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用 NumPy 在 Python 中处理数字

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Apr 15, 2023 pm 05:55 PM

python编程语言numpy

这篇文章讨论了安装 NumPy，然后创建、读取和排序 NumPy 数组。

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>class</span><span> </span><span>'numpy.ndarray'</span><span>></span></span></code></li>
</ol>

这里要注意的另一件事是 “形状shape”。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rank”。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 <u21> 的字符串 ndarray，意味着我们的 ndarray 包含 unicode 字符串：</u21>

<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></u21></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broadcasting”：

<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。

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