Graphic array calculation module numpy (trigonometric function, rounding function, converting radian to angle, statistical analysis function, median, array sorting, argsort(), lexport())

• This article is from 《Python Data analysis goes from beginner to proficient 》—— Edited by tomorrow Technology

8.5 NumPy Common statistical analysis functions

8.5.1 Mathematical operation function

• NumPy Functions that contain a large number of mathematical operations , Including trigonometric functions 、 Arithmetic operation function 、 Complex processing functions, etc , As shown in the table 8.2 Shown .
  

1. Arithmetic functions

（1） Add 、 reduce 、 ride 、 except

• NumPy Arithmetic functions contain simple addition 、 reduce 、 ride 、 In addition to the operation , Such as add() function 、subtract() function 、multiply() Functions and divide() function . What we should pay attention to here is , Arrays must have the same shape or conform to array broadcast rules .

import numpy as np
n1 = np.array([[1,2,3],[4,5,6],[7,8,9]])  # Create array 
n2 = np.array([10, 10, 10])
print(' Add two arrays ：')
print(np.add(n1, n2))
print(' Two arrays subtract ：')
print(np.subtract(n1, n2))
print(' Multiply two arrays ：')
print(np.multiply(n1, n2))
print(' Divide two arrays ：')
print(np.divide(n1, n2))

 Add two arrays ：
[[11 12 13]
 [14 15 16]
 [17 18 19]]
 Two arrays subtract ：
[[-9 -8 -7]
 [-6 -5 -4]
 [-3 -2 -1]]
 Multiply two arrays ：
[[10 20 30]
 [40 50 60]
 [70 80 90]]
 Divide two arrays ：
[[0.1 0.2 0.3]
 [0.4 0.5 0.6]

（2） Reciprocal

• reciprocal() Function is used to return the reciprocal of each element in the array .

import numpy as np
a = np.array([0.25, 1.75, 2, 100])
print(np.reciprocal(a))

[4.         0.57142857 0.5        0.01      ]

（3） Exponentiation

import numpy as np
n1 = np.array([10, 100, 1000])
print(np.power(n1, 3))
n2= np.array([1, 2, 3])
print(np.power(n1, n2))

[      1000    1000000 1000000000]
[        10      10000 1000000000]

（4） Remainder

• mod() Function is used to calculate the remainder after dividing the corresponding elements between arrays .

import numpy as np
n1 = np.array([10, 20, 30])
n2 = np.array([4, 5, -8])
print(np.mod(n1, n2))

[ 2  0 -2]

2. Rounding function

（1） rounding around() function

numpy.around(a,decimals)

• a: Array
• decimals: The number of decimal places rounded , The default value is 0, If a negative , Integers are rounded to the left of the decimal point .

import numpy as np
n = np.array([1.55, 6.823,100,0.1189,3.1415926,-2.345])  # Create array 
print(np.around(n))  # Round to the nearest whole 
print(np.around(n, decimals=2)) # Round to two decimal places 
print(np.around(n, decimals=-1))# Round to the left of the decimal point 

[  2.   7. 100.   0.   3.  -2.]
[  1.55   6.82 100.     0.12   3.14  -2.35]
[  0.  10. 100.   0.   0.  -0.]

（2） Rounding up ceil() function

• ceil() Function is used to return the smallest integer greater than or equal to the specified expression , That is, round up .

import numpy as np
n = np.array([-1.8, 1.66, -0.2, 0.888, 15])  # Create array 
print(np.ceil(n)) # Rounding up 

[-1.  2. -0.  1. 15.]

（3） Rounding down floor() function

import numpy as np
n = np.array([-1.8, 1.66, -0.2, 0.888, 15])  # Create array 
print(np.floor(n)) # Rounding down 

[-2.  1. -1.  0. 15.]

3. Trigonometric functions

import numpy as np
n= np.array([0, 30, 45, 60, 90])
print(' Sine of different angles ：')
#  By riding  pi/180  Into radians 
print(np.sin(n * np.pi / 180))
print(' The cosine of the angle in the array ：')
print(np.cos(n * np.pi / 180))
print(' The tangent of the angle in the array ：')
print(np.tan(n * np.pi / 180))

 Sine of different angles ：
[0.         0.5        0.70710678 0.8660254  1.        ]
 The cosine of the angle in the array ：
[1.00000000e+00 8.66025404e-01 7.07106781e-01 5.00000000e-01
 6.12323400e-17]
 The tangent of the angle in the array ：
[0.00000000e+00 5.77350269e-01 1.00000000e+00 1.73205081e+00
 1.63312394e+16]

Convert radians to degrees

import numpy as np
n = np.array([0, 30, 45, 60, 90])
print(' Sine of different angles ：')
sin = np.sin(n * np.pi / 180)
print(sin)
print(' Calculate the inverse sine of the angle , The return value is in radians ：')
inv = np.arcsin(sin)
print(inv)
print(' Radians are converted to angles ：')
print(np.degrees(inv))

 Sine of different angles ：
[0.         0.5        0.70710678 0.8660254  1.        ]
 Calculate the inverse sine of the angle , The return value is in radians ：
[0.         0.52359878 0.78539816 1.04719755 1.57079633]
 Radians are converted to angles ：
[ 0. 30. 45. 60. 90.]

