Prev

Next

Index-> contents reference index search external

Up-> CppAD ADFun FunEval Reverse reverse_one

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

FunEval-> Forward Reverse Sparse

Reverse-> reverse_one reverse_two reverse_any

reverse_one-> reverse_one.cpp

Headings-> Syntax Purpose f x w dw Vector Example

First Order Reverse Mode
Syntax
dw = f.Reverse(1, w)

Purpose
We use  F : B^n \rightarrow B^m to denote the AD function corresponding to f . The function  W : B^n \rightarrow B is defined by  \[
     W(x) = w_0 * F_0 ( x ) + \cdots + w_{m-1} * F_{m-1} (x)
\]  The result of this operation is the derivative  dw = W^{(1)} (x) ; i.e.,  \[
     dw = w_0 * F_0^{(1)} ( x ) + \cdots + w_{m-1} * F_{m-1}^{(1)} (x)
\]  Note that if  w is the i-th elementary vector ,  dw = F_i^{(1)} (x) .

f
The object f has prototype
     const ADFun<Base> f
Before this call to Reverse, the value returned by
     f.size_taylor()
must be greater than or equal one (see size_taylor ).

x
The vector x in expression for dw above corresponds to the previous call to ForwardZero using this ADFun object f ; i.e.,
     f.Forward(0, x)
If there is no previous call with the first argument zero, the value of the independent variables during the recording of the AD sequence of operations is used for x .

w
The argument w has prototype
     const Vector &w
(see Vector below) and its size must be equal to m , the dimension of the range space for f .

dw
The result dw has prototype
     Vector dw
(see Vector below) and its value is the derivative  W^{(1)} (x) . The size of dw is equal to n , the dimension of the domain space for f .

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.

Example
The file reverse_one.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.

---

Input File: omh/reverse.omh