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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 rev_sparse_hes.cpp}
Reverse Mode Hessian Sparsity: Example and Test
###############################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end rev_sparse_hes.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------------
// expected sparsity pattern
bool check_f0[] = {
false, false, false, // partials w.r.t x0 and (x0, x1, x2)
false, false, false, // partials w.r.t x1 and (x0, x1, x2)
false, false, true // partials w.r.t x2 and (x0, x1, x2)
};
bool check_f1[] = {
false, true, false, // partials w.r.t x0 and (x0, x1, x2)
true, false, false, // partials w.r.t x1 and (x0, x1, x2)
false, false, false // partials w.r.t x2 and (x0, x1, x2)
};
// define the template function BoolCases<Vector> in empty namespace
template <class Vector> // vector class, elements of type bool
bool BoolCases(void)
{ bool ok = true;
using CppAD::AD;
// domain space vector
size_t n = 3;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 0.;
ax[1] = 1.;
ax[2] = 2.;
// declare independent variables and start recording
CppAD::Independent(ax);
// range space vector
size_t m = 2;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = sin( ax[2] );
ay[1] = ax[0] * ax[1];
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// sparsity pattern for the identity matrix
Vector r(n * n);
size_t i, j;
for(i = 0; i < n; i++)
{ for(j = 0; j < n; j++)
r[ i * n + j ] = (i == j);
}
// compute sparsity pattern for J(x) = F^{(1)} (x)
f.ForSparseJac(n, r);
// compute sparsity pattern for H(x) = F_0^{(2)} (x)
Vector s(m);
for(i = 0; i < m; i++)
s[i] = false;
s[0] = true;
Vector h(n * n);
h = f.RevSparseHes(n, s);
// check values
for(i = 0; i < n; i++)
for(j = 0; j < n; j++)
ok &= (h[ i * n + j ] == check_f0[ i * n + j ] );
// compute sparsity pattern for H(x) = F_1^{(2)} (x)
for(i = 0; i < m; i++)
s[i] = false;
s[1] = true;
h = f.RevSparseHes(n, s);
// check values
for(i = 0; i < n; i++)
for(j = 0; j < n; j++)
ok &= (h[ i * n + j ] == check_f1[ i * n + j ] );
// call that transposed the result
bool transpose = true;
h = f.RevSparseHes(n, s, transpose);
// This h is symmetric, because R is symmetric, not really testing here
for(i = 0; i < n; i++)
for(j = 0; j < n; j++)
ok &= (h[ j * n + i ] == check_f1[ i * n + j ] );
return ok;
}
// define the template function SetCases<Vector> in empty namespace
template <class Vector> // vector class, elements of type std::set<size_t>
bool SetCases(void)
{ bool ok = true;
using CppAD::AD;
// domain space vector
size_t n = 3;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 0.;
ax[1] = 1.;
ax[2] = 2.;
// declare independent variables and start recording
CppAD::Independent(ax);
// range space vector
size_t m = 2;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = sin( ax[2] );
ay[1] = ax[0] * ax[1];
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// sparsity pattern for the identity matrix
Vector r(n);
size_t i;
for(i = 0; i < n; i++)
{ assert( r[i].empty() );
r[i].insert(i);
}
// compute sparsity pattern for J(x) = F^{(1)} (x)
f.ForSparseJac(n, r);
// compute sparsity pattern for H(x) = F_0^{(2)} (x)
Vector s(1);
assert( s[0].empty() );
s[0].insert(0);
Vector h(n);
h = f.RevSparseHes(n, s);
// check values
std::set<size_t>::iterator itr;
size_t j;
for(i = 0; i < n; i++)
{ for(j = 0; j < n; j++)
{ bool found = h[i].find(j) != h[i].end();
ok &= (found == check_f0[i * n + j]);
}
}
// compute sparsity pattern for H(x) = F_1^{(2)} (x)
s[0].clear();
assert( s[0].empty() );
s[0].insert(1);
h = f.RevSparseHes(n, s);
// check values
for(i = 0; i < n; i++)
{ for(j = 0; j < n; j++)
{ bool found = h[i].find(j) != h[i].end();
ok &= (found == check_f1[i * n + j]);
}
}
// call that transposed the result
bool transpose = true;
h = f.RevSparseHes(n, s, transpose);
// This h is symmetric, because R is symmetric, not really testing here
for(i = 0; i < n; i++)
{ for(j = 0; j < n; j++)
{ bool found = h[j].find(i) != h[j].end();
ok &= (found == check_f1[i * n + j]);
}
}
return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool rev_sparse_hes(void)
{ bool ok = true;
// Run with Vector equal to four different cases
// all of which are Simple Vectors with elements of type bool.
ok &= BoolCases< CppAD::vector <bool> >();
ok &= BoolCases< CppAD::vectorBool >();
ok &= BoolCases< std::vector <bool> >();
ok &= BoolCases< std::valarray <bool> >();
// Run with Vector equal to two different cases both of which are
// Simple Vectors with elements of type std::set<size_t>
typedef std::set<size_t> set;
ok &= SetCases< CppAD::vector <set> >();
ok &= SetCases< std::vector <set> >();
// Do not use valarray because its element access in the const case
// returns a copy instead of a reference
// ok &= SetCases< std::valarray <set> >();
return ok;
}
// END C++
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