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// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin ode_err_control.cpp}
OdeErrControl: Example and Test
###############################
Define
:math:`X : \B{R} \rightarrow \B{R}^2` by
.. math::
:nowrap:
\begin{eqnarray}
X_0 (0) & = & 1 \\
X_1 (0) & = & 0 \\
X_0^{(1)} (t) & = & - \alpha X_0 (t) \\
X_1^{(1)} (t) & = & 1 / X_0 (t)
\end{eqnarray}
It follows that
.. math::
:nowrap:
\begin{eqnarray}
X_0 (t) & = & \exp ( - \alpha t ) \\
X_1 (t) & = & [ \exp( \alpha t ) - 1 ] / \alpha
\end{eqnarray}
This example tests OdeErrControl using the relations above.
Nan
***
Note that :math:`X_0 (t) > 0` for all :math:`t` and that the
ODE goes through a singularity between :math:`X_0 (t) > 0`
and :math:`X_0 (t) < 0`.
If :math:`X_0 (t) < 0`,
we return ``nan`` in order to inform
``OdeErrControl`` that its is taking to large a step.
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end ode_err_control.cpp}
*/
// BEGIN C++
# include <limits> // for quiet_NaN
# include <cstddef> // for size_t
# include <cmath> // for exp
# include <cppad/utility/ode_err_control.hpp> // CppAD::OdeErrControl
# include <cppad/utility/near_equal.hpp> // CppAD::NearEqual
# include <cppad/utility/vector.hpp> // CppAD::vector
# include <cppad/utility/runge_45.hpp> // CppAD::Runge45
namespace {
// --------------------------------------------------------------
class Fun {
private:
const double alpha_;
public:
// constructor
Fun(double alpha) : alpha_(alpha)
{ }
// set f = x'(t)
void Ode(
const double &t,
const CppAD::vector<double> &x,
CppAD::vector<double> &f)
{ f[0] = - alpha_ * x[0];
f[1] = 1. / x[0];
// case where ODE does not make sense
if( x[0] < 0. )
f[1] = std::numeric_limits<double>::quiet_NaN();
}
};
// --------------------------------------------------------------
class Method {
private:
Fun F;
public:
// constructor
Method(double alpha) : F(alpha)
{ }
void step(
double ta,
double tb,
CppAD::vector<double> &xa ,
CppAD::vector<double> &xb ,
CppAD::vector<double> &eb )
{ xb = CppAD::Runge45(F, 1, ta, tb, xa, eb);
}
size_t order(void)
{ return 4; }
};
}
bool OdeErrControl(void)
{ bool ok = true; // initial return value
double alpha = 10.;
Method method(alpha);
CppAD::vector<double> xi(2);
xi[0] = 1.;
xi[1] = 0.;
CppAD::vector<double> eabs(2);
eabs[0] = 1e-4;
eabs[1] = 1e-4;
// inputs
double ti = 0.;
double tf = 1.;
double smin = 1e-4;
double smax = 1.;
double scur = 1.;
double erel = 0.;
// outputs
CppAD::vector<double> ef(2);
CppAD::vector<double> xf(2);
CppAD::vector<double> maxabs(2);
size_t nstep;
xf = OdeErrControl(method,
ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);
double x0 = exp(-alpha*tf);
ok &= CppAD::NearEqual(x0, xf[0], 1e-4, 1e-4);
ok &= CppAD::NearEqual(0., ef[0], 1e-4, 1e-4);
double x1 = (exp(alpha*tf) - 1) / alpha;
ok &= CppAD::NearEqual(x1, xf[1], 1e-4, 1e-4);
ok &= CppAD::NearEqual(0., ef[1], 1e-4, 1e-4);
return ok;
}
// END C++
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