def find_fit_sigmoid(x, y):
model_gompertz = lm.models.Model(gompertz)
params_gompertz = lm.Parameters()
params_gompertz.add('asymptote', value=1E-3, min=1E-8)
params_gompertz.add('displacement', value=1E-3, min=1E-8)
params_gompertz.add('step_center', value=1E-3, min=1E-8)
result_gompertz = model_gompertz.fit(y, params_gompertz, x=x)
step_mod = StepModel(form='erf', prefix='step_')
line_mod = LinearModel(prefix='line_')
params_stln = line_mod.make_params(intercept=y.min(), slope=0)
params_stln += step_mod.guess(y, x=x, center=90)
model_stln = step_mod + line_mod
result_stln = model_stln.fit(y, params_stln, x=x)
ret_result = None
ret_model = None
if result_stln.chisqr < result_gompertz.chisqr:
ret_result = result_stln
ret_model = model_stln
else:
ret_result = result_gompertz
ret_model = model_gompertz
return ret_result, ret_model
def correct_data(xData, yData, startIdx=0, endIdx=-1):
y = yData
# start x at zero
x = xData - xData[0]
# linear model
lr = LinearModel()
params = lr.make_params()
# fit model
xSelection = x[startIdx:endIdx]
ySelection = y[startIdx:endIdx]
outParams = lr.fit(ySelection, params, x=xSelection)
# construct corrected data
linear_trend = x * outParams.best_values['slope'] + outParams.best_values[
'intercept']
yCorrected = y - linear_trend + y[0]
result = {
"correctedData":
json.loads(
pd.DataFrame({
"x": xData.tolist(),
"y": yCorrected.tolist()
}).to_json(orient='records'))
}
return result
def make_model(peak_positions,
fwhm=0.05,
max_fwhm=0.5,
pos_range=0.5,
amplitude=1000.):
n_peaks = len(peak_positions)
pars = Parameters()
bg = LinearModel(prefix='bg_')
pars.update(bg.make_params(slope=0, intercept=0))
mod = bg
#pars['bg_intercept'].set(vary=True)
#pars['bg_slope'].set(vary=True)
for i in range(n_peaks):
prefix = 'pk{}_'.format(i)
peak = PseudoVoigtModel(prefix=prefix)
# Set this zero
pars.update(peak.make_params())
pars[prefix + 'center'].set(peak_positions[i],
min=peak_positions[i] - pos_range,
max=peak_positions[i] + pos_range,
vary=True)
pars[prefix + 'sigma'].set(fwhm, min=0., max=max_fwhm, vary=True)
pars[prefix + 'amplitude'].set(amplitude, min=0., vary=True)
pars[prefix + 'fraction'].set(0.0, min=0., max=1., vary=True)
mod += peak
return mod, pars
def line_fit(x, y, errors=True):
"""
Simple helper function that speeds up line fitting. Uses lmfit
Parameters
----------
x, y (float)
Sample length x, y arrays of data to be fitted
Returns
-------
Returns slope and intercept, with uncertainties (use uncertainties package if availabe)
Also returns fit object out, can be dropped
"""
from lmfit.models import LinearModel
mod = LinearModel()
par = mod.guess(y, x=x)
out = mod.fit(y, par, x=x)
s = out.params['slope']
i = out.params['intercept']
if errors:
try:
from uncertainties import ufloat
return ufloat(s.value, s.stderr), ufloat(i.value, i.stderr), out
except:
return s.value, s.stderr, i.value, i.stderr, out
else:
return s.value, i.value, out
def line_fit(x, y, errors=True):
"""
Simple helper function that speeds up line fitting. Uses lmfit
Parameters
----------
x, y (float)
Sample length x, y arrays of data to be fitted
Returns
-------
Returns slope and intercept, with uncertainties (use uncertainties package if availabe)
Also returns fit object out, can be dropped
"""
from lmfit.models import LinearModel
mod = LinearModel()
par = mod.guess(y, x=x)
out = mod.fit(y, par, x=x)
s = out.params["slope"]
i = out.params["intercept"]
if errors:
try:
from uncertainties import ufloat
return ufloat(s.value, s.stderr), ufloat(i.value, i.stderr), out
except:
return s.value, s.stderr, i.value, i.stderr, out
else:
return s.value, i.value, out
def guess(self, data, x=None, **kwargs):
lm = LinearModel()
y_slope = lm.eval(x=x, params=lm.guess(np.abs(data), x=x))
center, hwhm, height = guess_peak(np.abs(np.abs(data) - y_slope), x=x)
pars = self.make_params(Ms=height, B_res=center, dB=hwhm)
return pars
def find_peaks(filename,
show_plots=False): #subtract background and find peaks
num_samp_left = 200
num_samp_right = 200
data = np.genfromtxt(filename)
x = data[:, 0]
y = data[:, 1]
x_bg = np.hstack([x[:num_samp_left], x[-num_samp_right:]])
y_bg = np.hstack([y[:num_samp_left], y[-num_samp_right:]])
model = LinearModel()
params = model.guess(y_bg, x=x_bg)
out = model.fit(y_bg, x=x_bg, params=params)
if show_plots:
plt.plot(x, y)
plt.plot(x_bg, y_bg, '.')
y_fit = out.model.func(x, **out.best_values)
data = y - y_fit
if show_plots:
plt.plot(x, data)
plt.show()
indexes = peakutils.indexes(-data, thres=0.25, min_dist=65)
print(indexes)
pplot(x, data, indexes)
peaks_x = peakutils.interpolate(x, data, ind=indexes)
print(peaks_x)
def rotational_temperature_analysis(L, E_upper):
"""
Function that will perform a rotational temperature analysis. This will perform a least-squares fit of log(L),
which is related to the theoretical line strength and integrated flux, and the upper state energy for the same
transition.
Parameters
----------
L - 1D array
Value L related to the line and theoretical line strength
E_upper - 1D array
The upper state energy in wavenumbers.
Returns
-------
ModelResult - object
Result of the least-squares fit
"""
# Convert the upper state energy
E_upper *= units.kbcm
logL = np.log(L)
model = LinearModel()
params = model.make_params()
result = model.fit(x=E_upper, y=logL, params=params)
return result
def get_db_pixel(tths, xs, ys):
"""Get direct beam pixel at TTH = 0 degrees. This is done by taking a
total of 40 images around TTH = 0, finding the direct beam pixel for each of them
and fitting these positions to a line to get the direct beam pixel position at TTH = 0
Arguments:
tths {[float]} -- array of 2th values
xs {[float]} -- array of the x positions of the direct beam pixel
ys {[float]} -- array of the y positions of the direct beam pixel
Returns:
tuple -- x0, y0 (direct beam pixel position at 2th = 0)
"""
n0 = len(tths)//2
s_ = np.s_[n0-20:n0+20]
xs, ys, tths = xs[s_], ys[s_], tths[s_]
mod_xs = LinearModel()
params_xs = mod_xs.guess(xs, x=tths)
fit_xs = mod_xs.fit(xs, params=params_xs, x=tths)
fit_xs = mod_xs.fit(xs, params=fit_xs.params, x=tths)
mod_ys = LinearModel()
params_ys = mod_ys.guess(ys, x=tths)
fit_ys = mod_ys.fit(ys, params=params_ys, x=tths)
fit_ys = mod_ys.fit(ys, params=fit_ys.params, x=tths)
x0 = fit_xs.eval(params=fit_xs.params, x=0.0)
y0 = fit_ys.eval(params=fit_ys.params, x=0.0)
return x0, y0
def basic_fit_FanoResonance(freq,
trace,
filename='untitled',
plot=True,
save=True):
start, stop = None, None #np.argmax(trace)-500,np.argmax(trace)+500# 27900,28200 #Specifies the window within the data to analyse. Set to None,None if you want the whole window
Lin_mod = LinearModel(
) #Linear lmfit model for background offset and slope
BW_mod = BreitWignerModel() #Breit-Wigner-Fano model
mod = BW_mod + Lin_mod
x = freq[start:stop] / 1E6 #Convert frequencies to MHz
trace = (10**(trace / 10)) #Convert decibel data to linear
y = trace[start:stop]
pars = BW_mod.guess(y, x=x) #Initialize fit params
pars += Lin_mod.guess(y, x=x, slope=0, vary=False)
pars['center'].set(
value=x[np.argmax(y)], vary=True, expr=''
) #Use numpy to find the highest transmission value. Corresponding frequency is used as a guess for the centre frequency
pars['sigma'].set(value=0.1, vary=True, expr='') #Linewidth
pars['q'].set(
value=1, vary=True,
expr='') #Fano factor (asymmetry term). q=infinite gives a Lorentzian
pars['amplitude'].set(value=-0.03, vary=True, expr='') #Amplitude
out = mod.fit(y, pars, x=x)
sigma = out.params['sigma']
centre = out.params['center']
return (x, y, out.best_fit, sigma.value, centre.value,
centre.value / sigma.value
) #Returns linewidth in GHz, centre in GHz and Q factor
def MTF(Y, X):
"""
Fit a polynomial to the MTF curve
"""
pow_mod = PowerLawModel(prefix='pow_')
lin_mod = LinearModel(prefix="lin_")
const_mod = Model(sigmoid)
poly_mod = PolynomialModel(3)
#X = list(reversed(X))
pars = poly_mod.guess(Y, x=X) + lin_mod.guess(Y, x=X)
model = poly_mod + lin_mod
result = model.fit(Y, pars, x=X)
# write error report
print result.fit_report()
c0 = result.best_values['c0']
c1 = result.best_values['c1']
c2 = result.best_values['c2']
slop = result.best_values['lin_slope']
inter = result.best_values['lin_intercept']
# c3 = result.best_values['c3']
# c4 = result.best_values['c4']
# c5 = result.best_values['c5']
# c6 = result.best_values['c6']
# A = result.best_values["amplitude"]
# k = result.best_values["exponent"]
limit = polynomial(c0,c1,c2,inter,slop,10.)
