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First Order Partial Derivative: Driver Routine

Syntax
dy = f.ForOne(xj)

Purpose
We use  F : B^n \rightarrow B^m to denote the AD function corresponding to f. The syntax above sets dy to the partial of  F with respect to  x_j ; i.e.,  \[
dy 
= \D{F}{ x_j } (x) 
= \left[ 
     \D{ F_0 }{ x_j } (x) , \cdots , \D{ F_{m-1} }{ x_j } (x) 
\right]
\] 


f
The object f has prototype
     ADFun<
Basef
Note that the ADFun object f is not const (see ForOne Uses Forward below).

x
The argument x has prototype
     const 
Vector &x
(see Vector below) and its size must be equal to n, the dimension of the domain space for f. It specifies that point at which to evaluate the partial derivative.

j
The argument j has prototype
     size_t 
j
an is less than n, domain space for f. It specifies the component of F for which we are computing the partial derivative.

dy
The result dy has prototype
     
Vector dy
(see Vector below) and its size is  m , the dimension of the range space for f. The value of dy is the partial of  F with respect to  x_j evaluated at x; i.e., for  i = 0 , \ldots , m - 1  \[.
     dy[i] = \D{ F_i }{ x_j } ( x )
\] 


Vector
The type Vector must be a SimpleVector class with elements of type Base. The routine CheckSimpleVector will generate an error message if this is not the case.

ForOne Uses Forward
After each call to Forward , the object f contains the corresponding Taylor coefficients . After ForOne, the previous calls to Forward are undefined.

Example
The routine ForOne is both an example and test. It returns true, if it succeeds and false otherwise.
Input File: cppad/local/for_one.hpp