/usr/include/ql/experimental/math/adaptiverungekutta.hpp is in libquantlib0-dev 1.4-2.
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/*
Copyright (C) 2012 Peter Caspers
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program 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 license for more details.
*/
/*! \file adaptiverungekutta.hpp
\brief Runge-Kutta ODE integration
Runge Kutta method with adaptive stepsize as described in
Numerical Recipes in C, Chapter 16.2
*/
#ifndef quantlib_adaptive_runge_kutta_hpp
#define quantlib_adaptive_runge_kutta_hpp
#include <ql/types.hpp>
#include <ql/errors.hpp>
#include <ql/utilities/disposable.hpp>
#include <boost/function.hpp>
#include <vector>
#include <cmath>
namespace QuantLib {
template <class T = Real>
class AdaptiveRungeKutta {
public:
typedef boost::function<
Disposable<std::vector<T> >(const Real,
const std::vector<T>&)> OdeFct;
typedef boost::function<T(const Real, const T)> OdeFct1d;
/*! The class is constructed with the following inputs:
- eps prescribed error for the solution
- h1 start step size
- hmin smallest step size allowed
*/
AdaptiveRungeKutta(const Real eps=1.0e-6,
const Real h1=1.0e-4,
const Real hmin=0.0)
: eps_(eps), h1_(h1), hmin_(hmin),
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),
ADAPTIVERK_MAXSTP(10000), ADAPTIVERK_TINY(1.0E-30),
ADAPTIVERK_SAFETY(0.9), ADAPTIVERK_PGROW(-0.2),
ADAPTIVERK_PSHRINK(-0.25), ADAPTIVERK_ERRCON(1.89E-4) {}
/*! Integrate the ode from \f$ x1 \f$ to \f$ x2 \f$ with
initial value condition \f$ f(x1)=y1 \f$.
The ode is given by a function \f$ F: R \times K^n
\rightarrow K^n \f$ as \f$ f'(x) = F(x,f(x)) \f$, $K=R,
C$ */
Disposable<std::vector<T> > operator()(const OdeFct& ode,
const std::vector<T>& y1,
const Real x1,
const Real x2);
T operator()(const OdeFct1d& ode,
const T y1,
const Real x1,
const Real x2);
private:
void rkqs(std::vector<T>& y,
const std::vector<T>& dydx,
Real& x,
const Real htry,
const Real eps,
const std::vector<Real>& yScale,
Real &hdid,
Real &hnext,
const OdeFct& derivs);
void rkck(const std::vector<T>& y,
const std::vector<T>& dydx,
Real x,
const Real h,
std::vector<T>& yout,
std::vector<T>& yerr,
const OdeFct& derivs);
const std::vector<T> yStart_;
const Real eps_, h1_, hmin_;
const Real a2,a3,a4,a5,a6,
b21,b31,b32,b41,b42,b43,b51,b52,b53,b54,b61,b62,b63,b64,b65,
c1,c3,c4,c6,dc1,dc3,dc4,dc5,dc6;
const Real ADAPTIVERK_MAXSTP, ADAPTIVERK_TINY, ADAPTIVERK_SAFETY,
ADAPTIVERK_PGROW, ADAPTIVERK_PSHRINK, ADAPTIVERK_ERRCON;
};
template<class T>
Disposable<std::vector<T> > AdaptiveRungeKutta<T>::operator()(
const OdeFct& ode,
const std::vector<T>& y1,
const Real x1,
const Real x2) {
Size n = y1.size();
std::vector<T> y(y1);
std::vector<Real> yScale(n);
Real x = x1;
Real h = h1_* (x1<=x2 ? 1 : -1);
Real hnext,hdid;
for (Size nstp=1; nstp<=ADAPTIVERK_MAXSTP; nstp++) {
std::vector<T> dydx=ode(x,y);
for (Size i=0;i<n;i++)