# limit = A*9**k
return result.best_fit, limit
def fitLorentzian(x,y):
signalGuess = max(y)-min(y)
# centerGuess = x[np.argmax(y)]
centerGuess = (max(x)+min(x))/2.
span = max(x)-min(x)
sigmaGuess = span/10.
x_bg = np.concatenate((x[:10],x[10:]))
y_bg = np.concatenate((y[:10],y[10:]))
background = LinearModel()
pars = background.guess(y_bg, x=x_bg)
peak = LorentzianModel()
pars.update( peak.make_params())
pars['center'].set(centerGuess)#,min=min(x),max=max(x))
pars['sigma'].set(sigmaGuess,max=span/2.)
pars['amplitude'].set(signalGuess*sigmaGuess*np.pi,min=0.00000001)
pars.add('signal', expr='amplitude/(sigma*pi)')
pars.add('background', expr='intercept+slope*center')
pars.add('contrast', expr='amplitude/(sigma*pi*background)')
pars.add('centerDoubled', expr='2*center')
pars.add('shift', expr='2*center-9192631770')
pars.add('fwhmDoubled', expr='4*sigma')
model = peak + background
init = model.eval(pars, x=x)
out = model.fit(y, pars, x=x)
#print out.fit_report()
return init,out
def calibrate_pitch(mono='111'):
BMMuser = user_ns['BMMuser']
# read content from INI file
datafile = os.path.join(BMMuser.DATA, 'edges%s.ini' % mono)
print(f'reading {datafile}')
config.read_file(open(datafile))
edges = dict()
for i in config.items('edges'):
el = i[0]
vals = [float(j) for j in i[1].split(',')
] # convert CSV string -> list of strings -> list of floats
edges[el] = vals
# organize the data from the INI file
ordered = [y[1] for y in sorted([(edges[x][1], x) for x in edges.keys()])]
ee = list()
tt = list()
for el in ordered:
ee.append(edges[el][1])
tt.append(edges[el][3])
mod = LinearModel()
pars = mod.guess(tt, x=ee)
out = mod.fit(tt, pars, x=ee)
print(whisper(out.fit_report(min_correl=0)))
out.plot()
def lmDDOFit(xdata,
ydata,
params,
ctr_range=1.2,
amp_range=3,
sig_range=6,
weightexponential=0):
x = xdata
y = ydata
#Define a linear model and a Damped Oscillator Model
line_mod = LinearModel(prefix='line_')
ddo_mod = DampedOscillatorModel(prefix='ddo_')
#Initial Pars for Linear Model
pars = line_mod.make_params(intercept=0, slope=0)
pars['line_intercept'].set(0, vary=True)
pars['line_slope'].set(0, vary=True)
#Extend param list to use multiple peaks. Currently unused.
peaks = []
#Add fit parameters, Center, Amplitude, and Sigma
for i in range(0, len(params) / 3):
peaks.append(DampedOscillatorModel(prefix='ddo' + str(i) + '_'))
pars.update(peaks[i].make_params())
ctr = params[3 * i]
amp = params[3 * i + 1]
sig = params[3 * i + 2]
pars['ddo' + str(i) + '_center'].set(ctr,
min=ctr / ctr_range,
max=ctr * ctr_range)
pars['ddo' + str(i) + '_amplitude'].set(amp,
min=amp / amp_range,
max=amp * amp_range)
pars['ddo' + str(i) + '_sigma'].set(sig,
min=sig / sig_range,
max=sig * sig_range)
#Create full model. Add linear model and all peaks
mod = line_mod
for i in xrange(len(peaks)):
mod = mod + peaks[i]
#Initialize fit
init = mod.eval(pars, x=x)
#Do the fit. The weight exponential can weight the points porportional to the
#amplitude of y point. In this way, points on peak can be given more weight.
out = mod.fit(y, pars, x=x, weights=y**weightexponential)
#Get the fit parameters
fittedsigma = out.params['ddo0_sigma'].value
fittedAmp = out.params['ddo0_amplitude'].value
fittedCenter = out.params['ddo0_center'].value
fittedIntercept = out.params['line_intercept'].value
fittedSlope = out.params['line_slope'].value
fittedQ = 1 / (2 * fittedsigma)
#Returns the output fit as well as an array of the fit parameters
"""Returns output fit as will as list of important fitting parameters"""
return out, [
fittedCenter, fittedAmp, fittedsigma, fittedQ, fittedIntercept,
fittedSlope
]
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 fitting_math(
self,
xfile: List[str],
yfile: List[str],
flag: int = 1,
) -> Any:
"""PeakLogic.fitting_math() fits the data to a cosh and a
gaussian, then subtracts the cosh to find peak current.."""
try:
center: float = self.app.peak_center_.get()
x: "np.ndarray[Any, np.dtype[np.float64]]" = np.array(
xfile, dtype=np.float64)
y: "np.ndarray[Any, np.dtype[np.float64]]" = np.array(
yfile, dtype=np.float64)
# cut out outliers
passingx: "np.ndarray[Any, np.dtype[np.float64]]"
passingy: "np.ndarray[Any, np.dtype[np.float64]]"
passingx, passingy = self.trunc_edges(xfile, yfile)
rough_peak_positions = [min(passingx), center]
min_y = float(min(passingy))
model = LinearModel(prefix="Background")
params = model.make_params() # a=0, b=0, c=0
params.add("slope", 0, min=0)
# params.add("b", 0, min=0)
params.add("intercept", 0, min=min_y)
for i, cen in enumerate(rough_peak_positions):
peak, pars = self.add_lz_peak(f"Peak_{i+1}", cen)
model = model + peak
params.update(pars)
_ = model.eval(params, x=passingx)
result = model.fit(passingy, params, x=passingx)
comps = result.eval_components()
ip = float(max(comps["Peak_2"]))
if flag == 1:
return ip
if flag == 0:
return (
x,
y,
result.best_fit,
comps["Background"],
comps["Peak_1"],
comps["Peak_2"],
ip,
passingx,
)
except Exception: # pragma: no cover
print("Error Fitting")
print(sys.exc_info())
return -1
def poly_gaussian():
gauss1 = Model(gaussian, independent_vars=['x'], prefix='gauss1_')
gauss2 = Model(gaussian, independent_vars=['x'], prefix='gauss2_')
gauss3 = Model(gaussian, independent_vars=['x'], prefix='gauss3_')
gauss4 = Model(gaussian, independent_vars=['x'], prefix='gauss4_')
linear1 = LinearModel(independent_vars=['x'], prefix='linear1_')
linear2 = LinearModel(independent_vars=['x'], prefix='linear2_')
model = gauss1 + gauss2 + linear1 + gauss3 + linear2 + gauss4
return model
def lenar_calc(x,y):
mod = LinearModel()
pars = mod.guess(y, x=x)
out = mod.fit(y, pars, x=x)
calc= out.best_values['slope']
stress=calc*multi()
stress=round(stress,3)
#plt.plot(x,out.bes_fit)
return stress, x , out.best_fit,out
def LorentzianFit(self, freq, trace, plot=True):
if np.any(np.iscomplex(trace)):
trace = trace.real
#print (len(trace))
start, stop = None, None #Specifies the window within the data to analyse.
Lin_mod = LinearModel(
) #Linear lmfit model for background offset and slope
BW_mod = BreitWignerModel() #Breit-Wigner-Fano model
mod = BW_mod + Lin_mod
x = freq[start:stop] / 1E6 #Convert frequencies to MHz
trace = (10**(trace / 10)) #Convert decibel data to linear
y = trace[start:stop]
pars = BW_mod.guess(y, x=x) #Initialize fit params
pars += Lin_mod.guess(y, x=x, slope=0, vary=False)
pars['center'].set(
value=x[np.argmax(y)], vary=True, expr=''
) #Find the highest transmission value. Corresponding frequency is used as a guess for the centre frequency
pars['sigma'].set(value=0.05, vary=True, expr='') #Linewidth
pars['q'].set(
value=0, vary=True,
expr='') #Fano factor (asymmetry term). q=0 gives a Lorentzian
pars['amplitude'].set(value=-0.03, vary=True, expr='') #Amplitude
out = mod.fit(y, pars, x=x)
# print (out.fit_report())
#print (out.params['amplitude'],out.params['q'],out.params['sigma'])
sigma = out.params['sigma']
centre = out.params['center']
dic = {
'x': x,
'y': y,
'fit': out.best_fit,
'out': out,
'sigma': sigma.value,
'centre': centre.value,
'Q': centre.value / sigma.value
}
df = pd.DataFrame(data=dic)
if plot == True:
print(out.params['amplitude'], out.params['q'],
out.params['sigma'])
plt.plot(x, y, color='orange', label='Data')
plt.plot(x,
out.best_fit,
color='darkslateblue',
label='Fano resonance fit')
# return(sigma.value,centre.value,centre.value/sigma.value) #Returns linewidth in GHz, centre in GHz and Q factor
return df
def line_mod(N):
'''
Returns a model consisting of N lines
'''
# initialize model
model = LinearModel(prefix='lin1_')
# Add N-1 lines
for i in range(N - 1):
model += LinearModel(prefix='lin' + str(i + 2) + '_')
return model
def lin_and_multi_gaussian(self, numOfComponents, cList, sList, aList, lS, lI, limits):
"""All lists should be the same length"""
gList = []
if self.xAxis == 'wave' and self.initVals == 'vel':
cList = vel_to_wave(self.restWave, vel=np.array(cList), flux=0)[0]
sList = vel_to_wave(self.restWave, vel=np.array(sList), flux=0, delta=True)[0]
aList = vel_to_wave(self.restWave, vel=0, flux=np.array(aList))[1]
elif self.xAxis == 'vel' and self.initVals == 'wave':
cList = wave_to_vel(self.restWave, wave=np.array(cList), flux=0)[0]
sList = wave_to_vel(self.restWave, wave=np.array(sList), flux=0, delta=True)[0]
aList = wave_to_vel(self.restWave, wave=0, flux=np.array(aList))[1]
lin = LinearModel(prefix='lin_')
self.linGaussParams = lin.guess(self.flux, x=self.x)
self.linGaussParams.update(lin.make_params())
self.linGaussParams['lin_slope'].set(lS, vary=True)
self.linGaussParams['lin_intercept'].set(lI, vary=True)
for i in range(numOfComponents):
if type(limits['c']) is list:
cLimit = limits['c'][i]
else:
cLimit = limits['c']
if type(limits['s']) is list:
sLimit = limits['s'][i]
else:
sLimit = limits['s']
if type(limits['a']) is list:
aLimit = limits['a'][i]
else:
aLimit = limits['a']
lims = {'c': cLimit, 's': sLimit, 'a': aLimit}
prefix = 'g{0}_'.format(i+1)
gList.append(self._gaussian_component(self.linGaussParams, prefix, cList[i], sList[i], aList[i], lims))
gList = np.array(gList)
mod = lin + gList.sum()
init = mod.eval(self.linGaussParams, x=self.x)
out = mod.fit(self.flux, self.linGaussParams, x=self.x, weights=self.weights)
f = open(os.path.join(constants.OUTPUT_DIR, self.rp.regionName, "{0}_Log.txt".format(self.rp.regionName)), "a")
print("######## %s %s Linear and Multi-gaussian Model ##########\n" % (self.rp.regionName, self.lineName))
print(out.fit_report())
f.write("######## %s %s Linear and Multi-gaussian Model ##########\n" % (self.rp.regionName, self.lineName))
f.write(out.fit_report())
f.close()
components = out.eval_components()
if not hasattr(self.rp, 'plotResiduals'):
self.rp.plotResiduals = True
self.plot_emission_line(numOfComponents, components, out, self.rp.plotResiduals, init=init, scaleFlux=self.rp.scaleFlux)
self._get_amplitude(numOfComponents, out)
return out, components
def get_linearmodel(slope=0.8, intercept=0.5, noise=1.5):
# create data to be fitted
np.random.seed(88)
x = np.linspace(0, 10, 101)
y = intercept + x*slope
y = y + np.random.normal(size=len(x), scale=noise)
model = LinearModel()
params = model.make_params(intercept=intercept, slope=slope)
return x, y, model, params
def get_linearmodel(slope=0.8, intercept=0.5, noise=1.5):
# create data to be fitted
np.random.seed(88)
x = np.linspace(0, 10, 101)
y = intercept + x * slope
y = y + np.random.normal(size=len(x), scale=noise)
model = LinearModel()
params = model.make_params(intercept=intercept, slope=slope)
return x, y, model, params
def fitsample(data, theta_initial, theta_final):
x = data[:,0]
y = data[:,1]
m = (x > theta_initial) & (x < theta_final)
x_fit = x[m]
y_fit = y[m]
pseudovoigt1 = VoigtModel(prefix = 'pv1_')
pars= pseudovoigt1.make_params()
pars['pv1_center'].set(13.5, min = 13.4, max = 13.6)
pars['pv1_sigma'].set(0.05, min= 0.01, max = 0.1)
pars['pv1_amplitude'].set(70, min = 1, max = 100)
#pars['pv1_fraction'].set(0.5)
lorentz2 = LorentzianModel(prefix = 'lor2_')
pars.update(lorentz2.make_params())
pars['lor2_center'].set(13.60, min = 13.4, max = 13.9)
pars['lor2_sigma'].set(0.1, min= 0.01)
pars['lor2_amplitude'].set(10, min = 1, max = 50 )
#pars['lor2_fraction'].set(0.5)
line1 = LinearModel(prefix ='l1_')
pars.update(line1.make_params())
pars['l1_slope'].set(0)
pars['l1_intercept'].set(240, min = 200, max = 280)
mod = pseudovoigt1 + lorentz2 + line1
v = pars.valuesdict()
result = mod.fit(y_fit, pars, x=x_fit)
#print(result.fit_report())
pv1_pos = result.params['pv1_center'].value
pv1_height = result.params['pv1_height'].value
lor2_pos = result.params['lor2_center'].value
lor2_height = result.params['lor2_height'].value
#peak_area = pars['gau1_fwhm'].value*peak_amp
#plt.xlim([theta_initial, theta_final])
#plt.ylim([100, 500])
#plt.semilogy(x_fit, y_fit, 'bo')
#plt.semilogy (x_fit, result.init_fit, 'k--')
#plt.semilogy(x_fit, result.best_fit, 'r-')
#plt.show()
return pv1_pos, pv1_height, lor2_pos, lor2_height
def lenar_calc(x, y):
global dados
mod = LinearModel()
pars = mod.guess(y, x=x)
out = mod.fit(y, pars, x=x)
## print out.best_values
plt.plot(x, out.best_fit)
calc = out.best_values['slope']
## print calc,multi()
stresslocal = calc * multi()
globalstress.append(stresslocal)
print 'Value:', dados, round(stresslocal, 3)
def direct_method(x,
y,
bin_sizes,
fractions,
num_samples,
weights=None,
shuffle_threshold=0.02,
return_slope=False,
return_for_graph=False):
if not x.shape[0] == y.shape[0]:
raise ValueError("x and y must have same length in first dimension.")
