计数和比例的转换矩阵python [英] transition matrix for counts and proportions python
问题描述
我有一个矩阵,其中包含不同年级的成绩(行的年份和成绩的列). 我想要的是建立一个年份之间变化的过渡矩阵.
I have a matrix with the grades from a class for different years(rows for years and columns for grades). What I want is to build a transition matrix with the change between years.
例如,我想在y轴上输入t-1年,在x轴上输入t年,然后我想要一个过渡矩阵,其中包含t-1年和t年之间A级人数的差异,在t-1和t年之间达到B级,依此类推. 然后是第二个具有比例的过渡矩阵,例如: -在t-1和t年之间,A/B/C/D/F级的人增加/减少了z%.
For instance, I want year t-1 on the y-axis and year t on the x-axis and then I want a transition matrix with the difference in the number of people with grade A between year t-1 and t, grade B between year t-1 and t, and so on. And then a second transition matrix with the proportions, for example: - Between year t-1 and t there z% more/less people with grade A/B/C/D/F.
显然,最重要的部分是对角线,它代表不同年份同一等级的变化.
Obviously the moest import part is the diagonal which would represent the change for the same grade for different years.
我希望使用Python完成此操作.
I want this to be done in Python.
非常感谢,我希望一切都清楚.
Thank you very much, I hope everything is clear.
结果示例: 在此处输入图片描述
推荐答案
您可以在df.diff
中使用pandas库. numpy可以使用np.subtract.outer
生成所有可能差异的矩阵.下面是一个示例.
You can use pandas library with df.diff
. numpy can generate the matrix of all possible differences using np.subtract.outer
. below is an example.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
years = ['2015', '2016', '2017']
grades = ['A', 'B', 'C', 'D']
df = pd.DataFrame(np.random.randint(0, 10, (3, 4)), columns=grades, index=years)
print(df)
A B C D
2015 5 0 2 0
2016 7 2 0 2
2017 3 7 6 7
df_diff = df.diff(axis=0)
print(df_diff)
df_diff
中的每一行是当前行与原始df的前一行之差
each row here in df_diff
is the difference between current row and the preceding one from original df
A B C D
2015 NaN NaN NaN NaN
2016 2.0 2.0 -2.0 2.0
2017 -4.0 5.0 6.0 5.0
a = np.array([])
differences = []
for i, y in enumerate(years):
for j, g in enumerate(grades):
differences.append(y+g)
a = np.append(a, df.iloc[i,j])
df3 = pd.DataFrame(np.subtract.outer(a, a), columns=differences, index=differences)
print(df3)
2015A 2015B 2015C 2015D 2016A 2016B 2016C 2016D 2017A 2017B 2017C 2017D
2015A 0.0 5.0 3.0 5.0 -2.0 3.0 5.0 3.0 2.0 -2.0 -1.0 -2.0
2015B -5.0 0.0 -2.0 0.0 -7.0 -2.0 0.0 -2.0 -3.0 -7.0 -6.0 -7.0
2015C -3.0 2.0 0.0 2.0 -5.0 0.0 2.0 0.0 -1.0 -5.0 -4.0 -5.0
2015D -5.0 0.0 -2.0 0.0 -7.0 -2.0 0.0 -2.0 -3.0 -7.0 -6.0 -7.0
2016A 2.0 7.0 5.0 7.0 0.0 5.0 7.0 5.0 4.0 0.0 1.0 0.0
2016B -3.0 2.0 0.0 2.0 -5.0 0.0 2.0 0.0 -1.0 -5.0 -4.0 -5.0
2016C -5.0 0.0 -2.0 0.0 -7.0 -2.0 0.0 -2.0 -3.0 -7.0 -6.0 -7.0
2016D -3.0 2.0 0.0 2.0 -5.0 0.0 2.0 0.0 -1.0 -5.0 -4.0 -5.0
2017A -2.0 3.0 1.0 3.0 -4.0 1.0 3.0 1.0 0.0 -4.0 -3.0 -4.0
2017B 2.0 7.0 5.0 7.0 0.0 5.0 7.0 5.0 4.0 0.0 1.0 0.0
2017C 1.0 6.0 4.0 6.0 -1.0 4.0 6.0 4.0 3.0 -1.0 0.0 -1.0
2017D 2.0 7.0 5.0 7.0 0.0 5.0 7.0 5.0 4.0 0.0 1.0 0.0
使用matplotlib
plt.matshow(df3)
plt.colorbar()
plt.show()
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