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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
// ----------------------------------------------------------------------------
# include <cppad/cppad.hpp>
namespace {
typedef CPPAD_TESTVECTOR(size_t) svector;
typedef CppAD::sparse_rc<svector> sparsity;
//
using CppAD::AD;
typedef CPPAD_TESTVECTOR(AD<double>) avector;
// ========================================================================
// algorithm that will be checkpointed
void g_algo(const avector& u, avector& v)
{ for(size_t j = 0; j < size_t( u.size() ); ++j)
v[0] += u[j];
}
// will be a pointer to atomic version of g_algo
CppAD::checkpoint<double>* atom_g = nullptr;
// ------------------------------------------------------------------------
// record function
void record_function(
bool optimize ,
size_t& n ,
size_t& m ,
CppAD::ADFun<double>& fun )
{
// declare checkpoint function
avector au(3), av(1);
for(size_t j = 0; j < 3; j++)
au[j] = AD<double>(j);
if( atom_g == nullptr )
atom_g = new CppAD::checkpoint<double>("atom_g", g_algo, au, av);
//
// domain space vector
n = 6;
CPPAD_TESTVECTOR(AD<double>) ax(n);
for(size_t j = 0; j < n; j++)
ax[j] = AD<double>(j);
// declare independent variables and start recording
CppAD::Independent(ax);
// range space vector
m = 8;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = 0.0; // does not depend on anything
ay[1] = ax[1]; // is equal to an independent variable
AD<double> sum = ax[1] + ax[1]; // only uses ax[1]
ay[2] = sum * ax[2]; // operator(variable, variable)
ay[3] = sin(ax[1]); // operator(variable)
ay[4] = ax[4] / 2.0; // operator(variable, parameter)
ay[5] = 2.0 / ax[3]; // operator(parameter, variable)
//
// a atomic function call
for(size_t j = 0; j < size_t(au.size()); ++j)
au[j] = ax[j + 3];
(*atom_g)(au, av);
ay[6] = av[0];
//
// variable + variable operatros that optimizer will change to
// cumulative summation
ay[7] = 0.0;
for(size_t j = 0; j < n; ++j)
ay[7] += ax[j];
//
// create f: x -> y and stop tape recording
fun.Dependent(ax, ay);
//
if( optimize )
fun.optimize();
return;
}
// ------------------------------------------------------------------------
bool compare_subgraph_sparsity(
CppAD::sparse_rc<svector> subgraph ,
CppAD::sparse_rc<svector> check )
{ bool ok = true;
// check nnz
size_t sub_nnz = subgraph.nnz();
size_t chk_nnz = check.nnz();
ok &= sub_nnz == chk_nnz;
size_t nnz = std::min(sub_nnz, chk_nnz);
// row major order
svector sub_order = subgraph.row_major();
svector chk_order = check.row_major();
// check row indices
const svector& sub_row( subgraph.row() );
const svector& chk_row( check.row() );
for(size_t k = 0; k < nnz; k++)
ok &= sub_row[ sub_order[k] ] == chk_row[ chk_order[k] ];
// check column indices
const svector& sub_col( subgraph.col() );
const svector& chk_col( check.col() );
for(size_t k = 0; k < nnz; k++)
ok &= sub_col[ sub_order[k] ] == chk_col[ chk_order[k] ];
/*
std::cout << "\nsub_row = " << sub_row << "\n";
std::cout << "chk_row = " << chk_row << "\n";
std::cout << "sub_col = " << sub_col << "\n";
std::cout << "chk_col = " << chk_col << "\n";
*/
return ok;
}
// ------------------------------------------------------------------------
bool test_subgraph_sparsity(bool optimize)
{ bool ok = true;
// create f: x -> y
size_t n, m;
CppAD::ADFun<double> f;
record_function(optimize, n, m, f);
// --------------------------------------------------------------------
// Entire sparsity pattern
// compute sparsity using subgraph_sparsity
CPPAD_TESTVECTOR(bool) select_domain(n), select_range(m);
for(size_t j = 0; j < n; j++)
select_domain[j] = true;
for(size_t i = 0; i < m; i++)
select_range[i] = true;
bool transpose = false;
sparsity subgraph_out;
f.subgraph_sparsity(
select_domain, select_range, transpose, subgraph_out
);
// compute sparsity using for_jac_sparsity
sparsity pattern_in(n, n, n);
for(size_t k = 0; k < n; k++)
