def fit2DnormalDistribution(detector, fitFlag):
X, Z = getDetectorHitData(detector)
# Descriptive statistics
skew_x_dim = skew(X)
skew_z_dim = skew(Z)
med = [np.median(X), np.median(Z)]
if fitFlag == 1:
# Bivariate normal fit
(mu_nr, sigmaX_nr,
sigmaZ_nr, alpha_nr) = fit_bivariate_normal(X, Z, robust=True)
elif fitFlag == 0:
sigmaX_nr = np.std(X)
sigmaZ_nr = np.std(Z)
alpha_nr = None
mu_nr = [np.mean(X), np.mean(Z)]
Gauss2D_dist = {'Mean': mu_nr, 'Median': med,
'Sigma X': sigmaX_nr,
'Sigma Z': sigmaZ_nr, 'Alpha': alpha_nr,
'Skew X': skew_x_dim, 'Skew Z': skew_z_dim}
return Gauss2D_dist
def check_fit_bivariate_normal(sigma1, sigma2, mu, alpha, N=1000):
# poisson stats
rtol = 2 * np.sqrt(N) / N
x, y = bivariate_normal(mu, sigma1, sigma2, alpha, N).T
mu_fit, sigma1_fit, sigma2_fit, alpha_fit = fit_bivariate_normal(x, y)
if alpha_fit > np.pi / 2:
alpha_fit -= np.pi
elif alpha_fit < -np.pi / 2:
alpha_fit += np.pi
# Circular degeneracy in alpha: test sin(2*alpha) instead
assert_allclose(np.sin(2 * alpha_fit), np.sin(2 * alpha), atol=2 * rtol)
assert_allclose(mu, mu_fit, rtol=rtol)
assert_allclose(sigma1_fit, sigma1, rtol=rtol)
assert_allclose(sigma2_fit, sigma2, rtol=rtol)
def check_fit_bivariate_normal(sigma1, sigma2, mu, alpha, N=1000):
# poisson stats
rtol = 2 * np.sqrt(N) / N
x, y = bivariate_normal(mu, sigma1, sigma2, alpha, N).T
mu_fit, sigma1_fit, sigma2_fit, alpha_fit = fit_bivariate_normal(x, y)
if alpha_fit > np.pi / 2:
alpha_fit -= np.pi
elif alpha_fit < -np.pi / 2:
alpha_fit += np.pi
# Circular degeneracy in alpha: test sin(2*alpha) instead
assert_allclose(np.sin(2 * alpha_fit), np.sin(2 * alpha), atol=2 * rtol)
assert_allclose(mu, mu_fit, rtol=rtol)
assert_allclose(sigma1_fit, sigma1, rtol=rtol)
assert_allclose(sigma2_fit, sigma2, rtol=rtol)
def calc(camera_id, frames):
pc = np.zeros((3, 5, 5))
fig, ax = plt.subplots()
for r in range(3):
print(r)
for c in range(5):
X = []
Y = []
for index in range(150):
iteration = int(index // 15)
row = int((index % 15) // 5)
col = int(index % 5)
if row == r and col == c:
[frame, x, y] = frames[index]
X.append(x)
Y.append(y)
n_std = 3
xc, x_std = np.mean(X), np.std(X)
yc, y_std = np.mean(Y), np.std(Y)
pack = zip(X.copy(), Y.copy())
X = []
Y = []
for x, y in pack:
if abs(x-xc) <= n_std * x_std and abs(y-yc) <= n_std * y_std:
X.append(x)
Y.append(y)
X = np.array(X)
Y = np.array(Y)
assert(len(X) > 0)
print('R = %d, C = %d, NUM = %d' % (r,c,len(X)))
(center, a, b, theta) = fit_bivariate_normal(X, Y, robust=True)
xc, yc = center
ell = Ellipse(center, a * n_std, b * n_std, (theta * 180. / np.pi), ec='k', fc='none', color='red')
index = r * 5 + c + 1
plt.scatter(X, Y, color=('C'+str(index)), s = 5)
plt.scatter(xc, yc, color='red', s = 10)
ax.add_patch(ell)
pc[r,c] = [xc, yc, a, b, theta]
plt.show()
pickle.dump(pc, open('models/' + str(camera_id) + '.regist', 'wb'))
def fitBinsRobust(u, o):
gaussSamples = 5000
noiseSamples = 500
#Draw random samples
np.random.seed(1)
gauss = np.random.multivariate_normal(u, o, gaussSamples)
noise = np.random.multivariate_normal([0,8], [[2, 1],[1,2]], noiseSamples)
#Add noise and flatten data
xData = np.concatenate((gauss.ravel()[::2], noise.ravel()[::2]))
