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<div class="title">levenberg_marquardt.h File Reference<div class="ingroups"><a class="el" href="group__non__linear__algebra.html">NON_LINEAR_ALGEBRA</a> » <a class="el" href="group__optimization.html">OPTIMIZATION</a></div></div> </div>
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<p>Implement the Levenberg–Marquardt (LVM) algorithm.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include <inttypes.h></code><br />
<code>#include "<a class="el" href="matrix_8h_source.html">matrix.h</a>"</code><br />
<code>#include "<a class="el" href="vector_8h_source.html">vector.h</a>"</code><br />
</div>
<p><a href="levenberg__marquardt_8h_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a2a72b2b6be15a9998b61a9c0097e3d5f"><td class="memItemLeft" align="right" valign="top">uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="levenberg__marquardt_8h.html#a2a72b2b6be15a9998b61a9c0097e3d5f">opt_levenberg_marquardt</a> (uint8_t f_length, uint8_t n, <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x0_vec[n], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> data_vec[f_length], <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> eps, <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> tau, <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> beta0, <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> beta1, uint8_t max_iter_num, <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> est_x_vec[n], void(*get_f_error)(<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x0_vec[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> data_vec[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f_vec[]), void(*get_jacobian)(<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x0_vec[], <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J[][n]))</td></tr>
<tr class="memdesc:a2a72b2b6be15a9998b61a9c0097e3d5f"><td class="mdescLeft"> </td><td class="mdescRight">Implements the Levenberg–Marquardt (LVM) algorithm. <a href="levenberg__marquardt_8h.html#a2a72b2b6be15a9998b61a9c0097e3d5f">More...</a><br /></td></tr>
<tr class="separator:a2a72b2b6be15a9998b61a9c0097e3d5f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a46fb5a9d6d185ff7f98c9cf34b56e34f"><td class="memItemLeft" align="right" valign="top"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="levenberg__marquardt_8h.html#a46fb5a9d6d185ff7f98c9cf34b56e34f">opt_levenberg_marquardt_get_mu0</a> (uint8_t n, <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> tau, <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> JTJ[][n])</td></tr>
<tr class="memdesc:a46fb5a9d6d185ff7f98c9cf34b56e34f"><td class="mdescLeft"> </td><td class="mdescRight">Compute the initial value <img class="formulaInl" alt="$ \mu_0 $" src="form_57.png"/> of the Levenberg–Marquardt (LVM) algorithm. <a href="levenberg__marquardt_8h.html#a46fb5a9d6d185ff7f98c9cf34b56e34f">More...</a><br /></td></tr>
<tr class="separator:a46fb5a9d6d185ff7f98c9cf34b56e34f"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implement the Levenberg–Marquardt (LVM) algorithm. </p>
<dl class="section note"><dt>Note</dt><dd>This function is generally implemented.</dd></dl>
<dl class="section author"><dt>Author</dt><dd>Zakaria Kasmi <a href="#" onclick="location.href='mai'+'lto:'+'zka'+'sm'+'i@i'+'nf'+'.fu'+'-b'+'erl'+'in'+'.de'; return false;">zkasm<span style="display: none;">.nosp@m.</span>i@in<span style="display: none;">.nosp@m.</span>f.fu-<span style="display: none;">.nosp@m.</span>berl<span style="display: none;">.nosp@m.</span>in.de</a> </dd>
<dd>
Naouar Guerchali </dd></dl>
<p class="definition">Definition in file <a class="el" href="levenberg__marquardt_8h_source.html">levenberg_marquardt.h</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a2a72b2b6be15a9998b61a9c0097e3d5f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a2a72b2b6be15a9998b61a9c0097e3d5f">◆ </a></span>opt_levenberg_marquardt()</h2>
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<td class="memname">uint8_t opt_levenberg_marquardt </td>
<td>(</td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>f_length</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>x0_vec</em>[n], </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>data_vec</em>[f_length], </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td>
<td class="paramname"><em>eps</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td>
<td class="paramname"><em>tau</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td>
<td class="paramname"><em>beta0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td>
<td class="paramname"><em>beta1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>max_iter_num</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>est_x_vec</em>[n], </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">void(*)(<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x0_vec[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> data_vec[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f_vec[]) </td>
<td class="paramname"><em>get_f_error</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">void(*)(<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x0_vec[], <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J[][n]) </td>
