简约而不简单|值得收藏的Numpy小抄表（含主要语法、代码）-CFANZ编程社区

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

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

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

简约而不简单|值得收藏的Numpy小抄表（含主要语法、代码）_html

简约而不简单|值得收藏的Numpy小抄表（含主要语法、代码）_python_02

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]