def main(a):
#arg = raw_input("Zipf & Pareto belongs to power law. Please select: 1: Pareto\'s Law, 2: Zipf\'s law") )
fig, ax = plt.subplots(1, 1)
mean, var, skew, kurt = powerlaw.stats(a, moments='mvsk')
x = power_law_dist(a)
ax.plot(x, powerlaw.pdf(x, a), 'r-', lw=5, alpha=0.6, label='powerlaw pdf')
rv = powerlaw(a)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
r = powerlaw.rvs(a, size=1000)
ax.legend(loc='best', frameon=False)
#plt.plt(x,y)
plt.show()
def matrix_inverse_unfolding(signal, detector_response_matrix):
"""
Unfold the signal using simple matrix unfolding
:param signal: The signal from the detector, in either total energy per chamber or energy per particle per chamber
:param detector_response_matrix: The detector Response Matrix, normalized by column
:return: The unfolded signal, sigma in the unfolding, the x error estimation, y error, and the unf - pdf / sigma_x
"""
if signal.ndim == 2:
sum_signal_per_chamber = np.sum(signal, axis=1)
y_vector = np.histogram(sum_signal_per_chamber,
bins=detector_response_matrix.shape[0])
else:
y_vector = [signal, 0]
x_pdf_space = np.linspace(powerlaw.ppf(0.01,
0.70), powerlaw.ppf(1.0, 0.70),
detector_response_matrix.shape[0])
x_vector = powerlaw.pdf(x_pdf_space, 0.70)
# Get the inverse of the detector response matrix
inv_detector_response_matrix = np.linalg.inv(detector_response_matrix)
x_vector_unf = np.dot(y_vector[0], inv_detector_response_matrix)
# Error propagation
V_y = np.diag(y_vector[0])
V_x_est = np.dot(inv_detector_response_matrix,
np.dot(V_y, inv_detector_response_matrix.T))
sigma_x_unf = np.sqrt(np.diag(V_x_est))
# print('x_unf \t\t= %s' % str(np.round(x_vector_unf, 2)))
# print('simga_x_unf \t\t= %s' % str(np.round(sigma_x_unf, 2)))
# print('(unf - pdf) / sigma_x \t= %s ' % str(np.round((x_vector_unf - x_vector) / sigma_x_unf, 2)))
unf_pdf_sigma = (x_vector_unf - x_vector) / sigma_x_unf
return x_vector_unf, sigma_x_unf, V_x_est, V_y, unf_pdf_sigma
from scipy.stats import powerlaw import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1) # Calculate a few first moments: a = 1.66 mean, var, skew, kurt = powerlaw.stats(a, moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(powerlaw.ppf(0.01, a), powerlaw.ppf(0.99, a), 100) ax.plot(x, powerlaw.pdf(x, a), 'r-', lw=5, alpha=0.6, label='powerlaw pdf') # Alternatively, the distribution object can be called (as a function) # to fix the shape, location and scale parameters. This returns a "frozen" # RV object holding the given parameters fixed. # Freeze the distribution and display the frozen ``pdf``: rv = powerlaw(a) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = powerlaw.ppf([0.001, 0.5, 0.999], a) np.allclose([0.001, 0.5, 0.999], powerlaw.cdf(vals, a)) # True # Generate random numbers:
def integrand(x):
pp = powerlaw.pdf(x, a=k, loc=a, scale=L)
v = pp * (powerlaw.logpdf(x, a=k, loc=a, scale=L) -
mix_logpdf(x, k, a, L))
return v
plt.scatter(ba_c2.keys(),ba_c2.values(),c='b',marker='x')
plt.xlim((1e-4,1e-1))
plt.ylim((.9,1e4))
plt.xlabel('Connections (normalized)')
plt.ylabel('Frequency')
plt.show()
from scipy.stats import powerlaw
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
a = 1.66
mean, var, skew, kurt = powerlaw.stats(a, moments='mvsk')
x = np.linspace(powerlaw.ppf(0.01, a), powerlaw.ppf(0.99, a), 100)
ax.plot(x, powerlaw.pdf(x, a),'r-', lw=5, alpha=0.6, label='powerlaw pdf')
# Dec 15, 2015 Ch4
import math
math.pi
import random
random.choice(['a','b','c','d'])
S = 'Spam'
S[:-1]
B = bytearray(b'spam')
B.extend(b'eggs')
B.decode()
plt.ylabel("Total length")
plt.title("Trajectory of Search for Min Total Length, Average Min = %.1f" %
np.mean(mins))
#------------------------ Power Law Networks ----------------------------------
o_dist2 = data[1][1]
f_dist2 = data[1][2]
#original and final length
original_len = sum(o_dist2) / realizations
final_len = sum(f_dist2) / realizations
#fitting
r = powerlaw.fit(o_dist2)
rx = np.linspace(0, max(o_dist2), 100)
rp = powerlaw.pdf(rx, *r)
l1_fit = 1 / r[1]
fig3, (ax1, ax2) = plt.subplots(2)
n2, bins2, patches2 = ax1.hist(o_dist2, bins=100, density=True, alpha=0)
ax1.set(xlabel="log(Edge Length)", ylabel="log(counts)")
ax1.set_title('Original Length Distribution length = %.2f' %
(sum(o_dist2) / realizations))
ax1.set_yscale('log')
ax1.set_xscale('log')
ax1.scatter(bins2[:-1] + 0.5 * (bins2[1:] - bins2[:-1]),
n2,
marker='x',
c='red',
s=40,
alpha=1)
# plot distn of r for diff D, also do same for uniform ball
x = np.linspace(0, 2.0, 1000)
plt.figure()
for dim, color in zip(D, colors):
pdf = chi.pdf(np.sqrt(dim) * x, df=dim)
plt.plot(x, pdf / np.max(pdf), color, label='$D=%d$' % dim)
plt.xlabel('$r$ (rescaled)')
plt.ylabel('$\chi$ pdf (rescaled)')
plt.legend()
plt.title('distributions on radius in gaussians')
plt.savefig('fig0' + ext, dpi=300)
plt.figure()
for dim, color in zip(D, colors):
pdf = powerlaw.pdf(np.sqrt(dim) * x, a=dim, loc=0, scale=np.sqrt(dim))
plt.plot(x, pdf / np.max(pdf), color, label='$D=%d$' % dim)
plt.xlabel('$r$ (rescaled)')
plt.ylabel('power law pdf (rescaled)')
plt.legend()
plt.title('distributions on radius in uniform ball')
plt.savefig('fig1' + ext, dpi=300)
# warp 2D gauss to look like diff D
n = 500
plt.figure()
for dim, color in zip(D, colors):
R = np.sqrt(np.random.chisquare(df=dim, size=n))
R = R / np.median(R)