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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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@@ -124,12 +141,13 @@ Include dependency graph for brent_method_extrema.cpp:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d0e/brent__method__extrema_8cpp__incl.svg" width="515" 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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<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:a525335710b53cb064ca56b936120431e" id="r_a525335710b53cb064ca56b936120431e"><td class="memItemLeft" align="right" valign="top"><a id="a525335710b53cb064ca56b936120431e" name="a525335710b53cb064ca56b936120431e"></a>
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#define </td><td class="memItemRight" valign="bottom"><b>_USE_MATH_DEFINES</b></td></tr>
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<tr class="memdesc:a525335710b53cb064ca56b936120431e"><td class="mdescLeft"> </td><td class="mdescRight">required for MS Visual C++ <br /></td></tr>
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<tr class="memitem:a525335710b53cb064ca56b936120431e" id="r_a525335710b53cb064ca56b936120431e"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="#a525335710b53cb064ca56b936120431e">_USE_MATH_DEFINES</a></td></tr>
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<tr class="memdesc:a525335710b53cb064ca56b936120431e"><td class="mdescLeft"> </td><td class="mdescRight">required for MS Visual C++ <br /></td></tr>
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||||
<tr class="separator:a525335710b53cb064ca56b936120431e"><td class="memSeparator" colspan="2"> </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></td></tr>
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<tr class="memdesc:a002b2f4894492820fe708b1b7e7c5e70"><td class="mdescLeft"> </td><td class="mdescRight">system accuracy limit <br /></td></tr>
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@@ -137,7 +155,7 @@ 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:a1aa76a6d5fd4d333f9072beff1dc486b" id="r_a1aa76a6d5fd4d333f9072beff1dc486b"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>< double(double)> &f, double lim_a, double lim_b)</td></tr>
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<tr class="memitem:a1aa76a6d5fd4d333f9072beff1dc486b" id="r_a1aa76a6d5fd4d333f9072beff1dc486b"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a> (const std::function< double(double)> &f, double lim_a, double lim_b)</td></tr>
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<tr class="memdesc:a1aa76a6d5fd4d333f9072beff1dc486b"><td class="mdescLeft"> </td><td class="mdescRight">Get the real root of a function in the given interval. <br /></td></tr>
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<tr class="separator:a1aa76a6d5fd4d333f9072beff1dc486b"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0" id="r_a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
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@@ -162,7 +180,27 @@ Functions</h2></td></tr>
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</blockquote>
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||||
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d6/d7a/golden__search__extrema_8cpp.html" title="Find extrema of a univariate real function in a given interval using golden section search algorithm.">golden_search_extrema.cpp</a></dd></dl>
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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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||||
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||||
<p class="definition">Definition in file <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html">brent_method_extrema.cpp</a>.</p>
|
||||
</div><h2 class="groupheader">Macro Definition Documentation</h2>
|
||||
<a id="a525335710b53cb064ca56b936120431e" name="a525335710b53cb064ca56b936120431e"></a>
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||||
<h2 class="memtitle"><span class="permalink"><a href="#a525335710b53cb064ca56b936120431e">◆ </a></span>_USE_MATH_DEFINES</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">#define _USE_MATH_DEFINES</td>
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||||
</tr>
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||||
</table>
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||||
</div><div class="memdoc">
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||||
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||||
<p>required for MS Visual C++ </p>
|
||||
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||||
<p class="definition">Definition at line <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html#l00016">16</a> of file <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html">brent_method_extrema.cpp</a>.</p>
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||||
</div>
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</div>
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||||
<a id="a002b2f4894492820fe708b1b7e7c5e70" name="a002b2f4894492820fe708b1b7e7c5e70"></a>
|
||||
<h2 class="memtitle"><span class="permalink"><a href="#a002b2f4894492820fe708b1b7e7c5e70">◆ </a></span>EPSILON</h2>
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@@ -174,15 +212,15 @@ Functions</h2></td></tr>
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</tr>
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</table>
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</div><div class="memdoc">
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||||
<b>Value:</b><div class="fragment"><div class="line"> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>( \</div>
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<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits<double>::epsilon</a>())</div>
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||||
<div class="ttc" id="anumeric_limits_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits</a></div></div>
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||||
<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
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||||
<b>Value:</b><div class="fragment"><div class="line"> std::sqrt( \</div>
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<div class="line"> std::numeric_limits<double>::epsilon())</div>
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</div><!-- fragment -->
