causality_for_spaceweather/notebooks/_build/jupyter_execute/chapter1_it/jidt.py

#!/usr/bin/env python
# coding: utf-8

# # jidt 基本使用教程

# In[1]:


get_ipython().run_line_magic('reload_ext', 'autoreload')
get_ipython().run_line_magic('autoreload', '2')
get_ipython().run_line_magic('matplotlib', 'inline')


# 导入基本库

# In[2]:


import os, sys
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from pathlib import Path
Path.ls = lambda x: list(x.iterdir())
from tqdm import tqdm


# 打开java虚拟机

# In[3]:


import jpype
from jpype import *
try :
    jarLocation = "/home/fsf/software/inforDynamics-dist-1.5/infodynamics.jar"
    jpype.startJVM(jpype.getDefaultJVMPath(), "-ea", "-Djava.class.path=" + jarLocation)
except:
    print("JVM  has already started !")


# 添加jidt源码路径

# In[4]:


sys.path.append('../../srcs')


# ## 加载数据

# In[5]:


from jidt.data import example1, example2


# In[6]:


x1,y1 = example1(length=3600,delay=10)
x2,y2 = example2(length=3600,noise_level=[0.1,0.15])


# In[7]:


fig, axs = plt.subplots(2,1,figsize=(12,3))
axs[0].plot(x1-20,label='x',color='r')
axs[0].plot(y1,label='y',color='b')
axs[0].legend()
axs[1].plot(x2,label='sin',color='blue')
axs[1].plot(y2,label='cos',color='red')
axs[1].legend()
plt.tight_layout()
plt.show()


# ## 计算转移熵

# In[8]:


from jidt.TransferEntropyCalculatorBinned import TransferEntropyCalculatorBinned
from jidt.TransferEntropyCalculatorGaussian import TransferEntropyCalculatorGaussian
from jidt.TransferEntropyCalculatorKraskov import TransferEntropyCalculatorKraskov
from jidt.TransferEntropyCalculatorKernel import TransferEntropyCalculatorKernel


# In[9]:


estimator_ksg = TransferEntropyCalculatorKraskov(ALG_NUM=2)
estimator_bin = TransferEntropyCalculatorBinned(base=2)
estimator_gauss = TransferEntropyCalculatorGaussian()
estimator_kernel = TransferEntropyCalculatorKernel()


# In[10]:


estimator_ksg(x1,y1,tau=3), estimator_bin(x1,y1,tau=1), estimator_gauss(x1,y1,tau=1), estimator_kernel(x1,y1,tau=1)


# 计算重要性

# In[11]:


test_sig = TransferEntropyCalculatorKraskov(cal_sig=True,sig_num=10)


# In[12]:


test_sig(x1,y1,tau=10)


# In[13]:


value, [mean, std, pvalue] = test_sig(x1,y1,tau=1)


# 这里的pvalue应该是越小越说明计算得到的转移熵比较合理，因为假设的是他们之间不存在转移熵，或者说是`null hypothesis`，
# 
# p-value的定义：P值就是当原假设为真时所得到的样本观察结果或更极端结果出现的概率。
# 
# 如果p值越小，说明原假设情况的发生的概率很小，而如果出现了，根据小概率原理，我们就有理由拒绝原假设，P值越小，我们拒绝原假设的理由约充分。
# 
# 总之，P值越小，表明结果越显著。小的pvalue说明一件事，不是小概率事件发生了，就是你的原假设时错误的。

# 比较ksg算法的两个不同形式：

# In[14]:


es1 = TransferEntropyCalculatorKraskov(ALG_NUM=1)
es2 = TransferEntropyCalculatorKraskov(ALG_NUM=2)


# In[15]:


es1(x1,y1,10),es2(x1,y1,10)


# In[16]:


fig, ax = plt.subplots(1,1,figsize=(6,2))
TE_XY = []
TE_YX = []
taus = list(range(1,101))
for tau in tqdm(taus):
    TE_XY.append(estimator_ksg(x1,y1,tau))
    TE_YX.append(estimator_ksg(y1,x1,tau))
ax.plot(taus, TE_XY, label='X->Y', color='blue')
ax.plot(taus, TE_YX, label='Y->X', color='red')
ax.set_xlabel(r'Time Delay : $\tau$')
ax.set_ylabel('Transfer Entropy')
ax.legend()
plt.show()


# In[17]:


fig, ax = plt.subplots(1,1,figsize=(6,2))
TE_XY = []
TE_YX = []
taus = list(range(1,361))
for tau in tqdm(taus):
    TE_XY.append(estimator_ksg(x2,y2,tau))
    TE_YX.append(estimator_ksg(y2,x2,tau))
ax.plot(taus, TE_XY, label='X->Y', color='blue')
ax.plot(taus, TE_YX, label='Y->X', color='red')
ax.set_xlabel(r'Time Delay : $\tau$')
ax.set_ylabel('Transfer Entropy')
ax.legend()
plt.show()


# In[18]:


fig, ax = plt.subplots(1,1,figsize=(6,2))
TE_XY = []
TE_YX = []
taus = list(range(1,361))
for tau in tqdm(taus):
    TE_XY.append(estimator_bin(x2,y2,tau))
    TE_YX.append(estimator_bin(y2,x2,tau))
ax.plot(taus, TE_XY, label='X->Y', color='blue')
ax.plot(taus, TE_YX, label='Y->X', color='red')
ax.set_xlabel(r'Time Delay : $\tau$')
ax.set_ylabel('Transfer Entropy')
ax.legend()
plt.show()


# 不同estimator得到的结果并不一样

# ## 计算互信息

#