import pylab
pylab.rcParams['xtick.major.pad']='8'
pylab.rcParams['ytick.major.pad']='8'
#import matplotlib.gridspec as gridspec
from matplotlib import rc
rc('text', usetex=False)
rc('font', family='serif')
from os import listdir
files = listdir('.')
if 'blackouts.txt' not in files:
import urllib
urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/blackouts.txt', 'blackouts.txt')
if 'words.txt' not in files:
import urllib
urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/words.txt', 'words.txt')
if 'worm.txt' not in files:
import urllib
urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/worm.txt', 'worm.txt')
from numpy import genfromtxt
blackouts = genfromtxt('blackouts.txt')#/10**3
words = genfromtxt('words.txt')
worm = genfromtxt('worm.txt')
worm = worm[worm>0]
def plot_basics(data, data_inst, fig, units):
from powerlaw import plot_pdf, Fit, pdf
annotate_coord = (-.4, .95)
ax1 = fig.add_subplot(n_graphs,n_data,data_inst)
plot_pdf(data[data>0], ax=ax1, linear_bins=True, color='r', linewidth=.5)
x, y = pdf(data, linear_bins=True)
ind = y>0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)
from pylab import setp
setp( ax1.get_xticklabels(), visible=False)
#ax1.set_xticks(ax1.get_xticks()[::2])
ax1.set_yticks(ax1.get_yticks()[::2])
locs,labels = yticks()
#yticks(locs, map(lambda x: "%.0f" % x, log10(locs)))
if data_inst==1:
ax1.annotate("A", annotate_coord, xycoords="axes fraction", fontsize=14)
from mpl_toolkits.axes_grid.inset_locator import inset_axes
ax1in = inset_axes(ax1, width = "30%", height = "30%", loc=3)
ax1in.hist(data, normed=True, color='b')
ax1in.set_xticks([])
ax1in.set_yticks([])
ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst, sharex=ax1)
plot_pdf(data, ax=ax2, color='b', linewidth=2)
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')
p = fit.power_law.pdf()
#ax2.set_ylim(min(p), max(p))
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
from pylab import setp
setp( ax2.get_xticklabels(), visible=False)
#ax2.set_xticks(ax2.get_xticks()[::2])
if ax2.get_ylim()[1] >1:
ax2.set_ylim(ax2.get_ylim()[0], 1)
ax2.set_yticks(ax2.get_yticks()[::2])
#locs,labels = yticks()
#yticks(locs, map(lambda x: "%.0f" % x, log10(locs)))
if data_inst==1:
ax2.annotate("B", annotate_coord, xycoords="axes fraction", fontsize=14)
ax2.set_ylabel(r"$p(X)$")# (10^n)")
ax3 = fig.add_subplot(n_graphs,n_data,n_data*2+data_inst)#, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
#p = fit.power_law.pdf()
ax3.set_ylim(ax2.get_ylim())
ax3.set_yticks(ax3.get_yticks()[::2])
ax3.set_xlim(ax1.get_xlim())
#locs,labels = yticks()
#yticks(locs, map(lambda x: "%.0f" % x, log10(locs)))
if data_inst==1:
ax3.annotate("C", annotate_coord, xycoords="axes fraction", fontsize=14)
#if ax2.get_xlim()!=ax3.get_xlim():
# zoom_effect01(ax2, ax3, ax3.get_xlim()[0], ax3.get_xlim()[1])
ax3.set_xlabel(units)
n_data = 3
n_graphs = 4
f = figure(figsize=(8,11))
data = words
data_inst = 1
units = 'Word Frequency'
plot_basics(data, data_inst, f, units)
data_inst = 2
#data = city
#units = 'City Population'
data = worm
units = 'Neuron Connections'
plot_basics(data, data_inst, f, units)
data = blackouts
data_inst = 3
units = 'Population Affected\nby Blackouts'
plot_basics(data, data_inst, f, units)
f.subplots_adjust(left=None, bottom=None, right=None, top=None, wspace=.3, hspace=.2)
f.savefig('FigWorkflow.eps', bbox_inches='tight')
Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit
blackouts = blackouts/10**3
data = blackouts
####
import powerlaw
fit = powerlaw.Fit(data)
fit.power_law.alpha
fit.power_law.sigma
fit.distribution_compare('power_law', 'exponential')
Calculating best minimal value for power law fit
(12.754562675882063, 0.1522925560442657)
data = words
####
figPDF = powerlaw.plot_pdf(data, color='b')
