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PCA主成分分析

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主成分分析的目的：特征降维

1.为什么要进行特征降维？ 
直观上通常认为样本向量的维数越高，就了解样本更多方面的属性，应该对提高识别率有利，然而事实并非如此。 
对于已知的样本数目，存在着一个特征数目的最大值，当实际使用的特征数目超过这个最大值时，分类器的性能不是得到改善而是退化。这种现象是模式是被中的“维度灾难”。 
最好的一个例子是：一对双胞胎，其中一个额头上有痣，另外一个额头上没痣，那么区分这对双胞胎谁是谁最好的方法是，看痣就可以了。

2.降维的目的 
1.减少预测变量的个数 
2.确保这些变量是相互独立的 
3.提供一个框架来解释结果 
如1中举的例子，人们可以根据经验把痣当做区分双胞胎的关键因素，然而机器不会。 
PCA算法是一种无监督学习，无须实现训练就可以找到区分于其他数据的“痣”。这便是PCA的核心，找出主成分。

3.PCA追根溯源 
要想搞清楚PCA为什么能提取主成分，首先得弄清它的源头，K-L变换—最优正交变换，PCA可以通过K-L变换得到互不相关的向量，K-L变换的变换矩阵可以有很多种（二阶矩阵、协方差矩阵、总类内离散度矩阵等等），当K-L变换矩阵为协方差矩阵时，等同于PCA。 
问题描述：对于d维空间的n个样本（该样本有d个特征），x1，…xn ,考虑如何能在低维空间最好地表示他们。 
这里写图片描述 
其中yj系数，uj是相互正交的基向量，X是原始的n维表示n和特征的向量，将X用相互正交的向量表示。 
可以推出系数的推导公式。 
这里写图片描述 
这个公式由来我想应该是任一n维欧式空间V均存在正交基，利用施密特正交化过程即可构建这个正交基。 
现在我们希望用d个有限项来估计向量x，公式如下： 
这里写图片描述 
该估计的准确度，取决于该估计所带来的误差，误差越小的话，估计越准确，那么误差是怎么计算的呢？ 
使用均方误差来表示该误差，那么误差的计算公式为： 
使用原始值减去估计值的然后平方。 
这里写图片描述 
要使用均方误差最小，我们采用Langrange乘子法进行求解： 
这里写图片描述 
得： 
这里写图片描述 
于是 
这里写图片描述 
K-L变换定义：当取矩阵R的d个最大特征值对应的特征向量来展开x时，其截断均方误差最小。这d个特征向量组成的正交坐标系称作x所在的D维空间的d维K-L变换坐标系， x在K-L坐标系上的展开系数向量y称作x的K-L变换。 
矩阵形式： 
这里写图片描述 
所以 
这里写图片描述 
向量y就是变换（降维）后的系数向量，在人脸识别Eigenface算法中就是用系数向量y代替原始特征向量x进行识别。

现在问题来了，相关矩阵R是个什么鬼，之前在代换中用到公式： 
这里写图片描述 
表达成矩阵的形式为： 
这里写图片描述 
该矩阵为实对称矩阵，实对称矩阵特征值对应的特征向量必然相互正交。 
最终结论： 
这里写图片描述 
推理过程来到了这里，还有一个问题没有解决，跟协方差有什么关系？相关矩阵和协方差矩阵其实并没有什么关系，但是我们观察协方差矩阵的计算公式。 
这里写图片描述 
这里写图片描述 
然后，相关矩阵呢？还记得均方误差的计算公式吗？ 
这里写图片描述 
一毛一样。 
于是呢，在计算PCA的时候，需要算出样本的协方差矩阵。 
由这里写图片描述 
得到新的特征矩阵.

