\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)
Discrete¶
View page sourceDiscrete AD Functions¶
Syntax¶
CPPAD_DISCRETE_FUNCTION ( Base , name )Purpose¶
Record the evaluation of a discrete function as part
of an AD < Base >
operation sequence .
The value of a discrete function can depend on the
independent variables ,
but its derivative is identically zero.
For example, suppose that the integer part of
a Variable x is the
index into an array of values.
Base¶
This is the
base type
corresponding to the operations sequence;
i.e., use of the name with arguments of type
AD < Base > can be recorded in an operation sequence.
name¶
This is the name of the function (as it is used in the source code).
The user must provide a version of name
where the argument has type Base .
CppAD uses this to create a version of name
where the argument has type AD < Base > .
x¶
The argument x has prototype
constBase & x
It is the value at which the user provided version of name is to be evaluated.
y¶
The result y has prototype
Base y
It is the return value for the user provided version of name .
ax¶
The argument ax has prototype
const AD< Base >& ax
It is the value at which the CppAD provided version of name is to be evaluated.
ay¶
The result ay has prototype
AD< Base > ay
It is the return value for the CppAD provided version of name .
Create AD Version¶
The preprocessor macro invocation
CPPAD_DISCRETE_FUNCTION( Base , name )
defines the AD < Base > version of name .
This can be with in a namespace (not the CppAD namespace)
but must be outside of any routine.
Operation Sequence¶
This is an AD of Base atomic operation and hence is part of the current AD of Base operation sequence .
Derivatives¶
During a zero order Forward operation, an ADFun object will compute the value of name using the user provided Base version of this routine. All the derivatives of name will be evaluated as zero.
Parallel Mode¶
The first call to
name ( ax )
must not be in parallel execution mode.
Example¶
The file tape_index.cpp contains an example and test that uses a discrete function to vary an array index during Forward mode calculations. The file interp_onetape.cpp contains an example and test that uses discrete functions to avoid retaping a calculation that requires interpolation. (The file interp_retape.cpp shows how interpolation can be done with retaping.)
CppADCreateDiscrete Deprecated 2007-07-28¶
The preprocessor symbol CppADCreateDiscrete
is defined to be the same as CPPAD_DISCRETE_FUNCTION
but its use is deprecated.