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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
// ----------------------------------------------------------------------------
/*
Atomic function
g( x ) = [ x_2, x_0 * x_1 ]
\] $$
*/
# include <cppad/cppad.hpp>
namespace { // isolate items below to this file
using CppAD::vector; // vector
typedef vector< std::set<size_t> > set_vector; // atomic_sparsity
//
// a utility to compute the union of two sets.
using CppAD::set_union;
//
class atomic_set_sparsity : public CppAD::atomic_base<double> {
public:
// constructor
atomic_set_sparsity(const std::string& name) :
// this example only uses set sparsity patterns
CppAD::atomic_base<double>(name, set_sparsity_enum )
{ }
private:
// forward
virtual bool forward(
size_t p ,
size_t q ,
const vector<bool>& vx ,
vector<bool>& vy ,
const vector<double>& tx ,
vector<double>& ty
)
{
size_t n = tx.size() / (q + 1);
# ifndef NDEBUG
size_t m = ty.size() / (q + 1);
# endif
assert( n == 3 );
assert( m == 2 );
// only order zero
bool ok = q == 0;
if( ! ok )
return ok;
// check for defining variable information
if( vx.size() > 0 )
{ ok &= vx.size() == n;
vy[0] = vx[2];
vy[1] = vx[0] || vx[1];
}
// Order zero forward mode.
// y[0] = x[2], y[1] = x[0] * x[1]
if( p <= 0 )
{ ty[0] = tx[2];
ty[1] = tx[0] * tx[1];
}
return ok;
}
// for_sparse_jac
virtual bool for_sparse_jac(
size_t p ,
const set_vector& r ,
set_vector& s ,
const vector<double>& x )
{ // This function needed if using f.ForSparseJac
# ifndef NDEBUG
size_t n = r.size();
size_t m = s.size();
# endif
assert( n == x.size() );
assert( n == 3 );
assert( m == 2 );
// sparsity for S(x) = f'(x) * R = [ 0, 0, 1 ] * R
s[0] = r[2];
// s[1] = union(r[0], r[1])
s[1] = set_union(r[0], r[1]);
//
return true;
}
virtual bool rev_sparse_jac(
size_t p ,
const set_vector& rt ,
set_vector& st ,
const vector<double>& x )
{ // This function needed if using RevSparseJac or optimize
# ifndef NDEBUG
size_t n = st.size();
size_t m = rt.size();
# endif
assert( n == x.size() );
assert( n == 3 );
assert( m == 2 );
// [ 0, x1 ]
// sparsity for S(x)^T = f'(x)^T * R^T = [ 0, x0 ] * R^T
// [ 1, 0 ]
st[0] = rt[1];
st[1] = rt[1];
st[2] = rt[0];
return true;
}
virtual bool for_sparse_hes(
const vector<bool>& vx,
const vector<bool>& r ,
const vector<bool>& s ,
set_vector& h ,
const vector<double>& x )
{
size_t n = r.size();
# ifndef NDEBUG
size_t m = s.size();
# endif
assert( x.size() == n );
assert( h.size() == n );
assert( n == 3 );
assert( m == 2 );
// initialize h as empty
for(size_t i = 0; i < n; i++)
h[i].clear();
// only f_1 has a non-zero hessian
if( ! s[1] )
return true;
// only the cross term between x[0] and x[1] is non-zero
if( ! ( r[0] && r[1] ) )
return true;
// set the possibly non-zero terms in the hessian
h[0].insert(1);
h[1].insert(0);
return true;
}
virtual bool rev_sparse_hes(
const vector<bool>& vx,
const vector<bool>& s ,
vector<bool>& t ,
size_t p ,
const set_vector& r ,
const set_vector& u ,
set_vector& v ,
const vector<double>& x )
{ // This function needed if using RevSparseHes
# ifndef NDEBUG
size_t m = s.size();
size_t n = t.size();
# endif
assert( x.size() == n );
assert( r.size() == n );
assert( u.size() == m );
assert( v.size() == n );
assert( n == 3 );
assert( m == 2 );
// sparsity for T(x) = S(x) * f'(x) = S(x) * [ 0, 0, 1 ]
// [ x1, x0, 0 ]
t[0] = s[1];
t[1] = s[1];
t[2] = s[0];
// V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R
// U(x) = g''(y) * f'(x) * R
// S(x) = g'(y)
// [ 0, x1 ]
// sparsity for W(x) = f'(x)^T * U(x) = [ 0, x0 ] * U(x)
// [ 1, 0 ]
v[0] = u[1];
v[1] = u[1];
v[2] = u[0];
//
// [ 0, 1, 0 ]
// sparsity for V(x) = W(x) + S_1 (x) * [ 1, 0, 0 ] * R
// [ 0, 0, 0 ]
if( s[1] )
{ // v[0] = union( v[0], r[1] )
v[0] = set_union(v[0], r[1]);
// v[1] = union( v[1], r[0] )
v[1] = set_union(v[1], r[0]);
}
return true;
}
}; // End of atomic_set_sparsity class
// f(u) = g( u_0 + u_1 , u_0 + u_1 , u_2 )
// = [ u_2 , (u_0 + u_1)^2 ]
bool test_one(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * std::numeric_limits<double>::epsilon();
// Create the atomic get_started object
atomic_set_sparsity afun("atomic_set_sparsity");
size_t n = 3;
size_t m = 2;
vector< AD<double> > au(n), ay(m);
for(size_t j = 0; j < n; j++)
