Arbitrary order, one direction, forward mode Taylor coefficieints.
- Template Parameters:
-
Base | The type used during the forward mode computations; i.e., the corresponding recording of operations used the type AD<Base>. |
Vector | is a Simple Vector class with eleements of type Base. |
- Parameters:
-
q | is the hightest order for this forward mode computation; i.e., after this calculation there will be q+1 Taylor coefficients per variable. |
xq | contains Taylor coefficients for the independent variables. The size of xq must either be n or (q+1)*n , We define p = q + 1 - xq.size()/n . For j = 0 , ... , n-1 , k = p, ... , q , are xq[ (q+1-p)*j + k - p ] is the k-th order coefficient for the j-th independent variable. |
s | Is the stream where output corresponding to PriOp operations will written. |
- Returns:
- contains Taylor coefficients for the independent variables. The size of the return value y is
m*(q+1-p)
. For i = 0, ... , m-1
, k = p, ..., q
, y[(q+1-p)*i + (k-p)]
is the k-th order coefficient for the i-th dependent variable.
- taylor_
- The Taylor coefficients up to order p-1 are inputs and the coefficents from order p through q are outputs. Let
N = num_var_tape_
, and C = cap_order_taylor_
. Note that for i = 1 , ..., N-1
, k = 0 , ..., q
, taylor_[ C*i + k ]
is the k-th order cofficent, for the i-th varaible on the tape. (The first independent variable has index one on the tape and there is no variable with index zero.)
Definition at line 78 of file forward.hpp.