powerlaw.plot_pdf(data, linear_bins=True, color='r', ax=figPDF)
####
figPDF.set_ylabel(r"$p(X)$")
figPDF.set_xlabel(r"Word Frequency")
savefig('FigPDF.eps', bbox_inches='tight')
data = words
fit = powerlaw.Fit(data, discrete=True)
####
figCCDF = fit.plot_pdf(color='b', linewidth=2)
fit.power_law.plot_pdf(color='b', linestyle='--', ax=figCCDF)
fit.plot_ccdf(color='r', linewidth=2, ax=figCCDF)
fit.power_law.plot_ccdf(color='r', linestyle='--', ax=figCCDF)
####
figCCDF.set_ylabel(r"$p(X)$, $p(X\geq x)$")
figCCDF.set_xlabel(r"Word Frequency")
savefig('FigCCDF.eps', bbox_inches='tight')
Calculating best minimal value for power law fit
data = blackouts
fit = powerlaw.Fit(data)
###
x, y = fit.cdf()
bin_edges, probability = fit.pdf()
y = fit.lognormal.cdf(data=[300,350])
y = fit.lognormal.pdf()
Calculating best minimal value for power law fit
data = blackouts
####
import powerlaw
fit = powerlaw.Fit(data)
fit.xmin
fit.fixed_xmin
fit.alpha
fit.D
fit = powerlaw.Fit(data, xmin=1.0)
fit.xmin
fit.fixed_xmin
fit.alpha
fit.D
Calculating best minimal value for power law fit
0.37601504850371759
data = blackouts
####
fit = powerlaw.Fit(data, xmin=(250.0, 300.0))
fit.fixed_xmin
fit.given_xmin
fit.xmin
Calculating best minimal value for power law fit
272.0
data = blackouts
fit = powerlaw.Fit(data)
####
fit = powerlaw.Fit(data, xmax=10000.0)
fit.xmax
fit.fixed_xmax
Calculating best minimal value for power law fit Calculating best minimal value for power law fit
True
data = words
#FigCCDFmax = powerlaw.plot_ccdf(data, linewidth=3)
fit = powerlaw.Fit(data, discrete=True, xmax=None)
FigCCDFmax = fit.plot_ccdf(color='b', label=r"Empirical, no $x_{max}$")
fit.power_law.plot_ccdf(color='b', linestyle='--', ax=FigCCDFmax, label=r"Fit, no $x_{max}$")
fit = powerlaw.Fit(data, discrete=True, xmax=1000)
fit.plot_ccdf(color='r', label=r"Empirical, $x_{max}=1000$")
fit.power_law.plot_ccdf(color='r', linestyle='--', ax=FigCCDFmax, label=r"Fit, $x_{max}=1000$")
#x, y = powerlaw.ccdf(data, xmax=max(data))
#fig1.plot(x,y)
####
FigCCDFmax.set_ylabel(r"$p(X\geq x)$")
FigCCDFmax.set_xlabel(r"Word Frequency")
handles, labels = FigCCDFmax.get_legend_handles_labels()
leg = FigCCDFmax.legend(handles, labels, loc=3)
leg.draw_frame(False)
savefig('FigCCDFmax.eps', bbox_inches='tight')
Calculating best minimal value for power law fit Calculating best minimal value for power law fit
data = blackouts
fit = powerlaw.Fit(data)
####
fit = powerlaw.Fit(data, xmin=230.0)
fit.discrete
fit = powerlaw.Fit(data, xmin=230.0, discrete=True)
fit.discrete
Calculating best minimal value for power law fit
True
data = blackouts
fit = powerlaw.Fit(data)
####
fit.power_law
fit.power_law.alpha
fit.power_law.parameter1
fit.power_law.parameter1_name
fit.lognormal.mu
fit.lognormal.parameter1_name
fit.lognormal.parameter2_name
fit.lognormal.parameter3_name == None
Calculating best minimal value for power law fit
True
data = blackouts
####
fit = powerlaw.Fit(data)
R, p = fit.distribution_compare('power_law', 'exponential', normalized_ratio=True)
print R, p
Calculating best minimal value for power law fit 1.43148048496 0.152292556044
data = worm
fit = powerlaw.Fit(data, discrete=True)
####
fit.distribution_compare('power_law', 'exponential')
fit.distribution_compare('power_law', 'truncated_power_law')
Calculating best minimal value for power law fit Assuming nested distributions
(-0.081336372762826459, 0.68670761175575712)
data = worm
fit = powerlaw.Fit(data, discrete=True)
####
fit.distribution_compare('power_law', 'exponential')
fit.distribution_compare('power_law', 'truncated_power_law')
Calculating best minimal value for power law fit Assuming nested distributions
(-422.43094963299131, 0.0)
data = words
fit = powerlaw.Fit(data, discrete=True)
####
print fit.distribution_compare('power_law', 'exponential', normalized_ratio=True)
