/*
* 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;
/**
* Title: RK45MultiStep
* Description: Perform multiple RK4/5 ODE steps so that a uniform step size is maintained
*
* @author Wolfgang Christian
* @version 1.0
*/
public class RK45MultiStep extends RK45 {
private static int maxMessages = 3; // maximum number of error messages
private double fixedStepSize = 0.1;
protected int maxIterations = 200;
/**
* Constructs the RK45MultiStep ODESolver for a system of ordinary differential equations.
*
* @param _ode the system of differential equations.
*/
public RK45MultiStep(ODE _ode) {
super(_ode);
}
/**
* 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.
*
* @return the step size
*/
public double step() {
error_code = NO_ERROR;
if(fixedStepSize>0) {
return fixedStepSize-plus();
}
return fixedStepSize-minus();
}
/**
* Sets the maximum number of iterations.
* @param n maximum
*/
public void setMaxIterations(int n) {
maxIterations = Math.max(1, n);
}
/**
* Steps the ode with a postive stepsize.
*
* @return the step size
*/
private double plus() { // positive step size
double remainder = fixedStepSize; // dt will keep track of the remaining time
if((super.getStepSize()<=0)||( // is the stepsize postive?
super.getStepSize()>fixedStepSize)||( // is the stepsize larger than what is requested?
fixedStepSize-super.getStepSize()==fixedStepSize // is the stepsize smaller than the precision?
)) {
super.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<super.getStepSize()) { // temporarily reduce the step size so that we hit the exact dt value
double tempStep = super.getStepSize(); // save the current optimum step size
super.setStepSize(remainder); // set the RK4/5 step size to the remainder
double delta = super.step();
remainder -= delta;
super.setStepSize(tempStep); // restore the original step size
} else {
remainder -= super.step(); // do a rk45 step and set the remainder
}
// check to see if roundoff error prevents further calculation.
if((error_code!=NO_ERROR)||(Math.abs(oldRemainder-remainder)<=Float.MIN_VALUE)||(tol*fixedStepSize/10.0>super.getStepSize())||(counter>maxIterations)) {
error_code = DID_NOT_CONVERGE;
if(enableExceptions) {
throw new ODESolverException("RK45 ODE solver did not converge."); //$NON-NLS-1$
}
maxMessages--;
System.err.println("Warning: RK45MultiStep did not converge. Remainder="+remainder); //$NON-NLS-1$
if(maxMessages==0) {
System.err.println("RK45 ODE solver did not converge. Further warnings suppressed."); //$NON-NLS-1$
}
break;
}
}
return remainder;
}
/**
* Steps the ode with a negative stepsize.
*
* @return the step size
*/
private double minus() { // negative step size
double remainder = fixedStepSize; // dt will keep track of the remaining time
if((super.getStepSize()>=0)||( // is the step negative?
super.getStepSize()<fixedStepSize)||( // is the stepsize larger than what is requested?
fixedStepSize-super.getStepSize()==fixedStepSize // is the stepsize smaller than the precision?
)) {
super.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>super.getStepSize()) {
double tempStep = super.getStepSize(); // save the current optimum step size
super.setStepSize(remainder); // set the step RK4/5 size to the remainder
double delta = super.step();
remainder -= delta;
super.setStepSize(tempStep); // restore the original step size
} else {
remainder -= super.step(); // do a rk45 step and set the remainder
}
// check to see if roundoff error prevents further calculation.
if((error_code!=NO_ERROR)||(Math.abs(oldRemainder-remainder)<=Float.MIN_VALUE)||(tol*fixedStepSize/10.0<super.getStepSize())||(counter>maxIterations)) {
error_code = DID_NOT_CONVERGE;
if(enableExceptions) {
throw new ODESolverException("RK45 ODE solver did not converge."); //$NON-NLS-1$
}
if(maxMessages<=0) {
break;
}
maxMessages--;
System.err.println("Warning: RK45MultiStep did not converge. Remainder="+remainder); //$NON-NLS-1$
if(maxMessages==0) {
System.err.println("Further warnings surppressed."); //$NON-NLS-1$
}
break;
}
}
return remainder;
}
/**
* Sets the number of error messages if ODE solver did not converge.
* @param n int
*/
public void setMaximumNumberOfErrorMessages(int n) {
maxMessages = n;
}
/**
* Initializes the ODE solver.
*
* Temporary state and rate arrays are allocated by invoking the superclass method.
*
* @param stepSize
*/
public void initialize(double stepSize) {
fixedStepSize = stepSize;
super.initialize(stepSize/2); // be conservative with the adaptive solver
}
/**
* Method setStepSize
*
* @param stepSize
*/
public void setStepSize(double stepSize) {
maxMessages = 4; // reset the message counter
fixedStepSize = stepSize; // the fixed step size
if(stepSize<0) {
super.setStepSize(Math.max(-Math.abs(super.getStepSize()), stepSize));
} else { // stepSize is positive
super.setStepSize(Math.min(super.getStepSize(), stepSize));
}
super.setStepSize(stepSize); // the variable step size
}
/**
* Gets the step size.
*
* The step size is the fixed step size, not the size of the RK4/5 steps that are combined into a single step.
*
* @return the step size
*/
public double getStepSize() {
return fixedStepSize;
}
/**
* Gets the error code.
* Error codes:
* ODEAdaptiveSolver.NO_ERROR
* ODEAdaptiveSolver.DID_NOT_CONVERGE
* @return int
*/
public int getErrorCode() {
return error_code;
}
}
/*
* 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
*/