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<center><b><big><big>Comparison Changes During Zero Order Forward Mode</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'>c</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'>.CompareChange()</span></font></code>

<code><span style='white-space: nowrap'><br/>
</span></code><b>See Also</b>
<a href="funcheck.xml" target="_top"><span style='white-space: nowrap'>FunCheck</span></a>



<br/>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
We use 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>F</mi>
<mo stretchy="false">:</mo>
<msup><mi mathvariant='italic'>B</mi>
<mi mathvariant='italic'>n</mi>
</msup>
<mo stretchy="false">&#x02192;</mo>
<msup><mi mathvariant='italic'>B</mi>
<mi mathvariant='italic'>m</mi>
</msup>
</mrow></math>

 to denote the
<a href="glossary.xml#AD Function" target="_top"><span style='white-space: nowrap'>AD&#xA0;function</span></a>
 corresponding to 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
.
This function may be not agree with the algorithm that was used
to create the corresponding
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>

because of changes in AD
<a href="compare.xml" target="_top"><span style='white-space: nowrap'>comparison</span></a>
 results.
The <code><font color="blue">CompareChange</font></code> function can be used to detect these changes.

<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>
<br/>
<b><big><a name="c" id="c">c</a></big></b>
<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>c</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'>c</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
It is the number of 

<code><font color="blue"><span style='white-space: nowrap'>AD&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="compare.xml" target="_top"><span style='white-space: nowrap'>comparison</span></a>
 
operations,
corresponding to the previous call to <a href="forward.xml" target="_top"><span style='white-space: nowrap'>Forward</span></a>
 

<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'>.Forward(0,&#xA0;</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 have a different result from
when 
<code><i><font color="black"><span style='white-space: nowrap'>F</span></font></i></code>
 was created by taping an algorithm.

<br/>
<br/>
<b><big><a name="Discussion" id="Discussion">Discussion</a></big></b>
<br/>
If 
<code><i><font color="black"><span style='white-space: nowrap'>c</span></font></i></code>
 is not zero, 
the boolean values resulting from some of the 
<a href="compare.xml" target="_top"><span style='white-space: nowrap'>comparison&#xA0;operations</span></a>
 corresponding to 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>

are different from when 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>
 was created.
In this case, you may want to re-tape the algorithm with the
<a href="glossary.xml#Tape.Independent Variable" target="_top"><span style='white-space: nowrap'>independent&#xA0;variables</span></a>
 
equal to the values in 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 
(so AD operation sequence properly represents the algorithm
for this value of independent variables).
On the other hand, re-taping the AD operation sequence usually takes 
significantly more time than evaluation using <a href="forward_zero.xml" target="_top"><span style='white-space: nowrap'>forward_zero</span></a>
.
If the functions values have not changed (see <a href="funcheck.xml" target="_top"><span style='white-space: nowrap'>FunCheck</span></a>
)
it may not be worth re-taping a new AD operation sequence. 

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

<br/>
Computation of this function requires extra operations in the tape.
If <a href="faq.xml#Speed.NDEBUG" target="_top"><span style='white-space: nowrap'>NDEBUG</span></a>
 is defined,
of if a tape <a href="optimize.xml" target="_top"><span style='white-space: nowrap'>optimization</span></a>
 has been preformed,
these operations are not included in the tape and
the value of 
<code><i><font color="black"><span style='white-space: nowrap'>c</span></font></i></code>
 is always zero (and does not correspond
to the actual number of comparison changes).

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

<br/>
The file
<a href="compare_change.cpp.xml" target="_top"><span style='white-space: nowrap'>compare_change.cpp</span></a>

contains an example and test of this operation.
They return true if they succeed and false otherwise.


<hr/>Input File: omh/forward/compare_change.omh

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