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import numpy as np
from mc_compute_stationary_mpmath import mc_compute_stationary_mpmath
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A = [[.4, .6], [.2, .8]]
mc_compute_stationary_mpmath(A) # default precision = 17
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type(_[0][0])
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mc_compute_stationary_mpmath(A, precision=100)
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B = np.identity(2)
mc_compute_stationary_mpmath(B)
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C = np.identity(3)
mc_compute_stationary_mpmath(C)
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Let us try matrices generated by the KMR model where action 1 is risk-dominant, so that the theory says that the unique stationary distribution is close to the distribution that concentrates on the state $N$ (where the state is the number of players playing action 1).
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from test_mc_compute_stationary import KMR_Markov_matrix_sequential, KMR_Markov_matrix_simultaneous
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P = KMR_Markov_matrix_sequential(N=3, p=1./3, epsilon=1e-14)
eigvecs_P = mc_compute_stationary_mpmath(P)
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eigvecs_P
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[np.dot(vec, P) for vec in eigvecs_P]
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Q = KMR_Markov_matrix_simultaneous(N=5, p=1./3, epsilon=1e-15)
mc_compute_stationary_mpmath(Q)
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mc_compute_stationary_mpmath(Q, precision=100)
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R = KMR_Markov_matrix_sequential(N=27, p=1./3, epsilon=1e-2)
eigvecs_R = mc_compute_stationary_mpmath(R)
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eigvecs_R
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[np.dot(vec, R) for vec in eigvecs_R]
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mc_compute_stationary_mpmath uses mpmath.eig from mpmath.
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import sympy.mpmath as mp
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mp.__version__
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The working precision is controlled by a context object called mp.
See: Setting the precision
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print mp.mp
The routine eig solves the eigenvalue problem.
See: The eigenvalue problem
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E_A, EL_A = mp.eig(mp.matrix(A), left=True, right=False)
E_A, EL_A[0, :]/sum(EL_A[0, :]), EL_A[1, :]/sum(EL_A[1, :])
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Let us see what happens if we increase the precision.
See: Setting the precision
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mp.mp.dps += 15
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E_A, EL_A = mp.eig(mp.matrix(A), left=True, right=False)
E_A, EL_A[0, :]/sum(EL_A[0, :]), EL_A[1, :]/sum(EL_A[1, :])
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Arithemtic seems to be more accurate if the mpf values are created from strings.
See: Providing correct input
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AA = np.array(A).astype('str')
AA
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E_AA, EL_AA = mp.eig(mp.matrix(AA), left=True, right=False)
E_AA, EL_AA
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EL_AA[1, :]/sum(EL_AA[1, :])
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KMR Markov matrices:
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E_P, EL_P = mp.eig(mp.matrix(P), left=True, right=False)
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E_P, EL_P
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E_Q, EL_Q = mp.eig(mp.matrix(Q), left=True, right=False)
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E_Q
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E_R, EL_R = mp.eig(mp.matrix(R), left=True, right=False)
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E_R
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