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<div class="title">damped_newton_raphson.h File Reference<div class="ingroups"><a class="el" href="group__non__linear__algebra.html">NON_LINEAR_ALGEBRA</a> » <a class="el" href="group__solve__non__linear__equations.html">SOLVE_NON_LINEAR_EQUATIONS</a></div></div> </div>
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<p>Implement the damped Newton–Raphson algorithm.
<a href="#details">More...</a></p>
<div class="textblock"><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="damped__newton__raphson_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:a0cf3dc5e334091bc43820fa1d8e86c14"><td class="memItemLeft" align="right" valign="top">uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="damped__newton__raphson_8h.html#a0cf3dc5e334091bc43820fa1d8e86c14">damped_newton_raphson</a> (uint8_t f_length, uint8_t n, <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x0_arr[], double min_lamda, double eps, uint8_t max_it_num, <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> est_x_arr[], void(*get_non_lin_sys)(<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], <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> x_arr[], <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J[][n]))</td></tr>
<tr class="memdesc:a0cf3dc5e334091bc43820fa1d8e86c14"><td class="mdescLeft"> </td><td class="mdescRight">Implements the damped Newton–Raphson algorithm. <a href="damped__newton__raphson_8h.html#a0cf3dc5e334091bc43820fa1d8e86c14">More...</a><br /></td></tr>
<tr class="separator:a0cf3dc5e334091bc43820fa1d8e86c14"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a46f90a02170f4f35f9b3bdbc5c65271a"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="damped__newton__raphson_8h.html#a46f90a02170f4f35f9b3bdbc5c65271a">get_damped_norm</a> (uint8_t m, uint8_t n, <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], void(*get_non_lin_sys)(<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], <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> x_arr[], <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J[][n]))</td></tr>
<tr class="memdesc:a46f90a02170f4f35f9b3bdbc5c65271a"><td class="mdescLeft"> </td><td class="mdescRight">Compute the norm of the damped Newton–Raphson algorithm. <a href="damped__newton__raphson_8h.html#a46f90a02170f4f35f9b3bdbc5c65271a">More...</a><br /></td></tr>
<tr class="separator:a46f90a02170f4f35f9b3bdbc5c65271a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acd5be84f1d01dfb379d85cc8aef8b65e"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="damped__newton__raphson_8h.html#acd5be84f1d01dfb379d85cc8aef8b65e">get_delta_x</a> (uint8_t m, uint8_t n, <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], void(*get_non_lin_sys)(<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], <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> x_arr[], <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J[][n]), <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> delta_x_arr[])</td></tr>
<tr class="memdesc:acd5be84f1d01dfb379d85cc8aef8b65e"><td class="mdescLeft"> </td><td class="mdescRight">Compute the correction vector the damped Newton–Raphson algorithm. <a href="damped__newton__raphson_8h.html#acd5be84f1d01dfb379d85cc8aef8b65e">More...</a><br /></td></tr>
<tr class="separator:acd5be84f1d01dfb379d85cc8aef8b65e"><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 damped Newton–Raphson algorithm. </p>
<p>The damped Newton–Raphson algorithm enables to solve multi-variant nonlinear equation systems.</p>
<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></dl>
<p class="definition">Definition in file <a class="el" href="damped__newton__raphson_8h_source.html">damped_newton_raphson.h</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0cf3dc5e334091bc43820fa1d8e86c14"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0cf3dc5e334091bc43820fa1d8e86c14">◆ </a></span>damped_newton_raphson()</h2>
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<td class="memname">uint8_t damped_newton_raphson </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_arr</em>[], </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double </td>
<td class="paramname"><em>min_lamda</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double </td>
<td class="paramname"><em>eps</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>max_it_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_arr</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> x_arr[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f_vec[]) </td>
<td class="paramname"><em>get_non_lin_sys</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> x_arr[], <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 damped Newton–Raphson algorithm. </p>
<p>The user should provide pointers to non-linear equation systems 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_arr[]</td><td>start vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">min_lamda</td><td>minimal damping factor. </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">max_it_num</td><td>maximal iteration number of the damped Newton–Raphson algorithm. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">est_x_arr[]</td><td>estimated (solution) vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">(*get_non_lin_sys)</td><td>pointer to non-linear equation systems. </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="damped__newton__raphson_8c_source.html#l00032">32</a> of file <a class="el" href="damped__newton__raphson_8c_source.html">damped_newton_raphson.c</a>.</p>
