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tdeartwork/tdescreensaver/kdesavers/rkodesolver.cpp

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//============================================================================
//
// Ordinary differential equation solver using the Runge-Kutta method.
// $Id$
// Copyright (C) 2004 Georg Drenkhahn
//
// This file is free software; you can redistribute it and/or modify it under
// the terms of the GNU General Public License version 2 as published by the
// Free Software Foundation.
//
//============================================================================
#include <kdebug.h>
#include "rkodesolver.h"
template<typename T>
RkOdeSolver<T>::RkOdeSolver(const T &x,
const std::valarray<T>& y,
const T &dx,
const T &eps)
: mX(x)
{
Y(y);
dX(dx);
Eps(eps);
}
// virtual dtor
template<typename T>
RkOdeSolver<T>::~RkOdeSolver(void)
{}
// accessors
template<typename T>
void
RkOdeSolver<T>::dX(const T &a)
{
if (a < 0.0)
{
kdDebug() << "RkOdeSolver: dx was negative, made it positive" << endl;
mStep = -a;
}
else if (a == 0.0)
{
mStep = 0.001; // a very arbitrary value
kdDebug() << "RkOdeSolver: dx == 0, set it to " << mStep << endl;
}
else
{
mStep = a;
}
}
template<typename T>
void
RkOdeSolver<T>::Eps(const T &a)
{
if (a < 0.0)
{
kdDebug() << "RkOdeSolver: eps was negative, made it positive" << endl;
mEps = -a;
}
else if (a == 0.0)
{
mEps = 1e-5; // a very arbitrary value
kdDebug() << "RkOdeSolver: eps == 0, set it to 1e-5" << endl;
}
else
{
mEps = a;
}
}
template<typename T>
void
RkOdeSolver<T>::Y(const std::valarray<T> &a)
{
mY.resize(a.size());
mY = a;
}
// public member functions
template<typename T>
void
RkOdeSolver<T>::integrate(const T &deltaX)
{
if (deltaX == 0)
{
return; // nothing to integrate
}
// init dydx if uninitialised
if (mDydx.size() != mY.size())
{
mDydx.resize(mY.size());
mDydx = f(mX,mY);
}
static const unsigned int maxiter = 10000;
const T x2 = mX + deltaX;
unsigned int iter;
for (iter=0;
iter<maxiter && rkStepCheck(x2-mX) == false;
++iter)
{}
if (iter>maxiter)
{
kdDebug() << "RkOdeSolver: More than " << maxiter
<< " iterations in RkOdeSolver::integrate" << endl;
// TODO throw exeption here
}
}
// private member functions
template<typename T>
bool
RkOdeSolver<T>::rkStepCheck(const T& dx_requested)
{
static const T safety = 0.9;
static const T pshrnk = -0.25;
static const T pgrow = -0.2;
// reduce step size by no more than a factor 10
static const T shrinkLimit = 0.1;
// enlarge step size by no more than a factor 5
static const T growthLimit = 5.0;
// errmax_sl = 6561.0
static const T errmax_sl = pow(shrinkLimit/safety, 1.0/pshrnk);
// errmax_gl = 1.89e-4
static const T errmax_gl = pow(growthLimit/safety, 1.0/pgrow);
static const unsigned int maxiter = 100;
if (dx_requested == 0)
{
return true; // integration done
}
std::valarray<T> ytmp(mY.size());
std::valarray<T> yerr(mY.size());
std::valarray<T> t(mY.size());
bool stepSizeWasMaximal;
T dx;
if (std::abs(dx_requested) > mStep)
{
stepSizeWasMaximal = true;
dx = dx_requested>0 ? mStep : -mStep;
}
else
{
stepSizeWasMaximal = false;
dx = dx_requested;
}
// generic scaling factor
std::valarray<T> yscal = std::abs(mY) + std::abs(dx*mDydx) + 1e-15;
unsigned int iter = 0;
T errmax = 0;
do
{
if (errmax >= 1.0)
{
// reduce step size
dx *= errmax<errmax_sl ? safety * pow(errmax, pshrnk) : shrinkLimit;
stepSizeWasMaximal = true;
if (mX == mX + dx)
{
// stepsize below numerical resolution
kdDebug() << "RkOdeSolver: stepsize underflow in rkStepCheck"
<< endl;
// TODO throw exeption here
exit(0);
}
// new dx -> update scaling vector
yscal = std::abs(mY) + std::abs(dx*mDydx) + 1e-15;
}
ytmp = rkStep(dx, yerr); // try to make a step forward
t = std::abs(yerr/yscal); // calc the error vector
errmax = t.max()/mEps; // calc the rel. maximal error
++iter;
} while (iter < maxiter && errmax >= 1.0);
if (iter >= maxiter)
{
kdDebug() << "RkOdeSolver: too many iterations in rkStepCheck" << endl;
// TODO throw exeption here
exit(0);
}
if (stepSizeWasMaximal == true)
{
// estimate next step size if used step size was maximal
mStep =
std::abs(dx)
* (errmax>errmax_gl ? safety * pow(errmax, pgrow) : growthLimit);
}
mX += dx; // make step forward
mY = ytmp; // save new function values
mDydx = f(mX,mY); // and update derivatives
return std::abs(dx) < std::abs(dx_requested);
}
template<typename T>
std::valarray<T>
RkOdeSolver<T>::rkStep(const T& dx, std::valarray<T>& yerr) const
{
static const T
a2=0.2, a3=0.3, a4=0.6, a5=1.0, a6=0.875,
b21=0.2,
b31=3.0/40.0, b32=9.0/40.0,
b41=0.3, b42=-0.9, b43=1.2,
b51=-11.0/54.0, b52=2.5, b53=-70.0/27.0, b54=35.0/27.0,
b61=1631.0/55296.0, b62=175.0/512.0, b63=575.0/13824.0,
b64=44275.0/110592.0, b65=253.0/4096.0,
c1=37.0/378.0, c3=250.0/621.0, c4=125.0/594.0, c6=512.0/1771.0,
dc1=c1-2825.0/27648.0, dc3=c3-18575.0/48384.0,
dc4=c4-13525.0/55296.0, dc5=-277.0/14336.0, dc6=c6-0.25;
std::valarray<T> ak2 = f(mX + a2*dx,
mY + dx*b21*mDydx); // 2. step
std::valarray<T> ak3 = f(mX + a3*dx,
mY + dx*(b31*mDydx + b32*ak2)); // 3.step
std::valarray<T> ak4 = f(mX + a4*dx,
mY + dx*(b41*mDydx + b42*ak2
+ b43*ak3)); // 4.step
std::valarray<T> ak5 = f(mX + a5*dx,
mY + dx*(b51*mDydx + b52*ak2
+ b53*ak3 + b54*ak4)); // 5.step
std::valarray<T> ak6 = f(mX + a6*dx,
mY + dx*(b61*mDydx + b62*ak2
+ b63*ak3 + b64*ak4
+ b65*ak5)); // 6.step
yerr = dx*(dc1*mDydx + dc3*ak3 + dc4*ak4 + dc5*ak5 + dc6*ak6);
return mY + dx*( c1*mDydx + c3*ak3 + c4*ak4 + c6*ak6);
}
// explicite instantiations
//template RkOdeSolver<long double>;
template class RkOdeSolver<double>;
//template RkOdeSolver<float>;