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||||
<p>system accuracy limit </p>
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||||
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||||
<p class="definition">Definition at line <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html#l00024">24</a> of file <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html">brent_method_extrema.cpp</a>.</p>
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||||
<div class="fragment"><div class="line"><span class="lineno"> 24</span><span class="preprocessor">#define EPSILON \</span></div>
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<div class="line"><span class="lineno"> 25</span><span class="preprocessor"> std::sqrt( \</span></div>
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<div class="line"><span class="lineno"> 26</span><span class="preprocessor"> std::numeric_limits<double>::epsilon()) </span><span class="comment">///< system accuracy limit</span></div>
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<div class="line"><span class="lineno"> 26</span><span class="preprocessor"> std::numeric_limits<double>::epsilon()) </span></div>
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</div><!-- fragment -->
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</div>
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</div>
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@@ -196,7 +234,7 @@ Functions</h2></td></tr>
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<tr>
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<td class="memname">double get_minima </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>< double(double)> &</td> <td class="paramname"><span class="paramname"><em>f</em></span>, </td>
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||||
<td class="paramtype">const std::function< double(double)> &</td> <td class="paramname"><span class="paramname"><em>f</em></span>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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@@ -221,18 +259,20 @@ Functions</h2></td></tr>
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</dd>
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||||
</dl>
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<dl class="section return"><dt>Returns</dt><dd>root found in the interval </dd></dl>
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||||
<p class="definition">Definition at line <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html#l00036">36</a> of file <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html">brent_method_extrema.cpp</a>.</p>
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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> uint32_t iters = 0;</div>
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<div class="line"><span class="lineno"> 39</span> </div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">if</span> (lim_a > lim_b) {</div>
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<div class="line"><span class="lineno"> 41</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(lim_a, lim_b);</div>
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<div class="line"><span class="lineno"> 41</span> std::swap(lim_a, lim_b);</div>
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<div class="line"><span class="lineno"> 42</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::abs(lim_a - lim_b) <= <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>) {</div>
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||||
<div class="line"><span class="lineno"> 43</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> << <span class="stringliteral">"Search range must be greater than "</span> << <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 43</span> std::cerr << <span class="stringliteral">"Search range must be greater than "</span> << <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">return</span> lim_a;</div>
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<div class="line"><span class="lineno"> 45</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="comment">// golden ratio value</span></div>
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<div class="line"><span class="lineno"> 48</span> <span class="keyword">const</span> <span class="keywordtype">double</span> M_GOLDEN_RATIO = (3.f - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(5.f)) / 2.f;</div>
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<div class="line"><span class="lineno"> 48</span> <span class="keyword">const</span> <span class="keywordtype">double</span> M_GOLDEN_RATIO = (3.f - std::sqrt(5.f)) / 2.f;</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> <span class="keywordtype">double</span> v = lim_a + M_GOLDEN_RATIO * (lim_b - lim_a);</div>
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<div class="line"><span class="lineno"> 51</span> <span class="keywordtype">double</span> u, w = v, x = v;</div>
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@@ -317,20 +357,13 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 130</span> iters++;</div>
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<div class="line"><span class="lineno"> 131</span> } <span class="keywordflow">while</span> (std::abs(x - mid_point) > (tolerance - (lim_b - lim_a) / 2.f));</div>
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<div class="line"><span class="lineno"> 132</span> </div>
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<div class="line"><span class="lineno"> 133</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">" (iters: "</span> << iters << <span class="stringliteral">") "</span>;</div>
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<div class="line"><span class="lineno"> 133</span> std::cout << <span class="stringliteral">" (iters: "</span> << iters << <span class="stringliteral">") "</span>;</div>
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<div class="line"><span class="lineno"> 134</span> </div>
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<div class="line"><span class="lineno"> 135</span> <span class="keywordflow">return</span> x;</div>
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<div class="line"><span class="lineno"> 136</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::cerr</a></div></div>
