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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 OdeRunge example now used just for valiadation testing of Runge45
*/
# include <cppad/cppad.hpp>
# include <iostream>
# include <cassert>
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)
{
using CppAD::exp;
size_t n = x.size();
size_t i;
f[0] = 0.;
for(i = 1; i < n-1; i++)
f[i] = w[i] * x[i-1];
f[n-1] = x[0] * x[1];
}
private:
CPPAD_TESTVECTOR(CppAD::AD<double>) w;
};
} // END Empty namespace
bool Runge45(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
size_t i;
size_t j;
size_t k;
size_t n = 6;
size_t m = n - 1;
CPPAD_TESTVECTOR(AD<double>) x(n);
AD<double> t0 = 0.;
AD<double> t1 = 2.;
size_t nstep = 2;
// vector of independent variables
CPPAD_TESTVECTOR(AD<double>) w(m);
for(i = 0; i < m; i++)
w[i] = double(i);
Independent(w);
// construct function object using independent variables
TestFun fun(w);
// initial value of x
CPPAD_TESTVECTOR(AD<double>) x0(n);
for(i = 0; i < n; i++)
x0[i] = 0.;
x0[0] = exp( w[0] );
// solve the differential equation
x = Runge45(fun, nstep, t0, t1, x0);
// 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() );
// for i < n-1,
// x[i](2) = exp( w[0] ) * (w[1] / 1) * ... * (w[i] / i) * 2^i
AD<double> xi2 = exp(w[0]);
for(i = 0; i < n-1; i++)
{ ok &= NearEqual(x[i], xi2, eps99, eps99);
if( i < n-2 )
xi2 *= w[i+1] * 2. / double(i+1);
}
// x[n-1](2) = exp(2 * w[0]) * w[1] * 2^2 / 2
xi2 = exp(2. * w[0]) * w[1] * 2.;
ok &= NearEqual(x[n-1], xi2, eps99, eps99);
// the partial of x[i](2) with respect to w[j] is
// x[i](2) / w[j] if 0 < j <= i < n-1
// x[i](2) if j == 0 and i < n-1
// 2*x[i](2) if j == 0 and i = n-1
// x[i](2) / w[j] if j == 1 and i = n-1
// zero otherwise
for(i = 0; i < n-1; i++)
{ // compute partials of x[i]
for(k = 0; k < n; k++)
r[k] = 0.;
r[i] = 1.;
q = f.Reverse(1,r);
for(j = 0; j < m; j++)
{ // check partial of x[i] w.r.t w[j]
if (j == 0 )
ok &= NearEqual(q[j], x[i], eps99, eps99);
else if( j <= i )
ok &= NearEqual(
q[j], x[i]/w[j], 1e-14, 1e-14);
else
ok &= NearEqual(q[j], 0., eps99, eps99);
}
}
// compute partials of x[n-1]
i = n-1;
for(k = 0; k < n; k++)
r[k] = 0.;
r[i] = 1.;
q = f.Reverse(1,r);
for(j = 0; j < m; j++)
{ // check partial of x[n-1] w.r.t w[j]
if (j == 0 )
ok &= NearEqual(q[j], 2.*x[i], eps99, eps99);
else if( j == 1 )
ok &= NearEqual(
q[j], x[i]/w[1], 1e-14, 1e-14);
else
ok &= NearEqual(q[j], 0., eps99, eps99);
}
return ok;
}
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