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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 sparse_hes.cpp}
Computing Sparse Hessian: Example and Test
##########################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end sparse_hes.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
bool sparse_hes(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
//
typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
typedef CPPAD_TESTVECTOR(double) d_vector;
typedef CPPAD_TESTVECTOR(size_t) s_vector;
typedef CPPAD_TESTVECTOR(bool) b_vector;
//
// domain space vector
size_t n = 12; // must be greater than or equal 3; see n_sweep below
a_vector a_x(n);
for(size_t j = 0; j < n; j++)
a_x[j] = AD<double> (0);
//
// declare independent variables and starting recording
CppAD::Independent(a_x);
//
// range space vector
size_t m = 1;
a_vector a_y(m);
a_y[0] = a_x[0] * a_x[1];
for(size_t j = 0; j < n; j++)
a_y[0] += a_x[j] * a_x[j] * a_x[j];
//
// create f: x -> y and stop tape recording
// (without executing zero order forward calculation)
CppAD::ADFun<double> f;
f.Dependent(a_x, a_y);
//
// new value for the independent variable vector, and weighting vector
d_vector w(m), x(n);
for(size_t j = 0; j < n; j++)
x[j] = double(j);
w[0] = 1.0;
//
// vector used to check the value of the hessian
d_vector check(n * n);
size_t ij = 0 * n + 1;
for(ij = 0; ij < n * n; ij++)
check[ij] = 0.0;
ij = 0 * n + 1;
check[ij] = 1.0;
ij = 1 * n + 0;
check[ij] = 1.0 ;
for(size_t j = 0; j < n; j++)
{ ij = j * n + j;
check[ij] = 6.0 * x[j];
}
//
// compute Hessian sparsity pattern
b_vector select_domain(n), select_range(m);
for(size_t j = 0; j < n; j++)
select_domain[j] = true;
select_range[0] = true;
//
CppAD::sparse_rc<s_vector> hes_pattern;
bool internal_bool = false;
f.for_hes_sparsity(
select_domain, select_range, internal_bool, hes_pattern
);
//
// compute entire sparse Hessian (really only need lower triangle)
CppAD::sparse_rcv<s_vector, d_vector> subset( hes_pattern );
CppAD::sparse_hes_work work;
std::string coloring = "cppad.symmetric";
size_t n_sweep = f.sparse_hes(x, w, subset, hes_pattern, coloring, work);
ok &= n_sweep == 2;
//
const s_vector row( subset.row() );
const s_vector col( subset.col() );
const d_vector val( subset.val() );
size_t nnz = subset.nnz();
ok &= nnz == n + 2;
for(size_t k = 0; k < nnz; k++)
{ ij = row[k] * n + col[k];
ok &= val[k] == check[ij];
}
return ok;
}
// END C++
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