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<div class="ttc" id="abrent__method__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition</b> brent_method_extrema.cpp:24</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a4251b4df4748a0b9c43a48f61bdd2397"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a></div><div class="ttdeci">double f(double x)</div><div class="ttdoc">A function f(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> composite_simpson_rule.cpp:113</div></div>
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<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(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="../../db/d01/brent__method__extrema_8cpp_a1aa76a6d5fd4d333f9072beff1dc486b_cgraph.svg" width="226" height="86"><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 class="ttc" id="abrent__method__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition</b> <a href="../../db/d01/brent__method__extrema_8cpp_source.html#l00024">brent_method_extrema.cpp:24</a></div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a4251b4df4748a0b9c43a48f61bdd2397"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a></div><div class="ttdeci">double f(double x)</div><div class="ttdoc">A function f(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00113">composite_simpson_rule.cpp:113</a></div></div>
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</div><!-- fragment -->
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@@ -348,10 +381,12 @@ Here is the call graph for this function:</div>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
<p>Main function </p>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html#l00205">205</a> of file <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html">brent_method_extrema.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 205</span> {</div>
|
||||
<div class="line"><span class="lineno"> 206</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(18);</div>
|
||||
<div class="line"><span class="lineno"> 206</span> std::cout.precision(18);</div>
|
||||
<div class="line"><span class="lineno"> 207</span> </div>
|
||||
<div class="line"><span class="lineno"> 208</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">"Computations performed with machine epsilon: "</span> << <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
|
||||
<div class="line"><span class="lineno"> 208</span> std::cout << <span class="stringliteral">"Computations performed with machine epsilon: "</span> << <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
|
||||
<div class="line"><span class="lineno"> 209</span> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 210</span> </div>
|
||||
<div class="line"><span class="lineno"> 211</span> <a class="code hl_function" href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
|
||||
@@ -360,15 +395,10 @@ Here is the call graph for this function:</div>
|
||||
<div class="line"><span class="lineno"> 214</span> </div>
|
||||
<div class="line"><span class="lineno"> 215</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 216</span>}</div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition</b> brent_method_extrema.cpp:166</div></div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result = 2.</div><div class="ttdef"><b>Definition</b> brent_method_extrema.cpp:144</div></div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdoc">Test function to find maxima for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition</b> brent_method_extrema.cpp:189</div></div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d01/brent__method__extrema_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="422" height="135"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
||||
</div>
|
||||
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition</b> <a href="../../db/d01/brent__method__extrema_8cpp_source.html#l00166">brent_method_extrema.cpp:166</a></div></div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result = 2.</div><div class="ttdef"><b>Definition</b> <a href="../../db/d01/brent__method__extrema_8cpp_source.html#l00144">brent_method_extrema.cpp:144</a></div></div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdoc">Test function to find maxima for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition</b> <a href="../../db/d01/brent__method__extrema_8cpp_source.html#l00189">brent_method_extrema.cpp:189</a></div></div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
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||||
<a id="a1440a7779ac56f47a3f355ce4a8c7da0" name="a1440a7779ac56f47a3f355ce4a8c7da0"></a>
|
||||
@@ -388,29 +418,25 @@ Here is the call graph for this function:</div>
|
||||
|
||||
<p>Test function to find root for the function \(f(x)= (x-2)^2\) in the interval \([1,5]\) <br />
|
||||
Expected result = 2. </p>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html#l00144">144</a> of file <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html">brent_method_extrema.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 144</span> {</div>
|
||||
<div class="line"><span class="lineno"> 145</span> <span class="comment">// define the function to minimize as a lambda function</span></div>
|
||||
<div class="line"><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a><double(<span class="keywordtype">double</span>)> f1 = [](<span class="keywordtype">double</span> x) {</div>
|
||||
<div class="line"><span class="lineno"> 146</span> std::function<double(<span class="keywordtype">double</span>)> f1 = [](<span class="keywordtype">double</span> x) {</div>
|
||||
<div class="line"><span class="lineno"> 147</span> <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
|
||||
<div class="line"><span class="lineno"> 148</span> };</div>
|
||||
<div class="line"><span class="lineno"> 149</span> </div>
|
||||
<div class="line"><span class="lineno"> 150</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">"Test 1.... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 150</span> std::cout << <span class="stringliteral">"Test 1.... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 151</span> </div>
|
||||
<div class="line"><span class="lineno"> 152</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(f1, -1, 5);</div>
|
||||
<div class="line"><span class="lineno"> 153</span> </div>
|
||||
<div class="line"><span class="lineno"> 154</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << minima << <span class="stringliteral">"..."</span>;</div>
|
||||
<div class="line"><span class="lineno"> 154</span> std::cout << minima << <span class="stringliteral">"..."</span>;</div>
|
