/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under the terms of the
             Eclipse Public License Version 2.0.

This Source Code may also be made available under the following
Secondary License when the conditions for such availability set forth
in the Eclipse Public License, Version 2.0 are satisfied:
      GNU General Public License, Version 2.0 or later.
---------------------------------------------------------------------------- */

/*
$begin ode_err_maxabs.cpp$$
$spell
    Runge
    Maxabs
$$

$section OdeErrControl: Example and Test Using Maxabs Argument$$


Define
$latex X : \B{R} \rightarrow \B{R}^2$$ by
$latex \[
\begin{array}{rcl}
X_0 (t) & = &  - \exp ( - w_0 t )  \\
X_1 (t) & = & \frac{w_0}{w_1 - w_0} [ \exp ( - w_0 t ) - \exp( - w_1 t )]
\end{array}
\] $$
It follows that $latex X_0 (0) = 1$$, $latex X_1 (0) = 0$$ and
$latex \[
\begin{array}{rcl}
    X_0^{(1)} (t) & = & - w_0 X_0 (t)  \\
    X_1^{(1)} (t) & = & + w_0 X_0 (t) - w_1 X_1 (t)
\end{array}
\] $$
Note that $latex X_1 (0)$$ is zero an if $latex w_0 t$$ is large,
$latex X_0 (t)$$ is near zero.
This example tests OdeErrControl using the $icode maxabs$$ argument.

$srcfile%example/utility/ode_err_maxabs.cpp%0%// BEGIN C++%// END C++%1%$$

$end
*/
// BEGIN C++

# 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:
         CppAD::vector<double> w;
    public:
        // constructor
        Fun(const CppAD::vector<double> &w_) : w(w_)
        { }

        // set f = x'(t)
        void Ode(
            const double                &t,
            const CppAD::vector<double> &x,
            CppAD::vector<double>       &f)
        {   f[0] = - w[0] * x[0];
            f[1] = + w[0] * x[0] - w[1] * x[1];
        }
    };

    // --------------------------------------------------------------
    class Method {
    private:
        Fun F;
    public:
        // constructor
        Method(const CppAD::vector<double> &w_) : F(w_)
        { }
        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 OdeErrMaxabs(void)
{   bool ok = true;     // initial return value

    CppAD::vector<double> w(2);
    w[0] = 10.;
    w[1] = 1.;
    Method method(w);

    CppAD::vector<double> xi(2);
    xi[0] = 1.;
    xi[1] = 0.;

    CppAD::vector<double> eabs(2);
    eabs[0] = 0.;
    eabs[1] = 0.;

    CppAD::vector<double> ef(2);
    CppAD::vector<double> xf(2);
    CppAD::vector<double> maxabs(2);

    double ti   = 0.;
    double tf   = 1.;
    double smin = .5;
    double smax = 1.;
    double scur = .5;
    double erel = 1e-4;

    bool accurate = false;
    while( ! accurate )
    {   xf = OdeErrControl(method,
            ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs);
        accurate = true;
        size_t i;
        for(i = 0; i < 2; i++)
            accurate &= ef[i] <= erel * maxabs[i];
        if( ! accurate )
            smin = smin / 2;
    }

    double x0 = exp(-w[0]*tf);
    ok &= CppAD::NearEqual(x0, xf[0], erel, 0.);
    ok &= CppAD::NearEqual(0., ef[0], erel, erel);

    double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]);
    ok &= CppAD::NearEqual(x1, xf[1], erel, 0.);
    ok &= CppAD::NearEqual(0., ef[1], erel, erel);

    return ok;
}

// END C++
