 0) ? null : new double[dimension]; + interpolatedDerivatives = (dimension < 0) ? null : new double[dimension]; + + finalized = true; + + return in.readDouble(); + + } + +} diff --git a/src/main/java/org/apache/commons/math/ode/sampling/DummyStepHandler.java b/src/main/java/org/apache/commons/math/ode/sampling/DummyStepHandler.java new file mode 100644 index 0000000..cc759b9 --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/sampling/DummyStepHandler.java @@ -0,0 +1,101 @@ +/* + * 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.sampling; + +/** + * This class is a step handler that does nothing. + + * <p>This class is provided as a convenience for users who are only + * interested in the final state of an integration and not in the + * intermediate steps. Its handleStep method does nothing.</p> + * + * <p>Since this class has no internal state, it is implemented using + * the Singleton design pattern. This means that only one instance is + * ever created, which can be retrieved using the getInstance + * method. This explains why there is no public constructor.</p> + * + * @see StepHandler + * @version $Revision: 811827 $ $Date: 2009-09-06 17:32:50 +0200 (dim. 06 sept. 2009) $ + * @since 1.2 + */ + +public class DummyStepHandler implements StepHandler { + + /** Private constructor. + * The constructor is private to prevent users from creating + * instances (Singleton design-pattern). + */ + private DummyStepHandler() { + } + + /** Get the only instance. + * @return the only instance + */ + public static DummyStepHandler getInstance() { + return LazyHolder.INSTANCE; + } + + /** Determines whether this handler needs dense output. + * Since this handler does nothing, it does not require dense output. + * @return always false + */ + public boolean requiresDenseOutput() { + return false; + } + + /** Reset the step handler. + * Initialize the internal data as required before the first step is + * handled. + */ + public void reset() { + } + + /** + * Handle the last accepted step. + * This method does nothing in this class. + * @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 + */ + public void handleStep(final StepInterpolator interpolator, final boolean isLast) { + } + + // CHECKSTYLE: stop HideUtilityClassConstructor + /** Holder for the instance. + * <p>We use here the Initialization On Demand Holder Idiom.</p> + */ + private static class LazyHolder { + /** Cached field instance. */ + private static final DummyStepHandler INSTANCE = new DummyStepHandler(); + } + // CHECKSTYLE: resume HideUtilityClassConstructor + + /** Handle deserialization of the singleton. + * @return the singleton instance + */ + private Object readResolve() { + // return the singleton instance + return LazyHolder.INSTANCE; + } + +} diff --git a/src/main/java/org/apache/commons/math/ode/sampling/DummyStepInterpolator.java b/src/main/java/org/apache/commons/math/ode/sampling/DummyStepInterpolator.java new file mode 100644 index 0000000..af28c13 --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/sampling/DummyStepInterpolator.java @@ -0,0 +1,150 @@ +/* + * 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.sampling; + +import java.io.IOException; +import java.io.ObjectInput; +import java.io.ObjectOutput; + +/** This class is a step interpolator that does nothing. + * + * <p>This class is used when the {@link StepHandler "step handler"} + * set up by the user does not need step interpolation. It does not + * recompute the state when {@link AbstractStepInterpolator#setInterpolatedTime + * setInterpolatedTime} is called. This implies the interpolated state + * is always the state at the end of the current step.</p> + * + * @see StepHandler + * + * @version $Revision: 1037327 $ $Date: 2010-11-20 21:57:37 +0100 (sam. 20 nov. 2010) $ + * @since 1.2 + */ + +public class DummyStepInterpolator + extends AbstractStepInterpolator { + + /** Serializable version identifier. */ + private static final long serialVersionUID = 1708010296707839488L; + + /** Current derivative. */ + private double[] currentDerivative; + + /** Simple constructor. + * This constructor builds an instance that is not usable yet, the + * <code>AbstractStepInterpolator.reinitialize</code> protected method + * should be called before using the instance in order to initialize + * the internal arrays. This constructor is used only in order to delay + * the initialization in some cases. As an example, the {@link + * org.apache.commons.math.ode.nonstiff.EmbeddedRungeKuttaIntegrator} uses + * the prototyping design pattern