/*
* Open Source Physics software is free software as described near the bottom of this code file.
*
* For additional information and documentation on Open Source Physics please see:
* <http://www.opensourcephysics.org/>
*/
package org.opensourcephysics.numerics;
/**
* ODEMultistepSolver performs multiple ODE steps so that a uniform step size is maintained.
*
* @author Wolfgang Christian
* @version 1.0
*/
public class ODEMultistepSolver implements ODEAdaptiveSolver {
private static int maxMessages = 3; // maximum number of error messages
protected int err_code = NO_ERROR;
protected int maxIterations = 200;
protected boolean enableExceptions = false;
protected String err_msg = ""; //$NON-NLS-1$
protected ODEAdaptiveSolver odeEngine;
protected double fixedStepSize = 0.1;
protected InternalODE internalODE;
/**
* Constructs an ODEMultiStep ODE solver for a system of ordinary differential equations.
*
* The default ODESolver is DormandPrince45. Other solvers can be selected using factory methods.
*
* @param ode
*/
public ODEMultistepSolver(ODE ode) {
odeEngine = new DormandPrince45(setODE(ode));
}
/**
* Constructs a ODEMultistepSolver without an ODE so that a factory method
* can create a custom solver.
*/
protected ODEMultistepSolver() {}
/**
* Sets the ODE for this solver.
* @param ode ODE
* @return MyODE
*/
protected InternalODE setODE(ODE ode) {
internalODE = new InternalODE(ode);
return internalODE;
}
/**
* A factory method that creates a multisetp solver using the RK45 engine.
* @param ode ODE
* @return ODESolver
*/
public static ODEAdaptiveSolver MultistepRK45(ODE ode) {
ODEMultistepSolver multistepSolver = new ODEMultistepSolver();
multistepSolver.odeEngine = new RK45(multistepSolver.setODE(ode));
return multistepSolver;
}
/**
* Enables runtime exceptions if the solver does not converge.
* @param enable boolean
*/
public void enableRuntimeExpecptions(boolean enable) {
enableExceptions = enable;
}
/**
* Sets the maximum number of iterations.
* @param n maximum
*/
public void setMaxIterations(int n) {
maxIterations = Math.max(1, n);
}
/**
* Sets the tolerance of the adaptive ODE solver.
* @param tol the tolerance
*/
public void setTolerance(double tol) {
tol = Math.abs(tol);
odeEngine.setTolerance(tol);
}
/**
* Gets the tolerance of the adaptive ODE solver.
* @return
*/
public double getTolerance() {
return odeEngine.getTolerance();
}
/**
* Gets the error code.
* Error codes:
* ODEAdaptiveSolver.NO_ERROR
* ODEAdaptiveSolver.DID_NOT_CONVERGE
* ODEAdaptiveSolver.BISECTION_EVENT_NOT_FOUND=2;
* @return int
*/
public int getErrorCode() {
return err_code;
}
/**
* Steps (advances) the differential equations by the stepSize.
*
* The ODESolver invokes the ODE's getRate method to obtain the initial state of the system.
* The ODESolver then advances the solution and copies the new state into the
* state array at the end of the solution step if desired tolerance was reached.
*
* @return the actual step
*/
public double step() {
err_code = NO_ERROR;
internalODE.setInitialConditions(); // stores the ode's initial conditions
double remainder = 0;
if(fixedStepSize>0) {
remainder = plus();
} else {
remainder = minus();
}
internalODE.update(); // updates the ode
return fixedStepSize-remainder; // the step size that was actually taken
}
/**
* Steps the ode with a postive stepsize.
*
* @return the step size
*/
private double plus() { // positive step size
double tol = odeEngine.getTolerance();
double remainder = fixedStepSize; // track the remaining step
if((odeEngine.getStepSize()<=0)||( // is the stepsize postive?
odeEngine.getStepSize()>fixedStepSize)||( // is the stepsize larger than what is requested?
fixedStepSize-odeEngine.getStepSize()==fixedStepSize // is the stepsize smaller than the precision?
)) {
odeEngine.setStepSize(fixedStepSize); // reset the step size and let it adapt to an optimum size
}
int counter = 0;
while(remainder>tol*fixedStepSize) { // check to see if we are close enough
counter++;
double oldRemainder = remainder;
if(remainder<odeEngine.getStepSize()) { // temporarily reduce the step size so that we hit the exact dt value
double tempStep = odeEngine.getStepSize(); // save the current optimum step size
odeEngine.setStepSize(remainder); // set the step size to the remainder
double delta = odeEngine.step();
remainder -= delta;
odeEngine.setStepSize(tempStep); // restore the original step size
} else {
remainder -= odeEngine.step(); // do a step and set the remainder
}
// check to see if roundoff error prevents further calculation.
if((odeEngine.getErrorCode()!=ODEAdaptiveSolver.NO_ERROR)||(Math.abs(oldRemainder-remainder)<=Float.MIN_VALUE)||(tol*fixedStepSize/10.0>odeEngine.getStepSize())||(counter>maxIterations)) {
err_msg = "ODEMultiStep did not converge. Remainder="+remainder; //$NON-NLS-1$
err_code = ODEAdaptiveSolver.DID_NOT_CONVERGE;
if(enableExceptions) {
throw new ODESolverException(err_msg);
}
if(maxMessages>0) {
maxMessages--;
System.out.println(err_msg);
//OSPLog.warning(err_msg);
}
break;
}
}
return remainder;
}
/**
* Steps the ode with a negative stepsize.
