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<option>f</option>
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<center><b><big><big>First Order Derivative: Driver Routine</big></big></b></center>
<br/>
<b><big><a name="Syntax" id="Syntax">Syntax</a></big></b>
<br/>
<code><font color="blue"></font></code><i><span style='white-space: nowrap'>dw</span></i><code><font color="blue"><span style='white-space: nowrap'> = </span></font></code><i><span style='white-space: nowrap'>f</span></i><code><font color="blue"><span style='white-space: nowrap'>.RevOne(</span></font></code><i><span style='white-space: nowrap'>x</span></i><code><font color="blue"><span style='white-space: nowrap'>, </span></font></code><i><span style='white-space: nowrap'>i</span></i><code><font color="blue"><span style='white-space: nowrap'>)</span></font></code>
<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">→</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 function</span></a>
corresponding to <i>f</i>.
The syntax above sets <i>dw</i> to the
derivative of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<msub><mi mathvariant='italic'>F</mi>
<mi mathvariant='italic'>i</mi>
</msub>
</mrow></math>
with respect to
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>x</mi>
</mrow></math>
; i.e.,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mi mathvariant='italic'>dw</mi>
<mo stretchy="false">=</mo>
<msubsup><mi mathvariant='italic'>F</mi>
<mi mathvariant='italic'>i</mi>
<mrow><mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</mrow>
</msubsup>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">=</mo>
<mrow><mo stretchy="true">[</mo><mrow><mfrac><mrow><mo stretchy="false">∂</mo>
<msub><mi mathvariant='italic'>F</mi>
<mi mathvariant='italic'>i</mi>
</msub>
</mrow>
<mrow><mo stretchy="false">∂</mo>
<msub><mi mathvariant='italic'>x</mi>
<mn>0</mn>
</msub>
</mrow>
</mfrac>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">,</mo>
<mo stretchy="false">⋯</mo>
<mo stretchy="false">,</mo>
<mfrac><mrow><mo stretchy="false">∂</mo>
<msub><mi mathvariant='italic'>F</mi>
<mi mathvariant='italic'>i</mi>
</msub>
</mrow>
<mrow><mo stretchy="false">∂</mo>
<msub><mi mathvariant='italic'>x</mi>
<mrow><mi mathvariant='italic'>n</mi>
<mn>-1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow><mo stretchy="true">]</mo></mrow>
</mrow></math>
<br/>
<b><big><a name="f" id="f">f</a></big></b>
<br/>
The object <i>f</i> has prototype
<code><font color="blue"><span style='white-space: nowrap'><br/>
     ADFun<</span></font></code><i><span style='white-space: nowrap'>Base</span></i><code><font color="blue"><span style='white-space: nowrap'>> </span></font></code><i><span style='white-space: nowrap'>f</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>Note that the <a href="adfun.xml" target="_top"><span style='white-space: nowrap'>ADFun</span></a>
object <i>f</i> is not <code><font color="blue">const</font></code>
(see <a href="revone.xml#RevOne Uses Forward" target="_top"><span style='white-space: nowrap'>RevOne Uses Forward</span></a>
below).
<br/>
<br/>
<b><big><a name="x" id="x">x</a></big></b>
<br/>
The argument <i>x</i> has prototype
<code><font color="blue"><span style='white-space: nowrap'><br/>
     const </span></font></code><i><span style='white-space: nowrap'>Vector</span></i><code><font color="blue"><span style='white-space: nowrap'> &</span></font></code><i><span style='white-space: nowrap'>x</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>(see <a href="revone.xml#Vector" target="_top"><span style='white-space: nowrap'>Vector</span></a>
below)
and its size
must be equal to <i>n</i>, the dimension of the
<a href="seq_property.xml#Domain" target="_top"><span style='white-space: nowrap'>domain</span></a>
space for <i>f</i>.
It specifies
that point at which to evaluate the derivative.
<br/>
<br/>
<b><big><a name="i" id="i">i</a></big></b>
<br/>
The index <i>i</i> has prototype
<code><font color="blue"><span style='white-space: nowrap'><br/>
     size_t </span></font></code><i><span style='white-space: nowrap'>i</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>and is less than
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>m</mi>
</mrow></math>
, the dimension of the
<a href="seq_property.xml#Range" target="_top"><span style='white-space: nowrap'>range</span></a>
space for <i>f</i>.
It specifies the
component of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>F</mi>
</mrow></math>
that we are computing the derivative of.
<br/>
<br/>
<b><big><a name="dw" id="dw">dw</a></big></b>
<br/>
The result <i>dw</i> has prototype
<code><font color="blue"><span style='white-space: nowrap'><br/>
     </span></font></code><i><span style='white-space: nowrap'>Vector</span></i><code><font color="blue"><span style='white-space: nowrap'> </span></font></code><i><span style='white-space: nowrap'>dw</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>(see <a href="revone.xml#Vector" target="_top"><span style='white-space: nowrap'>Vector</span></a>
below)
and its size is <i>n</i>, the dimension of the
<a href="seq_property.xml#Domain" target="_top"><span style='white-space: nowrap'>domain</span></a>
space for <i>f</i>.
The value of <i>dw</i> is the derivative of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<msub><mi mathvariant='italic'>F</mi>
<mi mathvariant='italic'>i</mi>
</msub>
</mrow></math>
evaluated at <i>x</i>; i.e.,
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">…</mo>
<mo stretchy="false">,</mo>
<mi mathvariant='italic'>n</mi>
<mo stretchy="false">-</mo>
<mn>1</mn>
</mrow></math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mo stretchy="false">.</mo>
<mi mathvariant='italic'>dw</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>j</mi>
<mo stretchy="false">]</mo>
<mo stretchy="false">=</mo>
<mfrac><mrow><mo stretchy="false">∂</mo>
<msub><mi mathvariant='italic'>F</mi>
<mi mathvariant='italic'>i</mi>
</msub>
</mrow>
<mrow><mo stretchy="false">∂</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>
</mrow></math>
<br/>
<b><big><a name="Vector" id="Vector">Vector</a></big></b>
<br/>
The type <i>Vector</i> must be a <a href="simplevector.xml" target="_top"><span style='white-space: nowrap'>SimpleVector</span></a>
class with
<a href="simplevector.xml#Elements of Specified Type" target="_top"><span style='white-space: nowrap'>elements of type</span></a>
<i>Base</i>.
The routine <a href="checksimplevector.xml" target="_top"><span style='white-space: nowrap'>CheckSimpleVector</span></a>
will generate an error message
if this is not the case.
<br/>
<br/>
<b><big><a name="RevOne Uses Forward" id="RevOne Uses Forward">RevOne Uses Forward</a></big></b>
<br/>
After each call to <a href="forward.xml" target="_top"><span style='white-space: nowrap'>Forward</span></a>
,
the object <i>f</i> contains the corresponding
<a href="glossary.xml#Taylor Coefficient" target="_top"><span style='white-space: nowrap'>Taylor coefficients</span></a>
.
After <code><font color="blue">RevOne</font></code>,
the previous calls to <a href="forward.xml" target="_top"><span style='white-space: nowrap'>Forward</span></a>
are undefined.
<br/>
<br/>
<b><big><a name="Example" id="Example">Example</a></big></b>
<br/>
The routine
<a href="revone.cpp.xml" target="_top"><span style='white-space: nowrap'>RevOne</span></a>
is both an example and test.
It returns <code><font color="blue">true</font></code>, if it succeeds and <code><font color="blue">false</font></code> otherwise.
<hr/>Input File: cppad/local/rev_one.hpp
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