to create the step interpolators by + * cloning an uninitialized model and latter initializing the copy. + */ + public DummyStepInterpolator() { + super(); + currentDerivative = null; + } + + /** Simple constructor. + * @param y reference to the integrator array holding the state at + * the end of the step + * @param yDot reference to the integrator array holding the state + * derivative at some arbitrary point within the step + * @param forward integration direction indicator + */ + public DummyStepInterpolator(final double[] y, final double[] yDot, final boolean forward) { + super(y, forward); + currentDerivative = yDot; + } + + /** Copy constructor. + * @param interpolator interpolator to copy from. The copy is a deep + * copy: its arrays are separated from the original arrays of the + * instance + */ + public DummyStepInterpolator(final DummyStepInterpolator interpolator) { + super(interpolator); + currentDerivative = interpolator.currentDerivative.clone(); + } + + /** Really copy the finalized instance. + * @return a copy of the finalized instance + */ + @Override + protected StepInterpolator doCopy() { + return new DummyStepInterpolator(this); + } + + /** Compute the state at the interpolated time. + * In this class, this method does nothing: the interpolated state + * is always the state at the end of the current step. + * @param theta normalized interpolation abscissa within the step + * (theta is zero at the previous time step and one at the current time step) + * @param oneMinusThetaH time gap between the interpolated time and + * the current time + */ + @Override + protected void computeInterpolatedStateAndDerivatives(final double theta, final double oneMinusThetaH) { + System.arraycopy(currentState, 0, interpolatedState, 0, currentState.length); + System.arraycopy(currentDerivative, 0, interpolatedDerivatives, 0, currentDerivative.length); + } + + /** Write the instance to an output channel. + * @param out output channel + * @exception IOException if the instance cannot be written + */ + @Override + public void writeExternal(final ObjectOutput out) + throws IOException { + + // save the state of the base class + writeBaseExternal(out); + + if (currentDerivative != null) { + for (int i = 0; i < currentDerivative.length; ++i) { + out.writeDouble(currentDerivative[i]); + } + } + + } + + /** Read the instance from an input channel. + * @param in input channel + * @exception IOException if the instance cannot be read + */ + @Override + public void readExternal(final ObjectInput in) + throws IOException { + + // read the base class + final double t = readBaseExternal(in); + + if (currentState == null) { + currentDerivative = null; + } else { + currentDerivative = new double[currentState.length]; + for (int i = 0; i < currentDerivative.length; ++i) { + currentDerivative[i] = in.readDouble(); + } + } + + // we can now set the interpolated time and state + setInterpolatedTime(t); + + } + +} diff --git a/src/main/java/org/apache/commons/math/ode/sampling/FixedStepHandler.java b/src/main/java/org/apache/commons/math/ode/sampling/FixedStepHandler.java new file mode 100644 index 0000000..190c999 --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/sampling/FixedStepHandler.java @@ -0,0 +1,62 @@ +/* + * 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.sampling; + +import org.apache.commons.math.ode.DerivativeException; + +/** + * This interface represents a handler that should be called after + * each successful fixed step. + + * <p>This interface should be implemented by anyone who is interested + * in getting the solution of an ordinary differential equation at + * fixed time steps. Objects implementing this interface should be + * wrapped within an instance of {@link StepNormalizer} that itself + * is used as the general {@link StepHandler} by the integrator. The + * {@link StepNormalizer} object is called according to the integrator + * internal algorithms and it calls objects implementing this + * interface as necessary at fixed time steps.