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

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2021-08-15 11:58

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

$ conda install numpy

本文目录

  1. 基础
    • 占位符
  2. 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
  3. 数学计算
    • 数学计算
    • 比较
    • 基础统计
    • 更多
  4. 切片和子集
  5. 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 dimensionalx = np.array([1,2,3])# 2 dimensionaly = 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 ordery = 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 arraya = 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 arrayprint(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 npa = np.array([1, 3, 5])b = np.array([2, 4, 6])
# Stack two arrays row-wiseprint(np.vstack((a,b)))>>> [[1 3 5] [2 4 6]]
# Stack two arrays column-wiseprint(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 ~3a = 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
https://docs.scipy.org/doc/numpy/reference/generated/numpy.add.html
np.substract(x,y)
x - y
https://docs.scipy.org/doc/numpy/reference/generated/numpy.subtract.html#numpy.subtract
np.divide(x,y)
x / y
https://docs.scipy.org/doc/numpy/reference/generated/numpy.divide.html#numpy.divide
np.multiply(x,y)
x @ y
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 dimensiona = 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 arraysz = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])c = z < 6print(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)Meanhttps://numpy.org/doc/stable/reference/generated/numpy.mean.html#numpy.mean
np.median(array)Medianhttps://numpy.org/doc/stable/reference/generated/numpy.median.html#numpy.median
array.corrcoef()Correlation Coefficienthttps://numpy.org/doc/stable/reference/generated/numpy.corrcoef.html#numpy.corrcoef
np.std(array)Standard Deviationhttps://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html#numpy.std

举例

# Statistics of an arraya = np.array([1, 1, 2, 5, 8, 10, 11, 12])
# Standard deviationprint(np.std(a))>>> 4.2938910093294167
# Medianprint(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 2https://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 npa1 = 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


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

往期精彩回顾




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