# TVDTemperingLift.py

(Difference between revisions)
 Revision as of 10:26, 8 September 2022Werner (Talk | contribs)← Previous diff Revision as of 08:31, 10 September 2022Werner (Talk | contribs) Next diff → Line 44: Line 44: else: else: PTrans[i, k] = 1.0 PTrans[i, k] = 1.0 - + PReplica = np.zeros((4 * n, 4 * n)) PReplica = np.zeros((4 * n, 4 * n)) for x in range(1, n + 1): for x in range(1, n + 1): Line 65: Line 65: PResampling[k, l] = 1.0 / (4.0 * n) PResampling[k, l] = 1.0 / (4.0 * n) PResampling[k, k] = 1 - 1. / (4.0 * n) PResampling[k, k] = 1 - 1. / (4.0 * n) - + P = PTrans @ PReplica @ PResampling P = PTrans @ PReplica @ PResampling Pit = np.zeros([4 * n]) Pit = np.zeros([4 * n])

## Revision as of 08:31, 10 September 2022

```import random
import pylab
import numpy as np
for n in [10, 20, 40, 80, 160, 320]:
ReplicaChange = 0.1
const = 4.0 / n ** 2
PiStat = {}
Table = []

for x in range(1, n + 1):
Table.append((x, -1, 0))
Table.append((x,  1, 0))
Table.append((x, -1, 1))
Table.append((x,  1, 1))
#
#   factor of 1/4 because the total must be normalized, with two liftings and
#   two replicas
#
PiStat[(x, -1,  0)] = 1.0 / float(n) / 4.0
PiStat[(x,  1,  0)] = 1.0 / float(n) / 4.0
PiStat[(x, -1, 1)] = const * abs( (n + 1) / 2 - x) / 4.0
PiStat[(x,  1, 1)] = const * abs( (n + 1) / 2 - x) / 4.0
PiStat[(0, -1, 0)] = 0.0
PiStat[(0,  1, 0)] = 0.0
PiStat[(0, -1, 1)] = 0.0
PiStat[(0,  1, 1)] = 0.0
PiStat[(n + 1, -1,  0)] = 0.0
PiStat[(n + 1,  1,  0)] = 0.0
PiStat[(n + 1, -1, 1)] = 0.0
PiStat[(n + 1,  1, 1)] = 0.0
Position = (1,  1, 0)
PTrans   = np.zeros((4 * n, 4 * n))
Pi = np.zeros([4 * n])
for x in range(1, n + 1):
for Dir in [-1, 1]:
for Rep in [0, 1]:
i = Table.index((x, Dir, Rep))
Pi[i] = PiStat[(x, Dir, Rep)]
k = Table.index((x, -Dir, Rep))
if PiStat[(x + Dir, Dir, Rep)] > 0.0:
j = Table.index((x + Dir, Dir, Rep))
PTrans[i, j] = min(1.0, PiStat[(x + Dir, Dir,  Rep)] / PiStat[(x, Dir, Rep)])
PTrans[i, k] = 1.0 - PTrans[i, j]
else:
PTrans[i, k] = 1.0

PReplica = np.zeros((4 * n, 4 * n))
for x in range(1, n + 1):
for Dir in [-1, 1]:
i = Table.index((x, Dir, 0))
j = Table.index((x, Dir, 1))
PReplica[i, j] = ReplicaChange * min(1.0, PiStat[(x, Dir, 1)] / PiStat[(x, Dir, 0)])
PReplica[i, i] = 1.0 - PReplica[i, j]
PReplica[j, i] = ReplicaChange * min(1.0, PiStat[(x, Dir,  0)] / PiStat[(x, Dir, 1)])
PReplica[j, j] = 1.0 - PReplica[j, i]
PResampling = np.zeros((4 * n, 4 * n))
for x in range(1, n + 1):
for Dir in [-1, 1]:
i = Table.index((x, Dir, 0))
j = Table.index((x, -Dir, 0))
k = Table.index((x, Dir, 1))
l = Table.index((x, -Dir, 1))
PResampling[i, j] = 1.0 / (4.0 * n)
PResampling[i, i] =  1 - 1. / (4.0 * n)
PResampling[k, l] = 1.0 / (4.0 * n)
PResampling[k, k] =  1 - 1. / (4.0 * n)

P = PTrans @ PReplica @ PResampling
Pit = np.zeros([4 * n])
Pit = 1.0
xvalues = []
yvalues = []
iter = 0
while True:
iter += 1
Pit = Pit @ P
TVD = sum(np.absolute(Pi - Pit) / 2.0)
xvalues.append(iter / float(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\$ (rescaled time) ")
pylab.ylabel("TVD")
pylab.title("TVD lift tempering on the path graph of \$n\$ sites")
pylab.show()
```