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 make_gaussian_model(self):
""" This method creates a model of a gaussian with an offset.
@return tuple: (object model, object params)
Explanation of the objects:
object lmfit.model.CompositeModel model:
A model the lmfit module will use for that fit. Here a
gaussian model. Returns an object of the class
lmfit.model.CompositeModel.
object lmfit.parameter.Parameters params:
It is basically an OrderedDict, so a dictionary, with keys
denoting the parameters as string names and values which are
lmfit.parameter.Parameter (without s) objects, keeping the
information about the current value.
The used model has the Parameter with the meaning:
'amplitude' : amplitude
'center' : center
'sigm' : sigma
'fwhm' : full width half maximum
'c' : offset
For further information have a look in:
http://cars9.uchicago.edu/software/python/lmfit/builtin_models.html#models.GaussianModel
"""
model = GaussianModel() + ConstantModel()
params = model.make_params()
return model, params
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 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 fit_profile(profile, guess):
"Fit a profile to a Gaussian + Contant"
x = np.arange(len(profile))
model = GaussianModel(missing='drop') + ConstantModel(missing='drop')
result = model.fit(profile, x=x, verbose=False, **guess)
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 GaussConst(signal, guess):
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 = gauss_mod.make_params(center=centre, sigma=stdev, amplitude=amp)
pars += const_mod.guess(Y, x=X)
pars['gauss_center'].min = centre - 5.
pars['gauss_center'].max = centre + 5.
pars['gauss_sigma'].max = stdev + 5.
mod = gauss_mod + const_mod
result = mod.fit(Y, pars, x=X)
fwhm = result.best_values['gauss_sigma'] #* 2.3548
centr = result.best_values['gauss_center']
# Values within two stdevs i.e. 95%
pl.plot(np.repeat(centr - fwhm * 2, len(Y)),
np.arange(len(Y)), 'b-')
pl.plot(np.repeat(centr + fwhm * 2, len(Y)),
np.arange(len(Y)), 'b-')
return X, result.best_fit, result.best_values['gauss_sigma'] * 4
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(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 test_default_inputs_gauss():
area = 1
cen = 0
std = 0.2
x = np.arange(-3, 3, 0.01)
y = gaussian(x, area, cen, std)
g = GaussianModel()
fit_option1 = {'maxfev': 5000, 'xtol': 1e-2}
result1 = g.fit(y,
x=x,
amplitude=1,
center=0,
sigma=0.5,
fit_kws=fit_option1)
fit_option2 = {'maxfev': 5000, 'xtol': 1e-6}
result2 = g.fit(y,
x=x,
amplitude=1,
center=0,
sigma=0.5,
fit_kws=fit_option2)
assert result1.values != result2.values
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 gaussFitFunction(fitOut,minimum,maximum,ptNumber=100,prefix=None): x = np.linspace(minimum,maximum,ptNumber) gaussian = GaussianModel() if prefix==None: params = fitOut.best_values else: params = getKeysWithoutPrefix(fitOut.best_values,prefix) gauss = gaussian.func(x=x,center=params["center"],sigma=params["sigma"],amplitude=params["amplitude"]) return x, gauss
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 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 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_lmfit():
""" load data """
wave, flux, flux_err = np.loadtxt(
'/hydrogen/projects/song/delCep_order20.dat').T
flux_sine = 1 - flux
flux_sine = flux_sine * sinebell_like(flux, 1.0)
flux_obs = flux_sine + np.random.randn(*flux_sine.shape) * 0.1
wave_mod = wave
wave_obs = wave
flux_mod = flux_sine
rv_grid = np.linspace(-500, 500, 1000)
# z_grid = rv_grid / constants.c.value * 1000
ccfv = xcorr_rvgrid(wave_obs,
flux_obs,
wave_mod,
flux_mod,
mask_obs=None,
rv_grid=rv_grid,
sinebell_idx=1)
# Gaussian fit using LMFIT
from lmfit.models import GaussianModel
mod = GaussianModel()
x, y = ccfv[0], ccfv[1]
# pars = mod.guess(y, x=x)
out = mod.fit(y, None, x=x, method="least_squares")
# out = mod.fit(y, pars, x=x, method="leastsq")
plt.figure()
plt.plot(x, y)
plt.plot(x, out.best_fit)
print(out.fit_report())
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 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 GaussConst(signal, guess):
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 = gauss_mod.make_params(center=centre, sigma=stdev, amplitude=amp)
pars += const_mod.guess(Y, x=X)
pars['gauss_center'].min = centre - 5.
pars['gauss_center'].max = centre + 5.
pars['gauss_sigma'].max = stdev + 5.
