generatorMatrix6.py

# 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
  for n in range(1, exactQ.shape[0] + 1):
    expMatrix = pd.DataFrame(
        np.linalg.matrix_power(
            exactQ, n
        ),
        index = exactQ.index,
        columns = exactQ.columns
    )
    expMatrix = expMatrix / math.factorial(n)
    if exactMatrix is None:
      exactMatrix = expMatrix.copy()
    else:
      exactMatrix += expMatrix
  exactMatrix = exactMatrix + I
  return exactMatrix