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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 DivEq example now used just for valiadation testing
*/
# include <cppad/cppad.hpp>
namespace { // BEGIN empty namespace
bool DivEqTestOne(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector, indices, values, and declaration
CPPAD_TESTVECTOR(AD<double>) U(2);
size_t s = 0;
size_t t = 1;
U[s] = 3.;
U[t] = 2.;
Independent(U);
// dependent variable vector and indices
CPPAD_TESTVECTOR(AD<double>) Z(2);
size_t x = 0;
size_t y = 1;
// some constants
AD<double> zero = 0.;
AD<double> one = 1.;
// dependent variable values
Z[x] = U[s];
Z[y] = U[t];
Z[x] /= U[t]; // AD<double> *= AD<double>
Z[y] /= 5.; // AD<double> *= double
zero /= Z[y]; // divide into a parameter equal to zero
Z[y] /= one; // divide by a parameter equal to one
Z[y] /= 1.; // divide by a double equal to one
// check that zero is still a parameter
// (must do this before creating f because it erases the tape)
ok &= Parameter(zero);
// create f : U -> Z and vectors for derivative calculations
ADFun<double> f(U, Z);
CPPAD_TESTVECTOR(double) v( f.Domain() );
CPPAD_TESTVECTOR(double) w( f.Range() );
// check that none of the components of f are parameters
size_t i;
for(i = 0; i < f.Range(); i++)
ok &= ! f.Parameter(i);
// check function values
ok &= NearEqual(Z[x] , 3. / 2. , eps99, eps99);
ok &= NearEqual(Z[y] , 2. / 5. , eps99, eps99);
// forward computation of partials w.r.t. t
v[s] = 0.;
v[t] = 1.;
w = f.Forward(1, v);
ok &= NearEqual(w[x] , -1.*U[s]/(U[t]*U[t]) , eps99, eps99); // dx/dt
ok &= NearEqual(w[y] , 1. / 5. , eps99, eps99); // dy/dt
// reverse computation of second partials of x
CPPAD_TESTVECTOR(double) r( f.Domain() * 2 );
w[x] = 1.;
w[y] = 0.;
r = f.Reverse(2, w);
ok &= NearEqual(r[2 * s + 1] // d^2 x / (dt ds)
, - 1. / (U[t] * U[t]) , eps99 , eps99 );
ok &= NearEqual(r[2 * t + 1] // d^2 x / (dt dt)
, 2. * U[s] / (U[t] * U[t] * U[t]) , eps99 , eps99 );
return ok;
}
bool DivEqTestTwo(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector
double u0 = .5;
CPPAD_TESTVECTOR(AD<double>) U(1);
U[0] = u0;
Independent(U);
// dependent variable vector
CPPAD_TESTVECTOR(AD<double>) Z(1);
Z[0] = U[0] * U[0]; // initial value
Z[0] /= 2; // AD<double> /= int
Z[0] /= 4.; // AD<double> /= double
Z[0] /= U[0]; // AD<double> /= AD<double>
// create f: U -> Z and vectors used for derivative calculations
ADFun<double> f(U, Z);
CPPAD_TESTVECTOR(double) v(1);
CPPAD_TESTVECTOR(double) w(1);
// check value
ok &= NearEqual(Z[0] , u0*u0/(2*4*u0), eps99, eps99);
// forward computation of partials w.r.t. u
size_t j;
size_t p = 5;
double jfac = 1.;
double value = 1./8.;
v[0] = 1.;
for(j = 1; j < p; j++)
{ jfac *= double(j);
w = f.Forward(j, v);
ok &= NearEqual(w[0], value/jfac, eps99, eps99); // d^jz/du^j
v[0] = 0.;
value = 0.;
}
// reverse computation of partials of Taylor coefficients
CPPAD_TESTVECTOR(double) r(p);
w[0] = 1.;
r = f.Reverse(p, w);
jfac = 1.;
value = 1./8.;
for(j = 0; j < p; j++)
{ ok &= NearEqual(r[j], value/jfac, eps99, eps99); // d^jz/du^j
jfac *= double(j + 1);
value = 0.;
}
return ok;
}
} // END empty namespace
bool DivEq(void)
{ bool ok = true;
ok &= DivEqTestOne();
ok &= DivEqTestTwo();
return ok;
}
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