if y.ndim == 1:
MIs = create_samples_1d(x,
y,
bin_sizes,
fractions,
num_samples,
weights=weights)
else:
MIs = create_samples_1d_dd(x,
y,
bin_sizes,
fractions,
num_samples,
weights=weights)
MIs = MIs.reshape((-1, len(fractions), 2))
params = fit_linear_to_array(MIs[..., 0], 1 / fractions, MIs[..., 1])
params = params.reshape((len(bin_sizes), 2, 4))
where_less = params[:, 1, 2] < shuffle_threshold
if where_less.sum() < 3:
where_less = np.zeros(params.shape[0], dtype=bool)
where_less[:3] = True
model = LinearModel()
result = model.fit(
data=params[where_less, 0, 2],
x=1 / bin_sizes[where_less]**2,
weights=params[where_less, 0, 3]**2,
)
mi = result.params["intercept"].value
mi_err = result.params["intercept"].stderr
if not return_for_graph:
if return_slope:
return mi, mi_err, result.params["slope"].value
else:
return mi, mi_err
else:
return (mi, mi_err, MIs.reshape(len(bin_sizes), 2, len(fractions), 2),
params, result.params["slope"].value, where_less)
def fF_plot(pressures, volumes, out_params):
p = pressures[:, 0]
sigP = pressures[:, 1]
V = volumes[:, 0]
sigV = volumes[:, 1]
results = out_params.params.valuesdict()
Vo = results['vo']
ko = results['ko']
kpo = results['kp']
sigVo = out_params.params['vo'].stderr
#ignore the divide by zero error if the first piece of data is at 0 GPa
np.seterr(divide='ignore', invalid='ignore')
#f = (1.0/2.0)*(((V/Vo)**(-2.0/3.0))-1.0)
f = (((Vo / V)**(2. / 3.)) - 1.) / 2.
F = p / (3. * f * (1. + (2. * f))**(5. / 2.))
eta = V / Vo
sigeta = np.abs(eta) * ((((sigV / V)**2.0) +
((sigVo / Vo)**2))**(1.0 / 2.0))
sigprime = ((7.0 * (eta**(-2.0 / 3.0)) - 5.0) *
sigeta) / (2.0 * (1.0 - (eta**-2.0 / 3.0)) * eta)
sigF = F * np.sqrt(((sigP / p)**2.0) + (sigprime**2))
line_mod = LinearModel()
pars = line_mod.guess(f)
out = line_mod.fit(F, pars, x=f)
plt.figure(4)
plt.plot(f, out.best_fit, '-', color='black')
plt.errorbar(f, F, fmt='ko', xerr=0, yerr=sigF, alpha=1.0, capsize=3.)
plt.xlabel('Eulerian strain $\mathit{f_E}$', fontweight='bold')
plt.ylabel('Normalized pressure $\mathbf{F_E}$ (GPa)', fontweight='bold')
plt.tick_params(direction='in', bottom=1, top=1, left=1, right=1)
plt.title("$\mathit{f_E}$-F", fontweight='bold')
#plt.savefig('Ff-plot.png',dpi=600,bbox_inches='tight')
print(out.fit_report())
slope = uct.ufloat(out.params['slope'], out.params['slope'].stderr)
inter = uct.ufloat(out.params['intercept'], out.params['intercept'].stderr)
k_p = ((2.0 * slope) / (3 * inter)) + 4
return k_p, f, F, sigF, out.best_fit
def plot_gauss(energy_data, cnts_data, energy_spectrum, channel_width):
'''
plot_gauss takes an input spectrum and plots the gaussian fit to the photopeaks
Make sure the spectrum is calibrated first.
plot_gauss(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
'''
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)
plt.figure()
plt.plot(x, real_y)
plt.plot(x, out.best_fit, 'k--')
energy_title = np.argmax(x)
max_y = np.argmax(real_y) # Find the maximum y value
max_x = x[(
max_y)] # Find the x value corresponding to the maximum y value
plt.title('Gaussian fit around %0.1f keV' % x[max_y])
plt.xlabel('Energy (keV)')
plt.ylabel('CPS')
plt.show()
gauss_x = []
gauss_y = []
parameter_list_1 = []
real_y_gauss = []
def fit_voigt_over_linear(q,
I,
cen=1,
sig=0.002,
sigmin=1e-4,
sigmax=0.01,
amplmin=0,
amplmax=500,
trim=0.06,
plot=False):
trim = logical_and(q < cen + trim, q > cen - trim)
q = q[trim]
I = I[trim]
mod = LinearModel()
mod.set_param_hint('slope', value=-20)
mod.set_param_hint('intercept', value=10)
lineout = mod.fit(I, x=q)
pars = lineout.params
mod += VoigtModel()
pars.add('center', value=cen)
pars.add('sigma', value=sig, max=sigmax, min=sigmin)
pars.add('amplitude',
value=amplmin / 2 + amplmax / 2,
min=amplmin,
max=amplmax)
out = mod.fit(I, pars, x=q)
return out
def linear_fit(x, y, u_y=None, slope_guess=None, intercept_guess=None):
""" General purpose linear fit function.
This function takes your x and y data (as numpy arrays) and returns a
:py:class:`lmfit.model.ModelResult` object from the `lmfit`_ Python library.
It attempts to fit your data to a model define by:
:math:`y=mx+c`
where :math:`m = slope` and :math:`c = intercept`.
If guesses for the slope and intercept are not explicitly provided when
calling this function, they will be inferred from the provided data arrays.
Arguments:
x: A 1D numpy array of x data points
y: A 1D numpy array of y data points
Keyword Arguments:
u_y: An optional argument for providing a 1D numpy array of uncertainty
values for the y data points
slope_guess: An optional argument for providing an initial guess for the
value of the slope parameter
intercept_guess: An optional argument for providing an initial guess for the
value of the intercept parameter
Returns:
A :py:class:`lmfit.model.ModelResult` object from the `lmfit`_ Python library
.. _`lmfit`: https://lmfit.github.io/lmfit-py/
"""
# Create Model
model = LinearModel()
guess_kwargs = {}
# Create parameter guesses
if slope_guess is not None:
guess_kwargs['slope'] = slope_guess
if intercept_guess is not None:
guess_kwargs['intercept'] = intercept_guess
initial_parameters = model.guess(y, x=x, **guess_kwargs)
fit_result = model_fit(model, initial_parameters, x, y, u_y)
if not fit_result.success:
raise MonashSPAFittingException("The call to 'linear_fit(...)' failed. Perhaps try specifying a good guess for the 'gradient_guess' and/or 'intercept_guess' keyword arguments? The error message returned by the fitting algorithm was: {error}".format(error = fit_result.message))
return fit_result
def fit_GC_residual(x, y, peak, peak_center):
mod = LinearModel(prefix='bkg_')
pars = mod.guess(y, x) # mod.make_params()
#pars['bkg_intercept'].value = 1e5#
#pars['bkg_slope'].value = 500
out = mod.fit(y, pars, x=x)
# if peak == 'H2':
# #print('Nfev = ', out.nfev)
# print(out.fit_report())
# #print(out.pars['peak_amplitude'].value)
return out
def fit_adev(tau, adev, err_lo, err_high):
fit_tau_over = 499
# If there are at least 2 datapoints to fit at large tau_values, fit them
if len(tau[np.where(tau > fit_tau_over)]) >= 2:
# TODO: take into account asymmetric errorbars
weights = (err_lo + err_high) / 2 # take naive 1-std errorbar average
x = np.array([t for t in tau
if t > fit_tau_over]) # only fit long tau values
y = np.array([a for i, a in enumerate(adev) if tau[i] > fit_tau_over
]) # take equivalent in adev array
w = np.array([
h for i, h in enumerate(weights) if tau[i] > fit_tau_over
]) # take equivalent in weights array
# Fit straight line on a log10 scale
x = np.log10(x)
y = np.log10(y)
w_log = np.log10(np.exp(1)) * (w / y
) # error propagation for log10(y +- w)
# Weighted Least Squares fit; ax + b
model = LinearModel()
params = model.make_params()
params['intercept'].max = -10
params['intercept'].value = -15
params['intercept'].min = -19
params['intercept'].brute_step = 0.005
params[
'slope'].value = -0.5 # assume white noise dominates on fitting range
params['slope'].vary = False # ... so we keep this parameter fixed
res = model.fit(y, params, weights=1 / w_log**2, x=x)
a = res.values['slope']
b = res.values['intercept']
x_smooth = np.logspace(0, 5, 20)
return x_smooth, 10**(res.eval(x=np.log10(x_smooth))), a, b
# Else if there are not enough large tau_values to fit, return empty arrays
else:
return [], [], 0.5, -1
def twoPeakLorentzianFit(self):
try:
nRow, nCol = self.dockedOpt.fileInfo()
self.gausFit.binFitData = zeros((nRow, 0))
self.gausFit.TwoPkGausFitData = 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 = arange(0, len(yy))
xx1 = arange(0, len(yy)/2)
xx2 = 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 = LorentzianModel(prefix='p1_')
mod2 = LorentzianModel(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.gausFit.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.gausFit.binFitData = np.concatenate((self.gausFit.binFitData, binFit), axis=1)
if self.gausFit.continueGraphingEachFit == True:
self.gausFit.graphEachFitRawData(xx, yy, out.best_fit, 'L')
return False
except Exception as e:
QMessageBox.warning(self.myMainWindow, "Error", "There was an error \n\n Exception: " + str(e))
return True
def init_dr_model(baseline=False, guess=None):
""" Function to serialize a Model object for DR fits.
