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@(@\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}} }@)@

*dw* = *f*.Reverse(1, *w*)

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)
@)@.
The object

*f*

has prototype

const ADFun<*Base*> *f*

Before this call to `Reverse`

, the value returned by

*f*.size_order()

must be greater than or equal one (see size_order
).
The vector

*x*

in expression for
*dw*

above
corresponds to the previous call to forward_zero
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*

.
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*

.
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*

.
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.
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/reverse_one.omh