def gauss(x, y):
print(
'Selecione a regiao do fit gaussiano quantas vezes for necessario')
l1, l2 = fit_gauss(x, y)
index1 = np.where(abs(x - l1) == min(abs(x - l1)))[0]
index1 = np.int(index1)
index2 = np.where(abs(x - l2) == min(abs(x - l2)))[0]
index2 = np.int(index2)
print(index1, index2)
x1 = x[index1:index2]
y1 = y[index1:index2]
mod = GaussianModel()
pars = mod.guess(y1, x=x1)
out = mod.fit(y1, pars, x=x1)
xgauss = copy.copy(x1)
ygauss = copy.copy(out.best_fit)
#-#######
x0 = x[0:index1]
y0 = np.zeros(len(y[0:index1]))
x2 = x[index2:]
y2 = np.zeros(len(y[index2:]))
x1 = np.append(x0, x1)
x1 = np.append(x1, x2)
y1 = np.append(y0, out.best_fit)
y1 = np.append(y1, y2)
print(out.fit_report(min_correl=0.25))
mod = GaussianModel()
pars = mod.guess(y1, x=x1)
out = mod.fit(y1, pars, x=x1)
#-#######
return x1, out.best_fit, xgauss, ygauss
def twoPeakGaussianFit(self):
try:
nRow, nCol = self.dockedOpt.fileInfo()
self.binFitData = np.zeros((nRow, 0))
self.TwoPkGausFitData = np.zeros((nCol, 12)) # Creates the empty 2D List
for j in range(nCol):
yy1 = []
yy2 = []
yy = self.dockedOpt.TT[:, j]
i = 0
for y in yy:
if i < len(yy) / 2:
yy1.append(y)
else:
yy2.append(y)
i += 1
xx = np.arange(0, len(yy))
xx1 = np.arange(0, len(yy) / 2)
xx2 = np.arange(len(yy) / 2, len(yy))
x1 = xx[0]
x2 = xx[-1]
y1 = yy[0]
y2 = yy[-1]
m = (y2 - y1) / (x2 - x1)
b = y2 - m * x2
mod1 = GaussianModel(prefix='p1_')
mod2 = GaussianModel(prefix='p2_')
pars1 = mod1.guess(yy1, x=xx1)
pars2 = mod2.guess(yy2, x=xx2)
mod = mod1 + mod2 + LinearModel()
pars = pars1 + pars2
pars.add('intercept', value=b, vary=True)
pars.add('slope', value=m, vary=True)
out = mod.fit(yy, pars, x=xx, slope=m)
self.TwoPkGausFitData[j, :] = (out.best_values['p1_amplitude'], 0, out.best_values['p1_center'],
0, out.best_values['p1_sigma'], 0,
out.best_values['p2_amplitude'], 0, out.best_values['p2_center'],
0, out.best_values['p2_sigma'], 0)
# Saves fitted data of each fit
fitData = out.best_fit
binFit = np.reshape(fitData, (len(fitData), 1))
self.binFitData = np.concatenate((self.binFitData, binFit), axis=1)
if self.continueGraphingEachFit == True:
self.graphEachFitRawData(xx, yy, out.best_fit, 'G')
return False
except Exception as ex:
qtWidgets.QMessageBox.warning(self.myMainWindow, "Error", "Please make sure the guesses are realistic when fitting."
"\n\nException: " + str(ex))
return True
def test_guess_requires_x():
"""Regression test for GH #747."""
x = np.arange(100)
y = np.exp(-(x - 50)**2 / (2 * 10**2))
mod = GaussianModel()
msg = r"guess\(\) missing 1 required positional argument: 'x'"
with pytest.raises(TypeError, match=msg):
mod.guess(y)
def fit_gaussians_to_emission_lines(spectra, centers, x=None, verbose=False):
# First, sort out x
if x is None: x = np.arange(spectra.shape[0])
# we know which peaks to calibrate off, we still need to fit a Gaussian to them so we can get the exact peak position instead of just the highest pixel
pars = []
Model = None
gaussmodel = GaussianModel(prefix='f{:}_'.format(0))
pars = gaussmodel.guess(x, spectra)
pars['f{:}_center'.format(0)].set(vary=True,
value=centers[0],
min=centers[0] - 2,
max=centers[0] + 2)
pars['f{:}_amplitude'.format(0)].set(
vary=True,
value=0.5,
)
pars['f{:}_sigma'.format(0)].set(vary=True, value=2, min=0.9, max=5)
for i in range(1, centers.shape[0]):
gaussmodel_ = GaussianModel(prefix='f{:}_'.format(i))
pars_ = gaussmodel_.guess(x, spectra)
pars_['f{:}_center'.format(i)].set(vary=True,
value=centers[i],
min=centers[i] - 5,
max=centers[i] + 5)
pars_['f{:}_amplitude'.format(i)].set(vary=True, value=0.5)
pars_['f{:}_sigma'.format(i)].set(vary=True, value=2, min=0.9, max=5)
gaussmodel = gaussmodel + gaussmodel_
pars = pars + pars_
out = gaussmodel.fit(spectra, pars, x=x, method='powell')
if verbose:
print('Gaussians fit to spectra:')
print(out.fit_report())
centers = np.array([
float(out.params['f{:}_center'.format(i)].value)
for i in range(len(centers))
])
aplitudes = np.array([
float(out.params['f{:}_amplitude'.format(i)].value)
for i in range(len(centers))
])
sigmas = np.array([
float(out.params['f{:}_sigma'.format(i)].value)
for i in range(len(centers))
])
return centers, aplitudes, sigmas, out
def fit_gauss(graph=False, cdf=False, residuals=False):
xranges, yranges, xrange, yrange, filename1, dat1 = range_to_list()
FitVals = DataFrame(columns=['Sigma', 'Center', 'Amplitude', 'FWHM', 'Height', 'Intercept', 'Slope', 'ChiSq',
'RedChiSq', 'Akaike', 'Bayesian'])
for i in range(0, len(xranges)):
mdl = GaussianModel()
params = mdl.guess(data=yranges[i], x=xranges[i])
result = mdl.fit(yranges[i], params, x=xranges[i])
print(result.fit_report())
FitVals.at[i, 'Sigma'] = ufloat(result.params['sigma'].value, result.params['sigma'].stderr)
FitVals.at[i, 'Center'] = ufloat(result.params['center'].value, result.params['center'].stderr)
FitVals.at[i, 'Amplitude'] = ufloat(result.params['amplitude'].value, result.params['amplitude'].stderr)
FitVals.at[i, 'FWHM'] = ufloat(result.params['fwhm'].value, result.params['fwhm'].stderr)
FitVals.at[i, 'Height'] = ufloat(result.params['height'].value, result.params['height'].stderr)
FitVals.at[i, 'ChiSq'] = result.chisqr
FitVals.at[i, 'RedChiSq'] = result.redchi
FitVals.at[i, 'Akaike'] = result.aic
FitVals.at[i, 'Bayesian'] = result.bic
if graph:
plt.plot(xranges[i], yranges[i], '.', markerfacecolor="None", color='#050505',
mew=1.4, ms=1, antialiased=True, label='Data from frequency sweep')
plt.plot(xranges[i], result.best_fit, lw=2, label='Gaussian + Line fit')
plt.legend()
plt.xlabel('Frequency (Hz)')
plt.ylabel('Variance (a.u)')
fullscreen()
plt.show()
if cdf:
values, base = np.histogram(yranges[i], bins='auto')
cumulative = np.cumsum(values)
plt.plot(base[:-1], cumulative)
plt.plot(base[:-1], values)
fullscreen()
plt.show()
if residuals:
values, base = np.histogram(result.residual, bins='fd')
cumulative = np.cumsum(values)
# plt.plot(xranges[i], result.residual)
# plt.plot(base[:-1], cumulative, '.')
mdl2 = GaussianModel()
params2 = mdl2.guess(data=values, x=base[:-1])
model2 = mdl2
result2 = model2.fit(values, params2, x=base[:-1])
plt.plot(base[:-1], values, '.')
