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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode;
import java.util.ArrayList;
import java.util.List;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
/**
* This class represents a combined set of first order differential equations,
* with at least a primary set of equations expandable by some sets of secondary
* equations.
*
* One typical use case is the computation of the Jacobian matrix for some ODE.
* In this case, the primary set of equations corresponds to the raw ODE, and we
* add to this set another bunch of secondary equations which represent the Jacobian
* matrix of the primary set.
*
*
* We want the integrator to use only the primary set to estimate the
* errors and hence the step sizes. It should not use the secondary
* equations in this computation. The {@link AbstractIntegrator integrator} will
* be able to know where the primary set ends and so where the secondary sets begin.
*
*
* @see FirstOrderDifferentialEquations
* @see JacobianMatrices
*
* @since 3.0
*/
public class ExpandableStatefulODE {
/** Primary differential equation. */
private final FirstOrderDifferentialEquations primary;
/** Mapper for primary equation. */
private final EquationsMapper primaryMapper;
/** Time. */
private double time;
/** State. */
private final double[] primaryState;
/** State derivative. */
private final double[] primaryStateDot;
/** Components of the expandable ODE. */
private List components;
/** Build an expandable set from its primary ODE set.
* @param primary the primary set of differential equations to be integrated.
*/
public ExpandableStatefulODE(final FirstOrderDifferentialEquations primary) {
final int n = primary.getDimension();
this.primary = primary;
this.primaryMapper = new EquationsMapper(0, n);
this.time = Double.NaN;
this.primaryState = new double[n];
this.primaryStateDot = new double[n];
this.components = new ArrayList();
}
/** Get the primary set of differential equations.
* @return primary set of differential equations
*/
public FirstOrderDifferentialEquations getPrimary() {
return primary;
}
/** Return the dimension of the complete set of equations.
*
* The complete set of equations correspond to the primary set plus all secondary sets.
*
* @return dimension of the complete set of equations
*/
public int getTotalDimension() {
if (components.isEmpty()) {
// there are no secondary equations, the complete set is limited to the primary set
return primaryMapper.getDimension();
} else {
// there are secondary equations, the complete set ends after the last set
final EquationsMapper lastMapper = components.get(components.size() - 1).mapper;
return lastMapper.getFirstIndex() + lastMapper.getDimension();
}
}
/** Get the current time derivative of the complete state vector.
* @param t current value of the independent time variable
* @param y array containing the current value of the complete state vector
* @param yDot placeholder array where to put the time derivative of the complete state vector
* @exception MaxCountExceededException if the number of functions evaluations is exceeded
* @exception DimensionMismatchException if arrays dimensions do not match equations settings
*/
public void computeDerivatives(final double t, final double[] y, final double[] yDot)
throws MaxCountExceededException, DimensionMismatchException {
// compute derivatives of the primary equations
primaryMapper.extractEquationData(y, primaryState);
primary.computeDerivatives(t, primaryState, primaryStateDot);
// Add contribution for secondary equations
for (final SecondaryComponent component : components) {
component.mapper.extractEquationData(y, component.state);
component.equation.computeDerivatives(t, primaryState, primaryStateDot,
component.state, component.stateDot);
component.mapper.insertEquationData(component.stateDot, yDot);
}
primaryMapper.insertEquationData(primaryStateDot, yDot);
}
/** Add a set of secondary equations to be integrated along with the primary set.
* @param secondary secondary equations set
* @return index of the secondary equation in the expanded state
*/
public int addSecondaryEquations(final SecondaryEquations secondary) {
final int firstIndex;
if (components.isEmpty()) {
// lazy creation of the components list
components = new ArrayList();
firstIndex = primary.getDimension();
} else {
final SecondaryComponent last = components.get(components.size() - 1);
firstIndex = last.mapper.getFirstIndex() + last.mapper.getDimension();
}
components.add(new SecondaryComponent(secondary, firstIndex));
return components.size() - 1;
}
/** Get an equations mapper for the primary equations set.
* @return mapper for the primary set
* @see #getSecondaryMappers()
*/
public EquationsMapper getPrimaryMapper() {
return primaryMapper;
}
/** Get the equations mappers for the secondary equations sets.
