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Up-> CppAD AD ADValued atomic atomic_base atomic_reciprocal.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_reciprocal.cpp

Headings-> Theory sparsity Start Class Definition Constructor forward reverse for_sparse_jac rev_sparse_jac rev_sparse_hes End Class Definition Use Atomic Function ---..Constructor ---..Recording ---..forward ---..reverse ---..for_sparse_jac ---..rev_sparse_jac ---..rev_sparse_hes

# include <cppad/cppad.hpp>
namespace {           // isolate items below to this file
using CppAD::vector;  // abbreviate as vector
//
// a utility to compute the union of two sets.
using CppAD::set_union;
//
class atomic_reciprocal : public CppAD::atomic_base<double> {

public:
     // constructor (could use const char* for name)
     atomic_reciprocal(const std::string& name) :
     // this exmaple only uses set sparsity patterns
     CppAD::atomic_base<double>(name, atomic_base<double>::set_sparsity_enum)
     { }
private:

     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
                vector<bool>&      vy ,
          const vector<double>&    tx ,
                vector<double>&    ty
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
# endif
          assert( n == 1 );
          assert( m == 1 );
          assert( p <= q );

          // return flag
          bool ok = q <= 2;

          // check for defining variable information
          // This case must always be implemented
          if( vx.size() > 0 )
               vy[0] = vx[0];

          // Order zero forward mode.
          // This case must always be implemented
          // y^0 = f( x^0 ) = 1 / x^0
          double f = 1. / tx[0];
          if( p <= 0 )
               ty[0] = f;
          if( q <= 0 )
               return ok;
          assert( vx.size() == 0 );

          // Order one forward mode.
          // This case needed if first order forward mode is used.
          // y^1 = f'( x^0 ) x^1
          double fp = - f / tx[0];
          if( p <= 1 )
               ty[1] = fp * tx[1];
          if( q <= 1 )
               return ok;

          // Order two forward mode.
          // This case needed if second order forward mode is used.
          // Y''(t) = X'(t)^\R{T} f''[X(t)] X'(t) + f'[X(t)] X''(t)
          // 2 y^2  = x^1 * f''( x^0 ) x^1 + 2 f'( x^0 ) x^2
          double fpp  = - 2.0 * fp / tx[0];
          ty[2] = tx[1] * fpp * tx[1] / 2.0 + fp * tx[2];
          if( q <= 2 )
               return ok;

          // Assume we are not using forward mode with order > 2
          assert( ! ok );
          return ok;
     }

     // reverse mode routine called by CppAD
     virtual bool reverse(
          size_t                    q ,
          const vector<double>&    tx ,
          const vector<double>&    ty ,
                vector<double>&    px ,
          const vector<double>&    py
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
# endif
          assert( px.size() == n * (q + 1) );
          assert( py.size() == m * (q + 1) );
          assert( n == 1 );
          assert( m == 1 );
          bool ok = q <= 2;

          double f, fp, fpp, fppp;
          switch(q)
          {     case 0:
               // This case needed if first order reverse mode is used
               // reverse: F^0 ( tx ) = y^0 = f( x^0 )
               f     = ty[0];
               fp    = - f / tx[0];
               px[0] = py[0] * fp;;
               assert(ok);
               break;

               case 1:
               // This case needed if second order reverse mode is used
               // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1
               f      = ty[0];
               fp     = - f / tx[0];
               fpp    = - 2.0 * fp / tx[0];
               px[1]  = py[1] * fp;
               px[0]  = py[1] * fpp * tx[1];
               // reverse: F^0 ( tx ) = y^0 = f( x^0 );
               px[0] += py[0] * fp;
               assert(ok);
               break;

               case 2:
               // This needed if third order reverse mode is used
               // reverse: F^2 ( tx ) = y^2 =
               //          = x^1 * f''( x^0 ) x^1 / 2 + f'( x^0 ) x^2
               f      = ty[0];
               fp     = - f / tx[0];
               fpp    = - 2.0 * fp / tx[0];
               fppp   = - 3.0 * fpp / tx[0];
               px[2]  = py[2] * fp;
               px[1]  = py[2] * fpp * tx[1];
               px[0]  = py[2] * tx[1] * fppp * tx[1] / 2.0 + fpp * tx[2];
               // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1
               px[1] += py[1] * fp;
               px[0] += py[1] * fpp * tx[1];
               // reverse: F^0 ( tx ) = y^0 = f( x^0 );
               px[0] += py[0] * fp;
               assert(ok);
               break;

               default:
               assert(!ok);
          }
          return ok;
     }

     // forward Jacobian set sparsity routine called by CppAD
     virtual bool for_sparse_jac(
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
                vector< std::set<size_t> >&     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 == 1 );
          assert( m == 1 );

          // sparsity for S(x) = f'(x) * R is same as sparsity for R
          s[0] = r[0];

          return true;
     }

     // reverse Jacobian set sparsity routine called by CppAD
     virtual bool rev_sparse_jac(
          size_t                                p  ,
          const vector< std::set<size_t> >&     rt ,
                vector< std::set<size_t> >&     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 == 1 );
          assert( m == 1 );

          // sparsity for S(x)^T = f'(x)^T * R^T is same as sparsity for R^T
          st[0] = rt[0];

          return true;
     }

     // reverse Hessian set sparsity routine called by CppAD
     virtual bool rev_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   s ,
                vector<bool>&                   t ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          const vector< std::set<size_t> >&     u ,
                vector< std::set<size_t> >&     v ,
          const vector<double>&                 x )
     {     // This function needed if using RevSparseHes
# ifndef NDEBUG
          size_t n = vx.size();
          size_t m = s.size();
# endif
          assert( x.size() == n );
          assert( t.size() == n );
          assert( r.size() == n );
          assert( u.size() == m );
          assert( v.size() == n );
          assert( n == 1 );
          assert( m == 1 );

          // There are no cross term second derivatives for this case,
          // so it is not necessary to vx.

          // sparsity for T(x) = S(x) * f'(x) is same as sparsity for S
          t[0] = 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)

          // back propagate the sparsity for U, note f'(x) may be non-zero;
          v[0] = u[0];

          // include forward Jacobian sparsity in Hessian sparsity
          // (note sparsty for f''(x) * R same as for R)
          if( s[0] )
               v[0] = set_union(v[0], r[0] );

          return true;
     }

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

bool reciprocal(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // --------------------------------------------------------------------
     // Create the atomic reciprocal object
     atomic_reciprocal afun("atomic_reciprocal");

     // 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);
     afun(ax, au);        // u = 1 / x

     // now use AD division to invert to invert the operation
     ay[0] = 1.0 / au[0]; // y = 1 / u = x

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

     // 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);

     // 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.RevSparseHes(p, s3);
     ok  &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero
     //
     return ok;
}