4.PCA过程 
以鸢尾花的分类为例： 
原始数据是一个150x4的矩阵，也就是有150个样本数据，每个样本四个特征。

<code class="hljs  has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;">5.1     3.5     1.4     0.24.9     3.0     1.4     0.24.7     3.2     1.3     0.24.6     3.1     1.5     0.25.0     3.6     1.4     0.25.4     3.9     1.7     0.44.6     3.4     1.4     0.35.0     3.4     1.5     0.24.4     2.9     1.4     0.24.9     3.1     1.5     0.15.4     3.7     1.5     0.24.8     3.4     1.6     0.24.8     3.0     1.4     0.14.3     3.0     1.1     0.15.8     4.0     1.2     0.25.7     4.4     1.5     0.45.4     3.9     1.3     0.45.1     3.5     1.4     0.35.7     3.8     1.7     0.35.1     3.8     1.5     0.35.4     3.4     1.7     0.25.1     3.7     1.5     0.44.6     3.6     1.0     0.25.1     3.3     1.7     0.54.8     3.4     1.9     0.25.0     3.0     1.6     0.25.0     3.4     1.6     0.45.2     3.5     1.5     0.25.2     3.4     1.4     0.24.7     3.2     1.6     0.24.8     3.1     1.6     0.25.4     3.4     1.5     0.45.2     4.1     1.5     0.15.5     4.2     1.4     0.24.9     3.1     1.5     0.15.0     3.2     1.2     0.25.5     3.5     1.3     0.24.9     3.1     1.5     0.14.4     3.0     1.3     0.25.1     3.4     1.5     0.25.0     3.5     1.3     0.34.5     2.3     1.3     0.34.4     3.2     1.3     0.25.0     3.5     1.6     0.65.1     3.8     1.9     0.44.8     3.0     1.4     0.35.1     3.8     1.6     0.24.6     3.2     1.4     0.25.3     3.7     1.5     0.25.0     3.3     1.4     0.27.0     3.2     4.7     1.46.4     3.2     4.5     1.56.9     3.1     4.9     1.55.5     2.3     4.0     1.36.5     2.8     4.6     1.55.7     2.8     4.5     1.36.3     3.3     4.7     1.64.9     2.4     3.3     1.06.6     2.9     4.6     1.35.2     2.7     3.9     1.45.0     2.0     3.5     1.05.9     3.0     4.2     1.56.0     2.2     4.0     1.06.1     2.9     4.7     1.45.6     2.9     3.6     1.36.7     3.1     4.4     1.45.6     3.0     4.5     1.55.8     2.7     4.1     1.06.2     2.2     4.5     1.55.6     2.5     3.9     1.15.9     3.2     4.8     1.86.1     2.8     4.0     1.36.3     2.5     4.9     1.56.1     2.8     4.7     1.26.4     2.9     4.3     1.36.6     3.0     4.4     1.46.8     2.8     4.8     1.46.7     3.0     5.0     1.76.0     2.9     4.5     1.55.7     2.6     3.5     1.05.5     2.4     3.8     1.15.5     2.4     3.7     1.05.8     2.7     3.9     1.26.0     2.7     5.1     1.65.4     3.0     4.5     1.56.0     3.4     4.5     1.66.7     3.1     4.7     1.56.3     2.3     4.4     1.35.6     3.0     4.1     1.35.5     2.5     4.0     1.35.5     2.6     4.4     1.26.1     3.0     4.6     1.45.8     2.6     4.0     1.25.0     2.3     3.3     1.05.6     2.7     4.2     1.35.7     3.0     4.2     1.25.7     2.9     4.2     1.36.2     2.9     4.3     1.35.1     2.5     3.0     1.15.7     2.8     4.1     1.36.3     3.3     6.0     2.55.8     2.7     5.1     1.97.1     3.0     5.9     2.16.3     2.9     5.6     1.86.5     3.0     5.8     2.27.6     3.0     6.6     2.14.9     2.5     4.5     1.77.3     2.9     6.3     1.86.7     2.5     5.8     1.87.2     