TVDMetroLift.py

From Werner KRAUTH

#
# TVD for the Lifted Metropolis algorithm on the path graph.
#
import random
import pylab
import numpy as np
model = 'Flat'
model = 'VShape'
for n in [10, 20, 40, 80, 160, 320]:
    const = 4.0 / n ** 2
    PiStat = {}
    Table = []
    for x in range(1, n + 1):
        Table.append((x, -1))
        Table.append((x,  1))
        if model == 'Flat':
            PiStat[(x, -1)] = 1.0 / float(n) / 2.0
            PiStat[(x, +1)] = 1.0 / float(n) / 2.0
        elif model == 'VShape':
            PiStat[(x, -1)] = const * abs( (n + 1) / 2 - x) / 2.0
            PiStat[(x,  1)] = const * abs( (n + 1) / 2 - x) / 2.0
    PiStat[(0, -1)] = 0.0
    PiStat[(0,  1)] = 0.0
    PiStat[(n + 1, -1)] = 0.0
    PiStat[(n + 1,  1)] = 0.0
    PTrans   = np.zeros((2 * n, 2 * n))
    Pi = np.zeros([2 * n])
    for x in range(1, n + 1):
        for Sigma in [-1, 1]:
            i = Table.index((x, Sigma))
            Pi[i] = PiStat[(x, Sigma)]
            k = Table.index((x, -Sigma))
            if PiStat[(x + Sigma, Sigma)] > 0.0:
                j = Table.index((x + Sigma, Sigma))
                PTrans[i, j] = min(1.0, PiStat[(x + Sigma, Sigma)] / PiStat[(x, Sigma)])
                PTrans[i, k] = 1.0 - PTrans[i, j]
            else:
                PTrans[i, k] = 1.0
    PResampling = np.zeros((2 * n, 2 * n))
    for x in range(1, n + 1):
        for Sigma in [-1, 1]:
            i = Table.index((x, Sigma))
            j = Table.index((x, -Sigma))
            PResampling[i, j] = 1.0 / n
            PResampling[i, i] = 1.0 - PResampling[i,j]

    P = PTrans @ PResampling
    Pit = np.zeros([2 * n])
    Pit[0] = 1.0
    xvalues = []
    yvalues = []
    iter = 0
    while True:
        iter += 1
        Pit = np.array(Pit)
        Pit = Pit@P
        TVD = sum(np.absolute(Pi - Pit) / 2.0)
        xvalues.append(iter / float(n ** 2))
        yvalues.append(TVD)
        if TVD < 0.1: break
    pylab.plot(xvalues,yvalues, label='$n =$ '+str(n))
pylab.legend(loc='upper right')
pylab.xlabel("$t/ n$ (rescaled time) ")
pylab.ylabel("TVD")
pylab.title("TVD for the lifted Metropolis algorithm on the path graph of $n$ sites")
pylab.show()

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