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

1. 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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