Defaults to a Gaussian line shape, but the option to include
a linear offset is available.
Additionally, if a guess is provided in the
lmfit convention then it will be incorporated.
args:
-----------------
baseline - boolean indicating if linear offset is included
guess - nested dict with keys corresponding to parameter name
and values corresponding to dicts with key/value
indicating the parameter value, range, and constraints
"""
model = GaussianModel()
if baseline:
model += LinearModel()
params = model.make_params()
if guess:
params.update(guess)
# Constrain amplitude to always be negative
# since we're measuring depletion.
params["amplitude"].set(max=0.0)
return model, params
def replaceSpike(x, y, I):
"""
y = replaceSpike(x, y, I)
Replace bad points in y by good ones.
I is the index of bad points.
Works by doing a linear fit over the data.
"""
mod = LinearModel()
params = mod.guess(data=np.delete(y, I), x=np.delete(x, I))
# print(params)
# print(np.delete(y, I))
result = mod.fit(np.delete(y, I), params, x=np.delete(x, I))
# print(result.fit_report())
# print(result.best_values)
yy = mod.eval(x=x, slope=result.best_values['slope'], intercept=result.best_values['intercept'])
y[I] = yy[I]
return y
def calculateSlope(self, x, y, numPoints = 50):
nop = self.__regPoints
if nop > len(x):
_x=x
_y=y
else:
_x = x[-nop:]
_y = y[-nop:]
mod = LinearModel()
pars = mod.make_params()
pars['slope'].set(0.0)
pars['intercept'].set(0.0)
out = mod.fit(_y, pars, x=_x)
slope = str("{0:.3f}".format(out.best_values['slope']*1000))
self.returnSlope.emit(slope)
_time = self.setTimeLabel(_x)
self.__Regres.setData(_time, out.best_fit)
def lmDDOFit(xdata, ydata, params, ctr_range = 1.2, amp_range = 3 , sig_range= 6, weightexponential = 0):
x = xdata
y = ydata
#Define a linear model and a Damped Oscillator Model
line_mod = LinearModel(prefix='line_')
ddo_mod = DampedOscillatorModel(prefix='ddo_')
#Initial Pars for Linear Model
pars = line_mod.make_params(intercept=0, slope=0)
pars['line_intercept'].set(0, vary=True)
pars['line_slope'].set(0, vary=True)
#Extend param list to use multiple peaks. Currently unused.
peaks=[]
#Add fit parameters, Center, Amplitude, and Sigma
for i in range(0, len(params)/3):
peaks.append(DampedOscillatorModel(prefix='ddo'+str(i)+'_'))
pars.update(peaks[i].make_params())
ctr=params[3*i]
amp=params[3*i+1]
sig=params[3*i+2]
pars['ddo'+str(i)+'_center'].set(ctr, min=ctr/ctr_range, max=ctr*ctr_range)
pars['ddo'+str(i)+'_amplitude'].set(amp,min=amp/amp_range, max=amp*amp_range)
pars['ddo'+str(i)+'_sigma'].set(sig, min=sig/sig_range, max=sig*sig_range)
#Create full model. Add linear model and all peaks
mod=line_mod
for i in xrange(len(peaks)):
mod=mod+peaks[i]
#Initialize fit
init = mod.eval(pars, x=x)
#Do the fit. The weight exponential can weight the points porportional to the
#amplitude of y point. In this way, points on peak can be given more weight.
out=mod.fit(y, pars,x=x, weights=y**weightexponential)
#Get the fit parameters
fittedsigma = out.params['ddo0_sigma'].value
fittedAmp = out.params['ddo0_amplitude'].value
fittedCenter = out.params['ddo0_center'].value
fittedIntercept = out.params['line_intercept'].value
fittedSlope = out.params['line_slope'].value
fittedQ=1/(2*fittedsigma)
#Returns the output fit as well as an array of the fit parameters
"""Returns output fit as will as list of important fitting parameters"""
return out, [fittedCenter, fittedAmp, fittedsigma, fittedQ, fittedIntercept, fittedSlope]
def fitDoubleLorentzian(x,y) :
signalGuess = 0.5*(max(y)-min(y))
centerGuess = (max(x)+min(x))/2.
span = max(x)-min(x)
sigmaGuess = span/10.
x_bg = np.concatenate((x[:10],x[10:]))
y_bg = np.concatenate((y[:10],y[10:]))
background = LinearModel()
pars = background.guess(y_bg, x=x_bg)
peak1 = LorentzianModel(prefix="p1_")
pars.update(peak1.make_params())
pars['p1_center'].set(centerGuess,min=min(x),max=max(x))
pars['p1_sigma'].set(sigmaGuess,max=span/2.)
pars['p1_amplitude'].set(signalGuess*sigmaGuess*np.pi,min=0.00000001)
pars.add('p1_signal', expr='p1_amplitude/(p1_sigma*pi)')
pars.add('background', expr='intercept+slope*p1_center')
pars.add('p1_contrast', expr='p1_amplitude/(p1_sigma*pi*background)')
pars.add('p1_centerDoubled', expr='2*p1_center')
pars.add('p1_shift', expr='2*p1_center-9192631770')
pars.add('p1_fwhmDoubled', expr='4*p1_sigma')
peak2 = LorentzianModel(prefix="p2_")
pars.update(peak2.make_params())
pars['p2_center'].set(centerGuess,min=min(x),max=max(x))
pars.add('broadScale',value=2.0, min=1.9, max=100.0)
pars['p2_sigma'].set(sigmaGuess*2,max=span/2.,expr='p1_sigma*broadScale')
pars['p2_amplitude'].set(signalGuess*sigmaGuess*np.pi,min=0.00000001)
pars.add('p2_signal', expr='p2_amplitude/(p2_sigma*pi)')
pars.add('p2_contrast', expr='p2_amplitude/(p2_sigma*pi*background)')
pars.add('p2_centerDoubled', expr='2*p2_center')
pars.add('p2_shift', expr='2*p2_center-9192631770')
pars.add('p2_fwhmDoubled', expr='4*p2_sigma')
model = peak1 + peak2 + background
init = model.eval(pars, x=x)
out = model.fit(y, pars, x=x)
print out.fit_report()
return init,out
def measure_line_index_recover_spectrum(wave, params, norm=False):
""" recover the fitted line profile from params
Parameters
----------
wave: array-like
the wavelength to which the recovered flux correspond
params: 5-element tuple
the 1 to 5 elements are:
mod_linear_slope
mod_linear_intercept
mod_gauss_amplitude
mod_gauss_center
mod_gauss_sigma
norm: bool
if True, linear model (continuum) is deprecated
else linear + Gaussian model is used
"""
from lmfit.models import LinearModel, GaussianModel
mod_linear = LinearModel(prefix='mod_linear_')
mod_gauss = GaussianModel(prefix='mod_gauss_')
par_linear = mod_linear.make_params()
par_gauss = mod_gauss.make_params()
par_linear['mod_linear_slope'].value = params[0]
par_linear['mod_linear_intercept'].value = params[1]
par_gauss['mod_gauss_amplitude'].value = params[2]
par_gauss['mod_gauss_center'].value = params[3]
par_gauss['mod_gauss_sigma'].value = params[4]
if not norm:
flux = 1 - mod_gauss.eval(params=par_gauss, x=wave)
else:
flux = \
(1 - mod_gauss.eval(params=par_gauss, x=wave)) * \
mod_linear.eval(params=par_linear, x=wave)
return flux
def __init__(self):
self.Calibration = None
self.c_AperS = 2.99792458e18 # A / s
self.planckCGS = 6.626068e-27 #erg s-1 cm-2
self.DataRoot = '/home/vital/git/Dazer/Dazer/dazer/libraries/Astro_Libraries/'
self.lineal_mod = LinearModel(prefix='lineal_')
gammafile = self.DataRoot + "HI_t3_elec.ascii"
f = open(gammafile,'r')
self.a_HI = f.readlines()
f.close()
gammafile = self.DataRoot + "HeI_t5_elec.ascii"
f = open(gammafile,'r')
self.a_HeI = f.readlines()
f.close()
gammafile = self.DataRoot + "HeII_t4_elec.ascii"
f = open(gammafile,'r')
self.a_HeII = f.readlines()
f.close()
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)
# <examples/doc_builtinmodels_stepmodel.py> import matplotlib.pyplot as plt import numpy as np from lmfit.models import LinearModel, StepModel x = np.linspace(0, 10, 201) y = np.ones_like(x) y[:48] = 0.0 y[48:77] = np.arange(77-48)/(77.0-48) np.random.seed(0) y = 110.2 * (y + 9e-3*np.random.randn(len(x))) + 12.0 + 2.22*x step_mod = StepModel(form='erf', prefix='step_') line_mod = LinearModel(prefix='line_') pars = line_mod.make_params(intercept=y.min(), slope=0) pars += step_mod.guess(y, x=x, center=2.5) mod = step_mod + line_mod out = mod.fit(y, pars, x=x) print(out.fit_report()) plt.plot(x, y, 'b') plt.plot(x, out.init_fit, 'k--') plt.plot(x, out.best_fit, 'r-') plt.show() # <end examples/doc_builtinmodels_stepmodel.py>
params.add("fwhm2", expr="2.354820045 * sigma2")
params.add("FWHM2", expr="(fwhm2/mu2) * 2.99792458e5")
params.add("Flux2", expr="(A2*fwhm2)/(2.35*0.3989)")
params.add("z2", expr="mu2/6562.7 - 1.0")
params.add("Vshift2", expr="((mu2-6562.7*3.92)/(6562.7*3.92))*2.99792458e5")
# Declaring the wide component
params.add("A4", value=-7.54e-17)
params.add("mu4", value=6562, min=6561, max=6563)
params.add("sigma4", value=5.0, min=0, vary=True)
# Declaring the continuum
params.add("zerolev", value=8.7e-17)
# Declaring a linear continuum uppon which the line is located
lineal_mod = LinearModel(prefix="lineal_")
Lineal_parameters = lineal_mod.guess(np.hstack([blue_flux, red_flux]), x=np.hstack([blue_wave, red_wave]))
lineal_zerolev = Lineal_parameters["lineal_slope"].value * line_wave + Lineal_parameters["lineal_intercept"].value
# Make the fitting
out = minimize(CompResid, params, args=(Wavelength, Flux))
report_fit(out.params)
# Make the plots
plt.plot(Wavelength, Flux, "-", color="black", label="Complete spectrum")
# Resample range:
x_resample = np.linspace(line_wave[0], line_wave[-1], 100)
lineal_resample = Lineal_parameters["lineal_slope"].value * x_resample + Lineal_parameters["lineal_intercept"].value
