def test_var(self):
"""
var(testcase) = 1.666666667 """
#y = stats.var(self.shoes[0])
#assert_approx_equal(y,6.009)
y = stats.var(self.testcase)
assert_approx_equal(y, 1.666666667)
def test_var(self):
"""
var(testcase) = 1.666666667 """
#y = stats.var(self.shoes[0])
#assert_approx_equal(y,6.009)
y = stats.var(self.testcase)
assert_approx_equal(y,1.666666667)
def regression(self):
"""
Perform linear regression
"""
stats = BasicStats()
n = len(self.data['x'])
x2_sum = stats.sum_squares(self.data['x'])
x_sum2 = sum(self.data['x'])*sum(self.data['x'])
x_sum = sum(self.data['x'])
y_sum = sum(self.data['y'])
xy_sum = stats.sum_xy(self.data)
self.alpha = (y_sum*x2_sum - x_sum*xy_sum)/(n*x2_sum-x_sum2)
self.beta = (n*xy_sum - x_sum*y_sum)/(n*x2_sum-x_sum2)
self.beta = stats.cov(self.data['x'],self.data['y'])/stats.var(self.data['x'])
self.alpha = stats.mean(self.data['y']) - self.beta * stats.mean(self.data['x'])
def gausspeak(cmap, start):
from scipy.stats import tvar as var
from scipy.stats.distributions import norm
from scipy import cumsum, log, exp, zeros, r_, dot, transpose, array
from scipy import linalg, nan
#(pseudo-)Gaussian peak fit: p(x,y) = exp(a + b*x + c*y + d*x*x + e*x*y + f*y*y)
global QMAT
rhs = zeros((9), dtype=float)
ind = 0
for j in r_[-1:2]:
for i in r_[-1:2]:
rhs[ind] = log(max(cmap[start[1] + j, start[0] + i], 1e-12))
ind = ind + 1
if var(rhs) == 0:
#right hand side was clipped everywhere: no good
peak = 0
shift = array([0, 0])
ok = -1
#solve normal equations for least squares problem
qr = dot(transpose(QMAT), transpose(rhs))
coeffs = linalg.solve(QQ, qr)
#unpack solution vector; find peak position from zero derivative
mmat = array([[2 * coeffs[3], coeffs[4]], [coeffs[4], 2 * coeffs[5]]])
mrhs = array([[-coeffs[1]], [-coeffs[2]]])
qvec = transpose(linalg.solve(mmat, mrhs)) #qvec = (mmat\mrhs)'
if norm(qvec) > 1:
#interpolated displacement is too large: no good
peak = 0
shift = array([0, 0])
ok = -1
ok = 1
shift = qvec + start
qvec = transpose(qvec)
peak = exp(coeffs[0] + coeffs[1] * qvec[0] + coeffs[2] * qvec[1] +
coeffs[3] * qvec[0] * qvec[0] + coeffs[4] * qvec[0] * qvec[1] +
coeffs[5] * qvec[1] * qvec[1])
return peak, shift, ok
def autocorrelation(series, k=1, biased=True):
"""Returns autocorrelation of order 'k' and corresponding two-tailed pvalue.
(Inspired by CLM pp.45-47)
@param series: The series on which to compute autocorrelation
@param k: The order to which compute autocorrelation
@param biased: If False, rho_k will be corrected according to Fuller (1976)
@return: rho_k, pvalue
"""
T = len(series)
mu = mean(series)
sigma = var(series)
# Centered observations
obs = series-mu
lagged = lag(obs, k)
truncated = obs[:-k]
assert len(lagged) == len(truncated)
# Multiplied by 'T' for numerical stability
gamma_k = T*add.reduce(truncated*lagged) # Numerator
gamma_0 = T*add.reduce(obs*obs) # Denominator
rho_k = (gamma_k / gamma_0)
if rho_k > 1.0: rho_k = 1.0 # Correct for numerical errors
# The standard normal random variable
Z = sqrt(T)*rho_k
# Bias correction?
if not biased:
rho_k += (1 - rho_k**2) * (T-k)/(T-1)**2
Z = rho_k * T/sqrt(T-k)
# The two-tailed p-value is twice the prob that value of a std normal r.v.
# turns out to be greater than the (absolute) value of Z
pvalue = 2*( 1 - norm.cdf(abs(Z)) )
assert pvalue >= 0.0 and pvalue <= 1.0
return rho_k, pvalue
def autocorrelation(series, k=1, biased=True):
"""Returns autocorrelation of order 'k' and corresponding two-tailed pvalue.
