A.append(arr[::2, 1])
arrE.append(arr[::2, 2:] / V)
arrM.append(arr[1::2, 2:] / V)
E.append(np.mean(arrE[i], axis=1))
M.append(np.mean(arrM[i], axis=1))
errE.append(errorAll(binning, arrE[i], Binning_K[i]))
errM.append(errorAll(binning, arrM[i], Binning_K[i]))
U.append(binderpar(arrM[i]))
print "Finished calculations."
# PLOTS ###################################################################################################
print "\n==Plots=="
p.new(title="Mean energy", xlabel="Temperature", ylabel="Energy")
p.plot(T_exact, E_exact, label="for L = 4, exact")
for i in range(len(Ising_L)):
p.errorbar(T[i], E[i], yerr=errE[i], label="L=%s, MC" % Ising_L[i])
p.new(title="Mean absolute magnetization", xlabel="Temperature", ylabel=r"$\vert Magnetization \vert$")
p.plot(T_exact, M_exact, label="for L = 4, exact")
for i in range(len(Ising_L)):
p.errorbar(T[i], M[i], yerr=errM[i], label="L=%s, MC" % Ising_L[i])
# p.make(ncols=1,show=False)
for i in range(len(Ising_L)):
p.new(title="Frequency of energies (L=%s)" % Ising_L[i], xlabel="Energy", ylabel="Temperature")
temp = (T[i] * np.ones_like(arrE[i]).T).T
H, xedges, yedges = np.histogram2d(temp.flatten(), arrE[i].flatten(), bins=(len(T[i]), 100))
p.imshow(
H,
MC_M = arrayM.ravel()
MC_P = arrayP
print 'Finished metropolis calculation (acceptance=%s).' % (MC_acceptance)
MC_errmE = errorAll(binning, arrayE)
MC_errmM = errorAll(binning, arrayM)
MC_errmMabs = errorAll(binning, abs(arrayM))
print 'Finished error calculation.'
'''
=== PLOTS ===
'''
p.new(title='Mean energy', xlabel='Temperature', ylabel='Energy')
if useExact:
p.plot(T, meanE, label='exact')
if useMC:
p.errorbar(T, MC_meanE, yerr=MC_errmE, label='metropolis')
p.new(title='Mean magnetization', xlabel='Temperature', ylabel='Magnetization')
if useExact:
p.plot(T, meanM, label='exact')
if useMC:
p.errorbar(T, MC_meanM, yerr=MC_errmM, label='metropolis')
p.new(title='Mean absolute magnetization',
xlabel='Temperature',
ylabel=r'$\vert Magnetization \vert$')
if useExact:
p.plot(T, meanMabs, label='exact')
if useMC:
# open the trajectory file
vtffile = open('./plots/vmd_4_ljfluid/ljfluid.vtf', 'w')
# write the structure of the system into the file:
# N particles ("atoms") with a radius of 0.5
vtffile.write('atom 0:%s radius 0.5\n' % (N-1))
vtffile.write('pbc %s %s %s\n' % (L, L, L))
# main loop
f = compute_forces(x, L)
while t < tmax:
x, v, f = step_vv(x, v, f, dt)
t += dt
E = compute_energy(x, v, L)
print "t=%s, E=%s" % (t, E)
ts.append(t)
Es.append(E)
# write out that a new timestep starts
vtffile.write('timestep\n')
# write out the coordinates of the particles
for i in range(N):
vtffile.write("%s %s %s\n" % (x[0,i], x[1,i], x[2,i]))
vtffile.close()
p.new()
p.plot(ts, Es)
p.make(ncols=1)
U = []
for i in range(len(Ising_L)):
arr = load(Ising_L[i])
V = Ising_L[i]**2
T.append(arr[::2,0])
A.append(arr[::2,1])
arrE.append(arr[::2,2:]/V)
arrM.append(arr[1::2,2:]/V)
E.append(np.mean(arrE[i],axis=1))
M.append(np.mean(arrM[i],axis=1))
errE.append(errorAll(binning,arrE[i],Binning_K[i]))
errM.append(errorAll(binning,arrM[i],Binning_K[i]))
U.append(binderpar(arrM[i]))
print 'Finished calculations.'
