【Python】简约而不简单|值得收藏的Numpy小抄表（含主要语法、代码）

Numpy是一个用python实现的科学计算的扩展程序库，包括：

• 1、一个强大的N维数组对象Array；
• 2、比较成熟的（广播）函数库；
• 3、用于整合C/C++和Fortran代码的工具包；
• 4、实用的线性代数、傅里叶变换和随机数生成函数。numpy和稀疏矩阵运算包scipy配合使用更加方便。

NumPy（Numeric Python）提供了许多高级的数值编程工具，如：矩阵数据类型、矢量处理，以及精密的运算库。专为进行严格的数字处理而产生。多为很多大型金融公司使用，以及核心的科学计算组织如：Lawrence Livermore，NASA用其处理一些本来使用C++，Fortran或Matlab等所做的任务。

本文整理了一个Numpy的小抄表，总结了Numpy的常用操作，可以收藏慢慢看。

安装Numpy

可以通过 Pip 或者 Anaconda安装Numpy:

$ pip install numpy

或

$ conda install numpy

本文目录

基础

• 占位符
• 数组

• 增加或减少元素
• 合并数组
• 分割数组
• 数组形状变化

• 拷贝 /排序
• 数组操作
• 其他

• 数学计算

• 数学计算
• 比较
• 基础统计
• 更多

• 切片和子集
• 小技巧

基础

NumPy最常用的功能之一就是NumPy数组：列表和NumPy数组的最主要区别在于功能性和速度。

列表提供基本操作，但NumPy添加了FTTs、卷积、快速搜索、基本统计、线性代数、直方图等。

两者数据科学最重要的区别是能够用NumPy数组进行元素级计算。

​​axis 0​​ 通常指行

​​axis 1​​ 通常指列

操作

描述

文档

​​np.array([1,2,3])​​

一维数组

​​https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array​​

​​np.array([(1,2,3),(4,5,6)])​​

二维数组

​​https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array​​

​​np.arange(start,stop,step)​​

等差数组

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html​​

占位符

操作

描述

文档

​​np.linspace(0,2,9)​​

数组中添加等差的值

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html​​

​​np.zeros((1,2))​​

创建全0数组

docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html

​​np.ones((1,2))​​

创建全1数组

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.ones.html#numpy.ones​​

​​np.random.random((5,5))​​

创建随机数的数组

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.random.html​​

​​np.empty((2,2))​​

创建空数组

​​https://numpy.org/doc/stable/reference/generated/numpy.empty.html​​

举例：

import numpy as np


# 1 dimensional
x = np.array([1,2,3])
# 2 dimensional
y = np.array([(1,2,3),(4,5,6)])


x = np.arange(3)
>>> array([0, 1, 2])


y = np.arange(3.0)
>>> array([ 0., 1., 2.])


x = np.arange(3,7)
>>> array([3, 4, 5, 6])


y = np.arange(3,7,2)
>>> array([3, 5])

数组属性

数组属性

语法

描述

文档

​​array.shape​​

维度(行,列)

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.shape.html​​

​​len(array)​​

数组长度

​​https://docs.python.org/3.5/library/functions.html#len​​

​​array.ndim​​

数组的维度数

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.ndim.html​​

​​array.size​​

数组的元素数

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.size.html​​

​​array.dtype​​

数据类型

​​https://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html​​

​​array.astype(type)​​

转换数组类型

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.astype.html​​

​​type(array)​​

显示数组类型

​​https://numpy.org/doc/stable/user/basics.types.html​​

拷贝 /排序

操作

描述

文档

​​np.copy(array)​​

创建数组拷贝

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.copy.html​​

​​other = array.copy()​​

创建数组深拷贝

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.copy.html​​

​​array.sort()​​

排序一个数组

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html​​

​​array.sort(axis=0)​​

按照指定轴排序一个数组

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html​​

举例

import numpy as np
# Sort sorts in ascending order
y = np.array([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])
y.sort()
print(y)
>>> [ 1 2 3 4 5 6 7 8 9 10]

数组操作例程

增加或减少元素

操作

描述

文档

​​np.append(a,b)​​

增加数据项到数组

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.append.html​​

​​np.insert(array, 1, 2, axis)​​

沿着数组0轴或者1轴插入数据项

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.insert.html​​

​​np.resize((2,4))​​

将数组调整为形状(2,4)

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.resize.html​​

​​np.delete(array,1,axis)​​

从数组里删除数据项

​​https://numpy.org/doc/stable/reference/generated/numpy.delete.html​​

举例

import numpy as np
# Append items to array
a = np.array([(1, 2, 3),(4, 5, 6)])
b = np.append(a, [(7, 8, 9)])
print(b)
>>> [1 2 3 4 5 6 7 8 9]