</p> + * + * @see StepHandler + * @see StepNormalizer + * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ + * @since 1.2 + */ + +public interface FixedStepHandler { + + /** + * Handle the last accepted step + * @param t time of the current step + * @param y state vector at t. For efficiency purposes, the {@link + * StepNormalizer} class reuses the same array 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 complete array of all + * steps), it should build a local copy store this copy. + * @param yDot derivatives of the state vector state vector at t. + * For efficiency purposes, the {@link StepNormalizer} class reuses + * the same array 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 complete array of all + * steps), it should build a local copy store this copy. + * @param isLast true if the step is the last one + * @throws DerivativeException if some error condition is encountered + */ + void handleStep(double t, double[] y, double[] yDot, boolean isLast) throws DerivativeException; + +} diff --git a/src/main/java/org/apache/commons/math/ode/sampling/NordsieckStepInterpolator.java b/src/main/java/org/apache/commons/math/ode/sampling/NordsieckStepInterpolator.java new file mode 100644 index 0000000..2090276 --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/sampling/NordsieckStepInterpolator.java @@ -0,0 +1,291 @@ +/* + * 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.sampling; + +import java.io.IOException; +import java.io.ObjectInput; +import java.io.ObjectOutput; +import java.util.Arrays; + +import org.apache.commons.math.ode.DerivativeException; +import org.apache.commons.math.linear.Array2DRowRealMatrix; +import org.apache.commons.math.util.FastMath; + +/** + * This class implements an interpolator for integrators using Nordsieck representation. + * + * <p>This interpolator computes dense output around the current point. + * The interpolation equation is based on Taylor series formulas. + * + * @see org.apache.commons.math.ode.nonstiff.AdamsBashforthIntegrator + * @see org.apache.commons.math.ode.nonstiff.AdamsMoultonIntegrator + * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ + * @since 2.0 + */ + +public class NordsieckStepInterpolator extends AbstractStepInterpolator { + + /** Serializable version identifier */ + private static final long serialVersionUID = -7179861704951334960L; + + /** State variation. */ + protected double[] stateVariation; + + /** Step size used in the first scaled derivative and Nordsieck vector. */ + private double scalingH; + + /** Reference time for all arrays. + * <p>Sometimes, the reference time is the same as previousTime, + * sometimes it is the same as currentTime, so we use a separate + * field to avoid any confusion. + * </p> + */ + private double referenceTime; + + /** First scaled derivative. */ + private double[] scaled; + + /** Nordsieck vector. */ + private Array2DRowRealMatrix nordsieck; + + /** Simple constructor. + * This constructor builds an instance that is not usable yet, the + * {@link AbstractStepInterpolator#reinitialize} method should be called + * before using the instance in order to initialize the internal arrays. This + * constructor is used only in order to delay the initialization in + * some cases. + */ + public NordsieckStepInterpolator() { + } + + /** Copy constructor. + * @param interpolator interpolator to copy from. The copy is a deep + * copy: its arrays are separated from the original arrays of the + * instance + */ + public NordsieckStepInterpolator(final NordsieckStepInterpolator interpolator) { + super(interpolator); + scalingH = interpolator.scalingH; + referenceTime = interpolator.referenceTime; + if (interpolator.scaled != null) { + scaled = interpolator.scaled.clone(); + } + if (interpolator.nordsieck != null) { + nordsieck = new Array2DRowRealMatrix(interpolator.nordsieck.getDataRef(), true); + } + if (interpolator.stateVariation != null) { + stateVariation = interpolator.stateVariation.clone(); + } + } + + /** {@inheritDoc} */ + @Override + protected StepInterpolator doCopy() { + return new NordsieckStepInterpolator(this); + } + + /** Reinitialize the instance. + * <p>Beware that all arrays <em>must</em> be references to integrator + * arrays, in order to ensure proper update without copy.</p> + * @param y reference to the integrator array holding the state at + * the end of the step + * @param forward integration direction indicator + */ + @Override + public void reinitialize(final double[] y, final boolean forward) { + super.reinitialize(y, forward); + stateVariation = new double[y.length]; + } + + /** Reinitialize the instance. + * <p>Beware that all arrays <em>must</em> be references to integrator + * arrays, in order to ensure proper update without copy.