# PLOTS ###################################################################################################
print '\n==Plots=='
for bm in np.linspace(-0.14,-0.07,8):
p.new(title='bm=%s'%bm,xlabel=r't*L^{-v}',ylabel=r'M*L^{bm/v}')
for i in range(len(Ising_L)):
X = (1-T[i]/Tc)*Ising_L[i]**(-v)
Y = M[i]*Ising_L[i]**(bm/v)
inx = np.abs(X)<20
p.plot(X[inx],Y[inx],'o',alpha=0.75,label='L=%s'%Ising_L[i])
p.make(ncols=2,savewindow=True)
print 'Finished plots.'
# main loop
while t < tmax:
x, v, f = step_vv(x, v, f, dt)
t += dt
traj.append(x.copy())
Es.append(compute_energy(x, v))
# write out that a new timestep starts
vtffile.write('timestep\n')
# write out the coordinates of the particles
for i in range(N):
vtffile.write("%s %s %s\n" % (x[0,i], x[1,i], x[2,i]))
vtffile.close()
traj = np.array(traj)
# ==== PLOTTING ====
# plot the trajectory
p.new(aspect='equal')
traj -= np.floor(traj/L)*L #BECAUSE OF PBC
for i in range(N):
p.plot(traj[:,0,i], traj[:,1,i], ",", label='%s'%i)
# plot the total energy
p.new()
p.plot(Es, label='energy')
p.make()
# open the trajectory file
vtffile = open('./plots/vmd_4_ljfluid/ljfluid.vtf', 'w')
# write the structure of the system into the file:
# N particles ("atoms") with a radius of 0.5
vtffile.write('atom 0:%s radius 0.5\n' % (N - 1))
vtffile.write('pbc %s %s %s\n' % (L, L, L))
# main loop
f = compute_forces(x, L)
while t < tmax:
x, v, f = step_vv(x, v, f, dt)
t += dt
E = compute_energy(x, v, L)
print "t=%s, E=%s" % (t, E)
ts.append(t)
Es.append(E)
# write out that a new timestep starts
vtffile.write('timestep\n')
# write out the coordinates of the particles
for i in range(N):
vtffile.write("%s %s %s\n" % (x[0, i], x[1, i], x[2, i]))
vtffile.close()
p.new()
p.plot(ts, Es)
p.make(ncols=1)
E = compute_energy(x, v)
print "t=%s, E=%s" % (t, E)
ts.append(t)
Es.append(E)
# write out that a new timestep starts
vtffile.write('timestep\n')
# write out the coordinates of the particles
for i in range(N):
vtffile.write("%s %s %s\n" % (x[0,i], x[1,i], x[2,i]))
# for plotting
traj = np.append(traj,[x[0:2,:] - np.floor(x[0:2,:]/L)*L],axis=0)
vtffile.close()
p.new()
for n in range(1,traj.shape[0]):
i = (traj[n-1,0,:] - traj[n,0,:])**2+(traj[n-1,1,:] - traj[n,1,:])**2 > 1
traj[n,:,i] = [None,None]
p.plot(traj[:,0,:],traj[:,1,:],'-', lw = 2, alpha=0.3)
p.plot(traj[0,0,:],traj[0,1,:],'ko', alpha=0.5 ,ms=10, mew = 4, label = 'start position')
p.plot(traj[-1,0,:],traj[-1,1,:],'wo', alpha=0.5 ,ms=10, mew = 4, label = 'end position')
p.new()
p.plot(ts, Es)
p.make(ncols=1)
MC_P = arrayP
print 'Finished metropolis calculation.'
MC_errmE = binningAll(arrayE)
MC_errmM = binningAll(arrayM)
MC_errmMabs = binningAll(abs(arrayM))
print 'Finished error calculation.'
