def _extract_plateau_mean_fit(fit_target, f, x, y, y_err, inverse_fit=False):
"""
Extract y0 with y0err at a given fit_target by using a line fitw ith y_err
as weights. If inverse, will return x0 with x0err at a given y0.
Args:
fit_target: float, value at which to extract a y0 and y0err.
f: function to fit against.
x: numpy float array, x-axis to fit against.
y: numpy float array, y values.
y_err: numpy float array, y standard deviation values.
inverse_fit: bool, optional. If True, will perform an inverse fit.
Default is False.
Returns:
y0, y0_error, chi_squared
"""
# Line fit from the mean values and their standard deviations
pol_line, polcov_line = sciopt.curve_fit(f, x, y, sigma=y_err,
absolute_sigma=False)
pol_line_err = np.sqrt(np.diag(polcov_line))
# Extract fit target values
lfit_default = lfit.LineFit(x, y, y_err)
lfit_default.set_fit_parameters(pol_line[1], pol_line_err[1],
pol_line[0], pol_line_err[0], weighted=True)
if inverse_fit:
y0, y0_error = lfit_default.inverse_fit(fit_target, weighted=True)
_, _, chi_squared = lfit_default(fit_target, weighted=True)
else:
y0, y0_error, chi_squared = lfit_default(fit_target, weighted=True)
y0_error = ((y0_error[1] - y0_error[0])/2)
# f_err = lambda _x, a_err, b_err: np.sqrt((_x*a_err)**2 + (b_err)**2 + 2*a_err*_x*b_err)
# y0_error = f_err(fit_target, pol_line_err[0], pol_line_err[1])
# print "OLD METHOD: %20.16f +/- %-18.16f, chi^2 %g" % (y0, y0_error, chi_squared)
# _a, _a_err = lfit_default.b1w, lfit_default.b1w_err
# _b, _b_err = lfit_default.b0w, lfit_default.b0w_err
# y_func = lambda _x: _a*_x + _b
# y_error_func = lambda _x: np.sqrt(
# (_a_err*_x)**2 + (_b_err)**2 + 2*_a_err*_x*_b_err)
# chi_squared = lfit_default.chi_squared(y_func(x), y_error_func(x), x)
# y0 = y_func(fit_target)
# y0_error = y_error_func(fit_target)
# print _a, _a_err, _b, _b_err
# print "WITH COVARIANCE TERM", y0, y0_error
if isinstance(y0, (tuple, list, np.ndarray)):
y0 = y0[0]
if isinstance(y0_error, (tuple, list, np.ndarray)):
y0_error = y0_error[0]
return y0, y0_error, chi_squared
def _test_plateau_mean(x, y, x0, _f=lambda _x, a, b: _x * a + b):
"""
Performs a line fit through points x points to get an exact value for x0.
"""
x_hat = x[0, :]
y_mean, y_err = y.mean(axis=0), y.std(axis=0)
# Line fit from the mean values and their standard deviations
pol_line, polcov_line = sciopt.curve_fit(_f,
x_hat,
y_mean,
sigma=y_err,
absolute_sigma=False)
pol_line_err = np.sqrt(np.diag(polcov_line))
x_fit_arr = np.linspace(x_hat[0], x_hat[-1], 1000)
# Extract fit target values
lfit_default = lfit.LineFit(x_hat, y_mean, y_err)
lfit_default.set_fit_parameters(pol_line[1],
pol_line_err[1],
pol_line[0],
pol_line_err[0],
weighted=True)
y0, y0_error, chi_squared = lfit_default(x0, weighted=True)
y0_error = ((y0_error[1] - y0_error[0]) / 2)
y_fit_mean, y_fit_err, _ = lfit_default(x_fit_arr, weighted=True)
y_fit_err = ((y_fit_err[1] - y_fit_err[0]) / 2.0)
