mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
synced 2026-03-30 16:51:57 +08:00
Documentation for c6af943508
This commit is contained in:
realstealthninja
@@ -114,13 +114,14 @@ $(function(){initNavTree('de/dd3/newton__raphson__method_8cpp.html','../../'); i
|
||||
<p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Newton%27s_method" target="_blank">Newton-Raphson method</a> for both real and complex solutions.
|
||||
<a href="#details">More...</a></p>
|
||||
<div class="textblock"><code>#include <cmath></code><br />
|
||||
<code>#include <cstdint></code><br />
|
||||
<code>#include <ctime></code><br />
|
||||
<code>#include <iostream></code><br />
|
||||
<code>#include <limits></code><br />
|
||||
</div><div class="textblock"><div class="dynheader">
|
||||
Include dependency graph for newton_raphson_method.cpp:</div>
|
||||
<div class="dyncontent">
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d38/newton__raphson__method_8cpp__incl.svg" width="318" height="126"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d38/newton__raphson__method_8cpp__incl.svg" width="402" height="126"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
||||
</div>
|
||||
</div><table class="memberdecls">
|
||||
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
|
||||
@@ -180,9 +181,9 @@ x_{i+1} = x_i - \frac{f(x_i)}{f'(x_i)}
|
||||
f(x) = x^3 - 4x - 9
|
||||
\]
|
||||
</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 29</span> {</div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 31</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 30</span> {</div>
|
||||
<div class="line"><span class="lineno"> 31</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>
|
||||
<div class="line"><span class="lineno"> 32</span>}</div>
|
||||
<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>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
@@ -219,9 +220,9 @@ Here is the call graph for this function:</div>
|
||||
f'(x) = 3x^2 - 4
|
||||
\]
|
||||
</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 39</span> {</div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 41</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 40</span> {</div>
|
||||
<div class="line"><span class="lineno"> 41</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>
|
||||
<div class="line"><span class="lineno"> 42</span>}</div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
||||
@@ -245,36 +246,36 @@ Here is the call graph for this function:</div>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
<p>Main function </p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 44</span> {</div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 46</span> </div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 48</span> <span class="keywordtype">int</span> i = 0;</div>
|
||||
<div class="line"><span class="lineno"> 49</span> </div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 51</span> </div>
|
||||
<div class="line"><span class="lineno"> 52</span> <span class="comment">// start iterations</span></div>
|
||||
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="#a5c5ff05b9f37ae59dad67e1d4f6cd51d">MAX_ITERATIONS</a>; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 54</span> m = <a class="code hl_function" href="#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(c);</div>
|
||||
<div class="line"><span class="lineno"> 55</span> n = <a class="code hl_function" href="#a3d3f7f41977394680af6ebbed96f3386">eq_der</a>(c);</div>
|
||||
<div class="line"><span class="lineno"> 56</span> </div>
|
||||
<div class="line"><span class="lineno"> 57</span> z = c - (m / n);</div>
|
||||
<div class="line"><span class="lineno"> 58</span> c = z;</div>
|
||||
<div class="line"><span class="lineno"> 59</span> </div>
|
||||
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">if</span> (std::abs(m) < <a class="code hl_variable" href="#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a>) { <span class="comment">// stoping criteria</span></div>
|
||||
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><span class="lineno"> 62</span> }</div>
|
||||
<div class="line"><span class="lineno"> 63</span> }</div>
|
||||
<div class="line"><span class="lineno"> 64</span> </div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 67</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 45</span> {</div>
|
||||
<div class="line"><span class="lineno"> 46</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>
|
||||
<div class="line"><span class="lineno"> 47</span> </div>
|
||||
