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683 lines
229 KiB
Markdown
683 lines
229 KiB
Markdown
# 生成数组的函数
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## arange
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`arange` 类似于**Python**中的 `range` 函数，只不过返回的不是列表，而是数组：
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```py
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arange(start, stop=None, step=1, dtype=None)
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```
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产生一个在区间 `[start, stop)` 之间，以 `step` 为间隔的数组，如果只输入一个参数，则默认从 `0` 开始，并以这个值为结束：
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In [1]:
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```py
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import numpy as np
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np.arange(4)
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```
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Out[1]:
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```py
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array([0, 1, 2, 3])
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```
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与 `range` 不同， `arange` 允许非整数值输入，产生一个非整型的数组：
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In [2]:
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```py
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np.arange(0, 2 * np.pi, np.pi / 4)
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```
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Out[2]:
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```py
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array([ 0\. , 0.78539816, 1.57079633, 2.35619449, 3.14159265,
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3.92699082, 4.71238898, 5.49778714])
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```
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数组的类型默认由参数 `start, stop, step` 来确定，也可以指定：
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In [3]:
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```py
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np.arange(0, 2 * np.pi, np.pi / 4, dtype=np.float32)
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```
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Out[3]:
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```py
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array([ 0\. , 0.78539819, 1.57079637, 2.3561945 , 3.14159274,
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3.92699099, 4.71238899, 5.49778748], dtype=float32)
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```
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由于存在精度问题，使用浮点数可能出现问题：
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In [4]:
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```py
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np.arange(1.5, 2.1, 0.3)
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```
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Out[4]:
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```py
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array([ 1.5, 1.8, 2.1])
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```
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`stop` 的值 `2.1` 出现在了数组中，所以使用浮点数的时候需要注意。
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## linspace
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```py
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linspace(start, stop, N)
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```
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产生 `N` 个等距分布在 `[start, stop]`间的元素组成的数组，包括 `start, stop`。
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In [5]:
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```py
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np.linspace(0, 1, 5)
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```
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Out[5]:
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```py
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array([ 0\. , 0.25, 0.5 , 0.75, 1\. ])
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```
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## logspace
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```py
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logspace(start, stop, N)
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```
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产生 N 个对数等距分布的数组，默认以10为底：
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In [6]:
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```py
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np.logspace(0, 1, 5)
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```
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Out[6]:
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```py
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array([ 1\. , 1.77827941, 3.16227766, 5.62341325, 10\. ])
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```
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产生的值为$\left[10^0, 10^{0.25},10^{0.5},10^{0.75},10^1\right]$。
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## meshgrid
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有时候需要在二维平面中生成一个网格，这时候可以使用 `meshgrid` 来完成这样的工作：
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In [7]:
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```py
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x_ticks = np.linspace(-1, 1, 5)
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y_ticks = np.linspace(-1, 1, 5)
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x, y = np.meshgrid(x_ticks, y_ticks)
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```
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这里产生的 `x, y`如下：
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In [8]:
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```py
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x
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```
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Out[8]:
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```py
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array([[-1\. , -0.5, 0\. , 0.5, 1\. ],
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[-1\. , -0.5, 0\. , 0.5, 1\. ],
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[-1\. , -0.5, 0\. , 0.5, 1\. ],
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[-1\. , -0.5, 0\. , 0.5, 1\. ],
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[-1\. , -0.5, 0\. , 0.5, 1\. ]])
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```
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In [9]:
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```py
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y
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```
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Out[9]:
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```py
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array([[-1\. , -1\. , -1\. , -1\. , -1\. ],
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[-0.5, -0.5, -0.5, -0.5, -0.5],
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[ 0\. , 0\. , 0\. , 0\. , 0\. ],
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[ 0.5, 0.5, 0.5, 0.5, 0.5],
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[ 1\. , 1\. , 1\. , 1\. , 1\. ]])
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```
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`x` 对应网格的第一维，`y` 对应网格的第二维。
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图例：
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In [10]:
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```py
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%matplotlib inline
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d import Axes3D
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from matplotlib import cm
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def f(x, y):
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# sinc 函数
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r = np.sqrt(x ** 2 + y ** 2)
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result = np.sin(r) / r
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result[r == 0] = 1.0
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return result
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x_ticks = np.linspace(-10, 10, 51)
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y_ticks = np.linspace(-10, 10, 51)
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x, y = np.meshgrid(x_ticks, y_ticks)
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z = f(x, y)
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fig = plt.figure()
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ax = fig.add_subplot(111, projection='3d')
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ax.plot_surface(x, y, z,
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rstride=1, cstride=1,
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cmap=cm.YlGnBu_r)
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_zlabel('z')
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```
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```py
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c:\Miniconda\lib\site-packages\IPython\kernel\__main__.py:9: RuntimeWarning: invalid value encountered in divide
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```
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Out[10]:
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```py
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<matplotlib.text.Text at 0x9ac1630>
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```
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事实上，`x, y` 中有很多冗余的元素，这里提供了一个 `sparse` 的选项：
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In [11]:
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```py
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x_ticks = np.linspace(-1, 1, 5)
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y_ticks = np.linspace(-1, 1, 5)
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x, y = np.meshgrid(x_ticks, y_ticks, sparse=True)
