ADFun Sequence Properties

@(@\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}} }@)@ADFun Sequence Properties
Syntax

n = f.Domain()

m = f.Range()

p = f.Parameter(i)

s = f.size_var()

s = f.size_par()

s = f.size_op()

s = f.size_op_arg()

s = f.size_text()

s = f.size_VecAD()

s = f.size_op_seq()

See Also
size_order , capacity_order , number_skip .

Purpose
The operations above return properties of the AD of Base operation sequence stored in the ADFun object f . (If there is no operation sequence stored in f , size_var returns zero.)

f
The object f has prototype



     const ADFun<Base> f

(see ADFun<Base> constructor ).

Domain
The result n has prototype



     size_t n

and is the dimension of the domain space corresponding to f . This is equal to the size of the vector x in the call



     Independent(x)

that starting recording the operation sequence currently stored in f (see FunConstruct and Dependent ).

Range
The result m has prototype



     size_t m

and is the dimension of the range space corresponding to f . This is equal to the size of the vector y in syntax



     ADFun<Base> f(x, y)



     f.Dependent(y)

depending on which stored the operation sequence currently in f (see FunConstruct and Dependent ).

Parameter
The argument i has prototype



     size_t i

and @(@ 0 \leq i < m @)@. The result p has prototype



     bool p

It is true if the i-th component of range space for @(@ F @)@ corresponds to a parameter in the operation sequence. In this case, the i-th component of @(@ F @)@ is constant and @[@ \D{F_i}{x_j} (x) = 0 @]@ for @(@ j = 0 , \ldots , n-1 @)@ and all @(@ x \in B^n @)@.

size_var
The result s has prototype



     size_t s

and is the number of variables in the operation sequence plus the following: one for a phantom variable with tape address zero, one for each component of the range that is a parameter. The amount of work and memory necessary for computing function values and derivatives using f is roughly proportional to s . (The function call f.size_order() returns the number of Taylor coefficient orders, per variable,direction, currently stored in f .)

If there is no operation sequence stored in f , size_var returns zero (see default constructor ).

size_par
The result s has prototype



     size_t s

and is the number of parameters in the operation sequence. Parameters differ from variables in that only values (and not derivatives) need to be stored for each parameter. These parameters are considered part of the operation sequence, as opposed to the Taylor coefficients which are considered extra data in the function object f . Note that one Base value is required for each parameter.

size_op
The result s has prototype



     size_t s

and is the number of operations in the operation sequence. Some operators, like comparison operators, do not correspond to a variable. Other operators, like the sine operator, correspond to two variables. Thus, this value will be different from size_var . Note that one enum value is required for each operator.

size_op_arg
The result s has prototype



     size_t s

and is the total number of operator arguments in the operation sequence. For example, Binary operators (e.g. addition) have two arguments. Note that one integer index is stored in the operation sequence for each argument. Also note that, as of 2013-10-20, there is an extra phantom argument with index 0 that is not used.

size_text
The result s has prototype



     size_t s

and is the total characters used in the PrintFor commands in this operation sequence.

size_VecAD
The result s has prototype



     size_t s

and is the number of VecAD vectors, plus the number of elements in the vectors. Only VecAD vectors that depend on the independent variables are stored in the operation sequence.

size_op_seq
The result s has prototype



     size_t s

and is the amount of memory required to store the operation sequence (not counting a small amount of memory required for every operation sequence). For the current version of CppAD, this is given by



     s = f.size_op()     * sizeof(CppAD::local::OpCode)

         + f.size_op_arg() * sizeof(tape_addr_type)

         + f.size_par()    * sizeof(Base)

         + f.size_text()   * sizeof(char)

         + f.size_VecAD()  * sizeof(tape_addr_type)

         + f.size_op()     * sizeof(tape_addr_type) * 3

see tape_addr_type . Note that this is the minimal amount of memory that can hold the information corresponding to an operation sequence. The actual amount of memory allocated (inuse ) for the operations sequence may be larger.

Example
The file seq_property.cpp contains an example and test of these operations. It returns true if it succeeds and false otherwise.

Input File: omh/seq_property.omh