Prev Next Index-> contents reference index search external Up-> CppAD AD ADValued atomic atomic_base atomic_set_sparsity.cpp ADValued-> Arithmetic unary_standard_math binary_math CondExp Discrete numeric_limits atomic atomic-> checkpoint atomic_base atomic_base-> atomic_ctor atomic_option atomic_afun atomic_forward atomic_reverse atomic_for_sparse_jac atomic_rev_sparse_jac atomic_for_sparse_hes atomic_rev_sparse_hes atomic_base_clear atomic_get_started.cpp atomic_norm_sq.cpp atomic_reciprocal.cpp atomic_set_sparsity.cpp atomic_tangent.cpp atomic_eigen_mat_mul.cpp atomic_eigen_mat_inv.cpp atomic_eigen_cholesky.cpp atomic_mat_mul.cpp atomic_set_sparsity.cpp Headings-> function set_sparsity_enum Start Class Definition Constructor forward for_sparse_jac rev_sparse_jac for_sparse_hes rev_sparse_hes End Class Definition Test Atomic Function ---..Constructor ---..Recording ---..for_sparse_jac ---..rev_sparse_jac ---..for_sparse_hes ---..rev_sparse_hes ---..Test Result

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Atomic Sparsity with Set Patterns: Example and Test

function
For this example, the atomic function $f : \B{R}^3 \rightarrow \B{R}^2$ is defined by $$f( x ) = \left( \begin{array}{c} x_2 \\ x_0 * x_1 \end{array} \right)$$

set_sparsity_enum
This example only uses set sparsity patterns.

Start Class Definition
# include <cppad/cppad.hpp>
namespace {   // isolate items below to this file
typedef vector< std::set<size_t> > set_vector;  // atomic_sparsity
//
// a utility to compute the union of two sets.
//
class atomic_set_sparsity : public CppAD::atomic_base<double> {

Constructor
public:
// constructor
atomic_set_sparsity(const std::string& name) :
// this exampel only uses set sparsity patterns
{ }
private:

forward
     // 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
     // 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;
}

rev_sparse_jac
     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;
}

for_sparse_hes
     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;
}

rev_sparse_hes
     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 Class Definition

}; // End of atomic_set_sparsity class
}  // End empty namespace


Test Atomic Function
bool set_sparsity(void)
{     bool ok = true;
double eps = 10. * std::numeric_limits<double>::epsilon();

Constructor

// Create the atomic get_started object
atomic_set_sparsity afun("atomic_set_sparsity");


Recording
     size_t n = 3;
size_t m = 2;
for(size_t j = 0; j < n; j++)
ax[j] = double(j + 1);

// declare independent variables and start tape recording

// call user function
afun(ax, ay);

// create f: x -> y and stop tape recording
f.Dependent (ax, ay);  // f(x) = x

// check function value
ok &= NearEqual(ay[0] , ax[2],  eps, eps);
ok &= NearEqual(ay[1] , ax[0] * ax[1],  eps, eps);

for_sparse_jac
     // 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];
}

rev_sparse_jac
     // 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];
}

for_sparse_hes
     // correct Hessian result
set_vector check_h(n);
check_h[0].insert(1);
check_h[1].insert(0);
// 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];
}

rev_sparse_hes
Note the previous call to ForSparseJac above stored its results in f .
     // 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];
}

Test Result

return ok;
}


Input File: example/atomic/set_sparsity.cpp