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<title>TheAlgorithms/C++: numerical_methods/newton_raphson_method.cpp File Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectname">TheAlgorithms/C++<span id="projectnumber"> 1.0.0</span>
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</div>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div id="projectbrief">All the algorithms implemented in C++</div>
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</td>
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</tr>
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</tbody>
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@@ -123,7 +140,9 @@ Include dependency graph for newton_raphson_method.cpp:</div>
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<div class="dyncontent">
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<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>
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</div><table class="memberdecls">
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</div>
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<p><a href="../../de/dd3/newton__raphson__method_8cpp_source.html">Go to the source code of this file.</a></p>
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<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="#a2003b5b2dcfff0769b957ab5c968b03d">eq</a> (double i)</td></tr>
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@@ -135,13 +154,11 @@ Functions</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="var-members" name="var-members"></a>
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Variables</h2></td></tr>
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<tr class="memitem:a75f355966e0a97665eaf5a4c79baa7af" id="r_a75f355966e0a97665eaf5a4c79baa7af"><td class="memItemLeft" align="right" valign="top"><a id="a75f355966e0a97665eaf5a4c79baa7af" name="a75f355966e0a97665eaf5a4c79baa7af"></a>
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constexpr double </td><td class="memItemRight" valign="bottom"><b>EPSILON</b> = 1e-10</td></tr>
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<tr class="memdesc:a75f355966e0a97665eaf5a4c79baa7af"><td class="mdescLeft"> </td><td class="mdescRight">system accuracy limit <br /></td></tr>
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<tr class="memitem:a75f355966e0a97665eaf5a4c79baa7af" id="r_a75f355966e0a97665eaf5a4c79baa7af"><td class="memItemLeft" align="right" valign="top">constexpr double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a> = 1e-10</td></tr>
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<tr class="memdesc:a75f355966e0a97665eaf5a4c79baa7af"><td class="mdescLeft"> </td><td class="mdescRight">system accuracy limit <br /></td></tr>
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<tr class="separator:a75f355966e0a97665eaf5a4c79baa7af"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a5c5ff05b9f37ae59dad67e1d4f6cd51d" id="r_a5c5ff05b9f37ae59dad67e1d4f6cd51d"><td class="memItemLeft" align="right" valign="top"><a id="a5c5ff05b9f37ae59dad67e1d4f6cd51d" name="a5c5ff05b9f37ae59dad67e1d4f6cd51d"></a>
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constexpr int16_t </td><td class="memItemRight" valign="bottom"><b>MAX_ITERATIONS</b> = INT16_MAX</td></tr>
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<tr class="memdesc:a5c5ff05b9f37ae59dad67e1d4f6cd51d"><td class="mdescLeft"> </td><td class="mdescRight">Maximum number of iterations. <br /></td></tr>
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<tr class="memitem:a5c5ff05b9f37ae59dad67e1d4f6cd51d" id="r_a5c5ff05b9f37ae59dad67e1d4f6cd51d"><td class="memItemLeft" align="right" valign="top">constexpr int16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="#a5c5ff05b9f37ae59dad67e1d4f6cd51d">MAX_ITERATIONS</a> = INT16_MAX</td></tr>
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<tr class="memdesc:a5c5ff05b9f37ae59dad67e1d4f6cd51d"><td class="mdescLeft"> </td><td class="mdescRight">Maximum number of iterations. <br /></td></tr>
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<tr class="separator:a5c5ff05b9f37ae59dad67e1d4f6cd51d"><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>
|
||||
@@ -153,6 +170,8 @@ x_{i+1} = x_i - \frac{f(x_i)}{f'(x_i)}
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</p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d7/d6a/bisection__method_8cpp.html" title="Solve the equation using bisection method">bisection_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> </dd></dl>
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<p class="definition">Definition in file <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html">newton_raphson_method.cpp</a>.</p>
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</div><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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@@ -181,16 +200,12 @@ x_{i+1} = x_i - \frac{f(x_i)}{f'(x_i)}
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f(x) = x^3 - 4x - 9
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\]
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||||
</p>
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||||
<div class="fragment"><div class="line"><span class="lineno"> 30</span> {</div>
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||||
<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>
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||||
<p class="definition">Definition at line <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html#l00030">30</a> of file <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html">newton_raphson_method.cpp</a>.</p>
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||||
<div class="fragment"><div class="line"><span class="lineno"> 30</span> {</div>
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||||
<div class="line"><span class="lineno"> 31</span> <span class="keywordflow">return</span> (std::pow(i, 3) - (4 * i) - 9); <span class="comment">// original equation</span></div>
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<div class="line"><span class="lineno"> 32</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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<div class="dyncontent">
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||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/dd3/newton__raphson__method_8cpp_a2003b5b2dcfff0769b957ab5c968b03d_cgraph.svg" width="168" height="36"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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</div>
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</div><!-- fragment -->
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</div>
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<a id="a3d3f7f41977394680af6ebbed96f3386" name="a3d3f7f41977394680af6ebbed96f3386"></a>
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@@ -220,15 +235,12 @@ Here is the call graph for this function:</div>
