python-numpy一些方法总结
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本文转自： http://blog.csdn.net/u010156024/article/details/50419338
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-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><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-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><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-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><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-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><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-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><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-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><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-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><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-radius: 0px; word-wrap: normal; background: transparent;">156</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><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-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><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-radius: 0px; word-wrap: normal; background: transparent;">4.916666666674.91666666667</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><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： 
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-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><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-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><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： 
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-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><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-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><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：
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-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><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-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><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-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><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-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><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-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><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-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><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-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><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-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><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-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, 102, 102); box-sizing: border-box;">2</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>): <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> i</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><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>
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-radius: 0px; word-wrap: normal; background: transparent;"><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;">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;">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-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;">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></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></ul><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></ul>
xrange用于循环中，参数为一个整数的话，可循环遍历小于该参数的值。两个参数，则循环遍历两个整数之间的值。
test[:]则表示获取test列表中的所有元素。
test[2:3]则表示获取从第2个位置到第三个位置间的元素。
12、strptime
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-radius: 0px; word-wrap: normal; background: transparent;">import <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">time</span>from datetime import datetime,datedd = datetime.strptime(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'2014-04-03T10:53:49.875Z'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%Y</span>-<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%m</span>-<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%dT</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%H</span>:<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%M</span>:<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%S</span>.<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%fZ</span>"</span>) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">time</span>.mktime(dd.timetuple())<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#1396493629.0</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><li style="box-sizing: border-box; padding: 0px 5px;">4</li></ul><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-radius: 0px; word-wrap: normal; background: transparent;">1396493629.0</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><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>
strptime把时间按照指定的格式转换。处理时间的时候会用到这个函数。
13、tuple和数组转换成字符串
例子：
<code class="hljs go 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;"> tuple =<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-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> tuple[<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">len</span>(tuple<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">)-1</span>] <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> tuple<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">[-1</span>] <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;"> 9.99</span>.__repr__() <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> str<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">(9.99</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><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 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;">339.999.99</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><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>
上面的示例中tuple是一个元组，访问元素的时候，可以通过[index]这种方式访问。
访问最后一个元素的时候，可以通过[-1]访问.
那么访问倒数第二个元素：
print tuple[-2]
输出结果：2
另外，数字转换成字符串有两种方式：
_ _ repr _ _()
str()
14、transpose和.T
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-radius: 0px; word-wrap: normal; background: transparent;"> aa =<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1],[2],[3]]</span> aa= mat(aa)#将列表转换成矩阵，并存放在aa中 <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> aa <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> aa.transpose()#将矩阵进行转置 <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> aa #transpose()进行矩阵的转置，aa并没有改变 <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'*'</span>*<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">20</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> aa.T <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> aa #T转置矩阵，也没有发生改变</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></ul><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></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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1] [2] [3]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1 2 3]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1] [2] [3]]</span>********************<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1 2 3]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1] [2] [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><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></ul><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></ul>
有两种方式实现矩阵的转置。