plt.plot(base[:-1], result2.best_fit)
plt.xlabel('Residuals')
plt.ylabel('Counts')
fullscreen()
plt.show()
def GaussCalc(x, y, x1, y1):
y = removerBackground(y)
y1 = removerBackground(y1)
mod = GaussianModel()
pars = mod.guess(y, x=x)
out = mod.fit(y, pars, x=x)
mod = GaussianModel()
pars1 = mod.guess(y1, x=x1)
out1 = mod.fit(y1, pars1, x=x1)
center = out.best_values['center']
sigma = Decon_Gau(out.best_values['sigma'], out1.best_values['sigma'])
return ScherrerEquation(sigma, center)
def fit(les_x_init, les_y_init, remove):
les_x = []
les_y = []
for i in range(len(les_x_init)):
if les_x_init[i] not in remove:
les_x.append(les_x_init[i])
les_y.append(les_y_init[i])
x = scipy.asarray(les_x)
y = scipy.asarray(les_y)
gmod = GaussianModel()
param = gmod.guess(y, x=x)
amplitude = param['amplitude'].value
center = param['center'].value
sigma = param['sigma'].value
the_fit = gmod.fit(y, x=x, amplitude=amplitude, center=center, sigma=sigma)
best_res = the_fit.chisqr
amplitude = the_fit.params['amplitude'].value
center = the_fit.params['center'].value
sigma = the_fit.params['sigma'].value
best_sol = [amplitude, center, sigma]
y_fit = []
for i in range(len(les_x_init)):
y_fit.append(
gmod.eval(x=les_x_init[i],
amplitude=amplitude,
center=center,
sigma=sigma))
return [best_sol, best_res, y_fit]
def GaussConst(signal, guess):
if guess == False:
return [0, 0, 0]
else:
amp, centre, stdev, offset = guess
data = np.array([range(len(signal)), signal]).T
X = data[:,0]
Y = data[:,1]
gauss_mod = GaussianModel(prefix='gauss_')
const_mod = ConstantModel(prefix='const_')
#pars = lorentz_mod.make_params(amplitude=amp, center=centre, sigma=stdev / 3.)
#lorentz_mod.set_param_hint('sigma', value = stdev / 3., min=0., max=stdev)
pars = gauss_mod.guess(Y, x=X, center=centre, sigma=stdev / 3., amplitude=amp)
#pars += step_mod.guess(Y, x=X, center=centre)
pars += const_mod.guess(Y, x=X)
pars['gauss_sigma'].vary = False
mod = gauss_mod + const_mod
result = mod.fit(Y, pars, x=X)
# write error report
#print result.fit_report()
fwhm = result.best_values['gauss_sigma'] * 2.3548
return X, result.best_fit, result.redchi, fwhm
def NewFit2(amp1, amp2, mu1, mu2, sig1, sig2, x, y):
'=========================================='
'Define the first gaussian'
gauss1 = GaussianModel(prefix='g1_') # Model first as a gaussian
pars = gauss1.guess(y, x=x) # Make a gautomatic guess of the parameters
'Set the Parameters values'
pars['g1_center'].set(mu1, vary=True)
pars['g1_sigma'].set(sig1, vary=True)
pars['g1_amplitude'].set(amp1, vary=True)
'==========================================='
'Define the second Gaussian'
gauss2 = GaussianModel(prefix='g2_')
pars.update(
gauss2.make_params()) #update the parameter list with another gaussian
pars['g2_center'].set(mu2, vary=True)
pars['g2_sigma'].set(sig2, vary=True)
pars['g2_amplitude'].set(amp2, vary=True)
'==========================================='
'Make the model as the sum of gaussians'
mod = gauss1 + gauss2
'Fit and print the data'
out = mod.fit(y, pars, x=x)
print(out.fit_report(min_correl=0.5))
plt.plot(x, out.best_fit, 'r-', linewidth=1.50)
plt.show()
return pars
def find_fraunhofer_center(field: np.ndarray,
ic: np.ndarray,
debug: bool = False) -> float:
"""Extract the field at which the Fraunhofer is centered.
Parameters
----------
field : np.ndarray
1D array of the magnetic field applied of the JJ.
ic : np.ndarray
1D array of the JJ critical current.
Returns
-------
float
Field at which the center of the pattern is located.
"""
max_loc = np.argmax(ic)
width, *_ = peak_widths(ic, [max_loc], rel_height=0.5)
width_index = int(round(width[0] * 0.65))
subset_field = field[max_loc - width_index:max_loc + width_index + 1]
subset_ic = ic[max_loc - width_index:max_loc + width_index + 1]
model = GaussianModel()
params = model.guess(subset_ic, subset_field)
out = model.fit(subset_ic, params, x=subset_field)
if debug:
plt.figure()
plt.plot(field, ic)
plt.plot(subset_field, out.best_fit)
plt.show()
return out.best_values["center"]
def refine_energies(self,
frame_width: int = 20) -> List[Tuple[float, Any]]:
"""
Refine energy locations using curve fitting. For every peak in `.energies`, a small slice of the data around it is curve fitted to a gaussian and the center used as the refined energy location.
Will set the property `.refined_energies` equal to function output
Note: The detector energy channel is a `float` here
Parameters:
frame_width (int): The width of the slice of data around the peak used for curve fitting
Returns:
(List[Tuple[float, Any]]): List of energy locations as tuple (detector energy channel, actual energy)
"""
model = GaussianModel()
refined = []
for energy in self.energies:
domain = (int(max(energy[0] - frame_width / 2, 0)),
int(
min(energy[0] + frame_width / 2,
self.data.shape[0] - 1)))
frame = self.data[domain[0]:domain[1]]
pars = model.guess(frame, x=np.arange(0, 20))
out = model.fit(frame, pars, x=np.arange(0, 20))
refined.append((out.params["center"].value + domain[0], energy[1]))
self.refined_energies = refined
self.polynomial_coefficients = None
return refined
def test_2gaussians(): x = np.linspace(0.0, 10.0, num=1000) y = gaussian(x, -1, 3, 0.75) + gaussian(x, -0.5, 5, 0.8) + np.random.normal(0, 0.01, x.shape[0]) gauss1 = GaussianModel(prefix='g1_') pars = gauss1.guess(y, x=x) pars['g1_amplitude'].set(-0.9) pars['g1_center'].set(2.5) pars['g1_sigma'].set(0.5) gauss2 = GaussianModel(prefix='g2_') pars.update(gauss2.make_params()) pars['g2_amplitude'].set(-0.4) pars['g2_center'].set(5) pars['g2_sigma'].set(0.5) mod = gauss1 + gauss2 init = mod.eval(pars, x=x) plt.plot(x, y) plt.plot(x, init, 'k--') out = mod.fit(y, pars, x=x) print(out.fit_report(min_correl=0.5)) plt.plot(x, out.best_fit, 'r-') plt.show()
def gaussian_model(self):
composite_model = None
composite_pars = None
x, y = self.background_correction()
for i in range(self.num_of_gaussians):
model = GaussianModel(prefix='g' + str(i + 1) + '_')
if composite_pars is None:
composite_pars = model.guess(y, x=x)
# composite_pars = model.make_params()
else:
composite_pars.update(model.make_params())
if composite_model is None:
composite_model = model
else:
composite_model += model
result = composite_model.fit(y,
composite_pars,
x=x,
nan_policy='propagate')
return result
def gaussian(x, y):
# Gaussian fit to a curve
x_shifted = x - x.min() # Shifting to 0
y_shifted = y - y.min() # Shifting to 0
mod = GaussianModel() # Setting model type
pars = mod.guess(y_shifted, x=x_shifted) # Estimating fit
out = mod.fit(y_shifted, pars, x=x_shifted) # Fitting fit
print(out.fit_report(min_correl=0.25)) # Outputting best fit results
#print("Gaussian FWHM = ", out.params['fwhm'].value) # Outputting only FWHM
out.plot() # Plotting fit
std = np.std(x_shifted)
mux = np.mean(x_shifted)
h_y = np.max(out.best_fit)
#print(std, mux, h_y)
y_x = h_y/2
x_i = mux - np.sqrt(2*(std**2)*
np.log((np.sqrt(2*np.pi)*y_x*std)/
(h_y)))
x_f = mux + np.sqrt(2*(std**2)*
np.log((np.sqrt(2*np.pi)*y_x*std)/
(h_y)))
fwhm = x_f-x_i
print(x_i, x_f, fwhm)
def fit_and_plot_scan(self):
# self.ui.result_textBrowser.append("Starting Scan Fitting")
print("Starting Scan Fitting")
try:
"""Define starting and stopping wavelength values here"""
start_nm = int(self.ui.start_nm_spinBox.value())
stop_nm = int(self.ui.stop_nm_spinBox.value())
ref = self.bck_file
index = (ref[:, 0] > start_nm) & (ref[:, 0] < stop_nm)
x = self.wavelengths
x = x[index]
data_array = self.intensities
result_dict = {}
for i in range(data_array.shape[0]):
y = data_array[i, index] # intensity
yref = ref[index, 1]
y = y - yref # background correction
y = y - np.mean(
y[(x > start_nm)
& (x < start_nm + 25)]) # removing any remaining bckgrnd
gmodel = GaussianModel(prefix='g1_') # calling gaussian model
pars = gmodel.guess(y,
x=x) # parameters - center, width, height
result = gmodel.fit(y, pars, x=x, nan_policy='propagate')
result_dict["result_" + str(i)] = result
# self.ui.result_textBrowser.append("Scan Fitting Complete!")
print("Scan Fitting Complete!")
