Prev

Next

Index-> contents reference index search external

Up-> cppad_swig library a_fun a_fun_forward

cppad_swig-> testing swig_xam.i library whats_new_2018

library-> module a_double vector a_fun sparse error xam.m4

a_fun-> independent abort_recording a_fun_ctor a_fun_jacobian a_fun_hessian a_fun_forward a_fun_reverse a_fun_optimize a_fun_property

a_fun_forward-> a_fun_forward_xam.cpp a_fun_forward_xam.m a_fun_forward_xam.pm a_fun_forward_xam.py

Headings-> Syntax Taylor Coefficient af f(x) X(t) Y(t) p xp yp Example

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@ Forward Mode AD
Syntax
yp = af.forward(p, xp)

Taylor Coefficient
For a function @(@ g(t) @)@ of a scalar argument @(@ t \in \B{R} @)@, the p-th order Taylor coefficient is its p-th order derivative divided by p factorial and evaluated at @(@ t = 0 @)@; i.e., @[@ g^{(p)} (0) / p ! @]@

af
This object has prototype
     a_fun af
Note that its state is changed by this operation because it keeps all the Taylor coefficient that it calculates for every variable in recording it stored. See more discussion of this fact under the heading p below.

f(x)
We use the notation @(@ f: \B{R}^n \rightarrow \B{R}^m @)@ for the function corresponding to af . Note that n is the size of ax and m is the size of ay in to the constructor for af .

X(t)
We use the notation @(@ X : \B{R} \rightarrow \B{R}^n @)@ for a function that the calling routine chooses.

Y(t)
We define the function @(@ Y : \B{R} \rightarrow \B{R}^n @)@ by @(@ Y(t) = f(X(t)) @)@.

p
This argument has prototype
     int p
i.e., it is a positive integer. Its value is the order of the Taylor coefficient being calculated. If there was no call to forward for this af , the value of p must be zero. Otherwise, it must be between zero and one greater that its value for the previous call using this af . After this call, the Taylor coefficients for orders zero though p , and for every variable in the recording, will be stored in af .

xp
This argument has prototype
     const vec_double& xp
and its size must be n . It specifies the p-th order Taylor coefficients for X(t) .

yp
The result has prototype
     vec_double yp
and its size is m . It is the p-th order Taylor coefficients for @(@ Y(t) @)@.

Example
C++ , Octave , Perl , Python .

---

Input File: lib/a_fun.cpp