# Remove index 2 from previous array
print(np.delete(b, 2))
>>> [1 2 4 5 6 7 8 9]

组合数组

操作

描述

文档

​​np.concatenate((a,b),axis=0)​​

连接2个数组，添加到末尾

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.concatenate.html​​

​​np.vstack((a,b))​​

按照行堆叠数组

​​https://numpy.org/doc/stable/reference/generated/numpy.vstack.html​​

​​np.hstack((a,b))​​

按照列堆叠数组

docs.scipy.org/doc/numpy/reference/generated/numpy.hstack.html#numpy.hstack

举例

import numpy as np
a = np.array([1, 3, 5])
b = np.array([2, 4, 6])


# Stack two arrays row-wise
print(np.vstack((a,b)))
>>> [[1 3 5]
[2 4 6]]


# Stack two arrays column-wise
print(np.hstack((a,b)))
>>> [1 3 5 2 4 6]

分割数组

操作

描述

文档

​​numpy.split()​​

分割数组

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.split.html​​

​​np.array_split(array, 3)​​

将数组拆分为大小（几乎）相同的子数组

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.array_split.html#numpy.array_split​​

​​numpy.hsplit(array, 3)​​

在第3个索引处水平拆分数组

​​https://numpy.org/doc/stable/reference/generated/numpy.hsplit.html#numpy.hsplit​​

举例

# Split array into groups of ~3
a = np.array([1, 2, 3, 4, 5, 6, 7, 8])
print(np.array_split(a, 3))
>>> [array([1, 2, 3]), array([4, 5, 6]), array([7, 8])]

数组形状变化

操作

操作

描述

文档

​​other = ndarray.flatten()​​

平铺一个二维数组到一维数组

​​https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flatten.html​​

numpy.flip()

翻转一维数组中元素的顺序

​​https://docs.scipy.org/doc/stable/reference/generated/numpy.flip.html​​

np.ndarray[::-1]

翻转一维数组中元素的顺序

reshape

改变数组的维数

​​https://docs.scipy.org/doc/stable/reference/generated/numpy.reshape.html​​

squeeze

从数组的形状中删除单维度条目

​​https://numpy.org/doc/stable/reference/generated/numpy.squeeze.html​​

expand_dims

扩展数组维度

​​https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.expand_dims.html​​

其他

操作

描述

文档

​​other = ndarray.flatten()​​

平铺2维数组到1维数组

​​https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flatten.html​​

​​array = np.transpose(other)​​​​array.T​​

数组转置

​​https://numpy.org/doc/stable/reference/generated/numpy.transpose.html​​

​​inverse = np.linalg.inv(matrix)​​

求矩阵的逆矩阵

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.inv.html​​

举例

# Find inverse of a given matrix
>>> np.linalg.inv([[3,1],[2,4]])
array([[ 0.4, -0.1],
[-0.2, 0.3]])

数学计算

操作

操作

描述

文档

​​np.add(x,y)​​​​x + y​​

加

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.add.html​​

​​np.substract(x,y)​​​​x - y​​

减

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.subtract.html#numpy.subtract​​

​​np.divide(x,y)​​​​x / y​​

除

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.divide.html#numpy.divide​​

​​np.multiply(x,y)​​​​x @ y​​

乘

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.multiply.html#numpy.multiply​​

​​np.sqrt(x)​​

平方根

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.sqrt.html#numpy.sqrt​​

​​np.sin(x)​​

元素正弦

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sin​​

​​np.cos(x)​​

元素余弦

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.cos.html#numpy.cos​​

​​np.log(x)​​

元素自然对数

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.log.html#numpy.log​​

​​np.dot(x,y)​​

点积

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html​​

​​np.roots([1,0,-4])​​

给定多项式系数的根

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.roots.html​​

举例

# If a 1d array is added to a 2d array (or the other way), NumPy
# chooses the array with smaller dimension and adds it to the one
# with bigger dimension
a = np.array([1, 2, 3])
b = np.array([(1, 2, 3), (4, 5, 6)])
print(np.add(a, b))
>>> [[2 4 6]
[5 7 9]]

# Example of np.roots
# Consider a polynomial function (x-1)^2 = x^2 - 2*x + 1
# Whose roots are 1,1
>>> np.roots([1,-2,1])
array([1., 1.])
# Similarly x^2 - 4 = 0 has roots as x=±2
>>> np.roots([1,0,-4])
array([-2., 2.])