au[j] = double(j + 1);
// declare independent variables and start tape recording
CppAD::Independent(au);
// ax
vector< AD<double> > ax(n);
ax[0] = au[0] + au[1];
ax[1] = au[0] + au[1];
ax[2] = au[2];
// call atomic function
afun(ax, ay);
// create f: u -> y and stop tape recording
CppAD::ADFun<double> f(au, ay);
// check function value
ok &= NearEqual(ay[0] , au[2], eps, eps);
ok &= NearEqual(ay[1] , (au[0] + au[1]) * (au[0] + au[1]), eps, eps);
// correct Jacobian result
set_vector check_s(m);
check_s[0].insert(2);
check_s[1].insert(0);
check_s[1].insert(1);
// compute and test forward mode
{ set_vector r(n), s(m);
for(size_t i = 0; i < n; i++)
r[i].insert(i);
s = f.ForSparseJac(n, r);
for(size_t i = 0; i < m; i++)
ok &= s[i] == check_s[i];
}
// compute and test reverse mode
{ set_vector r(m), s(m);
for(size_t i = 0; i < m; i++)
r[i].insert(i);
s = f.RevSparseJac(m, r);
for(size_t i = 0; i < m; i++)
ok &= s[i] == check_s[i];
}
// correct Hessian result for w_0 * f_0 (u) + w_1 * f_1(u)
set_vector check_h(n);
check_h[0].insert(0);
check_h[0].insert(1);
check_h[1].insert(0);
check_h[1].insert(1);
// compute and test forward mode
{ set_vector r(1), s(1), h(n);
for(size_t i = 0; i < m; i++)
s[0].insert(i);
for(size_t j = 0; j < n; j++)
r[0].insert(j);
h = f.ForSparseHes(r, s);
for(size_t i = 0; i < n; i++)
ok &= h[i] == check_h[i];
}
// compute and test reverse mode
{ set_vector s(1), h(n);
for(size_t i = 0; i < m; i++)
s[0].insert(i);
h = f.RevSparseHes(n, s);
for(size_t i = 0; i < n; i++)
ok &= h[i] == check_h[i];
}
return ok;
}
// f(u) = g( u_0 + u_1 , u_1 + u_2 , u_2 + u_0 )
// = [ u_2 + u_0 , (u_0 + u_1)*(u_1 + u_2) ]
bool test_two(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * std::numeric_limits<double>::epsilon();
// Create the atomic get_started object
atomic_set_sparsity afun("atomic_set_sparsity");
size_t n = 3;
size_t m = 2;
vector< AD<double> > au(n), ay(m);
for(size_t j = 0; j < n; j++)
au[j] = double(j + 1);
// declare independent variables and start tape recording
CppAD::Independent(au);
// ax
vector< AD<double> > ax(n);
ax[0] = au[0] + au[1];
ax[1] = au[1] + au[2];
ax[2] = au[2] + au[0];
// call atomic function
afun(ax, ay);
// create f: u -> y and stop tape recording
CppAD::ADFun<double> f(au, ay);
// check function value
ok &= NearEqual(ay[0] , au[2] + au[0], eps, eps);
ok &= NearEqual(ay[1] , (au[0] + au[1]) * (au[1] + au[2]), eps, eps);
// correct Jacobian result
set_vector check_s(m);
check_s[0].insert(2);
check_s[0].insert(0);
check_s[1].insert(0);
check_s[1].insert(1);
check_s[1].insert(2);
// compute and test forward mode
{ set_vector r(n), s(m);
for(size_t i = 0; i < n; i++)
r[i].insert(i);
s = f.ForSparseJac(n, r);
for(size_t i = 0; i < m; i++)
ok &= s[i] == check_s[i];
}
// compute and test reverse mode
{ set_vector r(m), s(m);
for(size_t i = 0; i < m; i++)
r[i].insert(i);
s = f.RevSparseJac(m, r);
for(size_t i = 0; i < m; i++)
ok &= s[i] == check_s[i];
}
// ----------------------------------------------------------------------
// correct Hessian result for f_0 (u)
set_vector check_h(n), s(1);
s[0].insert(0);
// compute and test forward mode
{ set_vector r(1), h(n);
for(size_t j = 0; j < n; j++)
r[0].insert(j);
h = f.ForSparseHes(r, s);
for(size_t i = 0; i < n; i++)
ok &= h[i] == check_h[i];
}
// compute and test reverse mode
{ set_vector h(n);
h = f.RevSparseHes(n, s);
for(size_t i = 0; i < n; i++)
ok &= h[i] == check_h[i];
}
// ----------------------------------------------------------------------
// correct Hessian result for f_1 (u)
s[0].clear();
s[0].insert(1);
check_h[0].insert(1);
check_h[0].insert(2);
check_h[1].insert(0);
check_h[1].insert(1);
check_h[1].insert(2);
check_h[2].insert(0);
check_h[2].insert(1);
// compute and test forward mode
{ set_vector r(1), h(n);
for(size_t j = 0; j < n; j++)
r[0].insert(j);
h = f.ForSparseHes(r, s);
for(size_t i = 0; i < n; i++)
ok &= h[i] == check_h[i];
}
// compute and test reverse mode
{ set_vector h(n);
h = f.RevSparseHes(n, s);
for(size_t i = 0; i < n; i++)
ok &= h[i] == check_h[i];
}
return ok;
}
} // End empty namespace
bool atomic_sparsity(void)
{ bool ok = true;
ok &= test_one();
ok &= test_two();
return ok;
}
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