15、zeros() 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-radius: 0px; word-wrap: normal; background: transparent;"> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> zeros((<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((<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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#参数指明了矩阵的行列数</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><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>
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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 0.] [ 0.]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 1. 1. 1.] [ 1. 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><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li></ul><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>
zeros返回指定行列全零矩阵
ones返回指定行列的全一矩阵
16、列表 数组 linspace
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-radius: 0px; word-wrap: normal; background: transparent;"> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#列表和数组的区别：</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#列表： [1, 2, 3, 4]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#数组： [1 2 3 4]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'*'</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*20</span> ll =[<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-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'列表：'</span>,ll arr = array(ll) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'数组：'</span>,arr <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'*'</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*20</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> linspace(<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;">3</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#返回的是数组</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><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></ul><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></ul>
输出结果：
<code class="hljs asciidoc 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;">********************列表： [1, 2, 3, 4]数组： [1 2 3 4]********************<span class="hljs-attribute" style="box-sizing: border-box;">[ 0. 0.6 1.2 1.8 2.4 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><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li></ul><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>
数组中间元素没有分隔符。列表逗号分割。
linspace返回的是指定的开始结束位置的指定个数的数。
linspace(0,3,6)返回0到3之间6个数字，且间隔均匀
17、argsort 排序索引
例子：
<code class="hljs python 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="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'**************数组排序问题****************'</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#数组的构建问题，初始化使用array()</span> ary=array(zeros(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>)) ary[<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;">0.1</span> ary[<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;">0.6</span> ary[<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;">0.5</span> ary[<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;">0.7</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#有-号，降序排列</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#无-号，升序排列</span> sortindex = argsort(ary) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> id <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> sortindex: <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'索引：'</span>,id <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> ary: <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> i</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></ul><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></ul>
结果：
<code class="hljs markdown 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="hljs-strong" style="box-sizing: border-box;">*****</span><span class="hljs-strong" style="box-sizing: border-box;">*****</span><span class="hljs-strong" style="box-sizing: border-box;">****数组排序问题**</span><span class="hljs-strong" style="box-sizing: border-box;">*****</span><span class="hljs-strong" style="box-sizing: border-box;">*****</span><span class="hljs-emphasis" style="box-sizing: border-box;">***</span>*索引： 0索引： 2索引： 1索引： 30.10.60.50.7</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></ul><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></ul>
argsort函数返回数组按照从小到大排序的位置的索引。
sortindex = argsort(-ary)
for id in sortindex:
print ‘索引：’,id
for i in sortindex:
print ary[i]输出结果：
索引： 1
索引： 2
索引： 0
0.7
0.6
0.5
0.1
18、 [:,:]矩阵元素切片
<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-radius: 0px; word-wrap: normal; background: transparent;"> #矩阵元素的获取 ll = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,2,3],[4,5,6],[7,8,9]]</span> #获取第二行第<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>个元素 <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> mat(ll)[<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;">0</span>] #第一个冒号代表获取行的起止行号 #第二个冒号代表获取列的起止行号 <span class="hljs-built_in" style="color: rgb(102, 0, 102); 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><li style="box-sizing: border-box; padding: 0px 5px;">7</li></ul><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>
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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1 2 3] [4 5 6] [7 8 9]]</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><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>
19、diag
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-radius: 0px; word-wrap: normal; background: transparent;"> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#构建对角矩阵 </span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#diag()参数为列表即可</span> dd = [<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>] dilogg = diag(dd) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'diag='</span>,dilogg</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><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 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-radius: 0px; word-wrap: normal; background: transparent;">diag= <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1 0 0] [0 2 0] [0 0 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><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>
diag构建对角矩阵
20、linalg.inv和.I 求逆矩阵
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-radius: 0px; word-wrap: normal; background: transparent;"> dd = [<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>] dilogg = diag(dd) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'diag='</span>,dilogg <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'dd:'</span>,linalg.inv(dilogg) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'I='</span>,mat(dilogg).I ll = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,2,3],[4,5,6],[7,8,9]]</span> #求逆矩阵 lv = linalg.inv(mat(ll)) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'inv:'</span>,lv <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'I:'</span>,mat(ll).I</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></ul><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></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-radius: 0px; word-wrap: normal; background: transparent;">diag= <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1 0 0] [0 2 0] [0 0 3]]</span>dd: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 1. 0. 0. ] [ 0. 0.5 0. ] [ 0. 0. 0.33333333]]</span>I= <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 1. 0. 0. ] [ 0. 0.5 0. ] [ 0. 0. 0.33333333]]</span>inv: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ -4.50359963e+15 9.00719925e+15 -4.50359963e+15] [ 9.00719925e+15 -1.80143985e+16 9.00719925e+15] [ -4.50359963e+15 9.00719925e+15 -4.50359963e+15]]</span>I: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ -4.50359963e+15 9.00719925e+15 -4.50359963e+15] [ 9.00719925e+15 -1.80143985e+16 9.00719925e+15] [ -4.50359963e+15 9.00719925e+15 -4.50359963e+15]]</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><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></ul><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></ul>
