def mean_u_err(ww, ff, N, method, golden_u):
toterr = 0.0
numseeds = 0
for seed in seeds:
t_u_cv_s_method = readandcompute.t_u_cv_s(ww, ff, N, method, seed)
if t_u_cv_s_method != None:
du = abs((t_u_cv_s_method[1] -
golden_u)[t_u_cv_s_method[0] > Tmax]).max()
lw = 0.01
if seed == 0:
plt.plot(t_u_cv_s_method[0],
(t_u_cv_s_method[1] - golden_u) / N,
styles.plot(method),
label=styles.title(method),
linewidth=lw)
else:
plt.plot(t_u_cv_s_method[0],
(t_u_cv_s_method[1] - golden_u) / N,
styles.plot(method),
linewidth=lw)
toterr += du
numseeds += 1
if numseeds > 0:
return toterr / numseeds / N
return None
def mean_u_err(ww, ff, N, method, golden_u):
toterr = 0.0
numseeds = 0
for seed in seeds:
t_u_cv_s_method = readandcompute.T_u_cv_s_minT(ww, ff, N, method, seed)
if t_u_cv_s_method != None:
du = abs((t_u_cv_s_method[1]-golden_u)[t_u_cv_s_method[0] > Tmax]).max()
lw = 0.01
if seed == 0:
plt.plot(t_u_cv_s_method[0], (t_u_cv_s_method[1]-golden_u)/N,
styles.plot(method), label=styles.title(method), linewidth=lw)
else:
plt.plot(t_u_cv_s_method[0], (t_u_cv_s_method[1]-golden_u)/N,
styles.plot(method), linewidth=lw)
toterr += du
numseeds += 1
if numseeds > 0:
return toterr/numseeds/N
return None
for method in [golden]+methods:
U[method] = numpy.zeros(array_len)
CV[method] = numpy.zeros(array_len)
S[method] = numpy.zeros(array_len)
for seed in seeds:
u_cv_s = readandcompute.u_cv_s(ww, ff, N, method, seed)
U[method] += u_cv_s[0] # internal energy
CV[method] += u_cv_s[1] # heat capacity
S[method] += u_cv_s[2] # entropy
U[method] /= len(seeds)
CV[method] /= len(seeds)
S[method] /= len(seeds)
plt.figure('u')
plt.plot(T_range,U[method]/N, styles.plot(method), label=styles.title(method))
if method != 'wang_landau':
plt.figure('hc')
plt.plot(T_range,CV[method]/N, styles.plot(method), label=styles.title(method))
plt.figure('s')
plt.plot(T_range,S[method]/N, styles.plot(method), label=styles.title(method))
methods.remove('wang_landau')
for method in methods:
plt.figure('u_err')
plt.plot(T_range,(U[method]-U[golden])/N, styles.plot(method),
label=styles.title(method))
if method not in cv_errors:
cv_errors[method] = numpy.array([[N, dcv]])
else:
cv_errors[method] = numpy.vstack([u_errors[method], [N, dcv]])
ds = abs(u_cv_s_method[2]-u_cv_s[2]).max()
if method not in s_errors:
s_errors[method] = numpy.array([[N, ds]])
else:
s_errors[method] = numpy.vstack([u_errors[method], [N, ds]])
min_T = 0.2 # FIXME maybe shouldn't hardcode this?
plt.figure()
for method in u_errors.keys():
plt.semilogy(u_errors[method][:,0], u_errors[method][:,1],
'.'+styles.plot(method),label=styles.title(method))
plt.title('Maximum error with $\lambda=%g$, $\eta=%g$, and $T_{min}=%g$' % (ww, ff, min_T))
plt.xlabel('$N$')
plt.ylabel('$\\Delta U/N\epsilon$')
plt.legend(loc='best').get_frame().set_alpha(0.25)
plt.tight_layout(pad=0.2)
plt.savefig("figs/periodic-ww%02.0f-ff%02.0f-u_errors.pdf" % (ww*100, ff*100))
plt.figure()
for method in cv_errors.keys():
plt.semilogy(cv_errors[method][:,0], cv_errors[method][:,1],
'.'+styles.plot(method),label=styles.title(method))
plt.title('Maximum error with $\lambda=%g$, $\eta=%g$, and $T_{min}=%g$' % (ww, ff, min_T))
plt.xlabel('$N$')
cv_errors[method] = numpy.vstack(
[u_errors[method], [N, dcv]])
ds = abs(u_cv_s_method[2] - u_cv_s[2]).max()
if method not in s_errors:
s_errors[method] = numpy.array([[N, ds]])
else:
s_errors[method] = numpy.vstack(
[u_errors[method], [N, ds]])
min_T = 0.2 # FIXME maybe shouldn't hardcode this?
