CppAD: A C++ Algorithmic Differentiation Package  20171217
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template<class Vector_set >
void CppAD::local::reverse_sparse_hessian_cond_op ( size_t  i_z,
const addr_t *  arg,
size_t  num_par,
bool *  jac_reverse,
Vector_set &  hes_sparsity 
)
inline

Compute reverse Hessian sparsity patterns for op = CExpOp.

This routine is given the sparsity patterns for a function G(z, y, x, ... ) and it uses them to compute the sparsity patterns for 

     H( y, x, w , u , ... ) = G[ z(x,y) , y , x , w , u , ... ]

where y represents the combination of y_0, y_1, y_2, and y_3.

The C++ source code coresponding to this operation is 

     z = CondExpRel(y_0, y_1, y_2, y_3)

where Rel is one of the following: Lt, Le, Eq, Ge, Gt.

Template Parameters
Vector_setis the type used for vectors of sets. It can be either sparse_pack or sparse_list.
Parameters
i_zis the AD variable index corresponding to the variable z.
arg
arg[0] is static cast to size_t from the enum type 
     enum CompareOp {
          CompareLt,
          CompareLe,
          CompareEq,
          CompareGe,
          CompareGt,
          CompareNe
     }
for this operation. Note that arg[0] cannot be equal to CompareNe.

arg[1] & 1
If this is zero, y_0 is a parameter. Otherwise it is a variable.

arg[1] & 2
If this is zero, y_1 is a parameter. Otherwise it is a variable.

arg[1] & 4
If this is zero, y_2 is a parameter. Otherwise it is a variable.

arg[1] & 8
If this is zero, y_3 is a parameter. Otherwise it is a variable.

arg[2 + j ] for j = 0, 1, 2, 3
is the index corresponding to y_j.
num_paris the total number of values in the vector parameter.
Checked Assertions
  • NumArg(CExpOp) == 6
  • NumRes(CExpOp) == 1
  • arg[0] < static_cast<size_t> ( CompareNe )
  • arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters.
  • For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par.
Parameters
jac_reversejac_reverse[i_z] is false (true) if the Jacobian of G with respect to z is always zero (may be non-zero).

jac_reverse[ arg[4] ] If y_2 is a variable, jac_reverse[ arg[4] ] is false (true) if the Jacobian with respect to y_2 is always zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H.

jac_reverse[ arg[5] ] If y_3 is a variable, jac_reverse[ arg[5] ] is false (true) if the Jacobian with respect to y_3 is always zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H.
hes_sparsityThe set with index i_z in hes_sparsity is the Hessian sparsity pattern for the function G where one of the partials is with respect to z.

If y_2 is a variable, the set with index arg[4] in hes_sparsity is the Hessian sparsity pattern where one of the partials is with respect to y_2. On input, this pattern corresponds to the function G. On output, this pattern corresponds to the function H.

If y_3 is a variable, the set with index arg[5] in hes_sparsity is the Hessian sparsity pattern where one of the partials is with respect to y_3. On input, this pattern corresponds to the function G. On output, this pattern corresponds to the function H.

Definition at line 1279 of file cond_op.hpp.

Referenced by rev_hes_sweep().