'''
=== PLOTS ===
'''
p = Plotter(show=True, pdf=False, pgf=False, name='ising')
p.new(name='Mean energy', xlabel='Temperature', ylabel='Energy')
if useExact:
p.plot(T, meanE, label='exact')
if useMC:
p.errorbar(T, MC_meanE, yerr=MC_errmE, label='metropolis')
p.new(name='Mean magnetization', xlabel='Temperature', ylabel='Magnetization')
if useExact:
p.plot(T, meanM, label='exact')
if useMC:
p.errorbar(T, MC_meanM, yerr=MC_errmM, label='metropolis')
p.new(name='Mean absolute magnetization',
xlabel='Temperature',
ylabel=r'\vertMagnetization\vert')
if useExact:
p.plot(T, meanMabs, label='exact')
if useMC:
print "... total energy" jks0 = jke_seq(s0) print "... potential energy" jks1 = jke_seq(s1) print "... kinetic energy" jks2 = jke_seq(s2) print "... temperature" jks3 = jke_seq(s3) print "... pressure" jks4 = jke_seq(s4) """==== PLOTTING ====""" print "Plotting..." # first 1000 values of the data series s0, s1, s2, s3, s4 over time p.new(xlabel='time', ylabel='value') p.plot(s0, label='total energy') p.plot(s1, label='potential energy') p.plot(s2, label='kinetic energy') p.plot(s3, label='temperature') p.plot(s4, label='pressure') s0 = Es s1 = Epots s2 = Ekins s3 = Ts s4 = Ps # plot autocorrelation of s0, s1, s2, s3, s4 over k p.new(xlabel='k', ylabel='normalized autocorrelation') p.plot(acfn0, label='acf of total energy') p.plot(acfn1, label='acf of potential energy')
jks1 = jke_seq(s1) print "... dataset 3" jks2 = jke_seq(s2) print "... dataset 4" jks3 = jke_seq(s3) print "... dataset 5" jks4 = jke_seq(s4) """==== PLOTTING ====""" print "Plotting..." # first 1000 values of the data series s0, s1, s2, s3, s4 over time p.new(xlabel='time',ylabel='value') p.plot(s0[0:1000], label='dataset 1') p.plot(s1[0:1000], label='dataset 2') p.plot(s2[0:1000], label='dataset 3') p.plot(s3[0:1000], label='dataset 4') p.plot(s4[0:1000], label='dataset 5') # plot autocorrelation of s0, s1, s2, s3, s4 over k p.new(xlabel='k',ylabel='normalized autocorrelation') p.plot(acfn0[0:100000], label='acf of dataset 1') p.plot(acfn1[0:100000], label='acf of dataset 2') p.plot(acfn2[0:100000], label='acf of dataset 3') p.plot(acfn3[0:100000], label='acf of dataset 4') p.plot(acfn4[0:100000], label='acf of dataset 5') # plot autocorrelation via fft of s0, s1, s2, s3, s4 over k p.new(xlabel='k',ylabel='normalized autocorrelation via fft')
U = []
for i in range(len(Ising_L)):
arr = load(Ising_L[i])
V = Ising_L[i]**2
T.append(arr[::2, 0])
A.append(arr[::2, 1])
arrE.append(arr[::2, 2:] / V)
arrM.append(arr[1::2, 2:] / V)
E.append(np.mean(arrE[i], axis=1))
M.append(np.mean(arrM[i], axis=1))
errE.append(errorAll(binning, arrE[i], Binning_K[i]))
errM.append(errorAll(binning, arrM[i], Binning_K[i]))
U.append(binderpar(arrM[i]))
print 'Finished calculations.'
# PLOTS ###################################################################################################
print '\n==Plots=='
for bm in np.linspace(-0.14, -0.07, 8):
p.new(title='bm=%s' % bm, xlabel=r't*L^{-v}', ylabel=r'M*L^{bm/v}')
for i in range(len(Ising_L)):
X = (1 - T[i] / Tc) * Ising_L[i]**(-v)
Y = M[i] * Ising_L[i]**(bm / v)
inx = np.abs(X) < 20
p.plot(X[inx], Y[inx], 'o', alpha=0.75, label='L=%s' % Ising_L[i])
p.make(ncols=2, savewindow=True)
print 'Finished plots.'
for i in range(len(Ising_L)):
arr = load(Ising_L[i])
V = Ising_L[i]**2
T.append(arr[::2,0])
A.append(arr[::2,1])
arrE.append(arr[::2,2:]/V)
arrM.append(arr[1::2,2:]/V)
E.append(np.mean(arrE[i],axis=1))
M.append(np.mean(arrM[i],axis=1))
errE.append(errorAll(binning,arrE[i],Binning_K[i]))
errM.append(errorAll(binning,arrM[i],Binning_K[i]))
U.append(binderpar(arrM[i]))
print 'Finished calculations.'