pattern_in.set(k, k, k);
bool dependency = true;
bool internal_bool = true;
sparsity check_out;
f.for_jac_sparsity(
pattern_in, transpose, dependency, internal_bool, check_out
);
// compare results
ok &= compare_subgraph_sparsity(subgraph_out, check_out);
// --------------------------------------------------------------------
// Exclude ax[1]
select_domain[1] = false;
f.subgraph_sparsity(
select_domain, select_range, transpose, subgraph_out
);
pattern_in.resize(n, n, n-1);
for(size_t k = 0; k < n-1; k++)
{ if( k < 1 )
pattern_in.set(k, k, k);
else
pattern_in.set(k, k+1, k+1);
}
f.for_jac_sparsity(
pattern_in, transpose, dependency, internal_bool, check_out
);
// compare results
ok &= compare_subgraph_sparsity(subgraph_out, check_out);
return ok;
}
// ------------------------------------------------------------------------
bool compare_subgraph_reverse(
const CPPAD_TESTVECTOR(size_t)& col ,
const CPPAD_TESTVECTOR(double)& dw ,
const CPPAD_TESTVECTOR(double)& check )
{ bool ok = true;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
//
size_t n = size_t( check.size() );
//
// check order in col
for(size_t c = 1; c < size_t( col.size() ); c++)
ok &= col[c] > col[c-1];
//
size_t c = 0;
for(size_t j = 1; j < n; j++)
{ while( c < size_t( col.size() ) && col[c] < j )
++c;
if( c < size_t( col.size() ) && col[c] == j )
ok &= CppAD::NearEqual(dw[j], check[j], eps99, eps99);
else
ok &= CppAD::NearEqual(0.0, check[j], eps99, eps99);
}
return ok;
}
// ------------------------------------------------------------------------
bool test_subgraph_reverse(bool optimize)
{ bool ok = true;
// create f: x -> y
size_t n, m;
CppAD::ADFun<double> f;
record_function(optimize, n, m, f);
// value of x at which to compute derivatives
CPPAD_TESTVECTOR(double) x(n);
for(size_t j = 0; j < n; ++j)
x[j] = double(n) / double(j + 1);
f.Forward(0, x);
// exclude x[4] from the derivative calculations
CPPAD_TESTVECTOR(bool) select_domain(n);
for(size_t j = 0; j < n; j++)
select_domain[j] = true;
select_domain[4] = false;
f.subgraph_reverse(select_domain);
// vector used to check results
CPPAD_TESTVECTOR(double) check(n);
for(size_t j = 0; j < n; j++)
check[j] = 0.0;
// derivative of y[0]
CPPAD_TESTVECTOR(size_t) col;
CPPAD_TESTVECTOR(double) dw;
size_t q = 1;
size_t ell = 0;
f.subgraph_reverse(q, ell, col, dw);
ok &= compare_subgraph_reverse(col, dw, check);
//
// derivative of y[1]
check[1] = 1.0;
ell = 1;
f.subgraph_reverse(q, ell, col, dw);
ok &= compare_subgraph_reverse(col, dw, check);
//
// derivative of y[2]
check[1] = 2.0 * x[2];
check[2] = 2.0 * x[1];
ell = 2;
f.subgraph_reverse(q, ell, col, dw);
ok &= compare_subgraph_reverse(col, dw, check);
//
// derivative of y[3]
check[1] = cos( x[1] );
check[2] = 0.0;
ell = 3;
f.subgraph_reverse(q, ell, col, dw);
ok &= compare_subgraph_reverse(col, dw, check);
//
// derivative of y[4] (x[4] is not selected)
check[1] = 0.0;
ell = 4;
f.subgraph_reverse(q, ell, col, dw);
ok &= compare_subgraph_reverse(col, dw, check);
//
// derivative of y[5]
check[3] = -2.0 / (x[3] * x[3]);
ell = 5;
f.subgraph_reverse(q, ell, col, dw);
ok &= compare_subgraph_reverse(col, dw, check);
//
// derivative of y[6] (x[4] is not selected)
check[3] = 1.0;
check[5] = 1.0;
ell = 6;
f.subgraph_reverse(q, ell, col, dw);
ok &= compare_subgraph_reverse(col, dw, check);
//
// derivative of y[7] (x[4] is not selected)
for(size_t j = 0; j < n; ++j)
check[j] = 1.0;
check[4] = 0.0;
ell = 7;
f.subgraph_reverse(q, ell, col, dw);
ok &= compare_subgraph_reverse(col, dw, check);
//
return ok;
}
}
bool subgraph_1(void)
{ bool ok = true;
bool optimize = false;
ok &= test_subgraph_sparsity(optimize);
ok &= test_subgraph_reverse(optimize);
optimize = true;
ok &= test_subgraph_sparsity(optimize);
ok &= test_subgraph_reverse(optimize);
//
ok &= atom_g != nullptr;
delete atom_g;
//
return ok;
}
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