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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}} }@)@

*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_random()

*s* = *f*.size_dyn_ind()

*s* = *f*.size_dyn_par()

*s* = *f*.size_dyn_arg()

*s* = *f*.size_op_seq()

See Also

function_name , size_order , capacity_order , number_skip .

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.)
The object

*f*

has prototype

const ADFun<*Base*> *f*

(see
`ADFun<`*Base*>

constructor
).
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
).
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*)*

or

*f*.Dependent(*y*)

depending on which stored the operation sequence currently in
*f*

(see FunConstruct
and Dependent
).
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{R}^n
@)@.
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
).
The result

*s*

has prototype

size_t *s*

and is the number of parameters in the operation sequence
(include a phantom parameter at index zero that is not used).
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.
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.
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.
The result

*s*

has prototype

size_t *s*

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

*s*

has prototype

size_t *s*

and is the amount of memory currently holding information
for randomly access the operator sequence.
Random access is only used by the following routines
subgraph_sparsity
,
subgraph_reverse
, and
optimize
.
The optimize routine replaces the operation sequence, so the extra
memory is automatically dropped.
The subgraph routines hold onto this information
so that it does not need to be recalculated between calls.
The routine
clear_subgraph
will free this extra memory.
The result

*s*

has prototype

size_t *s*

and is the number of independent
dynamic
parameters
in the operation sequence.
This is the size of the
dynamic
parameter in the
corresponding call to `Independent`

.
The result

*s*

has prototype

size_t *s*

and is the number of
dynamic
parameters.
The dynamic parameters depend on the value of
the independent dynamic parameters but not on the value of the variables.
This includes the independent dynamic parameters.
The result

*s*

has prototype

size_t *s*

and is the total number of dynamic parameter 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.
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_VEC_ENUM_TYPE)

+ *f*.size_op_arg() * sizeof(*tape_addr_type*)

+ *f*.size_par() * sizeof(*Base*)

+ *f*.size_par() * sizeof(bool)

+ *f*.size_dyn_par() * sizeof(CPPAD_VEC_ENUM_TYPE)

+ *f*.size_dyn_par() * sizeof(*tape_addr_type*)

+ *f*.size_dyn_arg() * sizeof(*tape_addr_type*)

+ *f*.size_text() * sizeof(char)

+ *f*.size_VecAD() * sizeof(*tape_addr_type*)

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.
Also note that `CPPAD_VEC_ENUM_TYPE`

is not part
of the CppAD API and may change.
The file fun_property.cpp contains an example and test of these operations.

Input File: include/cppad/core/fun_property.omh