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<a href="#func-members">Functions</a> </div>
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<div class="title">fsolve_test.c File Reference</div> </div>
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<p>Examples of solving non-linear equation systems.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include <stdio.h></code><br />
<code>#include <stdlib.h></code><br />
<code>#include <math.h></code><br />
<code>#include <complex.h></code><br />
<code>#include <float.h></code><br />
<code>#include "<a class="el" href="vector_8h_source.html">vector.h</a>"</code><br />
<code>#include "<a class="el" href="matrix_8h_source.html">matrix.h</a>"</code><br />
<code>#include "<a class="el" href="damped__newton__raphson_8h_source.html">damped_newton_raphson.h</a>"</code><br />
<code>#include "<a class="el" href="newton__raphson_8h_source.html">newton_raphson.h</a>"</code><br />
<code>#include "<a class="el" href="fsolve_8h_source.html">fsolve.h</a>"</code><br />
</div>
<p><a href="fsolve__test_8c_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:aefd0d3fa000963221de289a3933b7c9b"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="fsolve__test_8c.html#aefd0d3fa000963221de289a3933b7c9b">get_non_lin_sys_f1_</a> (<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f1_vec[])</td></tr>
<tr class="memdesc:aefd0d3fa000963221de289a3933b7c9b"><td class="mdescLeft"> </td><td class="mdescRight">The non-linear system f1. <a href="fsolve__test_8c.html#aefd0d3fa000963221de289a3933b7c9b">More...</a><br /></td></tr>
<tr class="separator:aefd0d3fa000963221de289a3933b7c9b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a3344cde9f5060d7ab962fbaaf1cdd88f"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="fsolve__test_8c.html#a3344cde9f5060d7ab962fbaaf1cdd88f">get_non_lin_sys_J1_</a> (<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J1[][2])</td></tr>
<tr class="memdesc:a3344cde9f5060d7ab962fbaaf1cdd88f"><td class="mdescLeft"> </td><td class="mdescRight">The Jacobian matrix of the non-linear system <img class="formulaInl" alt="$ f_1 $" src="form_23.png"/>. <a href="fsolve__test_8c.html#a3344cde9f5060d7ab962fbaaf1cdd88f">More...</a><br /></td></tr>
<tr class="separator:a3344cde9f5060d7ab962fbaaf1cdd88f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae36fe8e55d180d348ef331efbbc5b908"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="fsolve__test_8c.html#ae36fe8e55d180d348ef331efbbc5b908">get_non_lin_sys_f2_</a> (<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f2_vec[])</td></tr>
<tr class="memdesc:ae36fe8e55d180d348ef331efbbc5b908"><td class="mdescLeft"> </td><td class="mdescRight">The non-linear system <img class="formulaInl" alt="$ f_2 $" src="form_26.png"/>. <a href="fsolve__test_8c.html#ae36fe8e55d180d348ef331efbbc5b908">More...</a><br /></td></tr>
<tr class="separator:ae36fe8e55d180d348ef331efbbc5b908"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab95955c80b1896b9e75a04faa4ce742e"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="fsolve__test_8c.html#ab95955c80b1896b9e75a04faa4ce742e">get_non_lin_sys_J2_</a> (<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J2[][3])</td></tr>
<tr class="memdesc:ab95955c80b1896b9e75a04faa4ce742e"><td class="mdescLeft"> </td><td class="mdescRight">The Jacobian matrix of the non-linear system <img class="formulaInl" alt="$ f_2 $" src="form_26.png"/>. <a href="fsolve__test_8c.html#ab95955c80b1896b9e75a04faa4ce742e">More...</a><br /></td></tr>
<tr class="separator:ab95955c80b1896b9e75a04faa4ce742e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8f8a1fe785d5304202601b95e1e6871a"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="fsolve__test_8c.html#a8f8a1fe785d5304202601b95e1e6871a">get_non_lin_sys_f3_</a> (<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], <a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f3_vec[])</td></tr>