y_hat, _, _ = lfit_default(x_hat, weighted=True)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x_fit_arr, y_fit_mean, label="Line fit", color="tab:blue")
ax.fill_between(x_fit_arr,
y_fit_mean - y_fit_err,
y_fit_mean + y_fit_err,
alpha=0.5,
color="tab:blue")
ax.errorbar(x_hat,
y_mean,
yerr=y_err,
marker=".",
linestyle="none",
color="tab:orange",
label=r"Signal")
ax.set_ylim(0, 5)
ax.set_title(r"$\chi^2=%g$" %
lfit.LineFit.chi_squared(y_mean, y_err, y_hat))
ax.axvline(x0, color="tab:grey", linestyle=":", label=r"$x_0$ fit target")
ax.legend(loc="best", prop={"size": 8})
fig.savefig("tests/plateau_mean_inverse_fit.pdf", dpi=400)
# plt.show()
plt.close(fig)
return _extract_plateau_mean_fit(x0, _f, x_hat, y_mean, y_err)[:2]
# cov2 = lftools._get_covariance_matrix_from_raw(V, iscov=True)
cov2 = cov_nearest(V, method="nearest", threshold=9e-16, n_fact=500)
pol_raw2, polcov_raw2 = sciopt.curve_fit(f,
x,
y,
sigma=cov2,
p0=[intercept, slope],
maxfev=1200)
pol_raw_err2 = np.sqrt(np.diag(polcov_raw2))
print slope, pol_raw0[0]
print slope, pol_raw1[0]
print slope, pol_raw2[0]
# Extract fit target values
lfit_raw = lfit.LineFit(x, y, y_err)
fig1 = plt.figure()
ax1 = fig1.add_subplot(111)
ax1.errorbar(x, y, yerr=y_err, label="Original", color="tab:blue")
lfit_raw.set_fit_parameters(pol_raw0[1],
pol_raw_err0[1],
pol_raw0[0],
pol_raw_err0[0],
weighted=True)
# y1, _, _ = lfit_raw(x, weighted=True)
y0 = f(x, pol_raw0[0], pol_raw0[1])
y0_err = f_err(x, pol_raw_err0[0], pol_raw_err0[1])
ax1.plot(x, y0, label=r"Method 0: $w=y_{err}$", color="tab:brown")
def _test_inverse_line_fit():
"""
Function for testing the inverse line fit.
"""
import scipy.optimize as sciopt
np.random.seed(1)
# Generates signal with noise
x_start = 0
x_end = 5
a = 0.65
b = 1.1
N = 10 # Number of data points
M = 40 # Number of observations at each data point
x = np.linspace(x_start, x_end, N)
x_matrix = np.ones((M, N)) * x
signal_spread = 0.5
signal = np.cos(np.random.uniform(-signal_spread, signal_spread, (M, N)))
signal = np.random.uniform(-signal_spread, signal_spread, (M, N))
signal += a*x_matrix + b
signal_err = np.std(signal, axis=0)
signal_mean = np.mean(signal, axis=0)
# My line fit
x_hat = np.linspace(x_start, x_end, 10)
X_values = np.linspace(x_start, x_end, 1000)
def _f(_x, a, b):
return _x*a + b
from autocorrelation import Autocorrelation
# print help(Autocorrelation)
_ac_array = np.zeros((N, M/2))
_tau_ints = np.zeros(N)
print signal.shape, M
for i in xrange(N):
ac = Autocorrelation(signal[:, i])
_ac_array[i] = ac.R
_tau_ints[i] = ac.integrated_autocorrelation_time()
def autocov(x, y):
n = len(x)
# variance = x.var()
x = x-x.mean()
y = y-y.mean()
G = np.correlate(x, y, mode="full")[-n:]
G /= np.arange(n, 0, -1)
return G
cov_mat = np.cov(signal.T)
print cov_mat.shape
for i in xrange(N):
cov_mat[i, i] *= 2*_tau_ints[i]
l = lfit.LineFit(x, signal_mean, y_err=signal_err)
signal_err_corrected = np.sqrt(np.diag(cov_mat))