</p> + * @param time time at which all arrays are defined + * @param stepSize step size used in the scaled and nordsieck arrays + * @param scaledDerivative reference to the integrator array holding the first + * scaled derivative + * @param nordsieckVector reference to the integrator matrix holding the + * nordsieck vector + */ + public void reinitialize(final double time, final double stepSize, + final double[] scaledDerivative, + final Array2DRowRealMatrix nordsieckVector) { + this.referenceTime = time; + this.scalingH = stepSize; + this.scaled = scaledDerivative; + this.nordsieck = nordsieckVector; + + // make sure the state and derivatives will depend on the new arrays + setInterpolatedTime(getInterpolatedTime()); + + } + + /** Rescale the instance. + * <p>Since the scaled and Nordiseck arrays are shared with the caller, + * this method has the side effect of rescaling this arrays in the caller too.</p> + * @param stepSize new step size to use in the scaled and nordsieck arrays + */ + public void rescale(final double stepSize) { + + final double ratio = stepSize / scalingH; + for (int i = 0; i < scaled.length; ++i) { + scaled[i] *= ratio; + } + + final double[][] nData = nordsieck.getDataRef(); + double power = ratio; + for (int i = 0; i < nData.length; ++i) { + power *= ratio; + final double[] nDataI = nData[i]; + for (int j = 0; j < nDataI.length; ++j) { + nDataI[j] *= power; + } + } + + scalingH = stepSize; + + } + + /** + * Get the state vector variation from current to interpolated state. + * <p>This method is aimed at computing y(t<sub>interpolation</sub>) + * -y(t<sub>current</sub>) accurately by avoiding the cancellation errors + * that would occur if the subtraction were performed explicitly.</p> + * <p>The returned vector is a reference to a reused array, so + * it should not be modified and it should be copied if it needs + * to be preserved across several calls.</p> + * @return state vector at time {@link #getInterpolatedTime} + * @see #getInterpolatedDerivatives() + * @throws DerivativeException if this call induces an automatic + * step finalization that throws one + */ + public double[] getInterpolatedStateVariation() + throws DerivativeException { + // compute and ignore interpolated state + // to make sure state variation is computed as a side effect + getInterpolatedState(); + return stateVariation; + } + + /** {@inheritDoc} */ + @Override + protected void computeInterpolatedStateAndDerivatives(final double theta, final double oneMinusThetaH) { + + final double x = interpolatedTime - referenceTime; + final double normalizedAbscissa = x / scalingH; + + Arrays.fill(stateVariation, 0.0); + Arrays.fill(interpolatedDerivatives, 0.0); + + // apply Taylor formula from high order to low order, + // for the sake of numerical accuracy + final double[][] nData = nordsieck.getDataRef(); + for (int i = nData.length - 1; i >= 0; --i) { + final int order = i + 2; + final double[] nDataI = nData[i]; + final double power = FastMath.pow(normalizedAbscissa, order); + for (int j = 0; j < nDataI.length; ++j) { + final double d = nDataI[j] * power; + stateVariation[j] += d; + interpolatedDerivatives[j] += order * d; + } + } + + for (int j = 0; j < currentState.length; ++j) { + stateVariation[j] += scaled[j] * normalizedAbscissa; + interpolatedState[j] = currentState[j] + stateVariation[j]; + interpolatedDerivatives[j] = + (interpolatedDerivatives[j] + scaled[j] * normalizedAbscissa) / x; + } + + } + + /** {@inheritDoc} */ + @Override + public void writeExternal(final ObjectOutput out) + throws IOException { + + // save the state of the base class + writeBaseExternal(out); + + // save the local attributes + out.writeDouble(scalingH); + out.writeDouble(referenceTime); + + final int n = (currentState == null) ? -1 : currentState.length; + if (scaled == null) { + out.writeBoolean(false); + } else { + out.writeBoolean(true); + for (int j = 0; j < n; ++j) { + out.writeDouble(scaled[j]); + } + } + + if (nordsieck == null) { + out.writeBoolean(false); + } else { + out.writeBoolean(true); + out.writeObject(nordsieck); + } + + // we don't save state variation, it will be recomputed + + } + + /** {@inheritDoc} */ + @Override + public void readExternal(final ObjectInput in) + throws IOException, ClassNotFoundException { + + // read the base class + final double t = readBaseExternal(in); + + // read the local attributes + scalingH = in.readDouble(); + referenceTime = in.readDouble(); + + final int n = (currentState == null) ? -1 : currentState.length; + final boolean hasScaled = in.readBoolean(); + if (hasScaled) { + scaled = new double[n]; + for (int j = 0; j < n; ++j) { + scaled[j] = in.readDouble(); + } + } else { + scaled = null; + } + + final boolean hasNordsieck = in.readBoolean(); + if (hasNordsieck) { + nordsieck = (Array2DRowRealMatrix) in.readObject(); + } else { + nordsieck = null; + } + + if (hasScaled && hasNordsieck) { + // we can now set the interpolated time and state + stateVariation = new double[n]; + setInterpolatedTime(t); + } else { + stateVariation = null; + } + + } + +} diff --git a/src/main/java/org/apache/commons/math/ode/sampling/StepHandler.java b/src/main/java/org/apache/commons/math/ode/sampling/StepHandler.java new file mode 100644 index 0000000..53c2fbe --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/sampling/StepHandler.java @@ -0,0 +1,78 @@ +/* + * 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.sampling; + +import org.apache.commons.math.ode.DerivativeException; + +/** + * This interface represents a handler that should be called after + * each successful step. + * + * <p>The ODE integrators compute the evolution of the state vector at + * some grid points that depend on their own internal algorithm. Once + * they have found a new grid point (possibly after having computed + * several evaluation of the derivative at intermediate points), they + * provide it to objects implementing this interface. These objects + * typically either ignore the intermediate steps and wait for the + * last one, store the points in an ephemeris, or forward them to + * specialized processing or output methods.</p> + * + * @see org.apache.commons.math.ode.FirstOrderIntegrator + * @see org.apache.commons.math.ode.SecondOrderIntegrator + * @see StepInterpolator + * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ + * @since 1.2 + */ + +public interface StepHandler { + + /** Determines whether this handler needs dense output. + * <p>This method allows the integrator to avoid performing extra + * computation if the handler does not need dense output. If this + * method returns false, the integrator will call the {@link + * #handleStep} method with a {@link DummyStepInterpolator} rather + * than a custom interpolator.</p> + * @return true if the handler needs dense output + */ + boolean requiresDenseOutput(); + + /** Reset the step handler. + * Initialize the internal data as required before the first step is + * handled. + */ + void reset(); + + /** + * 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, as the + * {@link org.apache.commons.math.ode.ContinuousOutputModel + * ContinuousOutputModel} class does), it should build a local copy + * using the clone method of the interpolator and store this copy. + * Keeping only a reference to the interpolator and reusing it will + * result in unpredictable behavior (potentially crashing the application). + * @param isLast true if the step is the last one + * @exception DerivativeException if user code called from step interpolator + * finalization triggers one + */ + void handleStep(StepInterpolator interpolator, boolean isLast) throws DerivativeException; + +} diff --git a/src/main/java/org/apache/commons/math/ode/sampling/StepInterpolator.java b/src/main/java/org/apache/commons/math/ode/sampling/StepInterpolator.java new file mode 100644 index 0000000..ceb5a86 --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/sampling/StepInterpolator.java @@ -0,0 +1,132 @@ +/* + * 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.sampling; + +import java.io.Externalizable; + +import org.apache.commons.math.ode.DerivativeException; + +/** This interface represents an interpolator over the last step + * during an ODE integration. + * + * <p>The various ODE integrators provide objects implementing this + * interface to the step handlers. These objects are often custom + * objects tightly bound to the integrator internal algorithms. The + * handlers can use these objects to retrieve the state vector at + * intermediate times between the previous and the current grid points + * (this feature is often called dense output).</p> + * <p>One important thing to note is that the step handlers may be so + * tightly bound to the integrators that they often share some internal + * state arrays. This imply that one should <em>never</em> use a direct + * reference to a step interpolator outside of the step handler, either + * for future use or for use in another thread. If such a need arise, the + * step interpolator <em>must</em> be copied using the dedicated + * {@link #copy()} method. + * </p> + * + * @see org.apache.commons.math.ode.FirstOrderIntegrator + * @see org.apache.commons.math.ode.SecondOrderIntegrator + * @see StepHandler + * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ + * @since 1.2 + */ + +public interface StepInterpolator extends Externalizable { + + /** + * Get