# PLOTS ###################################################################################################
print '\n==Plots=='
p.new(title='Binder parameter',xlabel='Temperature',ylabel='Binder parameter')
n = np.shape(T)[0]
for i in range(n): p.plot(T[i],U[i],label='for L = %s'%Ising_L[i])
p.new(title='Binder parameter',xlabel='1/Temperature = beta*k_B',ylabel='Binder parameter')
n = np.shape(T)[0]
for i in range(n): p.plot(1./T[i],U[i],label='for L = %s'%Ising_L[i])
p.make(ncols=2)
print 'Finished plots.'
MC_errmM = calcError(MC_meanM)
MC_errmMabs = calcError(MC_meanMabs)
print "error of MC mean E:", MC_errmE
print "error of MC mean M:", MC_errmM
print "error of MC mean |M|:", MC_errmMabs
print 'Finished metropolis calculation.'
'''
=== PLOTS ===
'''
p = Plotter(show = True, pdf = False, pgf = False, name='ising')
p.new(name='Mean energy',xlabel='Temperature',ylabel='Energy')
if useExact:
p.plot(T,meanE,label='exact')
if useMC:
p.errorbar(T, MC_meanE, yerr=MC_errmE, label='metropolis')
p.new(name='Mean magnetization',xlabel='Temperature',ylabel='Magnetization')
if useExact:
p.plot(T,meanM,label='exact')
if useMC:
p.errorbar(T, MC_meanM, yerr=MC_errmM, label='metropolis')
p.new(name='Mean absolute magnetization',xlabel='Temperature',ylabel=r'\vertMagnetization\vert')
if useExact:
p.plot(T,meanMabs,label='exact')
if useMC:
p.errorbar(T, MC_meanMabs, yerr=MC_errmMabs, label='metropolis')
MC_P = arrayP
print 'Finished metropolis calculation (acceptance=%s).'%(MC_acceptance)
MC_errmE = errorAll(binning,arrayE)
MC_errmM = errorAll(binning,arrayM)
MC_errmMabs = errorAll(binning,abs(arrayM))
print 'Finished error calculation.'
'''
=== PLOTS ===
'''
p.new(title='Mean energy',xlabel='Temperature',ylabel='Energy')
if useExact:
p.plot(T,meanE,label='exact')
if useMC:
p.errorbar(T, MC_meanE, yerr=MC_errmE, label='metropolis')
p.new(title='Mean magnetization',xlabel='Temperature',ylabel='Magnetization')
if useExact:
p.plot(T,meanM,label='exact')
if useMC:
p.errorbar(T, MC_meanM, yerr=MC_errmM, label='metropolis')
p.new(title='Mean absolute magnetization',xlabel='Temperature',ylabel=r'$\vert Magnetization \vert$')
if useExact:
p.plot(T,meanMabs,label='exact')
if useMC:
p.errorbar(T, MC_meanMabs, yerr=MC_errmMabs, label='metropolis')
errM = []
U = []
for i in range(len(Ising_L)):
arr = load(Ising_L[i])
V = Ising_L[i]**2
T.append(arr[::2,0])
A.append(arr[::2,1])
arrE.append(arr[::2,2:]/V)
arrM.append(arr[1::2,2:]/V)
E.append(np.mean(arrE[i],axis=1))
M.append(np.mean(arrM[i],axis=1))
errE.append(errorAll(binning,arrE[i],Binning_K[i]))
errM.append(errorAll(binning,arrM[i],Binning_K[i]))
U.append(binderpar(arrM[i]))
print 'Finished calculations.'
# PLOTS ###################################################################################################
print '\n==Plots=='
p.new(title='magnetization',xlabel='L',ylabel='magnetization M',xscale='log',yscale='log')
func = lambda x, *p: x**(-p[0]/v)*p[1]
f = Fitter(func, [-0.25,1])
f.loadData(np.array(Ising_L), np.array(M).ravel(), scale='linear')
p.plot(Ising_L,M,'o',label='Output of the simulation')
p.plot(f.x,f.y,'-',label=r'Fitt M = L^-{bm/v)*C with ...'+'\n'+'bm = %.4f, v = %.4f, C = %.4f'%(f.params[0],v,f.params[1]))
p.make(ncols=2)
print 'Finished plots.'
