# include <cppad/cppad.hpp>
namespace { // Begin empty namespace
using CppAD::AD;
using CppAD::ADFun;
using CppAD::vector;
// ----------------------------------------------------------------------
// function that computes reciprocal
ADFun<double>* r_ptr_;
void create_r(void)
{ vector< AD<double> > ax(1), ay(1);
ax[0] = 1;
CppAD::Independent(ax);
ay[0] = 1.0 / ax[0];
r_ptr_ = new ADFun<double>(ax, ay);
}
void destroy_r(void)
{ delete r_ptr_;
r_ptr_ = CPPAD_NULL;
}
// ----------------------------------------------------------------------
// forward mode routine called by CppAD
bool reciprocal_forward(
size_t id ,
size_t k ,
size_t n ,
size_t m ,
const vector<bool>& vx ,
vector<bool>& vy ,
const vector<double>& tx ,
vector<double>& ty
)
{ assert( id == 0 );
assert( n == 1 );
assert( m == 1 );
assert( k == 0 || vx.size() == 0 );
bool ok = true;
vector<double> x_q(1), y_q(1);
// check for special case
if( vx.size() > 0 )
vy[0] = vx[0];
// make sure r_ has proper lower order Taylor coefficients stored
// then compute ty[k]
for(size_t q = 0; q <= k; q++)
{ x_q[0] = tx[q];
y_q = r_ptr_->Forward(q, x_q);
if( q == k )
ty[k] = y_q[0];
assert( q == k || ty[q] == y_q[0] );
}
return ok;
}
// ----------------------------------------------------------------------
// reverse mode routine called by CppAD
bool reciprocal_reverse(
size_t id ,
size_t k ,
size_t n ,
size_t m ,
const vector<double>& tx ,
const vector<double>& ty ,
vector<double>& px ,
const vector<double>& py
)
{ assert( id == 0 );
assert( n == 1 );
assert( m == 1 );
bool ok = true;
vector<double> x_q(1), w(k+1), dw(k+1);
// make sure r_ has proper forward mode coefficients
size_t q;
for(q = 0; q <= k; q++)
{ x_q[0] = tx[q];
# ifdef NDEBUG
r_ptr_->Forward(q, x_q);
# else
vector<double> y_q(1);
y_q = r_ptr_->Forward(q, x_q);
assert( ty[q] == y_q[0] );
# endif
}
for(q = 0; q <=k; q++)
w[q] = py[q];
dw = r_ptr_->Reverse(k+1, w);
for(q = 0; q <=k; q++)
px[q] = dw[q];
return ok;
}
// ----------------------------------------------------------------------
// forward Jacobian sparsity routine called by CppAD
bool reciprocal_for_jac_sparse(
size_t id ,
size_t n ,
size_t m ,
size_t p ,
const vector< std::set<size_t> >& r ,
vector< std::set<size_t> >& s )
{ assert( id == 0 );
assert( n == 1 );
assert( m == 1 );
bool ok = true;
vector< std::set<size_t> > R(1), S(1);
R[0] = r[0];
S = r_ptr_->ForSparseJac(p, R);
s[0] = S[0];
return ok;
}
// ----------------------------------------------------------------------
// reverse Jacobian sparsity routine called by CppAD
bool reciprocal_rev_jac_sparse(
size_t id ,
size_t n ,
size_t m ,
size_t p ,
vector< std::set<size_t> >& r ,
const vector< std::set<size_t> >& s )
{
assert( id == 0 );
assert( n == 1 );
assert( m == 1 );
bool ok = true;
vector< std::set<size_t> > R(p), S(p);
size_t q;
for(q = 0; q < p; q++)
S[q] = s[q];
R = r_ptr_->RevSparseJac(p, S);
for(q = 0; q < p; q++)
r[q] = R[q];
return ok;
}
// ----------------------------------------------------------------------
// reverse Hessian sparsity routine called by CppAD
bool reciprocal_rev_hes_sparse(
size_t id ,
size_t n ,
size_t m ,
size_t p ,
const vector< std::set<size_t> >& r ,
const vector<bool>& s ,
vector<bool>& t ,
const vector< std::set<size_t> >& u ,
vector< std::set<size_t> >& v )
{ // Can just return false if not use RevSparseHes.