print "signal_err_corrected: ", signal_err_corrected[:5]
def get_err(_err): return (_err[1] - _err[0])/2
pol1, polcov1 = np.polyfit(
x, signal_mean, 1, w=1/np.diag(cov_mat), cov=True)
l.set_fit_parameters(pol1[1], np.sqrt(polcov1[1, 1]), pol1[0],
np.sqrt(polcov1[0, 0]), weighted=True)
y_hat, y_hat_err, chi_squared = l(X_values, weighted=True)
print "With polyfit: ", np.sqrt(np.diag(polcov1)), \
get_err(y_hat_err)[:5]
pol1, polcov1 = scipy.optimize.curve_fit(_f, x, signal_mean,
sigma=np.sqrt(np.diag(cov_mat)))
l.set_fit_parameters(pol1[1], np.sqrt(polcov1[1, 1]), pol1[0],
np.sqrt(polcov1[0, 0]), weighted=True)
y_hat, y_hat_err, chi_squared = l(X_values, weighted=True)
print "With naive autocorr: ", np.sqrt(np.diag(polcov1)), \
get_err(y_hat_err)[:5]
pol1, polcov1 = sciopt.curve_fit(
_f, x, signal_mean, sigma=np.cov(signal.T))
l.set_fit_parameters(pol1[1], np.sqrt(polcov1[1, 1]), pol1[0],
np.sqrt(polcov1[0, 0]), weighted=True)
y_hat, y_hat_err, chi_squared = l(X_values, weighted=True)
print "With cov(signal.T): ", np.sqrt(np.diag(polcov1)), \
get_err(y_hat_err)[:5]
pol1, polcov1 = sciopt.curve_fit(_f, x, signal_mean, sigma=signal_err)
l.set_fit_parameters(pol1[1], np.sqrt(polcov1[1, 1]), pol1[0],
np.sqrt(polcov1[0, 0]), weighted=True)
y_hat, y_hat_err, chi_squared = l(X_values, weighted=True)
print "With only signal errors: ", np.sqrt(np.diag(polcov1)), \
get_err(y_hat_err)[:5]
def _test_simple_line_fit():
"""
Function for testing the case where one compares the curve_fit module in
scipy.optimize with what I have created.
SciPy and lfit.LineFit should fit exact down to around 8th digit.
"""
import random
import scipy.optimize as sciopt
np.random.seed(1234)
def _fit_var_printer(var_name, var, var_error, w=16):
return "{0:<s} = {1:<.{w}f} +/- {2:<.{w}f}".format(var_name, var,
var_error, w=w)
# Generates signal with noise
a = 0.65
b = 1.1
N = 8
M = 10
x_start = 0
x_end = 5
x = np.linspace(x_start, x_end, N)
x_matrix = np.ones((M, N)) * x
signal_spread = 0.7
signal = a*x + b + np.random.uniform(-signal_spread, signal_spread, (M, N))
signal_err = np.std(signal, axis=0)
signal_mean = np.mean(signal, axis=0)
fit_target = 2.5
# # Generates signal with noise
# a = 0.65
# b = 1.1
# N = 5
# x = np.linspace(0, 5, N)
# signal_spread = 0.5
# signal_mean = a*x + b + np.random.uniform(-signal_spread, signal_spread, N)
# signal_err = np.random.uniform(0.1, 0.3, N)
# Fits without any weights first
pol1, polcov1 = sciopt.curve_fit(lambda x, a, b: x*a + b, x, signal_mean)
scipy_lfit = lfit.LineFit(x, signal_mean, signal_err)
scipy_lfit.set_fit_parameters(pol1[1], np.sqrt(polcov1[1, 1]), pol1[0],
np.sqrt(polcov1[0, 0]), weighted=False)
y_scipy = scipy_lfit(fit_target, weighted=False)
# Numpy polyfit
polyfit1, polyfitcov1 = np.polyfit(x, signal_mean, 1, cov=True)
polyfit_err = np.sqrt(np.diag(polyfitcov1))
fit = lfit.LineFit(x, signal_mean, signal_err)
x_hat = np.linspace(0, 5, 100)