<tr class="memdesc:a8f8a1fe785d5304202601b95e1e6871a"><td class="mdescLeft"> </td><td class="mdescRight">The non-linear system <img class="formulaInl" alt="$ f_3 $" src="form_31.png"/>. <a href="fsolve__test_8c.html#a8f8a1fe785d5304202601b95e1e6871a">More...</a><br /></td></tr>
<tr class="separator:a8f8a1fe785d5304202601b95e1e6871a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6686e4624961ca943bebb616e763a100"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="fsolve__test_8c.html#a6686e4624961ca943bebb616e763a100">get_non_lin_sys_J3_</a> (<a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_arr[], <a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J3[][3])</td></tr>
<tr class="memdesc:a6686e4624961ca943bebb616e763a100"><td class="mdescLeft"> </td><td class="mdescRight">The Jacobian matrix of the non-linear system <img class="formulaInl" alt="$ f_3 $" src="form_31.png"/>. <a href="fsolve__test_8c.html#a6686e4624961ca943bebb616e763a100">More...</a><br /></td></tr>
<tr class="separator:a6686e4624961ca943bebb616e763a100"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a53bbdeb6ad57eeb4b512c4620b64cc37"><td class="memItemLeft" align="right" valign="top"><a id="a53bbdeb6ad57eeb4b512c4620b64cc37"></a>
void </td><td class="memItemRight" valign="bottom"><a class="el" href="fsolve__test_8c.html#a53bbdeb6ad57eeb4b512c4620b64cc37">fsolve_test</a> (void)</td></tr>
<tr class="memdesc:a53bbdeb6ad57eeb4b512c4620b64cc37"><td class="mdescLeft"> </td><td class="mdescRight">Examples of solving non-linear equation systems. <br /></td></tr>
<tr class="separator:a53bbdeb6ad57eeb4b512c4620b64cc37"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Examples of solving non-linear equation systems. </p>
<p>Solving non-linear equation systems examples (see <a class="el" href="fsolve_8h.html">fsolve</a> functions).</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="fsolve__test_8c_source.html">fsolve_test.c</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="aefd0d3fa000963221de289a3933b7c9b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aefd0d3fa000963221de289a3933b7c9b">◆ </a></span>get_non_lin_sys_f1_()</h2>
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<tr>
<td class="memname">void get_non_lin_sys_f1_ </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"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>f1_vec</em>[] </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>The non-linear system f1. </p>
<p><img class="formulaInl" alt="$ f_1 \left(x_1, x_2 \right) = \begin{bmatrix} x_1^3 + x_2 - 1 \\ x_2^3 - x_1 + 1 \\ \end{bmatrix} $" src="form_20.png"/></p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">x_arr[]</td><td>pointer to the <img class="formulaInl" alt="$ x_1 $" src="form_21.png"/> and <img class="formulaInl" alt="$ x_2 $" src="form_22.png"/> values. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">f1_vec[]</td><td>pointer to the <img class="formulaInl" alt="$ f_1 $" src="form_23.png"/> function values. </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="fsolve__test_8c_source.html#l00054">54</a> of file <a class="el" href="fsolve__test_8c_source.html">fsolve_test.c</a>.</p>
<p class="reference">Referenced by <a class="el" href="fsolve__test_8c_source.html#l00245">fsolve_test()</a>.</p>
</div>
</div>
<a id="ae36fe8e55d180d348ef331efbbc5b908"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae36fe8e55d180d348ef331efbbc5b908">◆ </a></span>get_non_lin_sys_f2_()</h2>
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<td class="memname">void get_non_lin_sys_f2_ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>x_arr</em>[], </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>f2_vec</em>[] </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>The non-linear system <img class="formulaInl" alt="$ f_2 $" src="form_26.png"/>. </p>