# ==== DEFINITIONS ====
EPS = 1
SIG = 1
NParticles = 1000
# ==== FUNCTIONS ====
def compute_lj_potential(rij, eps=EPS, sig=SIG):
q = sig / np.linalg.norm(rij)
return 4 * eps * (q ** 12 - q ** 6)
def compute_lj_force(rij, eps=EPS, sig=SIG):
norm = np.linalg.norm(rij)
q = sig / norm
return 4 * eps * (12 * q ** 11 - 6 * q ** 5) * q / norm ** 2 * rij
# ==== CALCULATION ====
d = np.zeros((NParticles, 3))
d[:, 0] = np.linspace(0.85, 2.5, NParticles)
potential = np.array(map(compute_lj_potential, d))
force = np.array(map(compute_lj_force, d))
# ==== PLOTTING ====
p.new(title=u"LJ potential", xlabel="distance", ylabel="potential")
p.plot(d[:, 0], potential, "-", label=u"potential")
p.new(title=u"LJ force", xlabel="distance", ylabel="1st component of force")
p.plot(d[:, 0], force[:, 0], "-", label=u"force")
p.make()
Ekins = np.append(Ekins_old, Ekins, axis=0)
Ts = np.append(Ts_old, Ts, axis=0)
Ps = np.append(Ps_old, Ps, axis=0)
traj = np.append(traj_old, traj, axis=0)
datafile = open(datafilename, "w")
pickle.dump([ts, Es, Epots, Ekins, Ts, Ps, traj], datafile)
datafile.close()
"""==== PLOTTING ===="""
print "Plotting..."
# Trajectories
p.new(aspect="equal", xlabel="x-coordinate", ylabel="y-coordinate")
traj -= np.floor(traj / L) * L
p.plot([0, L, L, 0, 0], [0, 0, L, L, 0], "b-", lw=2)
p.plot(traj[-1, 0, :], traj[-1, 1, :], "wo", alpha=0.1, ms=7, mew=2)
p.plot(traj[0, 0, :], traj[0, 1, :], "+", c=[0.8, 0.8, 0.8], alpha=0.5)
i = range(traj.shape[2])
np.random.shuffle(i)
tpart = np.array(traj[:, :, i[:3]])
for n in range(1, tpart.shape[0]):
i = (tpart[n - 1, 0, :] - tpart[n, 0, :]) ** 2 + (tpart[n - 1, 1, :] - tpart[n, 1, :]) ** 2 > L * L * 0.5
tpart[n, :, i] = [None, None, None]
nmax = tpart.shape[2]
cm = cm.get_cmap("Dark2")
colors = [cm(1.0 * i / nmax) for i in range(nmax)]
for n in range(nmax):
p.plot(tpart[:, 0, n], tpart[:, 1, n], "-", c=colors[n], alpha=0.8)
p.plot(tpart[-1, 0, n], tpart[-1, 1, n], "o", c=colors[n], alpha=0.8, ms=7, mew=2)
vtffile.write('atom 0:%s radius 0.5\n' % (N-1))
# main loop
while t < tmax:
x, v, f = step_vv(x, v, f, dt)
t += dt
traj.append(x.copy())
Es.append(compute_energy(x, v))
# write out that a new timestep starts
vtffile.write('timestep\n')
# write out the coordinates of the particles
for i in range(N):
vtffile.write("%s %s %s\n" % (x[0,i], x[1,i], x[2,i]))
vtffile.close()
traj = np.array(traj)
# ==== PLOTTING ====
# plot the trajectory
p.new(aspect='equal')
for i in range(N):
p.plot(traj[:,0,i], traj[:,1,i], label='%s'%i)
# plot the total energy
p.new()
p.plot(Es, label='energy')
p.make()
meanEpots=np.mean(Epots[:10])
print "meanEpots=", meanEpots
meanEkins=np.mean(Ekins[:10])
print "meanEkins=", meanEkins
meanTs=np.mean(Ts[:10])
print "meanTs=", meanTs
meanPs=np.mean(Ps[:10])
print "meanPs=", meanPs
print "Plotting..."
