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<title>Algorithms_in_C++: numerical_methods/bisection_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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@@ -161,9 +161,9 @@ Functions</h2></td></tr>
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</table>
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</div><div class="memdoc">
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<p >define \(f(x)\) to find root for </p>
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<div class="fragment"><div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> {</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</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="l00028" name="l00028"></a><span class="lineno"> 28</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 26</span> {</div>
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<div class="line"><span class="lineno"> 27</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"> 28</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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@@ -190,45 +190,45 @@ 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="l00037" name="l00037"></a><span class="lineno"> 37</span> {</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordtype">double</span> a = -1, b = 1, x, z;</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordtype">int</span> i;</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// loop to find initial intervals a, b</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < <a class="code hl_define" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> z = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(a);</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> x = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(z) == <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(x)) { <span class="comment">// same signs, increase interval</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> b++;</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> a--;</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> } <span class="keywordflow">else</span> { <span class="comment">// if opposite signs, we got our interval</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</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> </div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</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">"\nFirst initial: "</span> << a;</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</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">"\nSecond initial: "</span> << b;</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// start iterations</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_define" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> x = (a + b) / 2;</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> z = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(x);</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</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\nz: "</span> << z << <span class="stringliteral">"\t["</span> << a << <span class="stringliteral">" , "</span> << b</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> << <span class="stringliteral">" | Bisect: "</span> << x << <span class="stringliteral">"]"</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> <span class="keywordflow">if</span> (z < 0) {</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> a = x;</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> b = x;</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="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">if</span> (std::abs(z) < <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="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</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> << x << <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="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 37</span> {</div>
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<div class="line"><span class="lineno"> 38</span> <span class="keywordtype">double</span> a = -1, b = 1, x, z;</div>
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<div class="line"><span class="lineno"> 39</span> <span class="keywordtype">int</span> i;</div>
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<div class="line"><span class="lineno"> 40</span> </div>
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<div class="line"><span class="lineno"> 41</span> <span class="comment">// loop to find initial intervals a, b</span></div>
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<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < <a class="code hl_define" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
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<div class="line"><span class="lineno"> 43</span> z = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(a);</div>
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<div class="line"><span class="lineno"> 44</span> x = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
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<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(z) == <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(x)) { <span class="comment">// same signs, increase interval</span></div>
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<div class="line"><span class="lineno"> 46</span> b++;</div>
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<div class="line"><span class="lineno"> 47</span> a--;</div>
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<div class="line"><span class="lineno"> 48</span> } <span class="keywordflow">else</span> { <span class="comment">// if opposite signs, we got our interval</span></div>
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<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><span class="lineno"> 50</span> }</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> </div>
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<div class="line"><span class="lineno"> 53</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">"\nFirst initial: "</span> << a;</div>
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<div class="line"><span class="lineno"> 54</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">"\nSecond initial: "</span> << b;</div>
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<div class="line"><span class="lineno"> 55</span> </div>
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<div class="line"><span class="lineno"> 56</span> <span class="comment">// start iterations</span></div>
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<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_define" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
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<div class="line"><span class="lineno"> 58</span> x = (a + b) / 2;</div>
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<div class="line"><span class="lineno"> 59</span> z = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(x);</div>
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||||
<div class="line"><span class="lineno"> 60</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\nz: "</span> << z << <span class="stringliteral">"\t["</span> << a << <span class="stringliteral">" , "</span> << b</div>
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<div class="line"><span class="lineno"> 61</span> << <span class="stringliteral">" | Bisect: "</span> << x << <span class="stringliteral">"]"</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> <span class="keywordflow">if</span> (z < 0) {</div>
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<div class="line"><span class="lineno"> 64</span> a = x;</div>
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<div class="line"><span class="lineno"> 65</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 66</span> b = x;</div>
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<div class="line"><span class="lineno"> 67</span> }</div>
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<div class="line"><span class="lineno"> 68</span> </div>
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<div class="line"><span class="lineno"> 69</span> <span class="keywordflow">if</span> (std::abs(z) < <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"> 70</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><span class="lineno"> 71</span> }</div>
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<div class="line"><span class="lineno"> 72</span> </div>
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<div class="line"><span class="lineno"> 73</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> << x << <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"> 74</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 75</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="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> bisection_method.cpp:22</div></div>
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<div class="ttc" id="abisection__method_8cpp_html_a1ab31b90bc584c635ec159468ceed9b2"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a></div><div class="ttdeci">int sgn(T val)</div><div class="ttdef"><b>Definition:</b> bisection_method.cpp:32</div></div>
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@@ -262,9 +262,9 @@ template<typename T > </div>
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</table>
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||||
</div><div class="memdoc">
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<p >get the sign of any given number </p>
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<div class="fragment"><div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> {</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordflow">return</span> (T(0) < val) - (val < T(0));</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 32</span> {</div>
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<div class="line"><span class="lineno"> 33</span> <span class="keywordflow">return</span> (T(0) < val) - (val < T(0));</div>
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<div class="line"><span class="lineno"> 34</span>}</div>
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</div><!-- fragment -->
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</div>
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</div>
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@@ -274,7 +274,7 @@ template<typename T > </div>
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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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="../../d7/d6a/bisection__method_8cpp.html">bisection_method.cpp</a></li>
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<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
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<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
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