def call_cont(x, y): cont = LinearModel(prefix='cont_') pars = cont.guess(y, x=x) return cont, pars
min_index = argrelextrema(line_flux, np.less)[0] Minima_fluxes = line_flux[min_index] Minima_waves = line_wave[min_index] #Lmfit parameters Ncomps = 3 Initial_guesses_dic = OrderedDict() Initial_guesses_dic['A'] = np.array([peak_fluxes[0], peak_fluxes[1], peak_fluxes[2], peak_fluxes[1]/20]) Initial_guesses_dic['mu'] = np.array([peak_waves[0], peak_waves[1], peak_waves[2], peak_waves[1]]) Initial_guesses_dic['sigma'] = np.array([1.0, 1.0, 1.0, 5.0]) Initial_guesses_dic['min_sigma'] = np.zeros(Ncomps + 1) params = Load_lmfit_parameters(Ncomps, Initial_guesses_dic, wide_component = True, mu_precission = mu_precission) #Declaring a linear continuum uppon which the line is located lineal_mod = LinearModel(prefix='lineal_') Continuum_wave, Continuum_flux = np.hstack([blue_wave, red_wave]), np.hstack([blue_flux, red_flux]) Lineal_parameters = lineal_mod.guess(Continuum_flux, x=Continuum_wave) lineal_zerolev = Lineal_parameters['lineal_slope'].value * line_wave + Lineal_parameters['lineal_intercept'].value err_continuum = np.std(Lineal_parameters['lineal_slope'].value * Continuum_wave + Lineal_parameters['lineal_intercept'].value - Continuum_flux) Lineal_parameters_scale = lineal_mod.guess(Continuum_flux * Max_Flux, x=Continuum_wave + Max_wavelength) lineal_zerolev_scale = Lineal_parameters['lineal_slope'].value * line_wave + Lineal_parameters['lineal_intercept'].value #Make the fitting out = minimize(CompResid_zerolev, params, args=(line_wave, line_flux, lineal_zerolev, Ncomps + 1, err_continuum)) report_fit(out.params) #Rescale the parameters scale_params = rescale_parameters(out.params, Max_wavelength, Max_Flux, Ncomps, wide_component = True)
def linFitFunc(fitOut,minimum,maximum,ptNumber=100): x = np.linspace(minimum,maximum,ptNumber) background = LinearModel() bg = background.func(x=x,intercept=fitOut.best_values["intercept"],slope=fitOut.best_values["slope"]) return x,bg
def produce_taufits(filepath,meth='iso',pulseperiod=None,snr_cut=None,
verbose=True, plotparams=False, plotflux=False, savefigure=False):
pulsar, nch, nbins,nsub, lm_rms, tsub = read_headerfull(filepath)
if verbose == True:
verboseTag = True
else:
verboseTag = False
print0 = "Pulsar name: %s" %pulsar
print1 = "Number of freq. channels: %d \nFreq channels will be labeled 0 - %d" %(nch, nch-1)
print2 = "Number of bins: %d" %nbins
print3 = "RMS: %.2f" %lm_rms
print4 = "Tsub: %.2f sec" %tsub
for k in range(5):
print eval('print{0}'.format(k))
print"--------------------------------------------------------"
if pulseperiod==None:
## Define time axis, and time/bins conversions
print ("Using Tsub in header to convert bins to time. Assumption is that tsub corresponds to 1.0 phase, corresponding to nbins. This should be adapted for search data.")
pulseperiod = tsub
else:
pulseperiod = pulseperiod #set to provided pulseperiod in seconds
profilexaxis = np.linspace(0,pulseperiod,nbins)
pbs = pulseperiod/nbins
tbs = tsub/nbins
"""Initialise vector outputs"""
obtainedtaus, lmfittausstds = [], []
"""freqmsMHz will correctly associate scattering time values
(tau) with frequency, taking into account frequency integration
across a sub-band. Whereas freqcsMHz is the centre freq. to the subband"""
freqmsMHz, freqcsMHz = [], []
noiselessmodels =[]
results, datas, comp_SNRs, comp_rmss = [], [], [], []
redchis, paramset, paramset_std, correls = [], [], [], []
halfway = nbins/2.
for i in range(nch):
print"--------------------------------------------------------"
print "Channel %d" %i
"""Read in (pdv) data"""
data, freqc, freqm = read_data(filepath,i,nbins)
freqmsMHz.append(freqm)
freqcsMHz.append(freqc)
# roll the data of lowest freq channel to middle of bins
if i ==0:
peakbin = np.argmax(data)
shift = int(halfway -int(peakbin))
if verboseTag:
print 'peak bin at lowest freq channel:%d' %peakbin
else:
peakbin = peakbin
shift = int(halfway - int(peakbin))
data = np.roll(data,shift)
if verboseTag:
print "Rolling data by -%d bins" %shift
comp_rms = find_rms(data,nbins)
if meth is None:
print "No fitting method was chosen. Will default to an isotropic fitting model. \n Use option -m with 'onedim' to change."
result, noiselessmodel, besttau, taustd, bestparams, bestparams_std, redchi, corsig = tau_fitter(data,nbins,verbose=verboseTag)
elif meth == 'iso':
result, noiselessmodel, besttau, taustd, bestparams, bestparams_std, redchi, corsig = tau_fitter(data,nbins,verbose=verboseTag)
elif meth == 'onedim':
result, noiselessmodel, besttau, taustd, bestparams, bestparams_std, redchi, corsig = tau_1D_fitter(data,nbins)
comp_SNR_model = find_peaksnr(noiselessmodel,comp_rms)
if verboseTag:
print 'Estimated SNR (from model peak and data rms): %.2f' % comp_SNR_model
comp_SNR = find_peaksnr_smooth(data,comp_rms)
print 'Estimated SNR (from data peak and rms): %.2f' % comp_SNR
print 'Channel Tau (ms): %.2f \pm %.2f ms' %(besttau,taustd)
obtainedtaus.append(besttau)
lmfittausstds.append(taustd)
noiselessmodels.append(noiselessmodel)
results.append(result)
datas.append(data)
comp_SNRs.append(comp_SNR)
#new:
comp_rmss.append(comp_rms)
redchis.append(redchi)
paramset.append(bestparams)
paramset_std.append(bestparams_std)
# if plotflux == True:
# correls.append(corsig)
#if plotflux == True:
# cor_sigA = np.zeros(len(correls))
# for i in range(len(correls)):
# cor_sigA[i] = correls[i]['A']
paramset = np.transpose(paramset)
paramset_std = np.transpose(paramset_std)
"""Next check if any of the subbands contain only zeros. This happens with high RFI excision in LOFAR bands"""
zero_ch = []
for i in range(nch):
all_zeros = not np.any(datas[i])
if all_zeros:
zero_ch.append(i)
print"--------------------------------------------------------"
if zero_ch:
print "\n"
print "%d channels have all zeroes (channels(s):" %len(zero_ch), zero_ch, ") and will be removed."
if verboseTag:
print "All zero channels are assigned SNR of 0"
if snr_cut:
print "Using SNR cutoff of %.2f" %snr_cut
comp_SNRs = np.nan_to_num(comp_SNRs)
(ind_lowSNR,) = np.where(np.array(comp_SNRs) < snr_cut)
print "SNR cutoff will exclude %d channels (channel(s): %s)" %(len(ind_lowSNR), ind_lowSNR)
data_highsnr = np.delete(np.array(datas),ind_lowSNR,0)
model_highsnr = np.delete(np.array(noiselessmodels),ind_lowSNR,0)
taus_highsnr = np.delete(np.array(obtainedtaus),ind_lowSNR)
lmfitstds_highsnr = np.delete(np.array(lmfittausstds),ind_lowSNR)
freqMHz_highsnr = np.delete(np.array(freqmsMHz),ind_lowSNR)
#New:
comp_rmss_highsnr = np.delete(np.array(comp_rmss),ind_lowSNR)
redchis_highsnr = np.delete(np.array(redchis),ind_lowSNR)
#corsigA_highsnr = np.delete(np.array(cor_sigA),ind_lowSNR)
paramset_highsnr = np.zeros([len(paramset),len(data_highsnr)])
paramsetstd_highsnr = np.zeros([len(paramset),len(data_highsnr)])
for i in range(len(paramset)):
paramset_highsnr[i]= np.delete(paramset[i],ind_lowSNR)
paramsetstd_highsnr[i]= np.delete(paramset_std[i],ind_lowSNR)
elif (snr_cut == None) and (zero_ch != []):
print "Used no SNR cutoff"
"""Rename array to be same as when cut-off is used"""
"""If no SNR cutoff is used, remove channels with all zeroes
-- these will automatically be removed by any snr_cut > 0"""
data_highsnr = np.delete(np.array(datas),zero_ch,0)
model_highsnr = np.delete(np.array(noiselessmodels),zero_ch,0)
taus_highsnr = np.delete(np.array(obtainedtaus),zero_ch)
lmfitstds_highsnr = np.delete(np.array(lmfittausstds),zero_ch)
freqMHz_highsnr = np.delete(np.array(freqmsMHz),zero_ch)
# New:
comp_rmss_highsnr = np.delete(np.array(comp_rmss),zero_ch)
redchis_highsnr = np.delete(np.array(redchis),zero_ch)
#corsigA_highsnr = np.delete(np.array(cor_sigA),zero_ch)
paramset_highsnr = np.zeros([len(paramset),len(data_highsnr)])
paramsetstd_highsnr = np.zeros([len(paramset),len(data_highsnr)])
for i in range(len(paramset)):
paramset_highsnr[i]= np.delete(paramset[i],zero_ch)
paramsetstd_highsnr[i]= np.delete(paramset_std[i],zero_ch)
else:
print "Used no SNR cutoff and there are no empty channels"
data_highsnr = np.array(datas)
model_highsnr = np.array(noiselessmodels)
taus_highsnr = np.array(obtainedtaus)
lmfitstds_highsnr = np.array(lmfittausstds)
freqMHz_highsnr = np.array(freqmsMHz)
# New:
comp_rmss_highsnr = np.array(comp_rmss)
redchis_highsnr = np.array(redchis)
paramset_highsnr = np.array(paramset)
paramsetstd_highsnr = np.array(paramset_std)
taussec_highsnr = taus_highsnr*pbs
lmfitstdssec_highsnr = lmfitstds_highsnr*pbs
number_of_plotted_channels = len(data_highsnr)
npch = number_of_plotted_channels
print "Will plot remaining %d/%d channels" %(npch, nch)
"""Plotting starts"""
#plot onedim in blue dashed
#else plot in red
if meth == 'onedim':
prof = 'b--'
lcol='b'
else:
prof = 'r-'
lcol ='r'
"""1. PLOT PROFILES"""
dimx, dimy = 3., 3.
