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<title>Algorithms_in_C++: numerical_methods/newton_raphson_method.cpp File Reference</title>
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
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@@ -164,9 +164,9 @@ constexpr int16_t </td><td class="memItemRight" valign="bottom"><b>MAX_ITER
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<p >define \(f(x)\) to find root for. Currently defined as: </p><p class="formulaDsp">
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\[ f(x) = x^3 - 4x - 9 \]
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</p>
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<div class="fragment"><div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> {</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordflow">return</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 3) - (4 * i) - 9); <span class="comment">// original equation</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 29</span> {</div>
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<div class="line"><span class="lineno"> 30</span> <span class="keywordflow">return</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 3) - (4 * i) - 9); <span class="comment">// original equation</span></div>
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<div class="line"><span class="lineno"> 31</span>}</div>
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<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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@@ -203,9 +203,9 @@ Here is the call graph for this function:</div>
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<p >define the derivative function \(f'(x)\) For the current problem, it is: </p><p class="formulaDsp">
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\[ f'(x) = 3x^2 - 4 \]
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</p>
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<div class="fragment"><div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> {</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">return</span> ((3 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 2)) - 4); <span class="comment">// derivative of equation</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 39</span> {</div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">return</span> ((3 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 2)) - 4); <span class="comment">// derivative of equation</span></div>
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<div class="line"><span class="lineno"> 41</span>}</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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@@ -231,30 +231,30 @@ Here is the call graph for this function:</div>
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</table>
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</div><div class="memdoc">
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<p >Main function </p>
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<div class="fragment"><div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> {</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>)); <span class="comment">// initialize randomizer</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordtype">double</span> z = NAN, c = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, m = NAN, n = NAN;</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordtype">int</span> i = 0;</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\nInitial approximation: "</span> << c;</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// start iterations</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="../../de/dd3/newton__raphson__method_8cpp.html#a5c5ff05b9f37ae59dad67e1d4f6cd51d">MAX_ITERATIONS</a>; i++) {</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> m = <a class="code hl_function" href="../../de/dd3/newton__raphson__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(c);</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> n = <a class="code hl_function" href="../../de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">eq_der</a>(c);</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> z = c - (m / n);</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> c = z;</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">if</span> (std::abs(m) < <a class="code hl_variable" href="../../de/dd3/newton__raphson__method_8cpp.html#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a>) { <span class="comment">// stoping criteria</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> }</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> }</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\n\nRoot: "</span> << z << <span class="stringliteral">"\t\tSteps: "</span> << i << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 44</span> {</div>
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<div class="line"><span class="lineno"> 45</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>)); <span class="comment">// initialize randomizer</span></div>
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<div class="line"><span class="lineno"> 46</span> </div>
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<div class="line"><span class="lineno"> 47</span> <span class="keywordtype">double</span> z = NAN, c = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, m = NAN, n = NAN;</div>
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<div class="line"><span class="lineno"> 48</span> <span class="keywordtype">int</span> i = 0;</div>
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<div class="line"><span class="lineno"> 49</span> </div>
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<div class="line"><span class="lineno"> 50</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\nInitial approximation: "</span> << c;</div>
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<div class="line"><span class="lineno"> 51</span> </div>
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<div class="line"><span class="lineno"> 52</span> <span class="comment">// start iterations</span></div>
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<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="../../de/dd3/newton__raphson__method_8cpp.html#a5c5ff05b9f37ae59dad67e1d4f6cd51d">MAX_ITERATIONS</a>; i++) {</div>
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<div class="line"><span class="lineno"> 54</span> m = <a class="code hl_function" href="../../de/dd3/newton__raphson__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(c);</div>
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<div class="line"><span class="lineno"> 55</span> n = <a class="code hl_function" href="../../de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">eq_der</a>(c);</div>
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<div class="line"><span class="lineno"> 56</span> </div>
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<div class="line"><span class="lineno"> 57</span> z = c - (m / n);</div>
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<div class="line"><span class="lineno"> 58</span> c = z;</div>
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<div class="line"><span class="lineno"> 59</span> </div>
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<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">if</span> (std::abs(m) < <a class="code hl_variable" href="../../de/dd3/newton__raphson__method_8cpp.html#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a>) { <span class="comment">// stoping criteria</span></div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><span class="lineno"> 62</span> }</div>
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<div class="line"><span class="lineno"> 63</span> }</div>
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<div class="line"><span class="lineno"> 64</span> </div>
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<div class="line"><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\n\nRoot: "</span> << z << <span class="stringliteral">"\t\tSteps: "</span> << i << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 67</span>}</div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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<div class="ttc" id="anewton__raphson__method_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:29</div></div>
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@@ -279,7 +279,7 @@ Here is the call graph for this function:</div>
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<ul>
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<li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html">newton_raphson_method.cpp</a></li>
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