filename = QtWidgets.QFileDialog.getSaveFileName(self)
pickle.dump(result_dict,
open(filename[0] + "_fit_result_dict.pkl", "wb"))
# self.ui.result_textBrowser.append("Data Saved!")
print("Data Saved!")
except Exception as e:
self.ui.result_textBrowser2.append(str(e))
pass
# self.ui.result_textBrowser.append("Loading Fit Data and Plotting")
print("Loading Fit Data and Plotting")
try:
self.fit_scan_file = pickle.load(
open(filename[0] + "_fit_result_dict.pkl", 'rb'))
self.plot_fit_scan()
except Exception as e:
self.ui.result_textBrowser2.append(str(e))
pass
def gaussian_model_w_lims(self, peak_pos, sigma, min_max_range):
#center_initial_guesses - list containing initial guesses for peak centers. [center_guess1, center_guess2]
#sigma_initial_guesses - list containing initial guesses for sigma. [sigma1, sigma2]
#min_max_range - list containing lists of min and max for peak center. [ [min1, max1], [min2, max2] ]
x, y = self.background_correction()
gmodel_1 = GaussianModel(prefix='g1_') # calling gaussian model
pars = gmodel_1.guess(y, x=x) # parameters - center, width, height
pars['g1_center'].set(peak_pos[0],
min=min_max_range[0][0],
max=min_max_range[0][1])
pars['g1_sigma'].set(sigma[0])
pars['g1_amplitude'].set(min=0)
gmodel_2 = GaussianModel(prefix='g2_')
pars.update(gmodel_2.make_params()
) # update parameters - center, width, height
pars['g2_center'].set(peak_pos[1],
min=min_max_range[1][0],
max=min_max_range[1][1])
pars['g2_sigma'].set(sigma[1], min=composite_pars['g1_sigma'].value)
pars['g2_amplitude'].set(min=0)
gmodel = gmodel_1 + gmodel_2
result = gmodel.fit(y, pars, x=x, nan_policy='propagate')
return result
def peakFit(self, x, y, model = 'gau', pi = None, di = None):
ti = time.time()
if pi:
NumPeaks = len(pi)
center = []
fwhm = []
amp = []
numVal = len(x)
for i in range(NumPeaks):
pImin = pi[i]-di
if pImin < 0:
pImin = 0
pImax = pi[i] + di
if pImax > (numVal-1):
pImax = numVal-1
__y = y[pImin:pImax]
__x = x[pImin:pImax]
__y = np.power(10,__y/10) #np.array(y)- np.min(y)
mod = GaussianModel()
pars = mod.guess(__y, x=__x)
out = mod.fit(__y, pars, x=__x)
center.append(out.best_values['center'])
fwhm.append(out.best_values['sigma']*2.3548)
amp.append(out.best_values['amplitude'])
#print 'fit:', time.time()-ti
return center, fwhm ,amp
def fit(self, xx, yy, fitType):
xx = np.asarray(xx)
yy = np.asarray(yy)
print("XX", xx)
print("YY", yy)
print(len(xx))
print(len(yy))
print("XX", xx)
x1 = xx[0]
x2 = xx[-1]
y1 = yy[0]
y2 = yy[-1]
m = (y2 - y1) / (x2 - x1)
b = y2 - m * x2
if fitType == "Gaussian":
mod = GaussianModel()
elif fitType == "Lorentzian":
mod = LorentzianModel()
else:
mod = VoigtModel()
pars = mod.guess(yy, x=xx, slope=m)
print(pars)
mod = mod + LinearModel()
pars.add('intercept', value=b, vary=True)
pars.add('slope', value=m, vary=True)
out = mod.fit(yy, pars, x=xx)
return out.best_fit
def test_2gaussians():
x = np.linspace(0.0, 10.0, num=1000)
y = gaussian(x, -1, 3, 0.75) + gaussian(
x, -0.5, 5, 0.8) + np.random.normal(0, 0.01, x.shape[0])
gauss1 = GaussianModel(prefix='g1_')
pars = gauss1.guess(y, x=x)
pars['g1_amplitude'].set(-0.9)
pars['g1_center'].set(2.5)
pars['g1_sigma'].set(0.5)
gauss2 = GaussianModel(prefix='g2_')
pars.update(gauss2.make_params())
pars['g2_amplitude'].set(-0.4)
pars['g2_center'].set(5)
pars['g2_sigma'].set(0.5)
mod = gauss1 + gauss2
init = mod.eval(pars, x=x)
plt.plot(x, y)
plt.plot(x, init, 'k--')
out = mod.fit(y, pars, x=x)
print(out.fit_report(min_correl=0.5))
plt.plot(x, out.best_fit, 'r-')
plt.show()
def lmfit_ngauss(x, y, *params):
params = params[0]
mods = []
prefixes = []
for i in range(0, len(params), 3):
pref = "g%02i_" % (i / 3)
gauss_i = GaussianModel(prefix=pref)
if i == 0:
pars = gauss_i.guess(y, x=x)
else:
pars.update(gauss_i.make_params())
A = params[i]
l_cen = params[i + 1]
sigma = params[i + 2]
pars[pref + 'amplitude'].set(A)
pars[pref + 'center'].set(l_cen)
pars[pref + 'sigma'].set(sigma)
mods.append(gauss_i)
prefixes.append(pref)
mod = mods[0]
if len(mods) > 1:
for m in mods[1:]:
mod += m
print mod
init = mod.eval(pars, x=x)
out = mod.fit(y, pars, x=x)
return mod, out, init
def lmfit_ngauss(x,y, *params):
params = params[0]
mods = []
prefixes = []
for i in range(0, len(params), 3):
pref = "g%02i_" % (i/3)
gauss_i = GaussianModel(prefix=pref)
if i == 0:
pars = gauss_i.guess(y, x=x)
else:
pars.update(gauss_i.make_params())
A = params[i]
l_cen = params[i+1]
sigma = params[i+2]
pars[pref+'amplitude'].set(A)
pars[pref+'center'].set(l_cen)
pars[pref+'sigma'].set(sigma)
mods.append(gauss_i)
prefixes.append(pref)
mod = mods[0]
if len(mods) > 1:
for m in mods[1:]:
mod += m
print mod
init = mod.eval(pars, x=x)
out = mod.fit(y, pars, x=x)
return mod, out, init
def fit_to_gaussian(self, x, y):
gmodel = GaussianModel()
params = gmodel.guess(y, x=x)
c = params['center'].value
n = len(y)
q3 = ((np.max(x) - c) / 2) + c
min_x = np.min(x)
q1 = ((params['center'].value - min_x) / 2) + min_x
s = params['sigma'].value
h = params['height'].value
max_y = np.max(y)
if np.max([h, max_y]) < 0.5:
amp = 1 / n
diff_h = 0.6 - h
gmodel.set_param_hint('amplitude', value=amp)
gmodel.set_param_hint('amplitude', max=amp * (1 + diff_h))
gmodel.set_param_hint('amplitude', min=amp * diff_h)
gmodel.set_param_hint('center', value=c)
gmodel.set_param_hint('center', max=q3)
gmodel.set_param_hint('center', min=q1)
gmodel.set_param_hint('sigma', value=s)
gmodel.set_param_hint('sigma', min=s / 2)
gmodel.set_param_hint('sigma', max=s * 1.5)
gmodel.set_param_hint('height', min=0.6)
result = gmodel.fit(y, x=x)
# gmodel.print_param_hints()
report = result.fit_report()
chi_re = re.compile(r'chi-square\s+=\s+([0-9.]+)')
cor_re = re.compile(r'C\(sigma, amplitude\)\s+=\s+([0-9.-]+)')
chis = np.float32(chi_re.findall(report))
cors = np.float32(cor_re.findall(report))
coeffs = np.concatenate((chis, cors))
mse_model = self.assess_fit(y, result.init_fit - result.best_fit)
mse_yhat = self.assess_fit(y, result.residual)
return mse_model, mse_yhat, result, report, coeffs
def _fit_gauss(xval, yval):
model = GaussianModel()
result = model.fit(yval, model.guess(yval, x=xval,
amplitude=np.max(yval)), x=xval)
return result
def gauss_peak_fit(energy_data, cnts_data, energy_spectrum, channel_width):
'''
spectrum_gauss_fit takes an input spectrum and finds the peaks of the
spectrum and fits a gaussian curve to the photopeaks and returns the
amplitude and sigma of the gaussian peak.