<p class="reference">References <a class="el" href="damped__newton__raphson_8c_source.html#l00104">get_damped_norm()</a>, <a class="el" href="damped__newton__raphson_8c_source.html#l00120">get_delta_x()</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>, <a class="el" href="vector_8c_source.html#l00141">vector_scalar_mul()</a>, and <a class="el" href="vector_8h_source.html#l00033">vector_t</a>.</p>
<p class="reference">Referenced by <a class="el" href="fsolve_8c_source.html#l00029">fsolve()</a>.</p>
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</div>
<a id="a46f90a02170f4f35f9b3bdbc5c65271a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a46f90a02170f4f35f9b3bdbc5c65271a">◆ </a></span>get_damped_norm()</h2>
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<td class="memname">double get_damped_norm </td>
<td>(</td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>m</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>x_arr</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> x_arr[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f_vec[]) </td>
<td class="paramname"><em>get_non_lin_sys</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> x_arr[], <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>Compute the norm of the damped Newton–Raphson algorithm. </p>
<p>The user should provide pointers to non-linear equation systems 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">m</td><td>number of the non-linear equations. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>length of the guess vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">x_arr[]</td><td>guess vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">(*get_non_lin_sys)</td><td>pointer to non-linear equation systems. </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>norm of the damped Newton–Raphson algorithm. </dd></dl>
<p class="definition">Definition at line <a class="el" href="damped__newton__raphson_8c_source.html#l00104">104</a> of file <a class="el" href="damped__newton__raphson_8c_source.html">damped_newton_raphson.c</a>.</p>
<p class="reference">References <a class="el" href="damped__newton__raphson_8c_source.html#l00120">get_delta_x()</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="damped__newton__raphson_8c_source.html#l00032">damped_newton_raphson()</a>.</p>
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<a id="acd5be84f1d01dfb379d85cc8aef8b65e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acd5be84f1d01dfb379d85cc8aef8b65e">◆ </a></span>get_delta_x()</h2>
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<td class="memname">void get_delta_x </td>
<td>(</td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>m</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>x_arr</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> x_arr[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f_vec[]) </td>
<td class="paramname"><em>get_non_lin_sys</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> x_arr[], <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 class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>delta_x_arr</em>[] </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p>Compute the correction vector the damped Newton–Raphson algorithm. </p>
<p>The user should provide pointers to non-linear equation systems 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">m</td><td>number of the non-linear equations. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>length of the guess vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">x_arr[]</td><td>guess vector. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">(*get_non_lin_sys)</td><td>pointer to non-linear equation systems. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">(*get_jacobian)</td><td>pointer to the Jacobian matrix. </td></tr>
<tr><td class="paramdir">[in,out]</td><td class="paramname">delta_x_arr[]</td><td>the correction vector (term). </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="damped__newton__raphson_8c_source.html#l00120">120</a> of file <a class="el" href="damped__newton__raphson_8c_source.html">damped_newton_raphson.c</a>.</p>
<p class="reference">References <a class="el" href="matrix_8c_source.html#l00434">matrix_mul_vec()</a>, <a class="el" href="matrix_8h_source.html#l00038">matrix_t</a>, <a class="el" href="moore__penrose__pseudo__inverse_8c_source.html#l00038">moore_penrose_get_pinv()</a>, <a class="el" href="vector_8c_source.html#l00131">vector_in_place_scalar_mul()</a>, and <a class="el" href="vector_8h_source.html#l00033">vector_t</a>.</p>
<p class="reference">Referenced by <a class="el" href="damped__newton__raphson_8c_source.html#l00032">damped_newton_raphson()</a>, and <a class="el" href="damped__newton__raphson_8c_source.html#l00104">get_damped_norm()</a>.</p>
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