1.背景
計算機視覺/computer vision是一個火了N年的topic。持續化升溫的原因也非常簡單：在搜索/影像內容理解/醫學應用/地圖識別等等領域應用太多，大家都有一個願景『讓計算機能夠像人一樣去”看”一張圖片，甚至”讀懂”一張圖片』。
有幾個比較重要的計算機視覺任務，比如圖片的分類,物體識別，物體定位於檢測等等。而近年來的神經網絡/深度學習使得上述任務的準確度有了非常大的提升。加之最近做了幾個不大不小的計算機視覺上的項目，愛湊熱鬧的博主自然不打算放過此領域，也邊學邊做點筆記總結，寫點東西，寫的不正確的地方，歡迎大家提出和指正。
2.基礎知識
爲了簡單易讀易懂，這個課程筆記系列中絕大多數的代碼都使用Python完成。這裏稍微介紹一下python和Numpy/Scipy(python中的科學計算包)的一些基礎。
2.1 python基礎
python是一種長得像僞代碼，具備高可讀性的編程語言。
優點挺多：可讀性相當好，寫起來也簡單，所想立馬可以轉爲實現代碼，且社區即爲活躍，可用的package相當多；缺點：效率一般。
2.1.1 基本數據類型
最常用的有數值型(Numbers),布爾型(Booleans)和字符串(String)三種。
- 數值型(Numbers)
可進行簡單的運算，如下：
<code class="language-python 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;">x = <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> type(x) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "<type 'int'>"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "5"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x + <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;"># 加; prints "6"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x - <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;"># 減; prints "4"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x * <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;"># 乘; prints "10"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x ** <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;"># 冪; prints "25"</span> x += <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;">#自加</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "6"</span> x *= <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;">#自乘</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "12"</span> y = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.5</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> type(y) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "<type 'float'>"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> y, y + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>, y * <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>, y ** <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;"># Prints "2.5 3.5 5.0 6.25"</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>
PS：python中沒有x++ 和 x– 操作
- 布爾型(Booleans)
包含True False和常見的與或非操作
<code class="language-python 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;">t = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">True</span> f = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">False</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> type(t) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "<type 'bool'>"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> t <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">and</span> f <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 邏輯與; prints "False"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> t <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">or</span> f <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 邏輯或; prints "True"</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;">not</span> t <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 邏輯非; prints "False"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> t != f <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># XOR; prints "True" </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>
- 字符串型(String)
字符串可以用單引號/雙引號/三引號聲明
<code class="language-python 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;">hello = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'hello'</span> world = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"world"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> hello <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "hello"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> len(hello) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 字符串長度; prints "5"</span> hw = hello + <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">' '</span> + world <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 字符串連接</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> hw <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># prints "hello world"</span> hw2015 = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'%s %s %d'</span> % (hello, world, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2015</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 格式化字符串</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> hw2015 <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># prints "hello world 2015"</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>
字符串對象有很有有用的函數：
<code class="language-python 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;">s = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"hello"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> s.capitalize() <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 首字母大寫; prints "Hello"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> s.upper() <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 全大寫; prints "HELLO"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> s.rjust(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 以7爲長度右對齊，左邊補空格; prints " hello"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> s.center(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 居中補空格; prints " hello "</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> s.replace(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'l'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'(ell)'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 字串替換;prints "he(ell)(ell)o"</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;">' world '</span>.strip() <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 去首位空格; prints "world"</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>
2.1.2 基本容器
- 列表/List
和數組類似的一個東東，不過可以包含不同類型的元素，同時大小也是可以調整的。
<code class="language-python 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;">xs = [<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;">2</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 創建</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> xs, xs[<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;"># Prints "[3, 1, 2] 2"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> xs[-<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;"># 第-1個元素，即最後一個</span> xs[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>] = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'foo'</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 下標從0開始，這是第3個元素</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> xs <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 可以有不同類型，Prints "[3, 1, 'foo']"</span> xs.append(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'bar'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 尾部添加一個元素</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> xs <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints </span> x = xs.pop() <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 去掉尾部的元素</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x, xs <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "bar [3, 1, 'foo']"</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>
列表最常用的操作有：
切片/slicing
即取子序列/一部分元素，如下：
<code class="language-python 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;">nums = range(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 從1到5的序列</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> nums <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[0, 1, 2, 3, 4]"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> nums[<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;">4</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 下標從2到4-1的元素 prints "[2, 3]"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> nums[<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;"># 下標從2到結尾的元素</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> nums[:<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;"># 從開頭到下標爲2-1的元素 [0, 1]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> nums[:] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 恩，就是全取出來了</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> nums[:-<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;"># 從開始到第-1個元素(最後的元素)</span> nums[<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;">4</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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 對子序列賦值</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> nums <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[0, 1, 8, 8, 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>
循環/loops
即遍歷整個list，做一些操作，如下：
<code class="language-python 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;">animals = [<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'cat'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'dog'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'monkey'</span>]
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> animal <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> animals:
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> animal
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 依次輸出 "cat", "dog", "monkey"，每個一行.</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>
可以用enumerate取出元素的同時帶出下標
<code class="language-python 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;">animals = [<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'cat'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'dog'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'monkey'</span>]
