ForOne

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First Order Partial Derivative: Driver Routine

Syntax

dy = f . ForOne ( x , j )

Purpose

We use \(F : \B{R}^n \rightarrow \B{R}^m\) 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 < Base > f

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 a call to ForOne , the zero order Taylor coefficients correspond to f . Forward (0, x ) and the other coefficients are unspecified.

Example

The routine ForOne is both an example and test. It returns true , if it succeeds and false otherwise.