numsubplots = dimx*dimy
numplots = int(np.ceil(npch/numsubplots))
print "Num profile plots:", numplots
"""Compute residuals"""
#"""Plot 1: Pulse profiles and fits"""
if npch > 0:
resdata = data_highsnr - model_highsnr
resnormed = (resdata-resdata.mean())/resdata.std()
if taussec_highsnr[0] > 1:
taulabel = taussec_highsnr
taulabelerr = lmfitstdssec_highsnr
taustring = 'sec'
else:
taulabel = taussec_highsnr*1000
taulabelerr = lmfitstdssec_highsnr*1000
taustring = 'ms'
for k in range(numplots):
j = int(numsubplots*k)
figg = plt.figure(k+1,figsize=(int(4*dimx),int(3*dimy)))
plots_remaining = int(npch - numsubplots*k)
#print "Plots remaining", plots_remaining
for i in range(np.min([int(numsubplots),int(plots_remaining)])):
figg.subplots_adjust(left = 0.08, right = 0.98, wspace=0.35,hspace=0.35,bottom=0.15)
#plt.rc('text', usetex=True)
plt.rc('font', family='serif')
plt.subplot(dimx,dimy,i+1)
plt.plot(profilexaxis,data_highsnr[j+i],alpha = 0.20)
plt.plot(profilexaxis,model_highsnr[j+i],lw = 2.0, alpha = 0.85, label=r'$\tau: %.2f \pm%.2f$ %s' %(taulabel[j+i], taulabelerr[j+i], taustring))
plt.title('%s at %.1f MHz' %(pulsar, freqMHz_highsnr[j+i]))
plt.ylim(ymax=1.3*np.max(data_highsnr[j+i]))
plt.xlim(xmax=pulseperiod)
plt.xticks(fontsize=11)
plt.yticks(fontsize=11)
plt.xlabel('time (s)',fontsize=11)
plt.legend(fontsize=11,numpoints=1)
plt.ylabel('normalized intensity',fontsize=11)
plt.tight_layout()
if savefigure == True:
figname = '%s_%s_%s_%d.png' %(os.path.basename(filepath),'fitted_profiles', meth, k)
plt.savefig(figname, dpi=200)
print "Saved figure %s in ./" %figname
if noshow == False:
plt.show()
if verboseTag:
for i in range(npch):
print "Channel %d" %i
print'Tau (ms): %.2f' %(1000*taussec_highsnr[i])
tau1GHz = tauatfreq(freqMHz_highsnr[i]/1000.,taussec_highsnr[i],1.0,4)
print 'tau1GHz_alpha_4 (ms) ~ %.4f' %(tau1GHz*1000)
lmfitstdssec_highsnr = lmfitstdssec_highsnr[np.nonzero(lmfitstdssec_highsnr)]
taussec_highsnr = taussec_highsnr[np.nonzero(lmfitstdssec_highsnr)]
freqMHz_highsnr = freqMHz_highsnr[np.nonzero(lmfitstdssec_highsnr)]
"""Plot 2: Plot Gaussian fitting parameters and DM if selected"""
if plotparams==True:
print "\nPlotting Gaussian fit parameters w.r.t frequency\n"
"""Set plotting parameters"""
alfval = 0.6
markr= '*'
msize=12
plt.figure(numplots+1, figsize=(12,8))
plt.subplots_adjust(left = 0.055, right=0.98,wspace=0.35,hspace=0.4,bottom=0.08)
"""Fit models to sigma"""
powmod = PowerLawModel()
powpars = powmod.guess(paramset_highsnr[0], x=freqMHz_highsnr)
powout = powmod.fit(paramset_highsnr[0], powpars, x=freqMHz_highsnr, weights=1/((paramsetstd_highsnr[0])**2))
linmod = LinearModel()
if len(freqMHz_highsnr) < 3:
raise RuntimeError("plotparams == True: Less than three frequency channels. Cannot compute quadratic or exponential fit for width evolution. Consider lowering snr_cut.")
else:
quadmod = QuadraticModel()
quadpars = quadmod.guess(paramset_highsnr[0], x=freqMHz_highsnr)
quadout = quadmod.fit(paramset_highsnr[0], quadpars, x=freqMHz_highsnr, weights=1/((paramsetstd_highsnr[0])**2))
expmod = ExponentialModel()
exppars = expmod.guess(paramset_highsnr[0], x=freqMHz_highsnr)
expout = expmod.fit(paramset_highsnr[0], exppars, x=freqMHz_highsnr, weights=1/((paramsetstd_highsnr[0])**2))
"""Fit a DM model to delta mu"""
delnuarray = [-(1/freqMHz_highsnr[-1]**2-1/freqMHz_highsnr[i]**2) for i in range(npch)] ##in MHz
delmuarray = [(paramset_highsnr[1][-1] - paramset_highsnr[1][i])*pbs for i in range(npch)] ##in seconds
delmu_stdarray = [(paramsetstd_highsnr[1][-1] - paramsetstd_highsnr[1][i])*pbs for i in range(npch)]
DM_linpars = linmod.guess(delmuarray, x=delnuarray)
DM_linout = linmod.fit(delmuarray, DM_linpars, x=delnuarray)
DM_CCval = DM_linout.best_values['slope']
DM_CCvalstd = DM_linout.params['slope'].stderr
DMmodelfit = DM_linout.best_fit ##model gives deltime in seconds (used to shift data)
DMconstant = 4148.808
#uncertainty in the constant is 0.003 - only affects the Delta DM value in the 9th decimal
DMval = (DM_CCval/DMconstant)
DMvalstd = (DM_CCvalstd/DMconstant)
#DMcheck = psr.DM_checker(freqmsMHz,bestpT_highSNR[1]*pbs)
## Plot reduced chi square:
plt.subplot(2,3,1)
plt.plot(freqMHz_highsnr, redchis_highsnr/np.power(comp_rmss_highsnr,2), markr,alpha=alfval,markersize = msize)
plt.title(r'Reduced $\chi^2$ values', fontsize=12)
plt.yticks(fontsize=12)
plt.xticks(fontsize=12)
plt.xlabel(r'$\nu$ MHz',fontsize=12)
plt.ylabel(r'$\chi^2$',fontsize=12)
## Plot sigma:
plt.subplot(2,3,2)
#plt.errorbar(freqMHz_highsnr,paramset_highsnr[0]*pbs)
plt.errorbar(freqMHz_highsnr,paramset_highsnr[0]*pbs,yerr =paramsetstd_highsnr[0]*pbs, fmt = markr,markersize=msize,capthick=2,linewidth=1.5,alpha=alfval)
plt.plot(freqMHz_highsnr,powout.best_fit*pbs,'-', alpha=alfval,label='pow = %.2f' %powout.best_values['exponent'])
plt.plot(freqMHz_highsnr,quadout.best_fit*pbs,'-',alpha=alfval, label='quad: a,b = %.3f,%.3f' %(quadout.best_values['a'],quadout.best_values['b']))
plt.ylabel(r'$\sigma$ (sec)')
plt.title(r'Width evolution', fontsize=12)
plt.yticks(fontsize=12)
plt.xticks(fontsize=12)
plt.xlabel(r'$\nu$ MHz',fontsize=14)
plt.legend(fontsize = 10, loc='best')
## Plot mean:
plt.subplot(2,3,3)
#plt.errorbar(freqMHz_highsnr,paramset_highsnr[1]*pbs)
plt.errorbar(freqMHz_highsnr,paramset_highsnr[1]*pbs,yerr =paramsetstd_highsnr[1]*pbs, fmt = markr,markersize=msize,capthick=2,linewidth=1.5,alpha=alfval)
plt.ylabel(r'$\mu$ (sec)')
plt.title(r'Centroid evolution', fontsize=12)
plt.yticks(fontsize=12)
plt.xticks(fontsize=12)
plt.xlabel(r'$\nu$ MHz',fontsize=14)
#plt.legend(fontsize = 9, loc='best')
## Plot amplitude:
plt.subplot(2,3,4)
#plt.errorbar(freqMHz_highsnr,paramset_highsnr[2]*pbs)
plt.errorbar(freqMHz_highsnr,paramset_highsnr[2]*pbs,yerr =paramsetstd_highsnr[2]*pbs, fmt = markr,markersize=msize,capthick=2,linewidth=1.5,alpha=alfval)
plt.ylabel(r'$\mu$ (sec)')
plt.title(r'Amplitude evolution', fontsize=12)
plt.yticks(fontsize=12)
plt.xticks(fontsize=12)
plt.xlabel(r'$\nu$ MHz',fontsize=14)
#plt.legend(fontsize = 9, loc='best')
## Plot DC:
plt.subplot(2,3,5)
#plt.errorbar(freqMHz_highsnr,paramset_highsnr[2]*pbs)
plt.errorbar(freqMHz_highsnr,paramset_highsnr[3]*pbs,yerr =paramsetstd_highsnr[3]*pbs, fmt = markr,markersize=msize,capthick=2,linewidth=1.5,alpha=alfval)
plt.ylabel(r'$\mu$ (sec)')
plt.title(r'DC offset', fontsize=12)
plt.yticks(fontsize=12)
plt.xticks(fontsize=12)
plt.xlabel(r'$\nu$ MHz',fontsize=14)
#plt.legend(fontsize = 9, loc='best')
## Plot DM:
plt.subplot(2,3,6)
plt.errorbar(delmuarray,freqMHz_highsnr, fmt = markr, xerr=delmu_stdarray, alpha = alfval, markersize=msize)
plt.plot(DMmodelfit,freqMHz_highsnr, '-', label=r'DM: $%.3f \pm %.3f$ $\rm{pc.cm}^{-3}$' %(DMval,DMvalstd), alpha = alfval)
plt.xlabel(r'$\Delta \mu$ (sec)', fontsize =12)
plt.yticks(fontsize=12)
plt.xticks(fontsize=12)
plt.title('Delta DM', fontsize=12)
plt.ylabel(r'$\nu$ (MHz)',fontsize=14)
plt.ticklabel_format(style='sci', axis='x',scilimits=(0,0))
plt.legend(fontsize = 10, loc='best')
plt.tight_layout()
if savefigure == True:
figname2 = '%s_%s.png' %(os.path.basename(filepath),'fitting_parameters')
plt.savefig(figname2, dpi=200)
print "Saved figure %s in ./" %figname2
if noshow == False:
plt.show()
if plotflux == True: ##Flux section needs debugging
ls = 'solid'
"""Plot flux, and corrected flux spectrum"""
"""Create unscattered profiles, i.e. Guassians"""
bins, profiles = [],[makeprofile(nbins = nbins, ncomps = 1, amps = paramset_highsnr[2][j], means = paramset_highsnr[1][j], sigmas = paramset_highsnr[0][j]) for j in range(npch)]
unscatflux = []
for i in range(npch):
unscatfl = np.sum(profiles[j])/nbins
unscatflux.append(unscatfl)
#smootheddata = smooth(data_highsnr[j],int(0.05*nbins))
scatflux = [find_modelflux(model_highsnr[i],nbins) for i in range(npch)]
climbvals = []
for i in range(npch):
climb = returnclimb(np.linspace(1,nbins,nbins),paramset_highsnr[1][i],paramset_highsnr[0][i],paramset_highsnr[2][i],taussec_highsnr[i],paramset_highsnr[3][i],nbins)
climbvals.append(climb)
correctedflux = np.array([scatflux[i] + climbvals[i] for i in range(npch)])
print scatflux
print climbvals