上面求逆矩阵有两种方式。
linalg.inv()和 矩阵.I
两种方式均可。
21、dot矩阵点积
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-radius: 0px; word-wrap: normal; background: transparent;"> ll = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,2,3],[4,5,6],[7,8,9]]</span> ld = dot(ll,ll) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'dot:'</span>,ld <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> mat(ll)*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></ul><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 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-radius: 0px; word-wrap: normal; background: transparent;">dot: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 30 36 42] [ 66 81 96] [102 126 150]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 30 36 42] [ 66 81 96] [102 126 150]]</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><li style="box-sizing: border-box; padding: 0px 5px;">6</li></ul><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>
22、eye 单元矩阵
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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'eye:'</span>,eye(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>)<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#单元矩阵</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><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>
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-radius: 0px; word-wrap: normal; background: transparent;">eye: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 1. 0.] [ 0. 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><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>
23 eig 矩阵的特征值和特征向量
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-radius: 0px; word-wrap: normal; background: transparent;"> A=mat(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,0,0,0,2],[0,0,3,0,0],[0,0,0,0,0],[0,4,0,0,0]]</span>) U =A*A.T lamda,hU=linalg.eig(U) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'hU:'</span>,hU <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> lamda</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><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 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-radius: 0px; word-wrap: normal; background: transparent;">hU: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 1. 0. 0. 0.] [ 0. 1. 0. 0.] [ 0. 0. 1. 0.] [ 0. 0. 0. 1.]]</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;">9.</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;">16.</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><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>
24 sorted 排序
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-radius: 0px; word-wrap: normal; background: transparent;"> ll=[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</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;">3</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;">1</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;">5</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;">8</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span>] <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> sorted(ll,reverse=<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">True</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#降序</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> sorted(ll,reverse=<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">False</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#升序</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><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 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-radius: 0px; word-wrap: normal; background: transparent;">[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</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;">5</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;">3</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;">0</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;">0</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;">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;">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-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</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><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>
25、linalg.svd 奇异值分解
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-radius: 0px; word-wrap: normal; background: transparent;"> A=mat(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,0,0,0,2],[0,0,3,0,0],[0,0,0,0,0],[0,4,0,0,0]]</span>) U,S,VT =linalg.svd(A) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'U:'</span>,U <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'V:'</span>,VT <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'s:'</span>,S <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'==='</span>,U*(mat(diag(S))*eye(<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>))*VT</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><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-radius: 0px; word-wrap: normal; background: transparent;">U: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 0. 0. 1. 0.] [ 0. 1. 0. 0.] [ 0. 0. 0. -1.] [ 1. 0. 0. 0.]]</span>V: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 0. 1. -0. -0. -0. ] [ 0. 0. 1. -0. -0. ] [ 0.4472136 0. -0. -0. 0.89442719] [ 0. 0. -0. 1. -0. ] [-0.89442719 0. -0. -0. 0.4472136 ]]</span>s: [ <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;">3.</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.23606798</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.</span> ]=== <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 1. 0. 0. 0. 2.] [ 0. 0. 3. 0. 0.] [ 0. 0. 0. 0. 0.] [ 0. 4. 0. 0. 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><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></ul><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></ul>
关于什么是奇异值分解，请参考奇异值分解
26、random.rand
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-radius: 0px; word-wrap: normal; background: transparent;"> A=mat(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,0,0,0,2],[0,0,3,0,0],[0,0,0,0,0],[0,4,0,0,0]]</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> A[:,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] #获取<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;">3</span>个<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;">1</span>之间的数字 rr=random.rand(<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;">3</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> rr <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> (rr-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>*(rr-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</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><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></ul><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></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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[0] [0] [0] [4]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 0.30446153 0.40653841 0.40143809] [ 0.77970727 0.57491894 0.85801586] [ 0.33509491 0.64652856 0.48276137]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[-0.19553847 -0.09346159 -0.09856191] [ 0.27970727 0.07491894 0.35801586] [-0.16490509 0.14652856 -0.01723863]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[-0.39107693 -0.18692318 -0.19712383] [ 0.55941453 0.14983789 0.71603172] [-0.32981018 0.29305712 -0.03447726]]</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><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></ul><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></ul>