<td class="paramname"><em>get_jacobian</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Implements the Levenberg–Marquardt (LVM) algorithm. </p>
<p>The user should provide pointers to the error and Jacobian functions. </p><dl class="section note"><dt>Note</dt><dd>This function is generally implemented.</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">f_length</td><td>length of the error functions vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>length of the start vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">x0_vec[]</td><td>start vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">data_vec[]</td><td>data vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">eps</td><td>accuracy bound. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">tau</td><td><img class="formulaInl" alt="$ \tau $" src="form_52.png"/> factor. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">beta0</td><td><img class="formulaInl" alt="$ \beta_0 $" src="form_53.png"/> factor. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">beta1</td><td><img class="formulaInl" alt="$ \beta_1 $" src="form_54.png"/> factor. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">max_iter_num</td><td>maximal iteration number of the LVM algorithm. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">est_x_vec[]</td><td>estimated (optimized) vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">(*get_f_error)</td><td>pointer to the error function. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">(*get_jacobian)</td><td>pointer to the Jacobian matrix.</td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>required iteration number. </dd></dl>
<p class="definition">Definition at line <a class="el" href="levenberg__marquardt_8c_source.html#l00143">143</a> of file <a class="el" href="levenberg__marquardt_8c_source.html">levenberg_marquardt.c</a>.</p>
<p class="reference">References <a class="el" href="matrix_8c_source.html#l00353">matrix_add_to_diag()</a>, <a class="el" href="matrix_8c_source.html#l00602">matrix_mul_scalar()</a>, <a class="el" href="matrix_8h_source.html#l00038">matrix_t</a>, <a class="el" href="matrix_8c_source.html#l00545">matrix_trans_mul_itself()</a>, <a class="el" href="matrix_8c_source.html#l00511">matrix_trans_mul_vec()</a>, <a class="el" href="levenberg__marquardt_8c_source.html#l00053">opt_levenberg_marquardt_correction()</a>, <a class="el" href="levenberg__marquardt_8c_source.html#l00227">opt_levenberg_marquardt_get_mu0()</a>, <a class="el" href="solve_8c_source.html#l00077">solve_householder()</a>, <a class="el" href="vector_8c_source.html#l00104">vector_add()</a>, <a class="el" href="vector_8c_source.html#l00037">vector_copy()</a>, <a class="el" href="vector_8c_source.html#l00042">vector_get_norm2()</a>, and <a class="el" href="vector_8h_source.html#l00033">vector_t</a>.</p>
<p class="reference">Referenced by <a class="el" href="optimization__test_8c_source.html#l00264">optimization_exponential_data_test()</a>, <a class="el" href="optimization__test_8c_source.html#l00376">optimization_sinusoidal_data_test()</a>, and <a class="el" href="optimization__test_8c_source.html#l00101">optimization_test()</a>.</p>
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<a id="a46fb5a9d6d185ff7f98c9cf34b56e34f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a46fb5a9d6d185ff7f98c9cf34b56e34f">◆ </a></span>opt_levenberg_marquardt_get_mu0()</h2>
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<td class="memname"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> opt_levenberg_marquardt_get_mu0 </td>
<td>(</td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td>
<td class="paramname"><em>tau</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td>
<td class="paramname"><em>JTJ</em>[][n] </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Compute the initial value <img class="formulaInl" alt="$ \mu_0 $" src="form_57.png"/> of the Levenberg–Marquardt (LVM) algorithm. </p>
<p>The user should provide a pointer to the matrix <img class="formulaInl" alt="$ J_f^{T} J_{f} $" src="form_40.png"/>.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>column number of the matrix <img class="formulaInl" alt="$J_f^T J_f$" src="form_61.png"/>. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">tau</td><td><img class="formulaInl" alt="$ \tau $" src="form_52.png"/> factor. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">JTJ[][]</td><td>pointer to the matrix <img class="formulaInl" alt="$J_f^T J_f$" src="form_61.png"/>.</td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>parameter <img class="formulaInl" alt="$ \rho_{\mu} $" src="form_56.png"/> </dd></dl>
<p class="definition">Definition at line <a class="el" href="levenberg__marquardt_8c_source.html#l00227">227</a> of file <a class="el" href="levenberg__marquardt_8c_source.html">levenberg_marquardt.c</a>.</p>
<p class="reference">References <a class="el" href="matrix_8h_source.html#l00038">matrix_t</a>.</p>
<p class="reference">Referenced by <a class="el" href="levenberg__marquardt_8c_source.html#l00143">opt_levenberg_marquardt()</a>.</p>
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