CppAD: A C++ Algorithmic Differentiation Package  20171217
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template<class Base >
void CppAD::local::reverse_cosh_op ( size_t  d,
size_t  i_z,
size_t  i_x,
size_t  cap_order,
const Base *  taylor,
size_t  nc_partial,
Base *  partial 
)
inline

Compute reverse mode partial derivatives for result of op = CoshOp.

The C++ source code corresponding to this operation is

     z = cosh(x)

The auxillary result is

     y = sinh(x)

The value of y is computed along with the value of z.

This routine is given the partial derivatives of a function G( z , y , x , w , ... ) and it uses them to compute the partial derivatives of

     H( x , w , u , ... ) = G[ z(x) , y(x), x , w , u , ... ]
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
dhighest order Taylor coefficient that we are computing the partial derivatives with respect to.
i_zvariable index corresponding to the last (primary) result for this operation; i.e. the row index in taylor to z. The auxillary result is called y and has index i_z - 1.
i_xvariable index corresponding to the argument for this operation; i.e. the row index in taylor corresponding to x.
cap_ordermaximum number of orders that will fit in the taylor array.
taylortaylor [ i_x * cap_order + k ] for k = 0 , ... , d is the k-th order Taylor coefficient corresponding to x.
taylor [ i_z * cap_order + k ] for k = 0 , ... , d is the k-th order Taylor coefficient corresponding to z.
taylor [ ( i_z - 1) * cap_order + k ] for k = 0 , ... , d is the k-th order Taylor coefficient corresponding to the auxillary variable y.
nc_partialnumber of colums in the matrix containing all the partial derivatives.
partialInput: partial [ i_x * nc_partial + k ] for k = 0 , ... , d is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for x.
Input: partial [ i_z * nc_partial + k ] for k = 0 , ... , d is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for z.
Input: partial [ ( i_z - 1) * nc_partial + k ] for k = 0 , ... , d is the partial derivative of G( z , x , w , u , ... ) with respect to the k-th order Taylor coefficient for the auxillary variable y.
Output: partial [ i_x * nc_partial + k ] for k = 0 , ... , d is the partial derivative of H( x , w , u , ... ) with respect to the k-th order Taylor coefficient for x.
Output: partial [ ( i_z - j ) * nc_partial + k ] for j = 0 , 1 , and for k = 0 , ... , d may be used as work space; i.e., may change in an unspecified manner.
Checked Assumptions
  • NumArg(op) == 1
  • NumRes(op) == 2
  • i_x + 1 < i_z
  • d < cap_order
  • d < nc_partial

Definition at line 186 of file cosh_op.hpp.

Referenced by reverse_sweep().