# Unweighted fit
y_hat, y_hat_err, f_params, chi_unweighted = fit.fit(x_hat)
b0, b0_err, b1, b1_err = f_params
# Fit target
x_fit, x_fit_err = fit.inverse_fit(fit_target)
print "UNWEIGTHED LINE FIT"
print "Numpy polyfit:"
print _fit_var_printer("a", polyfit1[0], polyfit_err[0])
print _fit_var_printer("b", polyfit1[1], polyfit_err[1])
print "SciPy curve_fit:"
print _fit_var_printer("a", pol1[0], polcov1[0, 0])
print _fit_var_printer("b", pol1[1], polcov1[1, 1])
print "Extraction point x0 value: ", y_scipy[0][0], ((y_scipy[1][-1] - y_scipy[1][0])/2.0)[0]
print "lfit.LineFit:"
print _fit_var_printer("a", b1, b1_err)
print _fit_var_printer("b", b0, b0_err)
print "Goodness of fit: %f" % chi_unweighted
# print "b = {0:<.10f} +/- {1:<.10f}".format(b0, self.b0_err)
fig1 = plt.figure()
ax1 = fig1.add_subplot(211)
ax1.axhline(fit_target, linestyle="dashed", color="tab:grey")
ax1.plot(x_hat, y_hat, label="Unweighted fit", color="tab:blue")
ax1.fill_between(x_hat, y_hat_err[0], y_hat_err[1], alpha=0.5,
color="tab:blue")
ax1.errorbar(x, signal_mean, yerr=signal_err, marker="o", label="Signal",
linestyle="none", color="tab:orange")
ax1.set_ylim(0, 5)
ax1.axvline(x_fit, color="tab:orange")
ax1.fill_betweenx(np.linspace(0, 6, 100), x_fit - x_fit_err, x_fit + x_fit_err,
label=r"$x_0\pm\sigma_{x_0}$", alpha=0.5, color="tab:orange")
ax1.legend(loc="best", prop={"size": 8})
ax1.set_title("Fit test")
# Weighted curve_fit
print "WEIGTHED LINE FIT"
# Numpy polyfit
polyfit1, polyfitcov1 = np.polyfit(x, signal_mean, 1, cov=True,
w=1/signal_err)
polyfit_err = np.sqrt(np.diag(polyfitcov1))
print "Numpy polyfit:"
print _fit_var_printer("a", polyfit1[0], polyfit_err[0])
print _fit_var_printer("b", polyfit1[1], polyfit_err[1])
# SciPy curve fit
polw, polcovw = sciopt.curve_fit(lambda x, a, b: x*a + b, x, signal_mean,
sigma=signal_err)
scipy_lfit_w = lfit.LineFit(x, signal_mean, y_err=signal_err)
scipy_lfit_w.set_fit_parameters(polw[1], np.sqrt(polcovw[1, 1]), polw[0],
np.sqrt(polcovw[0, 0]), weighted=True)
y_scipy_w = scipy_lfit_w(fit_target, weighted=True)
print "SciPy curve_fit:"
print _fit_var_printer("a", polw[0], polcovw[0, 0])
print _fit_var_printer("b", polw[1], polcovw[1, 1])
print "Extraction point x0 value: ", y_scipy_w[0][0], \
((y_scipy_w[1][-1] - y_scipy_w[1][0])/2.0)[0]
signal_cov = _get_covariance_matrix_from_raw(signal.T)
polwc, polcovwc = sciopt.curve_fit(lambda _x, _a, _b: _x*_a + _b, x,
signal_mean, sigma=signal_cov)
scipy_lfit_wc = lfit.LineFit(x, signal_mean, y_err=signal_err)
scipy_lfit_wc.set_fit_parameters(polwc[1], np.sqrt(polcovwc[1, 1]),
polwc[0], np.sqrt(polcovwc[0, 0]), weighted=True)
_a, _a_err = scipy_lfit_wc.b1w, scipy_lfit_wc.b1w_err
_b, _b_err = scipy_lfit_wc.b0w, scipy_lfit_wc.b0w_err
# y = a*x + b
# dy = da*x + db
# dy**2 = np.sqrt((da*x)**2 + db**2 + 2*da*x*db)
_y = _a*fit_target + _b
_y_err = np.sqrt(
(_a_err*fit_target)**2 + (_b_err)**2 + 2*_a_err*fit_target*_b_err)
