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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 example for deprecated interface.
$spell
CppAD
Jac
$$
$section Computing Dependency: Example and Test$$
$head Discussion$$
The partial of an dependent variable with respect to an independent variable
might always be zero even though the dependent variable depends on the
value of the dependent variable. Consider the following case
$latex \[
f(x) = {\rm sign} (x) =
\left\{ \begin{array}{rl}
+1 & {\rm if} \; x > 0 \\
0 & {\rm if} \; x = 0 \\
-1 & {\rm if} \; x < 0
\end{array} \right.
\] $$
In this case the value of $latex f(x)$$ depends on the value of $latex x$$
but CppAD always returns zero for the derivative of the $cref sign$$ function.
$head Dependency Pattern$$
If the $th i$$ dependent variables depends on the
value of the $th j$$ independent variable,
the corresponding entry in the dependency pattern is non-zero (true).
Otherwise it is zero (false).
CppAD uses $cref/sparsity patterns/glossary/Sparsity Pattern/$$
to represent dependency matrices.
The $icode dependency$$ argument to
$cref/ForSparseJac/ForSparseJac/dependency/$$ and
$cref/RevSparseJac/RevSparseJac/dependency/$$ is a flag that signals
that the dependency pattern (instead of the sparsity pattern) is computed.
$srcthisfile%0%// BEGIN C++%// END C++%1%$$
$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>
namespace {
double heavyside(const double& x)
{ if( x <= 0.0 )
return 0.0;
return 1.0;
}
CPPAD_DISCRETE_FUNCTION(double, heavyside)
}
bool dependency(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// VecAD object for use later
CppAD::VecAD<double> vec_ad(2);
vec_ad[0] = 0.0;
vec_ad[1] = 1.0;
// domain space vector
size_t n = 5;
CPPAD_TESTVECTOR(AD<double>) ax(n);
for(size_t j = 0; j < n; j++)
ax[j] = AD<double>(j + 1);
// declare independent variables and start tape recording
CppAD::Independent(ax);
// some AD constants
AD<double> azero(0.0), aone(1.0);
// range space vector
size_t m = n;
size_t m1 = n - 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[m1-0] = sign( ax[0] );
ay[m1-1] = CondExpLe( ax[1], azero, azero, aone);
ay[m1-2] = CondExpLe( azero, ax[2], azero, aone);
ay[m1-3] = heavyside( ax[3] );
ay[m1-4] = vec_ad[ ax[4] - AD<double>(4.0) ];
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// -----------------------------------------------------------
// ForSparseJac and bool dependency
bool transpose = false;
bool dependency;
// could replace CppAD::vectorBooll by CPPAD_TESTVECTOR<bool>
CppAD::vectorBool eye_bool(n * n), depend_bool(m * n);
for(size_t i = 0; i < n; i++)
{ for(size_t j = 0; j < n; j++)
eye_bool[i * n + j] = (i == j);
}
dependency = true;
depend_bool = f.ForSparseJac(n, eye_bool, transpose, dependency);
for(size_t i = 0; i < m; i++)
{ for(size_t j = 0; j < n; j++)
ok &= depend_bool[i * n + j] == (i == (m1-j));
}
dependency = false;
depend_bool = f.ForSparseJac(n, eye_bool, transpose, dependency);
for(size_t i = 0; i < m; i++)
{ for(size_t j = 0; j < n; j++)
ok &= depend_bool[i * n + j] == false;
}
// -----------------------------------------------------------
// RevSparseJac and set dependency
CppAD::vector< std::set<size_t> > eye_set(m), depend_set(m);
for(size_t i = 0; i < m; i++)
{ ok &= eye_set[i].empty();
eye_set[i].insert(i);
}
dependency = true;
depend_set = f.RevSparseJac(n, eye_set, transpose, dependency);
for(size_t i = 0; i < m; i++)
{ std::set<size_t> check;
check.insert(m1 - i);
ok &= depend_set[i] == check;
}
dependency = false;
depend_set = f.RevSparseJac(n, eye_set, transpose, dependency);
for(size_t i = 0; i < m; i++)
ok &= depend_set[i].empty();
return ok;
}
// END C++
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