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> idx, animal <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> enumerate(animals):
<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;">'#%d: %s'</span> % (idx + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>, animal)
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 輸出 "#1: cat", "#2: dog", "#3: monkey"，一個一行。</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>
List comprehension
這個相當相當相當有用，在很長的list生成過程中，效率完勝for循環：
<code class="language-python 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;"><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># for 循環</span>
nums = [<span class="hljs-number" style="color: 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>]
squares = []
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> x <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> nums:
squares.append(x ** <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> squares <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints [0, 1, 4, 9, 16]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># list comprehension</span>
nums = [<span class="hljs-number" style="color: 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>]
squares = [x ** <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;">for</span> x <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> nums]
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> squares <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints [0, 1, 4, 9, 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><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>
你猜怎麼着，list comprehension也是可以加多重條件的：
<code class="language-python 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;">nums = [<span class="hljs-number" style="color: 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>] even_squares = [x ** <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;">for</span> x <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> nums <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> x % <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-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> even_squares <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[0, 4, 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></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>
- 字典/Dict
和Java中的Map一樣的東東，用於存儲key-value對：
<code class="language-python 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;">d = {<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'cat'</span>: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'cute'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'dog'</span>: <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'furry'</span>} <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 創建</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> d[<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'cat'</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 根據key取出value</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;">'cat'</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> d <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 判斷是否有'cat'這個key</span>
d[<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'fish'</span>] = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'wet'</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 添加元素</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> d[<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'fish'</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "wet"</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># print d['monkey'] # KeyError: 'monkey'非本字典的key</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> d.get(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'monkey'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'N/A'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 有key返回value，無key返回"N/A"</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> d.get(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'fish'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'N/A'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># prints "wet"</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">del</span> d[<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'fish'</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 刪除某個key以及對應的value</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> d.get(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'fish'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'N/A'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># prints "N/A"</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></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>
對應list的那些操作，你在dict裏面也能找得到：
循環/loops
<code class="language-python 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;"><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># for循環</span>
d = {<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'person'</span>: <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'cat'</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;">'spider'</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;">for</span> animal <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> d:
legs = d[animal]
<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;">'A %s has %d legs'</span> % (animal, legs)
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "A person has 2 legs", "A spider has 8 legs", "A cat has 4 legs"</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 通過iteritems</span>
d = {<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'person'</span>: <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'cat'</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;">'spider'</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;">for</span> animal, legs <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> d.iteritems():
<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;">'A %s has %d legs'</span> % (animal, legs)
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "A person has 2 legs", "A spider has 8 legs", "A cat has 4 legs"</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><code class="language-python 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;"><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Dictionary comprehension</span>
nums = [<span class="hljs-number" style="color: 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>]
even_num_to_square = {x: x ** <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;">for</span> x <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> nums <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> x % <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-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> even_num_to_square <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "{0: 0, 2: 4, 4: 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></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>
- 元組/turple
本質上說，還是一個list，只不過裏面的每個元素都是一個兩元組對。
<code class="language-python 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;">d = {(x, x + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>): x <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> x <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;">10</span>)} <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 創建</span>
t = (<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;"># Create a tuple</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> type(t) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "<type 'tuple'>"</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> d[t] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "5"</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> d[(<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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "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><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>
2.1.3 函數
用def可以定義一個函數：
<code class="language-python 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;"><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> <span class="hljs-title" style="box-sizing: border-box;">sign</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(x)</span>:</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> x > <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>:
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'positive'</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">elif</span> x < <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>:
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'negative'</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>:
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'zero'</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> x <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</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;">1</span>]:
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> sign(x)
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "negative", "zero", "positive"</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="language-python 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;"><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> <span class="hljs-title" style="box-sizing: border-box;">hello</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(name, loud=False)</span>:</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> loud:
