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<a href="#define-members">Macros</a> &#124;
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<p><a href="https://en.wikipedia.org/wiki/Secant_method" target="_blank">Secant Method</a> implementation.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;assert.h&gt;</code><br />
<code>#include &lt;math.h&gt;</code><br />
<code>#include &lt;stdio.h&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for secant_method.c:</div>
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Macros</h2></td></tr>
<tr class="memitem:a30c17564229ec2e37dfea9c6c9ad643e" id="r_a30c17564229ec2e37dfea9c6c9ad643e"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a>&#160;&#160;&#160;0.0001</td></tr>
<tr class="memdesc:a30c17564229ec2e37dfea9c6c9ad643e"><td class="mdescLeft">&#160;</td><td class="mdescRight">for assert <br /></td></tr>
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<tr class="memitem:a5de5d183f9a6a8d53316f743e1ca6dc2" id="r_a5de5d183f9a6a8d53316f743e1ca6dc2"><td class="memItemLeft" align="right" valign="top"><a id="a5de5d183f9a6a8d53316f743e1ca6dc2" name="a5de5d183f9a6a8d53316f743e1ca6dc2"></a>
#define&#160;</td><td class="memItemRight" valign="bottom"><b>NMAX</b>&#160;&#160;&#160;100</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:aba60904b56a5dce7e291d2f7d62e9782" id="r_aba60904b56a5dce7e291d2f7d62e9782"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d72/secant__method_8c.html#aba60904b56a5dce7e291d2f7d62e9782">func</a> (double x)</td></tr>
<tr class="memdesc:aba60904b56a5dce7e291d2f7d62e9782"><td class="mdescLeft">&#160;</td><td class="mdescRight">Continuous function for which we want to find the root. <br /></td></tr>
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<tr class="memitem:a213829e8511060395c4a31ad8920ef0a" id="r_a213829e8511060395c4a31ad8920ef0a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d72/secant__method_8c.html#a213829e8511060395c4a31ad8920ef0a">secant_method</a> (double x0, double x1, double tolerance)</td></tr>
<tr class="memdesc:a213829e8511060395c4a31ad8920ef0a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Root-finding method for a continuous function given two points. <br /></td></tr>
<tr class="separator:a213829e8511060395c4a31ad8920ef0a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d72/secant__method_8c.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d72/secant__method_8c.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Secant_method" target="_blank">Secant Method</a> implementation. </p>
<p>Find a continuous function's root by using a succession of roots of secant lines to approximate it, starting from the given points' secant line. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/disnoca" target="_blank">Samuel Pires</a> </dd></dl>
</div><h2 class="groupheader">Macro Definition Documentation</h2>
<a id="a30c17564229ec2e37dfea9c6c9ad643e" name="a30c17564229ec2e37dfea9c6c9ad643e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a30c17564229ec2e37dfea9c6c9ad643e">&#9670;&#160;</a></span>TOLERANCE</h2>
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<td class="memname">#define TOLERANCE&#160;&#160;&#160;0.0001</td>
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<p>for assert </p>
<p>for fabs for io operations </p>
</div>
</div>
<h2 class="groupheader">Function Documentation</h2>
<a id="aba60904b56a5dce7e291d2f7d62e9782" name="aba60904b56a5dce7e291d2f7d62e9782"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aba60904b56a5dce7e291d2f7d62e9782">&#9670;&#160;</a></span>func()</h2>
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<td class="memname">double func </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
</tr>
</table>
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<p>Continuous function for which we want to find the root. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>Real input variable </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The evaluation result of the function using the input value </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 22</span>{</div>
<div class="line"><span class="lineno"> 23</span> <span class="keywordflow">return</span> x * x - 3.; <span class="comment">// x^2 = 3 - solution is sqrt(3)</span></div>
<div class="line"><span class="lineno"> 24</span>}</div>
</div><!-- fragment -->
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 77</span>{</div>
<div class="line"><span class="lineno"> 78</span> <a class="code hl_function" href="../../db/d72/secant__method_8c.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 79</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 80</span>}</div>
<div class="ttc" id="asecant__method_8c_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../db/d72/secant__method_8c.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> secant_method.c:61</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a213829e8511060395c4a31ad8920ef0a">&#9670;&#160;</a></span>secant_method()</h2>
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<td class="memname">double secant_method </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>tolerance</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Root-finding method for a continuous function given two points. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x0</td><td>One of the starting secant points </td></tr>
<tr><td class="paramname">x1</td><td>One of the starting secant points </td></tr>
