Markov discrete Algo | Python Fiddle

'''
From Algorithms and Computations by Werner Krauth
code the following algorithms in python

Markov discrete-pebble
procedure markov-discrete-pebble
input k (position of pebble)
n ← Nran (1, 4)
if (Nbr(n, k) 6 = 0) then (see Table 1.3)
k ← Nbr(n, k)
output k (next position)
——
Algorithm 1.6 markov-discrete-pebble. Discrete Markov-chain
Monte Carlo algorithm for the pebble game.

procedure transfer-matrix
input {p(a → b)} (matrix in eqn (1.14))
input {i(1), . . . , i(9)} for a = 1, . . . , 9 do 


i+1(a) ← 0
for b = 1, . . . , 9 do
i+1(a) ← i+1(a) + p(b → a)i(b)
output {i+1(1), . . . , i+1(9)} ——
Algorithm 1.7 transfer-matrix. Computing pebble-game probabilities
at iteration i + 1 from the probabilities at iteration i.

procedure markov-two-site
input k (either 0 or 1)
if (k = 0) l ← 1
if (k = 1) l ← 0
 ← (l)/(k)
if (ran (0, 1) < ) k ← l
output k (next site)
——
Algorithm 1.8 markov-two-site. Sampling sites 0 and 1 with station-
ary probabilities (0) and (1) by the Metropolis algorithm.

'''

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