/*!
Link from user_atomic to forward sparse Jacobian
\copydetails atomic_base::rev_sparse_hes
*/
virtual bool rev_sparse_hes(
const vector<bool>& vx ,
const vector<bool>& s ,
vector<bool>& t ,
size_t q ,
const vector< std::set<size_t> >& r ,
const vector< std::set<size_t> >& u ,
vector< std::set<size_t> >& v )
{ size_t n = v.size();
size_t m = u.size();
CPPAD_ASSERT_UNKNOWN( r.size() == v.size() );
CPPAD_ASSERT_UNKNOWN( s.size() == m );
CPPAD_ASSERT_UNKNOWN( t.size() == n );
bool ok = true;
bool transpose = true;
std::set<size_t>::const_iterator itr;
// compute sparsity pattern for T(x) = S(x) * f'(x)
t = f_.RevSparseJac(1, s);
# ifndef NDEBUG
for(size_t j = 0; j < n; j++)
CPPAD_ASSERT_UNKNOWN( vx[j] || ! t[j] )
# endif
// 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)
// compute sparsity pattern for A(x) = f'(x)^T * U(x)
vector< std::set<size_t> > a(n);
a = f_.RevSparseJac(q, u, transpose);
// set version of s
vector< std::set<size_t> > set_s(1);
CPPAD_ASSERT_UNKNOWN( set_s[0].empty() );
size_t i;
for(i = 0; i < m; i++)
if( s[i] )
set_s[0].insert(i);
// compute sparsity pattern for H(x) = (S(x) * F)''(x) * R
// (store it in v)
f_.ForSparseJac(q, r);
v = f_.RevSparseHes(q, set_s, transpose);
// compute sparsity pattern for V(x) = A(x) + H(x)
for(i = 0; i < n; i++)
{ for(itr = a[i].begin(); itr != a[i].end(); itr++)
{ size_t j = *itr;
CPPAD_ASSERT_UNKNOWN( j < q );
v[i].insert(j);
}
}
// no longer need the forward mode sparsity pattern
// (have to reconstruct them every time)
f_.size_forward_set(0);
return ok;
}
/*!
Link from user_atomic to forward sparse Jacobian
\copydetails atomic_base::rev_sparse_hes
*/
virtual bool rev_sparse_hes(
const vector<bool>& vx ,
const vector<bool>& s ,
vector<bool>& t ,
size_t q ,
const vector<bool>& r ,
const vector<bool>& u ,
vector<bool>& v )
{
CPPAD_ASSERT_UNKNOWN( r.size() == v.size() );
CPPAD_ASSERT_UNKNOWN( s.size() == u.size() / q );
CPPAD_ASSERT_UNKNOWN( t.size() == v.size() / q );
size_t n = t.size();
bool ok = true;
bool transpose = true;
std::set<size_t>::const_iterator itr;
size_t i, j;
// compute sparsity pattern for T(x) = S(x) * f'(x)
t = f_.RevSparseJac(1, s);
# ifndef NDEBUG
for(j = 0; j < n; j++)
CPPAD_ASSERT_UNKNOWN( vx[j] || ! t[j] )
# endif
// 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)
// compute sparsity pattern for A(x) = f'(x)^T * U(x)
vector<bool> a(n * q);
a = f_.RevSparseJac(q, u, transpose);
// compute sparsity pattern for H(x) =(S(x) * F)''(x) * R
// (store it in v)
f_.ForSparseJac(q, r);
v = f_.RevSparseHes(q, s, transpose);
// compute sparsity pattern for V(x) = A(x) + H(x)
for(i = 0; i < n; i++)
{ for(j = 0; j < q; j++)
v[ i * q + j ] |= a[ i * q + j];
}
// no longer need the forward mode sparsity pattern
// (have to reconstruct them every time)
f_.size_forward_set(0);
return ok;
}
bool old_usead_2(void)
{ bool ok = true;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// --------------------------------------------------------------------
// Create the ADFun<doulbe> r_
create_r();
// --------------------------------------------------------------------
// domain and range space vectors
size_t n = 3, m = 2;
vector< AD<double> > au(n), ax(n), ay(m);
au[0] = 0.0; // value of z_0 (t) = t, at t = 0
ax[1] = 0.0; // value of z_1 (t) = t^2/2, at t = 0
au[2] = 1.0; // final t
CppAD::Independent(au);
size_t M = 2; // number of r steps to take
ax[0] = au[0]; // value of z_0 (t) = t, at t = 0
ax[1] = au[1]; // value of z_1 (t) = t^2/2, at t = 0
AD<double> dt = au[2] / double(M); // size of each r step
ax[2] = dt;
for(size_t i_step = 0; i_step < M; i_step++)
{ size_t id = 0; // not used
solve_ode(id, ax, ay);