<div class="line"><span class="lineno"> 48</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>
|
||||
<div class="line"><span class="lineno"> 49</span> <span class="keywordtype">int</span> i = 0;</div>
|
||||
<div class="line"><span class="lineno"> 50</span> </div>
|
||||
<div class="line"><span class="lineno"> 51</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>
|
||||
<div class="line"><span class="lineno"> 52</span> </div>
|
||||
<div class="line"><span class="lineno"> 53</span> <span class="comment">// start iterations</span></div>
|
||||
<div class="line"><span class="lineno"> 54</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="#a5c5ff05b9f37ae59dad67e1d4f6cd51d">MAX_ITERATIONS</a>; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 55</span> m = <a class="code hl_function" href="#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(c);</div>
|
||||
<div class="line"><span class="lineno"> 56</span> n = <a class="code hl_function" href="#a3d3f7f41977394680af6ebbed96f3386">eq_der</a>(c);</div>
|
||||
<div class="line"><span class="lineno"> 57</span> </div>
|
||||
<div class="line"><span class="lineno"> 58</span> z = c - (m / n);</div>
|
||||
<div class="line"><span class="lineno"> 59</span> c = z;</div>
|
||||
<div class="line"><span class="lineno"> 60</span> </div>
|
||||
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">if</span> (std::abs(m) < <a class="code hl_variable" href="#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a>) { <span class="comment">// stoping criteria</span></div>
|
||||
<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><span class="lineno"> 63</span> }</div>
|
||||
<div class="line"><span class="lineno"> 64</span> }</div>
|
||||
<div class="line"><span class="lineno"> 65</span> </div>
|
||||
<div class="line"><span class="lineno"> 66</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>
|
||||
<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 68</span>}</div>
|
||||
<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>
|
||||
<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>
|
||||
<div class="ttc" id="anewton__raphson__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> newton_raphson_method.cpp:29</div></div>
|
||||
<div class="ttc" id="anewton__raphson__method_8cpp_html_a3d3f7f41977394680af6ebbed96f3386"><div class="ttname"><a href="#a3d3f7f41977394680af6ebbed96f3386">eq_der</a></div><div class="ttdeci">static double eq_der(double i)</div><div class="ttdef"><b>Definition</b> newton_raphson_method.cpp:39</div></div>
|
||||
<div class="ttc" id="anewton__raphson__method_8cpp_html_a5c5ff05b9f37ae59dad67e1d4f6cd51d"><div class="ttname"><a href="#a5c5ff05b9f37ae59dad67e1d4f6cd51d">MAX_ITERATIONS</a></div><div class="ttdeci">constexpr int16_t MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations.</div><div class="ttdef"><b>Definition</b> newton_raphson_method.cpp:21</div></div>
|
||||
<div class="ttc" id="anewton__raphson__method_8cpp_html_a75f355966e0a97665eaf5a4c79baa7af"><div class="ttname"><a href="#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a></div><div class="ttdeci">constexpr double EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition</b> newton_raphson_method.cpp:20</div></div>
|
||||
<div class="ttc" id="anewton__raphson__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> newton_raphson_method.cpp:30</div></div>
|
||||
<div class="ttc" id="anewton__raphson__method_8cpp_html_a3d3f7f41977394680af6ebbed96f3386"><div class="ttname"><a href="#a3d3f7f41977394680af6ebbed96f3386">eq_der</a></div><div class="ttdeci">static double eq_der(double i)</div><div class="ttdef"><b>Definition</b> newton_raphson_method.cpp:40</div></div>
|
||||
<div class="ttc" id="anewton__raphson__method_8cpp_html_a5c5ff05b9f37ae59dad67e1d4f6cd51d"><div class="ttname"><a href="#a5c5ff05b9f37ae59dad67e1d4f6cd51d">MAX_ITERATIONS</a></div><div class="ttdeci">constexpr int16_t MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations.</div><div class="ttdef"><b>Definition</b> newton_raphson_method.cpp:22</div></div>
|
||||
<div class="ttc" id="anewton__raphson__method_8cpp_html_a75f355966e0a97665eaf5a4c79baa7af"><div class="ttname"><a href="#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a></div><div class="ttdeci">constexpr double EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition</b> newton_raphson_method.cpp:21</div></div>
|
||||
<div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
|
||||
<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
|
||||
<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
|
||||
|
||||
Reference in New Issue
Block a user