print fit.distribution_compare('power_law', 'truncated_power_law')
Calculating best minimal value for power law fit (9.1359147187770002, 6.4856142413795328e-20) Assuming nested distributions (-0.91712308337346782, 0.17562683168707593)
print fit.distribution_compare('power_law', 'truncated_power_law')
Assuming nested distributions (-13026.994760437048, 0.0)
data = words
fit = powerlaw.Fit(data, discrete=True)
####
fit.distribution_compare('power_law', 'lognormal')
fig = fit.plot_ccdf(linewidth=3, label='Empirical Data')
fit.power_law.plot_ccdf(ax=fig, color='r', linestyle='--', label='Power law fit')
fit.lognormal.plot_ccdf(ax=fig, color='g', linestyle='--', label='Lognormal fit')
####
fig.set_ylabel(r"$p(X\geq x)$")
fig.set_xlabel(r"Word Frequency")
handles, labels = fig.get_legend_handles_labels()
fig.legend(handles, labels, loc=3)
savefig('FigLognormal.eps', bbox_inches='tight')
Calculating best minimal value for power law fit
empirical_data = blackouts
####
fit = powerlaw.Fit(empirical_data)
simulated_data = fit.power_law.generate_random(10000)
theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5])
simulated_data = theoretical_distribution.generate_random(10000)
Calculating best minimal value for power law fit
theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5])
simulated_data = theoretical_distribution.generate_random(10000)
####
fit = powerlaw.Fit(simulated_data)
fit.power_law.xmin, fit.power_law.alpha
Calculating best minimal value for power law fit
(5.5253208595576631, 2.5298369451264975)
powerlaw.plot_pdf(simulated_data,linewidth=3)
fit.power_law.plot_pdf(simulated_data,linestyle='--',color='r')
<matplotlib.axes.AxesSubplot at 0xd829dd0>
data = blackouts
####
fit = powerlaw.Fit(data, discrete=True, estimate_discrete=True)
fit.power_law.alpha
fit.power_law.estimate_discrete
fit = powerlaw.Fit(data, discrete=True, estimate_discrete=False)
fit.power_law.alpha
fit.power_law.estimate_discrete
Calculating best minimal value for power law fit Calculating best minimal value for power law fit
2.2691417084814285
data = blackouts
####
fit = powerlaw.Fit(data, discrete=True, xmin=230.0, xmax=9000, discrete_approximation='xmax')
fit.lognormal.mu
fit = powerlaw.Fit(data, discrete_approximation=100000, xmin=230.0, discrete=True)
fit.lognormal.mu
fit = powerlaw.Fit(data, discrete_approximation='round', xmin=230.0, discrete=True)
fit.lognormal.mu
0.39905257607693184
theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5], discrete=True)
simulated_data = theoretical_distribution.generate_random(10000, estimate_discrete=True)
empirical_data = blackouts
####
theoretical_distributionibution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5], discrete=True, estimate_discrete=False)
simulated_data = theoretical_distribution.generate_random(10000)
fit = powerlaw.Fit(empirical_data, discrete=True, estimate_discrete=True)
simulated_data = fit.power_law.generate_random(10000)
Calculating best minimal value for power law fit
data = blackouts
fit = powerlaw.Fit(data)
####
fit.distribution_compare('power_law', 'truncated_power_law')
fit.distribution_compare('exponential', 'stretched_exponential')
Calculating best minimal value for power law fit Assuming nested distributions Assuming nested distributions
(-13.018342321459194, 3.3499122220614908e-07)
data = blackouts
####
fit = powerlaw.Fit(data)
fit.power_law.alpha, fit.power_law.sigma, fit.xmin
fit = powerlaw.Fit(data, sigma_threshold=.1)
fit.power_law.alpha, fit.power_law.sigma, fit.xmin
Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit
(1.8833765811180314, 0.094168259953067143, 124.0)
parameter_range = {'alpha': [2.3, None], 'sigma': [None, .2]}
fit = powerlaw.Fit(data, parameter_range=parameter_range)
fit.power_law.alpha, fit.power_law.sigma, fit.xmin
