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⚡️ Speed up function KMR_Markov_matrix_sequential by 194% #16

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⚡️ Speed up function KMR_Markov_matrix_sequential by 194% #16

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49 changes: 37 additions & 12 deletions quantecon/markov/tests/test_core.py
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Original file line number Diff line number Diff line change
Expand Up @@ -47,19 +47,44 @@ def KMR_Markov_matrix_sequential(N, p, epsilon):
References:
KMRMarkovMatrixSequential is contributed from https://github.com/oyamad
"""
# Precompute constants
half_epsilon = 0.5 * epsilon
one_minus_epsilon = 1.0 - epsilon
N_float = float(N)
N_minus_1 = N - 1

P = np.zeros((N+1, N+1), dtype=float)
P[0, 0], P[0, 1] = 1 - epsilon * (1/2), epsilon * (1/2)
for n in range(1, N):
P[n, n-1] = \
(n/N) * (epsilon * (1/2) +
(1 - epsilon) * (((n-1)/(N-1) < p) + ((n-1)/(N-1) == p) * (1/2))
)
P[n, n+1] = \
((N-n)/N) * (epsilon * (1/2) +
(1 - epsilon) * ((n/(N-1) > p) + (n/(N-1) == p) * (1/2))
)
P[n, n] = 1 - P[n, n-1] - P[n, n+1]
P[N, N-1], P[N, N] = epsilon * (1/2), 1 - epsilon * (1/2)
P[0, 0] = 1.0 - half_epsilon
P[0, 1] = half_epsilon

if N_minus_1 > 0:
idx = np.arange(1, N)
idx_float = idx.astype(float)
idx_minus1_float = (idx - 1).astype(float)

# (n-1)/(N-1)
n1_frac = idx_minus1_float / N_minus_1
cond_left = n1_frac < p
cond_eq_left = n1_frac == p

left_term = cond_left.astype(float) + cond_eq_left.astype(float) * 0.5
P_left = (idx_float / N_float) * (half_epsilon + one_minus_epsilon * left_term)

# n/(N-1)
n_frac = idx_float / N_minus_1
cond_right = n_frac > p
cond_eq_right = n_frac == p

right_term = cond_right.astype(float) + cond_eq_right.astype(float) * 0.5
P_right = ((N_float - idx_float) / N_float) * (half_epsilon + one_minus_epsilon * right_term)

P[idx, idx - 1] = P_left
P[idx, idx + 1] = P_right
P[idx, idx] = 1.0 - P_left - P_right

# Final row assignment
P[N, N-1] = half_epsilon
P[N, N] = 1.0 - half_epsilon
return P


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