用 NumPy 在 Python 中处理数字
NumPy（即 Numerical Python）是一个库，它使得在 Python 中对线性数列和矩阵进行统计和集合操作变得容易。我在 Python 数据类型的笔记中介绍过，它比 Python 的列表快几个数量级。NumPy 在数据分析和科学计算中使用得相当频繁。
我将介绍安装 NumPy，然后创建、读取和排序 NumPy 数组。NumPy 数组也被称为 ndarray，即 N 维数组的缩写。
安装 NumPy
使用 pip 安装 NumPy 包非常简单，可以像安装其他软件包一样进行安装：
<ol ><li ><code><span >pip install numpy</span></code></li></ol>
安装了 NumPy 包后，只需将其导入你的 Python 文件中：
<ol ><li ><code><span >import</span><span > numpy </span><span >as</span><span > np</span></code></li></ol>
将 numpy 以 np 之名导入是一个标准的惯例，但你可以不使用 np，而是使用你想要的任何其他别名。
为什么使用 NumPy? 因为它比 Python 列表要快好几个数量级
当涉及到处理大量的数值时，NumPy 比普通的 Python 列表快几个数量级。为了看看它到底有多快，我首先测量在普通 Python 列表上进行 min() 和 max() 操作的时间。
我将首先创建一个具有 999,999,999 项的 Python 列表：
<ol ><li ><code><span >>>></span><span > my_list </span><span >=</span><span > range</span><span >(</span><span >1</span><span >,</span><span > </span><span >1000000000</span><span >)</span></code></li><li ><code><span >>>></span><span > len</span><span >(</span><span >my_list</span><span >)</span></code></li><li ><code><span >999999999</span></code></li></ol>
现在我将测量在这个列表中找到最小值的时间：
<ol ><li ><code><span >>>></span><span > start </span><span >=</span><span > </span><span >time</span><span >.</span><span >time</span><span >()</span></code></li><li ><code><span >>>></span><span > min</span><span >(</span><span >my_list</span><span >)</span></code></li><li ><code><span >1</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >'Time elapsed in milliseconds: '</span><span > </span><span >+</span><span > str</span><span >((</span><span >time</span><span >.</span><span >time</span><span >()</span><span > </span><span >-</span><span > start</span><span >)</span><span > </span><span >*</span><span > </span><span >1000</span><span >))</span></code></li><li ><code><span >Time</span><span > elapsed </span><span >in</span><span > milliseconds</span><span >:</span><span > </span><span >27007.00879096985</span></code></li></ol>
这花了大约 27,007 毫秒，也就是大约 27 秒。这是个很长的时间。现在我试着找出寻找最大值的时间：
<ol ><li ><code><span >>>></span><span > start </span><span >=</span><span > </span><span >time</span><span >.</span><span >time</span><span >()</span></code></li><li ><code><span >>>></span><span > max</span><span >(</span><span >my_list</span><span >)</span></code></li><li ><code><span >999999999</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >'Time elapsed in milliseconds: '</span><span > </span><span >+</span><span > str</span><span >((</span><span >time</span><span >.</span><span >time</span><span >()</span><span > </span><span >-</span><span > start</span><span >)</span><span > </span><span >*</span><span > </span><span >1000</span><span >))</span></code></li><li ><code><span >Time</span><span > elapsed </span><span >in</span><span > milliseconds</span><span >:</span><span > </span><span >28111.071348190308</span></code></li></ol>
这花了大约 28,111 毫秒，也就是大约 28 秒。
现在我试试用 NumPy 找到最小值和最大值的时间：
<ol ><li ><code><span >>>></span><span > my_list </span><span >=</span><span > np</span><span >.</span><span >arange</span><span >(</span><span >1</span><span >,</span><span > </span><span >1000000000</span><span >)</span></code></li><li ><code><span >>>></span><span > len</span><span >(</span><span >my_list</span><span >)</span></code></li><li ><code><span >999999999</span></code></li><li ><code><span >>>></span><span > start </span><span >=</span><span > </span><span >time</span><span >.</span><span >time</span><span >()</span></code></li><li ><code><span >>>></span><span > my_list</span><span >.</span><span >min</span><span >()</span></code></li><li ><code><span >1</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >'Time elapsed in milliseconds: '</span><span > </span><span >+</span><span > str</span><span >((</span><span >time</span><span >.</span><span >time</span><span >()</span><span > </span><span >-</span><span > start</span><span >)</span><span > </span><span >*</span><span > </span><span >1000</span><span >))</span></code></li><li ><code><span >Time</span><span > elapsed </span><span >in</span><span > milliseconds</span><span >:</span><span > </span><span >1151.1778831481934</span></code></li><li ><code><span >>>></span></code></li><li ><code><span >>>></span><span > start </span><span >=</span><span > </span><span >time</span><span >.</span><span >time</span><span >()</span></code></li><li ><code><span >>>></span><span > my_list</span><span >.</span><span >max</span><span >()</span></code></li><li ><code><span >999999999</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >'Time elapsed in milliseconds: '</span><span > </span><span >+</span><span > str</span><span >((</span><span >time</span><span >.</span><span >time</span><span >()</span><span > </span><span >-</span><span > start</span><span >)</span><span > </span><span >*</span><span > </span><span >1000</span><span >))</span></code></li><li ><code><span >Time</span><span > elapsed </span><span >in</span><span > milliseconds</span><span >:</span><span > </span><span >1114.8970127105713</span></code></li></ol>
