# TVDMetroPath.py

```#
# TVD for the 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)
#
#   flat stationary probability distribution.
#
if model == 'Flat':
PiStat[x] = 1.0 / float(n)
elif model == 'VShape':
PiStat[x] = const * abs( (n + 1) / 2 - x)
PiStat[0] = 0.0
PiStat[n + 1] = 0.0
PTrans   = np.eye(n)
Pi = np.zeros([n])
for x in range(1, n + 1):
i = Table.index(x)
Pi[i] = PiStat[x]
for Dir in [-1, 1]:
if PiStat[x + Dir] > 0:
j = Table.index(x + Dir)
PTrans[i, j] = min(1.0, PiStat[x + Dir] / PiStat[x]) / 2.0
PTrans[i, i] -= PTrans[i, j]
Pit = np.zeros([n])
Pit[0] = 1.0
xvalues = []
yvalues = []
iter = 0
while True:
iter += 1
Pit = np.array(Pit)
Pit = Pit@PTrans
TVD = sum(np.absolute(Pi - Pit) / 2.0)
xvalues.append(iter / float(n ** 2 * np.log(n)))
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^2\$ (rescaled time) ")
pylab.ylabel("TVD")
pylab.title("TVD for the Metropolis algorithm on the path graph of \$n\$ sites")
pylab.show()
```