the previous grid point time. + * @return previous grid point time + */ + double getPreviousTime(); + + /** + * Get the current grid point time. + * @return current grid point time + */ + double getCurrentTime(); + + /** + * Get the time of the interpolated point. + * If {@link #setInterpolatedTime} has not been called, it returns + * the current grid point time. + * @return interpolation point time + */ + double getInterpolatedTime(); + + /** + * Set the time of the interpolated point. + * <p>Setting the time outside of the current step is now allowed, but + * should be used with care since the accuracy of the interpolator will + * probably be very poor far from this step. This allowance has been + * added to simplify implementation of search algorithms near the + * step endpoints.</p> + * <p>Setting the time changes the instance internal state. If a + * specific state must be preserved, a copy of the instance must be + * created using {@link #copy()}.</p> + * @param time time of the interpolated point + */ + void setInterpolatedTime(double time); + + /** + * Get the state vector of the interpolated point. + * <p>The returned vector is a reference to a reused array, so + * it should not be modified and it should be copied if it needs + * to be preserved across several calls.</p> + * @return state vector at time {@link #getInterpolatedTime} + * @see #getInterpolatedDerivatives() + * @exception DerivativeException if user code called from step interpolator + * finalization triggers one + */ + double[] getInterpolatedState() throws DerivativeException; + + /** + * Get the derivatives of the state vector of the interpolated point. + * <p>The returned vector is a reference to a reused array, so + * it should not be modified and it should be copied if it needs + * to be preserved across several calls.</p> + * @return derivatives of the state vector at time {@link #getInterpolatedTime} + * @see #getInterpolatedState() + * @exception DerivativeException if user code called from step interpolator + * finalization triggers one + * @since 2.0 + */ + double[] getInterpolatedDerivatives() throws DerivativeException; + + /** Check if the natural integration direction is forward. + * <p>This method provides the integration direction as specified by + * the integrator itself, it avoid some nasty problems in + * degenerated cases like null steps due to cancellation at step + * initialization, step control or discrete events + * triggering.</p> + * @return true if the integration variable (time) increases during + * integration + */ + boolean isForward(); + + /** Copy the instance. + * <p>The copied instance is guaranteed to be independent from the + * original one. Both can be used with different settings for + * interpolated time without any side effect.</p> + * @return a deep copy of the instance, which can be used independently. + * @exception DerivativeException if user code called from step interpolator + * finalization triggers one + * @see #setInterpolatedTime(double) + */ + StepInterpolator copy() throws DerivativeException; + +} diff --git a/src/main/java/org/apache/commons/math/ode/sampling/StepNormalizer.java b/src/main/java/org/apache/commons/math/ode/sampling/StepNormalizer.java new file mode 100644 index 0000000..73bcc23 --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/sampling/StepNormalizer.java @@ -0,0 +1,161 @@ +/* + * 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.sampling; + +import org.apache.commons.math.ode.DerivativeException; +import org.apache.commons.math.util.FastMath; + +/** + * This class wraps an object implementing {@link FixedStepHandler} + * into a {@link StepHandler}. + + * <p>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.</p> + * + * <p>The stepsize used is selected at construction time. The {@link + * FixedStepHandler#handleStep handleStep} method of the underlying + * {@link FixedStepHandler} object is called at the beginning time of + * the integration t0 and also at times t0+h, t0+2h, ... If the + * integration range is an integer multiple of the stepsize, then the + * last point handled will be the endpoint of the integration tend, if + * not, the last point will belong to the interval [tend - h ; + * tend].</p> + * + * <p>There is no constraint on the integrator, it can use any + * timestep it needs (time steps longer or shorter than the fixed time + * step and non-integer ratios are all allowed).