找到最小值花了大约 1151 毫秒，找到最大值 1114 毫秒。这大约是 1 秒。
正如你所看到的，使用 NumPy 可以将寻找一个大约有 10 亿个值的列表的最小值和最大值的时间 从大约 28 秒减少到 1 秒。这就是 NumPy 的强大之处。
使用 Python 列表创建 ndarray
有几种方法可以在 NumPy 中创建 ndarray。
你可以通过使用元素列表来创建一个 ndarray：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([</span><span >1</span><span >,</span><span > </span><span >2</span><span >,</span><span > </span><span >3</span><span >,</span><span > </span><span >4</span><span >,</span><span > </span><span >5</span><span >])</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[</span><span >1</span><span > </span><span >2</span><span > </span><span >3</span><span > </span><span >4</span><span > </span><span >5</span><span >]</span></code></li></ol>
有了上面的 ndarray 定义，我将检查几件事。首先，上面定义的变量的类型是 numpy.ndarray。这是所有 NumPy ndarray 的类型：
<ol ><li ><code><span >>>></span><span > type</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span ><</span><span >class</span><span > </span><span >'numpy.ndarray'</span><span >></span></code></li></ol>
这里要注意的另一件事是 “形状”。ndarray 的形状是 ndarray 的每个维度的长度。你可以看到，my_ndarray 的形状是 (5,)。这意味着 my_ndarray 包含一个有 5 个元素的维度（轴）。
<ol ><li ><code><span >>>></span><span > np</span><span >.</span><span >shape</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >(</span><span >5</span><span >,)</span></code></li></ol>
数组中的维数被称为它的 “秩”。所以上面的 ndarray 的秩是 1。
我将定义另一个 ndarray my_ndarray2 作为一个多维 ndarray。那么它的形状会是什么呢？请看下面：
<ol ><li ><code><span >>>></span><span > my_ndarray2 </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([(</span><span >1</span><span >,</span><span > </span><span >2</span><span >,</span><span > </span><span >3</span><span >),</span><span > </span><span >(</span><span >4</span><span >,</span><span > </span><span >5</span><span >,</span><span > </span><span >6</span><span >)])</span></code></li><li ><code><span >>>></span><span > np</span><span >.</span><span >shape</span><span >(</span><span >my_ndarray2</span><span >)</span></code></li><li ><code><span >(</span><span >2</span><span >,</span><span > </span><span >3</span><span >)</span></code></li></ol>
这是一个秩为 2 的 ndarray。另一个要检查的属性是 dtype，也就是数据类型。检查我们的 ndarray 的 dtype 可以得到以下结果：
<ol ><li ><code><span >>>></span><span > my_ndarray</span><span >.</span><span >dtype</span></code></li><li ><code><span >dtype</span><span >(</span><span >'int64'</span><span >)</span></code></li></ol>
int64 意味着我们的 ndarray 是由 64 位整数组成的。NumPy 不能创建混合类型的 ndarray，必须只包含一种类型的元素。如果你定义了一个包含混合元素类型的 ndarray，NumPy 会自动将所有的元素类型转换为可以包含所有元素的最高元素类型。
例如，创建一个 int 和 float 的混合序列将创建一个 float64 的 ndarray：
<ol ><li ><code><span >>>></span><span > my_ndarray2 </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([</span><span >1</span><span >,</span><span > </span><span >2.0</span><span >,</span><span > </span><span >3</span><span >])</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2</span><span >)</span></code></li><li ><code><span >[</span><span >1.</span><span > </span><span >2.</span><span > </span><span >3.</span><span >]</span></code></li><li ><code><span >>>></span><span > my_ndarray2</span><span >.</span><span >dtype</span></code></li><li ><code><span >dtype</span><span >(</span><span >'float64'</span><span >)</span></code></li></ol>
另外，将其中一个元素设置为 string 将创建 dtype 等于
<ol ><li ><code><span >>>></span><span > my_ndarray2 </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([</span><span >1</span><span >,</span><span > </span><span >'2'</span><span >,</span><span > </span><span >3</span><span >])</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2</span><span >)</span></code></li><li ><code><span >[</span><span >'1'</span><span > </span><span >'2'</span><span > </span><span >'3'</span><span >]</span></code></li><li ><code><span >>>></span><span > my_ndarray2</span><span >.</span><span >dtype</span></code></li><li ><code><span >dtype</span><span >(</span><span >'<U21'</span><span >)</span></code></li></ol>