3.6     6.1     2.56.5     3.2     5.1     2.06.4     2.7     5.3     1.96.8     3.0     5.5     2.15.7     2.5     5.0     2.05.8     2.8     5.1     2.46.4     3.2     5.3     2.36.5     3.0     5.5     1.87.7     3.8     6.7     2.27.7     2.6     6.9     2.36.0     2.2     5.0     1.56.9     3.2     5.7     2.35.6     2.8     4.9     2.07.7     2.8     6.7     2.06.3     2.7     4.9     1.86.7     3.3     5.7     2.17.2     3.2     6.0     1.86.2     2.8     4.8     1.86.1     3.0     4.9     1.86.4     2.8     5.6     2.17.2     3.0     5.8     1.67.4     2.8     6.1     1.97.9     3.8     6.4     2.06.4     2.8     5.6     2.26.3     2.8     5.1     1.56.1     2.6     5.6     1.47.7     3.0     6.1     2.36.3     3.4     5.6     2.46.4     3.1     5.5     1.86.0     3.0     4.8     1.86.9     3.1     5.4     2.16.7     3.1     5.6     2.46.9     3.1     5.1     2.35.8     2.7     5.1     1.96.8     3.2     5.9     2.36.7     3.3     5.7     2.56.7     3.0     5.2     2.36.3     2.5     5.0     1.96.5     3.0     5.2     2.06.2     3.4     5.4     2.35.9     3.0     5.1     1.8</code><ul class="pre-numbering" style="box-sizing: border-box; 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padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li><li style="box-sizing: border-box; padding: 0px 5px;">122</li><li style="box-sizing: border-box; padding: 0px 5px;">123</li><li style="box-sizing: border-box; padding: 0px 5px;">124</li><li style="box-sizing: border-box; padding: 0px 5px;">125</li><li style="box-sizing: border-box; padding: 0px 5px;">126</li><li style="box-sizing: border-box; padding: 0px 5px;">127</li><li style="box-sizing: border-box; padding: 0px 5px;">128</li><li style="box-sizing: border-box; padding: 0px 5px;">129</li><li style="box-sizing: border-box; padding: 0px 5px;">130</li><li style="box-sizing: border-box; padding: 0px 5px;">131</li><li style="box-sizing: border-box; padding: 0px 5px;">132</li><li style="box-sizing: border-box; padding: 0px 5px;">133</li><li style="box-sizing: border-box; padding: 0px 5px;">134</li><li style="box-sizing: border-box; padding: 0px 5px;">135</li><li style="box-sizing: border-box; padding: 0px 5px;">136</li><li style="box-sizing: border-box; padding: 0px 5px;">137</li><li style="box-sizing: border-box; padding: 0px 5px;">138</li><li style="box-sizing: border-box; padding: 0px 5px;">139</li><li style="box-sizing: border-box; padding: 0px 5px;">140</li><li style="box-sizing: border-box; padding: 0px 5px;">141</li><li style="box-sizing: border-box; padding: 0px 5px;">142</li><li style="box-sizing: border-box; padding: 0px 5px;">143</li><li style="box-sizing: border-box; padding: 0px 5px;">144</li><li style="box-sizing: border-box; padding: 0px 5px;">145</li><li style="box-sizing: border-box; padding: 0px 5px;">146</li><li style="box-sizing: border-box; padding: 0px 5px;">147</li><li style="box-sizing: border-box; padding: 0px 5px;">148</li><li style="box-sizing: border-box; padding: 0px 5px;">149</li><li style="box-sizing: border-box; padding: 0px 5px;">150</li></ul>

