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<div class="headertitle"><div class="title">brent_method_extrema.cpp</div></div>
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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>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <cassert></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <cmath></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <functional></span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <iostream></span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include <limits></span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
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<div class="foldopen" id="foldopen00024" data-start="" data-end="">
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<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>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor"> std::sqrt( \</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor"> std::numeric_limits<double>::epsilon()) </span></div>
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</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span></div>
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<div class="foldopen" id="foldopen00036" data-start="{" data-end="}">
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<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>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordtype">double</span> lim_b) {</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> uint32_t iters = 0;</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">if</span> (lim_a > lim_b) {</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> std::swap(lim_a, lim_b);</div>
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<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) <= EPSILON) {</div>
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<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> << EPSILON << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> lim_a;</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> }</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// golden ratio value</span></div>
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<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>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
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<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>
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<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>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordtype">double</span> fu, fv = f(v);</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordtype">double</span> fw = fv, fx = fv;</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
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<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>
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<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>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordtype">double</span> d, e = 0;</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordtype">double</span> tolerance, tolerance2;</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">do</span> {</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> mid_point = (lim_a + lim_b) / 2.f;</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> tolerance = EPSILON * std::abs(x);</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> tolerance2 = 2 * tolerance;</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">if</span> (std::abs(e) > tolerance2) {</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// fit parabola</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> r = (x - w) * (fx - fv);</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> q = (x - v) * (fx - fw);</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> p = (x - v) * q - (x - w) * r;</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> q = 2.f * (q - r);</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">if</span> (q > 0)</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> p = -p;</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">else</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> q = -q;</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> r = e;</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> e = d;</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
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<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>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// parabolic interpolation step</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> d = p / q;</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> u = x + d;</div>
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<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>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> d = x < mid_point ? tolerance : -tolerance;</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// golden section interpolation step</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> e = (x < mid_point ? lim_b : lim_a) - x;</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> d = M_GOLDEN_RATIO * e;</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> }</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
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<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>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">if</span> (std::abs(d) >= tolerance)</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> u = d;</div>
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<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>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> u = tolerance;</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">else</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> u = -tolerance;</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> u += x;</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> fu = f(u);</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> </div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// update variables</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">if</span> (fu <= fx) {</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">if</span> (u < x)</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> lim_b = x;</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordflow">else</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> lim_a = x;</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> v = w;</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> fv = fw;</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> w = x;</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> fw = fx;</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> x = u;</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> fx = fu;</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordflow">if</span> (u < x)</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> lim_a = u;</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">else</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> lim_b = u;</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">if</span> (fu <= fw || x == w) {</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> v = w;</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> fv = fw;</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> w = u;</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> fw = fu;</div>
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<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>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> v = u;</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> fv = fu;</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> }</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> iters++;</div>
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<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>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> </div>
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<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>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordflow">return</span> x;</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span>}</div>
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</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span></div>
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<div class="foldopen" id="foldopen00144" data-start="{" data-end="}">
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<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>
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<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>
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<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>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> };</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> </div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> std::cout << <span class="stringliteral">"Test 1.... "</span>;</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> </div>
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<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>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> std::cout << minima << <span class="stringliteral">"..."</span>;</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> </div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> assert(std::abs(minima - 2) < EPSILON);</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span>}</div>
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</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span></div>
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<div class="foldopen" id="foldopen00166" data-start="{" data-end="}">
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<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>
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<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>
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<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>
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<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>
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<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>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> };</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> </div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> std::cout << <span class="stringliteral">"Test 2.... "</span>;</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> </div>
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<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>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
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<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>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> </div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> assert(std::abs(minima - M_E) < EPSILON);</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span>}</div>
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</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span></div>
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<div class="foldopen" id="foldopen00189" data-start="{" data-end="}">
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<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>
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<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>
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<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>
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<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>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> </div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> std::cout << <span class="stringliteral">"Test 3.... "</span>;</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> </div>
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<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>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> </div>
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<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>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> </div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> assert(std::abs(minima - M_PI) < EPSILON);</div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span>}</div>
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</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span></div>
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<div class="foldopen" id="foldopen00205" data-start="{" data-end="}">
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<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>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> std::cout.precision(18);</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
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<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> << EPSILON</div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> </div>
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<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>
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<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>
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<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>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> </div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span>}</div>
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</div>
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<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>
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<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>
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<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>
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<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>
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<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>
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