size 属性将显示我们的 ndarray 中存在的元素总数：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([</span><span >1</span><span >,</span><span > </span><span >2</span><span >,</span><span > </span><span >3</span><span >,</span><span > </span><span >4</span><span >,</span><span > </span><span >5</span><span >])</span></code></li><li ><code><span >>>></span><span > my_ndarray</span><span >.</span><span >size</span></code></li><li ><code><span >5</span></code></li></ol>
使用 NumPy 方法创建 ndarray
如果你不想直接使用列表来创建 ndarray，还有几种可以用来创建它的 NumPy 方法。
你可以使用 np.zeros() 来创建一个填满 0 的 ndarray。它需要一个“形状”作为参数，这是一个包含行数和列数的列表。它还可以接受一个可选的 dtype 参数，这是 ndarray 的数据类型：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >zeros</span><span >([</span><span >2</span><span >,</span><span >3</span><span >],</span><span > dtype</span><span >=</span><span >int</span><span >)</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[[</span><span >0</span><span > </span><span >0</span><span > </span><span >0</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span >0</span><span > </span><span >0</span><span > </span><span >0</span><span >]]</span></code></li></ol>
你可以使用 np. ones() 来创建一个填满 1 的 ndarray：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >ones</span><span >([</span><span >2</span><span >,</span><span >3</span><span >],</span><span > dtype</span><span >=</span><span >int</span><span >)</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[[</span><span >1</span><span > </span><span >1</span><span > </span><span >1</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span >1</span><span > </span><span >1</span><span > </span><span >1</span><span >]]</span></code></li></ol>
你可以使用 np.full() 来给 ndarray 填充一个特定的值：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >full</span><span >([</span><span >2</span><span >,</span><span >3</span><span >],</span><span > </span><span >10</span><span >,</span><span > dtype</span><span >=</span><span >int</span><span >)</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[[</span><span >10</span><span > </span><span >10</span><span > </span><span >10</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span >10</span><span > </span><span >10</span><span > </span><span >10</span><span >]]</span></code></li></ol>
你可以使用 np.eye() 来创建一个单位矩阵 / ndarray，这是一个沿主对角线都是 1 的正方形矩阵。正方形矩阵是一个行数和列数相同的矩阵：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >eye</span><span >(</span><span >3</span><span >,</span><span > dtype</span><span >=</span><span >int</span><span >)</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[[</span><span >1</span><span > </span><span >0</span><span > </span><span >0</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span >0</span><span > </span><span >1</span><span > </span><span >0</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span >0</span><span > </span><span >0</span><span > </span><span >1</span><span >]]</span></code></li></ol>
你可以使用 np.diag() 来创建一个沿对角线有指定数值的矩阵，而在矩阵的其他部分为 0：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >diag</span><span >([</span><span >10</span><span >,</span><span > </span><span >20</span><span >,</span><span > </span><span >30</span><span >,</span><span > </span><span >40</span><span >,</span><span > </span><span >50</span><span >])</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[[</span><span >10</span><span ></span><span >0</span><span ></span><span >0</span><span ></span><span >0</span><span ></span><span >0</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span > </span><span >0</span><span > </span><span >20</span><span ></span><span >0</span><span ></span><span >0</span><span ></span><span >0</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span > </span><span >0</span><span ></span><span >0</span><span > </span><span >30</span><span ></span><span >0</span><span ></span><span >0</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span > </span><span >0</span><span ></span><span >0</span><span ></span><span >0</span><span > </span><span >40</span><span ></span><span >0</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span > </span><span >0</span><span ></span><span >0</span><span ></span><span >0</span><span ></span><span >0</span><span > </span><span >50</span><span >]]</span></code></li></ol>