||||
<div class="line"><span class="lineno"> 155</span> </div>
|
||||
<div class="line"><span class="lineno"> 156</span> assert(std::abs(minima - 2) < <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
|
||||
<div class="line"><span class="lineno"> 157</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">"passed\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 157</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 158</span>}</div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function< double(double)> &f, double lim_a, double lim_b)</div><div class="ttdoc">Get the real root of a function in the given interval.</div><div class="ttdef"><b>Definition</b> brent_method_extrema.cpp:36</div></div>
|
||||
<div class="ttc" id="afunction_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a></div></div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d01/brent__method__extrema_8cpp_a1440a7779ac56f47a3f355ce4a8c7da0_cgraph.svg" width="324" height="86"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
||||
</div>
|
||||
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function< double(double)> &f, double lim_a, double lim_b)</div><div class="ttdoc">Get the real root of a function in the given interval.</div><div class="ttdef"><b>Definition</b> <a href="../../db/d01/brent__method__extrema_8cpp_source.html#l00036">brent_method_extrema.cpp:36</a></div></div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
<a id="a0283886819c7c140a023582b7269e2d0" name="a0283886819c7c140a023582b7269e2d0"></a>
|
||||
@@ -430,29 +456,25 @@ Here is the call graph for this function:</div>
|
||||
|
||||
<p>Test function to find root for the function \(f(x)= x^{\frac{1}{x}}\) in the interval \([-2,10]\) <br />
|
||||
Expected result: \(e\approx 2.71828182845904509\). </p>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html#l00166">166</a> of file <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html">brent_method_extrema.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 166</span> {</div>
|
||||
<div class="line"><span class="lineno"> 167</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
|
||||
<div class="line"><span class="lineno"> 168</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
|
||||
<div class="line"><span class="lineno"> 169</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a><double(<span class="keywordtype">double</span>)> func = [](<span class="keywordtype">double</span> x) {</div>
|
||||
<div class="line"><span class="lineno"> 170</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>(x, 1.f / x);</div>
|
||||
<div class="line"><span class="lineno"> 169</span> std::function<double(<span class="keywordtype">double</span>)> func = [](<span class="keywordtype">double</span> x) {</div>
|
||||
<div class="line"><span class="lineno"> 170</span> <span class="keywordflow">return</span> -std::pow(x, 1.f / x);</div>
|
||||
<div class="line"><span class="lineno"> 171</span> };</div>
|
||||
<div class="line"><span class="lineno"> 172</span> </div>
|
||||
<div class="line"><span class="lineno"> 173</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">"Test 2.... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 173</span> std::cout << <span class="stringliteral">"Test 2.... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 174</span> </div>
|
||||
<div class="line"><span class="lineno"> 175</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -2, 5);</div>
|
||||
<div class="line"><span class="lineno"> 176</span> </div>
|
||||
<div class="line"><span class="lineno"> 177</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << minima << <span class="stringliteral">" ("</span> << M_E << <span class="stringliteral">")..."</span>;</div>
|
||||
<div class="line"><span class="lineno"> 177</span> std::cout << minima << <span class="stringliteral">" ("</span> << M_E << <span class="stringliteral">")..."</span>;</div>
|
||||
<div class="line"><span class="lineno"> 178</span> </div>
|
||||
<div class="line"><span class="lineno"> 179</span> assert(std::abs(minima - M_E) < <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
|
||||
<div class="line"><span class="lineno"> 180</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">"passed\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 180</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 181</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>
|
||||
<div class="dyncontent">
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d01/brent__method__extrema_8cpp_a0283886819c7c140a023582b7269e2d0_cgraph.svg" width="324" height="110"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
||||
</div>
|
||||
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
<a id="a6d0455dd5c30adda100e95f0423c786e" name="a6d0455dd5c30adda100e95f0423c786e"></a>
|
||||
@@ -472,27 +494,23 @@ Here is the call graph for this function:</div>
|
||||
|
||||
<p>Test function to find <em>maxima</em> for the function \(f(x)= \cos x\) in the interval \([0,12]\) <br />
|
||||
Expected result: \(\pi\approx 3.14159265358979312\). </p>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html#l00189">189</a> of file <a class="el" href="../../db/d01/brent__method__extrema_8cpp_source.html">brent_method_extrema.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 189</span> {</div>
|
||||
<div class="line"><span class="lineno"> 190</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
|
||||
<div class="line"><span class="lineno"> 191</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
|
||||
<div class="line"><span class="lineno"> 192</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a><double(<span class="keywordtype">double</span>)> func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x); };</div>
|
||||
<div class="line"><span class="lineno"> 192</span> std::function<double(<span class="keywordtype">double</span>)> func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> std::cos(x); };</div>
|
||||
<div class="line"><span class="lineno"> 193</span> </div>
|
||||
<div class="line"><span class="lineno"> 194</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">"Test 3.... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 194</span> std::cout << <span class="stringliteral">"Test 3.... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 195</span> </div>
|
||||
<div class="line"><span class="lineno"> 196</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -4, 12);</div>
|
||||
<div class="line"><span class="lineno"> 197</span> </div>