# Trajectories
p.new(title='Trajectories', aspect='equal',xlabel='x-coordinate',ylabel='y-coordinate')
traj -= np.floor(traj/L)*L
p.plot([0,L,L,0,0],[0,0,L,L,0],'b-', lw=2)
p.plot(traj[-1,0,:],traj[-1,1,:],'wo', alpha=0.1 ,ms=7, mew = 2)
p.plot(traj[0,0,:],traj[0,1,:],'+', c=[0.8,0.8,0.8], alpha=0.1)
i = range(traj.shape[2])
np.random.shuffle(i)
tpart = np.array(traj[:,:,i[:3]])
for n in range(1,tpart.shape[0]):
i = (tpart[n-1,0,:] - tpart[n,0,:])**2+(tpart[n-1,1,:] - tpart[n,1,:])**2 > 50
tpart[n,:,i] = [None,None,None]
nmax = tpart.shape[2]
cm = cm.get_cmap('Dark2')
colors=[cm(1.*i/nmax) for i in range(nmax)]
for n in range(nmax):
p.plot(tpart[:,0,n],tpart[:,1,n],'-', c = colors[n], alpha=0.8)
p.plot(tpart[-1,0,n],tpart[-1,1,n],'o', c = colors[n], alpha=0.8 ,ms=7, mew = 2)
A.append(arr[::2,1])
arrE.append(arr[::2,2:]/V)
arrM.append(arr[1::2,2:]/V)
E.append(np.mean(arrE[i],axis=1))
M.append(np.mean(arrM[i],axis=1))
errE.append(errorAll(binning,arrE[i],Binning_K[i]))
errM.append(errorAll(binning,arrM[i],Binning_K[i]))
U.append(binderpar(arrM[i]))
print 'Finished calculations.'
# PLOTS ###################################################################################################
print '\n==Plots=='
p.new(title='Mean energy',xlabel='Temperature',ylabel='Energy')
p.plot(T_exact,E_exact,label='for L = 4, exact')
for i in range(len(Ising_L)): p.errorbar(T[i], E[i], yerr=errE[i], label='L=%s, MC'%Ising_L[i])
p.new(title='Mean absolute magnetization',xlabel='Temperature',ylabel=r'$\vert Magnetization \vert$')
p.plot(T_exact,M_exact,label='for L = 4, exact')
for i in range(len(Ising_L)): p.errorbar(T[i], M[i], yerr=errM[i], label='L=%s, MC'%Ising_L[i])
#p.make(ncols=1,show=False)
for i in range(len(Ising_L)):
p.new(title='Frequency of energies (L=%s)'%Ising_L[i],xlabel='Energy',ylabel='Temperature')
temp = (T[i]*np.ones_like(arrE[i]).T).T
H, xedges, yedges = np.histogram2d(temp.flatten(), arrE[i].flatten(), bins=(len(T[i]),100))
p.imshow(H, extent=[yedges[0], yedges[-1], xedges[0], xedges[-1]], interpolation='nearest',aspect='auto',origin='lower',norm=LogNorm())
p.new(title='Frequency of magnetizations (L=%s)'%Ising_L[i],xlabel='Absolute magnetization',ylabel='Temperature')
temp = (T[i]*np.ones_like(arrM[i]).T).T
print "Finished metropolis calculation."
MC_errmE = binningAll(arrayE)
MC_errmM = binningAll(arrayM)
MC_errmMabs = binningAll(abs(arrayM))
print "Finished error calculation."
