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<td>link_sparse_jacobian</td>
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<option>Headings-&gt;</option>
<option>Prototype</option>
<option>Method</option>
<option>size</option>
<option>repeat</option>
<option>m</option>
<option>row</option>
<option>col</option>
<option>x</option>
<option>jacobian</option>
<option>n_sweep</option>
<option>---..double</option>
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<center><b><big><big>Speed Testing Sparse Jacobian</big></big></b></center>
<br/>
<b><big><a name="Prototype" id="Prototype">Prototype</a></big></b>

<br/>

<code><font color="blue"><span style='white-space: nowrap'>extern&#xA0;bool&#xA0;link_sparse_jacobian(<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>size</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;,<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>repeat</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&#xA0;&#xA0;&#xA0;,<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>m</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;,<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;CppAD::vector&lt;size_t&gt;&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>row</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;,<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;CppAD::vector&lt;size_t&gt;&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>col</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;,&#xA0;<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;CppAD::vector&lt;double&gt;&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;,<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;CppAD::vector&lt;double&gt;&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>jacobian</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&#xA0;,<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;size_t&amp;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>n_sweep</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
);<br/>
</span></font></code>
<br/>
<b><big><a name="Method" id="Method">Method</a></big></b>
<br/>
Given a range space dimension 
<code><i><font color="black"><span style='white-space: nowrap'>m</span></font></i></code>

the row index vector 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>row</mi>
</mrow></math>

, and column index vector 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>col</mi>
</mrow></math>

,
a corresponding function 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">:</mo>
<msup><mrow><mstyle mathvariant='bold'><mi mathvariant='bold'>R</mi>
</mstyle></mrow>
<mi mathvariant='italic'>n</mi>
</msup>
<mo stretchy="false">&#x02192;</mo>
<msup><mrow><mstyle mathvariant='bold'><mi mathvariant='bold'>R</mi>
</mstyle></mrow>
<mi mathvariant='italic'>m</mi>
</msup>
</mrow></math>

 
is defined by <a href="sparse_jac_fun.xml" target="_top"><span style='white-space: nowrap'>sparse_jac_fun</span></a>
.
The non-zero entries in the Jacobian of this function have the form

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>row</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>k</mi>
<mo stretchy="false">]</mo>
<mo stretchy="false">]</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>col</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>k</mi>
<mo stretchy="false">]</mo>
<mo stretchy="false">]</mo>
<mo stretchy="false">]</mo>
</mrow>
</mfrac>
</mrow></math>

for some 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>k</mi>
</mrow></math>

 between zero and 
<code><i><font color="black"><span style='white-space: nowrap'>K</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>row</span></font></i><font color="blue"><span style='white-space: nowrap'>.size()-1</span></font></code>
.
All the other terms of the Jacobian are zero.


<br/>
<br/>
<b><big><a name="size" id="size">size</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>size</span></font></i></code>
, referred to as 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>n</mi>
</mrow></math>

 below,
is the dimension of the domain space for 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow></math>

.

<br/>
<br/>
<b><big><a name="repeat" id="repeat">repeat</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>repeat</span></font></i></code>
 is the number of different functions

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

 for which the Jacobian is computed for.
Each function corresponds to a randomly chosen index vectors, i.e.,
for each repetition a random choice is made for

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>row</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>k</mi>
<mo stretchy="false">]</mo>
</mrow></math>

 and 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>col</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>k</mi>
<mo stretchy="false">]</mo>
</mrow></math>

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

.

<br/>
<br/>
<b><big><a name="m" id="m">m</a></big></b>
<br/>
Is the dimension of the range space for the function 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow></math>

.

<br/>
<br/>
<b><big><a name="row" id="row">row</a></big></b>
<br/>
The size of the vector 
<code><i><font color="black"><span style='white-space: nowrap'>row</span></font></i></code>
 defines the value 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>K</mi>
</mrow></math>

.
All the elements of 
<code><i><font color="black"><span style='white-space: nowrap'>row</span></font></i></code>
 are between zero and 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>m</mi>
<mn>-1</mn>
</mrow></math>

.