Make sure the spectrum is calibrated first.
sigma_list, amplitude_list = spectrum_gauss_fit(energy_data, cnts_data, energy_spectrum, channel_width)
energy_data: .energies_kev that has been calibrated from becquerel
cnts_data: .cps_vals from becquerel spectrum
energy_spectrum: an array of gamma energies generated from gamma_energies
channel_width: width of the peak for analysis purposes
'''
sigma_list = []
amplitude_list = []
for erg in energy_spectrum:
x_loc = list(
filter(lambda x: (erg - 3) < energy_data[x] < (erg + 3),
range(len(energy_data))))
x_loc_pk = range(int(x_loc[0] - 5), int(x_loc[0] + 5))
pk_cnt = np.argmax(cnts_data[x_loc_pk])
ch_width = range(int(x_loc_pk[pk_cnt] - channel_width),
int(x_loc_pk[pk_cnt] + channel_width))
calibration = energy_data[ch_width]
real_y_gauss = cnts_data[ch_width]
x = np.asarray(calibration)
real_y = np.asarray(real_y_gauss)
mod_gauss = GaussianModel(prefix='g1_')
line_mod = LinearModel(prefix='line')
pars = mod_gauss.guess(real_y, x=x)
pars.update(line_mod.make_params(intercept=real_y.min(), slope=0))
pars.update(mod_gauss.make_params())
pars['g1_center'].set(x[np.argmax(real_y)], min=x[np.argmax(real_y)]\
- 3)
pars['g1_sigma'].set(3, min=0.25)
pars['g1_amplitude'].set(max(real_y), min=max(real_y) - 10)
mod = mod_gauss + line_mod
out = mod.fit(real_y, pars, x=x)
#print("The amplitude sum is %0.2f" % sum(real_y))
gauss_x = []
gauss_y = []
parameter_list_1 = []
real_y_gauss = []
#print(out.fit_report(min_correl=10))
sigma = out.params['g1_sigma'].value
amplitude = out.params['g1_amplitude'].value
sigma_list.append(sigma)
amplitude_list.append(amplitude)
fit_params = {}
#gauss_fit_parameters = [out.params[key].value for k in out.params]
#print(key, "=", out.params[key].value, "+/-", out.params[key].stderr)
gauss_fit_parameters = []
return sigma_list, amplitude_list
def get_plume_gaussian_model(dat, img_width):
'''returns a single gaussian fit for the pd series provided
dat = horizontal row of plume time average df'''
mod = GaussianModel()
pars = mod.guess(dat, x=img_width) # guesses starting value for gaussian
out = mod.fit(dat, pars, x=img_width) # finds best fit of gaussian
return out
def fit_s21mag(x_val, y_val):
peak = GaussianModel()
offset = ConstantModel()
model = peak + offset
pars = offset.make_params(c=np.median(y_val))
pars += peak.guess(y_val, x=x_val, amplitude=-0.5)
result = model.fit(y_val, pars, x=x_val)
return result
def fitSimpleHist(array,
title='E5XX',
nbins=25,
xlabel='mytit',
verbose=False,
savedir=None,
fileappendix='',
ax=None):
""" Simple Gaussian fit to an array of datapoints. Output can be saved to file if wanted
Input Argument:
array -- np.array of input points
title -- title of graph. Will also be the filename
nbins -- number of histogram bins
xlabel -- label on x-axis
verbose -- T/F print the fit report
savedir -- Directory to save output to, if not specified nothing will be saved. Suggest os.getcwd() or '.'
fileappendix -- will add "_fileappendix" to the filename specified by title.
"""
gausfit = GaussianModel()
if (ax == None):
fig, ax = plt.subplots(figsize=(15, 3), nrows=1, ncols=1)
redarray = array[array >= (array.mean() - 5 * array.std()
)] # and array<= (array.mean()+ 5*array.std())]
n, bins, patches = ax.hist(
redarray[redarray <= array.mean() + 5 * array.std()], nbins)
cbins = np.zeros(len(bins) - 1)
for k in (range(0, len(bins) - 1)):
cbins[k] = (bins[k] + bins[k + 1]) / 2
pars = gausfit.guess(n, x=cbins)
fitresult = gausfit.fit(n, pars, x=cbins)
if (verbose):
print(fitresult.fit_report())
ax.plot(cbins, fitresult.best_fit, 'r-', linewidth=2)
mean = fitresult.best_values['center']
fwhm = 2.35 * fitresult.best_values['sigma']
textstring = ' Mean : ' + '{:4.3f}'.format(mean) + '\n'
textstring += ' FWHM : ' + '{:4.3f}'.format(fwhm)
props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
ax.text(0.05,
0.95,
textstring,
transform=ax.transAxes,
fontsize=14,
verticalalignment='top',
bbox=props)
ax.set_xlabel(xlabel)
ax.set_ylabel('Frequency')
ax.set_title(title)
if savedir != None:
filename = os.path.join(savedir, title)
if (fileappendix != ''):
filename += '_' + fileappendix
filename += '.png'
plt.savefig(filename, dpi=200, bbox_inches='tight')
# plt.show()
# return
return fitresult
def fit_gaussian(self, array_x, array_y, figure_number):
mod = GaussianModel()
pars = mod.guess(array_y, x=array_x)
out = mod.fit(array_y, pars, x=array_x)
self.sigma_temp = out.params['sigma'].value
self.amplitude_temp = out.params['amplitude'].value
self.center_temp = out.params['center'].value
self.plot_fit_function(array_x, figure_number)
return self.sigma_temp, self.amplitude_temp, self.center_temp
def gaussian_model_w_lims(self, peak_pos, sigma, min_max_range):
x, y = self.background_correction()
gmodel = GaussianModel(prefix='g1_') # calling gaussian model
pars = gmodel.guess(y, x=x) # parameters - center, width, height
pars['g1_center'].set(peak_pos,
min=min_max_range[0],
max=min_max_range[1])
pars['g1_sigma'].set(sigma)
result = gmodel.fit(y, pars, x=x, nan_policy='propagate')
return result #770 760 780 sigma 15
def fit_gaussian(self):
mod = GaussianModel()
pars = mod.guess(self.result[:, 1], x=self.result[:, 0])
out = mod.fit(self.result[:, 1], pars, x=self.result[:, 0])
self.sigma = out.params['sigma'].value
self.amp = out.params['amplitude'].value
self.center = out.params['center'].value
print('sigma:' + str(self.sigma), 'amp:' + str(self.amp), 'center' + str(self.center))
self.plot_fit_function(1)
return self.sigma, self.amp, self.center
def bootg(data,
flareinds,
ind,
st=40,
end=130,
indiv=False,
num=100,
offset=0):
'''Bootstrap gaussian fit for one flare.
