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
wildfilename = "data/s%03d/periodic-ww%04.2f-ff%04.2f-N%d-%s-%%s.dat" \
% (seed, ww, ff, N, method)
with open(filename, 'r') as content_file:
content = content_file.read()
init_iters[method].append(int(initialization_iters_regex.findall(content)[0]))
E_data = numpy.loadtxt(wildfilename % 'E', ndmin=2)
Emins[method].append(E_data[:, 0].max())
sample_data = numpy.loadtxt(wildfilename % 'ps', ndmin=2)
samples[method].append(sample_data[len(sample_data[:,1])-1, 1])
plt.figure('iters')
plt.semilogy(all_Ns, init_iters[method], styles.color(method)+'.-',
label=styles.title(method))
plt.figure('emin')
plt.plot(all_Ns, Emins[method],styles.color(method)+'.-', label=styles.title(method))
plt.figure('iters')
plt.xlabel('$N$')
plt.ylabel('Initialization iterations')
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-scaling.pdf" % (ww*100, ff*100))
plt.figure('emin')
plt.xlabel('$N$')
plt.ylabel('Emin')
plt.legend(loc='best').get_frame().set_alpha(0.25)
plt.tight_layout(pad=0.2)
ff = float(sys.argv[2])
#arg ff = [0.1, 0.2, 0.3, 0.4]
N = int(sys.argv[3])
#arg N = range(5,21)+[100, 200, 1000]
methods = eval(sys.argv[4])
#arg methods = [["nw","kT0.4","kT0.5","wang_landau","simple_flat","tmmc","oetmmc"]]
seed = int(sys.argv[5])
#arg seed = [0]
# input: ["data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-E.dat" % (seed, ww, ff, N, version) for version in methods]
plt.title('Energy histogram for $\lambda=%g$, $\eta=%g$, and $N=%i$' %
(ww, ff, N))
for version in methods:
data = numpy.loadtxt("data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-E.dat" %
(seed, ww, ff, N, version))
energy = -data[:, 0] / N
DS = data[:, 1]
plt.semilogy(energy, DS, styles.dots(version), label=styles.title(version))
plt.xlabel('$U/N\epsilon$')
plt.ylabel('$H$')
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-N%i-E.pdf" %
(ww * 100, ff * 100, N))
with open(filename, 'r') as content_file:
content = content_file.read()
init_iters[method].append(
int(initialization_iters_regex.findall(content)[0]))
E_data = numpy.loadtxt(wildfilename % 'E', ndmin=2)
Emins[method].append(E_data[:, 0].max())
sample_data = numpy.loadtxt(wildfilename % 'ps', ndmin=2)
samples[method].append(sample_data[len(sample_data[:, 1]) - 1, 1])
plt.figure('iters')
plt.semilogy(all_Ns,
init_iters[method],
styles.color(method) + '.-',
label=styles.title(method))
plt.figure('emin')
plt.plot(all_Ns,
Emins[method],
styles.color(method) + '.-',
label=styles.title(method))
plt.figure('iters')
plt.xlabel('$N$')
plt.ylabel('Initialization iterations')
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-scaling.pdf" %
(ww * 100, ff * 100))
plt.figure('emin')
if reference_error == None:
continue
print ' ', reference, reference_error
for method in methods:
plt.figure(2)
method_err = mean_u_err(ww, ff, N, method, golden_u)
if method_err != None:
print ' ', method, method_err
plt.figure(1)
if method not in labels_added:
plt.loglog(reference_error,
method_err,
styles.dots(method),
markerfacecolor='none',
markeredgecolor=styles.color(method),
label=styles.title(method))
labels_added |= set([method])
else:
plt.loglog(reference_error,
method_err,
styles.dots(method),
markerfacecolor='none',
markeredgecolor=styles.color(method))
plt.figure(2)
plt.figure(2)
plt.legend(loc='best')
plt.savefig('figs/energy-for-debugging-ww%04.2f-ff%04.2f-N%i.pdf' %
(ww, ff, N))
min_T = 0.2 # FIXME maybe shouldn't hardcode this?