8.5.2 Statistical analysis function

1. Sum up sum() function

• Sum array elements 、 Sum the array elements by row and column , The program code is as follows ：
• Parameters axis＝0 when , Returns the sum of the columns of the array , Parameters axis＝1 when , Returns the sum of the rows of the array .
  

import numpy as np
n=np.array([[1,2,3],[4,5,6],[7,8,9]])
print(' Sum array elements ：')
print(n.sum())
print(' Sum array elements by line ：')
print(n.sum(axis=0))
print(' Sum array elements by column ：')
print(n.sum(axis=1))

 Sum array elements ：
45
 Sum array elements by line ：
[12 15 18]
 Sum array elements by column ：
[ 6 15 24]

2. averaging mean() function

import numpy as np
n=np.array([[1,2,3],[4,5,6],[7,8,9]])
print(' Average the array elements ：')
print(n.mean())
print(' Average the array elements by row ：')
print(n.mean(axis=0))
print(' Average the array elements by column ：')
print(n.mean(axis=1))

 Average the array elements ：
5.0
 Average the array elements by row ：
[4. 5. 6.]
 Average the array elements by column ：
[2. 5. 8.]

3. For maximum max() Functions and minimum values min() function

import numpy as np
n=np.array([[1,2,3],[4,5,6],[7,8,9]])
print(' Maximum value of array element ：')
print(n.max())
print(' The maximum value of each row in the array ：')
print(n.max(axis=0))
print(' The maximum value of each column in the array ：')
print(n.max(axis=1))
print(' Minimum value of array element ：')
print(n.min())
print(' The minimum value of each row in the array ：')
print(n.min(axis=0))
print(' The minimum value of each column in the array ：')
print(n.min(axis=1))

 Maximum value of array element ：
9
 The maximum value of each row in the array ：
[7 8 9]
 The maximum value of each column in the array ：
[3 6 9]
 Minimum value of array element ：
1
 The minimum value of each row in the array ：
[1 2 3]
 The minimum value of each column in the array ：
[1 4 7]

4. Take the weighted average average() function

Calculate the weighted average price of e-commerce activities

• An e-commerce company is in the school season 、6.18、 A double tenth 、 The prices of double twelve and other activities are different , Next, calculate the weighted average price , The program code is as follows ：

import numpy as np
price=np.array([34.5,36,37.8,39,39.8,33.6])  # establish “ The unit price ” Array 
number=np.array([900,580,230,150,120,1800])  # establish “ sales volumes ” Array 
print(' Weighted average price ：')
print(np.average(price,weights=number))

 Weighted average price ：
34.84920634920635

5. Median median() function

• The median is used to measure the medium or general level of data value , It can avoid the influence of extreme values . In data processing , When there are a few outliers in the data , It is not affected by it , Based on this feature , The median is generally used to evaluate the analysis results .

import numpy as np
n=np.array([34.5,36,37.8,39,39.8,33.6])  # establish “ The unit price ” Array 
#  After array sorting , Find the median 
sort_n = np.msort(n)
print(' Array sorting ：')
print(sort_n)
print(' The median of the array is ：')
print(np.median(sort_n))

 Array sorting ：
[33.6 34.5 36.  37.8 39.  39.8]
 The median of the array is ：
36.9

6. variance 、 Standard deviation

import numpy as np
n=np.array([34.5,36,37.8,39,39.8,33.6])  # establish “ The unit price ” Array 
print(' Array variance ：')
print(np.var(n))
print(' Array standard deviation ：')
print(np.std(n))

 Array variance ：
5.168055555555551
 Array standard deviation ：
2.2733357771247853

8.5.3 Sort of array

1.sort() function

• Use sort() Function to sort , Change the original array directly , Parameters axis Specify whether to sort by row or column .

import numpy as np
n=np.array([[4,7,3],[2,8,5],[9,1,6]])
print(' Array sorting ：')
print(np.sort(n))
print(' Sort by row ：')
print(np.sort(n,axis=0))
print(' Sort by column ：')
print(np.sort(n,axis=1))

