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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_hessian.cpp}
Sparse Hessian: Example and Test
################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end sparse_hessian.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
bool sparse_hessian(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
size_t i, j, k, ell;
typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
typedef CPPAD_TESTVECTOR(double) d_vector;
typedef CPPAD_TESTVECTOR(size_t) i_vector;
typedef CPPAD_TESTVECTOR(bool) b_vector;
typedef CPPAD_TESTVECTOR(std::set<size_t>) s_vector;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 12; // must be greater than or equal 3; see n_sweep below
a_vector a_x(n);
for(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(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(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);
for(ell = 0; ell < n * n; ell++)
check[ell] = 0.0;
ell = 0 * n + 1;
check[ell] = 1.0;
ell = 1 * n + 0;
check[ell] = 1.0 ;
for(j = 0; j < n; j++)
{ ell = j * n + j;
check[ell] = 6.0 * x[j];
}
// -------------------------------------------------------------------
// second derivative of y[0] w.r.t x
d_vector hes(n * n);
hes = f.SparseHessian(x, w);
for(ell = 0; ell < n * n; ell++)
ok &= NearEqual(w[0] * check[ell], hes[ell], eps, eps );
// --------------------------------------------------------------------
// example using vectors of bools to compute sparsity pattern for Hessian
b_vector r_bool(n * n);
for(i = 0; i < n; i++)
{ for(j = 0; j < n; j++)
r_bool[i * n + j] = false;
r_bool[i * n + i] = true;
}
f.ForSparseJac(n, r_bool);
//
b_vector s_bool(m);
for(i = 0; i < m; i++)
s_bool[i] = w[i] != 0;
b_vector p_bool = f.RevSparseHes(n, s_bool);
hes = f.SparseHessian(x, w, p_bool);
for(ell = 0; ell < n * n; ell++)
ok &= NearEqual(w[0] * check[ell], hes[ell], eps, eps );
// --------------------------------------------------------------------
// example using vectors of sets to compute sparsity pattern for Hessian
s_vector r_set(n);
for(i = 0; i < n; i++)
r_set[i].insert(i);
f.ForSparseJac(n, r_set);
//
s_vector s_set(m);
for(i = 0; i < m; i++)
if( w[i] != 0. )
s_set[0].insert(i);
s_vector p_set = f.RevSparseHes(n, s_set);
// example passing sparsity pattern to SparseHessian
hes = f.SparseHessian(x, w, p_set);
for(ell = 0; ell < n * n; ell++)
ok &= NearEqual(w[0] * check[ell], hes[ell], eps, eps );
// --------------------------------------------------------------------
// use row and column indices to specify upper triangle of
// non-zero elements of Hessian
size_t K = n + 1;
i_vector row(K), col(K);
hes.resize(K);
k = 0;
for(j = 0; j < n; j++)
{ // diagonal of Hessian
row[k] = j;
col[k] = j;
k++;
}
// only off diagonal non-zero elemenet in upper triangle
row[k] = 0;
col[k] = 1;
k++;
ok &= k == K;
CppAD::sparse_hessian_work work;
// can use p_set or p_bool.
size_t n_sweep = f.SparseHessian(x, w, p_set, row, col, hes, work);
for(k = 0; k < K; k++)
{ ell = row[k] * n + col[k];
ok &= NearEqual(w[0] * check[ell], hes[k], eps, eps );
}
ok &= n_sweep == 2;
// now recompute at a different x and w (using work from previous call
w[0] = 2.0;
x[1] = 0.5;
ell = 1 * n + 1;
check[ell] = 6.0 * x[1];
s_vector not_used;
n_sweep = f.SparseHessian(x, w, not_used, row, col, hes, work);
for(k = 0; k < K; k++)
{ ell = row[k] * n + col[k];
ok &= NearEqual(w[0] * check[ell], hes[k], eps, eps );
}
ok &= n_sweep == 2;
return ok;
}
// END C++
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