<br/>
<br/>
<b><big><a name="col" id="col">col</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>col</span></font></i></code>
 is a vector with size 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>K</mi>
</mrow></math>

.
The input value of its elements does not matter.
On output, it has been set the column index vector
for the last repetition.
All the elements of 
<code><i><font color="black"><span style='white-space: nowrap'>col</span></font></i></code>
 are between zero and 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>n</mi>
<mn>-1</mn>
</mrow></math>

.
<code><span style='white-space: nowrap'><br/>
<br/>
</span></code>There are no duplicate row and column entires; i.e., if 
<code><i><font color="black"><span style='white-space: nowrap'>j</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;!=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>k</span></font></i></code>
,

<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'>row</span></font></i><font color="blue"><span style='white-space: nowrap'>[</span></font><i><font color="black"><span style='white-space: nowrap'>j</span></font></i><font color="blue"><span style='white-space: nowrap'>]&#xA0;!=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>row</span></font></i><font color="blue"><span style='white-space: nowrap'>[</span></font><i><font color="black"><span style='white-space: nowrap'>k</span></font></i><font color="blue"><span style='white-space: nowrap'>]&#xA0;||&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>col</span></font></i><font color="blue"><span style='white-space: nowrap'>[</span></font><i><font color="black"><span style='white-space: nowrap'>j</span></font></i><font color="blue"><span style='white-space: nowrap'>]&#xA0;!=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>col</span></font></i><font color="blue"><span style='white-space: nowrap'>[</span></font><i><font color="black"><span style='white-space: nowrap'>k</span></font></i><font color="blue"><span style='white-space: nowrap'>]<br/>
</span></font></code>
<br/>
<b><big><a name="x" id="x">x</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;CppAD::vector&lt;double&gt;&amp;&#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>
and its size is 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>n</mi>
</mrow></math>

; i.e., 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>.size()&#xA0;==&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>size</span></font></i></code>
.
The input value of the elements of 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 does not matter.
On output, it has been set to the 
argument value for which the function,
or its derivative, is being evaluated and placed in 
<code><i><font color="black"><span style='white-space: nowrap'>jacobian</span></font></i></code>
.
The value of this vector need not change with each repetition.

<br/>
<br/>
<b><big><a name="jacobian" id="jacobian">jacobian</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>jacobian</span></font></i></code>
 is a vector with 

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

 elements.
The input value of its elements does not matter. 
The output value of its elements is the Jacobian of the function 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow></math>


that corresponds to output values of 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
.
To be more specific, for

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

,

<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>

,

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mfrac><mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>i</mi>
<mo stretchy="false">]</mo>
</mrow>
<mrow><mo stretchy="false">&#x02202;</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>j</mi>
<mo stretchy="false">]</mo>
</mrow>
</mfrac>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">=</mo>
<mi mathvariant='italic'>jacobian</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>i</mi>
<mo stretchy="false">*</mo>
<mi mathvariant='italic'>n</mi>
<mo stretchy="false">+</mo>
<mi mathvariant='italic'>j</mi>
<mo stretchy="false">]</mo>
</mrow></math>

<br/>
<b><big><a name="n_sweep" id="n_sweep">n_sweep</a></big></b>
<br/>
The input value of 
<code><i><font color="black"><span style='white-space: nowrap'>n_sweep</span></font></i></code>
 does not matter. On output,
it is the value <a href="sparse_jacobian.xml#n_sweep" target="_top"><span style='white-space: nowrap'>n_sweep</span></a>
 corresponding
to the evaluation of 
<code><i><font color="black"><span style='white-space: nowrap'>jacobian</span></font></i></code>
.
This is also the number of colors corresponding to the 
<a href="sparse_jacobian.xml#work.color_method" target="_top"><span style='white-space: nowrap'>coloring&#xA0;method</span></a>

which can be set to <a href="speed_main.xml#option_list.colpack" target="_top"><span style='white-space: nowrap'>colpack</span></a>

and is otherwise <code><font color="blue">cppad</font></code>.

<br/>
<br/>
<b><a name="n_sweep.double" id="n_sweep.double">double</a></b>
<br/>
In the case where 
<code><i><font color="black"><span style='white-space: nowrap'>package</span></font></i></code>
 is <code><font color="blue">double</font></code>,
only the first 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>m</mi>
</mrow></math>

 
elements of 
<code><i><font color="black"><span style='white-space: nowrap'>jacobian</span></font></i></code>
 are used and they are set to
the value of 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">)</mo>
</mrow></math>

.


<hr/>Input File: speed/src/link_sparse_jacobian.cpp

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