random.rand(3,3)随机获取3*3个0-1之间的数字
27、arange
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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-attribute" style="box-sizing: border-box;"> delta </span>=<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;"> 0.25 x = arange(-3.0, 3.0, delta) print x</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><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 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-radius: 0px; word-wrap: normal; background: transparent;">[-<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;">2.75</span> -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.5</span> -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.25</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;">1.75</span> -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.5</span> -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.25</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;">0.75</span> -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span> -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.25</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;">0.25</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.75</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;">1.25</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.5</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.75</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;">2.25</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.5</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.75</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><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>
arange获取指定起始位置，指定步长的一系列数。
28、nonzero()
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-radius: 0px; word-wrap: normal; background: transparent;"> x =<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,0,0,0,2],[0,0,3,0,0]]</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> x nz=nonzero(x) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> nz <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> nz[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">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><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li></ul><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 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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1, 0, 0, 0, 2], [0, 0, 3, 0, 0]]</span>(array([<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;">0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]), array([<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;">4</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;">0</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;">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><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>
nonzero（）函数返回矩阵中非0元素的位置
nz的返回值意义如下：
第一行是所有非零数所在行值
第二行是所有非零值所在列值
29、获取指定位置的元素
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-radius: 0px; word-wrap: normal; background: transparent;"> A=mat(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,0,0,0,2],[0,0,3,0,0],[0,0,0,0,0],[0,4,0,0,0]]</span>) sample =A[<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> sample <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> sample[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>] ll=mat([<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-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> range(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>): <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> sum(ll==i): <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> i</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></ul><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></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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1 0 0 0 2]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1 0 0 0 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></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><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>
A[0,:]的意义是获取第0行的所有元素
if sum(ll==i):的意义是只要i存在ll矩阵中，if就是True
ll必须是mat转换的矩阵。列表好像不行。并且还是单行的矩阵。
第二个例子：
<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-radius: 0px; word-wrap: normal; background: transparent;"> A=mat(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,0,0,0,2],[0,0,3,0,0],[0,0,0,0,0],[0,4,0,0,0]]</span>) #根据ind序列索引获取矩阵A中的数据 ind=[<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-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;">0</span>] <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> A[ind,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">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><li style="box-sizing: border-box; padding: 0px 5px;">4</li></ul><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 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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[0] [0] [0] [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><li style="box-sizing: border-box; padding: 0px 5px;">4</li></ul><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>
30、zip
例子：
<code class="hljs python 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;"> ll=[<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-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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#可以互换指定区域的位置</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> ll[<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;">6</span>]+ll[<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;">3</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#成对获取x、y的值</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;">for</span> x,y <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> zip(l1,l2): <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x,y</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></ul><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></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-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;">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;">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;">1</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;">2</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;">3</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">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><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>
print ll[3:6]+ll[0:3]这行代码实现指定位置的元素进行交换。
31、chr函数，获取指定的字符
例子：
<code class="hljs python 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="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#获取指定的字符</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> range(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">65</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">70</span>): <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> str(chr(i))</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><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 mathematica 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;">AB<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">C</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">D</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">E</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><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>
32、random.shuffle
