Prev Next

@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@
Jacobian: Driver Routine

jac = f.Jacobian(x)

We use @(@ F : B^n \rightarrow B^m @)@ to denote the AD function corresponding to f . The syntax above sets jac to the Jacobian of F evaluated at x ; i.e., @[@ jac = F^{(1)} (x) @]@

The object f has prototype
Note that the ADFun object f is not const (see Forward or Reverse below).

The argument x has prototype
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 Jacobian.

The result jac has prototype
Vector jac
(see Vector below) and its size is @(@ m * n @)@; i.e., the product of the domain and range dimensions for f . For @(@ i = 0 , \ldots , m - 1 @)@ and @(@ j = 0 , \ldots , n - 1 @)@ @[@ . jac[ i * n + j ] = \D{ F_i }{ x_j } ( x ) @]@

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.

Forward or Reverse
This will use order zero Forward mode and either order one Forward or order one Reverse to compute the Jacobian (depending on which it estimates will require less work). After each call to Forward , the object f contains the corresponding Taylor coefficients . After a call to Jacobian, the zero order Taylor coefficients correspond to f.Forward(0, x) and the other coefficients are unspecified.

The routine Jacobian is both an example and test. It returns true, if it succeeds and false otherwise.
Input File: cppad/core/jacobian.hpp