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Up-> CppAD ADFun Drivers Jacobian

CppAD-> Install Introduction AD ADFun multi_thread library cppad_ipopt_nlp Example preprocessor Appendix

ADFun-> Independent FunConstruct Dependent abort_recording seq_property FunEval Drivers FunCheck optimize

Drivers-> Jacobian ForOne RevOne Hessian ForTwo RevTwo sparse_jacobian sparse_hessian

Jacobian-> Jacobian.cpp

Headings-> Syntax Purpose f x jac Vector Forward or Reverse Example

Jacobian: Driver Routine
Syntax
jac = f.Jacobian(x)

Purpose
We use $\mathit{F}:{\mathit{B}}^{\mathit{n}}\to {\mathit{B}}^{\mathit{m}}$ to denote the AD function corresponding to f. The syntax above sets jac to the Jacobian of F evaluated at x; i.e., $$\mathit{jac}={\mathit{F}}^{(1)}(\mathit{x})$$
f
The object f has prototype
     ADFun<Base> f
Note that the ADFun object f is not const (see Forward or Reverse 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 Jacobian.

jac
The result jac has prototype
     Vector jac
(see Vector below) and its size is $\mathit{m}*\mathit{n}$ ; i.e., the product of the domain and range dimensions for f. For $\mathit{i}=0,\dots ,\mathit{m}-1$ and $\mathit{j}=0,\dots ,\mathit{n}-1$ $$.\mathit{jac}[\mathit{i}*\mathit{n}+\mathit{j}]=\frac{\partial {\mathit{F}}_{\mathit{i}}}{\partial {\mathit{x}}_{\mathit{j}}}(\mathit{x})$$
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.

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 each call to Jacobian, the previous calls to Forward are unspecified.

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

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Input File: cppad/local/jacobian.hpp