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-radius: 0px; word-wrap: normal; background: transparent;"> ll=range(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span>)<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#返回列表</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> ll <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#shuffle函数随机打乱列表中的元素顺序</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> random.shuffle(ll) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> 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></ul><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 scss 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="hljs-attr_selector" style="color: rgb(0, 136, 0); box-sizing: border-box;">[0, 1, 2, 3, 4, 5, 6, 7, 8]</span><span class="hljs-attribute" style="box-sizing: border-box;">None</span><span class="hljs-attr_selector" style="color: rgb(0, 136, 0); box-sizing: border-box;">[8, 5, 1, 4, 2, 6, 0, 3, 7]</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><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>
shuffle函数随机打乱列表中的元素顺序
33、vdot 点积
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-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>] 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> dot(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><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li></ul><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></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-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-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><li style="box-sizing: border-box; padding: 0px 5px;">5</li></ul><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>
vdot 和 dot都可以获取向量的点积。
区别：
<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-radius: 0px; word-wrap: normal; background: transparent;"> ll=<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,2,3],[4,5,6],[1,2,3]]</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> dot(mat(ll),mat(ll).T) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> vdot(mat(ll),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></ul><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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[14 32 14] [32 77 32] [14 32 14]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[105]]</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><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>
总结：对于向量来说，vdot dot向量的点积结果相同。
对于矩阵来说，dot是矩阵的点积。
而vdot是对应位置的元素乘积求和。
结果中的105=1^2+2^2+3^3+4^2+5^2+6^2+1^2+2^2+3^3
34、次方计算**
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-radius: 0px; word-wrap: normal; background: transparent;"> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*2</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">**</span><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*2</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">**</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;">5</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*2</span>)<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">**</span><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*2</span>)<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">**</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;">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><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-radius: 0px; word-wrap: normal; background: transparent;">124.24264068712362.44948974278</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><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>
可见 **次方计算优先级要高！
35、max函数
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-radius: 0px; word-wrap: normal; background: transparent;"> ll=[<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;">6</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;">89</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</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;">2</span>] <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> max(ll) l2=<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[3,4,6,2,89,9,3,2],[3,6,7,8,983,3,5,6]]</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> max(l2[<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> max(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><li style="box-sizing: border-box; padding: 0px 5px;">5</li></ul><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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">89</span><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">89</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;">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;">8</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">983</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>]</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><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>
对于矩阵的最大值的求法，还不知道怎么搞。稍后更新一下。
36、mgrid函数
<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-radius: 0px; word-wrap: normal; background: transparent;"> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#开始值，结束值，步长。如果步长为虚数，表示产生的个数长度</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mgrid[-<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;">5</span>:<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>j] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#结果：[-5. 0. 5.]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mgrid[-<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;">5</span>:<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#结果：[-5 -2 1 4]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'*'</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*20</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mgrid[-<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;">5</span>:<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>j,-<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;">5</span>:<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>j] <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'*'</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*20</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> mgrid[-<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;">5</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;">5</span>:<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><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><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>
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-radius: 0px; word-wrap: normal; background: transparent;">[-<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;">0.</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;">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;">1</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>]********************<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[[-5. -5. -5.] [ 0. 0. 0.] [ 5. 5. 5.]]</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[-5. 0. 5.] [-5. 0. 5.] [-5. 0. 5.]]</span>] ******************** <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[[-5 -5 -5 -5] [-2 -2 -2 -2] [ 1 1 1 1] [ 4 4 4 4]]</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[-5 -2 1 4] [-5 -2 1 4] [-5 -2 1 4] [-5 -2 1 4]]</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><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></ul><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></ul>
mgrid函数说明：开始值，结束值，步长。如果步长为虚数，表示产生的个数长度。
对照结果即可知道函数的功能。
37、ogrid函数
