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<option>jac</option>
<option>work</option>
<option>---..color_method</option>
<option>n_sweep</option>
<option>VectorBase</option>
<option>VectorSet</option>
<option>---..Restrictions</option>
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<center><b><big><big>Sparse Jacobian: Easy Driver</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'>jac</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'>.SparseJacobian(</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><i><font color="black"><span style='white-space: nowrap'>jac</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'>.SparseJacobian(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#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><i><font color="black"><span style='white-space: nowrap'>n_sweep</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'>.SparseJacobianForward(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>p</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#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;</span></font><i><font color="black"><span style='white-space: nowrap'>col</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>jac</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>work</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font><i><font color="black"><span style='white-space: nowrap'>n_sweep</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'>.SparseJacobianReverse(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>p</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#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;</span></font><i><font color="black"><span style='white-space: nowrap'>col</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>jac</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>work</span></font></i><font color="blue"><span style='white-space: nowrap'>)<br/>
</span></font></code>
<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'>n</mi>
</mrow></math>

 for the <a href="seq_property.xml#Domain" target="_top"><span style='white-space: nowrap'>domain</span></a>
 size,
and 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>m</mi>
</mrow></math>

 for the <a href="seq_property.xml#Range" target="_top"><span style='white-space: nowrap'>range</span></a>
 size of 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
.
We use 
<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>

 do 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>
. 
The syntax above sets 
<code><i><font color="black"><span style='white-space: nowrap'>jac</span></font></i></code>
 to the Jacobian 

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mi mathvariant='italic'>jac</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>

This routine takes advantage of the sparsity of the Jacobian
in order to reduce the amount of computation necessary.
If 
<code><i><font color="black"><span style='white-space: nowrap'>row</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>col</span></font></i></code>
 are present, it also takes
advantage of the reduced set of elements of the Jacobian that
need to be computed.
One can use speed tests (e.g. <a href="speed_test.xml" target="_top"><span style='white-space: nowrap'>speed_test</span></a>
)
to verify that results are computed faster
than when using the routine <a href="jacobian.xml" target="_top"><span style='white-space: nowrap'>Jacobian</span></a>
.

<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;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>
Note that the <a href="adfun.xml" target="_top"><span style='white-space: nowrap'>ADFun</span></a>
 object 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
 is not <code><font color="blue">const</font></code>
(see <a href="sparse_jacobian.xml#Uses Forward" target="_top"><span style='white-space: nowrap'>Uses&#xA0;Forward</span></a>
 below).

<br/>
<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;const&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>VectorBase</span></font></i><font color="blue"><span style='white-space: nowrap'>&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>
(see <a href="sparse_jacobian.xml#VectorBase" target="_top"><span style='white-space: nowrap'>VectorBase</span></a>
 below)
and its size 
must be equal to 
<code><i><font color="black"><span style='white-space: nowrap'>n</span></font></i></code>
, the dimension of the
<a href="seq_property.xml#Domain" target="_top"><span style='white-space: nowrap'>domain</span></a>
 space for 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
.
It specifies
that point at which to evaluate the Jacobian.

<br/>
<br/>
<b><big><a name="p" id="p">p</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>p</span></font></i></code>
 is optional and 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'>VectorSet</span></font></i><font color="blue"><span style='white-space: nowrap'>&amp;&#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>
(see <a href="sparse_jacobian.xml#VectorSet" target="_top"><span style='white-space: nowrap'>VectorSet</span></a>
 below).
If it has elements of type <code><font color="blue">bool</font></code>,
its size is 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>m</mi>
<mo stretchy="false">*</mo>
<mi mathvariant='italic'>n</mi>
</mrow></math>

.
If it has elements of type <code><font color="blue">std::set&lt;size_t&gt;</font></code>,
its size is 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>m</mi>
</mrow></math>

 and all its set elements are between
zero and 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>n</mi>
<mo stretchy="false">-</mo>
<mn>1</mn>
</mrow></math>

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

.
<code><span style='white-space: nowrap'><br/>
<br/>
</span></code>If this sparsity pattern does not change between calls to 

<code><font color="blue"><span style='white-space: nowrap'>SparseJacobian</span></font></code>
, it should be faster to calculate 
<code><i><font color="black"><span style='white-space: nowrap'>p</span></font></i></code>
 once 
(using <a href="forsparsejac.xml" target="_top"><span style='white-space: nowrap'>ForSparseJac</span></a>
 or <a href="revsparsejac.xml" target="_top"><span style='white-space: nowrap'>RevSparseJac</span></a>
)
and then pass 
<code><i><font color="black"><span style='white-space: nowrap'>p</span></font></i></code>
 to 
<code><font color="blue"><span style='white-space: nowrap'>SparseJacobian</span></font></code>
.
In addition,
if you specify 
<code><i><font color="black"><span style='white-space: nowrap'>p</span></font></i></code>
, CppAD will use the same
type of sparsity representation 
(vectors of <code><font color="blue">bool</font></code> or vectors of <code><font color="blue">std::set&lt;size_t&gt;</font></code>)
for its internal calculations.
Otherwise, the representation
for the internal calculations is unspecified.

