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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: 2003-24 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
Old SparseHessian example
*/
# include <cppad/cppad.hpp>
namespace { // ---------------------------------------------------------
bool rc_tridiagonal(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
size_t i, j, k, ell;
double eps10 = 10. * CppAD::epsilon<double>();
size_t n = 12; // must be greater than or equal 3; see n_sweep.
size_t m = n - 1;
CPPAD_TESTVECTOR(AD<double>) a_x(n), a_y(m);
CPPAD_TESTVECTOR(double) x(n), check(n * n), w(m);
for(j = 0; j < n; j++)
a_x[j] = x[j] = double(j+1);
// declare independent variables and start taping
CppAD::Independent(a_x);
for(ell = 0; ell < n * n; ell++)
check[ell] = 0.0;
for(i = 0; i < m; i++)
{ AD<double> diff = a_x[i+1] - a_x[i];
a_y[i] = 0.5 * diff * diff / double(i+2);
w[i] = double(i+1);
ell = i * n + i;
check[ell] += w[i] / double(i+2);
ell = (i+1) * n + i+1;
check[ell] += w[i] / double(i+2);
ell = (i+1) * n + i;
check[ell] -= w[i] / double(i+2);
ell = i * n + i+1;
check[ell] -= w[i] / double(i+2);
}
// create f: x -> y
CppAD::ADFun<double> f(a_x, a_y);
// determine the sparsity pattern p for Hessian of w^T f
typedef CppAD::vector< std::set<size_t> > SetVector;
SetVector p_r(n);
for(j = 0; j < n; j++)
p_r[j].insert(j);
f.ForSparseJac(n, p_r);
//
SetVector p_s(1);
for(i = 0; i < m; i++)
if( w[i] != 0 )
p_s[0].insert(i);
SetVector p_h = f.RevSparseHes(n, p_s);
// requires the upper triangle of the Hessian
size_t K = 2 * n - 1;
CPPAD_TESTVECTOR(size_t) r(K), c(K);
CPPAD_TESTVECTOR(double) hes(K);
k = 0;
for(i = 0; i < n; i++)
{ r[k] = i;
c[k] = i;
k++;
if( i < n-1 )
{ r[k] = i;
c[k] = i+1;
k++;
}
}
ok &= k == K;
// test computing sparse Hessian
CppAD::sparse_hessian_work work;
size_t n_sweep = f.SparseHessian(x, w, p_h, r, c, hes, work);
ok &= n_sweep == 3;
for(k = 0; k < K; k++)
{ ell = r[k] * n + c[k];
ok &= NearEqual(check[ell], hes[k], eps10, eps10);
ell = c[k] * n + r[k];
ok &= NearEqual(check[ell], hes[k], eps10, eps10);
}
return ok;
}
template <class BaseVector, class BoolVector>
bool bool_case()
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
size_t i, j, k;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 3;
CPPAD_TESTVECTOR(AD<double>) X(n);
for(i = 0; i < n; i++)
X[i] = AD<double> (0);
// declare independent variables and starting recording
CppAD::Independent(X);
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) Y(m);
Y[0] = X[0] * X[0] + X[0] * X[1] + X[1] * X[1] + X[2] * X[2];
// create f: X -> Y and stop tape recording
CppAD::ADFun<double> f(X, Y);
// new value for the independent variable vector
BaseVector x(n);
for(i = 0; i < n; i++)
x[i] = double(i);
// second derivative of y[1]
BaseVector w(m);
w[0] = 1.;
BaseVector h( n * n );
h = f.SparseHessian(x, w);
/*
[ 2 1 0 ]
h = [ 1 2 0 ]
[ 0 0 2 ]
*/
BaseVector check(n * n);
check[0] = 2.; check[1] = 1.; check[2] = 0.;
check[3] = 1.; check[4] = 2.; check[5] = 0.;
check[6] = 0.; check[7] = 0.; check[8] = 2.;
for(k = 0; k < n * n; k++)
ok &= NearEqual(check[k], h[k], eps99, eps99 );
// determine the sparsity pattern p for Hessian of w^T F
BoolVector r(n * n);
for(j = 0; j < n; j++)
{ for(k = 0; k < n; k++)
r[j * n + k] = false;
r[j * n + j] = true;
}
f.ForSparseJac(n, r);
//
BoolVector s(m);
for(i = 0; i < m; i++)
s[i] = w[i] != 0;
BoolVector p = f.RevSparseHes(n, s);
// test passing sparsity pattern
h = f.SparseHessian(x, w, p);
for(k = 0; k < n * n; k++)
ok &= NearEqual(check[k], h[k], eps99, eps99 );
return ok;
}
template <class BaseVector, class SetVector>
bool set_case()
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
size_t i, j, k;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 3;
CPPAD_TESTVECTOR(AD<double>) X(n);
for(i = 0; i < n; i++)
X[i] = AD<double> (0);
// declare independent variables and starting recording
CppAD::Independent(X);
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) Y(m);
Y[0] = X[0] * X[0] + X[0] * X[1] + X[1] * X[1] + X[2] * X[2];
// create f: X -> Y and stop tape recording
CppAD::ADFun<double> f(X, Y);
// new value for the independent variable vector
BaseVector x(n);
for(i = 0; i < n; i++)
x[i] = double(i);
// second derivative of y[1]
BaseVector w(m);
w[0] = 1.;
BaseVector h( n * n );
h = f.SparseHessian(x, w);
/*
[ 2 1 0 ]
h = [ 1 2 0 ]
[ 0 0 2 ]
*/
BaseVector check(n * n);
check[0] = 2.; check[1] = 1.; check[2] = 0.;
check[3] = 1.; check[4] = 2.; check[5] = 0.;
check[6] = 0.; check[7] = 0.; check[8] = 2.;
for(k = 0; k < n * n; k++)
ok &= NearEqual(check[k], h[k], eps99, eps99 );
// determine the sparsity pattern p for Hessian of w^T F
SetVector r(n);
for(j = 0; j < n; j++)
r[j].insert(j);
f.ForSparseJac(n, r);
//
SetVector s(1);
for(i = 0; i < m; i++)
if( w[i] != 0 )
s[0].insert(i);
SetVector p = f.RevSparseHes(n, s);
// test passing sparsity pattern
h = f.SparseHessian(x, w, p);
for(k = 0; k < n * n; k++)
ok &= NearEqual(check[k], h[k], eps99, eps99 );
return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool sparse_hessian(void)
{ bool ok = true;
ok &= rc_tridiagonal();
// ---------------------------------------------------------------
// vector of bool cases
ok &= bool_case< CppAD::vector <double>, CppAD::vectorBool >();
ok &= bool_case< std::vector <double>, CppAD::vector<bool> >();
ok &= bool_case< std::valarray <double>, std::vector<bool> >();
// ---------------------------------------------------------------
// vector of set cases
typedef std::vector< std::set<size_t> > std_vector_set;
typedef CppAD::vector< std::set<size_t> > cppad_vector_set;
//
ok &= set_case< CppAD::vector<double>, std_vector_set >();
ok &= set_case< std::valarray<double>, std_vector_set >();
ok &= set_case< std::vector<double>, cppad_vector_set >();
ok &= set_case< CppAD::vector<double>, cppad_vector_set >();
//
// According to section 26.3.2.3 of the 1998 C++ standard
// a const valarray does not return references to its elements.
// so do not include it in the testing for sets.
// ---------------------------------------------------------------
return ok;
}
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