Inputs:
-------
data: sog4
flareinds: flareinds
ind: index of flare to bootstrap (used to get inds from flareinds if indiv False)
st: used as start index if indiv True
end: used as end index if indiv True
indiv: use individual index arguments (st,end) rather than ind, which then references flareinds (default False)
num: number of bootstrap iterations (default 100)
offset: gaussian vertical offset
Outputs:
--------
bsouts: list of bootstrap model results
bsfits: DataFrame with parameters from each bootstrap iteration
'''
if indiv:
ind1, ind2 = st, end
else:
ind1, ind2 = flareinds[ind][0], flareinds[ind][1]
bsouts = []
for i in range(num):
#bootstrap indices of first flare
bs = sk.resample(np.arange(ind1, ind2))
bst = np.array(data['MJD-50000'][bs])
bsi = np.array(data['I mag'][bs])
x = bst
#uses original (not detrended) data
y = np.max(bsi) - bsi + offset
mod = GaussianModel()
pars = mod.guess(y, x=x)
out = mod.fit(y, pars, x=x)
bsouts.append(out)
bsfits = pd.DataFrame(columns=['center', 'sigma', 'fwhm', 'height', 'amp'])
bsfits['center'] = np.zeros(num)
#adding to DataFrame
i = 0
for b in bsouts:
bsfits['center'][i] = b.params['center'].value
bsfits['fwhm'][i] = b.params['fwhm'].value
bsfits['height'][i] = b.params['height'].value
bsfits['amp'][i] = b.params['amplitude'].value
bsfits['sigma'][i] = b.params['sigma'].value
i += 1
#returns list of model results and DataFrame with compiled best fit parameter values
return bsouts, bsfits
def fit_curve(ps_list):
#--input:ps_list, (x,y)
x = np.array([r[0] for r in ps_list])
y = np.array([r[1] for r in ps_list])
mod = GaussianModel()
pars = mod.guess(y, x=x)
bestresult = mod.fit(y, pars, x=x)
return (bestresult.best_fit,x,y,getfloat_attr(bestresult, 'chisqr'),bestresult)
def gaussian_fit(x, y, title_name):
mod = GaussianModel()
pars = mod.guess(y, x=x)
out = mod.fit(y, pars, x=x)
plt.figure()
plt.plot(x, y)
plt.plot(x, out.best_fit, 'r-')
plt.title(title_name)
print(out.fit_report(min_correl=0.25))
print('Center at ' + str(out.best_values['center']) + ' Angstrom')
plt.show()
def gaussian_fit(x, y, title_name):
mod = GaussianModel()
pars = mod.guess(y, x=x)
out = mod.fit(y, pars, x=x)
plt.figure()
plt.plot(x, y)
plt.plot(x, out.best_fit, 'r-')
plt.title(title_name)
print(out.fit_report(min_correl = 0.25))
print('Center at ' + str(out.best_values['center']) + ' Angstrom')
plt.show()
def gaussian_fit(x, y, title_name):
mod = GaussianModel()
pars = mod.guess(y, x=x)
#pars = mod.make_params(amplitude = -2000, sigma = 1, center = 6562.801)
out = mod.fit(y, pars, x=x)
plt.figure()
plt.plot(x, y)
plt.plot(x, out.best_fit, 'r-')
plt.title(title_name)
print(out.fit_report(min_correl = 0.25))
print('Center at ' + str(out.best_values['center']) + ' Angstrom')
plt.show()
def fluxError(counts, wavelength, error, continuum):
flux_vector = []
E_W_vector = []
cont_avg = np.mean(continuum)
#plt.close('all')
for i in range(100):
#plt.errorbar(wavelength, counts, yerr=error)
new_counts=[]
j = 0
for point in counts:
new_counts.append(np.random.normal(point, error[j]))
j = j + 1
new_counts = np.array(new_counts)
#So for each N in 1000 a new counts vector is generated randomly
#Take this data against the wavelength values and fit a gaussian
#each time to compute the flux. Append this to a vector and then
#find the standard deviation to get the flux error for that emission line
#Note this is to be encorporated in the fitLines module so that each of the emission
#lines is fit in turn. Next step here is to construct the model with lmfit,
#guess the initial parameters and then fit the gaussian and take
#out.best_values('amplitude') as the flux and store in flux_vector
#Now use the lmfit package to perform gaussian fits to the data
#Construct the gaussian model
mod = GaussianModel()
#Take an initial guess at what the model parameters are
#In this case the gaussian model has three parameters,
#Which are amplitude, center and sigma
pars = mod.guess(new_counts, x=wavelength)
#We know from the redshift what the center of the gaussian is, set this
#And choose the option not to vary this parameter
#Leave the guessed values of the other parameters
pars['center'].set(value = np.mean(wavelength))
#Now perform the fit to the data using the set and guessed parameters
#And the inverse variance weights form the fits file
out = mod.fit(new_counts, pars, x=wavelength)
flux = out.best_values['amplitude']
E_W = out.best_values['amplitude'] / cont_avg
flux_vector.append(flux)
E_W_vector.append(E_W)
#plt.scatter(wavelength, new_counts)
#plt.plot(wavelength, out.best_fit)
print 'Hello', flux_vector
#Now return the standard deviation of the flux_vector as the flux error
return {'flux_error' : np.std(flux_vector), 'E_W_error' : np.std(E_W_vector)}
def fit_gaussian(y,x):
x=array(x)
y=array(y)
mod=GaussianModel()
pars=mod.guess(y,x=x)
result=mod.fit(y,pars,x=x)
a=result.params['amplitude'].value
b=result.params['center'].value
c=result.params['sigma'].value
best=result.best_fit
chsqred=result.redchi
chisq=result.chisqr
fwhm=result.params['fwhm'].value
return a,b,c,best,fwhm,chisq,chsqred
def peakFit(self, x, y):
if len(x) == 0:
y = self.getdBmSpec()
y = y[self.__scalePos]
x = self.__scaledWavelength
y = np.power(10,y/10)
mod = GaussianModel()
pars = mod.guess(y, x=x)
out = mod.fit(y, pars, x=x)
print(out.fit_report(min_correl=0.25))
center = out.best_values['center']
fwhm = out.best_values['sigma']*2.3548
return center, fwhm#, amp
def lmfit_ngauss_constrains(x,y, params, constrains):
"""
INPUT:
x - is the wavelength array
y - is the normalized flux
params - is a list/array of initial guess values for the parameters
(this controls the number of gaussians to be fitted
number of gaussians: len(params)/3 - 3 parameters per Gaussian)
contrains - the limits of the constrains for the fit of the parameters
OUTPUT:
mod - the lmfit model object used for the fit
out - the lmfit fit object that contains all the results of the fit
init- array with the initial guess model (usefull to see the initial guess when plotting)
"""
mods = []
prefixes = []
for i in range(0, len(params), 3):
pref = "g%02i_" % (i/3)
gauss_i = GaussianModel(prefix=pref)
if i == 0:
pars = gauss_i.guess(y, x=x)
else:
pars.update(gauss_i.make_params())
A = params[i]
limA = constrains[i]
l_cen = params[i+1]
limL = constrains[i+1]
sigma = params[i+2]
limS = constrains[i+2]
pars[pref+'amplitude'].set(A, min=limA[0], max=limA[1])
pars[pref+'center'].set(l_cen, min=limL[0], max=limL[1])
pars[pref+'sigma'].set(sigma, min=limS[0], max=limS[1])
mods.append(gauss_i)
prefixes.append(pref)
mod = mods[0]
if len(mods) > 1:
for m in mods[1:]:
mod += m
init = mod.eval(pars, x=x)
out = mod.fit(y, pars, x=x)
return mod, out, init
def gaussian_fit(x, y, bounds=None):
"""Fit a gaussian background to `field` in `scan`
Parameters
----------
x : array
independent variable
y : array
dependent variable
bounds : iterable
The +/- range to fit the data to
Returns
-------
fit : lmfit.model.ModelFit
The results of fitting the data to a gaussian peak
Examples
--------
>>> fit = fit_gaussian(scan.scan_data)
>>> fit.plot()
"""
gaussian = GaussianModel()
center = x[np.argmax(y)]
if bounds is None:
lower, upper = 0, len(x)
else:
lower = center - bounds
upper = center + bounds
if lower < 0:
lower = 0
if upper > len(x):
upper = len(x)
bounds = slice(lower, upper)
y = y[bounds]
x = x[bounds]
gaussian_params = gaussian.guess(y, x=x, center=center)
model = gaussian
return model.fit(y, x=x, params=gaussian_params)
def lmfit_ngauss_constrains(x,y, params, constrains):
#params = params[0]
#constrains = constrains[0]
mods = []
prefixes = []
for i in range(0, len(params), 3):
pref = "g%02i_" % (i/3)
gauss_i = GaussianModel(prefix=pref)
if i == 0:
pars = gauss_i.guess(y, x=x)
else:
pars.update(gauss_i.make_params())
A = params[i]
limA = constrains[i]
l_cen = params[i+1]
limL = constrains[i+1]
sigma = params[i+2]
limS = constrains[i+2]
pars[pref+'amplitude'].set(A, min=limA[0], max=limA[1])
pars[pref+'center'].set(l_cen, min=limL[0], max=limL[1])
pars[pref+'sigma'].set(sigma, min=limS[0], max=limS[1])
mods.append(gauss_i)
prefixes.append(pref)
mod = mods[0]
if len(mods) > 1:
for m in mods[1:]:
mod += m
init = mod.eval(pars, x=x)
out = mod.fit(y, pars, x=x)
return mod, out, init
def fitLines(self, flux, wavelength, z, weights):
#Convert all into numpy arrays
flux = np.array(flux)
wavelength = np.array(wavelength)
z = np.array(z)
weights = np.array(weights)
error = np.sqrt(1 / weights)
#Fit a polynomial to the continuum background emission of the galaxy
#This is the crude way to do it
continuum_poly = self.fitPoly(flux, wavelength)
#Can also compute the continuum in the more advanced way
#masking the emission lines and using a moving average
#Define the wavelength values of the relevant emission lines
OII3727 = 3727.092
OII3729 = 3729.875
H_beta = 4862.721
OIII4959 = 4960.295
OIII5007 = 5008.239
H_alpha = 6564.614
NII6585 = 6585.27
SII6718 = 6718.29
SII6732 = 6732.68
