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<div id="projectname">Templates -- Meow
 <span id="projectnumber">1.1.2</span>
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<div id="projectbrief">不能,也不應該先編譯成obj-file的templates</div>
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<div class="title">utility.h</div> </div>
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<a href="math_2utility_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="preprocessor">#ifndef math_utility_H__</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor"></span><span class="preprocessor">#define math_utility_H__</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="preprocessor">#include <cstdlib></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="preprocessor">#include <algorithm></span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="preprocessor">#include <cmath></span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> </div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="keyword">namespace </span>meow{</div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a name="l00012"></a><span class="lineno"><a class="code" href="namespacemeow.html#aa86d5920087a4e73078b759bc3996f76"> 12</a></span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="namespacemeow.html#aa86d5920087a4e73078b759bc3996f76" title="圓周率...">PI</a> = 3.14159265358979323846264338327950288;</div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00018"></a><span class="lineno"><a class="code" href="namespacemeow.html#ab9456533c0ae85fba812bfb5b017c8d2"> 18</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#ab9456533c0ae85fba812bfb5b017c8d2" title="如果abs(輸入的數值) < eps, 則回傳0, 否則回傳輸入的數值">noEPS</a>(T value, T eps = 1e-9){</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  T epsp((eps < T(0)) ? -eps : eps);</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  <span class="keywordflow">return</span> ((value < -epsp || value > epsp) ? value : T(0));</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> }</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00027"></a><span class="lineno"><a class="code" href="namespacemeow.html#aebe1ad335556790c578c4cf7836fd9ca"> 27</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#aebe1ad335556790c578c4cf7836fd9ca" title="(value-lower)/(upper-lower)">normalize</a>(T lower, T upper, T value){</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="keywordflow">return</span> (value - lower) / (upper - lower);</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> }</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00035"></a><span class="lineno"><a class="code" href="namespacemeow.html#af95cfca15ad7a51ed4d07b06e1296080"> 35</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#af95cfca15ad7a51ed4d07b06e1296080" title="(lower+_ratio*(upper-lower))">denormalize</a>(T lower, T upper, T _ratio){</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">return</span> lower + _ratio * (upper - lower);</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> }</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00043"></a><span class="lineno"><a class="code" href="namespacemeow.html#a3b01a91eb4a02909a61a35e406fa5732"> 43</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#a3b01a91eb4a02909a61a35e406fa5732" title="denormalize(l2,u2,normalize(l1,u1,m1))">ratioMapping</a>(T l1, T u1, T m1, T l2, T u2){</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">return</span> <a class="code" href="namespacemeow.html#af95cfca15ad7a51ed4d07b06e1296080" title="(lower+_ratio*(upper-lower))">denormalize</a>(l2, u2, <a class="code" href="namespacemeow.html#aebe1ad335556790c578c4cf7836fd9ca" title="(value-lower)/(upper-lower)">normalize</a>(l1, u1, m1));</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00051"></a><span class="lineno"><a class="code" href="namespacemeow.html#a98d838d338a3e6f3c57e94562fab3fa7"> 51</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#a98d838d338a3e6f3c57e94562fab3fa7" title="std::min(mx,std::max(mn,v))">inRange</a>(T <span class="keyword">const</span>& mn, T <span class="keyword">const</span>& mx, T <span class="keyword">const</span>& v){</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">return</span> std::min(mx, std::max(mn, v));</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> }</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00059"></a><span class="lineno"><a class="code" href="namespacemeow.html#a1954e235973a2ac79a7a72a4b7d25573"> 59</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#a1954e235973a2ac79a7a72a4b7d25573" title="x*x ">squ</a>(T <span class="keyword">const</span>& x){</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordflow">return</span> x * x;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00067"></a><span class="lineno"><a class="code" href="namespacemeow.html#a10a8cca705773b7d9f6f91d3fb08c104"> 67</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#a10a8cca705773b7d9f6f91d3fb08c104" title="x*x*x ">cub</a>(T <span class="keyword">const</span>& x){</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">return</span> x * x * x;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> }</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="code" href="namespacemeow.html#ad4d1e5fa951e5534204a0ee3eee22777"> 75</a></span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="namespacemeow.html#ad4d1e5fa951e5534204a0ee3eee22777" title="只將 sigs 個標準差以內的數據拿來取平均">average</a>(T <span class="keyword">const</span>& beg, T <span class="keyword">const</span>& end, <span class="keywordtype">double</span> sigs){</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordtype">int</span> N = 0;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordtype">double</span> av = 0;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">for</span>(T it = beg; it != end; it++, N++){</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  av += *it;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  }</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  av /= N;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordtype">double</span> sig = 0;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">for</span>(T it = beg; it != end; it++){</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  sig += (*it - av) * (*it - av);</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  }</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  sig = sqrt(sig / N);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordtype">double</span> lower = av - sig * sigs, upper = av + sig * sigs;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordtype">double</span> ret = 0, retn = 0;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordflow">for</span>(T it = beg; it != end; it++){</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">if</span>(lower <= *it && *it <= upper){</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  ret += *it;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  retn++;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  }</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  }</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">return</span> ret / retn;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> }</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00102"></a><span class="lineno"><a class="code" href="namespacemeow.html#a6ae78e60d507c85de003f8fa8423b650"> 102</a></span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="namespacemeow.html#ad4d1e5fa951e5534204a0ee3eee22777" title="只將 sigs 個標準差以內的數據拿來取平均">average</a>(T <span class="keyword">const</span>& beg, T <span class="keyword">const</span>& end, T <span class="keyword">const</span>& p, <span class="keywordtype">double</span> sigs){</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordtype">int</span> N = 0;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordtype">double</span> ps = 0;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">for</span>(T it = beg, ip = p; it != end; it++, N++, ip++){</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  ps += *ip;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  }</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordtype">double</span> av = 0;</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">for</span>(T it = beg, ip = p; it != end; it++, ip++){</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  av += *it * *ip / ps;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  }</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordtype">double</span> sig = 0;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">for</span>(T it = beg, ip = p; it != end; it++, ip++){</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  sig += *ip / ps * (*it - av) * (*it - av);</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  }</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  sig = sqrt(sig);</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordtype">double</span> lower = av - sig * sigs, upper = av + sig * sigs;</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordtype">double</span> ret = 0, retn = 0;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordflow">for</span>(T it = beg, ip = p; it != end; it++, ip++){</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">if</span>(lower <= *it && *it <= upper){</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  ret += *it * *ip;</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  retn += *ip;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  }</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  }</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">if</span>(retn <= 1e-10) <span class="keywordflow">return</span> av;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">return</span> ret / retn;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> }</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="keyword">template</span><<span class="keyword">class</span> T></div>
<div class="line"><a name="l00133"></a><span class="lineno"><a class="code" href="namespacemeow.html#ae880337dfdcc67984a0dccdb50e5c5d0"> 133</a></span> <span class="keyword">inline</span> T <a class="code" href="namespacemeow.html#ae880337dfdcc67984a0dccdb50e5c5d0" title="就只是個取絕對值">tAbs</a>(T <span class="keyword">const</span>& t){</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">return</span> (t < 0 ? -t : t);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> }</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> }</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> </div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="preprocessor">#endif // math_utility_H__</span></div>
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