#per bin
meancorflux = np.mean(correctedflux)
meancorfluxerr = np.sqrt(np.sum(correctedflux**2))/len(correctedflux)
"""Calculate error in Flux"""
sigmaWIDTH = paramsetstd_highsnr[0]*pbs #in seconds
sigmaAMP = paramsetstd_highsnr[2] #in mJy
WIDTHS =paramset_highsnr[0]*pbs #in seconds
AMPS =paramset_highsnr[2] #in mJy
Expr1 = np.sqrt(2*np.pi)*AMPS
Expr2 = np.sqrt(WIDTHS)
AreaExpression = Expr1*Expr2
sigmaEx1 = np.sqrt(2*np.pi)*sigmaAMP
sigmaEx2 = Expr2*0.5*sigmaWIDTH/WIDTHS
sigmaFlux =AreaExpression*np.sqrt(np.power(sigmaEx1/Expr1,2)+ np.power(sigmaEx2/Expr2,2))#+ 2*corsigA_highsnr*sigmaEx1*sigmaEx2/(Expr1*Expr2)
plt.figure(figsize=(10,6))
plt.plot(freqMHz_highsnr, correctedflux,'k-', linewidth=2.0)
plt.plot(freqMHz_highsnr, scatflux,'r--', linewidth=2.0)
plt.fill_between(freqMHz_highsnr,scatflux,correctedflux, alpha=alfval,facecolor='r')
eb = plt.errorbar(freqMHz_highsnr,correctedflux,yerr=sigmaFlux, fmt=markr,markersize=10.0, alpha=1.0,capthick=2,linewidth=1.5)
eb[-1][0].set_linestyle(ls)
#plt.errorbar(freqMHz_highsnr, unscatflux,yerr=sigmaFlux, fmt=markr,markersize=10.0, alpha=alfval)
plt.title('Flux Spectrum', fontsize=12)
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)
plt.xlabel(r'$\nu$ (MHz)',fontsize=12)
plt.ylabel(r'Calibrated flux (mJy)',fontsize=12)
return freqMHz_highsnr, taussec_highsnr, lmfitstdssec_highsnr
"""Array with all the other fitting parameters: sigma, A, etc.""" bestpT = np.transpose(bestparamsall) bestpT_std = np.transpose(bestparams_stdall) print "Number of plotted channels: %d/%d" %(npch, nch) bestpT_highSNR = bestpT bestpT_std_highSNR = bestpT_std """Calculate fits for parameters sigma and mu""" """Fit a DM model to delta mu""" delnuarray = [-(1/freqMHz_highsnr[-1]**2-1/freqMHz_highsnr[i]**2) for i in range(npch)] ##in MHz delmuarray = [(bestpT_highSNR[1][-1] - bestpT_highSNR[1][i])*pbs for i in range(npch)] ##in seconds delmu_stdarray = [(bestpT_std_highSNR[1][-1] - bestpT_std_highSNR[1][i])*pbs for i in range(npch)] linmod = LinearModel() DM_linpars = linmod.guess(delmuarray, x=delnuarray) # DM_linout = linmod.fit(delmuarray, DM_linpars, x=delnuarray, weights=1/(np.power(delmu_stdarray,2))) DM_linout = linmod.fit(delmuarray, DM_linpars, x=delnuarray) DM_CCval = DM_linout.best_values['slope'] DM_CCvalstd = DM_linout.params['slope'].stderr DMmodelfit = DM_linout.best_fit ##model gives deltime in seconds (used to shift data) DMconstant = 4148.808 #uncertainty in the constant is 0.003 - only affects the Delta DM value in the 9th decimal DMval = (DM_CCval/DMconstant) DMvalstd = (DM_CCvalstd/DMconstant) DMcheck = psr.DM_checker(freqmsMHz,bestpT_highSNR[1]*pbs)
class Nebular_Bayesian():
def __init__(self):
self.Calibration = None
self.c_AperS = 2.99792458e18 # A / s
self.planckCGS = 6.626068e-27 #erg s-1 cm-2
self.DataRoot = '/home/vital/git/Dazer/Dazer/dazer/libraries/Astro_Libraries/'
self.lineal_mod = LinearModel(prefix='lineal_')
gammafile = self.DataRoot + "HI_t3_elec.ascii"
f = open(gammafile,'r')
self.a_HI = f.readlines()
f.close()
gammafile = self.DataRoot + "HeI_t5_elec.ascii"
f = open(gammafile,'r')
self.a_HeI = f.readlines()
f.close()
gammafile = self.DataRoot + "HeII_t4_elec.ascii"
f = open(gammafile,'r')
self.a_HeII = f.readlines()
f.close()
def calculate_wavelength_intervals(self, total_wavelength, total_flux, lineslog_frame):
#Another value
empty_array = zeros(len(total_wavelength), dtype = bool)
for j in range(len(lineslog_frame.index)):
blue_limit = lineslog_frame.iloc[j]['Wave3']
red_limit = lineslog_frame.iloc[j]['Wave4']
if lineslog_frame.index.values[j] in ['O2_3726A', 'O3_4959A', 'O3_5007A', 'H1_6563A']:
tolerance = 15
else:
tolerance = 4
indeces_line = (total_wavelength >= blue_limit - tolerance) & (total_wavelength <= red_limit + tolerance)
empty_array = empty_array + indeces_line
#Extra for weird lines
for interval in [[3630,3640],[3655, 3677], [3816, 3824], [3537, 3542], [6990,7010], [5238, 5330]]:
blue_limit = interval[0]
red_limit = interval[1]
tolerance = 0
indeces_line = (total_wavelength >= blue_limit - tolerance) & (total_wavelength <= red_limit + tolerance)
empty_array = empty_array + indeces_line
self.clean_indeces = invert(empty_array)
#Calculating the error on the continuum
self.linear_indeces = argwhere(diff(r_[False, self.clean_indeces, False])).reshape(-1, 2)
self.linear_indeces[:, 1] -= 1
std_arrays = []
for interval in self.linear_indeces:
#dz.data_plot(wave_obs[interval[0]:interval[1]], flux_obs[interval[0]:interval[1]], 'initial', 'blue', markerstyle='o')
#dz.data_plot(wave_obs[interval[0]], flux_obs[interval[0]], 'initial', 'blue', markerstyle='o')
#dz.data_plot(wave_obs[interval[1]], flux_obs[interval[1]], 'final', 'red', markerstyle='o')
try:
if (interval[1] - interval[0]) > 1:
x_region = total_wavelength[interval[0]:interval[1]]
y_region = total_flux[interval[0]:interval[1]]
lin_param = self.lineal_mod.guess(y_region, x=x_region)
y_lineal = lin_param['lineal_slope'].value * x_region + lin_param['lineal_intercept'].value
std_arrays.append(std(y_lineal - y_region))
#dz.data_plot(x_region, y_lineal, 'lineal fit', 'black')
except:
print 'fallo', interval[1] - interval[0]
self.continuum_error = mean(std_arrays)
return total_wavelength[self.clean_indeces], total_flux[self.clean_indeces]
def model_parameters(self, obs_wave, obs_flux, err_obs):
y_plus = pymc.Uniform('He_abud', 0.050, 0.15)
# Te = pymc.Uniform('Te', self.ObjectData_dict['TOIII'] -2000, self.ObjectData_dict['TOIII']+2000)
Te = pymc.TruncatedNormal('Te', self.ObjectData_dict['TOIII'], self.ObjectData_dict['TOIII_error']**-2, a=self.ObjectData_dict['TOIII']- 6 * self.ObjectData_dict['TOIII_error'], b=self.ObjectData_dict['TOIII'] + 6 * self.ObjectData_dict['TOIII_error'])
# Flux_Recomb = pymc.Uniform('Flux_Recomb', self.ObjectData_dict['Flux_Hbeta_Normalize'] - 4*self.ObjectData_dict['Error_Hbeta_Normalize'], self.ObjectData_dict['Flux_Hbeta_Normalize']+4 * self.ObjectData_dict['Error_Hbeta_Normalize'])
Flux_Recomb = pymc.Normal('Flux_Recomb', self.ObjectData_dict['Flux_Hbeta_Normalize'], self.ObjectData_dict['Error_Hbeta_Normalize']**-2)
#Calculate nebular continuum
@pymc.deterministic
def Calculate_Continuum(y_plus=y_plus, Te=Te, Flux_Recomb=Flux_Recomb, Wavelength_Range = obs_wave):
return self.Calculate_Nebular_gamma(Te, Flux_Recomb, y_plus, HeIII_HII = 0.0, Wavelength_Range = Wavelength_Range)
#Likelihood
@pymc.stochastic(observed=True)
def Likelihood_model(value=obs_flux, nebInt_cont = Calculate_Continuum, sigmaLines = err_obs):
chi_F = np_sum(square(nebInt_cont - value) / square(sigmaLines))
return - chi_F / 2
return locals()
def Calculate_Nebular_gamma(self, Te, Flux_Recomb, HeII_HII, HeIII_HII, Wavelength_Range):
HII_HI = 1.0
Frac = 1 + HeII_HII*4 + HeIII_HII*4
Gamma_2q = self.TwoPhotonContinuum(Te, Wavelength_Range)
Gamma_FF_HI = self.FreeFreeContinuum('HI', Te, Wavelength_Range)
Gamma_FF = Frac * Gamma_FF_HI
Gamma_FB_HI = self.FreeBoundContinuum_EP("HI", Te, Wavelength_Range)
Gamma_FB_HeI = self.FreeBoundContinuum_EP("HeI", Te, Wavelength_Range)
Gamma_FB_HeII = self.FreeBoundContinuum_EP("HeII", Te, Wavelength_Range)
Gamma_FB = HII_HI * Gamma_FB_HI + HeII_HII * Gamma_FB_HeI + HeIII_HII * Gamma_FB_HeII
Gamma_Total = Gamma_FB + Gamma_FF + Gamma_2q
Gamma_lambda = Gamma_Total * (self.c_AperS / power(Wavelength_Range,2))
# NebularFlux_lambda = self.Zanstra_Calibration_Hbeta(Te, Flux_Recomb, Gamma_Total, Wavelength_Range)
NebularFlux_lambda = self.Zanstra_Calibration_Halpha(Te, Flux_Recomb, Gamma_Total, Wavelength_Range)
return NebularFlux_lambda
def TwoPhotonContinuum(self, Te, Wavelength_Range):
Gamma_2q = []
#Coefficients for calculating A_2q The total radiative probability 2s -> 1s (s^-1)
alpha_A = 0.88
beta_A = 1.53
gamma_A = 0.8
C_A = 202.0 # (s^-1)
c_CGS = 2.99792458e10 #cm / s
h = 6.626068e-27 #erg s
H0_Ionization_Energy = 13.6 #eV
eV2erg = 1.602177e-12
nu_0 = H0_Ionization_Energy * eV2erg / h #Hz
A2q = 8.2249 #(s^-1) Transition probability at lambda = 1215.7
alpha_eff_2q = 6.5346e-11 * Te**-0.72315 #(cm^3 s^-1) Effective Recombination coefficient (Este es mi ajuste. El de Molla es: 0.647e-10 * Te**-0.722)