#Now apply the redshift formula to find where this will be observed
#Note that for these SDSS spectra the OII doublet is not in range
OII3727_shifted = OII3727 * (1 + z)
OII3729_shifted = OII3729 * (1 + z)
H_beta_shifted = H_beta * (1 + z)
OIII4959_shifted = OIII4959 * (1 + z)
OIII5007_shifted = OIII5007 * (1 + z)
H_alpha_shifted = H_alpha * (1 + z)
NII6585_shifted = NII6585 * (1 + z)
SII6718_shifted = SII6718 * (1 + z)
SII6732_shifted = SII6732 * (1 + z)
#hellofriend
#Will choose to mask pm 15 for each of the lines
H_beta_index = np.where(np.logical_and(wavelength>=(H_beta_shifted - 15), wavelength<=(H_beta_shifted + 15)))
OIII_one_index = np.where(np.logical_and(wavelength>=(OIII4959_shifted - 15), wavelength<=(OIII4959_shifted + 15)))
OIII_two_index = np.where(np.logical_and(wavelength>=(OIII5007_shifted - 15), wavelength<=(OIII5007_shifted + 15)))
NII_one_index = np.where(np.logical_and(wavelength>=(NII6585_shifted - 15), wavelength<=(NII6585_shifted + 15)))
H_alpha_index = np.where(np.logical_and(wavelength>=(H_alpha_shifted - 15), wavelength<=(H_alpha_shifted + 15)))
SII_one_index = np.where(np.logical_and(wavelength>=(SII6718_shifted - 15), wavelength<=(SII6718_shifted + 15)))
SII_two_index = np.where(np.logical_and(wavelength>=(SII6732_shifted - 15), wavelength<=(SII6732_shifted + 15)))
#define the mask 1 values from the index values
mask = np.zeros(len(flux))
mask[H_beta_index] = 1
mask[OIII_one_index] = 1
mask[OIII_two_index] = 1
mask[NII_one_index] = 1
mask[H_alpha_index] = 1
mask[SII_one_index] = 1
mask[SII_two_index] = 1
#Now apply these to the flux to mask
masked_flux = ma.masked_array(flux, mask=mask)
#Make my own with np.mean()
continuum = np.empty(len(masked_flux))
for i in range(len(masked_flux)):
if (i + 5) < len(masked_flux):
continuum[i] = ma.mean(masked_flux[i:i+5])
if np.isnan(continuum[i]):
continuum[i] = continuum[i - 1]
else:
continuum[i] = ma.mean(masked_flux[i-5:i])
if np.isnan(continuum[i]):
continuum[i] = continuum[i - 1]
#Subtract the continuum from the flux, just use polynomial fit right now
counts = flux - continuum_poly
#Construct a dictionary housing these shifted emission line values
#Note that values for the OII doublet are not present
line_dict = {'H_beta' : H_beta_shifted, 'OIII4959' : OIII4959_shifted,
'OIII5007' : OIII5007_shifted, 'H_alpha' : H_alpha_shifted, 'NII6585' : NII6585_shifted,
'SII6718' : SII6718_shifted, 'SII6732' : SII6732_shifted}
#Plot the initial continuum subtracted spectrum
plt.plot(wavelength, counts)
#Initialise a dictionary for the results in the for loop
results_dict = {}
#Begin for loop to fit an arbitrary number of emission lines
for key in line_dict:
########################################################################
#FITTING EACH OF THE EMISSION LINES IN TURN
########################################################################
#We don't want to include all the data in the gaussian fit
#Look for the indices of the points closes to the wavelength value
#The appropriate range is stored in fit_wavelength etc.
#Use np.where to find the indices of data surrounding the gaussian
new_index = np.where(np.logical_and(wavelength > (line_dict[key] - 10) ,
wavelength < (line_dict[key] + 10)))
#Select only data for the fit with these indices
fit_wavelength = wavelength[new_index]
fit_counts = counts[new_index]
fit_weights = weights[new_index]
fit_continuum = continuum[new_index]
fit_error = error[new_index]
#Now use the lmfit package to perform gaussian fits to the data
#Construct the gaussian model
mod = GaussianModel()
#Take an initial guess at what the model parameters are
#In this case the gaussian model has three parameters,
#Which are amplitude, center and sigma
pars = mod.guess(fit_counts, x=fit_wavelength)
#We know from the redshift what the center of the gaussian is, set this
#And choose the option not to vary this parameter
#Leave the guessed values of the other parameters
pars['center'].set(value = line_dict[key])
pars['center'].set(vary = 'False')
#Now perform the fit to the data using the set and guessed parameters
#And the inverse variance weights form the fits file
out = mod.fit(fit_counts, pars, weights = fit_weights, x=fit_wavelength)
#print(out.fit_report(min_correl=0.25))
#Plot the results and the spectrum to check the fit
plt.plot(fit_wavelength, out.best_fit, 'r-')
#Return the error on the flux
error_dict = self.fluxError(fit_counts, fit_wavelength, fit_error, continuum_poly)
#Compute the equivalent width
con_avg = np.mean(continuum_poly)
E_w = out.best_values['amplitude'] / con_avg
#The amplitude parameter is the area under the curve, equivalent to the flux
results_dict[key] = [out.best_values['amplitude'], error_dict['flux_error'], out.best_values['sigma'],
2.3548200*out.best_values['sigma'], E_w, error_dict['E_W_error']]
plt.show()
#plt.savefig('fitted_spectrum.png')
#The return dictionary for this method is a sequence of results vectors
return results_dict
def lmfit_mngauss(x,y, *params):
"""
Fit multiple gaussians from two spectra that are multiplied together
INPUT:
x - is the wavelength array
y - is the normalized flux
params - is a tuple of 2 list/arrays of initial guess values for the each spectras parameters
(this controls the number of gaussians to be fitted
number of gaussians: len(params)/3 - 3 parameters per Gaussian)
OUTPUT:
mod - the lmfit model object used for the fit
out - the lmfit fit object that contains all the results of the fit
init- array with the initial guess model (usefull to see the initial guess when plotting)
"""
m_params = params[0]
m_mods = []
prefixes = []
for i in range(0, len(m_params), 3):
pref = "gm%02i_" % (i/3)
gauss_i = GaussianModel(prefix=pref)
if i == 0:
pars = gauss_i.guess(y, x=x)
else:
pars.update(gauss_i.make_params())
A = m_params[i]
l_cen = m_params[i+1]
sigma = m_params[i+2]
pars[pref+'amplitude'].set(A)
pars[pref+'center'].set(l_cen)
pars[pref+'sigma'].set(sigma)
m_mods.append(gauss_i)
prefixes.append(pref)
m_mod = m_mods[0]
if len(m_mods) > 1:
for m in m_mods[1:]:
m_mod += m
m_one = ConstantModel(prefix="m_one_")
prefixes.append("m_one_")
pars.update(m_one.make_params())
pars['m_one_c'].set(value=1, vary=False)
try:
n_params = params[1]
n_mods = []
#prefixes = []
for j in range(0, len(n_params), 3):
pref = "gn%02i_" % (j/3)
gauss_j = GaussianModel(prefix=pref)
pars.update(gauss_j.make_params())
A = n_params[j]
l_cen = n_params[j+1]
sigma = n_params[j+2]
pars[pref+'amplitude'].set(A)
pars[pref+'center'].set(l_cen)
pars[pref+'sigma'].set(sigma)
n_mods.append(gauss_j)
prefixes.append(pref)
n_mod = n_mods[0]
if len(n_mods) > 1:
for n in n_mods[1:]:
n_mod += n
n_one = ConstantModel(prefix="n_one_")
prefixes.append("n_one_")
pars.update(n_one.make_params())
pars['n_one_c'].set(value=1, vary=False)
mod = (m_one + m_mod) * (n_one + n_mod)
except:
print("Error with second spectra, only fitting first")
mod = m_one + m_mod
init = mod.eval(pars, x=x)
out = mod.fit(y, pars, x=x)
print("Printed prefixes", prefixes)
#print(init)
return mod, out, init
exp_mod = ExponentialModel(prefix='exp_')
gauss1 = GaussianModel(prefix='g1_')
gauss2 = GaussianModel(prefix='g2_')
def index_of(arrval, value):
"return index of array *at or below* value "
if value < min(arrval): return 0
return max(np.where(arrval<=value)[0])
ix1 = index_of(x, 75)
ix2 = index_of(x, 135)
ix3 = index_of(x, 175)
pars1 = exp_mod.guess(y[:ix1], x=x[:ix1])
pars2 = gauss1.guess(y[ix1:ix2], x=x[ix1:ix2])
pars3 = gauss2.guess(y[ix2:ix3], x=x[ix2:ix3])
pars = pars1 + pars2 + pars3
mod = gauss1 + gauss2 + exp_mod
out = mod.fit(y, pars, x=x)
print(out.fit_report(min_correl=0.5))
plt.plot(x, y)
plt.plot(x, out.init_fit, 'k--')
plt.plot(x, out.best_fit, 'r-')
plt.show()
#<end examples/doc_nistgauss2.py>
#Module Preparing
import numpy as np
import matplotlib.pyplot as plt
'''
也可以使用import pylab as pl
'''
from lmfit.models import GaussianModel
#Read data from file
data=np.loadtxt('**实验数据文件**')
x=data[:,0]
y=data[:,1]
#Preparing the Model
model=GaussianModel()
pars=model.guess(y,x=x)
#Do the fit
result=model.fit(y,pars,x=x)
#Print the fit result
print(result.fit_report(min_correl=0.25))
#Draw the plot
pl.plot(x,y,color='red',linestyle='--')
pl.plot(x,result.best_fit,color='blue',linestyle='-')
#Tobe Continue
def measure_line_index(wave,
flux,
flux_err=None,
mask=None,
z=None,
line_info=None,
num_refit=(100, None),
filepath=None,
return_type='dict',
verbose=False):
""" Measure line index / EW and have it plotted
Parameters
----------
wave: array-like
wavelength vector
flux: array-like
flux vector
flux_err: array-like
flux error vector (optional)
If un-specified, auto-generate an np.ones array
mask: array-like
andmask or ormask (optional)
If un-specified, auto-generate an np.ones array (evenly weighted)
line_info: dict
information about spectral line, eg:
line_info_dib5780 = {'line_center': 5780,
'line_range': (5775, 5785),
'line_shoulder_left': (5755, 5775),
'line_shoulder_right': (5805, 5825)}
num_refit: non-negative integer
number of refitting.