|
||||
<div class="line"><span class="lineno"> 198</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << minima << <span class="stringliteral">" ("</span> << M_PI << <span class="stringliteral">")..."</span>;</div>
|
||||
<div class="line"><span class="lineno"> 198</span> std::cout << minima << <span class="stringliteral">" ("</span> << M_PI << <span class="stringliteral">")..."</span>;</div>
|
||||
<div class="line"><span class="lineno"> 199</span> </div>
|
||||
<div class="line"><span class="lineno"> 200</span> assert(std::abs(minima - M_PI) < <a class="code hl_define" href="#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
|
||||
<div class="line"><span class="lineno"> 201</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">"passed\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 201</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 202</span>}</div>
|
||||
<div class="ttc" id="acos_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a></div><div class="ttdeci">T cos(T... args)</div></div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
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|
||||
<div class="dyncontent">
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d01/brent__method__extrema_8cpp_a6d0455dd5c30adda100e95f0423c786e_cgraph.svg" width="324" height="110"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
||||
</div>
|
||||
|
||||
</div><!-- fragment -->
|
||||
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|
||||
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|
||||
</div><!-- contents -->
|
||||
|
||||
@@ -1,11 +0,0 @@
|
||||
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<div class="contents">
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<a href="../../db/d01/brent__method__extrema_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
|
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"><a class="line" href="../../db/d01/brent__method__extrema_8cpp.html#a525335710b53cb064ca56b936120431e"> 16</a></span><span class="preprocessor">#define _USE_MATH_DEFINES </span></div>
|
||||
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <cassert></span></div>
|
||||
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <cmath></span></div>
|
||||
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <cstdint></span></div>
|
||||
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <functional></span></div>
|
||||
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <iostream></span></div>
|
||||
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include <limits></span></div>
|
||||
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
|
||||
<div class="foldopen" id="foldopen00024" data-start="" data-end="">
|
||||
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"><a class="line" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70"> 24</a></span><span class="preprocessor">#define EPSILON \</span></div>
|
||||
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor"> std::sqrt( \</span></div>
|
||||
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor"> std::numeric_limits<double>::epsilon()) </span></div>
|
||||
</div>
|
||||
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
|
||||
<div class="foldopen" id="foldopen00036" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"><a class="line" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b"> 36</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(<span class="keyword">const</span> std::function<<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)> &f, <span class="keywordtype">double</span> lim_a,</div>
|
||||
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordtype">double</span> lim_b) {</div>
|
||||
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> uint32_t iters = 0;</div>
|
||||
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
|
||||
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">if</span> (lim_a > lim_b) {</div>
|
||||
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> std::swap(lim_a, lim_b);</div>
|
||||
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::abs(lim_a - lim_b) <= <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>) {</div>
|
||||
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> std::cerr << <span class="stringliteral">"Search range must be greater than "</span> << <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> lim_a;</div>
|
||||
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> }</div>
|
||||
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
|
||||
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// golden ratio value</span></div>
|
||||
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">const</span> <span class="keywordtype">double</span> M_GOLDEN_RATIO = (3.f - std::sqrt(5.f)) / 2.f;</div>
|
||||
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
|
||||
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordtype">double</span> v = lim_a + M_GOLDEN_RATIO * (lim_b - lim_a);</div>
|
||||
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordtype">double</span> u, w = v, x = v;</div>
|
||||
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordtype">double</span> fu, fv = f(v);</div>
|
||||
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordtype">double</span> fw = fv, fx = fv;</div>
|
||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
|
||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">double</span> mid_point = (lim_a + lim_b) / 2.f;</div>
|
||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordtype">double</span> p = 0, q = 0, r = 0;</div>
|
||||
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
|
||||
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordtype">double</span> d, e = 0;</div>
|
||||
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordtype">double</span> tolerance, tolerance2;</div>
|
||||
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
|
||||
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">do</span> {</div>
|
||||
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> mid_point = (lim_a + lim_b) / 2.f;</div>
|
||||
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> tolerance = <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> * std::abs(x);</div>
|
||||
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> tolerance2 = 2 * tolerance;</div>
|
||||
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
|
||||
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">if</span> (std::abs(e) > tolerance2) {</div>
