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<center><b><big><big>ADFun Sequence Properties</big></big></b></center>
<br/>
<b><big><a name="Syntax" id="Syntax">Syntax</a></big></b>

<br/>

<code><i><font color="black"><span style='white-space: nowrap'>n</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.Domain()<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>m</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.Range()<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>p</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.Parameter(</span></font><i><font color="black"><span style='white-space: nowrap'>i</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_var()<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_par()<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_op()<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_op_arg()<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_text()<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_VecAD()<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_op_seq()<br/>
</span></font></code>
<br/>
<b><a name="Syntax.See Also" id="Syntax.See Also">See Also</a></b>

<br/>
<a href="size_order.xml" target="_top"><span style='white-space: nowrap'>size_order</span></a>
, <a href="capacity_order.xml" target="_top"><span style='white-space: nowrap'>capacity_order</span></a>
.

<br/>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
The operations above return properties of the
AD of 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>

<a href="glossary.xml#Operation.Sequence" target="_top"><span style='white-space: nowrap'>operation&#xA0;sequence</span></a>

stored in the ADFun object 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
. 
(If there is no operation sequence stored in 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
,
<code><font color="blue">size_var</font></code> returns zero.)

<br/>
<br/>
<b><big><a name="f" id="f">f</a></big></b>
<br/>
The object 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;ADFun&lt;</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>&gt;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
(see 
<code><font color="blue"><span style='white-space: nowrap'>ADFun&lt;</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>&gt;</span></font></code>
 <a href="funconstruct.xml" target="_top"><span style='white-space: nowrap'>constructor</span></a>
).

<br/>
<br/>
<b><big><a name="Domain" id="Domain">Domain</a></big></b>


<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>n</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>n</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
and is the dimension of the domain space corresponding to 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
.
This is equal to the size of the vector 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 in the call

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;Independent(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font></code>
that starting recording the operation sequence 
currently stored in 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>

(see <a href="funconstruct.xml" target="_top"><span style='white-space: nowrap'>FunConstruct</span></a>
 and <a href="dependent.xml" target="_top"><span style='white-space: nowrap'>Dependent</span></a>
). 

<br/>
<br/>
<b><big><a name="Range" id="Range">Range</a></big></b>


<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>m</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>m</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
and is the dimension of the range space corresponding to 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
.
This is equal to the size of the vector 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 in syntax

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;ADFun&lt;</span></font><i><font color="black"><span style='white-space: nowrap'>Base&gt;&#xA0;</span></font></i><font color="blue"><span style='white-space: nowrap'>f</span></font><i><font color="black"><span style='white-space: nowrap'>(</span></font></i><font color="blue"><span style='white-space: nowrap'>x</span></font><i><font color="black"><span style='white-space: nowrap'>,&#xA0;</span></font></i><font color="blue"><span style='white-space: nowrap'>y</span></font><i><font color="black"><span style='white-space: nowrap'>)<br/>
</span></font></i></code>
or

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.Dependent(</span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font></code>
depending on which stored the operation sequence currently in 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>

(see <a href="funconstruct.xml" target="_top"><span style='white-space: nowrap'>FunConstruct</span></a>
 and <a href="dependent.xml" target="_top"><span style='white-space: nowrap'>Dependent</span></a>
). 

<br/>
<br/>
<b><big><a name="Parameter" id="Parameter">Parameter</a></big></b>


<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>i</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>i</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
and 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mn>0</mn>
<mo stretchy="false">&#x02264;</mo>
<mi mathvariant='italic'>i</mi>
<mo stretchy="false">&lt;</mo>
<mi mathvariant='italic'>m</mi>
</mrow></math>