(Inspired by CLM pp.45-47)
@param series: The series on which to compute autocorrelation
@param k: The order to which compute autocorrelation
@param biased: If False, rho_k will be corrected according to Fuller (1976)
@return: rho_k, pvalue
"""
T = len(series)
mu = mean(series)
sigma = var(series)
# Centered observations
obs = series - mu
lagged = lag(obs, k)
truncated = obs[:-k]
assert len(lagged) == len(truncated)
# Multiplied by 'T' for numerical stability
gamma_k = T * add.reduce(truncated * lagged) # Numerator
gamma_0 = T * add.reduce(obs * obs) # Denominator
rho_k = (gamma_k / gamma_0)
if rho_k > 1.0: rho_k = 1.0 # Correct for numerical errors
# The standard normal random variable
Z = sqrt(T) * rho_k
# Bias correction?
if not biased:
rho_k += (1 - rho_k**2) * (T - k) / (T - 1)**2
Z = rho_k * T / sqrt(T - k)
# The two-tailed p-value is twice the prob that value of a std normal r.v.
# turns out to be greater than the (absolute) value of Z
pvalue = 2 * (1 - norm.cdf(abs(Z)))
assert pvalue >= 0.0 and pvalue <= 1.0
return rho_k, pvalue
from __future__ import division
from mcmchammer import *
from scipy import stats
datafilename = "faculty.dat"
nsamples = 10000
burn = 0
mean_candsd = 0.2
var_candsd = 0.15
# Read in Data
data = [float(line) for line in open(datafilename)]
# Use point estimators from the data to come up with starting values.
estimated_mean = stats.mean(data)
estimated_var = stats.var(data)
# Create Nodes and Links in Network
meannode = NormalNode(estimated_mean, name="Mean", candsd=mean_candsd, mean=5, var=(1 / 3) ** 2)
varprior_mean = 1 / 4
varprior_stddev = 1 / 12
varprior_shape = MomentsInvGammaShape(varprior_mean, varprior_stddev ** 2)
varprior_scale = MomentsInvGammaScale(varprior_mean, varprior_stddev ** 2)
varnode = InvGammaNode(estimated_var, name="Variance", candsd=var_candsd, shape=varprior_shape, scale=varprior_scale)
for datum in data:
NormalNode(datum, observed=True, mean=meannode, var=varnode)
# Perform simulations and plot results
currentnetwork.simulate(nsamples, burn)
meannode.plotmixing()
sims.plot_susceptibility(N)
sims.plot_absmag(N)
sims.plot_energies(N)
"""
###########################
# Plotting P(E) for L=20 an T = [1, 2.4]
###########################
sim = Simulation(20, 2.4, "/scratch/henriasv/FYS3150/IsingModel_once/N20/T2.4")
sim.set_thermalization(0.2)
sim.calculate_properties()
sim.plot_pe()
title("Probability density function for the energy at T=2.4 (not normalized)")
xlabel("E")
ylabel("Count")
variance = stats.var(sim.e_array)
print "variance = %f" % variance, sim.var_E
hold("on")
sim = Simulation(20, 1, "/scratch/henriasv/FYS3150/IsingModel_once/N20/T1")
sim.set_thermalization(0.2)
sim.calculate_properties()
sim.plot_pe()
title("Probability density function for the energy at T=1 (not normalized)")
xlabel("E")
ylabel("Count")
"""
###########################
# Plotting convergence with ordered or random initialization for T = [1, 2.4]
###########################
# Random, T=1
sim1 = Simulation(20, 1, "/scratch/henriasv/FYS3150/IsingModel_once_rand/N20/T1")
def approximate_hmean(dest_values): A = stats.mean(dest_values) varD = stats.var(dest_values) h_mean = 1/((1/A)+(varD)*pow((1/A),3)) return h_mean
def printParam(par, parString):
mean = stats.mean(par)
sd = sqrt(stats.var(par))
print parString, ' = ', mean, ' +/- ', sd
sims.plot_susceptibility(N)
sims.plot_absmag(N)
sims.plot_energies(N)
"""
###########################
# Plotting P(E) for L=20 an T = [1, 2.4]
###########################
sim = Simulation(20, 2.4, "/scratch/henriasv/FYS3150/IsingModel_once/N20/T2.4")
sim.set_thermalization(0.2)
sim.calculate_properties()
sim.plot_pe()
title("Probability density function for the energy at T=2.4 (not normalized)")
xlabel("E")
ylabel("Count")
variance = stats.var(sim.e_array)
print "variance = %f" % variance, sim.var_E
hold("on")
sim = Simulation(20, 1, "/scratch/henriasv/FYS3150/IsingModel_once/N20/T1")
sim.set_thermalization(0.2)
sim.calculate_properties()
sim.plot_pe()
title("Probability density function for the energy at T=1 (not normalized)")
xlabel("E")
ylabel("Count")
"""
###########################
# Plotting convergence with ordered or random initialization for T = [1, 2.4]
###########################
# Random, T=1