1.特征值中心化，即每一维的数据都减去该维的均值。目的是使得变换之后的每一维的均值都为0. 
Matlab程序： 
function result = pca(source) 
for i=1:4 
mean = sum(source(:,i))/150; 
temp(:,i) = source(:,i)-mean; 
end 
result = temp; 
结果：

<code class="hljs haml has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;">-<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.1433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.4587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.2433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.2433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.4433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.1587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.5433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.6587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.5587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.4587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.2433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.7587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.8587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.1587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.1587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.1433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.1587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.1587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.1460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.5587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.4587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.4433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.4587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.4587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.3433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.4587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.4433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.4587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.1587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.8587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.1587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.2433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2460</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9987</span></span>    1.1567    0.1460    0.9413    0.2013    0.5567    0.1460    0.7413    0.3013    1.0567    0.0460    1.1413    0.3013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1013</span></span>    0.6567   -0.2540    0.8413    0.3013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1013</span></span>    0.4567    0.2460    0.9413    0.4013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1987</span></span>    0.7567   -0.1540    0.8413    0.1013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2013</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1987</span></span>    0.0567   -0.0540    0.4413    0.3013    0.1567   -0.8540    0.2413   -0.1987    0.2567   -0.1540    0.9413    0.2013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1587</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1013</span></span>    0.8567    0.0460    0.6413    0.2013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3013</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3413</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1987</span></span>    0.3567   -0.8540    0.7413    0.3013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1413</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.0987</span>    0.0567    0.1460    1.0413    0.6013    0.2567   -0.2540    0.2413    0.1013    0.4567   -0.5540    1.1413    0.3013    0.2567   -0.2540    0.9413    0.0013    0.5567   -0.1540    0.5413    0.1013    0.7567   -0.0540    0.6413    0.2013    0.9567   -0.2540    1.0413    0.2013    0.8567   -0.0540    1.2413    0.5013    0.1567   -0.1540    0.7413    0.3013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0413</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.0987</span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">05</span>87   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0013</span></span>    0.1567   -0.3540    1.3413    0.4013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3013</span></span>    0.1567    0.3460    0.7413    0.4013    0.8567    0.0460    0.9413    0.3013    0.4567   -0.7540    0.6413    0.1013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1013</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1013</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0013</span></span>    0.2567   -0.0540    0.8413    0.2013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0013</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1987</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1013</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0013</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1013</span></span>    0.3567   -0.1540    0.5413    