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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
// ----------------------------------------------------------------------------
/*
@begin sparse_sub_hes.cpp$$
$spell
$$
$section Sparse Hessian on Subset of Variables: Example and Test$$
$head Purpose$$
This example uses a
$cref/column subset/sparse_hessian/p/Column Subset/$$ of the sparsity pattern
to compute the Hessian for a subset of the variables.
The values in the rest of the sparsity pattern do not matter.
$head See Also$$
$cref sub_sparse_hes.cpp$$
$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>
namespace { // BEGIN_EMPTY_NAMESPACE
// --------------------------------------------------------------------------
void record_function(CppAD::ADFun<double>& f, size_t n)
{ // must be greater than or equal 3; see n_sweep below
assert( n >= 3 );
//
using CppAD::AD;
typedef CppAD::vector< AD<double> > a_vector;
//
// domain space vector
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] = 0.0;
for(size_t j = 1; j < n; j++)
a_y[0] += a_x[j-1] * a_x[j] * a_x[j];
// create f: x -> y and stop tape recording
// (without executing zero order forward calculation)
f.Dependent(a_x, a_y);
//
return;
}
// --------------------------------------------------------------------------
bool test_set(const char* color_method)
{ bool ok = true;
//
typedef CppAD::vector< double > d_vector;
typedef CppAD::vector<size_t> i_vector;
typedef CppAD::vector< std::set<size_t> > s_vector;
//
size_t n = 12;
CppAD::ADFun<double> f;
record_function(f, n);
//
// sparsity patteren for the sub-set of variables we are computing
// the hessian w.r.t.
size_t n_sub = 4;
s_vector r(n);
for(size_t j = 0; j < n_sub; j++)
{ assert( r[j].empty() );
r[j].insert(j);
}
// store forward sparsity for J(x) = F^{(1)} (x) * R
f.ForSparseJac(n_sub, r);
// compute sparsity pattern for H(x) = (S * F)^{(2)} ( x ) * R
s_vector s(1);
assert( s[0].empty() );
s[0].insert(0);
bool transpose = true;
s_vector h = f.RevSparseHes(n_sub, s, transpose);
// set the row and column indices that correspond to lower triangle
i_vector row, col;
for(size_t i = 0; i < n_sub; i++)
{ if( i > 0 )
{ // diagonal element
row.push_back(i);
col.push_back(i);
// lower diagonal element
row.push_back(i);
col.push_back(i-1);
}
}
// weighting for the Hessian
d_vector w(1);
w[0] = 1.0;
// compute Hessian
CppAD::sparse_hessian_work work;
work.color_method = color_method;
d_vector x(n), hes( row.size() );
for(size_t j = 0; j < n; j++)
x[j] = double(j+1);
f.SparseHessian(x, w, h, row, col, hes, work);
// check the values in the sparse hessian
for(size_t ell = 0; ell < row.size(); ell++)
{ size_t i = row[ell];
size_t j = col[ell];
if( i == j )
ok &= hes[ell] == 2.0 * x[i-1];
else
{ ok &= j+1 == i;
ok &= hes[ell] == 2.0 * x[i];
}
}
return ok;
}
// --------------------------------------------------------------------------
bool test_bool(const char* color_method)
{ bool ok = true;
//
typedef CppAD::vector< double > d_vector;
typedef CppAD::vector<size_t> i_vector;
typedef CppAD::vector<bool> s_vector;
//
size_t n = 12;
CppAD::ADFun<double> f;
record_function(f, n);
//
// sparsity patteren for the sub-set of variables we are computing
// the hessian w.r.t.
size_t n_sub = 4;
s_vector r(n * n_sub);
for(size_t i = 0; i < n; i++)
{ for(size_t j = 0; j < n_sub; j++)
r[ i * n_sub + j ] = (i == j);
}
// store forward sparsity for J(x) = F^{(1)} (x) * R
f.ForSparseJac(n_sub, r);
// compute sparsity pattern for H(x) = (S * F)^{(2)} ( x ) * R
s_vector s(1);
s[0] = true;
bool transpose = true;
s_vector h = f.RevSparseHes(n_sub, s, transpose);
// set the row and column indices that correspond to lower triangle
i_vector row, col;
for(size_t i = 0; i < n_sub; i++)
{ if( i > 0 )
{ // diagonal element
row.push_back(i);
col.push_back(i);
// lower diagonal element
row.push_back(i);
col.push_back(i-1);
}
}
// weighting for the Hessian
d_vector w(1);
w[0] = 1.0;
// extend sparsity pattern (values in extended columns do not matter)
s_vector h_extended(n * n);
for(size_t i = 0; i < n; i++)
{ for(size_t j = 0; j < n_sub; j++)
h_extended[ i * n + j ] = h[ i * n_sub + j ];
for(size_t j = n_sub; j < n; j++)
h_extended[ i * n + j ] = false;
}
// compute Hessian
CppAD::sparse_hessian_work work;
work.color_method = color_method;
d_vector x(n), hes( row.size() );
for(size_t j = 0; j < n; j++)
x[j] = double(j+1);
f.SparseHessian(x, w, h_extended, row, col, hes, work);
// check the values in the sparse hessian
for(size_t ell = 0; ell < row.size(); ell++)
{ size_t i = row[ell];
size_t j = col[ell];
if( i == j )
ok &= hes[ell] == 2.0 * x[i-1];
else
{ ok &= j+1 == i;
ok &= hes[ell] == 2.0 * x[i];
}
}
return ok;
}
} // END_EMPTY_NAMESPACE
bool sparse_sub_hes(void)
{ bool ok = true;
ok &= test_set("cppad.symmetric");
ok &= test_set("cppad.general");
//
ok &= test_bool("cppad.symmetric");
ok &= test_bool("cppad.general");
return ok;
}
// END C++
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