 Array sorting ：
[[3 4 7]
 [2 5 8]
 [1 6 9]]
 Sort by row ：
[[2 1 3]
 [4 7 5]
 [9 8 6]]
 Sort by column ：
[[3 4 7]
 [2 5 8]
 [1 6 9]]

2.argsort() function

• Use argsort() Function to sort the array , Returns the index value from small to large after ascending sorting .

import numpy as np
x=np.array([4,7,3,2,8,5,1,9,6])
print(' Index value after ascending sort ：')
y = np.argsort(x)
print(y)
print(' Reconstruct the original array in the sorted order ：')
print(x[y])

 Index value after ascending sort ：
[6 3 2 0 5 8 1 4 7]
 Reconstruct the original array in the sorted order ：
[1 2 3 4 5 6 7 8 9]

3.lexsort() function

• lexsort() Function to sort multiple sequences . Think of it as sorting a spreadsheet , Each column represents a sequence , When sorting, priority is given to the next column .

Solve the admission problem of students with the same grades by sorting

• A key high school , The students admitted to the elite class are admitted according to the total score . Due to the limited number of places , So when the total score is the same , Those with high math scores are preferred ; When the total score and math score are the same , Those with high English scores are preferred . Use lexsort() Function to sort student grades , The program code is as follows ：

import numpy as np
math=np.array([101,109,115,108,118,118])
en=np.array([117,105,118,108,98,109])
total=np.array([621,623,620,620,615,615])
sort_total=np.lexsort((en,math,total))
print(' The sorted index value ')
print(sort_total)
print (' Get the sorted array through the sorted index ：')
print(np.array([[en[i],math[i],total[i]] for i in sort_total]))

 The sorted index value 
[4 5 3 2 0 1]
 Get the sorted array through the sorted index ：
[[ 98 118 615]
 [109 118 615]
 [108 108 620]
 [118 115 620]
 [117 101 621]
 [105 109 623]]

8.6 Comprehensive application

8.6.1 NumPy Achieve normal distribution

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
plt.rcParams['axes.unicode_minus'] = False  #  Used to display negative sign normally 
sns.set_style('darkgrid')
n = np.random.normal(0, 0.1, 1000)   # The mean value of the generation is 0, The standard deviation is 0.1 One dimensional normal distribution sample 1000 individual 
print(n)
sns.distplot(n)                      # Histogram 
plt.show()#  Show 

8.6.2 NumPy For image gray processing

• First, let's look at the image , The image is actually composed of several pixels , Each pixel has a specific position and assigned color value , Therefore, an image constitutes a pixel matrix . for example , A gray pixel block , Pictured 8.32 Shown .
• From the picture 8.32 hear ： The data of the grayscale image is a two-dimensional array , The color value is 0~255, among 0 For the black ,255 White . from 0-255 Gradually from dark to bright . thus it can be seen , Can image grayscale processing be realized by array calculation ？
• Next , Understand a formula ,RGB Common formula for converting to gray image ：

Gray = R*0.299 + G*0.587 + G*0.114

• among ,Gray Represents the grayscale value ,R、G、B It means red 、 green 、 Blue color value ,0.299、0.587、0.114 Represents the fixed value of the grayscale formula .
• Use NumPy combination Matplotlib Realize the gray processing of the image , The program code is as follows ：

import numpy as np
import matplotlib.pyplot as plt
n1=plt.imread("flower.jpg")   # Read the picture 
plt.imshow(n1)   # The incoming array displays the corresponding color 
#n1 Is a three-dimensional array , The highest dimension is the height of the image , The next higher dimension is the width of the image , Minimum dimension [R,G,B] It's the color value 
n2=np.array([0.299,0.587,0.114])   # Fixed value of gray formula 
x=np.dot(n1,n2) # Will array n1（RGB Color value ） And an array n2（ Fixed value of gray formula ） Point multiplication is performed on each element in 
plt.imshow(x,cmap="gray")   # The incoming array displays grayscale 
plt.show()  # Display images 

• The above code , When displaying grayscale images , Need to be in imshow() Set parameters in function parameters camp=‘gray’.
• Run the program , The contrast effect is as follows ：
  
  

8.7 Summary

• Through the study of this chapter , Be able to master NumPy Common operations of , That is, the basic operations and operations from array creation to array . For data statistical analysis , That's enough ; And for AI 、 machine learning , More in-depth study is needed NumPy Related knowledge . in addition , When the amount of data is very large ,NumPy It can bring more than a hundred times the speed increase .