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```
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In [12]:
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```py
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x
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```
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Out[12]:
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```py
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array([[-1\. , -0.5, 0\. , 0.5, 1\. ]])
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```
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In [13]:
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```py
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y
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```
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Out[13]:
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```py
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array([[-1\. ],
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[-0.5],
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[ 0\. ],
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[ 0.5],
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[ 1\. ]])
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```
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在这个选项下，`x, y` 变成了单一的行向量和列向量。
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但这并不影响结果：
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In [14]:
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```py
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x_ticks = np.linspace(-10, 10, 51)
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y_ticks = np.linspace(-10, 10, 51)
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x, y = np.meshgrid(x_ticks, y_ticks, sparse=True)
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z = f(x, y)
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fig = plt.figure()
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ax = fig.add_subplot(111, projection='3d')
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ax.plot_surface(x, y, z,
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rstride=1, cstride=1,
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cmap=cm.YlGnBu_r)
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_zlabel('z')
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```
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```py
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c:\Miniconda\lib\site-packages\IPython\kernel\__main__.py:9: RuntimeWarning: invalid value encountered in divide
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```
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Out[14]:
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```py
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<matplotlib.text.Text at 0xba147f0>
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```
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`meshgrid` 可以设置轴排列的先后顺序：
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* 默认为 `indexing='xy'` 即笛卡尔坐标，对于2维数组，返回行向量 `x` 和列向量 `y`
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* 或者使用 `indexing='ij'` 即矩阵坐标，对于2维数组，返回列向量 `x` 和行向量 `y`。
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## ogrid , mgrid
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**Matlab**中有 `meshgrid` 的用法：
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```py
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meshgrid(-1:.5:1, -1:.5:1)
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```
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**Numpy**的 `meshgrid` 并不支持这样的用法，但我们可以使用 `ogrid / mgrid` 来实现类似这样的用法。
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`ogrid` 与 `mgrid` 的区别在于：
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* `ogrid` 相当于 `meshgrid(indexing='ij', sparse=True)`
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* `mgrid` 相当于 `meshgrid(indexing='ij', sparse=False)`
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In [15]:
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```py
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x, y = np.ogrid[-1:1:.5, -1:1:.5]
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```
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In [16]:
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```py
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x
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```
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Out[16]:
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```py
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array([[-1\. ],
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[-0.5],
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[ 0\. ],
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[ 0.5]])
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```
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In [17]:
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```py
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y
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```
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Out[17]:
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```py
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array([[-1\. , -0.5, 0\. , 0.5]])
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```
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注意：
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* 这里使用的是中括号
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* **Matlab** 使用的是 `start:step:end` 的表示，**Numpy** 使用的是 `start:end:step` 的表示
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* 这里的结果不包括 `end` 的值
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为了包含 `end` 的值，我们可以使用这样的技巧：
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In [18]:
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```py
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x, y = np.ogrid[-1:1:5j, -1:1:5j]
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```
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In [19]:
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```py
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x, y
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```
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Out[19]:
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```py
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(array([[-1\. ],
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[-0.5],
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[ 0\. ],
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[ 0.5],
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[ 1\. ]]), array([[-1\. , -0.5, 0\. , 0.5, 1\. ]]))
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```
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我们在 `step` 的位置传入一个复数 `5j` ，表示我们需要一个 `5` 个值的数组，此时返回值就会包含 `end` 的值。
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重复之前的画图：
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In [20]:
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```py
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# exchange here
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y, x = np.ogrid[-10:10:51j, -10:10:51j]
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z = f(x, y)
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fig = plt.figure()
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ax = fig.add_subplot(111, projection='3d')
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ax.plot_surface(x, y, z,
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rstride=1, cstride=1,
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cmap=cm.YlGnBu_r)
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_zlabel('z')
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```
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```py
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c:\Miniconda\lib\site-packages\IPython\kernel\__main__.py:9: RuntimeWarning: invalid value encountered in divide
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```
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Out[20]:
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```py
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<matplotlib.text.Text at 0x9e34278>
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```
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这里，我们交换了 `x, y` 输出值的顺序。
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## r`_` , c`_`
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我们可以使用 `r_ / c_` 来产生行向量或者列向量。
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使用切片产生：
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In [21]:
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```py
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np.r_[0:1:.1]
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```
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Out[21]:
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```py
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array([ 0\. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])
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```
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复数步长制定数组长度：
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In [22]:
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```py
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np.r_[0:1:5j]
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```
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Out[22]:
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```py
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array([ 0\. , 0.25, 0.5 , 0.75, 1\. ])
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```
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连接多个序列，产生数组：
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In [23]:
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```py
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np.r_[(3,22,11), 4.0, [15, 6]]
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```
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Out[23]:
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```py
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array([ 3., 22., 11., 4., 15., 6.])