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f'(x) = 3x^2 - 4
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||||
\]
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||||
</p>
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||||
<div class="fragment"><div class="line"><span class="lineno"> 40</span> {</div>
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||||
<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>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html#l00040">40</a> of file <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html">newton_raphson_method.cpp</a>.</p>
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||||
<div class="fragment"><div class="line"><span class="lineno"> 40</span> {</div>
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||||
<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">return</span> ((3 * std::pow(i, 2)) - 4); <span class="comment">// derivative of equation</span></div>
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||||
<div class="line"><span class="lineno"> 42</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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<div class="dyncontent">
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||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/dd3/newton__raphson__method_8cpp_a3d3f7f41977394680af6ebbed96f3386_cgraph.svg" width="191" height="36"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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</div>
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</div><!-- fragment -->
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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@@ -246,13 +258,15 @@ 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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||||
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||||
<p class="definition">Definition at line <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html#l00045">45</a> of file <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html">newton_raphson_method.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 45</span> {</div>
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||||
<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>
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<div class="line"><span class="lineno"> 46</span> std::srand(std::time(<span class="keyword">nullptr</span>)); <span class="comment">// initialize randomizer</span></div>
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<div class="line"><span class="lineno"> 47</span> </div>
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<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>
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||||
<div class="line"><span class="lineno"> 48</span> <span class="keywordtype">double</span> z = NAN, c = std::rand() % 100, m = NAN, n = NAN;</div>
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<div class="line"><span class="lineno"> 49</span> <span class="keywordtype">int</span> i = 0;</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> <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> std::cout << <span class="stringliteral">"\nInitial approximation: "</span> << c;</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> <span class="comment">// start iterations</span></div>
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<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>
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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> </div>
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<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>
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<div class="line"><span class="lineno"> 66</span> std::cout << <span class="stringliteral">"\n\nRoot: "</span> << z << <span class="stringliteral">"\t\tSteps: "</span> << i << std::endl;</div>
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<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 68</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>
|
||||
<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>
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<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>
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<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>
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||||
<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>
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</div><!-- fragment --><div class="dynheader">
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<div class="dyncontent">
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||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/dd3/newton__raphson__method_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="307" height="283"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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||||
<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> <a href="../../de/dd3/newton__raphson__method_8cpp_source.html#l00030">newton_raphson_method.cpp:30</a></div></div>
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<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> <a href="../../de/dd3/newton__raphson__method_8cpp_source.html#l00040">newton_raphson_method.cpp:40</a></div></div>
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<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> <a href="../../de/dd3/newton__raphson__method_8cpp_source.html#l00022">newton_raphson_method.cpp:22</a></div></div>
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<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> <a href="../../de/dd3/newton__raphson__method_8cpp_source.html#l00021">newton_raphson_method.cpp:21</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a75f355966e0a97665eaf5a4c79baa7af">◆ </a></span>EPSILON</h2>
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<p>system accuracy limit </p>
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<p class="definition">Definition at line <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html#l00021">21</a> of file <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html">newton_raphson_method.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a5c5ff05b9f37ae59dad67e1d4f6cd51d">◆ </a></span>MAX_ITERATIONS</h2>
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<td class="memname">int16_t MAX_ITERATIONS = INT16_MAX</td>
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<p>Maximum number of iterations. </p>
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<p class="definition">Definition at line <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html#l00022">22</a> of file <a class="el" href="../../de/dd3/newton__raphson__method_8cpp_source.html">newton_raphson_method.cpp</a>.</p>
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