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372 lines
21 KiB
Markdown
372 lines
21 KiB
Markdown
# Numpy 简介
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## 导入numpy
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**Numpy**是**Python**的一个很重要的第三方库，很多其他科学计算的第三方库都是以**Numpy**为基础建立的。
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**Numpy**的一个重要特性是它的数组计算。
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在使用**Numpy**之前，我们需要导入`numpy`包：
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In [1]:
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```py
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from numpy import *
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```
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使用前一定要先导入 Numpy 包，导入的方法有以下几种：
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```py
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import numpy
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import numpy as np
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from numpy import *
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from numpy import array, sin
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```
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事实上，在**ipython**中可以使用magic命令来快速导入**Numpy**的内容。
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In [2]:
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```py
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%pylab
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```
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```py
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Using matplotlib backend: Qt4Agg
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Populating the interactive namespace from numpy and matplotlib
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```
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## 数组上的数学操作
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假如我们想将列表中的每个元素增加`1`，但列表不支持这样的操作（报错）：
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In [3]:
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```py
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a = [1, 2, 3, 4]
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a + 1
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```
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```py
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---------------------------------------------------------------------------
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TypeError Traceback (most recent call last)
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<ipython-input-3-068856d2a224> in <module>()
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1 a = [1, 2, 3, 4]
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----> 2 a + 1
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TypeError: can only concatenate list (not "int") to list
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```
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转成 `array` ：
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In [4]:
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```py
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a = array(a)
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a
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```
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Out[4]:
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```py
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array([1, 2, 3, 4])
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```
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`array` 数组支持每个元素加 `1` 这样的操作：
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In [5]:
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```py
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a + 1
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```
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Out[5]:
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```py
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array([2, 3, 4, 5])
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```
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与另一个 `array` 相加，得到对应元素相加的结果：
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In [6]:
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```py
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b = array([2, 3, 4, 5])
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a + b
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```
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Out[6]:
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```py
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array([3, 5, 7, 9])
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```
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对应元素相乘：
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In [7]:
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```py
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a * b
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```
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Out[7]:
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```py
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array([ 2, 6, 12, 20])
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```
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对应元素乘方：
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In [8]:
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```py
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a ** b
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```
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Out[8]:
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```py
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array([ 1, 8, 81, 1024])
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```
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## 提取数组中的元素
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提取第一个元素：
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In [9]:
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```py
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a[0]
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```
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Out[9]:
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```py
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1
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```
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提取前两个元素：
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In [10]:
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```py
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a[:2]
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```
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Out[10]:
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```py
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array([1, 2])
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```
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最后两个元素：
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In [11]:
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```py
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a[-2:]
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```
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Out[11]:
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```py
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array([3, 4])
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```
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将它们相加：
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In [12]:
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```py
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a[:2] + a[-2:]
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```
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Out[12]:
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```py
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array([4, 6])
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```
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## 修改数组形状
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查看 `array` 的形状：
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In [13]:
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```py
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a.shape
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```
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Out[13]:
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```py
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(4L,)
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```
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修改 `array` 的形状：
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In [14]:
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```py
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a.shape = 2,2
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a
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```
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Out[14]:
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```py
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array([[1, 2],
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[3, 4]])
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```
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## 多维数组
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`a` 现在变成了一个二维的数组，可以进行加法：
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In [15]:
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```py
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a + a
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```
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Out[15]:
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```py
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array([[2, 4],
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[6, 8]])
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```
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乘法仍然是对应元素的乘积，并不是按照矩阵乘法来计算：
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In [16]:
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```py
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a * a
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```
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Out[16]:
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```py
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array([[ 1, 4],
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[ 9, 16]])
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```
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## 画图
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linspace 用来生成一组等间隔的数据：
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In [17]:
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```py
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a = linspace(0, 2*pi, 21)
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%precision 3
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a
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```
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Out[17]:
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```py
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array([ 0\. , 0.314, 0.628, 0.942, 1.257, 1.571, 1.885, 2.199,
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2.513, 2.827, 3.142, 3.456, 3.77 , 4.084, 4.398, 4.712,
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5.027, 5.341, 5.655, 5.969, 6.283])
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```
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三角函数：
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In [18]:
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```py
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b = sin(a)
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b
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```
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Out[18]:
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```py
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array([ 0.000e+00, 3.090e-01, 5.878e-01, 8.090e-01, 9.511e-01,
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1.000e+00, 9.511e-01, 8.090e-01, 5.878e-01, 3.090e-01,
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1.225e-16, -3.090e-01, -5.878e-01, -8.090e-01, -9.511e-01,
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-1.000e+00, -9.511e-01, -8.090e-01, -5.878e-01, -3.090e-01,
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-2.449e-16])
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```
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画出图像：
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In [19]:
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```py
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%matplotlib inline
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plot(a, b)
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```
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Out[19]:
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```py
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[<matplotlib.lines.Line2D at 0xa128ba8>]
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```
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## 从数组中选择元素
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假设我们想选取数组b中所有非负的部分，首先可以利用 `b` 产生一组布尔值：
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In [20]:
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```py
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b >= 0
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```
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Out[20]:
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```py
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array([ True, True, True, True, True, True, True, True, True,
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True, True, False, False, False, False, False, False, False,
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False, False, False], dtype=bool)
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```
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In [21]:
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```py
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mask = b >= 0
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```
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画出所有对应的非负值对应的点：
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In [22]:
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```py
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plot(a[mask], b[mask], 'ro')
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```
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Out[22]:
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```py
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[<matplotlib.lines.Line2D at 0xa177be0>]
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```
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