0.1013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5540</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7587</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.0987</span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1013</span></span>    0.4567    0.2460    2.2413    1.3013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.3413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7013</span></span>    1.2567   -0.0540    2.1413    0.9013    0.4567   -0.1540    1.8413    0.6013    0.6567   -0.0540    2.0413    1.0013    1.7567   -0.0540    2.8413    0.9013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5013</span></span>    1.4567   -0.1540    2.5413    0.6013    0.8567   -0.5540    2.0413    0.6013    1.3567    0.5460    2.3413    1.3013    0.6567    0.1460    1.3413    0.8013    0.5567   -0.3540    1.5413    0.7013    0.9567   -0.0540    1.7413    0.9013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.2413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8013</span></span>   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.3413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.2013</span></span>    0.5567    0.1460    1.5413    1.1013    0.6567   -0.0540    1.7413    0.6013    1.8567    0.7460    2.9413    1.0013    1.8567   -0.4540    3.1413    1.1013    0.1567   -0.8540    1.2413    0.3013    1.0567    0.1460    1.9413    1.1013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.1413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8013</span></span>    1.8567   -0.2540    2.9413    0.8013    0.4567   -0.3540    1.1413    0.6013    0.8567    0.2460    1.9413    0.9013    1.3567    0.1460    2.2413    0.6013    0.3567   -0.2540    1.0413    0.6013    0.2567   -0.0540    1.1413    0.6013    0.5567   -0.2540    1.8413    0.9013    1.3567   -0.0540    2.0413    0.4013    1.5567   -0.2540    2.3413    0.7013    2.0567    0.7460    2.6413    0.8013    0.5567   -0.2540    1.8413    1.0013    0.4567   -0.2540    1.3413    0.3013    0.2567   -0.4540    1.8413    0.2013    1.8567   -0.0540    2.3413    1.1013    0.4567    0.3460    1.8413    1.2013    0.5567    0.0460    1.7413    0.6013    0.1567   -0.0540    1.0413    0.6013    1.0567    0.0460    1.6413    0.9013    0.8567    0.0460    1.8413    1.2013    1.0567    0.0460    1.3413    1.1013   -<span class="ruby" style="box-sizing: border-box;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0433</span>   -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3540</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.3413</span>    <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7013</span></span>    0.9567    0.1460    2.1413    1.1013    0.8567    0.2460    1.9413    1.3013    0.8567   -0.0540    1.4413    1.1013    0.4567   -0.5540    1.2413    0.7013    0.6567   -0.0540    1.4413    0.8013    0.3567    0.3460    1.6413    1.1013    0.0567   -0.0540    1.3413    0.6013</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; 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padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li><li style="box-sizing: border-box; padding: 0px 5px;">122</li><li style="box-sizing: border-box; padding: 0px 5px;">123</li><li style="box-sizing: border-box; padding: 0px 5px;">124</li><li style="box-sizing: border-box; padding: 0px 5px;">125</li><li style="box-sizing: border-box; padding: 0px 5px;">126</li><li style="box-sizing: border-box; padding: 0px 5px;">127</li><li style="box-sizing: border-box; padding: 0px 5px;">128</li><li style="box-sizing: border-box; padding: 0px 5px;">129</li><li style="box-sizing: border-box; padding: 0px 5px;">130</li><li style="box-sizing: border-box; padding: 0px 5px;">131</li><li style="box-sizing: border-box; padding: 0px 5px;">132</li><li style="box-sizing: border-box; padding: 0px 5px;">133</li><li style="box-sizing: border-box; padding: 0px 5px;">134</li><li style="box-sizing: border-box; padding: 0px 5px;">135</li><li style="box-sizing: border-box; padding: 0px 5px;">136</li><li style="box-sizing: border-box; padding: 0px 5px;">137</li><li style="box-sizing: border-box; padding: 0px 5px;">138</li><li style="box-sizing: border-box; padding: 0px 5px;">139</li><li style="box-sizing: border-box; padding: 0px 5px;">140</li><li style="box-sizing: border-box; padding: 0px 5px;">141</li><li style="box-sizing: border-box; padding: 0px 5px;">142</li><li style="box-sizing: border-box; padding: 0px 5px;">143</li><li style="box-sizing: border-box; padding: 0px 5px;">144</li><li style="box-sizing: border-box; padding: 0px 5px;">145</li><li style="box-sizing: border-box; padding: 0px 5px;">146</li><li style="box-sizing: border-box; padding: 0px 5px;">147</li><li style="box-sizing: border-box; padding: 0px 5px;">148</li><li style="box-sizing: border-box; padding: 0px 5px;">149</li><li style="box-sizing: border-box; padding: 0px 5px;">150</li></ul>