<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;">'HELLO, %s'</span> % name.upper()
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</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;">'Hello, %s!'</span> % name
hello(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'Bob'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "Hello, Bob"</span>
hello(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'Fred'</span>, loud=<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;"># Prints "HELLO, FRED!"</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>
- 類/Class
python裏面的類定義非常的直接和簡潔：
<code class="language-python 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;"><span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">class</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Greeter</span>:</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Constructor</span>
<span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> <span class="hljs-title" style="box-sizing: border-box;">__init__</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(self, name)</span>:</span>
self.name = name <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Create an instance variable</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Instance method</span>
<span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> <span class="hljs-title" style="box-sizing: border-box;">greet</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(self, loud=False)</span>:</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> loud:
<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;">'HELLO, %s!'</span> % self.name.upper()
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</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;">'Hello, %s'</span> % self.name
g = Greeter(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'Fred'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Construct an instance of the Greeter class</span>
g.greet() <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Call an instance method; prints "Hello, Fred"</span>
g.greet(loud=<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;"># Call an instance method; prints "HELLO, FRED!"</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>
2.2.NumPy基礎
NumPy是Python的科學計算的一個核心庫。它提供了一個高性能的多維數組(矩陣)對象，可以完成在其之上的很多操作。很多機器學習中的計算問題，把數據vectorize之後可以進行非常高效的運算。
2.2.1 數組
一個NumPy數組是一些類型相同的元素組成的類矩陣數據。用list或者層疊的list可以初始化：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np a = np.array([<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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 一維Numpy數組</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> type(a) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "<type 'numpy.ndarray'>"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a.shape <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "(3,)"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>], a[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>], a[<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;"># Prints "1 2 3"</span> a[<span class="hljs-number" style="color: 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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 重賦值</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[5, 2, 3]"</span> b = np.array([[<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;"># 二維Numpy數組</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> b.shape <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "(2, 3)"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> b[<span class="hljs-number" style="color: 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>], b[<span class="hljs-number" style="color: 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>], 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;">0</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "1 2 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></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>
生成一些特殊的Numpy數組(矩陣)時，我們有特定的函數可以調用：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np
a = np.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;">2</span>)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 全0的2*2 Numpy數組</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[ 0. 0.]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 0. 0.]]"</span>
b = np.ones((<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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 全1 Numpy數組</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;"># Prints "[[ 1. 1.]]"</span>
c = np.full((<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</span>), <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 固定值Numpy數組</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> c <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[ 7. 7.]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 7. 7.]]"</span>
d = np.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;"># 2*2 對角Numpy數組</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> d <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[ 1. 0.]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 0. 1.]]"</span>
e = np.random.random((<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</span>)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 2*2 的隨機Numpy數組</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> e <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 隨機輸出</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></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></ul>
2.2.2 Numpy數組索引與取值
可以通過像list一樣的分片/slicing操作取出需要的數值部分。
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 創建如下的3*4 Numpy數組</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[ 1 2 3 4]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 5 6 7 8]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 9 10 11 12]]</span> a = np.array([[<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-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>]]) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 通過slicing取出前兩行的2到3列:</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[2 3]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [6 7]]</span> b = a[:<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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 需要注意的是取出的b中的數據實際上和a的這部分數據是同一份數據.</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a[<span class="hljs-number" style="color: 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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "2"</span> b[<span class="hljs-number" style="color: 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;">77</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># b[0, 0] 和 a[0, 1] 是同一份數據</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a[<span class="hljs-number" style="color: 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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># a也被修改了，Prints "77"</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></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></ul>
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np
a = np.array([[<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-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>]])
row_r1 = a[<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;"># a 的第二行 </span>
row_r2 = a[<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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 同上</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> row_r1, row_r1.shape <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[5 6 7 8] (4,)"</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> row_r2, row_r2.shape <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[5 6 7 8]] (1, 4)"</span>
col_r1 = a[:, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]
col_r2 = a[:, <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-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> col_r1, col_r1.shape <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[ 2 6 10] (3,)"</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> col_r2, col_r2.shape <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[ 2]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 6]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [10]] (3, 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><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></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></ul>
還可以這麼着取：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np a = np.array([[<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;"># 取出(0,0) (1,1) (2,0)三個位置的值</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a[[<span class="hljs-number" style="color: 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;">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;">0</span>]] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[1 4 5]"</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 和上面一樣</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.array([a[<span class="hljs-number" style="color: 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>], a[<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>], a[<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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[1 4 5]"</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 取出(0,1) (0,1) 兩個位置的值</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a[[<span class="hljs-number" style="color: 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;">1</span>]] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[2 2]"</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 同上</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.array([a[<span class="hljs-number" style="color: 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>], a[<span class="hljs-number" style="color: 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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[2 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><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></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></ul>
