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python如何实现MK突变检验方法,代码复制修改可用

2023-05-19 09:05

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需求

已知年份和历年最大冻土深度，计算最大冻土深度Mk突变检验。

原理

请添加图片描述

工具和语言

python
jupter notebook

代码过程

定义函数

def mktest(inputdata):
    import numpy as np
    inputdata = np.array(inputdata)
    n=inputdata.shape[0]
    Sk = np.zeros(n)
    UFk = np.zeros(n)
    r = 0
    for i in range(1,n):
        for j in range(i):
            if inputdata[i] > inputdata[j]:
                r = r+1
        Sk[i] = r
        E = (i+1)*i/4
        Var = (i+1)*i*(2*(i+1)+5)/72
        UFk[i] = (Sk[i] - E)/np.sqrt(Var)
    Sk2 = np.zeros(n)
    UBk = np.zeros(n)
    inputdataT = inputdata[::-1]
    r = 0
    for i in range(1,n):
        for j in range(i):
            if inputdataT[i] > inputdataT[j]:
                r = r+1
        Sk2[i] = r
        E = (i+1)*(i/4)
        Var = (i+1)*i*(2*(i+1)+5)/72
        UBk[i] = -(Sk2[i] - E)/np.sqrt(Var)
    UBk2 = UBk[::-1]
    return UFk, UBk2
定义函数计算变量
```python
def mktest(inputdata):
    import numpy as np
    inputdata = np.array(inputdata)
    n=inputdata.shape[0]
    s              =  0
    Sk = np.zeros(n)
    UFk = np.zeros(n)
    for i in range(1,n):
        for j in range(i):
            if inputdata[i] > inputdata[j]:
                s = s+1
            else:
                s = s+0
        Sk[i] = s
        E = (i+1)*(i/4)
        Var = (i+1)*i*(2*(i+1)+5)/72
        UFk[i] = (Sk[i] - E)/np.sqrt(Var)
    Sk2 = np.zeros(n)
    UBk = np.zeros(n)
    s  =  0
    inputdataT = inputdata[::-1]
    for i in range(1,n):
        for j in range(i):
            if inputdataT[i] > inputdataT[j]:
                s = s+1
            else:
                s = s+0
        Sk2[i] = s
        E = (i+1)*(i/4)
        Var = (i+1)*i*(2*(i+1)+5)/72
        UBk[i] = -(Sk2[i] - E)/np.sqrt(Var)
    UBk2 = UBk[::-1]
    return UFk, UBk2

导入变量，形成突变检验图

import matplotlib.dates as mdates    #處理日期
import matplotlib.pyplot as plt
import numpy as np
from pylab import mpl
from matplotlib.pyplot import MultipleLocator
mpl.rcParams['font.sans-serif'] = ['SimHei'] #防止标题出现乱码。
plt.rcParams['axes.unicode_minus'] = False   #防止出现图上的负数为方框。
# y值和x值   分别输入六个站点的最大冻土深度值，将值以列表的方式导入
a = [150,150,114,109,96,95,83,76,109,80,115,80,94,86,133,91,110,116,114,128,172,172,
162,121,175,151,110,92,116,156,134,110,89,97,109,157,153,105,76,87,122,78,97,93,141,162,
123,133,161,128,138,104,133,102,140,109,118,86,126,92,121,149,116]  #这个部分值可以替换成为要检验的气温、水文等值
x_values=list(range(1961,2022))
uf,ub = mktest(a)
plt.figure(figsize=(8,4))   #图片的大小
plt.plot(uf,'r',label='UFk')
plt.plot(ub,'b',label='UBk')
plt.xticks([0,5,10,15,20,25,30,35,40,45,50,55,60],['1960','1965','1970','1975','1980','1985','1990','1995','2000','2005','2010','2015','2020',])
#将默认的x轴数值替换为年份的X轴，默认是0-61，一共62个值，代表X轴内容。
# 0.01显著性检验
plt.legend()
plt.axhline(1.96)
plt.axhline(-1.96)
#设置图片的标签（标题）
plt.title("富蕴点最大冻土深度突变检验结果")#x轴上的名字
plt.xlabel("年份（1960年-2022年）")#x轴上的名字
plt.ylabel("突变值波动参数")#y轴上的名字
plt.grid() #形成网格线输出
x_major_locator=MultipleLocator(5)
plt.show()