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Up-> CppAD ADFun Drivers RevTwo

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

RevTwo-> RevTwo.cpp

Headings-> Syntax Purpose f x i j ddw VectorBase VectorSize_t RevTwo Uses Forward Examples

Reverse Mode Second Partial Derivative Driver
Syntax
ddw = f.RevTwo(x, i, j)

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 $$\mathit{ddw}[\mathit{k}*\mathit{p}+\ell ]=\frac{{\partial }^2{\mathit{F}}_{\mathit{i}[\ell ]}}{\partial {\mathit{x}}_{\mathit{j}[\ell ]}\partial {\mathit{x}}_{\mathit{k}}}(\mathit{x})$$ for $\mathit{k}=0,\dots ,\mathit{n}-1$ and $\ell =0,\dots ,\mathit{p}$ , where $\mathit{p}$ is the size of the vectors i and j .

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

x
The argument x has prototype
     const VectorBase &x
(see VectorBase 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 derivatives listed above.

i
The argument i has prototype
     const VectorSize_t &i
(see VectorSize_t below) We use p to denote the size of the vector i . All of the indices in i must be less than m , the dimension of the range space for f ; i.e., for $\ell =0,\dots ,\mathit{p}-1$ , $\mathit{i}[\ell ]<\mathit{m}$ .

j
The argument j has prototype
     const VectorSize_t &j
(see VectorSize_t below) and its size must be equal to p , the size of the vector i . All of the indices in j must be less than n ; i.e., for $\ell =0,\dots ,\mathit{p}-1$ , $\mathit{j}[\ell ]<\mathit{n}$ .

ddw
The result ddw has prototype
     VectorBase ddw
(see VectorBase below) and its size is $\mathit{n}*\mathit{p}$ . It contains the requested partial derivatives; to be specific, for $\mathit{k}=0,\dots ,\mathit{n}-1$ and $\ell =0,\dots ,\mathit{p}-1$ $$\mathit{ddw}[\mathit{k}*\mathit{p}+\ell ]=\frac{{\partial }^2{\mathit{F}}_{\mathit{i}[\ell ]}}{\partial {\mathit{x}}_{\mathit{j}[\ell ]}\partial {\mathit{x}}_{\mathit{k}}}(\mathit{x})$$
VectorBase
The type VectorBase must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

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

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

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

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Input File: cppad/local/rev_two.hpp