你可以使用 np.range() 来创建一个具有特定数值范围的 ndarray。它是通过指定一个整数的开始和结束（不包括）范围以及一个步长来创建的：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >arange</span><span >(</span><span >1</span><span >,</span><span > </span><span >20</span><span >,</span><span > </span><span >3</span><span >)</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[</span><span > </span><span >1</span><span ></span><span >4</span><span ></span><span >7</span><span > </span><span >10</span><span > </span><span >13</span><span > </span><span >16</span><span > </span><span >19</span><span >]</span></code></li></ol>
读取 ndarray
ndarray 的值可以使用索引、分片或布尔索引来读取。
使用索引读取 ndarray 的值
在索引中，你可以使用 ndarray 的元素的整数索引来读取数值，就像你读取 Python 列表一样。就像 Python 列表一样，索引从 0 开始。
例如，在定义如下的 ndarray 中：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >arange</span><span >(</span><span >1</span><span >,</span><span > </span><span >20</span><span >,</span><span > </span><span >3</span><span >)</span></code></li></ol>
第四个值将是 my_ndarray[3]，即 10。最后一个值是 my_ndarray[-1]，即 19：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >arange</span><span >(</span><span >1</span><span >,</span><span > </span><span >20</span><span >,</span><span > </span><span >3</span><span >)</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[</span><span >0</span><span >])</span></code></li><li ><code><span >1</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[</span><span >3</span><span >])</span></code></li><li ><code><span >10</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[-</span><span >1</span><span >])</span></code></li><li ><code><span >19</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[</span><span >5</span><span >])</span></code></li><li ><code><span >16</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[</span><span >6</span><span >])</span></code></li><li ><code><span >19</span></code></li></ol>
使用分片读取 ndarray
你也可以使用分片来读取 ndarray 的块。分片的工作方式是用冒号（:）操作符指定一个开始索引和一个结束索引。然后，Python 将获取该开始和结束索引之间的 ndarray 片断：
<ol ><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[:])</span></code></li><li ><code><span >[</span><span > </span><span >1</span><span ></span><span >4</span><span ></span><span >7</span><span > </span><span >10</span><span > </span><span >13</span><span > </span><span >16</span><span > </span><span >19</span><span >]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[</span><span >2</span><span >:</span><span >4</span><span >])</span></code></li><li ><code><span >[</span><span > </span><span >7</span><span > </span><span >10</span><span >]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[</span><span >5</span><span >:</span><span >6</span><span >])</span></code></li><li ><code><span >[</span><span >16</span><span >]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[</span><span >6</span><span >:</span><span >7</span><span >])</span></code></li><li ><code><span >[</span><span >19</span><span >]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[:-</span><span >1</span><span >])</span></code></li><li ><code><span >[</span><span > </span><span >1</span><span ></span><span >4</span><span ></span><span >7</span><span > </span><span >10</span><span > </span><span >13</span><span > </span><span >16</span><span >]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >[-</span><span >1</span><span >:])</span></code></li><li ><code><span >[</span><span >19</span><span >]</span></code></li></ol>
分片创建了一个 ndarray 的引用（或视图）。这意味着，修改分片中的值也会改变原始 ndarray 的值。
比如说：
<ol ><li ><code><span >>>></span><span > my_ndarray</span><span >[-</span><span >1</span><span >:]</span><span > </span><span >=</span><span > </span><span >100</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[</span><span ></span><span >1</span><span > </span><span >4</span><span > </span><span >7</span><span ></span><span >10</span><span ></span><span >13</span><span ></span><span >16</span><span > </span><span >100</span><span >]</span></code></li></ol>
对于秩超过 1 的 ndarray 的分片，可以使用 [行开始索引:行结束索引, 列开始索引:列结束索引] 语法：
<ol ><li ><code><span >>>></span><span > my_ndarray2 </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([(</span><span >1</span><span >,</span><span > </span><span >2</span><span >,</span><span > </span><span >3</span><span >),</span><span > </span><span >(</span><span >4</span><span >,</span><span > </span><span >5</span><span >,</span><span > </span><span >6</span><span >)])</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2</span><span >)</span></code></li><li ><code><span >[[</span><span >1</span><span > </span><span >2</span><span > </span><span >3</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span >4</span><span > </span><span >5</span><span > </span><span >6</span><span >]]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2</span><span >[</span><span >0</span><span >:</span><span >2</span><span >,</span><span >1</span><span >:</span><span >3</span><span >])</span></code></li><li ><code><span >[[</span><span >2</span><span > </span><span >3</span><span >]</span></code></li><li ><code><span > </span><span >[</span><span >5</span><span > </span><span >6</span><span >]]</span></code></li></ol>
