numpy学习

Posted 2020-08-02 技术从未如此性感

tags:

篇首语：本文由小常识网(cha138.com)小编为大家整理，主要介绍了numpy学习相关的知识，希望对你有一定的参考价值。

1、multiply
例子：

<code class="hljs fix 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-attribute" style="box-sizing: border-box;">x1</span>=<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[1,2,3];x2=[4,5,6]
print multiply(x1,x2)</span></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></ul>

输出：

<code class="hljs json 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">[ <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">10</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">18</span>]</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></ul>

multiply函数得到的结果是对应位置上面的元素进行相乘。

2、std 标准方差 ,var 方差
例子：

<code class="hljs lua 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">b=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>]
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> var(b)
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> power(std(b),<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>)
ll=<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,2,3,4,5,6],[3,4,5,6,7,8]]</span>
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> var(ll[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>])
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> var(ll,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>)#第二个参数为<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>，表示按列求方差
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> var(ll,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>)#第二个参数为<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>，表示按行求方差</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></ul>

输出：

<code class="hljs json 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.6875</span>
<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.6875</span>
<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.91666666667</span>
[ <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.</span>]
[ <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.91666667</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.91666667</span>]</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></ul>

var输出向量的方差，std输出向量的标准方差。

3、mean
例子：

<code class="hljs php 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">b=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>]
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mean(b)
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mean(ll) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#全部元素求均值</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mean(ll,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>)<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#按列求均值</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mean(ll,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>)<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#按行求均值</span></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></ul>

结果：

<code class="hljs json 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.75</span>
<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.5</span>
[ <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6.</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7.</span>]
[ <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.5</span>  <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5.5</span>]</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></ul>

mean函数得到向量的均值。

4、sum
求和
例子

<code class="hljs lua 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">x=<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[0, 1, 2],[2, 1, 0]]</span>
b=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>]
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> sum(b)
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> sum(x)</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></ul>

输出：

<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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">15
6</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></ul>

sum求向量的和。也可以求矩阵所有元素的和

5、cov()

例子：

<code class="hljs perl 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">b=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>]
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> cov(b)
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> sum((multiply(b,b))-mean(b)<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*mean</span>(b))/<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span></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></ul>

输出：

<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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">4.91666666667
4.91666666667</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></ul>

cov求的是样本协方差
公式如下：
这里写图片描述
公式一是样本均值
公式二是样本方差
公式三是样本协方差。
上面的函数cov就是使用样本协方差求得的。

例子：

<code class="hljs lua 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">x=<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[0, 1, 2],[2, 1, 0]]</span>
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> cov(x)
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> sum((multiply(x[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>],x[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]))-mean(x[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>])*mean(x[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]))/<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span></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></ul>

输出结果：

<code class="hljs lua 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 1. -1.]
 [-1.  1.]]</span>
-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span></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></ul>

cov的参数是矩阵，输出结果也是矩阵！输出的矩阵为协方差矩阵！
计算过程如下：
这里写图片描述
截图来源维基百科：协方差矩阵

6、corrcoef
该函数得到相关系数矩阵。
例子：

<code class="hljs perl 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">    vc=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">39</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;">8</span>]
    vb=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">38</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;">8</span>]
    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mean(multiply((vc-mean(vc)),(vb-mean(vb))))/(std(vb)<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*std</span>(vc))
    <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#corrcoef得到相关系数矩阵（向量的相似程度）</span>
    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> corrcoef(vc,vb)</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></ul>

输出结果：

<code class="hljs lua 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.999986231331</span>
<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 1.          0.99998623]
 [ 0.99998623  1.        ]]</span></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></ul>

相关系数公式：
这里写图片描述

对应着公式理解上面的代码，应该是很容易的。

7、vdot 向量的点积
例子：

<code class="hljs php 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">    <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#vdot 返回两向量的点积</span>
    l1=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>]
    l2=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>]
    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span>  vdot(l1,l2)</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></ul>

结果：

<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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">32</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></ul>

点积没什么说的，对应位置相乘求和。

8、mat
例子：

<code class="hljs perl 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">    l1=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>]
    l2=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>]
    ll=[l1,l2]
    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span>  vdot(l1,l2)
    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mat(l1)<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*mat</span>(l2).T
    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mat(ll)</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></ul>

结果：

<code class="hljs lua 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">32</span>
<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[32]]</span>
<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1 2 3]
 [4 5 6]]</span></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></ul>

mat函数把列表转换成矩阵形式。这在矩阵运算中不可缺少。

9、shape
例子：

<code class="hljs lua 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">    #矩阵有一个shape属性，是一个(行，列)形式的元组
    a = array(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,2,3],[4,5,6]]</span>)
    <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> a.shape</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></ul>

结果：

<code class="hljs clojure 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-list" style="box-sizing: border-box;">(<span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">2</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;"> 3</span>)</span></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></ul>

shape返回矩阵的行列数

10、ones
例子：

<code class="hljs php 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">    <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#返回按要求的矩阵</span>
    ones = ones((<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>))
    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> ones</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></ul>

结果：

<code class="hljs lua 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 1.]
 [ 1.]]</span></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></ul>

ones返回指定行列数的全一矩阵

11、xrange
例子：

<code class="hljs lua 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-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background: transparent;">    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> i <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> xrange(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>):
        <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> i
    test=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>]
    <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> test[:]
    <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> test[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>:<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>]
    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> i <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> xrange(<span class="hljs-number" style="color: rgb(0以上是关于numpy学习的主要内容，如果未能解决你的问题，请参考以下文章 
 Numpy学习:《Python数据分析基础教程NumPy学习指南第2版》中文PDF+英文PDF+代码
 《Python机器学习及实践》----无监督学习之数据聚类
 《Python机器学习及实践》----无监督学习之数据聚类
 Numpy学习笔记
 Numpy学习一：array数组对象
 Numpy学习练习代码 ——