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link_sparse_jacobian.xml @upstream/2015.00.00.7 — raw · history · blame
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xmlns:math='http://www.w3.org/1998/Math/MathML' > <head> <title>Speed Testing Sparse Jacobian</title> <meta http-equiv='Content-Type' content='text/html' charset='utf-8'/> <meta name="description" id="description" content="Speed Testing Sparse Jacobian"/> <meta name="keywords" id="keywords" content=" link_sparse_jacobian sparse speed test testing jacobian prototype method size repeat m row col x n_sweep double "/> <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='_link_sparse_jacobian_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="link_sparse_hessian.xml" target="_top">Prev</a> </td><td><a href="microsoft_timer.xml" target="_top">Next</a> </td><td> <select onchange='choose_across0(this)'> <option>Index-></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-></option> <option>CppAD</option> <option>speed</option> <option>speed_main</option> <option>link_sparse_jacobian</option> </select> </td> <td> <select onchange='choose_down3(this)'> <option>CppAD-></option> <option>Install</option> <option>Introduction</option> <option>AD</option> <option>ADFun</option> <option>preprocessor</option> <option>multi_thread</option> <option>library</option> <option>ipopt_solve</option> <option>Example</option> <option>speed</option> <option>Appendix</option> </select> </td> <td> <select onchange='choose_down2(this)'> <option>speed-></option> <option>speed_main</option> <option>speed_utility</option> <option>speed_double</option> <option>speed_adolc</option> <option>speed_cppad</option> <option>speed_fadbad</option> <option>speed_sacado</option> </select> </td> <td> <select onchange='choose_down1(this)'> <option>speed_main-></option> <option>link_det_lu</option> <option>link_det_minor</option> <option>link_mat_mul</option> <option>link_ode</option> <option>link_poly</option> <option>link_sparse_hessian</option> <option>link_sparse_jacobian</option> <option>microsoft_timer</option> </select> </td> <td>link_sparse_jacobian</td> <td> <select onchange='choose_current0(this)'> <option>Headings-></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> </select> </td> </tr></table><br/> <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 bool link_sparse_jacobian(<br/>      size_t                       </span></font><i><font color="black"><span style='white-space: nowrap'>size</span></font></i><font color="blue"><span style='white-space: nowrap'>      ,<br/>      size_t                       </span></font><i><font color="black"><span style='white-space: nowrap'>repeat</span></font></i><font color="blue"><span style='white-space: nowrap'>    ,<br/>      size_t                       </span></font><i><font color="black"><span style='white-space: nowrap'>m</span></font></i><font color="blue"><span style='white-space: nowrap'>         ,<br/>      const CppAD::vector<size_t>& </span></font><i><font color="black"><span style='white-space: nowrap'>row</span></font></i><font color="blue"><span style='white-space: nowrap'>       ,<br/>      const CppAD::vector<size_t>& </span></font><i><font color="black"><span style='white-space: nowrap'>col</span></font></i><font color="blue"><span style='white-space: nowrap'>       , <br/>            CppAD::vector<double>& </span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>         ,<br/>            CppAD::vector<double>& </span></font><i><font color="black"><span style='white-space: nowrap'>jacobian</span></font></i><font color="blue"><span style='white-space: nowrap'>  ,<br/>            size_t&                </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">→</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">∂</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">∂</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'> = </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">…</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'> != </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/>      </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'>] != </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'>] || </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'>] != </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/>         CppAD::vector<double>& </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() == </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">×</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">…</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">…</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">∂</mo> <mi mathvariant='italic'>f</mi> <mo stretchy="false">[</mo> <mi mathvariant='italic'>i</mi> <mo stretchy="false">]</mo> </mrow> <mrow><mo stretchy="false">∂</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 method</span></a> which can be set to <a href="speed_main.xml#Sparsity Options.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 </body> </html> |