"""
=== PLOTS ===
"""
p = Plotter(show=True, pdf=False, pgf=False, name="ising")
p.new(name="Mean energy", xlabel="Temperature", ylabel="Energy")
if useExact:
p.plot(T, meanE, label="exact")
if useMC:
p.errorbar(T, MC_meanE, yerr=MC_errmE, label="metropolis")
p.new(name="Mean magnetization", xlabel="Temperature", ylabel="Magnetization")
if useExact:
p.plot(T, meanM, label="exact")
if useMC:
p.errorbar(T, MC_meanM, yerr=MC_errmM, label="metropolis")
p.new(name="Mean absolute magnetization", xlabel="Temperature", ylabel=r"\vertMagnetization\vert")
if useExact:
p.plot(T, meanMabs, label="exact")
if useMC:
p.errorbar(T, MC_meanMabs, yerr=MC_errmMabs, label="metropolis")
T.append(arr[::2,0])
A.append(arr[::2,1])
arrE.append(arr[::2,2:]/V)
arrM.append(arr[1::2,2:]/V)
E.append(np.mean(arrE[i],axis=1))
M.append(np.mean(arrM[i],axis=1))
errE.append(errorAll(binning,arrE[i],Binning_K[i]))
errM.append(errorAll(binning,arrM[i],Binning_K[i]))
print 'Finished calculations.'
# PLOTS ###################################################################################################
print '\n==Plots=='
p.new(title='Mean energy',xlabel='Temperature',ylabel='Energy')
p.plot(T_exact,E_exact,label='L = 4, exact')
for i in range(len(Ising_L)): p.errorbar(T[i], E[i], yerr=errE[i], label='L=%s, MC'%Ising_L[i])
p.new(title='Mean absolute magnetization',xlabel='Temperature',ylabel=r'$\vert Magnetization \vert$')
p.plot(T_exact,M_exact,label='L = 4, exact')
for i in range(len(Ising_L)): p.errorbar(T[i], M[i], yerr=errM[i], label='L=%s, MC'%Ising_L[i])
#p.make(ncols=1,show=False)
for i in range(len(Ising_L)):
p.new(title='Frequency of energies (L=%s)'%Ising_L[i],xlabel='Energy',ylabel='Temperature')
temp = (T[i]*np.ones_like(arrE[i]).T).T
H, xedges, yedges = np.histogram2d(temp.flatten(), arrE[i].flatten(), bins=(len(T[i]),100))
p.imshow(H, extent=[yedges[0], yedges[-1], xedges[0], xedges[-1]], interpolation='nearest',aspect='auto',origin='lower',norm=LogNorm())
p.new(title='Frequency of magnetizations (L=%s)'%Ising_L[i],xlabel='Absolute magnetization',ylabel='Temperature')
temp = (T[i]*np.ones_like(arrM[i]).T).T
T.append(arr[::2, 0])
A.append(arr[::2, 1])
arrE.append(arr[::2, 2:] / V)
arrM.append(arr[1::2, 2:] / V)
E.append(np.mean(arrE[i], axis=1))
M.append(np.mean(arrM[i], axis=1))
errE.append(errorAll(binning, arrE[i], Binning_K[i]))
errM.append(errorAll(binning, arrM[i], Binning_K[i]))
print 'Finished calculations.'
# PLOTS ###################################################################################################
print '\n==Plots=='
p.new(title='Mean energy', xlabel='Temperature', ylabel='Energy')
p.plot(T_exact, E_exact, label='L = 4, exact')
for i in range(len(Ising_L)):
p.errorbar(T[i], E[i], yerr=errE[i], label='L=%s, MC' % Ising_L[i])
p.new(title='Mean absolute magnetization',
xlabel='Temperature',
ylabel=r'$\vert Magnetization \vert$')
p.plot(T_exact, M_exact, label='L = 4, exact')
for i in range(len(Ising_L)):
p.errorbar(T[i], M[i], yerr=errM[i], label='L=%s, MC' % Ising_L[i])
#p.make(ncols=1,show=False)
for i in range(len(Ising_L)):
p.new(title='Frequency of energies (L=%s)' % Ising_L[i],
xlabel='Energy',
ylabel='Temperature')
Epots = np.append(Epots_old, Epots, axis=0)
Ekins = np.append(Ekins_old, Ekins, axis=0)
Ts = np.append(Ts_old, Ts, axis=0)
Ps = np.append(Ps_old, Ps, axis=0)
traj = np.append(traj_old, traj, axis=0)
datafile = open(datafilename, 'w')
pickle.dump([ts, Es, Epots, Ekins, Ts, Ps, traj], datafile)
datafile.close()
"""==== PLOTTING ===="""
print "Plotting..."