If 0, no refit will be performed
If positive, refits will be performed after adding normal random noise
z: float
redshift (only specify when z is large)
filepath: string
path of the diagnostic figure
if None, do nothing, else print diagnostic figure
return_type: string
'dict' or 'array'
if 'array', np.array(return dict.values())
verbose: bool
if True, print details
Returns
-------
line_indx: dict
A dictionary type result of line index.
If any problem encountered, return the default result (filled with nan).
"""
try:
# 0. do some input check
# 0.1> check line_info
line_info_keys = line_info.keys()
assert 'line_range' in line_info_keys
assert 'line_shoulder_left' in line_info_keys
assert 'line_shoulder_right' in line_info_keys
# 0.2> check line range/shoulder in spectral range
assert np.min(wave) <= line_info['line_shoulder_left'][0]
assert np.max(wave) >= line_info['line_shoulder_right'][0]
# 1. get line information
# line_center = line_info['line_center'] # not used
line_range = line_info['line_range']
line_shoulder_left = line_info['line_shoulder_left']
line_shoulder_right = line_info['line_shoulder_right']
# 2. shift spectra to rest-frame
wave = np.array(wave)
flux = np.array(flux)
if z is not None:
wave /= 1. + z
# 3. estimate the local continuum
# 3.1> shoulder wavelength range
ind_shoulder = np.any([
np.all([wave > line_shoulder_left[0],
wave < line_shoulder_left[1]], axis=0),
np.all([wave > line_shoulder_right[0],
wave < line_shoulder_right[1]], axis=0)], axis=0)
wave_shoulder = wave[ind_shoulder]
flux_shoulder = flux[ind_shoulder]
# 3.2> integrated/fitted wavelength range
ind_range = np.logical_and(wave > line_range[0], wave < line_range[1])
wave_range = wave[ind_range]
flux_range = flux[ind_range]
# flux_err_range = flux_err[ind_range] # not used
mask_range = mask[ind_range]
flux_err_shoulder = flux_err[ind_shoulder]
# mask_shoulder = mask[ind_shoulder] # not used
# 4. linear model
mod_linear = LinearModel(prefix='mod_linear_')
par_linear = mod_linear.guess(flux_shoulder, x=wave_shoulder)
# ############################################# #
# to see the parameter names: #
# model_linear.param_names #
# {'linear_fun_intercept', 'linear_fun_slope'} #
# ############################################# #
out_linear = mod_linear.fit(flux_shoulder,
par_linear,
x=wave_shoulder,
method='leastsq')
# 5. estimate continuum
cont_shoulder = out_linear.best_fit
noise_std = np.std(flux_shoulder / cont_shoulder)
cont_range = mod_linear.eval(out_linear.params, x=wave_range)
resi_range = 1 - flux_range / cont_range
# 6.1 Integrated EW (
# estimate EW_int
wave_diff = np.diff(wave_range)
wave_step = np.mean(np.vstack([np.hstack([wave_diff[0], wave_diff]),
np.hstack([wave_diff, wave_diff[-1]])]),
axis=0)
EW_int = np.dot(resi_range, wave_step)
# estimate EW_int_err
num_refit_ = num_refit[0]
if num_refit_ is not None and num_refit_>0:
EW_int_err = np.std(np.dot(
(resi_range.reshape(1, -1).repeat(num_refit_, axis=0) +
np.random.randn(num_refit_, resi_range.size) * noise_std),
wave_step))
# 6.2 Gaussian model
# estimate EW_fit
mod_gauss = GaussianModel(prefix='mod_gauss_')
par_gauss = mod_gauss.guess(resi_range, x=wave_range)
out_gauss = mod_gauss.fit(resi_range, par_gauss, x=wave_range)
line_indx = collections.OrderedDict([
('SN_local_flux_err', np.median(flux_shoulder / flux_err_shoulder)),
('SN_local_flux_std', 1. / noise_std),
('num_bad_pixel', np.sum(mask_range != 0)),
('EW_int', EW_int),
('EW_int_err', EW_int_err),
('mod_linear_slope', out_linear.params[mod_linear.prefix + 'slope'].value),
('mod_linear_slope_err', out_linear.params[mod_linear.prefix + 'slope'].stderr),
('mod_linear_intercept', out_linear.params[mod_linear.prefix + 'intercept'].value),
('mod_linear_intercept_err', out_linear.params[mod_linear.prefix + 'intercept'].stderr),
('mod_gauss_amplitude', out_gauss.params[mod_gauss.prefix + 'amplitude'].value),
('mod_gauss_amplitude_err', out_gauss.params[mod_gauss.prefix + 'amplitude'].stderr),
('mod_gauss_center', out_gauss.params[mod_gauss.prefix + 'center'].value),
('mod_gauss_center_err', out_gauss.params[mod_gauss.prefix + 'center'].stderr),
('mod_gauss_sigma', out_gauss.params[mod_gauss.prefix + 'sigma'].value),
('mod_gauss_sigma_err', out_gauss.params[mod_gauss.prefix + 'sigma'].stderr),
('mod_gauss_amplitude_std', np.nan),
('mod_gauss_center_std', np.nan),
('mod_gauss_sigma_std', np.nan)])
# estimate EW_fit_err
num_refit_ = num_refit[1]
if num_refit_ is not None and num_refit_ > 2:
# {'mod_gauss_amplitude',
# 'mod_gauss_center',
# 'mod_gauss_fwhm',
# 'mod_gauss_sigma'}
out_gauss_refit_amplitude = np.zeros(num_refit_)
out_gauss_refit_center = np.zeros(num_refit_)
out_gauss_refit_sigma = np.zeros(num_refit_)
# noise_fit = np.random.randn(num_refit,resi_range.size)*noise_std
for i in range(int(num_refit_)):
# resi_range_with_noise = resi_range + noise_fit[i,:]
resi_range_with_noise = resi_range + \
np.random.randn(resi_range.size) * noise_std
out_gauss_refit = mod_gauss.fit(resi_range_with_noise,
par_gauss,
x=wave_range)
out_gauss_refit_amplitude[i],\
out_gauss_refit_center[i],\
out_gauss_refit_sigma[i] =\
out_gauss_refit.params[mod_gauss.prefix + 'amplitude'].value,\
out_gauss_refit.params[mod_gauss.prefix + 'center'].value,\
out_gauss_refit.params[mod_gauss.prefix + 'sigma'].value
print(out_gauss_refit_amplitude[i], out_gauss_refit_center[i], out_gauss_refit_sigma[i])
line_indx.update({'mod_gauss_amplitude_std': np.nanstd(out_gauss_refit_amplitude),
'mod_gauss_center_std': np.nanstd(out_gauss_refit_center),
'mod_gauss_sigma_std': np.nanstd(out_gauss_refit_sigma)})
# 7. plot and save image
if filepath is not None and os.path.exists(os.path.dirname(filepath)):
save_image_line_indice(filepath, wave, flux, ind_range, cont_range,
ind_shoulder, line_info)
