data = data[5:] # no outliers x = data['x'] y = data['y'] sigma_x = data['sigma_x'] sigma_y = data['sigma_y'] rho_xy = data['rho_xy'] #------------------------------------------------------------ # Find best-fit parameters X = np.vstack((x, y)).T dX = np.zeros((len(x), 2, 2)) dX[:, 0, 0] = sigma_x**2 dX[:, 1, 1] = sigma_y**2 dX[:, 0, 1] = dX[:, 1, 0] = rho_xy * sigma_x * sigma_y min_func = lambda beta: -TLS_logL(beta, X, dX) beta_fit = optimize.fmin(min_func, x0=[-1, 1]) #------------------------------------------------------------ # Plot the data and fits fig = plt.figure(figsize=(8, 4)) fig.subplots_adjust(left=0.1, right=0.95, wspace=0.25, bottom=0.15, top=0.9) #------------------------------------------------------------ # first let's visualize the data ax = fig.add_subplot(121) ax.scatter(x, y, c='k') plot_ellipses(x, y, sigma_x, sigma_y, rho_xy, ax=ax) #------------------------------------------------------------ # plot the best-fit line
def min_func(beta):
return -TLS_logL(beta, X, dX)
def plot_regressions(ksi,
eta,
x,
y,
sigma_x,
sigma_y,
add_regression_lines=False,
alpha_in=1,
beta_in=0.5,
basis='linear'):
figure = plt.figure(figsize=(8, 6))
ax = figure.add_subplot(111)
ax.scatter(x, y, alpha=0.5)
ax.errorbar(x, y, xerr=sigma_x, yerr=sigma_y, alpha=0.3, ls='')
ax.set_xlabel('x')
ax.set_ylabel('y')
x0 = np.linspace(np.min(x) - 0.5, np.max(x) + 0.5, 20)
# True regression line
if alpha_in is not None and beta_in is not None:
if basis == 'linear':
y0 = alpha_in + x0 * beta_in
elif basis == 'poly':
y0 = alpha_in + beta_in[0] * x0 + beta_in[1] * x0 * x0 + beta_in[
2] * x0 * x0 * x0
ax.plot(x0, y0, color='black', label='True regression')
else:
y0 = None
if add_regression_lines:
for label, data, *target in [['fit no errors', x, y, 1],
['fit y errors only', x, y, sigma_y],
['fit x errors only', y, x, sigma_x]]:
linreg = LinearRegression()
linreg.fit(data[:, None], *target)
if label == 'fit x errors only' and y0 is not None:
x_fit = linreg.predict(y0[:, None])
ax.plot(x_fit, y0, label=label)
else:
y_fit = linreg.predict(x0[:, None])
ax.plot(x0, y_fit, label=label)
# TLS
X = np.vstack((x, y)).T
dX = np.zeros((len(x), 2, 2))
dX[:, 0, 0] = sigma_x
dX[:, 1, 1] = sigma_y
min_func = lambda beta: -TLS_logL(beta, X, dX)
beta_fit = optimize.fmin(min_func, x0=[-1, 1])
m_fit, b_fit = get_m_b(beta_fit)
x_fit = np.linspace(-10, 10, 20)
ax.plot(x_fit, m_fit * x_fit + b_fit, label='TLS')
ax.set_xlim(np.min(x) - 0.5, np.max(x) + 0.5)
ax.set_ylim(np.min(y) - 0.5, np.max(y) + 0.5)
ax.legend()