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-radius: 0px; word-wrap: normal; background: transparent;"> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> ogrid[-<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;">5</span>:<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>j] <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> ogrid[-<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;">5</span>:<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> ogrid[-<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;">5</span>:<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>j,-<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;">5</span>:<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>j] <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> ogrid[-<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;">5</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;">5</span>:<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><li style="box-sizing: border-box; padding: 0px 5px;">4</li></ul><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 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-radius: 0px; word-wrap: normal; background: transparent;">[-<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;">0.</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;">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;">1</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>][array([[-<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;">0.</span>], [ <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5.</span>]]), array([[-<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;">0.</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5.</span>]])][array([[-<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;">2</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;">4</span>]]), array([[-<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;">2</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;">4</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><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></ul><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></ul>
ogrid跟mgrid一样。不同的是，一个数矩阵，一个数组形式。第三个擦数如果是实数，说明是步长。如果是虚数，说明是个数。
ogrid[-5:5:3,-5:5:3]第一部分产生多行一列，第二部分产生一行多列。这与mgrid不同。
38、random函数
<code class="hljs rsl 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;"> print <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">random</span>.seed(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>) <span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#要每次产生随机数相同就要设置种子，相同种子数的Random对象，相同次数生成的随机数字是完全相同的</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><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>
<code class="hljs glsl 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="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#用于生成一个指定范围内的随机符点数</span> print random.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">uniform</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;">5</span>) <span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#结果：[ 0.40254497 -0.42350395 -0.67640645 -0.54075394 -0.99584028]</span> <span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#均匀分布</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><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>
<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-radius: 0px; word-wrap: normal; background: transparent;"> #用于生成一个<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>到<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>的随机符点数: <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> <= n < <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> random.random() <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> random.random(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> random.rand(<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;">2</span>行<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>列结果： None<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.417022004703</span>[ <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7.20324493e-01</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.14374817e-04</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.02332573e-01</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.46755891e-01</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9.23385948e-02</span>]<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 0.18626021 0.34556073 0.39676747] [ 0.53881673 0.41919451 0.6852195 ]]</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><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></ul><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></ul>
<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-radius: 0px; word-wrap: normal; background: transparent;"> #用于生成一个指定范围内的整数。其中参数a是下限，参数b是上限，生成的随机数n: a <= n <= b <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> random.randint(<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;">10</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> random.randint(<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;">10</span>,size=(<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;">5</span>))结果： None<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[9 5 6 8 5] [5 6 9 9 6] [7 9 7 9 8] [9 7 9 7 9] [6 6 5 6 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><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></ul><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></ul>
更多关于random的函数的解析，请参看这篇文章：http://blog.csdn.net/pipisorry/article/details/39086463
39、tofile、fromfile
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-radius: 0px; word-wrap: normal; background: transparent;"> a =arange(<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;">12</span>) a.shape = <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-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a a.tofile(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"a.bin"</span>) b = fromfile(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"a.bin"</span>, dtype=float) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 按照float类型读入数据</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> b <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 读入的数据是错误的</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a.dtype <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 查看a的dtype</span> b = fromfile(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"a.bin"</span>, dtype=int32) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 按照int32类型读入数据</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> b <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 数据是一维的</span> b.shape = <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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 按照a的shape修改b的shape</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> b</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></ul><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></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-radius: 0px; word-wrap: normal; background: transparent;">None<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]]</span>[ <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.12199579e-314</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6.36598737e-314</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.06099790e-313</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.48539705e-313</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.90979621e-313</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.33419537e-313</span>]int32[ <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;">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-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;">8</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</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;">11</span>]<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]]</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><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></ul><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></ul>
使用数组的方法函数tofile可以方便地将数组中数据以二进制的格式写进文件。tofile输出的数据没有格式，因此用numpy.fromfile读回来的时候需要自己格式化数据。
Note:
1. 读入的时候设置正确的dtype和shape才能保证数据一致。
并且tofile函数不管数组的排列顺序是C语言格式的还是Fortran语言格式的，统一使用C语言格式输出。
2. sep关键字参数:此外如果fromfile和tofile函数调用时指定了sep关键字参数的话，
数组将以文本格式输入输出。{这样就可以通过notepad++打开查看, 不过数据是一行显示，不便于查看}
user_item_mat.tofile(user_item_mat_filename, sep=’ ‘)
40、numpy.load和numpy.save