|
||||
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// fit parabola</span></div>
|
||||
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> r = (x - w) * (fx - fv);</div>
|
||||
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> q = (x - v) * (fx - fw);</div>
|
||||
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> p = (x - v) * q - (x - w) * r;</div>
|
||||
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> q = 2.f * (q - r);</div>
|
||||
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">if</span> (q > 0)</div>
|
||||
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> p = -p;</div>
|
||||
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">else</span></div>
|
||||
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> q = -q;</div>
|
||||
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> r = e;</div>
|
||||
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> e = d;</div>
|
||||
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
|
||||
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
|
||||
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">if</span> (std::abs(p) < std::abs(0.5 * q * r) && p < q * (lim_b - x)) {</div>
|
||||
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// parabolic interpolation step</span></div>
|
||||
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> d = p / q;</div>
|
||||
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> u = x + d;</div>
|
||||
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordflow">if</span> (u - lim_a < tolerance2 || lim_b - u < tolerance2)</div>
|
||||
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> d = x < mid_point ? tolerance : -tolerance;</div>
|
||||
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// golden section interpolation step</span></div>
|
||||
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> e = (x < mid_point ? lim_b : lim_a) - x;</div>
|
||||
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> d = M_GOLDEN_RATIO * e;</div>
|
||||
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> }</div>
|
||||
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
|
||||
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// evaluate not too close to x</span></div>
|
||||
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">if</span> (std::abs(d) >= tolerance)</div>
|
||||
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> u = d;</div>
|
||||
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (d > 0)</div>
|
||||
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> u = tolerance;</div>
|
||||
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">else</span></div>
|
||||
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> u = -tolerance;</div>
|
||||
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> u += x;</div>
|
||||
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> fu = f(u);</div>
|
||||
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> </div>
|
||||
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// update variables</span></div>
|
||||
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">if</span> (fu <= fx) {</div>
|
||||
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">if</span> (u < x)</div>
|
||||
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> lim_b = x;</div>
|
||||
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordflow">else</span></div>
|
||||
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> lim_a = x;</div>
|
||||
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> v = w;</div>
|
||||
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> fv = fw;</div>
|
||||
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> w = x;</div>
|
||||
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> fw = fx;</div>
|
||||
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> x = u;</div>
|
||||
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> fx = fu;</div>
|
||||
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordflow">if</span> (u < x)</div>
|
||||
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> lim_a = u;</div>
|
||||
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">else</span></div>
|
||||
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> lim_b = u;</div>
|
||||
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">if</span> (fu <= fw || x == w) {</div>
|
||||
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> v = w;</div>
|
||||
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> fv = fw;</div>
|
||||
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> w = u;</div>
|
||||
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> fw = fu;</div>
|
||||
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (fu <= fv || v == x || v == w) {</div>
|
||||
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> v = u;</div>
|
||||
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> fv = fu;</div>
|
||||
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
|
||||
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> }</div>
|
||||
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
|
||||
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> iters++;</div>
|
||||
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> } <span class="keywordflow">while</span> (std::abs(x - mid_point) > (tolerance - (lim_b - lim_a) / 2.f));</div>
|
||||
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> </div>
|
||||
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> std::cout << <span class="stringliteral">" (iters: "</span> << iters << <span class="stringliteral">") "</span>;</div>
|
||||
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
|
||||
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordflow">return</span> x;</div>
|
||||
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> </div>
|
||||
<div class="foldopen" id="foldopen00144" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"><a class="line" href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0"> 144</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>() {</div>
|
||||
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="comment">// define the function to minimize as a lambda function</span></div>
|
||||
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> std::function<double(<span class="keywordtype">double</span>)> f1 = [](<span class="keywordtype">double</span> x) {</div>
|
||||
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
|
||||