Calculating best minimal value for power law fit
(2.3000107113942141, 0.17069976919260452, 234.0)
parameter_range = lambda(self): self.sigma/self.alpha < .05
fit = powerlaw.Fit(data, parameter_range=parameter_range)
fit.power_law.alpha, fit.power_law.sigma, fit.xmin
Calculating best minimal value for power law fit
(1.8833765811180314, 0.094168259953067143, 124.0)
data = blackouts
fit = powerlaw.Fit(data, sigma_threshold=.1)
print fit.xmin, fit.D, fit.alpha
fit = powerlaw.Fit(data)
print fit.xmin, fit.D, fit.alpha
####
from matplotlib.pylab import plot
plot(fit.xmins, fit.Ds, label=r'$D$')
plot(fit.xmins, fit.sigmas, label=r'$\sigma$', linestyle='--')
plot(fit.xmins, fit.sigmas/fit.alphas, label=r'$\sigma /\alpha$', linestyle='--')
####
ylim(0, .4)
legend(loc=4)
xlabel(r'$x_{min}$')
ylabel(r'$D,\sigma,\alpha$')
savefig('FigD.eps', bbox_inches='tight')
Calculating best minimal value for power law fit 50.0 0.0998297854528 1.78313986533 Calculating best minimal value for power law fit 230.0 0.0606737962944 2.27263721983
data = blackouts
####
fit = powerlaw.Fit(data, sigma_threshold=.001)
fit.power_law.alpha, fit.power_law.sigma, fit.xmin, fit.noise_flag
Calculating best minimal value for power law fit No valid fits found. No valid fits found.
(10.500000000422041, 5.1423189016918585, False)
fit.lognormal.mu, fit.lognormal.sigma
range_dict = {'mu': [10.5, None]}
fit.lognormal.parameter_range(range_dict)
fit.lognormal.mu, fit.lognormal.sigma, fit.lognormal.noise_flag
initial_parameters = (12, .7)
fit.lognormal.parameter_range(range_dict, initial_parameters)
fit.lognormal.mu, fit.lognormal.sigma, fit.lognormal.noise_flag
from numpy import logspace
from scipy.stats import variation
import pandas as pd
def validate(xmin, alpha, discrete='continuous', n_data=10000, n_trials=1):
if n_trials>1:
return array([validate(xmin, alpha, discrete=discrete, n_data=n_data, n_trials=1) for trial in arange(n_trials)]).T
if discrete=='continuous':
discrete = False
estimate_discrete = False
elif discrete == 'discrete':
discrete = True
estimate_discrete = False
elif discrete == 'discrete_estimate':
discrete = True
estimate_discrete = True
theoretical_distribution = powerlaw.Power_Law(xmin=xmin, parameters=[alpha], discrete=discrete)
simulated_data = theoretical_distribution.generate_random(n_data, estimate_discrete=estimate_discrete)
fit = powerlaw.Fit(simulated_data, discrete=discrete, estimate_discrete=estimate_discrete)
return fit.xmin, fit.alpha
%%prun
xmin=1
alpha=1.5
n_data=10000
discrete='continuous'
validate(xmin, alpha, discrete=discrete, n_data=n_data, n_trials=10)
Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit
theoretical_xmins = unique(floor(logspace(0.0,2.0,num=20)))
theoretical_alphas = array([1.5,2.0,2.5,3.0,3.5])
#theoretical_xmins = [2]
#theoretical_alphas = [2.5]
distribution_types = ['continuous','discrete']
n_trials = 10
n_data = 10000
ind = [(d,a,x) for d in distribution_types for a in theoretical_alphas for x in theoretical_xmins]
ind = pd.MultiIndex.from_tuples(ind, names=['type', 'alpha','xmin'])
df = pd.DataFrame(columns=['alpha_mean', 'alpha_sd', 'xmin_mean', 'xmin_sd'], index=ind)
i = 0
for dt, alpha, xmin in ind:
i += 1
print(i)
data = validate(xmin, alpha, discrete=dt, n_data=n_data, n_trials=n_trials)
df.ix[dt,alpha,xmin] = (mean(data[1]), std(data[1]), mean(data[0]), std(data[0]))
filename = 'powerlaw_validation_%itrials_%idata.h5'%(int(n_trials),int(n_data))
df.to_hdf(filename,'df')
