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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
// ----------------------------------------------------------------------------
/*
{xrst_begin atomic_four_lin_ode_sparsity.cpp}
{xrst_spell
cccc
}
Atomic Linear ODE Sparsity Calculations: Example and Test
#########################################################
Purpose
*******
This example demonstrates calculating sparsity patterns with
the :ref:`atomic_four_lin_ode-name` class.
f(u)
****
For this example, the function :math:`f(u) = z(r, u)` where
:math:`z(t, u)` solves the following ODE
.. math::
z_t (t, u) =
\left( \begin{array}{cccc}
0 & 0 & 0 & 0 \\
u_4 & 0 & 0 & 0 \\
0 & u_5 & 0 & 0 \\
0 & 0 & u_6 & 0 \\
\end{array} \right)
z(t, u)
\W{,}
z(0, u) =
\left( \begin{array}{c}
u_0 \\
u_1 \\
u_2 \\
u_3 \\
\end{array} \right)
Solution
********
The actual solution to this ODE is
.. math::
z(t, u) =
\left( \begin{array}{l}
u_0 \\
u_1 + u_4 u_0 t \\
u_2 + u_5 u_1 t + u_5 u_4 u_0 t^2 / 2 \\
u_3 + u_6 u_2 t + u_6 u_5 u_1 t^2 / 2 + u_6 u_5 u_4 u_0 t^3 / 6
\end{array} \right)
Source
******
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end atomic_four_lin_ode_sparsity.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# include <cppad/example/atomic_four/lin_ode/lin_ode.hpp>
namespace { // BEGIN_EMPTY_NAMESPACE
template <class Scalar, class Vector>
Vector Z(Scalar t, const Vector& u)
{ size_t nz = 4;
Vector z(nz);
//
z[0] = u[0];
z[1] = u[1] + u[4]*u[0]*t;
z[2] = u[2] + u[5]*u[1]*t + u[5]*u[4]*u[0]*t*t/2.0;
z[3] = u[3] + u[6]*u[2]*t + u[6]*u[5]*u[1]*t*t/2.0
+ u[6]*u[5]*u[4]*u[0]*t*t*t/6.0;
//
return z;
}
} // END_EMPTY_NAMESPACE
bool sparsity(void)
{ // ok
bool ok = true;
//
// sparse_rc, AD
typedef CppAD::sparse_rc< CppAD::vector<size_t> > sparse_rc;
using CppAD::AD;
// -----------------------------------------------------------------------
// Record f
// -----------------------------------------------------------------------
//
// afun
CppAD::atomic_lin_ode<double> afun("atomic_lin_ode");
//
// m, r
size_t m = 4;
double r = 2.0;
double step = 0.5;
//
// pattern, transpose
size_t nr = m;
size_t nc = m;
size_t nnz = 3;
CppAD::sparse_rc< CppAD::vector<size_t> > pattern(nr, nc, nnz);
for(size_t k = 0; k < nnz; ++k)
{ size_t i = k + 1;
size_t j = k;
pattern.set(k, i, j);
}
bool transpose = false;
//
// ny, ay
size_t ny = m;
CPPAD_TESTVECTOR( AD<double> ) ay(ny);
//
// nu, au
size_t nu = nnz + m;
CPPAD_TESTVECTOR( AD<double> ) au(nu);
for(size_t j = 0; j < nu; ++j)
au[j] = AD<double>(j + 1);
CppAD::Independent(au);
//
// ax
CPPAD_TESTVECTOR( AD<double> ) ax(nnz + m);
for(size_t k = 0; k < nnz; ++k)
ax[k] = au[m + k];
for(size_t i = 0; i < m; ++i)
ax[nnz + i] = au[i];
//
// ay
size_t call_id = afun.set(r, step, pattern, transpose);
afun(call_id, ax, ay);
//
// f
CppAD::ADFun<double> f(au, ay);
// -----------------------------------------------------------------------
// ar, check_f
CppAD::Independent(au);
AD<double> ar = r;
ay = Z(ar, au);
CppAD::ADFun<double> check_f(au, ay);
// -----------------------------------------------------------------------
// Jacobian Sparsity
// -----------------------------------------------------------------------
//
// eye_sparsity
// nu by nu identitty matrix
sparse_rc eye_sparsity(nu, nu, nu);
for(size_t i = 0; i < nu; ++i)
eye_sparsity.set(i, i, i);
//
// internal_bool
bool internal_bool = false;
//
// jac_sparsity
transpose = false;
bool dependency = false;
sparse_rc jac_sparsity;
f.for_jac_sparsity(
eye_sparsity, transpose, dependency, internal_bool, jac_sparsity
);
//
// check_jac_sparsity
sparse_rc check_jac_sparsity;
check_f.for_jac_sparsity(
eye_sparsity, transpose, dependency, internal_bool, check_jac_sparsity
);
//
// ok
ok &= jac_sparsity == check_jac_sparsity;
// -----------------------------------------------------------------------
// Hessian Sparsity
// -----------------------------------------------------------------------
//
// select_domain
CPPAD_TESTVECTOR(bool) select_domain(nu);
for(size_t j = 0; j < nu; ++j)
select_domain[j] = true;
//
// select_range
CPPAD_TESTVECTOR(bool) select_range(ny);
for(size_t i = 0; i < ny; ++i)
select_range[i] = false;
select_range[1] = true;
//
// hes_sparsity
sparse_rc hes_sparsity;
f.for_hes_sparsity(
select_domain, select_range, internal_bool, hes_sparsity
);
//
// check_hes_sparsity
sparse_rc check_hes_sparsity;
check_f.for_hes_sparsity(
select_domain, select_range, internal_bool, check_hes_sparsity
);
//
// ok
ok &= hes_sparsity == check_hes_sparsity;
// -----------------------------------------------------------------------
return ok;
}
// END C++
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