ax[0] = ay[0];
ax[1] = ay[1];
}
// create f: u -> y and stop tape recording
// y_0(t) = u_0 + t = u_0 + u_2
// y_1(t) = u_1 + u_0 * t + t^2 / 2 = u_1 + u_0 * u_2 + u_2^2 / 2
// where t = u_2
ADFun<double> f;
f.Dependent(au, ay);
// --------------------------------------------------------------------
// Check forward mode results
//
// zero order forward
vector<double> up(n), yp(m);
size_t q = 0;
double u0 = 0.5;
double u1 = 0.25;
double u2 = 0.75;
double check;
up[0] = u0;
up[1] = u1;
up[2] = u2;
yp = f.Forward(q, up);
check = u0 + u2;
ok &= NearEqual( yp[0], check, eps, eps);
check = u1 + u0 * u2 + u2 * u2 / 2.0;
ok &= NearEqual( yp[1], check, eps, eps);
//
// forward mode first derivative w.r.t t
q = 1;
up[0] = 0.0;
up[1] = 0.0;
up[2] = 1.0;
yp = f.Forward(q, up);
check = 1.0;
ok &= NearEqual( yp[0], check, eps, eps);
check = u0 + u2;
ok &= NearEqual( yp[1], check, eps, eps);
//
// forward mode second order Taylor coefficient w.r.t t
q = 2;
up[0] = 0.0;
up[1] = 0.0;
up[2] = 0.0;
yp = f.Forward(q, up);
check = 0.0;
ok &= NearEqual( yp[0], check, eps, eps);
check = 1.0 / 2.0;
ok &= NearEqual( yp[1], check, eps, eps);
// --------------------------------------------------------------------
// reverse mode derivatives of \partial_t y_1 (t)
vector<double> w(m * q), dw(n * q);
w[0 * q + 0] = 0.0;
w[1 * q + 0] = 0.0;
w[0 * q + 1] = 0.0;
w[1 * q + 1] = 1.0;
dw = f.Reverse(q, w);
// derivative of y_1(u) = u_1 + u_0 * u_2 + u_2^2 / 2, w.r.t. u
// is equal deritative of \partial_u2 y_1(u) w.r.t \partial_u2 u
check = u2;
ok &= NearEqual( dw[0 * q + 1], check, eps, eps);
check = 1.0;
ok &= NearEqual( dw[1 * q + 1], check, eps, eps);
check = u0 + u2;
ok &= NearEqual( dw[2 * q + 1], check, eps, eps);
// derivative of \partial_t y_1 w.r.t u = u_0 + t, w.r.t u
check = 1.0;
ok &= NearEqual( dw[0 * q + 0], check, eps, eps);
check = 0.0;
ok &= NearEqual( dw[1 * q + 0], check, eps, eps);
check = 1.0;
ok &= NearEqual( dw[2 * q + 0], check, eps, eps);
// --------------------------------------------------------------------
// forward mode sparsity pattern for the Jacobian
// f_u = [ 1, 0, 1 ]
// [ u_2, 1, u_2 ]
size_t i, j, p = n;
CppAD::vectorBool r(n * p), s(m * p);
// r = identity sparsity pattern
for(i = 0; i < n; i++)
for(j = 0; j < p; j++)
r[i*n +j] = (i == j);
s = f.ForSparseJac(p, r);
ok &= s[ 0 * p + 0] == true;
ok &= s[ 0 * p + 1] == false;
ok &= s[ 0 * p + 2] == true;
ok &= s[ 1 * p + 0] == true;
ok &= s[ 1 * p + 1] == true;
ok &= s[ 1 * p + 2] == true;
// --------------------------------------------------------------------
// reverse mode sparsity pattern for the Jacobian
q = m;
s.resize(q * m);
r.resize(q * n);
// s = identity sparsity pattern
for(i = 0; i < q; i++)
for(j = 0; j < m; j++)
s[i*m +j] = (i == j);
r = f.RevSparseJac(q, s);
ok &= r[ 0 * n + 0] == true;
ok &= r[ 0 * n + 1] == false;
ok &= r[ 0 * n + 2] == true;
ok &= r[ 1 * n + 0] == true;
ok &= r[ 1 * n + 1] == true;
ok &= r[ 1 * n + 2] == true;
// --------------------------------------------------------------------
// Hessian sparsity for y_1 (u) = u_1 + u_0 * u_2 + u_2^2 / 2
s.resize(m);
s[0] = false;
s[1] = true;
r.resize(n * n);
for(i = 0; i < n; i++)
for(j = 0; j < n; j++)
r[ i * n + j ] = (i == j);
CppAD::vectorBool h(n * n);
h = f.RevSparseHes(n, s);
ok &= h[0 * n + 0] == false;
ok &= h[0 * n + 1] == false;
ok &= h[0 * n + 2] == true;
ok &= h[1 * n + 0] == false;
ok &= h[1 * n + 1] == false;
ok &= h[1 * n + 2] == false;
ok &= h[2 * n + 0] == true;
ok &= h[2 * n + 1] == false;
ok &= h[2 * n + 2] == true;
// --------------------------------------------------------------------
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;
}