比较

操作

描述

文档

​​==​​

等于

​​https://docs.python.org/2/library/stdtypes.html​​

​​!=​​

不等于

​​https://docs.python.org/2/library/stdtypes.html​​

​​<​​

小于

​​https://docs.python.org/2/library/stdtypes.html​​

​​>​​

大于

​​https://docs.python.org/2/library/stdtypes.html​​

​​<=​​

小于等于

​​https://docs.python.org/2/library/stdtypes.html​​

​​>=​​

大于等于

​​https://docs.python.org/2/library/stdtypes.html​​

​​np.array_equal(x,y)​​

数组比较

​​https://numpy.org/doc/stable/reference/generated/numpy.array_equal.html​​

举例：

# Using comparison operators will create boolean NumPy arrays
z = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
c = z < 6
print(c)
>>> [ True True True True True False False False False False]

基本的统计

操作

描述

文档

​​np.mean(array)​​

Mean

​​https://numpy.org/doc/stable/reference/generated/numpy.mean.html#numpy.mean​​

​​np.median(array)​​

Median

​​https://numpy.org/doc/stable/reference/generated/numpy.median.html#numpy.median​​

​​array.corrcoef()​​

Correlation Coefficient

​​https://numpy.org/doc/stable/reference/generated/numpy.corrcoef.html#numpy.corrcoef​​

​​np.std(array)​​

Standard Deviation

​​https://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html#numpy.std​​

举例

# Statistics of an array
a = np.array([1, 1, 2, 5, 8, 10, 11, 12])


# Standard deviation
print(np.std(a))
>>> 4.2938910093294167


# Median
print(np.median(a))
>>> 6.5

更多

操作

描述

文档

​​array.sum()​​

数组求和

​​https://numpy.org/doc/stable/reference/generated/numpy.sum.html​​

​​array.min()​​

数组求最小值

​​https://numpy.org/doc/stable/reference/generated/numpy.ndarray.min.html​​

​​array.max(axis=0)​​

数组求最大值（沿着0轴）

​​array.cumsum(axis=0)​​

指定轴求累计和

​​https://numpy.org/doc/stable/reference/generated/numpy.cumsum.html​​

切片和子集

操作

描述

文档

​​array[i]​​

索引i处的一维数组

​​https://numpy.org/doc/stable/reference/arrays.indexing.html​​

​​array[i,j]​​

索引在[i][j]处的二维数组

​​https://numpy.org/doc/stable/reference/arrays.indexing.html​​

​​array[i<4]​​

布尔索引

​​https://numpy.org/doc/stable/reference/arrays.indexing.html​​

​​array[0:3]​​

选择索引为 0, 1和 2

​​https://numpy.org/doc/stable/reference/arrays.indexing.html​​

​​array[0:2,1]​​

选择第0,1行，第1列

​​https://numpy.org/doc/stable/reference/arrays.indexing.html​​

​​array[:1]​​

选择第0行数据项 (与[0:1, :]相同)

​​https://numpy.org/doc/stable/reference/arrays.indexing.html​​

​​array[1:2, :]​​

选择第1行

​​https://numpy.org/doc/stable/reference/arrays.indexing.html​​

[comment]: <> "

​​array[1,...]​​

等同于 array[1,:,:]

​​array[ : :-1]​​

反转数组

同上

举例

b = np.array([(1, 2, 3), (4, 5, 6)])


# The index *before* the comma refers to *rows*,
# the index *after* the comma refers to *columns*
print(b[0:1, 2])
>>> [3]


print(b[:len(b), 2])
>>> [3 6]


print(b[0, :])
>>> [1 2 3]


print(b[0, 2:])
>>> [3]


print(b[:, 0])
>>> [1 4]


c = np.array([(1, 2, 3), (4, 5, 6)])
d = c[1:2, 0:2]
print(d)
>>> [[4 5]]

切片举例

import numpy as np
a1 = np.arange(0, 6)
a2 = np.arange(10, 16)
a3 = np.arange(20, 26)
a4 = np.arange(30, 36)
a5 = np.arange(40, 46)
a6 = np.arange(50, 56)
a = np.vstack((a1, a2, a3, a4, a5, a6))

生成矩阵和切片图示

小技巧

例子将会越来越多的，欢迎大家提交。

布尔索引 

# Index trick when working with two np-arrays
a = np.array([1,2,3,6,1,4,1])
b = np.array([5,6,7,8,3,1,2])


# Only saves a at index where b == 1
other_a = a[b == 1]
#Saves every spot in a except at index where b != 1
other_other_a = a[b != 1]import numpy as np
x = np.array([4,6,8,1,2,6,9])
y = x > 5
print(x[y])
>>> [6 8 6 9]


# Even shorter
x = np.array([1, 2, 3, 4, 4, 35, 212, 5, 5, 6])
print(x[x < 5])
>>> [1 2 3 4 4]

• 【参考】

​​https://github.com/juliangaal/python-cheat-sheet​​

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