<tr><td class="paramname">tolerance</td><td>Determines how accurate the returned value is. The returned value will be within <code>tolerance</code> of the actual root </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><code>root of the function</code> if secant method succeed within the maximum number of iterations </dd>
<dd>
<code>-1</code> if secant method fails </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 37</span>{</div>
<div class="line"><span class="lineno"> 38</span> <span class="keywordtype">int</span> n = 1; <span class="comment">// step counter</span></div>
<div class="line"><span class="lineno"> 39</span> </div>
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">while</span> (n++ &lt; NMAX)</div>
<div class="line"><span class="lineno"> 41</span> {</div>
<div class="line"><span class="lineno"> 42</span> <span class="comment">// calculate secant line root</span></div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordtype">double</span> x2 = x1 - <a class="code hl_function" href="../../db/d72/secant__method_8c.html#aba60904b56a5dce7e291d2f7d62e9782">func</a>(x1) * (x1 - x0) / (<a class="code hl_function" href="../../db/d72/secant__method_8c.html#aba60904b56a5dce7e291d2f7d62e9782">func</a>(x1) - <a class="code hl_function" href="../../db/d72/secant__method_8c.html#aba60904b56a5dce7e291d2f7d62e9782">func</a>(x0));</div>
<div class="line"><span class="lineno"> 44</span> </div>
<div class="line"><span class="lineno"> 45</span> <span class="comment">// update values</span></div>
<div class="line"><span class="lineno"> 46</span> x0 = x1;</div>
<div class="line"><span class="lineno"> 47</span> x1 = x2;</div>
<div class="line"><span class="lineno"> 48</span> </div>
<div class="line"><span class="lineno"> 49</span> <span class="comment">// return value if it meets tolerance</span></div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">if</span> (fabs(x1 - x0) &lt; tolerance)</div>
<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">return</span> x2;</div>
<div class="line"><span class="lineno"> 52</span> }</div>
<div class="line"><span class="lineno"> 53</span> </div>
<div class="line"><span class="lineno"> 54</span> <span class="keywordflow">return</span> -1; <span class="comment">// method failed (maximum number of steps exceeded)</span></div>
<div class="line"><span class="lineno"> 55</span>}</div>
<div class="ttc" id="asecant__method_8c_html_aba60904b56a5dce7e291d2f7d62e9782"><div class="ttname"><a href="../../db/d72/secant__method_8c.html#aba60904b56a5dce7e291d2f7d62e9782">func</a></div><div class="ttdeci">double func(double x)</div><div class="ttdoc">Continuous function for which we want to find the root.</div><div class="ttdef"><b>Definition</b> secant_method.c:21</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">static void test </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 62</span>{</div>
<div class="line"><span class="lineno"> 63</span> <span class="comment">// compares root values found by the secant method within the tolerance</span></div>
<div class="line"><span class="lineno"> 64</span> assert(<a class="code hl_function" href="../../db/d72/secant__method_8c.html#a213829e8511060395c4a31ad8920ef0a">secant_method</a>(0.2, 0.5, <a class="code hl_define" href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a>) - sqrt(3) &lt; <a class="code hl_define" href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a>);</div>
<div class="line"><span class="lineno"> 65</span> assert(fabs(<a class="code hl_function" href="../../db/d72/secant__method_8c.html#a213829e8511060395c4a31ad8920ef0a">secant_method</a>(-2, -5, <a class="code hl_define" href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a>)) - sqrt(3) &lt; <a class="code hl_define" href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a>);</div>
<div class="line"><span class="lineno"> 66</span> assert(<a class="code hl_function" href="../../db/d72/secant__method_8c.html#a213829e8511060395c4a31ad8920ef0a">secant_method</a>(-3, 2, <a class="code hl_define" href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a>) - sqrt(3) &lt; <a class="code hl_define" href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a>);</div>
<div class="line"><span class="lineno"> 67</span> assert(fabs(<a class="code hl_function" href="../../db/d72/secant__method_8c.html#a213829e8511060395c4a31ad8920ef0a">secant_method</a>(1, -1.5, <a class="code hl_define" href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a>)) - sqrt(3) &lt; <a class="code hl_define" href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a>);</div>
<div class="line"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> printf(<span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</span>);</div>
<div class="line"><span class="lineno"> 70</span>}</div>
<div class="ttc" id="asecant__method_8c_html_a213829e8511060395c4a31ad8920ef0a"><div class="ttname"><a href="../../db/d72/secant__method_8c.html#a213829e8511060395c4a31ad8920ef0a">secant_method</a></div><div class="ttdeci">double secant_method(double x0, double x1, double tolerance)</div><div class="ttdoc">Root-finding method for a continuous function given two points.</div><div class="ttdef"><b>Definition</b> secant_method.c:36</div></div>
<div class="ttc" id="asecant__method_8c_html_a30c17564229ec2e37dfea9c6c9ad643e"><div class="ttname"><a href="../../db/d72/secant__method_8c.html#a30c17564229ec2e37dfea9c6c9ad643e">TOLERANCE</a></div><div class="ttdeci">#define TOLERANCE</div><div class="ttdoc">for assert</div><div class="ttdef"><b>Definition</b> secant_method.c:13</div></div>
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