09: Run copied code

Exercise sheet 9/latticescalar.py

@@ -1,71 +1,85 @@
 import numpy as np
+import argparse
+import time
+import h5py
+
+starttime = time.asctime()
+
 rng = np.random.default_rng()  
-import matplotlib.pylab as plt
-%matplotlib inline
 
 def potential_v(x,lamb):
-    '''Compute the potential function V(x).'''
-    return lamb*(x*x-1)*(x*x-1)+x*x
+	'''Compute the potential function V(x).'''
+	return lamb*(x*x-1)*(x*x-1)+x*x
 
 def neighbor_sum(phi,s):
-    '''Compute the sum of the state phi on all 8 neighbors of the site s.'''
-    w = len(phi)
-    return (phi[(s[0]+1)%w,s[1],s[2],s[3]] + phi[(s[0]-1)%w,s[1],s[2],s[3]] +
-            phi[s[0],(s[1]+1)%w,s[2],s[3]] + phi[s[0],(s[1]-1)%w,s[2],s[3]] +
-            phi[s[0],s[1],(s[2]+1)%w,s[3]] + phi[s[0],s[1],(s[2]-1)%w,s[3]] +
-            phi[s[0],s[1],s[2],(s[3]+1)%w] + phi[s[0],s[1],s[2],(s[3]-1)%w] )
+	'''Compute the sum of the state phi on all 8 neighbors of the site s.'''
+	w = len(phi)
+	return (phi[(s[0]+1)%w,s[1],s[2],s[3]] + phi[(s[0]-1)%w,s[1],s[2],s[3]] +
+			phi[s[0],(s[1]+1)%w,s[2],s[3]] + phi[s[0],(s[1]-1)%w,s[2],s[3]] +
+			phi[s[0],s[1],(s[2]+1)%w,s[3]] + phi[s[0],s[1],(s[2]-1)%w,s[3]] +
+			phi[s[0],s[1],s[2],(s[3]+1)%w] + phi[s[0],s[1],s[2],(s[3]-1)%w] )
 
 def scalar_action_diff(phi,site,newphi,lamb,kappa):
-    '''Compute the change in the action when phi[site] is changed to newphi.'''
-    return (2 * kappa * neighbor_sum(phi,site) * (phi[site] - newphi) +
-            potential_v(newphi,lamb) - potential_v(phi[site],lamb) )
+	'''Compute the change in the action when phi[site] is changed to newphi.'''
+	return (2 * kappa * neighbor_sum(phi,site) * (phi[site] - newphi) +
+			potential_v(newphi,lamb) - potential_v(phi[site],lamb) )
 
 def scalar_MH_step(phi,lamb,kappa,delta):
-    '''Perform Metropolis-Hastings update on state phi with range delta.'''
-    site = tuple(rng.integers(0,len(phi),4))
-    newphi = phi[site] + rng.uniform(-delta,delta)
-    deltaS = scalar_action_diff(phi,site,newphi,lamb,kappa)
-    if deltaS < 0 or rng.uniform() < np.exp(-deltaS):
-        phi[site] = newphi
-        return True
-    return False
+	'''Perform Metropolis-Hastings update on state phi with range delta.'''
+	site = tuple(rng.integers(0,len(phi),4))
+	newphi = phi[site] + rng.uniform(-delta,delta)
+	deltaS = scalar_action_diff(phi,site,newphi,lamb,kappa)
+	if deltaS < 0 or rng.uniform() < np.exp(-deltaS):
+		phi[site] = newphi
+		return True
+	return False
 
 def run_scalar_MH(phi,lamb,kappa,delta,n):
-    '''Perform n Metropolis-Hastings updates on state phi and return number of accepted transtions.'''
-    total_accept = 0
-    for _ in range(n):
-        total_accept += scalar_MH_step(phi,lamb,kappa,delta)
-    return total_accept
+	'''Perform n Metropolis-Hastings updates on state phi and return number of accepted transtions.'''
+	total_accept = 0
+	for _ in range(n):
+		total_accept += scalar_MH_step(phi,lamb,kappa,delta)
+	return total_accept
 
 def batch_estimate(data,observable,k):
-    '''Devide data into k batches and apply the function observable to each.
-    Returns the mean and standard error.'''
-    batches = np.reshape(data,(k,-1))
-    values = np.apply_along_axis(observable, 1, batches)
-    return np.mean(values), np.std(values)/np.sqrt(k-1)
+	'''Devide data into k batches and apply the function observable to each.
+	Returns the mean and standard error.'''
+	batches = np.reshape(data,(k,-1))
+	values = np.apply_along_axis(observable, 1, batches)
+	return np.mean(values), np.std(values)/np.sqrt(k-1)
 
 lamb = 1.5
 kappas = np.linspace(0.08,0.18,11)
 width = 3
 num_sites = width**4
 delta = 1.5  # chosen to have ~ 50% acceptance
-equil_sweeps = 1000
+equil_sweeps = 10
 measure_sweeps = 2
-measurements = 2000
+measurements = 20
 
 mean_magn = []
 for kappa in kappas:
-    phi_state = np.zeros((width,width,width,width))
-    run_scalar_MH(phi_state,lamb,kappa,delta,equil_sweeps * num_sites)
-    magnetizations = np.empty(measurements)
-    for i in range(measurements):
-        run_scalar_MH(phi_state,lamb,kappa,delta,measure_sweeps * num_sites)
-        magnetizations[i] = np.mean(phi_state)
-    mean, err = batch_estimate(np.abs(magnetizations),lambda x:np.mean(x),10)
-    mean_magn.append([mean,err])
+	phi_state = np.zeros((width,width,width,width))
+	run_scalar_MH(phi_state,lamb,kappa,delta,equil_sweeps * num_sites)
+	magnetizations = np.empty(measurements)
+	for i in range(measurements):
+		run_scalar_MH(phi_state,lamb,kappa,delta,measure_sweeps * num_sites)
+		magnetizations[i] = np.mean(phi_state)
+	mean, err = batch_estimate(np.abs(magnetizations),lambda x:np.mean(x),10)
+	mean_magn.append([mean,err])
 
-plt.errorbar(kappas,[m[0] for m in mean_magn],yerr=[m[1] for m in mean_magn],fmt='-o')
-plt.xlabel(r"$\kappa$")
-plt.ylabel(r"$|m|$")
-plt.title(r"Absolute field average on $3^4$ lattice, $\lambda = 1.5$")
-plt.show()
+output_filename = 'preliminary_simulation.h5'
+with h5py.File(output_filename,'a') as f:
+	if not "mean-magn" in f:
+		dataset = f.create_dataset("mean-magn", chunks=True, data=mean_magn)
+		# store some information as metadata for the data set
+		dataset.attrs["lamb"] = lamb
+		dataset.attrs["kappas"] = kappas
+		dataset.attrs["width"] = width
+		dataset.attrs["num_sites"] = num_sites
+		dataset.attrs["delta"] = delta
+		dataset.attrs["equil_sweeps"] = equil_sweeps
+		dataset.attrs["measure_sweeps"] = measure_sweeps
+		dataset.attrs["measurements"] = measurements
+		dataset.attrs["start time"] = starttime
+		dataset.attrs["stop time"] = time.asctime()