e_hist = numpy.loadtxt("data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-conv_T%g-E.dat"
% (seed, ww, ff, N, method, min_T), ndmin=2)
lnw_hist = numpy.loadtxt("data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-conv_T%g-lnw.dat"
% (seed, ww, ff, N, method, min_T), ndmin=2)
energy = -e_hist[:,0] # array of energies
lnw = lnw_hist[e_hist[:,0].astype(int),1] # look up the lnw for each actual energy
ln_dos = numpy.log(e_hist[:,1]) - lnw
log10w = lnw_hist[e_hist[:,0].astype(int),1]*numpy.log10(numpy.exp(1))
log10_dos = numpy.log10(e_hist[:,1]) - log10w
log10_dos -= log10_dos.max()
if log10_dos.min() < minlog:
minlog = log10_dos.min()
plt.figure('dos')
plt.plot(energy, log10_dos, styles.dots(method),label=styles.title(method))
Z = numpy.zeros(len(T_range)) # partition function
U[method] = numpy.zeros(len(T_range)) # internal energy
CV[method] = numpy.zeros(len(T_range)) # heat capacity
S[method] = numpy.zeros(len(T_range)) # entropy
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() \
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")
return energy, e_hist, log10w, log10_dos
for method in methods:
wildfilename = "../data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-%%s.dat" \
% (seed, ww, ff, N, method)
energy, e_hist, log10w, log10_dos = get_arrays(wildfilename)
if method != 'wang_landau':
plt.figure('dos-poster')
plt.plot(energy, log10_dos, styles.dots(method),
markerfacecolor='none', markeredgecolor=styles.color(method),
label=styles.title(method))
for ax in [ ax_dos, ax_dos_all ]:
ax.plot(energy[log10_dos > -cap], log10_dos[log10_dos > -cap],
styles.dots(method), markerfacecolor='none',
markeredgecolor=styles.color(method), label=styles.title(method))
for ax in [ ax_hist, ax_hist_all ]:
ax.semilogy(energy, e_hist[:,1], styles.dots(method),
markerfacecolor='none', markeredgecolor=styles.color(method),
label=styles.title(method))
for ax in [ ax_lnw, ax_lnw_all ]:
ax.plot(energy[log10w < cap], log10w[log10w < cap], styles.dots(method),
markerfacecolor='none', markeredgecolor=styles.color(method),
label=styles.title(method))
golden_u = t_u_cv_s[1]
reference_error = mean_u_err(ww, ff, N, reference, golden_u)
if reference_error == None:
continue
print ' ', reference, reference_error
for method in methods:
plt.figure(2)
method_err = mean_u_err(ww, ff, N, method, golden_u)
if method_err != None:
print ' ', method, method_err
plt.figure(1)
if method not in labels_added:
plt.loglog(reference_error, method_err, styles.dots(method),
markerfacecolor='none', markeredgecolor=styles.color(method),
label=styles.title(method))
labels_added |= set([method])
else:
plt.loglog(reference_error, method_err, styles.dots(method),
markerfacecolor='none', markeredgecolor=styles.color(method))
plt.figure(2)
plt.figure(2)
plt.legend(loc='best')
plt.savefig(
'figs/energy-for-debugging-ww%04.2f-ff%04.2f-N%i.pdf' % (ww, ff, N))
min_T = 0.2 # FIXME maybe shouldn't hardcode this?