y_scipy_wc = [_y, [_y-_y_err, _y+_y_err]]
y_scipy_wc = scipy_lfit_wc(fit_target, weighted=True)
print "SciPy curve_fit with covariance:"
print _fit_var_printer("a", polwc[0], polcovwc[0, 0])
print _fit_var_printer("b", polwc[1], polcovwc[1, 1])
print "Extraction point x0 value: ", y_scipy_wc[0], \
((y_scipy_wc[1][-1] - y_scipy_wc[1][0])/2.0)
# Weighted lfit.LineFit
yw_hat, yw_hat_err, f_params_weighted, chi_weighted = fit.fit_weighted(
x_hat)
b0, b0_err, b1, b1_err = f_params_weighted
xw_fit, xw_fit_error = fit.inverse_fit(fit_target, weighted=True)
print "lfit.LineFit:"
print _fit_var_printer("a", b1, b1_err)
print _fit_var_printer("b", b0, b0_err)
print "Goodness of fit: %f" % chi_weighted
ax2 = fig1.add_subplot(212)
ax2.axhline(fit_target, linestyle="dashed", color="tab:grey")
ax2.errorbar(x, signal_mean, yerr=signal_err, marker="o", label="Signal",
linestyle="none", color="tab:orange")
ax2.plot(x_hat, yw_hat, label="Weighted fit", color="tab:blue")
ax2.fill_between(x_hat, yw_hat_err[0], yw_hat_err[1], alpha=0.5,
color="tab:blue")
ax2.set_ylim(0, 5)
ax2.axvline(xw_fit, color="tab:orange")
ax2.fill_betweenx(np.linspace(0, 6, 100), xw_fit - xw_fit_error,
xw_fit + xw_fit_error, label=r"$x_{0,w}\pm\sigma_{x_0,w}$",
alpha=0.5, color="tab:orange")
ax2.legend(loc="best", prop={"size": 8})
fig1.savefig("tests/line_fit_example.png", dpi=400)
plt.show()
plt.close(fig1)
def __get_tau_int(x0, x, tau_int, tau_int_err):
"""Smal internal function for getting tau int at x0."""
tauFit = lfit.LineFit(x, tau_int, y_err=tau_int_err)
tau_int0, _, _, _ = tauFit.fit_weighted(x0)
return tau_int0[0]
def _extract_bootstrap_fit(fit_target, f, x, y, y_err, y_raw, tau_int=None,
tau_int_err=None, plot_samples=False, F=lambda _y: _y, FDer=lambda _y,
_yerr: _yerr, inverse_fit=False, full=False):
"""
Extract y0 with y0err at a given x0 by using line fitting the y_raw data.
Error will be corrected by line fitting tau int and getting the exact
value at x0.
Args:
fit_target: float, value at which to extract a y0 and y0err.
f: function to fit against.
x: numpy float array, x-axis to fit against.
y: numpy float array, y values.
y_err: numpy float array, y standard deviation values.
y_raw: numpy float array, y raw values. E.g. bootstrap, jackknifed or
analyzed values.
tau_int: optional, numpy float array, autocorrelation times.
tau_int_err: optional, numpy float array, autocorrelation time errors.
plot_bs: bool, optional. Will plot the bootstrapped line fits and show.
F: function, optional, will modify the bootstrap data after
samples has been taken by this function.
FDer: function, optional, will propagate the error of the bootstrapped
line fit. Should take y and yerr. Calculated by regular error
propagation.
inverse_fit: bool, optional. If True, will perform an inverse fit, with
the fit target as a y axis value. Default is False.
full: bool, optional. If True, returns the entire line, and not just
y0 with its errors.
