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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 atomic_four_vector_hes_sparsity.cpp}
Atomic Vector Sparsity Patterns Example
#######################################
f(u, v)
*******
For this example,
:math:`f : \B{R}^{3m} \rightarrow \B{R}^m`
is defined by :math:`f(u, v, w) = - u * v * w`.
where *u* , *v* , and *w* are in :math:`\B{R}^m`.
Source
******
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end atomic_four_vector_hes_sparsity.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# include <cppad/example/atomic_four/vector/vector.hpp>
bool hes_sparsity(void)
{ bool ok = true;
using CppAD::NearEqual;
using CppAD::AD;
//
// vec_op
// atomic vector_op object
CppAD::atomic_vector<double> vec_op("atomic_vector");
//
// m
// size of u, v, and w
size_t m = 6;
//
// n
size_t n = 3 * m;
//
// mul_op, neg_op
typedef CppAD::atomic_vector<double>::op_enum_t op_enum_t;
op_enum_t mul_op = CppAD::atomic_vector<double>::mul_enum;
op_enum_t neg_op = CppAD::atomic_vector<double>::neg_enum;
// -----------------------------------------------------------------------
// Record f(u, v, w) = - u * v * w
// -----------------------------------------------------------------------
// Independent variable vector
CPPAD_TESTVECTOR( CppAD::AD<double> ) auvw(n);
for(size_t j = 0; j < n; ++j)
auvw[j] = AD<double>(1 + j);
CppAD::Independent(auvw);
//
// au, av, aw
CPPAD_TESTVECTOR( CppAD::AD<double> ) au(m), av(m), aw(m);
for(size_t i = 0; i < m; ++i)
{ au[i] = auvw[0 * m + i];
av[i] = auvw[1 * m + i];
aw[i] = auvw[2 * m + i];
}
//
// ax = (au, av)
CPPAD_TESTVECTOR( CppAD::AD<double> ) ax(2 * m);
for(size_t i = 0; i < m; ++i)
{ ax[i] = au[i];
ax[m + i] = av[i];
}
//
// ay = u * v
CPPAD_TESTVECTOR( CppAD::AD<double> ) ay(m);
vec_op(mul_op, ax, ay);
//
// ax = (ay, aw)
for(size_t i = 0; i < m; ++i)
{ ax[i] = ay[i];
ax[m + i] = aw[i];
}
//
// az = ay * w
CPPAD_TESTVECTOR( CppAD::AD<double> ) az(m);
vec_op(mul_op, ax, az);
//
// ay = - az
vec_op(neg_op, az, ay);
//
// f
CppAD::ADFun<double> f(auvw, ay);
//
// size_vector, sparsity_pattern
typedef CPPAD_TESTVECTOR(size_t) size_vector;
typedef CppAD::sparse_rc<size_vector> sparsity_pattern;
// -----------------------------------------------------------------------
// Hessian sparsity
// -----------------------------------------------------------------------
for(size_t direction = 0; direction < 2; ++direction)
{ sparsity_pattern pattern_out;
//
// select_range
CPPAD_TESTVECTOR(bool) select_range(m);
for(size_t i = 0; i < m; ++i)
select_range[i] = true;
//
if( direction == 0 )
{ // Forward
//
// select_domain
CPPAD_TESTVECTOR(bool) select_domain(n);
for(size_t j = 0; j < n; ++j)
select_domain[j] = true;
//
// pattern_out
bool internal_bool = false;
f.for_hes_sparsity(
select_domain, select_range, internal_bool, pattern_out
);
}
else
{ // Reverse
//
// transpose, internal_bool
bool transpose = false;
bool dependency = false;
bool internal_bool = false;
//
// pattern_in
sparsity_pattern pattern_in(n, n, n);
for(size_t j = 0; j < n; ++j)
pattern_in.set(j, j, j);
//
// f stores forward Jacobian
f.for_jac_sparsity(
pattern_in, transpose, dependency, internal_bool, pattern_out
);
//
// pattern_out
f.rev_hes_sparsity(
select_range, transpose, internal_bool, pattern_out
);
}
//
// ok
ok &= pattern_out.nnz() == 2 * n;
ok &= pattern_out.nr() == n;
ok &= pattern_out.nc() == n;
//
// row, col, row_major
const size_vector& row = pattern_out.row();
const size_vector& col = pattern_out.col();
size_vector row_major = pattern_out.row_major();
//
// ok
size_t ell = 0;
for(size_t i = 0; i < m; ++i)
{ // first non-zero in row i
size_t k = row_major[ell++];
ok &= row[k] == i;
ok &= col[k] == m + i;
// second non-zero in row i
k = row_major[ell++];
ok &= row[k] == i;
ok &= col[k] == 2 * m + i;
}
for(size_t i = m; i < 2 * m; ++i)
{ // first non-zero in row i
size_t k = row_major[ell++];
ok &= row[k] == i;
ok &= col[k] == i - m;
// second non-zero in row i
k = row_major[ell++];
ok &= row[k] == i;
ok &= col[k] == i + m;
}
for(size_t i = 2 * m; i < 3 * m; ++i)
{ // first non-zero in row i
size_t k = row_major[ell++];
ok &= row[k] == i;
ok &= col[k] == i - 2 * m;
// second non-zero in row i
k = row_major[ell++];
ok &= row[k] == i;
ok &= col[k] == i - m;
}
}
//
return ok;
}
// END C++
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