我們還可以通過條件得到bool型的Numpy數組結果，再通過這個數組取出符合條件的值，如下：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np
a = np.array([[<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>]])
bool_idx = (a > <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;"># 判定a大於2的結果矩陣</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> bool_idx <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[False False]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ True True]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ True True]]"</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 再通過bool_idx取出我們要的值</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a[bool_idx] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[3 4 5 6]"</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 放在一起我們可以這麼寫</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> a[a > <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;"># Prints "[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><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></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></ul>
Numpy數組的類型
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np x = np.array([<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-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x.dtype <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "int64"</span> x = np.array([<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;">2.0</span>]) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x.dtype <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "float64"</span> x = np.array([<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>], dtype=np.int64) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 強制使用某個type</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x.dtype <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "int64"</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></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>
2.2.3 Numpy數組的運算
矩陣的加減開方和(元素對元素)乘除如下：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np x = np.array([[<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>]], dtype=np.float64) y = np.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;">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>]], dtype=np.float64) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[ 6.0 8.0]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [10.0 12.0]]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x + y <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.add(x, y) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[-4.0 -4.0]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [-4.0 -4.0]]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x - y <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.subtract(x, y) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 元素對元素，點對點的乘積</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[ 5.0 12.0]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [21.0 32.0]]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x * y <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.multiply(x, y) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 元素對元素，點對點的除法</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[ 0.2 0.33333333]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 0.42857143 0.5 ]]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x / y <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.divide(x, y) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 開方</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[ 1. 1.41421356]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 1.73205081 2. ]]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.sqrt(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><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li></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><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li></ul>
矩陣的內積是通過下列方法計算的：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np x = np.array([[<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>]]) y = np.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;">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>]]) v = np.array([<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>]) w = np.array([<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">11</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>]) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 向量內積，得到 219</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> v.dot(w) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.dot(v, w) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 矩陣乘法，得到 [29 67]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x.dot(v) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.dot(x, v) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 矩陣乘法</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[19 22]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [43 50]]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x.dot(y) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.dot(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><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li></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><li style="box-sizing: border-box; padding: 0px 5px;">21</li></ul>
特別特別有用的一個操作是，sum/求和(對某個維度)：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np x = np.array([[<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> np.sum(x) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 整個矩陣的和，得到 "10"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.sum(x, axis=<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;"># 每一列的和 得到 "[4 6]"</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.sum(x, axis=<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;"># 每一行的和 得到 "[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><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>
還有一個經常會用到操作是矩陣的轉置，在Numpy數組裏用.T實現：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np
x = np.array([[<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> x <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[1 2]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [3 4]]"</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x.T <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[1 3]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [2 4]]"</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 1*n的Numpy數組，用.T之後其實啥也沒做:</span>
v = np.array([<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-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> v <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[1 2 3]"</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> v.T <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[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>
2.2.4 Broadcasting
Numpy還有一個非常牛逼的機制，你想想，如果你現在有一大一小倆矩陣，你想使用小矩陣在大矩陣上做多次操作。額，舉個例子好了，假如你想將一個1*n的矩陣，加到m*n的矩陣的每一行上：
<code class="language-python 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;"><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#你如果要用for循環實現是醬紫的(下面用y的原因是，你不想改變原來的x)</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np
x = np.array([[<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-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>]])
v = np.array([<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;">1</span>])
y = np.empty_like(x) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 設置一個和x一樣維度的Numpy數組y</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 逐行相加</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;">4</span>):
y[i, :] = x[i, :] + v
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 恩，y就是你想要的了</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[ 2 2 4]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 5 5 7]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 8 8 10]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [11 11 13]]</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> 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><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></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></ul><code class="language-python 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;"><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#上一種方法如果for的次數非常多，會很慢，於是我們改進了一下</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np
x = np.array([[<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-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>]])
v = np.array([<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;">1</span>])
vv = np.tile(v, (<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;">1</span>)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 變形，重複然後疊起來</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> vv <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[1 0 1]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [1 0 1]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [1 0 1]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [1 0 1]]"</span>
