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<div class="header">
  <div class="headertitle"><div class="title">newton_raphson_method.cpp</div></div>
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<a href="../../de/dd3/newton__raphson__method_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="preprocessor">#include &lt;ctime&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="preprocessor">#include &lt;limits&gt;</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"><a class="line" href="../../de/dd3/newton__raphson__method_8cpp.html#a75f355966e0a97665eaf5a4c79baa7af">   21</a></span><span class="keyword">constexpr</span> <span class="keywordtype">double</span> EPSILON = 1e-10;              </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"><a class="line" href="../../de/dd3/newton__raphson__method_8cpp.html#a5c5ff05b9f37ae59dad67e1d4f6cd51d">   22</a></span><span class="keyword">constexpr</span> int16_t <a class="code hl_define" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a> = INT16_MAX;  </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span></div>
<div class="foldopen" id="foldopen00030" data-start="{" data-end="}">
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="../../de/dd3/newton__raphson__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">   30</a></span><span class="keyword">static</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(<span class="keywordtype">double</span> i) {</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <span class="keywordflow">return</span> (std::pow(i, 3) - (4 * i) - 9);  <span class="comment">// original equation</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>}</div>
</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span></div>
<div class="foldopen" id="foldopen00040" data-start="{" data-end="}">
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"><a class="line" href="../../de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">   40</a></span><span class="keyword">static</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">eq_der</a>(<span class="keywordtype">double</span> i) {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="keywordflow">return</span> ((3 * std::pow(i, 2)) - 4);  <span class="comment">// derivative of equation</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>}</div>
</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span></div>
<div class="foldopen" id="foldopen00045" data-start="{" data-end="}">
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"><a class="line" href="../../de/dd3/newton__raphson__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">   45</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    std::srand(std::time(<span class="keyword">nullptr</span>));  <span class="comment">// initialize randomizer</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordtype">double</span> z = NAN, c = std::rand() % 100, m = NAN, n = NAN;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="keywordtype">int</span> i = 0;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    std::cout &lt;&lt; <span class="stringliteral">&quot;\nInitial approximation: &quot;</span> &lt;&lt; c;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span> </div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="comment">// start iterations</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_define" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        m = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(c);</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        n = <a class="code hl_function" href="../../de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">eq_der</a>(c);</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        z = c - (m / n);</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        c = z;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <span class="keywordflow">if</span> (std::abs(m) &lt; EPSILON) {  <span class="comment">// stoping criteria</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        }</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    }</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    std::cout &lt;&lt; <span class="stringliteral">&quot;\n\nRoot: &quot;</span> &lt;&lt; z &lt;&lt; <span class="stringliteral">&quot;\t\tSteps: &quot;</span> &lt;&lt; i &lt;&lt; std::endl;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>}</div>
</div>
<div class="ttc" id="abisection__method_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a></div><div class="ttdeci">#define MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations to check.</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d6a/bisection__method_8cpp_source.html#l00022">bisection_method.cpp:22</a></div></div>
<div class="ttc" id="abisection__method_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d6a/bisection__method_8cpp_source.html#l00026">bisection_method.cpp:26</a></div></div>
<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
<div class="ttc" id="anewton__raphson__method_8cpp_html_a3d3f7f41977394680af6ebbed96f3386"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">eq_der</a></div><div class="ttdeci">static double eq_der(double i)</div><div class="ttdef"><b>Definition</b> <a href="#l00040">newton_raphson_method.cpp:40</a></div></div>
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