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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
// ----------------------------------------------------------------------------
// Check that multilevel reverse with conditional expressions works properly
// when using AD< AD<zdouble> >.
# include <cppad/cppad.hpp>
namespace {
using CppAD::AD;
using CppAD::zdouble;
using CppAD::ADFun;
using CppAD::vector;
typedef AD<zdouble> a1type;
typedef AD<a1type> a2type;
typedef vector<a2type> (*a2fun)(const vector<a2type>& a2x);
//
zdouble eps = 10. * std::numeric_limits<double>::epsilon();
size_t n_ = 2;
size_t m_ = 1;
//
void record(a2fun fun, ADFun<zdouble>& g)
{ vector<zdouble> x(n_);
vector<a1type> a1x(n_), a1w(m_), a1z(m_ * n_);
vector<a2type> a2x(n_), a2y(m_);
//
for(size_t j = 0; j < n_; j++)
{ x[j] = 0.0;
a1x[j] = a1type( x[j] );
a2x[j] = a2type( a1x[j] );
}
Independent(a2x);
// f(x) = x[0] / x[1] if x[1] > 0.0 else 0.0
a2y = fun(a2x);
ADFun<a1type> a1f;
a1f.Dependent(a2x, a2y);
// use reverse mode to calculate g(x) = f'(x)
a1w[0] = a1type(1.0);
Independent(a1x);
a1f.Forward(0, a1x);
a1z = a1f.Reverse(1, a1w);
g.Dependent(a1x, a1z);
//
return;
}
// ----------------------------------------------------------------------
vector<a2type> div(const vector<a2type>& a2x)
{ vector<a2type> a2y(m_);
a2type a2zero = a2type(0.0);
a2type a2four = a2type(4.0);
a2y[0] = CondExpGt(a2x[1], a2zero, a2x[0] / a2x[1], a2zero);
a2y[0] += CondExpGt(a2x[1], a2zero, a2four / a2x[1], a2zero);
return a2y;
}
bool check_div(void)
{ bool ok = true;
// record division operations
ADFun<zdouble> g;
record(div, g);
vector<zdouble> x(n_), z(n_);
// check result where x[1] <= 0.0 (would be nan without absolute zero)
x[0] = 0.0;
x[1] = 0.0;
z = g.Forward(0, x);
z = g.Forward(0, x);
ok &= z[0] == 0.0;
ok &= z[1] == 0.0;
// check result where x[1] > 0.0
x[0] = 2.0;
x[1] = 3.0;
z = g.Forward(0, x);
ok &= CppAD::NearEqual(z[0], 1.0/x[1], eps, eps);
ok &= CppAD::NearEqual(z[1], - (x[0]+4.0)/(x[1]*x[1]), eps, eps);
//
return ok;
}
// ----------------------------------------------------------------------
vector<a2type> mul(const vector<a2type>& a2x)
{ vector<a2type> a2y(m_);
a2type a2zero = a2type(0.0);
a2type a2four = a2type(4.0);
a2y[0] = CondExpLt(a2x[0], a2four, a2x[0] * a2x[1], a2zero);
a2y[0] += CondExpLt(a2x[0], a2four, a2four * a2x[1], a2zero);
a2y[0] += CondExpLt(a2x[0], a2four, a2x[1] * a2four, a2zero);
return a2y;
}
bool check_mul(void)
{ bool ok = true;
// record multiplication operations
ADFun<zdouble> g;
record(mul, g);
vector<zdouble> x(n_), z(n_);
// check result where x[0] > 4 (would be nan without absolute zero)
ok &= std::numeric_limits<double>::has_infinity;
x[0] = std::numeric_limits<double>::infinity();
x[1] = 0.0;
z = g.Forward(0, x);
ok &= z[0] == 0.0;
ok &= z[1] == 0.0;
// check result where x[0] < 4
x[0] = 2.0;
x[1] = 3.0;
z = g.Forward(0, x);
ok &= CppAD::NearEqual(z[0], x[1], eps, eps);
ok &= CppAD::NearEqual(z[1], x[0]+8.0, eps, eps);
//
return ok;
}
// ----------------------------------------------------------------------
bool check_numeric_limits(void)
{ bool ok = true;
//
double double_eps = std::numeric_limits<double>::epsilon();
zdouble zdouble_eps = CppAD::numeric_limits<zdouble>::epsilon();
ok &= double_eps == zdouble_eps;
//
double double_min = std::numeric_limits<double>::min();
zdouble zdouble_min = CppAD::numeric_limits<zdouble>::min();
ok &= double_min == zdouble_min;
//
double double_max = std::numeric_limits<double>::max();
zdouble zdouble_max = CppAD::numeric_limits<zdouble>::max();
ok &= double_max == zdouble_max;
//
return ok;
}
}
bool mul_zdouble(void)
{ bool ok = true;
ok &= check_div();
ok &= check_mul();
ok &= check_numeric_limits();
return ok;
}
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