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```
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列向量：
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In [24]:
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```py
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np.c_[1:3:5j]
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```
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Out[24]:
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```py
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array([[ 1\. ],
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[ 1.5],
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[ 2\. ],
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[ 2.5],
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[ 3\. ]])
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```
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## ones , zeros
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```py
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ones(shape, dtype=float64)
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zeros(shape, dtype=float64)
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```
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产生一个制定形状的全 `0` 或全 `1` 的数组，还可以制定数组类型：
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In [25]:
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```py
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np.zeros(3)
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```
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Out[25]:
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```py
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array([ 0., 0., 0.])
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```
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In [26]:
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```py
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np.ones([2,3], dtype=np.float32)
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```
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Out[26]:
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```py
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array([[ 1., 1., 1.],
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[ 1., 1., 1.]], dtype=float32)
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```
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产生一个全是 `5` 的数组：
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In [27]:
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```py
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np.ones([2,3]) * 5
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```
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Out[27]:
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```py
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array([[ 5., 5., 5.],
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[ 5., 5., 5.]])
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```
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## empty
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```py
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empty(shape, dtype=float64, order='C')
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```
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也可以使用 `empty` 方法产生一个制定大小的数组（数组所指向的内存未被初始化，所以值随机），再用 `fill` 方法填充：
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In [28]:
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```py
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a = np.empty(2)
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a
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```
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Out[28]:
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```py
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array([-0.03412165, 0.05516321])
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```
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In [29]:
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```py
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a.fill(5)
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a
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```
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Out[29]:
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```py
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array([ 5., 5.])
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```
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另一种替代方法使用索引，不过速度会稍微慢一些：
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In [30]:
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```py
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a[:] = 5
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a
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```
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Out[30]:
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```py
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array([ 5., 5.])
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```
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## empty`_`like, ones`_`like, zeros`_`like
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```py
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empty_like(a)
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ones_like(a)
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zeros_like(a)
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```
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产生一个跟 `a` 大小一样，类型一样的对应数组。
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In [31]:
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```py
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a = np.arange(0, 10, 2.5)
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a
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```
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Out[31]:
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```py
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array([ 0\. , 2.5, 5\. , 7.5])
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```
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In [32]:
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```py
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np.empty_like(a)
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```
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Out[32]:
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```py
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array([ 0., 0., 0., 0.])
|
||
```
|
||
|
||
In [33]:
|
||
|
||
```py
|
||
np.zeros_like(a)
|
||
|
||
```
|
||
|
||
Out[33]:
|
||
|
||
```py
|
||
array([ 0., 0., 0., 0.])
|
||
```
|
||
|
||
In [34]:
|
||
|
||
```py
|
||
np.ones_like(a)
|
||
|
||
```
|
||
|
||
Out[34]:
|
||
|
||
```py
|
||
array([ 1., 1., 1., 1.])
|
||
```
|
||
|
||
## identity
|
||
|
||
```py
|
||
indentity(n, dtype=float64)
|
||
```
|
||
|
||
产生一个 `n` 乘 `n` 的单位矩阵：
|
||
|
||
In [35]:
|
||
|
||
```py
|
||
np.identity(3)
|
||
|
||
```
|
||
|
||
Out[35]:
|
||
|
||
```py
|
||
array([[ 1., 0., 0.],
|
||
[ 0., 1., 0.],
|
||
[ 0., 0., 1.]])
|
||
``` |