<br/>
<br/>
<b><big><a name="row, col" id="row, col">row, col</a></big></b>
<br/>
The arguments 
<code><i><font color="black"><span style='white-space: nowrap'>row</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>col</span></font></i></code>
 are optional and have 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'>VectorSize</span></font></i><font color="blue"><span style='white-space: nowrap'>&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'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>VectorSize</span></font></i><font color="blue"><span style='white-space: nowrap'>&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'><br/>
</span></font></code>
(see <a href="sparse_jacobian.xml#VectorSize" target="_top"><span style='white-space: nowrap'>VectorSize</span></a>
 below).
They specify which rows and columns of 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<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>

 are
computes and in what order.
Not all the non-zero entries in 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<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>

 need be computed,
but all the entries specified by 
<code><i><font color="black"><span style='white-space: nowrap'>row</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>col</span></font></i></code>

must be possibly non-zero in the sparsity pattern.
We use 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>K</mi>
</mrow></math>

 to denote the value 
<code><i><font color="black"><span style='white-space: nowrap'>jac</span></font></i><font color="blue"><span style='white-space: nowrap'>.size()</span></font></code>

which must also equal the size of 
<code><i><font color="black"><span style='white-space: nowrap'>row</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>col</span></font></i></code>
.
Furthermore,
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>

, it must hold that

<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>
<mo stretchy="false">&lt;</mo>
<mi mathvariant='italic'>m</mi>
</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>
<mo stretchy="false">&lt;</mo>
<mi mathvariant='italic'>n</mi>
</mrow></math>

.

<br/>
<br/>
<b><big><a name="jac" id="jac">jac</a></big></b>
<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>jac</span></font></i></code>
 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'>VectorBase</span></font></i><font color="blue"><span style='white-space: nowrap'>&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>jac</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
In the case where the arguments 
<code><i><font color="black"><span style='white-space: nowrap'>row</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>col</span></font></i></code>
 are not present,
the size of 
<code><i><font color="black"><span style='white-space: nowrap'>jac</span></font></i></code>
 is 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>m</mi>
<mo stretchy="false">*</mo>
<mi mathvariant='italic'>n</mi>
</mrow></math>

 and
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>
<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>
<mi mathvariant='italic'>jac</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>
<mo stretchy="false">=</mo>
<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>
</mrow></math>

<code><span style='white-space: nowrap'><br/>
<br/>
</span></code>In the case where the arguments 
<code><i><font color="black"><span style='white-space: nowrap'>row</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>col</span></font></i></code>
 are present,
we use 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>K</mi>
</mrow></math>

 to denote the size of 
<code><i><font color="black"><span style='white-space: nowrap'>jac</span></font></i></code>
. 
The input value of its elements does not matter.
Upon return, 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>
<mo stretchy="false">-</mo>
<mn>1</mn>
</mrow></math>

,

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mi mathvariant='italic'>jac</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>k</mi>
<mo stretchy="false">]</mo>
<mo stretchy="false">=</mo>
<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>
<mspace width='.3em'/>
<mo stretchy="false">,</mo>
<mspace width='.3em'/>
<mspace width='.3em'/>
<mrow><mstyle mathvariant='normal'><mi mathvariant='normal'>where</mi>
</mstyle></mrow>
<mspace width='.3em'/>
<mi mathvariant='italic'>i</mi>
<mo stretchy="false">=</mo>
<mi mathvariant='italic'>row</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>k</mi>
<mo stretchy="false">]</mo>
<mspace width='.3em'/>
<mrow><mstyle mathvariant='normal'><mi mathvariant='normal'>and</mi>
</mstyle></mrow>
<mspace width='.3em'/>
<mi mathvariant='italic'>j</mi>
<mo stretchy="false">=</mo>
<mi mathvariant='italic'>col</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>k</mi>
<mo stretchy="false">]</mo>
</mrow></math>

<br/>
<b><big><a name="work" id="work">work</a></big></b>
<br/>
If this argument is present, it has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;sparse_jacobian_work&amp;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>work</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
This object can only be used with the routines 
<code><font color="blue">SparseJacobianForward</font></code> and <code><font color="blue">SparseJacobianReverse</font></code>.
During its the first use, information is stored in 
<code><i><font color="black"><span style='white-space: nowrap'>work</span></font></i></code>
.
This is used to reduce the work done by future calls to the same mode
(forward or reverse), 
the same 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
, 
<code><i><font color="black"><span style='white-space: nowrap'>p</span></font></i></code>
, 
<code><i><font color="black"><span style='white-space: nowrap'>row</span></font></i></code>
, and 
<code><i><font color="black"><span style='white-space: nowrap'>col</span></font></i></code>
.
If a future call is for a different mode,
or any of these values have changed,
you must first call 
<code><i><font color="black"><span style='white-space: nowrap'>work</span></font></i><font color="blue"><span style='white-space: nowrap'>.clear()</span></font></code>

to inform CppAD that this information needs to be recomputed.