* @return equations mappers for the secondary equations sets
* @see #getPrimaryMapper()
*/
public EquationsMapper[] getSecondaryMappers() {
final EquationsMapper[] mappers = new EquationsMapper[components.size()];
for (int i = 0; i < mappers.length; ++i) {
mappers[i] = components.get(i).mapper;
}
return mappers;
}
/** Set current time.
* @param time current time
*/
public void setTime(final double time) {
this.time = time;
}
/** Get current time.
* @return current time
*/
public double getTime() {
return time;
}
/** Set primary part of the current state.
* @param primaryState primary part of the current state
* @throws DimensionMismatchException if the dimension of the array does not
* match the primary set
*/
public void setPrimaryState(final double[] primaryState) throws DimensionMismatchException {
// safety checks
if (primaryState.length != this.primaryState.length) {
throw new DimensionMismatchException(primaryState.length, this.primaryState.length);
}
// set the data
System.arraycopy(primaryState, 0, this.primaryState, 0, primaryState.length);
}
/** Get primary part of the current state.
* @return primary part of the current state
*/
public double[] getPrimaryState() {
return primaryState.clone();
}
/** Get primary part of the current state derivative.
* @return primary part of the current state derivative
*/
public double[] getPrimaryStateDot() {
return primaryStateDot.clone();
}
/** Set secondary part of the current state.
* @param index index of the part to set as returned by {@link
* #addSecondaryEquations(SecondaryEquations)}
* @param secondaryState secondary part of the current state
* @throws DimensionMismatchException if the dimension of the partial state does not
* match the selected equations set dimension
*/
public void setSecondaryState(final int index, final double[] secondaryState)
throws DimensionMismatchException {
// get either the secondary state
double[] localArray = components.get(index).state;
// safety checks
if (secondaryState.length != localArray.length) {
throw new DimensionMismatchException(secondaryState.length, localArray.length);
}
// set the data
System.arraycopy(secondaryState, 0, localArray, 0, secondaryState.length);
}
/** Get secondary part of the current state.
* @param index index of the part to set as returned by {@link
* #addSecondaryEquations(SecondaryEquations)}
* @return secondary part of the current state
*/
public double[] getSecondaryState(final int index) {
return components.get(index).state.clone();
}
/** Get secondary part of the current state derivative.
* @param index index of the part to set as returned by {@link
* #addSecondaryEquations(SecondaryEquations)}
* @return secondary part of the current state derivative
*/
public double[] getSecondaryStateDot(final int index) {
return components.get(index).stateDot.clone();
}
/** Set the complete current state.
* @param completeState complete current state to copy data from
* @throws DimensionMismatchException if the dimension of the complete state does not
* match the complete equations sets dimension
*/
public void setCompleteState(final double[] completeState)
throws DimensionMismatchException {
// safety checks
if (completeState.length != getTotalDimension()) {
throw new DimensionMismatchException(completeState.length, getTotalDimension());
}
// set the data
primaryMapper.extractEquationData(completeState, primaryState);
for (final SecondaryComponent component : components) {
component.mapper.extractEquationData(completeState, component.state);
}
}
/** Get the complete current state.
* @return complete current state
* @throws DimensionMismatchException if the dimension of the complete state does not
* match the complete equations sets dimension
*/
public double[] getCompleteState() throws DimensionMismatchException {
// allocate complete array
double[] completeState = new double[getTotalDimension()];
// set the data
primaryMapper.insertEquationData(primaryState, completeState);
for (final SecondaryComponent component : components) {
component.mapper.insertEquationData(component.state, completeState);
}
return completeState;
}
/** Components of the compound stateful ODE. */
private static class SecondaryComponent {
/** Secondary differential equation. */
private final SecondaryEquations equation;
/** Mapper between local and complete arrays. */
private final EquationsMapper mapper;
/** State. */
private final double[] state;
/** State derivative. */
private final double[] stateDot;
/** Simple constructor.
* @param equation secondary differential equation
* @param firstIndex index to use for the first element in the complete arrays
*/
SecondaryComponent(final SecondaryEquations equation, final int firstIndex) {
final int n = equation.getDimension();
this.equation = equation;
mapper = new EquationsMapper(firstIndex, n);
state = new double[n];
stateDot = new double[n];
}
}
}