</p> + * + * @see StepHandler + * @see FixedStepHandler + * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ + * @since 1.2 + */ + +public class StepNormalizer implements StepHandler { + + /** Fixed time step. */ + private double h; + + /** Underlying step handler. */ + private final FixedStepHandler handler; + + /** Last step time. */ + private double lastTime; + + /** Last State vector. */ + private double[] lastState; + + /** Last Derivatives vector. */ + private double[] lastDerivatives; + + /** Integration direction indicator. */ + private boolean forward; + + /** Simple constructor. + * @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 = FastMath.abs(h); + this.handler = handler; + reset(); + } + + /** Determines whether this handler needs dense output. + * This handler needs dense output in order to provide data at + * regularly spaced steps regardless of the steps the integrator + * uses, so this method always returns true. + * @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() { + lastTime = Double.NaN; + lastState = null; + lastDerivatives = null; + forward = true; + } + + /** + * 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 + * @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 (lastState == null) { + + 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; + } + + } + + double nextTime = lastTime + h; + boolean nextInStep = forward ^ (nextTime > interpolator.getCurrentTime()); + while (nextInStep) { + + // output the stored previous step + handler.handleStep(lastTime, lastState, lastDerivatives, false); + + // store the next step + lastTime = nextTime; + interpolator.setInterpolatedTime(lastTime); + System.arraycopy(interpolator.getInterpolatedState(), 0, + lastState, 0, lastState.length); + System.arraycopy(interpolator.getInterpolatedDerivatives(), 0, + lastDerivatives, 0, lastDerivatives.length); + + nextTime += h; + nextInStep = forward ^ (nextTime > interpolator.getCurrentTime()); + + } + + if (isLast) { + // there will be no more steps, + // the stored one should be flagged as being the last + handler.handleStep(lastTime, lastState, lastDerivatives, true); + } + + } + +} diff --git a/src/main/java/org/apache/commons/math/ode/sampling/package.html b/src/main/java/org/apache/commons/math/ode/sampling/package.html new file mode 100644 index 0000000..46de4ef --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/sampling/package.html @@ -0,0 +1,60 @@ +<html> +<!-- + 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. + --> + <!-- $Revision: 613620 $ --> +<body> +<p> +This package provides classes to handle sampling steps during +Ordinary Differential Equations integration. +</p> + +<p> +In addition to computing the evolution of the state vector at some grid points, all +ODE integrators also build up interpolation models of this evolution <em>inside</em> the +last computed step. If users are interested in these interpolators, they can register a +{@link org.apache.commons.math.ode.sampling.StepHandler StepHandler} instance using the +{@link org.apache.commons.math.ode.FirstOrderIntegrator#addStepHandler addStepHandler} +method which is supported by all integrators. The integrator will call this instance +at the end of each accepted step and provide it the interpolator. The user can do +whatever he wants with this interpolator, which computes both the state and its +time-derivative. A typical use of step handler is to provide some output to monitor +the integration process. +</p> + +<p> +In a sense, this is a kind of Inversion Of Control: rather than having the master +application driving the slave integrator by providing the target end value for +the free variable, we get a master integrator scheduling the free variable +evolution and calling the slave application callbacks that were registered at +configuration time. +</p> + +<p> +Since some integrators may use variable step size, the generic {@link +org.apache.commons.math.ode.sampling.StepHandler StepHandler} interface can be called +either at regular or irregular rate. This interface allows to navigate to any location +within the last computed step, thanks to the provided {@link +org.apache.commons.math.ode.sampling.StepInterpolator StepInterpolator} object. +If regular output is desired (for example in order to write an ephemeris file), then +the simpler {@link org.apache.commons.math.ode.sampling.FixedStepHandler FixedStepHandler} +interface can be used. Objects implementing this interface should be wrapped within a +{@link org.apache.commons.math.ode.sampling.StepNormalizer StepNormalizer} instance +in order to be registered to the integrator. +</p> + +</body> +</html> |