以下文章来源于机器学习初学者 ,作者机器学习初学者

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 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
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 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