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value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 103 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 104 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 105 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 106 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 107 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 108 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 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best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 111 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 112 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 113 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 114 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 115 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 116 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 117 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 118 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 119 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 120 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 121 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 122 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 123 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 124 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 125 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit 126 Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law fit Calculating best minimal value for power law 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best minimal value for power law fit
#filename = 'powerlaw_validation_%itrials_%idata.h5'%(int(n_trials),int(n_data))
#df = pd.read_hdf(filename,'df')
subplot(2,2,1)
for a in theoretical_alphas:
y_vals = df.ix['continuous', a]['alpha_mean']
error = df.ix['continuous', a]['alpha_sd']
plot(theoretical_xmins, y_vals, label=a)
fill_between(theoretical_xmins, y_vals-error, y_vals+error, alpha=.1)
xscale('log')
#xlabel(r"$x_{min}$")
ylabel(r"Fitted $\alpha$")
yticks(theoretical_alphas)
setp(gca().get_xticklabels(), visible=False)
title("Continuous")
#########
subplot(2,2,2)
for a in theoretical_alphas:
y_vals = df.ix['discrete', a]['alpha_mean']
error = df.ix['discrete', a]['alpha_sd']
plot(theoretical_xmins, y_vals, label=a)
fill_between(theoretical_xmins, y_vals-error, y_vals+error, alpha=.1)
xscale('log')
#xlabel(r"$x_{min}$")
#ylabel(r"Fitted $\alpha$")
setp(gca().get_xticklabels(), visible=False)
setp(gca().get_yticklabels(), visible=False)
title("Discrete")
########
subplot(2,2,3)
for a in theoretical_alphas:
y_vals = df.ix['continuous', a]['xmin_mean']
error = df.ix['continuous', a]['xmin_sd']
up = y_vals+error
down = y_vals-error
ind = down<theoretical_xmins
down[ind] = theoretical_xmins[ind]
plot(theoretical_xmins, y_vals, label=a)
fill_between(theoretical_xmins, down, up, alpha=.1)
xlim(xmin=1)
ylim(ymin=1)
plot(xlim(),xlim(),linestyle='--', color='k')
xscale('log')
yscale('log')
xlabel(r"$x_{min}$ of Data")
ylabel(r"Fitted $x_{min}$")
########
legend_refs = []
########
subplot(2,2,4,sharey=gca())
for a in theoretical_alphas:
y_vals = df.ix['discrete', a]['xmin_mean']
error = df.ix['discrete', a]['xmin_sd']
up = y_vals+error
down = y_vals-error
ind = down<theoretical_xmins
down[ind] = theoretical_xmins[ind]
line = plot(theoretical_xmins, y_vals, label=a)
legend_refs += line
fill_between(theoretical_xmins, down, up, alpha=.1)
xlim(xmin=1)
ylim(ymin=1)
plot(xlim(),xlim(),linestyle='--', color='k')
xscale('log')
yscale('log')
xlabel(r"$x_{min}$ of Data")
#ylabel(r"Fitted $x_{min}$")
setp(gca().get_yticklabels(), visible=False)
#######
#figlegend(legend_refs[::-1], theoretical_alphas[::-1],'center right', title=r'$\alpha$ of Data')
subplots_adjust(wspace=.15, hspace=.1)
legend( legend_refs[::-1], theoretical_alphas[::-1], loc = 'center right', bbox_to_anchor = (.1,0,1,1),
bbox_transform = plt.gcf().transFigure, title=r'$\alpha$ of Data' )
savefig('Fig_powerlaw_validation_%itrials_%idata.pdf'%(int(n_trials),int(n_data)), bbox_inches='tight')