Returns:
y0, y0_error, tau_int0, chi_squared
"""
N, M = y_raw.shape # Points, samples
y0_sample = np.zeros(M)
y0_sample_err = np.zeros(M)
if plot_samples:
N_plot_values = 1000
x_plot = np.linspace(x[0], x[-1], N_plot_values)
fig_samples = plt.figure()
ax_samples = fig_samples.add_subplot(111)
# Empty arrays for storing plot means and errors
y_plot_points = np.zeros((N, M))
plot_ymean = np.zeros((N_plot_values, M))
plot_yerr = np.zeros((N_plot_values, M, 2))
# Gets the bootstrapped line fits
# for i, y_sample in enumerate(tqdm(y_raw.T, desc="Sample line fitting")):
for i, y_sample in enumerate(y_raw.T):
p, pcov = sciopt.curve_fit(f, x, y_sample, p0=[0.01, 0.18])
pfit_err = np.sqrt(np.diag(pcov))
# Fits sample
fit_sample = lfit.LineFit(x, y_sample)
fit_sample.set_fit_parameters(p[1], pfit_err[1], p[0], pfit_err[0])
if inverse_fit:
# Performs an inverse fit where y0 is the target value, and not x0.
# _x0_err is not needed, is error cannot be inflated by the
# autocorrelation.
try:
y0_sample[i], y0_sample_err[i] = \
fit_sample.inverse_fit(fit_target)
except IndexError as err:
print "Points included: %s" % y0_raw.shape
fit_sample.plot()
exit(err)
else:
y0_sample[i], _tmp_err, _ = fit_sample(fit_target)
y0_sample_err[i] = (_tmp_err[1] - _tmp_err[0])/2
if plot_samples:
# Retrieves at exactly sample values x
y_plot_points[:, i], _, _ = fit_sample(x)
# Retrieves a smooth set of y values.
plot_ymean[:, i], _p_err, _ = fit_sample(x_plot)
plot_yerr[:, i] = np.asarray(_p_err).T
ax_samples.fill_between(x_plot, plot_yerr[:, i, 0], plot_yerr[:, i, 1],
alpha=0.01, color="tab:red")
ax_samples.plot(
x_plot, plot_ymean[:, i], color="tab:red", alpha=0.1)
y0_mean = F(np.mean(y0_sample, axis=0))
# Gets the tau int. Asserted that is is provided.
if not isinstance(tau_int, types.NoneType) and \
not isinstance(tau_int_err, types.NoneType) and \
not inverse_fit:
tau_int0 = __get_tau_int(fit_target, x, tau_int, tau_int_err)
# tau_int0 = __get_tau_int(y0_mean, x, tau_int, tau_int_err)
else:
tau_int0 = 0.5
# # Using error propegation on the std of the fit and correcting by tau int
# y0_std = FDer(np.mean(y0_sample, axis=0),
# np.std(y0_sample, axis=0) * np.sqrt(2*tau_int0))
# print y0_std
# # Using error propegation on the fit errors and correcting by tau int
# y0_std = FDer(np.mean(y0_sample, axis=0),
# np.mean(y0_sample_err) * np.sqrt(2*tau_int0))
# print y0_std
# y0_std = np.mean(FDer(y0_sample, y0_sample_err * np.sqrt(2*tau_int0)))
# print y0_std
# y0_std = np.mean(FDer(y0_sample, y0_sample_err))*np.sqrt(2*tau_int0)
# print y0_std
# Using the mean of the line fit errors and correcting it by tau int
# y0_std = np.mean(F(y0_sample_err))*np.sqrt(2*tau_int0)
# print y0_std
# Using standard deviation of the line fits and correcting it by tau int
y0_std = np.std(F(y0_sample))*np.sqrt(2*tau_int0)
# print y0_std
# print y0_std
# exit(1)
if plot_samples:
sample_mean = F(np.mean(plot_ymean, axis=1))
sample_std = FDer(np.mean(plot_ymean, axis=1),
np.std(plot_ymean, axis=1) * np.sqrt(2*tau_int0))
y_sample_points = F(np.mean(y_plot_points, axis=1))
bs_chi2 = lfit.LineFit.chi_squared(y, y_err, y_sample_points)
# sample_mean = np.mean(plot_ymean, axis=1)
# sample_std = np.std(plot_ymean, axis=1)*np.sqrt(2*tau_int0)
# Sets up sample std edges
ax_samples.plot(x_plot, sample_mean - sample_std, x_plot,
sample_mean + sample_std, color="tab:blue", alpha=0.6)
# Plots sample mean
ax_samples.plot(x_plot, sample_mean, label="Averaged samples fit",
color="tab:blue")
# Plots original data with error bars
ax_samples.errorbar(x, y, yerr=y_err, marker=".",
linestyle="none", color="tab:orange", label="Original")
ax_samples.set_title(r"$\chi^2: %g$" % bs_chi2)
plt.show()
plt.close(fig_samples)
if full:
return y0_mean, y0_std, tau_int0, bs_chi2, x_plot, sample_mean, sample_std
else:
return y0_mean, y0_std, tau_int0
def _extract_plateau_fit(fit_target, f, x, y, y_err, y_raw, tau_int=None,
tau_int_err=None, inverse_fit=False):
"""
Extract y0 with y0err at a given x0 by using a line fit with the
covariance matrix from the raw y data.