q2 = 5.92e-4 - 6.1e-9 * Te #(cm^3 s^-1) Collisional transition rate coefficient for protons and electrons
Lambda_0 = 1215.7
for i in range(len(Wavelength_Range)):
Lambda = float(Wavelength_Range[i])
if Lambda > 1215.7:
nu = c_CGS / (Lambda * 1e-8)
nu_0 = 3.e18/Lambda_0
y = nu / nu_0
A_y = C_A * (
y*(1-y) * (1-(4*y*(1-y))**gamma_A)
+ alpha_A*(y*(1-y))**beta_A * (4*y*(1-y))**gamma_A
)
g_nu = h * nu / nu_0 / A2q * A_y # (erg Hz^-1)
Gamma_2q.append(alpha_eff_2q * g_nu / (1+q2/A2q)) # (erg cm^3 s^-1) We take the density of protons and electrons = n_e
else:
Gamma_2q.append(0.0)
Np_Gamma_2q = array(Gamma_2q)
Np_Gamma_2q[isnan(Np_Gamma_2q)] = 0.0
return Np_Gamma_2q
def FreeFreeContinuum(self, Ion, Te, Wavelength_Range):
#Browns and Seaton methodology
h = 6.626068e-27 #erg s
c_CGS = 2.99792458e10 #cm / s
eV2erg = 1.602177e-12
pi = 3.141592
masseCGS = 9.1096e-28
e_proton = 4.80320425e-10 #statCoulomb = 1 erg^1/2 cm^1/2 # Eperez definition electronCGS = 1.60217646e-19 * 3.e9 # Coulomb # 1eV = 1.60217646e-19 Jul
k = 1.3806503e-16 #erg / K
H0_Ionization_Energy = 13.6057 #eV
nu_0 = H0_Ionization_Energy * eV2erg / h #Hz
H_RydbergEnergy = h * nu_0
Flux_List = []
if Ion == "HI":
Z = 1
CteTotal = (32 * (Z**2) * (e_proton**4)*h) / (3*(masseCGS**2)*(c_CGS**3)) * ((pi * H_RydbergEnergy / (3 * k * Te))**0.5)
for i in range(len(Wavelength_Range)):
Wave = float(Wavelength_Range[i])
nu = 2.99792458e18 / Wave
Flux_Comp1 = exp(((-1*h*nu)/(k*Te))) #No unit
Flux_Comp2 = h*nu/(Z**2*e_proton*13.6057)
Flux_Comp3 = k*Te/(h*nu)
gff_mio = 1 + 0.1728*(Flux_Comp2)**0.33333*(1+2*Flux_Comp3) - 0.0496*(Flux_Comp2)**0.66667*(1+0.66667*Flux_Comp3+1.33333*(Flux_Comp3)**2)
FluxValue = CteTotal * Flux_Comp1 * gff_mio # This is gamma_nu
Flux_List.append(FluxValue)
return array(Flux_List)
def FreeBoundContinuum_EP(self, Ion, Te, Wavelength_Range):
planckCGS = 6.626068e-27 # cm2 g / s == erg s
cspeedA = 3.e18 # A / s
rydbergerg = 2.1798741e-11 # Rydberg to erg
t4 = Te/1.e4
PixelNumber = len(Wavelength_Range)
nu = zeros(PixelNumber)
eryd = zeros(PixelNumber)
eryd_low = zeros(PixelNumber)
for i in range(len(Wavelength_Range)):
wave = Wavelength_Range[i] # wavelength en Angstroms
nu[i] = cspeedA/wave # frecuencia en Hz
eryd[i] = planckCGS*cspeedA/(rydbergerg*wave) # energia en Rydbergs
if Ion == "HI":
a = self.a_HI
if Ion == "HeI":
a = self.a_HeI
if Ion == "HeII":
a = self.a_HeII
nTe = int(split(a[0])[0]) # number of Te columns
nener = int(split(a[0])[1]) # number of energy points rows
skip = int(1+ceil(nTe/8.)) # 8 es el numero de valores de Te por fila.
temp = zeros(nTe)
for i in range(1,skip) :
tt = split(a[i])
for j in range(0,len(tt)) :
temp[8*(i-1)+j] = tt[j]
rte2 = 0
if bisect_right(temp,log10(Te)) - bisect_left(temp,log10(Te)) == 1 :
rte1 = bisect_left(temp,log10(Te)) # Te existe
elif bisect_right(temp,log10(Te)) - bisect_left(temp,log10(Te)) == 0 :
rte1 = bisect_left(temp,log10(Te))-1 # interpola Te
rte2 = bisect_right(temp,log10(Te)) #
else :
print 'ERROR IN Te COLUMN DETECTION FOR Gamma_fb', Te
Gamma_fb_f = zeros(nener)
ener = zeros(nener)
gamma = zeros(nener)
thresh = zeros(nener)
ener_low = zeros(nener)
for i in range(skip,skip+nener) :
thresh[i-skip] = int(split(a[i])[0]) # indicador de threshold (1) o de punto nodal (0)
ener[i-skip] = float(split(a[i])[1]) # energia en Ryd
gamma[i-skip] = float(split(a[i])[2+rte1]) # [22] es para Te=1e4
if rte2 > 0 :
gamma[i-skip] = float(split(a[i])[2+rte1]) + (float(split(a[i])[2+rte2])-float(split(a[i])[2+rte1]))/(10**temp[rte2]-10**temp[rte1]) * (Te-10**temp[rte1])
ener_low = thresh*ener
atmp=thresh.nonzero()[0]
for i in range(1,len(atmp),2) : ener_low[atmp[i]] = ener_low[atmp[i-1]]
for i in range(0,len(ener_low)) :
if ener_low[i] == 0 : ener_low[i] = ener_low[i-1]
eryd_low = interp(eryd, ener, ener_low)
Gamma_fb_f = interp(eryd, ener, gamma) # linear interpolation at grid of interest
Gamma_fb_f = Gamma_fb_f * 1e-40*t4**-1.5*exp(-15.7887*(eryd-eryd_low)/t4)
return Gamma_fb_f
def Zanstra_Calibration_Hbeta(self, Te, Flux_EmLine, Gamma_nu, Wavelength_Range):
# Pequignot et al. 1991
t4 = Te / 10000
alfa_eff = 0.668e-13 * t4**-0.507 / (1 + 1.221*t4**0.653)
lambda_EmLine = 4862.683
NebularFlux_lambda = Gamma_nu * lambda_EmLine * Flux_EmLine / (alfa_eff * self.planckCGS * power(Wavelength_Range,2)) # erg s-1 [cm-2] A-1
return NebularFlux_lambda
def Zanstra_Calibration_Halpha(self, Te, Flux_EmLine, Gamma_nu, Wavelength_Range):
# Pequignot et al. 1991
t4 = Te / 10000
alfa_eff = 2.708e-13 * t4**-0.648 / (1 + 1.315*t4**0.523)
lambda_EmLine = 6562.819
NebularFlux_lambda = Gamma_nu * lambda_EmLine * Flux_EmLine / (alfa_eff * self.planckCGS * power(Wavelength_Range,2)) # erg s-1 [cm-2] A-1
return NebularFlux_lambda
color = Grid_Values['zGas'].index(parameter_divider)
label = r'$Z = {logage}$'.format(logage = Model_dict['zGas'])
#Calculate the grid point abundances
#x_values, y_values = Ar_S_model(Line_dict, threshold = 4, z = float(Model_dict['zGas']))
x_values, y_values = Ar_S_abundances_model(Line_dict, diags, Ar3, Ar4, S3, S4, 3)
if (x_values != None) and (y_values != None):
dz.data_plot(x_values, y_values, color=dz.ColorVector[2][color], label=label, markerstyle='o')
x_linealFitting = hstack([x_linealFitting, x_values])
y_linealFitting = hstack([y_linealFitting, y_values])
#Lineal model
lineal_mod = LinearModel(prefix='lineal_')
Lineal_parameters = lineal_mod.guess(y_linealFitting, x=x_linealFitting)
x_lineal = linspace(0, np_max(x_linealFitting), 100)
y_lineal = Lineal_parameters['lineal_slope'].value * x_lineal + Lineal_parameters['lineal_intercept'].value
dz.data_plot(x_lineal, y_lineal, label='Lineal fitting', color = 'black', linestyle='-')
# #Plot fitting formula
formula = r"$log\left(Ar^{{+2}}/Ar^{{+3}}\right) = {m} \cdot log\left(S^{{+2}}/S^{{+3}}\right) + {n}$".format(m=round(Lineal_parameters['lineal_slope'].value,3),
n=round(Lineal_parameters['lineal_intercept'].value, 3))
dz.Axis.text(0.50, 0.15, formula, transform=dz.Axis.transAxes, fontsize=20)
#Plot wording
xtitle = r'$log\left(S^{{+2}}/S^{{+3}}\right)$'
ytitle = r'$log\left(Ar^{{+2}}/Ar^{{+3}}\right)$'
title = 'Argon - Sulfur ionic abundances for several cluster ages and masses'
dz.FigWording(xtitle, ytitle, title, axis_Size = 20.0, title_Size = 20.0, legend_size=20.0, legend_loc='upper left')
plt.plot(line_wave[max_index], line_flux[max_index], 'o', color = 'purple', label = 'Maxima') plt.plot(line_wave[min_index], line_flux[min_index], 'o', color = 'orange', label = 'Minima') #Lmfit parameters Ncomps = 3 Initial_guesses_dic = OrderedDict() Initial_guesses_dic['A'] = np.array([peak_fluxes[0], peak_fluxes[1], peak_fluxes[2], peak_fluxes[1]/50]) Initial_guesses_dic['mu'] = np.array([peak_waves[0], peak_waves[1], peak_waves[2], peak_waves[1]]) Initial_guesses_dic['sigma'] = np.array([1.0, 1.0, 1.0, 5.0]) Initial_guesses_dic['min_sigma'] = np.zeros(Ncomps + 1) Initial_guesses_dic['min_sigma'][-1] = 5 params = Load_lmfit_parameters(Ncomps, Initial_guesses_dic, wide_component = True, mu_precission = mu_precission) #Declaring a linear continuum uppon which the line is located lineal_mod = LinearModel(prefix='lineal_') Continuum_wave, Continuum_flux = np.hstack([blue_wave, red_wave]), np.hstack([blue_flux, red_flux]) Lineal_parameters = lineal_mod.guess(Continuum_flux, x=Continuum_wave) lineal_zerolev = Lineal_parameters['lineal_slope'].value * line_wave + Lineal_parameters['lineal_intercept'].value err_continuum = np.std(Lineal_parameters['lineal_slope'].value * Continuum_wave + Lineal_parameters['lineal_intercept'].value - Continuum_flux) print 'error', err_continuum #Make the fitting out = minimize(CompResid_zerolev, params, args=(line_wave, line_flux, lineal_zerolev, Ncomps + 1, err_continuum)) report_fit(out.params) #Make the plots x_resample = np.linspace(line_wave[0], line_wave[-1], 100) lineal_resample = Lineal_parameters['lineal_slope'].value * x_resample + Lineal_parameters['lineal_intercept'].value plt.plot(Wavelength, Flux, '-', color= 'black', label = 'Complete spectrum') # plt.plot(x_resample, CompositeModel_zerolev(out.params, x_resample, lineal_resample, Ncomps + 1), 'r-', label = 'Fitted line')