CppAD: A C++ Algorithmic Differentiation Package  20171217
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template<class Base >
void CppAD::local::forward_pow_op_dir ( size_t  q,
size_t  r,
size_t  i_z,
const addr_t *  arg,
const Base *  parameter,
size_t  cap_order,
Base *  taylor 
)
inline

Prototype for multiple direction forward mode z = pow(x, y) (not used).

Template Parameters
Basebase type for the operator; i.e., this operation was recorded using AD< Base > and computations by this routine are done using type Base.
Parameters
qorder of the Taylor coefficient that we are computing.
ris the number of Taylor coefficient directions that we are computing
i_zvariable index corresponding to the last (primary) result for this operation; i.e. the row index in taylor corresponding to z. Note that there are three results for this operation, below they are referred to as z_0, z_1, z_2 and correspond to 
     z_0 = log(x)
     z_1 = z0 * y
     z_2 = exp(z1)
It follows that the final result is equal to z; i.e., z = z_2 = pow(x, y).
argarg[0] index corresponding to the left operand for this operator; i.e. the index corresponding to x.
arg[1] index corresponding to the right operand for this operator; i.e. the index corresponding to y.
parameterIf x is a parameter, parameter [ arg[0] ] is the value corresponding to x.
If y is a parameter, parameter [ arg[1] ] is the value corresponding to y.
cap_ordermaximum number of orders that will fit in the taylor array.
tpv
We use the notation tpv = (cap_order-1) * r + 1 which is the number of Taylor coefficients per variable
Parameters
taylorInput: If x is a variable, taylor [ arg[0] * tpv + 0 ] is the zero order coefficient corresponding to x and taylor [ arg[0] * tpv + (k-1)*r+1+ell ] for k = 1 , ... , q, ell = 0 , ... , r-1, is the k-th order Taylor coefficient corresponding to x for the ell-th direction.

Input: If y is a variable, taylor [ arg[1] * tpv + 0 ] is the zero order coefficient corresponding to y and taylor [ arg[1] * tpv + (k-1)*r+1+ell ] for k = 1 , ... , q, ell = 0 , ... , r-1, is the k-th order Taylor coefficient corresponding to y for the ell-th direction.

Input: taylor [ (i_z-2+j) * tpv + 0 ], is the zero order coefficient corresponding to z_j and taylor [ (i_z-2+j) * tpv + (k-1)*r+1+ell ], for j = 0, 1, 2 , k = 0 , ... , q-1, ell = 0, ... , r-1, is the k-th order Taylor coefficient corresponding to z_j for the ell-th direction.

Output: taylor [ (i_z-2+j) * tpv + (q-1)*r+1+ell ], for j = 0, 1, 2 , ell = 0, ... , r-1, is the q-th order Taylor coefficient corresponding to z_j for the ell-th direction.
Checked Assertions
  • NumArg(op) == 2
  • NumRes(op) == 3
  • If x is a variable, arg[0] < i_z - 2
  • If y is a variable, arg[1] < i_z - 2
  • 0 < q
  • q < cap_order

Definition at line 1100 of file prototype_op.hpp.