<p><img class="formulaInl" alt="$ f_2 \left( x_1, x_2, x_3 \right) = \begin{bmatrix} 3 x_1 - \cos\left( x_2 \times x_3 \right) - \dfrac{1}{2} \\ x_1^2 - 81 \left( x_2 + 0.1 \right)^2 + \sin(x_3) + 1.06 \\ \exp \left( -x1 \times x_2 \right) + 20 x_3 + \dfrac{10 \pi -3}{3} \\ \end{bmatrix} $" src="form_27.png"/></p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">x_arr[]</td><td>pointer to the <img class="formulaInl" alt="$ x_1 $" src="form_21.png"/>, <img class="formulaInl" alt="$ x_2 $" src="form_22.png"/>, and <img class="formulaInl" alt="$ x_3 $" src="form_28.png"/> values. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">f2_vec[]</td><td>pointer to the <img class="formulaInl" alt="$ f_2 $" src="form_26.png"/> function values. </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="fsolve__test_8c_source.html#l00110">110</a> of file <a class="el" href="fsolve__test_8c_source.html">fsolve_test.c</a>.</p>
<p class="reference">References <a class="el" href="matrix_8h_source.html#l00054">M_PI</a>.</p>
<p class="reference">Referenced by <a class="el" href="fsolve__test_8c_source.html#l00245">fsolve_test()</a>.</p>
</div>
</div>
<a id="a8f8a1fe785d5304202601b95e1e6871a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8f8a1fe785d5304202601b95e1e6871a">◆ </a></span>get_non_lin_sys_f3_()</h2>
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<td class="memname">void get_non_lin_sys_f3_ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>x_arr</em>[], </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>f3_vec</em>[] </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</table>
</div><div class="memdoc">
<p>The non-linear system <img class="formulaInl" alt="$ f_3 $" src="form_31.png"/>. </p>
<p><img class="formulaInl" alt="$ f_3 \left( x_1, x_2, x_3 \right) = \begin{bmatrix} \exp \left( -x_1 x_2 \right) + \log \left( x_1 \right)-\exp \left( -2 \right) \\ \exp \left( x_1 \right) - \dfrac{\sqrt{x_3}}{x_1} - \exp \left( 1 \right) + 2\\ x_1 + x_2 - x_2 x_3 + 5 \\ \end{bmatrix} $" src="form_32.png"/></p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">x_arr[]</td><td>pointer to the <img class="formulaInl" alt="$ x_1 $" src="form_21.png"/>, <img class="formulaInl" alt="$ x_2 $" src="form_22.png"/>, and <img class="formulaInl" alt="$ x_3 $" src="form_28.png"/> values. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">f3_vec[]</td><td>pointer to the <img class="formulaInl" alt="$ f_3 $" src="form_31.png"/> function values. </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="fsolve__test_8c_source.html#l00174">174</a> of file <a class="el" href="fsolve__test_8c_source.html">fsolve_test.c</a>.</p>
<p class="reference">Referenced by <a class="el" href="fsolve__test_8c_source.html#l00245">fsolve_test()</a>.</p>
</div>
</div>
<a id="a3344cde9f5060d7ab962fbaaf1cdd88f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3344cde9f5060d7ab962fbaaf1cdd88f">◆ </a></span>get_non_lin_sys_J1_()</h2>
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<td class="memname">void get_non_lin_sys_J1_ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>x_arr</em>[], </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td>
<td class="paramname"><em>J1</em>[][2] </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>The Jacobian matrix of the non-linear system <img class="formulaInl" alt="$ f_1 $" src="form_23.png"/>. </p>
<p><img class="formulaInl" alt="$ J_1 \left( x_1, x_2\right) = \begin{bmatrix} 3 \times x_1^2 & 1 \\ -1 & 3 \times x_2^2 \\ \end{bmatrix} $" src="form_24.png"/></p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">x_arr[]</td><td>pointer to the <img class="formulaInl" alt="$ x_1 $" src="form_21.png"/> and <img class="formulaInl" alt="$ x_2 $" src="form_22.png"/> values. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">J1[][]</td><td>pointer to the Jacobian function <img class="formulaInl" alt="$ J_1 $" src="form_25.png"/>. </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="fsolve__test_8c_source.html#l00080">80</a> of file <a class="el" href="fsolve__test_8c_source.html">fsolve_test.c</a>.</p>