使用布尔索引读取 ndarray 的方法
读取 ndarray 的另一种方法是使用布尔索引。在这种方法中，你在方括号内指定一个过滤条件，然后返回符合该条件的 ndarray 的一个部分。
例如，为了获得一个 ndarray 中所有大于 5 的值，你可以指定布尔索引操作 my_ndarray[my_ndarray > 5]。这个操作将返回一个包含所有大于 5 的值的 ndarray：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([</span><span >1</span><span >,</span><span > </span><span >2</span><span >,</span><span > </span><span >3</span><span >,</span><span > </span><span >4</span><span >,</span><span > </span><span >5</span><span >,</span><span > </span><span >6</span><span >,</span><span > </span><span >7</span><span >,</span><span > </span><span >8</span><span >,</span><span > </span><span >9</span><span >,</span><span > </span><span >10</span><span >])</span></code></li><li ><code><span >>>></span><span > my_ndarray2 </span><span >=</span><span > my_ndarray</span><span >[</span><span >my_ndarray </span><span >></span><span > </span><span >5</span><span >]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2</span><span >)</span></code></li><li ><code><span >[</span><span > </span><span >6</span><span ></span><span >7</span><span ></span><span >8</span><span ></span><span >9</span><span > </span><span >10</span><span >]</span></code></li></ol>
例如，为了获得一个 ndarray 中的所有偶数值，你可以使用如下的布尔索引操作：
<ol ><li ><code><span >>>></span><span > my_ndarray2 </span><span >=</span><span > my_ndarray</span><span >[</span><span >my_ndarray </span><span >%</span><span > </span><span >2</span><span > </span><span >==</span><span > </span><span >0</span><span >]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2</span><span >)</span></code></li><li ><code><span >[</span><span > </span><span >2</span><span ></span><span >4</span><span ></span><span >6</span><span ></span><span >8</span><span > </span><span >10</span><span >]</span></code></li></ol>
而要得到所有的奇数值，你可以用这个方法：
<ol ><li ><code><span >>>></span><span > my_ndarray2 </span><span >=</span><span > my_ndarray</span><span >[</span><span >my_ndarray </span><span >%</span><span > </span><span >2</span><span > </span><span >==</span><span > </span><span >1</span><span >]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2</span><span >)</span></code></li><li ><code><span >[</span><span >1</span><span > </span><span >3</span><span > </span><span >5</span><span > </span><span >7</span><span > </span><span >9</span><span >]</span></code></li></ol>
ndarray 的矢量和标量算术
NumPy 的 ndarray 允许进行矢量和标量算术操作。在矢量算术中，在两个 ndarray 之间进行一个元素的算术操作。在标量算术中，算术运算是在一个 ndarray 和一个常数标量值之间进行的。
如下的两个 ndarray：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([</span><span >1</span><span >,</span><span > </span><span >2</span><span >,</span><span > </span><span >3</span><span >,</span><span > </span><span >4</span><span >,</span><span > </span><span >5</span><span >])</span></code></li><li ><code><span >>>></span><span > my_ndarray2 </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([</span><span >6</span><span >,</span><span > </span><span >7</span><span >,</span><span > </span><span >8</span><span >,</span><span > </span><span >9</span><span >,</span><span > </span><span >10</span><span >])</span></code></li></ol>
如果你将上述两个 ndarray 相加，就会产生一个两个 ndarray 的元素相加的新的 ndarray。例如，产生的 ndarray 的第一个元素将是原始 ndarray 的第一个元素相加的结果，以此类推：
<ol ><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2 </span><span >+</span><span > my_ndarray</span><span >)</span></code></li><li ><code><span >[</span><span > </span><span >7</span><span ></span><span >9</span><span > </span><span >11</span><span > </span><span >13</span><span > </span><span >15</span><span >]</span></code></li></ol>
这里，7 是 1 和 6 的和，这是我相加的 ndarray 中的前两个元素。同样，15 是 5 和10 之和，是最后一个元素。
请看以下算术运算：