plt.figure()
for method in u_errors.keys():
plt.semilogy(u_errors[method][:, 0],
u_errors[method][:, 1],
'.' + styles.plot(method),
label=styles.title(method))
plt.title('Maximum error with $\lambda=%g$, $\eta=%g$, and $T_{min}=%g$' %
(ww, ff, min_T))
plt.xlabel('$N$')
plt.ylabel('$\\Delta U/N\epsilon$')
plt.legend(loc='best').get_frame().set_alpha(0.25)
plt.tight_layout(pad=0.2)
plt.savefig("figs/periodic-ww%02.0f-ff%02.0f-u_errors.pdf" %
(ww * 100, ff * 100))
plt.figure()
for method in cv_errors.keys():
plt.semilogy(cv_errors[method][:, 0],
cv_errors[method][:, 1],
Z_inf = sum(numpy.exp(ln_dos - ln_dos.max()))
S_inf = sum(-numpy.exp(ln_dos - ln_dos.max())*(-ln_dos.max() - numpy.log(Z_inf))) / Z_inf
for i in range(len(T_range)):
ln_dos_boltz = ln_dos - energy/T_range[i]
dos_boltz = numpy.exp(ln_dos_boltz - ln_dos_boltz.max())
Z[i] = sum(dos_boltz)
U[method][i] = sum(energy*dos_boltz)/Z[i]
S[method][i] = sum(-dos_boltz*(-energy/T_range[i] - ln_dos_boltz.max() \
- numpy.log(Z[i])))/Z[i]
S[method][i] -= S_inf
CV[method][i] = sum((energy/T_range[i])**2*dos_boltz)/Z[i] - \
(sum(energy/T_range[i]*dos_boltz)/Z[i])**2
plt.figure('u')
plt.plot(T_range,U[method]/N,styles.plot(method),label=styles.title(method))
plt.figure('hc')
plt.plot(T_range,CV[method]/N,styles.plot(method),label=styles.title(method))
plt.figure('S')
plt.plot(T_range,S[method]/N,styles.plot(method),label=styles.title(method))
plt.figure('dos')
plt.ylim(minlog, 0)
locs, labels = plt.yticks()
def tentothe(n):
if n == 0:
return '1'
if n == 10:
U = {} # internal energy
CV = {} # heat capacity
S = {} # entropy
for method in set(methods + [golden]):
u_cv_s = readandcompute.u_cv_s(ww, ff, N, method)
if u_cv_s != None:
U[method] = u_cv_s[0] # internal energy
CV[method] = u_cv_s[1] # heat capacity
S[method] = u_cv_s[2] # entropy
plt.figure('u')
plt.plot(T_range,
U[method] / N,
styles.plot(method),
label=styles.title(method))
plt.figure('hc')
plt.plot(T_range,
CV[method] / N,
styles.plot(method),
label=styles.title(method))
plt.figure('s')
plt.plot(T_range,
S[method] / N,
styles.plot(method),
label=styles.title(method))
for method in methods:
cv_errors[method][n] += dcv
s_errors[method][n] += ds
u_errors[method][n] /= len(seeds)
cv_errors[method][n] /= len(seeds)
s_errors[method][n] /= len(seeds)
os.chdir(thesis_dir)
### scaling figures
fig_size = (6,5)
plt.figure(figsize=fig_size)
for method in methods:
plt.semilogy(Ns, u_errors[method],'.'+styles.plot(method),
label=styles.title(method))
plt.xlabel('$N$')
plt.ylabel('$\\Delta U/N\epsilon$')
plt.legend(loc='best')
plt.tight_layout(pad=0.2)
plt.savefig("figs/u-scaling.pdf")
plt.figure(figsize=fig_size)
for method in methods:
plt.semilogy(Ns, cv_errors[method],'.'+styles.plot(method),
label=styles.title(method))
plt.xlabel('$N$')
cv_errors[method][n] += dcv
s_errors[method][n] += ds
u_errors[method][n] /= len(seeds)
cv_errors[method][n] /= len(seeds)
s_errors[method][n] /= len(seeds)
os.chdir(thesis_dir)
### scaling figures
fig_size = (6, 5)
plt.figure(figsize=fig_size)
for method in methods:
plt.semilogy(Ns, u_errors[method], "." + styles.plot(method), label=styles.title(method))
plt.xlabel("$N$")
plt.ylabel("$\\Delta U/N\epsilon$")
plt.legend(loc="best")
plt.tight_layout(pad=0.2)
plt.savefig("figs/u-scaling.pdf")
plt.figure(figsize=fig_size)
for method in methods:
plt.semilogy(Ns, cv_errors[method], "." + styles.plot(method), label=styles.title(method))
plt.xlabel("$N$")
plt.ylabel("$\\Delta C_V/N\epsilon$")
plt.legend(loc="best")
#methods = eval(sys.argv[4])
methods = ["tmmc", "oetmmc"]
#arg methods = [["tmmc"]]
#seed = int(sys.argv[5])
#arg seed = [0]
# input: ["../data/ww%04.2f-L%04.2f-N%i-%s.dat" % (ww, L, N, data) for data in ["E","lnw"]]
for method in set(methods):
T, U, CV, S, min_T = readandcompute.T_u_cv_s_minT('../data/ww%04.2f-L%04.2f-N%03d' % (ww, L, N))
plt.figure('u')
plt.plot(T,U/N,styles.plot(method),label=styles.title(method))
plt.figure('hc')
plt.plot(T,CV/N,styles.plot(method),label=styles.title(method))
plt.figure('s')
plt.plot(T,S/N,styles.plot(method),label=styles.title(method))
plt.figure('u')
plt.title('Specific internal energy for $\lambda=%g$, $L=%g$, and $N=%i$' % (ww, L, N))
plt.xlabel('$kT/\epsilon$')
plt.ylabel('$U/N\epsilon$')
plt.legend(loc='best')
plt.axvline(min_T,linewidth=1,color='k',linestyle=':')
plt.tight_layout(pad=0.2)
plt.savefig("ww%02.0f-L%02.0f-N%i-u.pdf" % (ww*100, L, N))