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<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>Atomic Reverse Jacobian Sparsity Patterns</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Atomic Reverse Jacobian Sparsity Patterns"/>
<meta name="keywords" id="keywords" content=" atomic reverse jacobian sparsity patterns rev_sparse_jac callback virtual syntax purpose implementation q rt st ok examples define use "/>
<style type='text/css'>
body { color : black }
body { background-color : white }
A:link { color : blue }
A:visited { color : purple }
A:active { color : purple }
</style>
<script type='text/javascript' language='JavaScript' src='_atomic_rev_sparse_jac_xml.js'>
</script>
</head>
<body>
<table><tr>
<td>
<a href="http://www.coin-or.org/CppAD/" target="_top"><img border="0" src="_image.gif"/></a>
</td>
<td><a href="atomic_for_sparse_jac.xml" target="_top">Prev</a>
</td><td><a href="atomic_rev_sparse_hes.xml" target="_top">Next</a>
</td><td>
<select onchange='choose_across0(this)'>
<option>Index-&gt;</option>
<option>contents</option>
<option>reference</option>
<option>index</option>
<option>search</option>
<option>external</option>
</select>
</td>
<td>
<select onchange='choose_up0(this)'>
<option>Up-&gt;</option>
<option>CppAD</option>
<option>AD</option>
<option>ADValued</option>
<option>atomic</option>
<option>atomic_base</option>
<option>atomic_rev_sparse_jac</option>
</select>
</td>
<td>
<select onchange='choose_down3(this)'>
<option>ADValued-&gt;</option>
<option>Arithmetic</option>
<option>std_math_ad</option>
<option>MathOther</option>
<option>CondExp</option>
<option>Discrete</option>
<option>atomic</option>
</select>
</td>
<td>
<select onchange='choose_down2(this)'>
<option>atomic-&gt;</option>
<option>checkpoint</option>
<option>atomic_base</option>
</select>
</td>
<td>
<select onchange='choose_down1(this)'>
<option>atomic_base-&gt;</option>
<option>atomic_ctor</option>
<option>atomic_option</option>
<option>atomic_afun</option>
<option>atomic_forward</option>
<option>atomic_reverse</option>
<option>atomic_for_sparse_jac</option>
<option>atomic_rev_sparse_jac</option>
<option>atomic_rev_sparse_hes</option>
<option>atomic_base_clear</option>
<option>atomic_get_started.cpp</option>
<option>atomic_norm_sq.cpp</option>
<option>atomic_reciprocal.cpp</option>
<option>atomic_tangent.cpp</option>
<option>atomic_hes_sparse.cpp</option>
<option>atomic_mat_mul.cpp</option>
</select>
</td>
<td>atomic_rev_sparse_jac</td>
<td>
<select onchange='choose_current0(this)'>
<option>Headings-&gt;</option>
<option>Syntax</option>
<option>Purpose</option>
<option>Implementation</option>
<option>---..q</option>
<option>---..rt</option>
<option>---..st</option>
<option>ok</option>
<option>Examples</option>
<option>---..Define rev_sparse_jac</option>
<option>---..Use rev_sparse_jac</option>
</select>
</td>
</tr></table><br/>



<center><b><big><big>Atomic Reverse Jacobian Sparsity Patterns</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'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>afun</span></font></i><font color="blue"><span style='white-space: nowrap'>.rev_sparse_jac(</span></font><i><font color="black"><span style='white-space: nowrap'>q</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>rt</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>st</span></font></i><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/>
This function is used by <a href="revsparsejac.xml" target="_top"><span style='white-space: nowrap'>RevSparseJac</span></a>
 to compute
Jacobian sparsity patterns.
For a fixed matrix 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>R</mi>
<mo stretchy="false">&#x02208;</mo>
<msup><mi mathvariant='italic'>B</mi>
<mrow><mi mathvariant='italic'>q</mi>
<mo stretchy="false">&#x000D7;</mo>
<mi mathvariant='italic'>m</mi>
</mrow>
</msup>
</mrow></math>

,
the Jacobian of 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>R</mi>
<mo stretchy="false">*</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow></math>

 with respect to 
<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'>q</mi>
</msup>
</mrow></math>

 is

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mi mathvariant='italic'>S</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">=</mo>
<mi mathvariant='italic'>R</mi>
<mo stretchy="false">*</mo>
<msup><mi mathvariant='italic'>f</mi>
<mrow><mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow></math>

Given a <a href="glossary.xml#Sparsity Pattern" target="_top"><span style='white-space: nowrap'>sparsity&#xA0;pattern</span></a>
 for 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>R</mi>
</mrow></math>

,
<code><font color="blue">rev_sparse_jac</font></code> computes a sparsity pattern for 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>S</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow></math>

.

<br/>
<br/>
<b><big><a name="Implementation" id="Implementation">Implementation</a></big></b>
<br/>
If you are using <a href="revsparsejac.xml" target="_top"><span style='white-space: nowrap'>RevSparseJac</span></a>
,
this virtual function must be defined by the
<a href="atomic_ctor.xml#atomic_user" target="_top"><span style='white-space: nowrap'>atomic_user</span></a>
 class.