Matlab语句： 
result = cov(temp);

结果： 
0.6857 -0.0393 1.2737 0.5169 
-0.0393 0.1880 -0.3217 -0.1180 
1.2737 -0.3217 3.1132 1.2964 
0.5169 -0.1180 1.2964 0.5824

3.计算协方差矩阵C的特征值和特征向量 
Matlab语句：

[v,D]= eig(error); 
display(v); 
display(D);

结果： 
特征向量 
v =

-0.3173 0.5810 0.6565 0.3616 
0.3241 -0.5964 0.7297 -0.0823 
0.4797 -0.0725 -0.1758 0.8566 
-0.7511 -0.5491 -0.0747 0.3588

特征值： 
D =

0.0237         0         0         0     0    0.0785         0         0     0         0    0.2422         0     0         0         0    4.2248

选取特征值4.2248和0.2422

4.选取大的特征值对应的特征向量，得到新的数据集 
Matlab语句： 
new(:,1)=v(:,3); 
new(:,2)=v(:,4);

result=source*new; 
结果：

5.6413    2.8271    5.1452    2.7960    5.1774    2.6215    5.0036    2.7649    5.6486    2.7828    6.0625    3.2314    5.2326    2.6905    5.4851    2.8849    4.7439    2.6234    5.2080    2.8375    5.9667    3.0048    5.3362    2.8982    5.0870    2.7239    4.8114    2.2861    6.5009    2.8678    6.6595    3.1275    6.1328    2.8888    5.6339    2.8630    6.1940    3.3123    5.8352    2.9240    5.7126    3.2008    5.7548    2.9681    5.4563    2.2955    5.4202    3.2082    5.2835    3.1552    5.1757    3.0034    5.4526    3.0423    5.6894    2.9490    5.6340    2.8715    5.1246    2.8785    5.1173    2.9229    5.7328    3.1013    6.1347    2.8637    6.4147    2.9142    5.2080    2.8375    5.3919    2.6443    5.9215    2.8861    5.2080    2.8375    4.8345    2.5295    5.5508    2.9210    5.5858    2.7412    4.3819    2.6591    4.9804    2.5130    5.5106    3.1058    5.7574    3.3025    5.0720    2.7957    5.8251    2.9738    5.0941    2.6710    5.9010    2.9687    5.4297    2.8074    6.0002    6.7961    5.6339    6.4438    5.8189    6.9754    4.4891    5.6923    5.3901    6.5985    4.8974    6.1518    5.5986    6.6066    4.3136    4.7599    5.5437    6.5546    4.5941    5.5012    4.0522    5.0003    5.2124    6.0224    4.7668    5.7737    5.1904    6.4954    5.0629    5.3365    5.7830    6.4389    4.9627    6.1709    4.9828    5.7459    4.7729    6.4537    4.7332    5.5546    5.2305    6.6276    5.2479    5.8681    4.9872    6.8078    5.1323    6.4318    5.4651    6.2254    5.6443    6.4110    5.5594    6.8424    5.5821    7.0687    5.1524    6.3238    4.9496    5.2040    4.6122    5.4410    4.6372    5.3195    5.0030    5.6463    4.8935    6.8901    4.8314    6.0986    5.5098    6.3185    5.7228    6.7318    4.9440    6.3242    5.0480    5.7565    4.6351    5.6759    4.6452    5.9744    5.2809    6.4015    4.9125    5.7402    4.3063    4.8043    4.8115    5.8669    5.1035    5.8425    5.0231    5.8866    5.3338    6.1530    4.5632    4.6029    4.9677    5.8092    5.3029    8.0431    4.7398    6.9254    5.6567    8.1278    5.1336    7.4822    5.2728    7.8611    5.8619    8.9082    4.1234    6.0307    5.6671    8.4433    5.0692    7.8310    6.0951    8.4295    5.5568    7.1733    5.0986    7.3137    5.5300    7.6767    4.5383    6.8559    4.7754    7.0966    5.4335    7.4161    5.3555    7.4606    6.4863    9.0001    5.5680    9.3060    4.5537    6.8097    5.6915    7.9395    4.7091    6.7094    5.7715    9.0106    5.1107    6.8990    5.6481    7.7872    5.8731    8.1255    5.1356    6.7690    5.1983    6.8020    5.1039    7.6342    5.7772    7.8989    5.6875    8.3523    6.6852    8.7437    5.0964    7.6701    5.1709    6.9544    4.8133    7.2910    6.0005    8.5879    5.4536    7.6563    5.3628    7.4162    5.1502    6.6802    5.6862    7.6190    5.4973    7.8256    5.7240    7.4338    4.7398    6.9254    5.5907    8.0747    5.6182    7.9307    5.5021    7.4554    4.9397    7.0370    5.3932    7.2754    5.4306    7.4130    5.0318    6.9010
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5.为什么要计算协方差矩阵请参考（3.PCA追根溯源）

5.matlab中对于PCA的实现

[COEFE,SCORE,latent]=princomp(s) 
其中参数： 
COEFE表示：主成分分量，也就是特征向量矩阵。 
SCORE表示：主成分，X的源特征数据的低维表示。 
latent表示：协方差矩阵。


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