y = x + vv <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 相加</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> y <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[ 2 2 4</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 5 5 7]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 8 8 10]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [11 11 13]]"</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></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></ul><code class="language-python 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;"><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#其實因爲Numpy的Broadcasting，你可以直接醬紫操作</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np
x = np.array([[<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-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>]])
v = np.array([<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;">1</span>])
y = x + v <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 直接加！！！</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> y <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># Prints "[[ 2 2 4]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 5 5 7]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 8 8 10]</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [11 11 13]]"</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></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>
更多Broadcasting的例子請看下面：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np v = np.array([<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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># v has shape (3,)</span> w = np.array([<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-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># w has shape (2,)</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 首先把v變成一個列向量</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># v現在的形狀是(3, 1);</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 作用在w上得到的結果形狀是(3, 2)，如下</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[ 4 5]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 8 10]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [12 15]]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> np.reshape(v, (<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>)) * w <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 逐行相加</span> x = np.array([[<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;"># 得到如下結果:</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[2 4 6]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [5 7 9]]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x + v <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 先逐行相加再轉置，得到以下結果:</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[ 5 6 7]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 9 10 11]]</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> (x.T + w).T <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 恩，也可以這麼做</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x + np.reshape(w, (<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>))</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li></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><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li></ul>
2.3 SciPy
Numpy提供了一個非常方便操作和計算的高維向量對象，並提供基本的操作方法，而Scipy是在Numpy的基礎上，提供很多很多的函數和方法去直接完成你需要的矩陣操作。有興趣可以瀏覽Scipy方法索引查看具體的方法，函數略多，要都記下來有點困難，隨用隨查吧。
向量距離計算
需要特別拎出來說一下的是，向量之間的距離計算，這個Scipy提供了很好的接口scipy.spatial.distance.pdist：
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">from</span> scipy.spatial.distance <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> pdist, squareform <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[0 1]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [1 0]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [2 0]]</span> x = np.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;">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;">0</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-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> x <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 計算矩陣每一行和每一行之間的歐氏距離</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># d[i, j] 是 x[i, :] 和 x[j, :] 之間的距離,</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 結果如下：</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [[ 0. 1.41421356 2.23606798]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 1.41421356 0. 1. ]</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># [ 2.23606798 1. 0. ]]</span> d = squareform(pdist(x, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'euclidean'</span>)) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">print</span> d</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></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></ul>
2.4 Matplotlib
這是python中的一個作圖工具包。如果你熟悉matlab的語法的話，應該會用得挺順手。可以通過matplotlib.pyplot.plot瞭解更多繪圖相關的設置和參數。
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> matplotlib.pyplot <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> plt <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 計算x和對應的sin值作爲y</span> x = np.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;">3</span> * np.pi, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.1</span>) y = np.sin(x) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 用matplotlib繪出點的變化曲線</span> plt.plot(x, y) plt.show() <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 只有調用plt.show()之後才能顯示</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></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>
結果如下：
<code class="language-python 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;"><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 在一個圖中畫出2條曲線</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> matplotlib.pyplot <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> plt <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 計算x對應的sin和cos值</span> x = np.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;">3</span> * np.pi, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.1</span>) y_sin = np.sin(x) y_cos = np.cos(x) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 用matplotlib作圖</span> plt.plot(x, y_sin) plt.plot(x, y_cos) plt.xlabel(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'x axis label'</span>) plt.ylabel(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'y axis label'</span>) plt.title(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'Sine and Cosine'</span>) plt.legend([<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'Sine'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'Cosine'</span>]) plt.show()</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></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></ul>
<code class="language-python 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;"><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 用subplot分到子圖裏</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> matplotlib.pyplot <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> plt <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 得到x對應的sin和cos值</span> x = np.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;">3</span> * np.pi, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.1</span>) y_sin = np.sin(x) y_cos = np.cos(x) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 2*1個子圖，第一個位置.</span> plt.subplot(<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;">1</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 畫第一個子圖</span> plt.plot(x, y_sin) plt.title(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'Sine'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 畫第2個子圖</span> plt.subplot(<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>) plt.plot(x, y_cos) plt.title(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'Cosine'</span>) plt.show()</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li></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><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li></ul>
2.5 簡單圖片讀寫
可以使用imshow來顯示圖片。
<code class="language-python 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;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> np <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">from</span> scipy.misc <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> imread, imresize <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> matplotlib.pyplot <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">as</span> plt img = imread(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'/Users/HanXiaoyang/Comuter_vision/computer_vision.jpg'</span>) img_tinted = img * [<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;">0.95</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.9</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 顯示原始圖片</span> plt.subplot(<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>) plt.imshow(img) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 顯示調色後的圖片</span> plt.subplot(<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;">2</span>) plt.imshow(np.uint8(img_tinted)) plt.show()</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>
參考資料與原文
作者：寒小陽
時間：2015年11月。
出處：http://blog.csdn.net/han_xiaoyang/article/details/49876119
聲明：版權所有，轉載請註明出處，謝謝。