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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
// ----------------------------------------------------------------------------
/*
Old OdeImplicit example now used just for valiadation testing of Rosen34
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# include <iostream>
# include <cassert>
/*
Case where
x[0](0) = 1, x[0]'(t) = - w[0] * x[0](t)
x[1](0) = 1, x[1]'(t) = - w[1] * x[1](t)
x[2](0) = 0, x[2]'(t) = w[2] * t
x[0](t) = exp( - w[0] * t )
x[1](t) = exp( - w[1] * t )
x[2](t) = w[2] * t^2 / 2
*/
namespace { // BEGIN Empty namespace
class TestFun {
public:
TestFun(const CPPAD_TESTVECTOR(CppAD::AD<double>) &w_)
{ w.resize( w_.size() );
w = w_;
}
void Ode(
const CppAD::AD<double> &t,
const CPPAD_TESTVECTOR(CppAD::AD<double>) &x,
CPPAD_TESTVECTOR(CppAD::AD<double>) &f)
{
f[0] = - w[0] * x[0];
f[1] = - w[1] * x[1];
f[2] = w[2] * t;
}
void Ode_ind(
const CppAD::AD<double> &t,
const CPPAD_TESTVECTOR(CppAD::AD<double>) &x,
CPPAD_TESTVECTOR(CppAD::AD<double>) &f_t)
{
f_t[0] = 0.;
f_t[1] = 0.;
f_t[2] = w[2];
}
void Ode_dep(
const CppAD::AD<double> &t,
const CPPAD_TESTVECTOR(CppAD::AD<double>) &x,
CPPAD_TESTVECTOR(CppAD::AD<double>) &f_x)
{
f_x[0] = - w[0]; f_x[1] = 0.; f_x[2] = 0.;
f_x[3] = 0.; f_x[4] = - w[1]; f_x[5] = 0.;
f_x[6] = 0.; f_x[7] = 0.; f_x[8] = 0.;
}
private:
CPPAD_TESTVECTOR(CppAD::AD<double>) w;
};
} // END empty namespace
bool Rosen34(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
CPPAD_TESTVECTOR(AD<double>) x(3);
CPPAD_TESTVECTOR(AD<double>) w(3);
size_t n = 3;
size_t nstep = 20;
AD<double> t0 = 0.;
AD<double> t1 = 1.;
// set independent variables
size_t i;
for(i = 0; i < n; i++)
w[i] = double(100 * i + 1);
Independent(w);
// construct the function object using the independent variables
TestFun fun(w);
// initial value of x
CPPAD_TESTVECTOR(AD<double>) xini(3);
xini[0] = 1.;
xini[1] = 1.;
xini[2] = 0.;
// integrate the differential equation
x = Rosen34(fun, nstep, t0, t1, xini);
// create f : w -> x and vectors for evaluating derivatives
ADFun<double> f(w, x);
CPPAD_TESTVECTOR(double) q( f.Domain() );
CPPAD_TESTVECTOR(double) r( f.Range() );
// check function values
AD<double> x0 = exp( - w[0] * t1 );
ok &= NearEqual(x[0], x0, 0., 1. / double(nstep * nstep) );
AD<double> x1 = exp( - w[1] * t1 );
ok &= NearEqual(x[1], x1, 0., 1. / double(nstep * nstep) );
AD<double> x2 = w[2] * t1 * t1 / 2.;
ok &= NearEqual(x[2], x2, eps99, eps99);
// check dx[0] / dw[0]
for(i = 0; i < size_t(w.size()); i++)
q[i] = 0.;
q[0] = 1.;
r = f.Forward(1, q);
ok &= NearEqual(r[0], - w[0] * x0, 0., 1. / double(nstep * nstep) );
// check dx[1] / dw[1]
q[0] = 0.;
q[1] = 1.;
r = f.Forward(1, q);
ok &= NearEqual(r[1], - w[1] * x1, 0., 1. / double(nstep * nstep) );
// check dx[2] / dw[2]
q[1] = 0.;
q[2] = 1.;
r = f.Forward(1, q);
ok &= NearEqual(r[2], x2 / w[2], eps99, eps99);
return ok;
}
// END C++
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