Args:
fit_target: float, value at which to extract a y0 and y0err.
f: function to fit against.
x: numpy float array, x-axis to fit against.
y: numpy float array, y values.
y_err: numpy float array, y standard deviation values.
y_raw: numpy float array, y raw values. E.g. bootstrap, jackknifed or
analyzed values.
tau_int: numpy float array, optional, autocorrelation times. Default
is None.
tau_int_err: numpy float array, optional, autocorrelation time errors.
Default is None.
inverse_fit: bool, optional. If True, will perform an inverse fit.
y0, y0err -> x0, x0err. Default is False.
Returns:
y0, y0_error, tau_int0, chi_squared
"""
assert not isinstance(y_raw, types.NoneType), \
"missing y_raw values."
assert not isinstance(tau_int, types.NoneType), \
"missing tau_int values."
assert not isinstance(tau_int_err, types.NoneType), \
"missing tau_int_err values."
cov_raw = _get_covariance_matrix_from_raw(y_raw)
# Line fit from the mean values and the raw values covariance matrix
pol_raw, polcov_raw = sciopt.curve_fit(f, x, y, sigma=cov_raw,
p0=[0.18, 0.0], maxfev=1200)
pol_raw_err = np.sqrt(np.diag(polcov_raw))
# Extract fit target values
lfit_raw = lfit.LineFit(x, y, y_err)
lfit_raw.set_fit_parameters(pol_raw[1], pol_raw_err[1], pol_raw[0],
pol_raw_err[0], weighted=True)
y0, y0_error, chi_squared = lfit_raw(fit_target, weighted=True)
if inverse_fit:
y0, y0_error = lfit_raw.inverse_fit(fit_target, weighted=True)
else:
y0 = y0[0] # y0 and y0_error both comes in form of arrays
def f_err(_x, a_err, b_err): return np.sqrt(
(_x*a_err)**2 + (b_err)**2 + 2*a_err*_x*b_err)
err = f_err(fit_target, pol_raw_err[0], pol_raw_err[1])
# If I want to include covariances in old fit model, assuming that
# y0_error is only a combination of a and b errors.
y0_error = (y0_error[1][0] - y0_error[0][0])/2
y0_error = np.sqrt(
y0_error**2 + 2*fit_target*pol_raw_err[0]*pol_raw_err[1])
# print y0_error, err, y0_error - err
y0_error = f_err(fit_target, pol_raw_err[0], pol_raw_err[1])
# y0_error = err
# print "Plateau fit: %20.16f +/- %-20.16f, chi^2 %g" % (
# y0, y0_error, chi_squared)
# exit(1)
# Gets the tau int using a line fit, given it is provide.
if not isinstance(tau_int, types.NoneType) and \
not isinstance(tau_int_err, types.NoneType):
if inverse_fit:
tau_int0 = __get_tau_int(y0, x, tau_int, tau_int_err)
else:
tau_int0 = __get_tau_int(fit_target, x, tau_int, tau_int_err)
else:
tau_int0 = 0.5
# Corrects error with the tau int
y0_error *= np.sqrt(2*tau_int0)
return y0, y0_error, tau_int0, chi_squared