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# Exact generator
exactMatrix  = ExactMatrix(exactGenerator)

# Show matrix
plotMatrix(exactMatrix, 'Exact transition matrix', 'Percent')

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# Define exact transition matrix
def ExactMatrix(exactQ):
  # Define identity matrix
  I = pd.DataFrame(
      np.identity(exactQ.shape[0]),
      index = exactQ.index,
      columns = exactQ.columns
  )
  # Exact transition matrix
  exactMatrix = None

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# Exact generator
exactGenerator  = ExactGenerator(generatorMatrix)

# Show matrix
plotMatrix(exactGenerator, 'Exact generator')

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# Define exact generator function
def ExactGenerator(Q):
  # Define Gi and Bi
  # Gi
  GiMatrix = Q.copy()
  for i in range(Q.shape[1]):
    for j in range(Q.shape[0]):
      if i == j: #Diagonal matrix
        GiMatrix.iloc[i, j] = abs(GiMatrix.iloc[i, j])
      else: #Non-Diagonal matrix

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# Generator matrix
generatorMatrix  = GeneratorMatrix(matrix)

# Show matrix
plotMatrix(generatorMatrix, 'Generator matrix')

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# Define generator matrix function
def GeneratorMatrix(P):
  # Define identity matrix
  I = pd.DataFrame(
      np.identity(P.shape[0]),
      index = P.index,
      columns = P.columns
  )
  # Generator matrix
  generatedMatrix = None

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# Set auto reload
%reload_ext autoreload
%autoreload 2

# Import libraries
import warnings
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

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# Export
pd.concat(
    [
        pd.DataFrame(X, columns = ['X1']),
        pd.DataFrame(y, columns = ['y'])
    ],
    axis = 1
).to_csv(
    'Theil-Sen_Data.csv',
    index = 0

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# Compare
plt.figure(figsize = (10, 6))
plt.scatter(
    X,
    y,
    c = 'teal'
)
plt.plot(
    X,
    OLS.predict(X),

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# Theil-Sen
TS = TheilSenRegressor()
TS.fit(X, y.ravel())

# Plot
plt.figure(figsize = (10, 6))
plt.scatter(
    X,
    y,
    c = 'teal'