assert( id == 0 );
assert( n == 1 );
assert( m == 1 );
bool ok = true;
// compute sparsity pattern for T(x) = S(x) * f'(x)
vector<bool> T(1), S(1);
S[0] = s[0];
T = r_ptr_->RevSparseJac(1, S);
t[0] = T[0];
// compute sparsity pattern for A(x) = U(x)^T * f'(x)
vector<bool> Ut(p), A(p);
size_t q;
for(q = 0; q < p; q++)
Ut[q] = false;
std::set<size_t>::iterator itr;
for(itr = u[0].begin(); itr != u[0].end(); itr++)
Ut[*itr] = true;
A = r_ptr_-> RevSparseJac(p, Ut);
// compute sparsity pattern for H(x) = R^T * (S * F)''(x)
vector<bool> H(p), R(n);
for(q = 0; q < p; q++)
R[q] = false;
for(itr = r[0].begin(); itr != r[0].end(); itr++)
R[*itr] = true;
r_ptr_->ForSparseJac(p, R);
H = r_ptr_->RevSparseHes(p, S);
// compute sparsity pattern for V(x) = A(x)^T + H(x)^T
v[0].clear();
for(q = 0; q < p; q++)
if( A[q] | H[q] )
v[0].insert(q);
return ok;
}
// ---------------------------------------------------------------------
// Declare the AD<double> routine reciprocal(id, ax, ay)
CPPAD_USER_ATOMIC(
reciprocal ,
CppAD::vector ,
double ,
reciprocal_forward ,
reciprocal_reverse ,
reciprocal_for_jac_sparse ,
reciprocal_rev_jac_sparse ,
reciprocal_rev_hes_sparse
)
} // End empty namespace
bool old_usead_1(void)
{ bool ok = true;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// --------------------------------------------------------------------
// Create the ADFun<doulbe> r_
create_r();
// --------------------------------------------------------------------
// Create the function f(x)
//
// domain space vector
size_t n = 1;
double x0 = 0.5;
vector< AD<double> > ax(n);
ax[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(ax);
// range space vector
size_t m = 1;
vector< AD<double> > ay(m);
// call user function and store reciprocal(x) in au[0]
vector< AD<double> > au(m);
size_t id = 0; // not used
reciprocal(id, ax, au); // u = 1 / x
// call user function and store reciprocal(u) in ay[0]
reciprocal(id, au, ay); // y = 1 / u = x
// create f: x -> y and stop tape recording
ADFun<double> f;
f.Dependent(ax, ay); // f(x) = x
// --------------------------------------------------------------------
// Check function value results
//
// check function value
double check = x0;
ok &= NearEqual( Value(ay[0]) , check, eps, eps);
// check zero order forward mode
size_t q;
vector<double> x_q(n), y_q(m);
q = 0;
x_q[0] = x0;
y_q = f.Forward(q, x_q);
ok &= NearEqual(y_q[0] , check, eps, eps);
// check first order forward mode
q = 1;
x_q[0] = 1;
y_q = f.Forward(q, x_q);
check = 1.;
ok &= NearEqual(y_q[0] , check, eps, eps);
// check second order forward mode
q = 2;
x_q[0] = 0;
y_q = f.Forward(q, x_q);
check = 0.;
ok &= NearEqual(y_q[0] , check, eps, eps);
// --------------------------------------------------------------------
// Check reverse mode results
//
// third order reverse mode
q = 3;
vector<double> w(m), dw(n * q);
w[0] = 1.;
dw = f.Reverse(q, w);
check = 1.;
ok &= NearEqual(dw[0] , check, eps, eps);
check = 0.;
ok &= NearEqual(dw[1] , check, eps, eps);
ok &= NearEqual(dw[2] , check, eps, eps);
// --------------------------------------------------------------------
// forward mode sparstiy pattern
size_t p = n;
CppAD::vectorBool r1(n * p), s1(m * p);
r1[0] = true; // compute sparsity pattern for x[0]
s1 = f.ForSparseJac(p, r1);
ok &= s1[0] == true; // f[0] depends on x[0]
// --------------------------------------------------------------------
// reverse mode sparstiy pattern
q = m;
CppAD::vectorBool s2(q * m), r2(q * n);
s2[0] = true; // compute sparsity pattern for f[0]
r2 = f.RevSparseJac(q, s2);
ok &= r2[0] == true; // f[0] depends on x[0]
// --------------------------------------------------------------------
// Hessian sparsity (using previous ForSparseJac call)
CppAD::vectorBool s3(m), h(p * n);
s3[0] = true; // compute sparsity pattern for f[0]
h = f.RevSparseJac(p, s3);
ok &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero
// -----------------------------------------------------------------
// Free all memory associated with the object r_ptr
destroy_r();
// -----------------------------------------------------------------
// Free all temporary work space associated with old_atomic objects.
// (If there are future calls to user atomic functions, they will
// create new temporary work space.)
CppAD::user_atomic<double>::clear();
return ok;
}
