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import numpy as np
import random as rd
class TransitionMatrixCalculator:
def __init__(self):
# Initialisation des matrices de transition pour les dés "safe", "normal" et "risky"
self.matrix_safe = np.zeros((15, 15))
self.matrix_normal = np.zeros((15, 15))
self.matrix_risky = np.zeros((15, 15))
# Probability to go from state k to k'
self.safe_dice = np.array([1/2, 1/2])
self.normal_dice = np.array([1/3, 1/3, 1/3])
self.risky_dice = np.array([1/4, 1/4, 1/4, 1/4])
def compute_transition_matrix(self, layout, circle=False):
self.matrix_safe.fill(0)
self.matrix_normal.fill(0)
self.matrix_risky.fill(0)
self._compute_safe_matrix()
self._compute_normal_matrix(layout, circle)
self._compute_risky_matrix(layout, circle)
return self.matrix_safe, self.matrix_normal, self.matrix_risky
def _compute_safe_matrix(self):
for k in range(15):
for s, p in enumerate(self.safe_dice):
if k == 9 and s == 1:
k_prime = 14
self.matrix_safe[k,k_prime] += p
elif k == 2 and s > 0:
p /= 2
k_prime = 10
self.matrix_safe[k,k_prime] += p
k_prime = 3
self.matrix_safe[k,k_prime] += p
else:
k_prime = k + s
k_prime = min(14, k_prime)
self.matrix_safe[k,k_prime] += p
return self.matrix_safe
def _compute_normal_matrix(self, layout, circle):
for k in range(15):
for s, p in enumerate(self.normal_dice):
if k == 8 and s == 2:
k_prime = 14
self.matrix_normal[k,k_prime] += p
continue
elif k == 9 and s in [1, 2]:
if not circle or s == 1:
k_prime = 14
self.matrix_normal[k,k_prime] += p
elif circle and s == 2:
k_prime = 0
self.matrix_normal[k,k_prime] += p
continue
# handle the fast lane
if k == 2 and s > 0:
p /= 2
k_prime = 10 + (s - 1) # rebalance the step before with s > 0
if layout[k_prime] in [0, 3]: # normal or prison square
self.matrix_normal[k,k_prime] += p
elif layout[k_prime] == 1: # handle type 1 trap
self.matrix_normal[k,k_prime] += p / 2
k_prime = 0
self.matrix_normal[k,k_prime] += p / 2
elif layout[k_prime] == 2: # handle type 2 trap
self.matrix_normal[k,k_prime] += p / 2
if k_prime == 10:
k_prime = 0
elif k_prime == 11:
k_prime = 1
elif k_prime == 12:
k_prime = 2
else:
k_prime = max(0, k_prime - 3)
self.matrix_normal[k,k_prime] += p / 2
k_prime = 3 + (s - 1) # rebalance the step before with s > 0
if layout[k_prime] in [0, 3]: # normal or prison square
self.matrix_normal[k,k_prime] += p
elif layout[k_prime] == 1: # handle type 1 trap
self.matrix_normal[k,k_prime] += p / 2
k_prime = 0
self.matrix_normal[k,k_prime] += p / 2
elif layout[k_prime] == 2: # handle type 2 trap
self.matrix_normal[k,k_prime] += p / 2
k_prime = max(0, k_prime - 3)
self.matrix_normal[k,k_prime] += p / 2
continue
k_prime = k + s
k_prime = k_prime % 15 if circle else min(14, k_prime) # modulo
if layout[k_prime] in [1, 2]:
p /= 2
if layout[k_prime] == 1:
k_prime = 0
self.matrix_normal[k,k_prime] += p
continue
elif layout[k_prime] == 2:
if k_prime == 10:
k_prime = 0
elif k_prime == 11:
k_prime = 1
elif k_prime == 12:
k_prime = 2
else:
k_prime = max(0, k_prime - 3)
self.matrix_normal[k,k_prime] += p
continue
self.matrix_normal[k,k_prime] += p
return self.matrix_normal
def _compute_risky_matrix(self, layout, circle):
for k in range(15):
for s, p in enumerate(self.risky_dice):
if k == 7 and s == 3:
k_prime = 14
self.matrix_risky[k,k_prime] += p
continue
elif k == 8 and s in [2, 3]:
if not circle or s == 2:
k_prime = 14
self.matrix_risky[k,k_prime] += p
elif circle:
k_prime = 0
self.matrix_risky[k,k_prime] += p
continue
elif k == 9 and s in [1, 2, 3]:
if not circle or s == 1:
k_prime = 14
self.matrix_risky[k,k_prime] += p
elif circle and s == 2:
k_prime = 0
self.matrix_risky[k,k_prime] += p
elif circle and s == 3:
k_prime = 1
if layout[k_prime] != 0:
if layout[k_prime] == 1:
k_prime = 0
self.matrix_risky[k,k_prime] += p
elif layout[k_prime] == 2:
k_prime = max(0, k_prime - 3)
self.matrix_risky[k,k_prime] += p
self.matrix_risky[k,k_prime] += p
continue
continue
if k == 2 and s > 0:
p /= 2
k_prime = 10 + (s - 1)
if layout[k_prime] == 1:
k_prime = 0
self.matrix_risky[k,k_prime] += p
elif layout[k_prime] == 2:
if k_prime == 10:
k_prime = 0
elif k_prime == 11:
k_prime = 1
elif k_prime == 12:
k_prime = 2
else:
k_prime = max(0, k_prime - 3)
self.matrix_risky[k,k_prime] += p
else:
self.matrix_risky[k,k_prime] += p
k_prime = 3 + (s - 1)
self.matrix_risky[k,k_prime] += p
continue
k_prime = k + s
k_prime = k_prime % 15 if circle else min(14, k_prime)
if layout[k_prime] in [1, 2]:
if layout[k_prime] == 1:
k_prime = 0
self.matrix_risky[k,k_prime] += p
continue
elif layout[k_prime] == 2:
if k_prime == 10:
k_prime = 0
elif k_prime == 11:
k_prime = 1
elif k_prime == 12:
k_prime = 2
else:
k_prime = max(0, k_prime - 3)
self.matrix_risky[k,k_prime] += p
continue
self.matrix_risky[k,k_prime] += p
return self.matrix_risky
def print_matrix_with_layout(self, title, matrix):
print(f"{title}:")
for i in range(matrix.shape[0]):
row_str = " | ".join(f"{matrix[i, j]:.3f}" for j in range(matrix.shape[1]))
print(row_str)
print()
# Example Usage:
layout_example = [0]*15
calculator = TransitionMatrixCalculator()
print(calculator.compute_transition_matrix(layout_example, circle=True))
#tmc = TransitionMatrixCalculator()
#tmc.tst_transition_matrix()