# Trajectories
p.new(aspect='equal', xlabel='x-coordinate', ylabel='y-coordinate')
traj -= np.floor(traj / L) * L
p.plot([0, L, L, 0, 0], [0, 0, L, L, 0], 'b-', lw=2)
p.plot(traj[-1, 0, :], traj[-1, 1, :], 'wo', alpha=0.1, ms=7, mew=2)
p.plot(traj[0, 0, :], traj[0, 1, :], '+', c=[0.8, 0.8, 0.8], alpha=0.5)
i = range(traj.shape[2])
np.random.shuffle(i)
tpart = np.array(traj[:, :, i[:3]])
for n in range(1, tpart.shape[0]):
i = (tpart[n - 1, 0, :] - tpart[n, 0, :])**2 + (
tpart[n - 1, 1, :] - tpart[n, 1, :])**2 > L * L * 0.5
tpart[n, :, i] = [None, None, None]
nmax = tpart.shape[2]
cm = cm.get_cmap('Dark2')
colors = [cm(1. * i / nmax) for i in range(nmax)]
for n in range(nmax):
p.plot(tpart[:, 0, n], tpart[:, 1, n], '-', c=colors[n], alpha=0.8)
# ==== DEFINITIONS ====
EPS = 1
SIG = 1
NParticles = 1000
# ==== FUNCTIONS ====
def compute_lj_potential(rij, eps=EPS, sig=SIG):
q = sig / np.linalg.norm(rij)
return 4 * eps * (q**12 - q**6)
def compute_lj_force(rij, eps=EPS, sig=SIG):
norm = np.linalg.norm(rij)
q = sig / norm
return 4 * eps * (12 * q**11 - 6 * q**5) * q / norm**2 * rij
# ==== CALCULATION ====
d = np.zeros((NParticles, 3))
d[:, 0] = np.linspace(0.85, 2.5, NParticles)
potential = np.array(map(compute_lj_potential, d))
force = np.array(map(compute_lj_force, d))
# ==== PLOTTING ====
p.new(title=u'LJ potential', xlabel='distance', ylabel='potential')
p.plot(d[:, 0], potential, '-', label=u'potential')
p.new(title=u'LJ force', xlabel='distance', ylabel='1st component of force')
p.plot(d[:, 0], force[:, 0], '-', label=u'force')
p.make()
E = compute_energy(x, v)
print "t=%s, E=%s" % (t, E)
ts.append(t)
Es.append(E)
# write out that a new timestep starts
vtffile.write("timestep\n")
# write out the coordinates of the particles
for i in range(N):
vtffile.write("%s %s %s\n" % (x[0, i], x[1, i], x[2, i]))
# for plotting
traj = np.append(traj, [x[0:2, :] - np.floor(x[0:2, :] / L) * L], axis=0)
vtffile.close()
p.new()
for n in range(1, traj.shape[0]):
i = (traj[n - 1, 0, :] - traj[n, 0, :]) ** 2 + (traj[n - 1, 1, :] - traj[n, 1, :]) ** 2 > 1
traj[n, :, i] = [None, None]
p.plot(traj[:, 0, :], traj[:, 1, :], "-", lw=2, alpha=0.3)
p.plot(traj[0, 0, :], traj[0, 1, :], "ko", alpha=0.5, ms=10, mew=4, label="start position")
p.plot(traj[-1, 0, :], traj[-1, 1, :], "wo", alpha=0.5, ms=10, mew=4, label="end position")
p.new()
p.plot(ts, Es)
p.make(ncols=1)
print "... potential energy" jks1 = jke_seq(s1) print "... kinetic energy" jks2 = jke_seq(s2) print "... temperature" jks3 = jke_seq(s3) print "... pressure" jks4 = jke_seq(s4) """==== PLOTTING ====""" print "Plotting..." # first 1000 values of the data series s0, s1, s2, s3, s4 over time p.new(xlabel='time',ylabel='value') p.plot(s0, label='total energy') p.plot(s1, label='potential energy') p.plot(s2, label='kinetic energy') p.plot(s3, label='temperature') p.plot(s4, label='pressure') s0 = Es s1 = Epots s2 = Ekins s3 = Ts s4 = Ps # plot autocorrelation of s0, s1, s2, s3, s4 over k p.new(xlabel='k',ylabel='normalized autocorrelation')
