atomic_three_hes_sparsity¶

Atomic Function Hessian Sparsity Patterns¶

Syntax¶

ok = afun . hes_sparsity (
      parameter_x , type_x , select_x , select_y , pattern_out
)

Prototype¶

template <class Base>
bool atomic_three<Base>::hes_sparsity(
   const vector<Base>&                     parameter_x  ,
   const vector<ad_type_enum>&             type_x       ,
   const vector<bool>&                     select_x     ,
   const vector<bool>&                     select_y     ,
   sparse_rc< vector<size_t> >&            pattern_out  )

Implementation¶

This function must be defined if afun is used to define an ADFun object f , and Hessian sparsity patterns are computed for f .

Base¶

See Base .

parameter_x¶

See parameter_x .

type_x¶

See type_x .

select_x¶

This argument has size equal to the number of arguments to this atomic function; i.e. the size of ax . It specifies which domain components are included in the calculation of pattern_out . If select_x [ j ] is false, then there will be no indices k such that either of the following hold:

pattern_out . row ()[ k ] == j

pattern_out . col ()[ k ] == j

select_y¶

This argument has size equal to the number of results to this atomic function; i.e. the size of ay . It specifies which range component functions \(g_i (x)\) are included in of pattern_out .

pattern_out¶

This input value of pattern_out does not matter. Upon return it is the union, with respect to i such that select_y [ i ] is true, of the sparsity pattern for Hessian of \(g_i (x)\). To be specific, there are non-negative indices i , r , c , and k such that

pattern_out . row ()[ k ] == r

pattern_out . col ()[ k ] == c

if and only if select_y [ i ] is true, select_x [ r ] is true, select_x [ c ] is true, and

\[\partial_{x(r)} \partial_{x(c)} g_i(x)\]

is possibly non-zero. Note that the sparsity pattern should be symmetric.

ok¶

If this calculation succeeded, ok is true. Otherwise it is false.

Examples¶

The file atomic_three_hes_sparsity.cpp contains an example and test that uses this routine.