例子：
<code class="hljs livecodeserver 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="hljs-operator" style="box-sizing: border-box;">a</span> =arange(<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;">12</span>) <span class="hljs-operator" style="box-sizing: border-box;">a</span>.shape = <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> print <span class="hljs-operator" style="box-sizing: border-box;">a</span> save(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'a.npy'</span>,<span class="hljs-operator" style="box-sizing: border-box;">a</span>) c=<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">load</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'a.npy'</span>) print c</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><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-radius: 0px; word-wrap: normal; background: transparent;">None<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]]</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]]</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><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li></ul><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>
numpy.load和numpy.save函数（推荐在不需要查看保存数据的情况下使用）
以NumPy专用的二进制类型保存数据，这两个函数会自动处理元素类型和shape等信息，
使用它们读写数组就方便多了，但是numpy.save输出的文件很难和其它语言编写的程序读入。
Note:
1. 文件要保存为.npy文件类型，否则会出错
2. 保存为numpy专用二进制格式后，就不能用notepad++打开（乱码）看了，这是相对tofile内建函数不好的一点
numpy.savez函数
如果你想将多个数组保存到一个文件中的话，可以使用numpy.savez函数。savez函数的第一个参数是文件名，其后的参数都是需要保存的数组，也可以使用关键字参数为数组起一个名字，非关键字参数传递的数组会自动起名为arr_0, arr_1, …。savez函数输出的是一个压缩文件(扩展名为npz)，其中每个文件都是一个save函数保存的npy文件，文件名对应于数组名。load函数自动识别npz文件，并且返回一个类似于字典的对象，可以通过数组名作为关键字获取数组的内容：
如果你用解压软件打开result.npz文件的话，会发现其中有三个文件：arr_0.npy， arr_1.npy， sin_array.npy，其中分别保存着数组a, b, c的内容。
<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-radius: 0px; word-wrap: normal; background: transparent;"> a = array(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1,2,3],[4,5,6]]</span>) b = arange(<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;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.1</span>) c = sin(b) savez(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"result.npz"</span>, a, b, sin_array = c) r =<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">load</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"result.npz"</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> r[<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"arr_0"</span>] # 数组a <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> r[<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"arr_1"</span>] # 数组b <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">print</span> r[<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"sin_array"</span>] # 数组c</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></ul><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></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-radius: 0px; word-wrap: normal; background: transparent;">None<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[1 2 3] [4 5 6]]</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;">0.1</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.2</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.3</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.4</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.6</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.7</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.8</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.9</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;">0.09983342</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.19866933</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.29552021</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.38941834</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.47942554</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.56464247</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.64421769</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.71735609</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.78332691</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><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li></ul><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>
numpy.savetxt和numpy.loadtxt（推荐需要查看保存数据时使用）
Note:savetxt缺省按照’%.18e’格式保存数据， 可以修改保存格式为‘%.8f’(小数点后保留8位的浮点数)， ’%d’(整数)等等
总结：
载入txt文件：numpy.loadtxt()/numpy.savetxt()
智能导入文本/csv文件：numpy.genfromtxt()/numpy.recfromcsv()
高速，有效率但numpy特有的二进制格式：numpy.save()/numpy.load()
39、40部分来源：http://blog.csdn.net/pipisorry/article/details/39088003。详细内容请参看这个链接。
41、permutation函数
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-radius: 0px; word-wrap: normal; background: transparent;"> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#混淆位置。如果是多维数组，则混淆一维的。例如下面的arr.</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> random.permutation(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">10</span>) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> random.permutation([<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;">4</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">15</span>]) arr=arange(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span>).reshape((<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;">3</span>)) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> arr <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> random.permutation(arr)</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><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>
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-radius: 0px; word-wrap: normal; background: transparent;">None[<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;">9</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;">4</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;">3</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;">7</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</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;">12</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;">4</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">15</span>]<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">[[0 1 2] [3 4 5] [6 7 8]]</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><li style="box-sizing: border-box; padding: 0px 5px;">6</li></ul><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>
permutation混淆位置。如果是多维数组，则混淆一维的。例如下面的arr.
42、complex构造复数
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-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> complex(<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;">100</span>)<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#结果：100j</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><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>
43、norm求范数
例子：
<code class="hljs python 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="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">from</span> scipy.linalg.misc <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> norm<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> norm([<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</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;">10</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><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>
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-radius: 0px; word-wrap: normal; background: transparent;">14.1421356237</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><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>
默认情况下，求二范数。也就是各个元素的平方和再开平方。
当然，也可以求取其他范数。例如p范数、无穷范数等。
我这里import写的是scipy。其实numpy里面也有这个函数。详细的其他范数的求法请参考官网http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.linalg.norm.html内容的介绍。对于求二范数的结果，我这里介绍的就够用了。
待续。。。。！！
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