# if necessary, convert to array
# NOTE: for a non-ordered dict the order of keys and values may change!
if return_type == 'array':
return np.array(line_indx.values())
return line_indx
except Exception:
return measure_line_index_null_result(return_type)
# ax_res_y2.set_yticks((ax_res.get_yticks() / 100) * yNorm)
for xticklabel in ax.get_xticklabels():
xticklabel.set_visible(False)
for xticklabel in axy2.get_xticklabels():
xticklabel.set_visible(False)
ax.get_yticklabels()[0].set_visible(False)
axy2.get_yticklabels()[0].set_visible(False)
ax_res.get_yticklabels()[-1].set_visible(False)
ax_res_y2.get_yticklabels()[-1].set_visible(False)
if legend:
ax.legend(loc='best')
ax_res.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
return fig, [ax, axy2, ax_res, ax_res_y2]
if __name__ == '__main__':
from functions import gaussian
from lmfit.models import GaussianModel
x = np.linspace(-3, 3, 200)
y = gaussian(x, sigma=0.5) * (1 + np.random.normal(0, 0.1, len(x)))
gmod = GaussianModel()
para = gmod.guess(y, x=x)
gfit = gmod.fit(y, para, x=x)
models = [gfit.init_fit, gfit.best_fit]
plt.close('all')
fig, axes = plotResidual(x, y, models, yNorm=1.0, yThresh=0.1)
axes[0].set_ylabel('relative [%]')
axes[1].set_ylabel('absolute')
axes[2].set_xlabel('xxx')
plt.show()
da = s / (np.pi*fac)
dmu = (2. * A * (xx-mu)*s)/(np.pi * fac**2)
return np.array([ds, dmu, da])
if __name__ == '__main__':
xs = np.linspace(-4, 4, 100)
print('**********************************')
print('***** Test Gaussian **************')
print('**********************************')
ys = gaussian(xs, 2.5, 0, 0.5)
yn = ys + 0.1*np.random.normal(size=len(xs))
mod = GaussianModel()
pars = mod.guess(yn, xs)
out = mod.fit(yn, pars, x=xs)
out2 = mod.fit(yn, pars, x=xs, fit_kws={'Dfun': dfunc_gaussian,
'col_deriv': 1})
print('lmfit without dfunc **************')
print('number of function calls: ', out.nfev)
print('params', out.best_values)
print('lmfit with dfunc *****************')
print('number of function calls: ', out2.nfev)
print('params', out2.best_values)
print('\n \n')
out2.plot(datafmt='.')
print('**********************************')
print('***** Test Lorentzian ************')
print('**********************************')
cont = 3.0 # continuum level
randamp = 3. # amplitude of gaussian noise
x = np.arange(0,xmax)
y = randamp * np.random.randn(xmax) + jrr.spec.onegaus(x, aa, bb, cc, cont)
err = randamp * np.random.randn(xmax)
plt.plot(x, y, color='black')
# Let's try fitting that gaussian w the python version of MPFIT
p0 = (50., xmax/2, 5, 2)
fa = {'x':x, 'y':y, 'err':err}
m = mpfit.mpfit(myfunct, p0, functkw=fa)
# There has got to be a less kludgy way to do line below
bestfit = jrr.spec.onegaus(x, m.params[0], m.params[1], m.params[2], m.params[3])
plt.plot(x, bestfit, color='blue')
# The same, but with LMFIT
mod1 = GaussianModel()
mod2 = ConstantModel() # The continuum level
mod = mod1 + mod2
pars = mod1.guess(y, x=x) + mod2.guess(y, x=x) # This is cool. It made rough guesses for us.
pars['c'].min = 0 # Set bounds on continuum
pars['c'].max = 10 # Set bounds on continuum
#pars['amplitude'].vary = False # Fix a parameter
out = mod.fit(y, pars, x=x, weights=1/err**2) # Fitting is done here.
plt.plot(x, out.best_fit, color='orange')
print(out.fit_report(min_correl=0.25))
plt.show()
# This is actually more elegant. I think I should learn LMFIT and use it...
def CurveFitting(self, frec, Pxx, iaf, ax):
'Non-Linear Least-Squares Minimization and Curve-Fitting for Python'
# ----- adjusting a model to the obtained PSD -----
# model 1: constante
g1 = ConstantModel(prefix = 'g1_')
pars = g1.guess(Pxx, x = frec)
pars['g1_c'].set(0)
# model 2: k2/f^-1
g2 = PowerLawModel(prefix = 'g2_')
pars += g2.guess(Pxx, x = frec)
pars['g2_exponent'].set(-1)
#model 3: probability density function
g3 = GaussianModel(prefix = 'g3_')
pars += g3.guess(Pxx, x = frec)
pars['g3_center'].set(iaf, min = iaf-2, max = iaf+2)
# model 4: probability density function
g4 = GaussianModel(prefix = 'g4_')
pars += g4.guess(Pxx, x = frec)
pars['g4_center'].set(20, min = 16, max = 25)
# final model
gA = g1 + g2 + g3 + g4
outA = gA.fit(Pxx, pars, x = frec)
diffA= np.sum(Pxx - outA.best_fit)
gB = g1 + g2 + g3
outB = gB.fit(Pxx, pars, x = frec)
diffB= np.sum(Pxx - outB.best_fit)
gC = g1 + g2
outC = gC.fit(Pxx, pars, x = frec)
diffC= np.sum(Pxx - outC.best_fit)
diffs= np.abs([diffA, diffB, diffC])
idx = np.where(diffs == np.min(diffs))[0][0]
out = [outA, outB, outC][idx]
# ----- plotting the desire PSD -----
# original and fitted curves
ax.plot(frec, Pxx, 'k', linewidth = 2, label = 'PSD')
ax.plot(frec, out.best_fit, 'b.-', linewidth = 2, markersize = 9, label ='BestModel')
ax.set_xlim(frec[0], 32)
ax.set_ylim(ymin = 0)
ax.tick_params(axis = 'both', labelsize = 16)
ax.set_xlabel('Frequency [Hz]', fontsize = 'x-large')
ax.grid()
# components of the fitted curved
comps = out.eval_components(x = frec)
g12 = comps['g1_'] + comps['g2_']
ax.plot(frec, g12, 'g--', linewidth = 2, label = 'PowerLawModel')
idx1, idx2 = np.where(frec >= 5)[0][0], np.where(frec <= 15)[0][-1]
# final value on the subplot
if out != outC:
diffs = out.best_fit[idx1:idx2] - g12[idx1:idx2]
peak1 = np.amax(diffs)
idx = np.where(diffs == peak1)[0]
idx+= len(out.best_fit[:idx1])
ax.plot((frec[idx],frec[idx]), (g12[idx],out.best_fit[idx]), 'r-o', linewidth = 3, markersize = 9)
ax.text(frec[idx], g12[idx], str(np.around(peak1, decimals=2)), horizontalalignment='right', verticalalignment='top', color='r', fontsize='xx-large')
else:
peak1 = 0
# optional valued on the subplot
diffs = Pxx[idx1:idx2] - g12[idx1:idx2]
peak2 = np.amax(diffs)
idx = np.where(peak2 == diffs)[0]
idx+= len(Pxx[:idx1])
ax.plot((frec[idx],frec[idx]), (g12[idx], Pxx[idx]), 'r-*', linewidth = 3, markersize = 11)
ax.text(frec[idx], Pxx[idx], str(np.around(peak2, decimals=2)), horizontalalignment='left', verticalalignment='top', color='r', fontsize='xx-large')
ax.legend(loc='upper right', shadow=True)
return peak1, peak2
# MODEL = 'loren'
# MODEL = 'voigt'
# gamma_free = True
if MODEL.lower().startswith('g'):
mod = GaussianModel()
gamma_free = False
figname = '../doc/_images/models_peak1.png'
elif MODEL.lower().startswith('l'):
mod = LorentzianModel()
gamma_free = False
figname = '../doc/_images/models_peak2.png'
elif MODEL.lower().startswith('v'):
mod = VoigtModel()
figname = '../doc/_images/models_peak3.png'
pars = mod.guess(y, x=x)
if gamma_free:
pars['gamma'].set(value=0.7, vary=True, expr='')
figname = '../doc/_images/models_peak4.png'
out = mod.fit(y, pars, x=x)
print(out.fit_report(min_correl=0.25))
plt.plot(x, y, 'b-')
plt.plot(x, out.best_fit, 'r-')
# plt.savefig(figname)
plt.show()
# <end examples/doc_builtinmodels_peakmodels.py>