<p class="reference">Referenced by <a class="el" href="fsolve__test_8c_source.html#l00245">fsolve_test()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ab95955c80b1896b9e75a04faa4ce742e">◆ </a></span>get_non_lin_sys_J2_()</h2>
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<table class="memname">
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<td class="memname">void get_non_lin_sys_J2_ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>x_arr</em>[], </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td>
<td class="paramname"><em>J2</em>[][3] </td>
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<td></td>
<td>)</td>
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<p>The Jacobian matrix of the non-linear system <img class="formulaInl" alt="$ f_2 $" src="form_26.png"/>. </p>
<p><img class="formulaInl" alt="$ J_2 \left( x_1, x_2, x_3 \right) = \begin{bmatrix} 3 & x_3 \sin\left( x_2 x_3 \right) & x_2 \sin\left( x_2 x_3 \right) \\ 2 x_1 & -162 x2 - \dfrac{81}{5} & \cos(x_3) \\ -x_2 \exp\left( -x_1 x_2 \right) & -x_1 \exp\left( -x_1 x_2 \right) & 20 \end{bmatrix} $" src="form_29.png"/></p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">x_arr[]</td><td>pointer to the <img class="formulaInl" alt="$ x_1 $" src="form_21.png"/>, <img class="formulaInl" alt="$ x_2 $" src="form_22.png"/>, and <img class="formulaInl" alt="$ x_3 $" src="form_28.png"/> values. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">J2[][]</td><td>pointer to the Jacobian function <img class="formulaInl" alt="$ J_2 $" src="form_30.png"/>. </td></tr>
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</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="fsolve__test_8c_source.html#l00139">139</a> of file <a class="el" href="fsolve__test_8c_source.html">fsolve_test.c</a>.</p>
<p class="reference">Referenced by <a class="el" href="fsolve__test_8c_source.html#l00245">fsolve_test()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a6686e4624961ca943bebb616e763a100">◆ </a></span>get_non_lin_sys_J3_()</h2>
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<td class="memname">void get_non_lin_sys_J3_ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> </td>
<td class="paramname"><em>x_arr</em>[], </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> </td>
<td class="paramname"><em>J3</em>[][3] </td>
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<td></td>
<td>)</td>
<td></td><td></td>
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<p>The Jacobian matrix of the non-linear system <img class="formulaInl" alt="$ f_3 $" src="form_31.png"/>. </p>
<p><img class="formulaInl" alt="$ J_3 \left( x_1, x_2, x_3 \right) = \begin{bmatrix} \dfrac{1}{x_1}-x_2 \exp\left(-x_1 x_2\right) & -x_1\exp\left(-x_1 x_2\right) & 0 \\ \exp\left(x_1\right) + \dfrac{\sqrt{x_3}}{x_1^2} & 0 & \dfrac{-1}{2x_1\sqrt{x_3}} \\ 1 & 1-x_3 & -x_2 \end{bmatrix} $" src="form_33.png"/></p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">x_arr[]</td><td>pointer to the <img class="formulaInl" alt="$ x_1 $" src="form_21.png"/>, <img class="formulaInl" alt="$ x_2 $" src="form_22.png"/>, and <img class="formulaInl" alt="$ x_3 $" src="form_28.png"/> values. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">J3[][]</td><td>pointer to the Jacobian function <img class="formulaInl" alt="$ J_3 $" src="form_34.png"/>. </td></tr>
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</dd>
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<p class="definition">Definition at line <a class="el" href="fsolve__test_8c_source.html#l00210">210</a> of file <a class="el" href="fsolve__test_8c_source.html">fsolve_test.c</a>.</p>
<p class="reference">Referenced by <a class="el" href="fsolve__test_8c_source.html#l00245">fsolve_test()</a>.</p>
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