49 lines
1.5 KiB
Python
49 lines
1.5 KiB
Python
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import numpy as np
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import numpy.linalg as la
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import matplotlib.pyplot as plt
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# Attack speed independent. Fast speed losses not accounted for
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mana_consumption = 3
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mana_steal = 10 # /3s
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mana_regen = 0 # /5s
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#mana_steal = 5 # /3s
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#mana_regen = 5 # /5s
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natural_regen = 1
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weight_natural = 8/15 # 4/5 * 2/3
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weight_mr = 2/15 # 1/5 * 2/3
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weight_ms = 4/15 # 4/5 * 1/3
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weight_mr_ms = 1/15 # 1/5 * 1/3
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MAX_MANA = 20
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transition_matrix = np.zeros((MAX_MANA, MAX_MANA))
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for i in range(MAX_MANA):
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natural_state = max(0, i - mana_consumption + natural_regen)
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mr_state = min(19, natural_state + mana_regen)
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ms_state = min(19, natural_state + mana_steal)
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mr_ms_state = min(19, natural_state + mana_regen + mana_steal)
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transition_matrix[natural_state, i] = weight_natural
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transition_matrix[mr_state, i] += weight_mr
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transition_matrix[ms_state, i] += weight_ms
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transition_matrix[mr_ms_state, i] += weight_mr_ms
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eigval, eigvec = la.eig(transition_matrix)
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print(eigval)
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eps = 0.00001
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ind = np.argwhere(abs(eigval - 1) < eps)
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steady_state = abs(eigvec[:, ind])
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steady_state /= np.sum(steady_state)
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cumulative = np.cumsum(steady_state)
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print("mana\tprob cumsum")
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for i in range(MAX_MANA):
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print(f"{i+1}\t{cumulative[i]}")
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plt.figure()
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plt.scatter(range(len(steady_state)), steady_state)
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plt.xlim(0, 19)
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plt.ylim(0, 0.2)
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plt.xlabel("Mana Value")
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plt.ylabel("Probability at t=infty")
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plt.title(f"Build={mana_regen}mr,{mana_steal}ms,{mana_consumption}mana/sec")
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plt.show()
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