.
The result 
<code><i><font color="black"><span style='white-space: nowrap'>p</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;bool&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>p</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
It is true if the <i>i</i>-th component of range space for 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>F</mi>
</mrow></math>


corresponds to a
<a href="glossary.xml#Parameter" target="_top"><span style='white-space: nowrap'>parameter</span></a>
 in the operation sequence.
In this case,
the <i>i</i>-th component of 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>F</mi>
</mrow></math>

 is constant and

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<msub><mi mathvariant='italic'>F</mi>
<mi mathvariant='italic'>i</mi>
</msub>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<msub><mi mathvariant='italic'>x</mi>
<mi mathvariant='italic'>j</mi>
</msub>
</mrow>
</mfrac>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">=</mo>
<mn>0</mn>
</mrow></math>

for 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>j</mi>
<mo stretchy="false">=</mo>
<mn>0</mn>
<mo stretchy="false">,</mo>
<mo stretchy="false">&#x02026;</mo>
<mo stretchy="false">,</mo>
<mi mathvariant='italic'>n</mi>
<mn>-1</mn>
</mrow></math>

 and all 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">&#x02208;</mo>
<msup><mi mathvariant='italic'>B</mi>
<mi mathvariant='italic'>n</mi>
</msup>
</mrow></math>

.

<br/>
<br/>
<b><big><a name="size_var" id="size_var">size_var</a></big></b>


<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
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 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
 is roughly proportional to 
<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i></code>
.
(The function call <a href="size_order.xml" target="_top"><span style='white-space: nowrap'>f.size_order()</span></a>
 
returns the number of Taylor coefficient orders, per variable,direction,
currently stored in 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
.)
<code><span style='white-space: nowrap'><br/>
<br/>
</span></code>If there is no operation sequence stored in 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
,
<code><font color="blue">size_var</font></code> returns zero
(see <a href="funconstruct.xml#Default Constructor" target="_top"><span style='white-space: nowrap'>default&#xA0;constructor</span></a>
).

<br/>
<br/>
<b><big><a name="size_par" id="size_par">size_par</a></big></b>


<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
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 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
.
Note that one 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
 value is required for each parameter.

<br/>
<br/>
<b><big><a name="size_op" id="size_op">size_op</a></big></b>
<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
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 
<a href="seq_property.xml#size_var" target="_top"><span style='white-space: nowrap'>size_var</span></a>
. 
Note that one <code><font color="blue">enum</font></code> value is required for each operator.

<br/>
<br/>
<b><big><a name="size_op_arg" id="size_op_arg">size_op_arg</a></big></b>
<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
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.

<br/>
<br/>
<b><big><a name="size_text" id="size_text">size_text</a></big></b>
<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
and is the total characters used in the <a href="printfor.xml" target="_top"><span style='white-space: nowrap'>PrintFor</span></a>
 commands
in this operation sequence.

<br/>
<br/>
<b><big><a name="size_VecAD" id="size_VecAD">size_VecAD</a></big></b>


<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
and is the number of <a href="vecad.xml" target="_top"><span style='white-space: nowrap'>VecAD</span></a>
 vectors,
plus the number of elements in the vectors.
Only <code><font color="blue">VecAD</font></code> vectors that depend on the 
independent variables are stored in the operation sequence.

<br/>
<br/>
<b><big><a name="size_op_seq" id="size_op_seq">size_op_seq</a></big></b>
<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
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

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>s</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_op()&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;*&#xA0;sizeof(CppAD::OpCode)<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;+&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_op_arg()&#xA0;*&#xA0;sizeof(</span></font><i><font color="black"><span style='white-space: nowrap'>tape_addr_type</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;+&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_par()&#xA0;&#xA0;&#xA0;&#xA0;*&#xA0;sizeof(</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;+&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_text()&#xA0;&#xA0;&#xA0;*&#xA0;sizeof(char)<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;+&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>f</span></font></i><font color="blue"><span style='white-space: nowrap'>.size_VecAD()&#xA0;&#xA0;*&#xA0;sizeof(</span></font><i><font color="black"><span style='white-space: nowrap'>tape_addr_type</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font></code>
see <a href="cmake.xml#cppad_tape_addr_type" target="_top"><span style='white-space: nowrap'>tape_addr_type</span></a>
.
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 (<a href="ta_inuse.xml" target="_top"><span style='white-space: nowrap'>inuse</span></a>
)
for the operations sequence may be larger.

<br/>
<br/>
<b><big><a name="Example" id="Example">Example</a></big></b>

<br/>
The file
<a href="seq_property.cpp.xml" target="_top"><span style='white-space: nowrap'>seq_property.cpp</span></a>
 
contains an example and test of these operations.
It returns true if it succeeds and false otherwise.



<hr/>Input File: omh/seq_property.omh

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