yScale[i] = std::abs(y[i])+std::abs(dydx[i]*h)+ADAPTIVERK_TINY;
if ((x+h-x2)*(x+h-x1) > 0.0)
h=x2-x;
rkqs(y,dydx,x,h,eps_,yScale,hdid,hnext,ode);
if ((x-x2)*(x2-x1) >= 0.0)
return y;
if (std::fabs(hnext) <= hmin_)
QL_FAIL("Step size (" << hnext << ") too small ("
<< hmin_ << " min) in AdaptiveRungeKutta");
h=hnext;
}
QL_FAIL("Too many steps (" << ADAPTIVERK_MAXSTP
<< ") in AdaptiveRungeKutta");
}
namespace detail {
template <class T>
struct OdeFctWrapper {
typedef typename AdaptiveRungeKutta<T>::OdeFct1d OdeFct1d;
OdeFctWrapper(const OdeFct1d& ode1d)
: ode1d_(ode1d) {}
Disposable<std::vector<T> > operator()(const Real x,
const std::vector<T>& y) {
std::vector<T> res(1,ode1d_(x,y[0]));
return res;
}
const OdeFct1d& ode1d_;
};
}
template<class T>
T AdaptiveRungeKutta<T>::operator()(const OdeFct1d& ode,
const T y1,
const Real x1,
const Real x2) {
return operator()(detail::OdeFctWrapper<T>(ode),
std::vector<T>(1,y1),x1,x2)[0];
}
template<class T>
void AdaptiveRungeKutta<T>::rkqs(std::vector<T>& y,
const std::vector<T>& dydx,
Real& x,
const Real htry,
const Real eps,
const std::vector<Real>& yScale,
Real& hdid,
Real& hnext,
const OdeFct& derivs) {
Size n=y.size();
Real errmax,htemp,xnew;
std::vector<T> yerr(n),ytemp(n);
Real h=htry;
for(;;) {
rkck(y,dydx,x,h,ytemp,yerr,derivs);
errmax=0.0;
for (Size i=0;i<n;i++)
errmax=std::max(errmax,std::abs(yerr[i]/yScale[i]));
errmax/=eps;
if (errmax>1.0) {
htemp=ADAPTIVERK_SAFETY*h*pow(errmax,ADAPTIVERK_PSHRINK);
h = (h>=0.0 ? std::max(htemp,h/10) : std::min(htemp,h/10));
xnew=x+h;
if (xnew==x)
QL_FAIL("Stepsize (" << xnew
<< ") underflow in AdaptiveRungeKutta::rkqs");
continue;
} else {
if (errmax>ADAPTIVERK_ERRCON)
hnext=ADAPTIVERK_SAFETY*h*pow(errmax,ADAPTIVERK_PGROW);
else
hnext=5.0*h;
x+=(hdid=h);
for (Size i=0;i<n;i++)
y[i]=ytemp[i];
break;
}
}
}
template <class T>
void AdaptiveRungeKutta<T>::rkck(const std::vector<T>& y,
const std::vector<T>& dydx,
Real x,
const Real h,
std::vector<T>& yout,
std::vector<T> &yerr,
const OdeFct& derivs) {
Size n=y.size();
std::vector<T> ak2(n),ak3(n),ak4(n),ak5(n),ak6(n),ytemp(n);
// first step
for (Size i=0;i<n;i++)
ytemp[i]=y[i]+b21*h*dydx[i];
// second step
ak2=derivs(x+a2*h,ytemp);
for (Size i=0;i<n;i++)
ytemp[i]=y[i]+h*(b31*dydx[i]+b32*ak2[i]);
// third step
ak3=derivs(x+a3*h,ytemp);
for (Size i=0;i<n;i++)
ytemp[i]=y[i]+h*(b41*dydx[i]+b42*ak2[i]+b43*ak3[i]);
// fourth step
ak4=derivs(x+a4*h,ytemp);
for (Size i=0;i<n;i++)
ytemp[i]=y[i]+h*(b51*dydx[i]+b52*ak2[i]+b53*ak3[i]+b54*ak4[i]);
// fifth step
ak5=derivs(x+a5*h,ytemp);
for (Size i=0;i<n;i++)
ytemp[i]=y[i]+h*(b61*dydx[i]+b62*ak2[i]+b63*ak3[i]+b64*ak4[i]+b65*ak5[i]);
// sixth step
ak6=derivs(x+a6*h,ytemp);
for (Size i=0;i<n;i++) {
yout[i]=y[i]+h*(c1*dydx[i]+c3*ak3[i]+c4*ak4[i]+c6*ak6[i]);
yerr[i]=h*(dc1*dydx[i]+dc3*ak3[i]+dc4*ak4[i]+dc5*ak5[i]+dc6*ak6[i]);
}
}
}
#endif
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