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@@ -117,8 +119,7 @@ Include dependency graph for bisection_method.cpp:</div>
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</div><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="define-members" name="define-members"></a>
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Macros</h2></td></tr>
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<tr class="memitem:a002b2f4894492820fe708b1b7e7c5e70" id="r_a002b2f4894492820fe708b1b7e7c5e70"><td class="memItemLeft" align="right" valign="top"><a id="a002b2f4894492820fe708b1b7e7c5e70" name="a002b2f4894492820fe708b1b7e7c5e70"></a>
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#define </td><td class="memItemRight" valign="bottom"><b>EPSILON</b>    1e-6</td></tr>
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<tr class="memitem:a002b2f4894492820fe708b1b7e7c5e70" id="r_a002b2f4894492820fe708b1b7e7c5e70"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>    1e-6</td></tr>
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#define </td><td class="memItemRight" valign="bottom"><b>MAX_ITERATIONS</b>   50000</td></tr>
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@@ -127,12 +128,12 @@ Macros</h2></td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a2003b5b2dcfff0769b957ab5c968b03d" id="r_a2003b5b2dcfff0769b957ab5c968b03d"><td class="memItemLeft" align="right" valign="top">static double </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a> (double i)</td></tr>
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<tr class="memitem:a2003b5b2dcfff0769b957ab5c968b03d" id="r_a2003b5b2dcfff0769b957ab5c968b03d"><td class="memItemLeft" align="right" valign="top">static double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a2003b5b2dcfff0769b957ab5c968b03d">eq</a> (double i)</td></tr>
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<tr class="separator:a2003b5b2dcfff0769b957ab5c968b03d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2" id="r_a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplItemLeft" align="right" valign="top">int </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a> (T val)</td></tr>
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<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplItemLeft" align="right" valign="top">int </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a1ab31b90bc584c635ec159468ceed9b2">sgn</a> (T val)</td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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@@ -144,7 +145,24 @@ x_{i+1} = \frac{a_i+b_i}{2}
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</p>
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<p> For the next iteration, the interval is selected as: \([a,x]\) if \(x>0\) or \([x,b]\) if \(x<0\). The Process is continued till a close enough approximation is achieved.</p>
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<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html" title="Solve the equation using Newton-Raphson method for both real and complex solutions.">newton_raphson_method.cpp</a>, <a class="el" href="../../dd/d29/false__position_8cpp.html" title="Solve the equation using false position method, also known as the Secant method.">false_position.cpp</a>, secant_method.cpp </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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</div><h2 class="groupheader">Macro Definition Documentation</h2>
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<a id="a002b2f4894492820fe708b1b7e7c5e70" name="a002b2f4894492820fe708b1b7e7c5e70"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a002b2f4894492820fe708b1b7e7c5e70">◆ </a></span>EPSILON</h2>
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<div class="memproto">
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<table class="memname">
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<td class="memname">#define EPSILON    1e-6</td>
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<div class="fragment"><div class="line"><span class="lineno"> 20</span><span class="preprocessor">#define EPSILON \</span></div>
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<div class="line"><span class="lineno"> 21</span><span class="preprocessor"> 1e-6 </span><span class="comment">// std::numeric_limits<double>::epsilon() ///< system accuracy limit</span></div>
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</div><!-- fragment -->
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<h2 class="groupheader">Function Documentation</h2>
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<a id="a2003b5b2dcfff0769b957ab5c968b03d" name="a2003b5b2dcfff0769b957ab5c968b03d"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a2003b5b2dcfff0769b957ab5c968b03d">◆ </a></span>eq()</h2>
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@@ -157,8 +175,7 @@ x_{i+1} = \frac{a_i+b_i}{2}
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<tr>
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<td class="memname">static double eq </td>
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<td>(</td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>i</em></td><td>)</td>
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<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>i</em></span></td><td>)</td>
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<td></td>
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<tr>
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void </td>
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<td class="paramname"></td><td>)</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"></span></td><td>)</td>
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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"> 42</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < <a class="code hl_define" href="#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="#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(a);</div>
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<div class="line"><span class="lineno"> 44</span> x = <a class="code hl_function" href="#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="#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(z) == <a class="code hl_function" href="#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"> 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"> 57</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_define" href="#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"> 59</span> z = <a class="code hl_function" href="#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"> 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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<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> bisection_method.cpp:26</div></div>
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<div class="ttc" id="abisection__method_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="#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="#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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<div class="ttc" id="abisection__method_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition</b> bisection_method.cpp:26</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><!-- fragment --><div class="dynheader">
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@@ -260,8 +276,7 @@ template<typename T > </div>
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<tr>
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<td class="memname">int sgn </td>
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<td>(</td>
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<td class="paramtype">T </td>
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<td class="paramname"><em>val</em></td><td>)</td>
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<td class="paramtype">T</td> <td class="paramname"><span class="paramname"><em>val</em></span></td><td>)</td>
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@@ -279,7 +294,7 @@ template<typename T > </div>
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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> 1.9.8 </li>
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