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> };</div>
|
||||
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> </div>
|
||||
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> std::cout << <span class="stringliteral">"Test 1.... "</span>;</div>
|
||||
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> </div>
|
||||
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(f1, -1, 5);</div>
|
||||
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
|
||||
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> std::cout << minima << <span class="stringliteral">"..."</span>;</div>
|
||||
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> </div>
|
||||
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> assert(std::abs(minima - 2) < <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
|
||||
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
|
||||
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> </div>
|
||||
<div class="foldopen" id="foldopen00166" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"><a class="line" href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0"> 166</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>() {</div>
|
||||
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
|
||||
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
|
||||
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> std::function<double(<span class="keywordtype">double</span>)> func = [](<span class="keywordtype">double</span> x) {</div>
|
||||
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="keywordflow">return</span> -std::pow(x, 1.f / x);</div>
|
||||
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> };</div>
|
||||
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> </div>
|
||||
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> std::cout << <span class="stringliteral">"Test 2.... "</span>;</div>
|
||||
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> </div>
|
||||
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -2, 5);</div>
|
||||
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
|
||||
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> std::cout << minima << <span class="stringliteral">" ("</span> << M_E << <span class="stringliteral">")..."</span>;</div>
|
||||
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> </div>
|
||||
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> assert(std::abs(minima - M_E) < <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
|
||||
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
|
||||
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> </div>
|
||||
<div class="foldopen" id="foldopen00189" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"><a class="line" href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e"> 189</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>() {</div>
|
||||
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
|
||||
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
|
||||
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> std::function<double(<span class="keywordtype">double</span>)> func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> std::cos(x); };</div>
|
||||
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> </div>
|
||||
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> std::cout << <span class="stringliteral">"Test 3.... "</span>;</div>
|
||||
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> </div>
|
||||
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -4, 12);</div>
|
||||
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> </div>
|
||||
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> std::cout << minima << <span class="stringliteral">" ("</span> << M_PI << <span class="stringliteral">")..."</span>;</div>
|
||||
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> </div>
|
||||
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> assert(std::abs(minima - M_PI) < <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
|
||||
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
|
||||
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> </div>
|
||||
<div class="foldopen" id="foldopen00205" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"><a class="line" href="../../db/d01/brent__method__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 205</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
|
||||
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> std::cout.precision(18);</div>
|
||||
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
|
||||
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> std::cout << <span class="stringliteral">"Computations performed with machine epsilon: "</span> << <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
|
||||
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> </div>
|
||||
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
|
||||
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
|
||||
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
|
||||
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> </div>
|
||||
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span>}</div>
|
||||
</div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition</b> <a href="#l00024">brent_method_extrema.cpp:24</a></div></div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition</b> <a href="#l00166">brent_method_extrema.cpp:166</a></div></div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result = 2.</div><div class="ttdef"><b>Definition</b> <a href="#l00144">brent_method_extrema.cpp:144</a></div></div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function< double(double)> &f, double lim_a, double lim_b)</div><div class="ttdoc">Get the real root of a function in the given interval.</div><div class="ttdef"><b>Definition</b> <a href="#l00036">brent_method_extrema.cpp:36</a></div></div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdoc">Test function to find maxima for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition</b> <a href="#l00189">brent_method_extrema.cpp:189</a></div></div>
|
||||
<div class="ttc" id="abrent__method__extrema_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition</b> <a href="#l00205">brent_method_extrema.cpp:205</a></div></div>
|
||||
</div><!-- fragment --></div><!-- contents -->
|
||||
</div><!-- doc-content -->
|
||||
<!-- start footer part -->
|
||||
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|
||||
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