*
* @return the step size
*/
private double minus() { // negative step size
double tol = odeEngine.getTolerance();
double remainder = fixedStepSize; // track the remaining step
if((odeEngine.getStepSize()>=0)||( // is the step negative?
odeEngine.getStepSize()<fixedStepSize)||( // is the stepsize larger than what is requested?
fixedStepSize-odeEngine.getStepSize()==fixedStepSize // is the stepsize smaller than the precision?
)) {
odeEngine.setStepSize(fixedStepSize); // reset the step size and let it adapt to an optimum size
}
int counter = 0;
while(remainder<tol*fixedStepSize) { // check to see if we are close enough
counter++;
double oldRemainder = remainder;
if(remainder>odeEngine.getStepSize()) {
double tempStep = odeEngine.getStepSize(); // save the current optimum step size
odeEngine.setStepSize(remainder); // set the step RK4/5 size to the remainder
double delta = odeEngine.step();
remainder -= delta;
odeEngine.setStepSize(tempStep); // restore the original step size
} else {
remainder -= odeEngine.step(); // do a step and set the remainder
}
// check to see if roundoff error prevents further calculation.
if((odeEngine.getErrorCode()!=ODEAdaptiveSolver.NO_ERROR)||(Math.abs(oldRemainder-remainder)<=Float.MIN_VALUE)||(tol*fixedStepSize/10.0<odeEngine.getStepSize())||(counter>maxIterations)) {
err_msg = "ODEMultiStep did not converge. Remainder="+remainder; //$NON-NLS-1$
err_code = ODEAdaptiveSolver.DID_NOT_CONVERGE;
if(enableExceptions) {
throw new ODESolverException(err_msg);
}
if(maxMessages>0) {
maxMessages--;
System.out.println(err_msg);
//OSPLog.warning(err_msg);
}
}
}
return remainder;
}
/**
* Initializes the ODE solver.
*
* Temporary arrays may be allocated within the ODE solver.
*
* @param stepSize
*/
public void initialize(double stepSize) {
maxMessages = 4; // reset the message counter to produce more messages
err_msg = ""; //$NON-NLS-1$
err_code = NO_ERROR;
fixedStepSize = stepSize;
internalODE.setInitialConditions();
odeEngine.initialize(stepSize);
}
/**
* Sets the fixed step size. Multi-step solvers will perform one or more internal steps
* in order to perform a step with the given size.
*
* @param stepSize
*/
public void setStepSize(double stepSize) {
maxMessages = 4; // reset the message counter to produce more messages
fixedStepSize = stepSize; // the fixed step size
if(stepSize<0) {
odeEngine.setStepSize(Math.max(-Math.abs(odeEngine.getStepSize()), stepSize));
} else { // stepSize is positive
odeEngine.setStepSize(Math.min(odeEngine.getStepSize(), stepSize));
}
}
/**
* Sets the number of error messages if ODE solver did not converge.
* @param n int
*/
public void setMaximumNumberOfErrorMessages(int n) {
maxMessages = n;
}
/**
* Gets the step size.
* The step size is the fixed step size, not the size of the ODEAdaptiveSolver steps that are combined into a single step.
*
* @return the step size
*/
public double getStepSize() {
return fixedStepSize;
}
/**
* A class that saves an internal state that may be different from the orginal ODE.
* This internal state is used with interpolation solvers.
*/
protected final class InternalODE implements ODE {
private ODE ode;
private double[] engineState = new double[0];
InternalODE(ODE ode) {
this.ode = ode;
setInitialConditions();
}
/**
* Gets the rate using the given state.
*
* @param state double[]
* @param rate double[]
*/
public void getRate(double[] state, double[] rate) {
ode.getRate(state, rate);
}
/**
* Gets the state.
*
* @return double[]
*/
public double[] getState() {
return engineState;
}
/**
* Sets the initial conditions using the current state of the ODE.
*
* @return double[]
*/
public void setInitialConditions() {
double[] state = ode.getState();
if(state==null) {
return;
}
if((engineState==null)||(engineState.length!=state.length)) {
engineState = new double[state.length]; // create an engine state with the correct size
}
System.arraycopy(state, 0, engineState, 0, state.length);
}
/**
* updates the ODE state using the engine's internal state.
*/
public void update() {
System.arraycopy(engineState, 0, ode.getState(), 0, engineState.length);
}
}
}
/*
* Open Source Physics software is free software; you can redistribute
* it and/or modify it under the terms of the GNU General Public License (GPL) as
* published by the Free Software Foundation; either version 2 of the License,
* or(at your option) any later version.
* Code that uses any portion of the code in the org.opensourcephysics package
* or any subpackage (subdirectory) of this package must must also be be released
* under the GNU GPL license.
*
* This software is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston MA 02111-1307 USA
* or view the license online at http://www.gnu.org/copyleft/gpl.html
*
* Copyright (c) 2007 The Open Source Physics project
* http://www.opensourcephysics.org
*/