<br/>
<br/>
<b><a name="Implementation.q" id="Implementation.q">q</a></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>q</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'>q</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
It specifies the number of rows in 

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>R</mi>
<mo stretchy="false">&#x02208;</mo>
<msup><mi mathvariant='italic'>B</mi>
<mrow><mi mathvariant='italic'>q</mi>
<mo stretchy="false">&#x000D7;</mo>
<mi mathvariant='italic'>m</mi>
</mrow>
</msup>
</mrow></math>

 and the Jacobian 

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>S</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">&#x02208;</mo>
<msup><mi mathvariant='italic'>B</mi>
<mrow><mi mathvariant='italic'>q</mi>
<mo stretchy="false">&#x000D7;</mo>
<mi mathvariant='italic'>n</mi>
</mrow>
</msup>
</mrow></math>

. 

<br/>
<br/>
<b><a name="Implementation.rt" id="Implementation.rt">rt</a></b>
<br/>
This argument has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>atomic_sparsity</span></font></i><font color="blue"><span style='white-space: nowrap'>&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>rt</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
and is a 
<a href="atomic_option.xml#atomic_sparsity" target="_top"><span style='white-space: nowrap'>atomic_sparsity</span></a>
 pattern for

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<msup><mi mathvariant='italic'>R</mi>
<mrow><mstyle mathvariant='normal'><mi mathvariant='normal'>T</mi>
</mstyle></mrow>
</msup>
<mo stretchy="false">&#x02208;</mo>
<msup><mi mathvariant='italic'>B</mi>
<mrow><mi mathvariant='italic'>m</mi>
<mo stretchy="false">&#x000D7;</mo>
<mi mathvariant='italic'>q</mi>
</mrow>
</msup>
</mrow></math>

.

<br/>
<br/>
<b><a name="Implementation.st" id="Implementation.st">st</a></b>
<br/>
This argument has prototype

<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'>atomic_sparsity</span></font></i><font color="blue"><span style='white-space: nowrap'>&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>st</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
The input value of its elements 
are not specified (must not matter).
Upon return, 
<code><i><font color="black"><span style='white-space: nowrap'>s</span></font></i></code>
 is a 
<a href="atomic_option.xml#atomic_sparsity" target="_top"><span style='white-space: nowrap'>atomic_sparsity</span></a>
 pattern for

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>S</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<msup><mo stretchy="false">)</mo>
<mrow><mstyle mathvariant='normal'><mi mathvariant='normal'>T</mi>
</mstyle></mrow>
</msup>
<mo stretchy="false">&#x02208;</mo>
<msup><mi mathvariant='italic'>B</mi>
<mrow><mi mathvariant='italic'>n</mi>
<mo stretchy="false">&#x000D7;</mo>
<mi mathvariant='italic'>q</mi>
</mrow>
</msup>
</mrow></math>

. 

<br/>
<br/>
<b><big><a name="ok" id="ok">ok</a></big></b>
<br/>
The return value 
<code><i><font color="black"><span style='white-space: nowrap'>ok</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'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
If it is <code><font color="blue">true</font></code>, the corresponding evaluation succeeded,
otherwise it failed.

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


<br/>
<br/>
<b><a name="Examples.Define rev_sparse_jac" id="Examples.Define rev_sparse_jac">Define rev_sparse_jac</a></b>
<br/>
The following files contain example atomic <code><font color="blue">rev_sparse_jac</font></code> functions:
<a href="atomic_norm_sq.cpp.xml#rev_sparse_jac" target="_top"><span style='white-space: nowrap'>norm_sq.cpp</span></a>
,
<a href="atomic_reciprocal.cpp.xml#rev_sparse_jac" target="_top"><span style='white-space: nowrap'>reciprocal.cpp</span></a>
,
<a href="atomic_tangent.cpp.xml#rev_sparse_jac" target="_top"><span style='white-space: nowrap'>tangent.cpp</span></a>
,
<a href="atomic_matrix_mul.hpp.xml#rev_sparse_jac" target="_top"><span style='white-space: nowrap'>matrix_mul.hpp</span></a>
.

<br/>
<br/>
<b><a name="Examples.Use rev_sparse_jac" id="Examples.Use rev_sparse_jac">Use rev_sparse_jac</a></b>
<br/>
The following are links to user atomic function constructor uses:
<a href="atomic_norm_sq.cpp.xml#Use Atomic Function.rev_sparse_jac" target="_top"><span style='white-space: nowrap'>norm_sq.cpp</span></a>
,
<a href="atomic_reciprocal.cpp.xml#Use Atomic Function.rev_sparse_jac" target="_top"><span style='white-space: nowrap'>reciprocal.cpp</span></a>
,
<a href="atomic_tangent.cpp.xml#Use Atomic Function.rev_sparse_jac" target="_top"><span style='white-space: nowrap'>tangent.cpp</span></a>
,
<a href="atomic_mat_mul.cpp.xml#Use Atomic Function.rev_sparse_jac" target="_top"><span style='white-space: nowrap'>mat_mul.cpp</span></a>
.


<hr/>Input File: cppad/local/atomic_base.hpp

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</html>