<br/>
<br/>
<b><a name="work.color_method" id="work.color_method">color_method</a></b>
<br/>
The coloring algorithm determines which columns (forward mode)
or rows (reverse mode) can be computed during the same sweep.
This field has prototype
<code><font color='blue'><pre style='display:inline'> 
	std::string %work%.color_method
</pre></font></code>

and its default value (after a constructor or <code><font color="blue">clear()</font></code>) 
is <code><font color="blue">&quot;cppad&quot;</font></code>.
If <a href="colpack_prefix.xml" target="_top"><span style='white-space: nowrap'>colpack_prefix</span></a>
 is specified on the
<a href="cmake.xml#CMake Command" target="_top"><span style='white-space: nowrap'>cmake&#xA0;command</span></a>
 line,
you can set this method to <code><font color="blue">&quot;colpack&quot;</font></code>.
This value only matters on the first call to <code><font color="blue">sparse_jacobian</font></code>
after the 
<code><i><font color="black"><span style='white-space: nowrap'>work</span></font></i></code>
 constructor or a call to <code><font color="blue">clear</font></code>.

<br/>
<br/>
<b><big><a name="n_sweep" id="n_sweep">n_sweep</a></big></b>
<br/>
The return value 
<code><i><font color="black"><span style='white-space: nowrap'>n_sweep</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_sweep</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
If <code><font color="blue">SparseJacobianForward</font></code> (<code><font color="blue">SparseJacobianReverse</font></code>) is used, 

<code><i><font color="black"><span style='white-space: nowrap'>n_sweep</span></font></i></code>
 is the number of first order forward (reverse) sweeps 
used to compute the requested Jacobian values. 
(This is also the number of colors determined by the coloring method
mentioned above).
This is proportional to the total work that <code><font color="blue">SparseJacobian</font></code> does, 
not counting the zero order forward sweep, 
or the work to combine multiple columns (rows) into a single sweep.

<br/>
<br/>
<b><big><a name="VectorBase" id="VectorBase">VectorBase</a></big></b>
<br/>
The type 
<code><i><font color="black"><span style='white-space: nowrap'>VectorBase</span></font></i></code>
 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&#xA0;of&#xA0;type</span></a>


<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
.
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="VectorSet" id="VectorSet">VectorSet</a></big></b>
<br/>
The type 
<code><i><font color="black"><span style='white-space: nowrap'>VectorSet</span></font></i></code>
 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&#xA0;of&#xA0;type</span></a>

<code><font color="blue">bool</font></code> or <code><font color="blue">std::set&lt;size_t&gt;</font></code>;
see <a href="glossary.xml#Sparsity Pattern" target="_top"><span style='white-space: nowrap'>sparsity&#xA0;pattern</span></a>
 for a discussion
of the difference.
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><a name="VectorSet.Restrictions" id="VectorSet.Restrictions">Restrictions</a></b>
<br/>
If 
<code><i><font color="black"><span style='white-space: nowrap'>VectorSet</span></font></i></code>
 has elements of <code><font color="blue">std::set&lt;size_t&gt;</font></code>,
then 
<code><i><font color="black"><span style='white-space: nowrap'>p</span></font></i><font color="blue"><span style='white-space: nowrap'>[</span></font><i><font color="black"><span style='white-space: nowrap'>i</span></font></i><font color="blue"><span style='white-space: nowrap'>]</span></font></code>
 must return a reference (not a copy) to the 
corresponding set.
According to section 26.3.2.3 of the 1998 C++ standard,
<code><font color="blue">std::valarray&lt; std::set&lt;size_t&gt; &gt;</font></code> does not satisfy
this condition. 

<br/>
<br/>
<b><big><a name="VectorSize" id="VectorSize">VectorSize</a></big></b>
<br/>
The type 
<code><i><font color="black"><span style='white-space: nowrap'>VectorSize</span></font></i></code>
 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&#xA0;of&#xA0;type</span></a>

<code><font color="blue">size_t</font></code>.
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="Uses Forward" id="Uses Forward">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 
<code><i><font color="black"><span style='white-space: nowrap'>f</span></font></i></code>
 contains the corresponding 
<a href="glossary.xml#Taylor Coefficient" target="_top"><span style='white-space: nowrap'>Taylor&#xA0;coefficients</span></a>
.
After a call to any of the sparse Jacobian routines,
the zero order Taylor coefficients correspond to

<code><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'>)</span></font></code>

and the other coefficients are unspecified.

After <code><font color="blue">SparseJacobian</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="sparse_jacobian.cpp.xml" target="_top"><span style='white-space: nowrap'>sparse_jacobian.cpp</span></a>

is examples and tests of <code><font color="blue">sparse_jacobian</font></code>.
It return <code><font color="blue">true</font></code>, if it succeeds and <code><font color="blue">false</font></code> otherwise.


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

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