plt.figure(1)
xmin,xmax = plt.xlim()
ymin,ymax = plt.ylim()
ww = float(sys.argv[1])
# arg ww = [1.3, 1.5, 2.0, 3.0]
ff = float(sys.argv[2])
# arg ff = [0.1, 0.2, 0.3, 0.4]
N = int(sys.argv[3])
# arg N = range(5,21)+[100, 200, 1000]
methods = eval(sys.argv[4])
# arg methods = [["nw","kT0.4","kT0.5","wang_landau","simple_flat","tmmc","oetmmc"]]
seed = int(sys.argv[5])
# arg seed = [0]
# input: ["data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-E.dat" % (seed, ww, ff, N, version) for version in methods]
plt.title("Energy histogram for $\lambda=%g$, $\eta=%g$, and $N=%i$" % (ww, ff, N))
for version in methods:
data = numpy.loadtxt("data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-E.dat" % (seed, ww, ff, N, version))
energy = -data[:, 0] / N
DS = data[:, 1]
plt.semilogy(energy, DS, styles.dots(version), label=styles.title(version))
plt.xlabel("$U/N\epsilon$")
plt.ylabel("$H$")
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-N%i-E.pdf" % (ww * 100, ff * 100, N))
# input: ["data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-%s.dat" % (seed, ww, ff, N, method, data) for method in methods for data in ["E","lnw"]]
minlog = 0
for method in methods:
e_hist = numpy.loadtxt("data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-E.dat"
% (seed, ww, ff, N, method))
lnw = numpy.loadtxt("data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-lnw.dat"
% (seed, ww, ff, N, method))
energy = -e_hist[:, 0]/N
log10w = lnw[e_hist[:, 0].astype(int), 1]*numpy.log10(numpy.exp(1))
log10_dos = numpy.log10(e_hist[:, 1]) - log10w
log10_dos -= log10_dos.max()
if log10_dos.min() < minlog:
minlog = log10_dos.min()
plt.figure('dos')
plt.plot(energy, log10_dos, styles.dots(method), label=styles.title(method))
log10w += log10w.min()
if log10w.min() < minlog:
minlog = log10w.min()
plt.figure('w')
plt.plot(energy, -log10w, styles.dots(method), label=styles.title(method))
def tentothe(n):
if n == 0:
return '1'
if n == 10:
return '10'
if int(n) == n:
return r'$10^{%d}$' % n
seed = int(sys.argv[5])
#arg seed = [0]
# input: ["data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-ps.dat" % (seed, ww, ff, N, method) for method in methods]
plt.title('Iterations per sample for $\lambda=%g$, $\eta=%g$, and $N=%i$' % (ww, ff, N))
for method in methods:
data_file = "data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-ps.dat" \
% (seed, ww, ff, N, method)
with open(data_file,'r') as file_handle:
for line in file_handle:
entries = line.split()
if 'iterations:' in entries:
iterations = int(entries[entries.index('iterations:')+1].replace(',',''))
continue
data = numpy.loadtxt(data_file)
energy = -data[:,0]/N
round_trips = data[:,1]
energy = energy[round_trips != 0]
round_trips = round_trips[round_trips != 0]
if sum(round_trips) > 0:
plt.semilogy(energy, iterations/round_trips, styles.dots(method),
label=styles.title(method))
plt.xlabel('$U/N\epsilon$')
plt.ylabel('Iterations per sample')
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-N%i-sample-rate.pdf" % (ww*100, ff*100, N))
# input: ["data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-%s.dat" % (seed, ww, ff, N, method, data) for method in methods for data in ["E","lnw"]]
minlog = 0
for method in methods:
e_hist = numpy.loadtxt("data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-E.dat"
% (seed, ww, ff, N, method))
lnw = numpy.loadtxt("data/s%03d/periodic-ww%04.2f-ff%04.2f-N%i-%s-lnw.dat"
% (seed, ww, ff, N, method))
energy = -e_hist[:,0]/N
log10w = lnw[e_hist[:,0].astype(int),1]*numpy.log10(numpy.exp(1))
log10_dos = numpy.log10(e_hist[:,1]) - log10w
log10_dos -= log10_dos.max()
if log10_dos.min() < minlog:
minlog = log10_dos.min()
plt.figure('dos')
plt.plot(energy, log10_dos, styles.dots(method),label=styles.title(method))
log10w += log10w.min()
if log10w.min() < minlog:
minlog = log10w.min()
plt.figure('w')
plt.plot(energy, -log10w, styles.dots(method),label=styles.title(method))
def tentothe(n):
if n == 0:
return '1'
if n == 10:
return '10'
if int(n) == n:
return r'$10^{%d}$' % n
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:
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))
#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))