<ol ><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2 </span><span >-</span><span > my_ndarray</span><span >)</span></code></li><li ><code><span >[</span><span >5</span><span > </span><span >5</span><span > </span><span >5</span><span > </span><span >5</span><span > </span><span >5</span><span >]</span></code></li><li ><code><span >>>></span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2 </span><span >*</span><span > my_ndarray</span><span >)</span></code></li><li ><code><span >[</span><span > </span><span >6</span><span > </span><span >14</span><span > </span><span >24</span><span > </span><span >36</span><span > </span><span >50</span><span >]</span></code></li><li ><code><span >>>></span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray2 </span><span >/</span><span > my_ndarray</span><span >)</span></code></li><li ><code><span >[</span><span >6.</span><span > </span><span >3.5</span><span ></span><span >2.66666667</span><span > </span><span >2.25</span><span > </span><span >2.</span><span ></span><span >]</span></code></li></ol>
在 ndarray 中加一个标量值也有类似的效果，标量值被添加到 ndarray 的所有元素中。这被称为“广播”：
<ol ><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray </span><span >+</span><span > </span><span >10</span><span >)</span></code></li><li ><code><span >[</span><span >11</span><span > </span><span >12</span><span > </span><span >13</span><span > </span><span >14</span><span > </span><span >15</span><span >]</span></code></li><li ><code><span >>>></span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray </span><span >-</span><span > </span><span >10</span><span >)</span></code></li><li ><code><span >[-</span><span >9</span><span > </span><span >-</span><span >8</span><span > </span><span >-</span><span >7</span><span > </span><span >-</span><span >6</span><span > </span><span >-</span><span >5</span><span >]</span></code></li><li ><code><span >>>></span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray </span><span >*</span><span > </span><span >10</span><span >)</span></code></li><li ><code><span >[</span><span >10</span><span > </span><span >20</span><span > </span><span >30</span><span > </span><span >40</span><span > </span><span >50</span><span >]</span></code></li><li ><code><span >>>></span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray </span><span >/</span><span > </span><span >10</span><span >)</span></code></li><li ><code><span >[</span><span >0.1</span><span > </span><span >0.2</span><span > </span><span >0.3</span><span > </span><span >0.4</span><span > </span><span >0.5</span><span >]</span></code></li></ol>
ndarray 的排序
有两种方法可以对 ndarray 进行原地或非原地排序。原地排序会对原始 ndarray 进行排序和修改，而非原地排序会返回排序后的 ndarray，但不会修改原始 ndarray。我将尝试这两个例子：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([</span><span >3</span><span >,</span><span > </span><span >1</span><span >,</span><span > </span><span >2</span><span >,</span><span > </span><span >5</span><span >,</span><span > </span><span >4</span><span >])</span></code></li><li ><code><span >>>></span><span > my_ndarray</span><span >.</span><span >sort</span><span >()</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[</span><span >1</span><span > </span><span >2</span><span > </span><span >3</span><span > </span><span >4</span><span > </span><span >5</span><span >]</span></code></li></ol>
正如你所看到的，sort() 方法对 ndarray 进行原地排序，并修改了原数组。
还有一个方法叫 np.sort()，它对数组进行非原地排序：
<ol ><li ><code><span >>>></span><span > my_ndarray </span><span >=</span><span > np</span><span >.</span><span >array</span><span >([</span><span >3</span><span >,</span><span > </span><span >1</span><span >,</span><span > </span><span >2</span><span >,</span><span > </span><span >5</span><span >,</span><span > </span><span >4</span><span >])</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >np</span><span >.</span><span >sort</span><span >(</span><span >my_ndarray</span><span >))</span></code></li><li ><code><span >[</span><span >1</span><span > </span><span >2</span><span > </span><span >3</span><span > </span><span >4</span><span > </span><span >5</span><span >]</span></code></li><li ><code><span >>>></span><span > </span><span >print</span><span >(</span><span >my_ndarray</span><span >)</span></code></li><li ><code><span >[</span><span >3</span><span > </span><span >1</span><span > </span><span >2</span><span > </span><span >5</span><span > </span><span >4</span><span >]</span></code></li></ol>
正如你所看到的，np.sort() 方法返回一个已排序的 ndarray，但没有修改它。
总结
我已经介绍了很多关于 NumPy 和 ndarray 的内容。我谈到了创建 ndarray，读取它们的不同方法，基本的向量和标量算术，以及排序。NumPy 还有很多东西可以探索，包括像 union() 和 intersection()这样的集合操作，像 min() 和 max() 这样的统计操作，等等。
我希望我上面演示的例子是有用的。祝你在探索 NumPy 时愉快。