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import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize
from astroML.linear_model import TLS_logL, LinearRegression
# TLS:
def get_m_b(beta):
b = np.dot(beta, beta) / beta[1]
m = -beta[0] / beta[1]
return m, b
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
def min_func(beta): return -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()
def plot_regression_from_trace(fitted, observed, ax=None, chains=None, multidim_ind=None):
traces = [fitted.trace, ]
xi, yi, sigx, sigy = observed
if multidim_ind is not None:
xi = xi[multidim_ind]
x = np.linspace(np.min(xi)-0.5, np.max(xi)+0.5, 50)
for i, trace in enumerate(traces):
if 'theta' in trace.varnames and 'slope' not in trace.varnames:
trace.add_values({'slope': np.tan(trace['theta'])})
if multidim_ind is not None:
trace_slope = trace['slope'][:, multidim_ind]
else:
trace_slope = trace['slope'][:, 0]
if chains is not None:
for chain in range(100, len(trace) * trace.nchains, chains):
y = trace['inter'][chain] + trace_slope[chain] * x
ax.plot(x, y, alpha=0.03, c='red')
# plot the best-fit line only
H2D, bins1, bins2 = np.histogram2d(trace_slope,
trace['inter'], bins=50)
w = np.where(H2D == H2D.max())
# choose the maximum posterior slope and intercept
slope_best = bins1[w[0][0]]
intercept_best = bins2[w[1][0]]
print("beta:", slope_best, "alpha:", intercept_best)
y = intercept_best + slope_best * x
# y_pre = fitted.predict(x[:, None])
ax.plot(x, y, ':', label='fitted')
ax.legend()
break
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