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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
// ----------------------------------------------------------------------------
/*
{xrst_begin optimize_cumulative_sum.cpp}
Optimize Cumulative Sum Operations: Example and Test
####################################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end optimize_cumulative_sum.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
namespace {
struct tape_size { size_t n_var; size_t n_op; };
template <class Vector> void fun(
const Vector& x, Vector& y, tape_size& before, tape_size& after
)
{ typedef typename Vector::value_type scalar;
// phantom variable with index 0 and independent variables
// begin operator, independent variable operators and end operator
before.n_var = 1 + x.size(); before.n_op = 2 + x.size();
after.n_var = 1 + x.size(); after.n_op = 2 + x.size();
// operators that are identical, and that will be made part of the
// cumulative summation. Make sure do not replace second variable
// using the first and then remove the first as part of the
// cumulative summation.
scalar first = x[0] + x[1];
scalar second = x[0] + x[1];
before.n_var += 2; before.n_op += 2;
after.n_var += 0; after.n_op += 0;
// test that subtractions are also included in cumulative summations
scalar third = x[1] - 2.0;
before.n_var += 1; before.n_op += 1;
after.n_var += 0; after.n_op += 0;
// the finial summation is converted to a cumulative summation
// the other is removed.
scalar csum = first + second + third;
before.n_var += 2; before.n_op += 2;
after.n_var += 1; after.n_op += 1;
// results for this operation sequence
y[0] = csum;
before.n_var += 0; before.n_op += 0;
after.n_var += 0; after.n_op += 0;
}
}
bool cumulative_sum(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps10 = 10.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 2;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 0.5;
ax[1] = 1.5;
// declare independent variables and start tape recording
CppAD::Independent(ax);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
tape_size before, after;
fun(ax, ay, before, after);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
ok &= f.size_order() == 1; // this constructor does 0 order forward
ok &= f.size_var() == before.n_var;
ok &= f.size_op() == before.n_op;
// Optimize the operation sequence
f.optimize();
ok &= f.size_order() == 0; // 0 order forward not present
ok &= f.size_var() == after.n_var;
ok &= f.size_op() == after.n_op;
// Check result for a zero order calculation for a different x,
CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
x[0] = 0.75;
x[1] = 2.25;
y = f.Forward(0, x);
fun(x, check, before, after);
ok &= CppAD::NearEqual(y[0], check[0], eps10, eps10);
return ok;
}
// END C++
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