yData = np.concatenate((gauss.ravel()[1::2], noise.ravel()[1::2]))
data = [xData, yData]
#Non-Robust Stats
#stats = ast.fit_bivariate_normal(xData, yData)
#Robust stats
stats = ast.fit_bivariate_normal(xData, yData, robust=True)
return data, stats
sigfit2_nonrob = np.ones(n_els) alpfit_rob = np.ones(n_els) alpfit_nonrob = np.ones(n_els) ax1 = fig.add_subplot(2, 2, 1) ax2 = fig.add_subplot(2, 2, 3) ax3 = fig.add_subplot(2, 2, 2) for i, f in enumerate(cont_frac): # add outliers distributed using a bivariate normal. X[:int(f * N)] = bivariate_normal((10, 10), 2, 4, 45 * np.pi / 180., int(f * N)) x, y = X.T # compute the non-robust statistics (mu_nr, sigma1_nr, sigma2_nr, alpha_nr) = fit_bivariate_normal(x, y, robust=False) sigfit_nonrob[i] = sigma1_nr sigfit2_nonrob[i] = sigma2_nr alpfit_nonrob[i] = alpha_nr # compute the robust statistics (mu_r, sigma1_r, sigma2_r, alpha_r) = fit_bivariate_normal(x, y, robust=True) sigfit_rob[i] = sigma1_r sigfit2_rob[i] = sigma2_r alpfit_rob[i] = alpha_r # scatter the points for i in range(n_els): print "%g\t%g\t%g" %(cont_frac[i], sigfit_rob[i], alpfit_rob[i]) ax1.plot(cont_frac, sigfit_rob, '-k', label='Robust')
# Create the figure showing the fits
fig = plt.figure(figsize=(10, 5))
fig.subplots_adjust(left=0.07, right=0.95, wspace=0.05, bottom=0.1, top=0.95)
# We'll create two figures, with two levels of contamination
for i, f in enumerate([0.05, 0.15]):
ax = fig.add_subplot(1, 2, i + 1)
# add outliers distributed using a bivariate normal.
X[:int(f * N)] = bivariate_normal((10, 10), 2, 5, 45 * np.pi / 180.,
int(f * N))
x, y = X.T
# compute the non-robust statistics
(mu_nr, sigma1_nr, sigma2_nr,
alpha_nr) = fit_bivariate_normal(x, y, robust=False)
# compute the robust statistics
(mu_r, sigma1_r, sigma2_r, alpha_r) = fit_bivariate_normal(x,
y,
robust=True)
# scatter the points
ax.scatter(x, y, s=4, lw=0, c='k', alpha=0.5)
# Draw elipses showing the fits
for Nsig in [1, 3]:
# True fit
E = Ellipse((10, 10),
sigma1 * Nsig,
sigma2 * Nsig,
# is drawn upon the data.
from astroML.stats import fit_bivariate_normal
import numpy as np
import matplotlib.pyplot as plt
import gauss
# Produce a number of points in x-y from 1 bi-variate gaussian
# distribution.
mean = [1,1]
cov = [[3,1],[1,3]]
N = 1000
x,y = np.random.multivariate_normal(mean,cov,N).T
# Fit method provided by astroML
mean_est,sigma1,sigma2,alpha = fit_bivariate_normal(x,y)
# Plot bi-variate gaussian with parameters and determine
# variances in x-y. The covariance and variances should
# approximate the original distribution drawn from.
domain = 10;
xCord = np.linspace(-domain,domain,N/domain)
yCord = np.linspace(-domain,domain,N/domain)
A = 1;
X,Y,Z,varx,vary,cov,rho,P1,P2,P = gauss.mult_gaussPrincipal(A,xCord,yCord,mean[0],mean[1],sigma1**2,sigma2**2,alpha)
sigma_x = np.sqrt(varx); sigma_y = np.sqrt(vary)
V = [cov, 2*cov]
plt.figure(1)
plt.xlabel('x'); plt.ylabel('y'); plt.title('Distribution of Points with Gaussian Fit (As Contours)')
lab = r'Estimated Parameters: $\sigma_x=%.2f$,$\sigma_y=%.2f$,$\sigma_{xy}=%.2f$,$\alpha=%.2f$' % (sigma_x,sigma_y,cov,alpha)
p1, = plt.plot(x,y,'x'); plt.axis('equal')