mod = gauss_mod + const_mod
result = mod.fit(Y, pars, x=X)
fwhm = result.best_values['gauss_sigma'] #* 2.3548
centr = result.best_values['gauss_center']
# Values within two stdevs i.e. 95%
pl.plot(np.repeat(centr - fwhm * 2, len(Y)), np.arange(len(Y)), 'b-')
pl.plot(np.repeat(centr + fwhm * 2, len(Y)), np.arange(len(Y)), 'b-')
return X, result.best_fit, result.best_values['gauss_sigma'] * 4
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 fitgaussian_sample(sample, components, svg, verbose, center, cmin, cmax,
amp, amin, sigma, smin):
'''Fits gaussian curve to dyad coverage for a single sample.'''
print('Fits gaussian curve to dyad coverage of sample {}'.format(sample))
input = sample + '-dyad.txt'
dyads = pd.read_csv(input, sep='\t', index_col=0, comment='#')
x = dyads.index.values
y = dyads['Relative Frequency'].values
if not amp:
amp = dyads['Relative Frequency'].max() * 100
if not center:
center = 0.0
if not sigma:
sigma = dyads.index.max() / 2
plt.figure()
plt.title(sample)
plt.xlabel('Position relative to dyad (bp)')
plt.ylabel('Relative Frequency')
plt.xlim(x[0], x[len(x) - 1])
plt.xticks(list(range(x[0], x[len(x) - 1] + 1, 25)))
plt.plot(dyads.index.values,
dyads['Relative Frequency'].values,
color='red')
plot_output = sample + '-dyad-gaussian.png'
try:
constant = ConstantModel(prefix='c_')
pars = constant.make_params()
pars['c_c'].set(value=dyads['Relative Frequency'].min(),
min=0.0,
max=dyads['Relative Frequency'].max())
gauss = GaussianModel(prefix='g_')
pars.update(gauss.make_params())
pars['g_center'].set(value=center, min=cmin, max=cmax)
pars['g_sigma'].set(value=sigma, min=smin)
pars['g_amplitude'].set(value=amp, min=amin)
mod = constant + gauss
init = mod.eval(pars, x=x)
out = mod.fit(y, pars, x=x)
if components:
plt.plot(x, init, 'b--', label='Initial fit')
if verbose:
print(out.fit_report(min_correl=0.5))
plt.plot(x, out.best_fit, 'b-', label='Best fit')
if components:
comps = out.eval_components(x=x)
plt.plot(x,
np.repeat(comps['c_'], len(x)),
'g--',
label='Constant component')
plt.plot(x, comps['g_'], 'm--', label='Gaussian component')
except Exception as e:
logging.warning(
'could not fit gaussian curve to sample {}'.format(sample), e)
if components:
plt.legend(loc='lower right')
plt.savefig(plot_output)
if svg:
plot_svg_output = sample + '-dyad-gaussian.svg'
plt.savefig(plot_svg_output, transparent=True)
plt.close()
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 call_gauss(x, y, cen, count, pars): label='g'+str(count)+'_' gauss = GaussianModel(prefix=label) pars.update(gauss.make_params()) pars[label+'center'].set(cen, min=cen-0.01, max=cen+0.01) pars[label+'amplitude'].set(-0.5, min=-10., max=0.0001) pars[label+'sigma'].set(0.1, min=0.005, max=0.25) return gauss
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 call_gauss(x, y, cen, count, pars): label='g'+str(count)+'_' gauss = GaussianModel(prefix=label) pars.update(gauss.make_params()) pars[label+'center'].set(cen, min=cen-0.01, max=cen+0.01) pars[label+'amplitude'].set(0, min=-(max(y)-min(y))*1.5, max=0.0001) pars[label+'sigma'].set(fw_set/4, min=0.005, max=fw_set/2.3548) return gauss
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 label_diff_lmfit(label1,
label2,
bins='auto',
bin_std=3,
plot=False,
emcee=True):
label1 = np.array(label1)
label2 = np.array(label2)
assert label1.shape == label2.shape
n_obs, n_dim = label1.shape
amp = np.zeros((n_dim, ), dtype=float)
bias = np.zeros((n_dim, ), dtype=float)
scatter = np.zeros((n_dim, ), dtype=float)
frs = np.zeros((n_dim, ), dtype=object)
for i_dim in range(n_dim):
data = label2[:, i_dim] - label1[:, i_dim]
theta, frs[i_dim] = \
gfit_bin_lmfit(data, bins=bins, bin_std=bin_std, plot=False)
amp[i_dim], bias[i_dim], scatter[i_dim] = theta
params = [fr.params for fr in frs]
if emcee:
frs = Parallel(n_jobs=-1)(
delayed(run_mcmc)(fr, steps=1000, nwalkers=50, burn=300, workers=1)
for fr in frs)
for i_dim in range(n_dim):
bias[i_dim] = np.median(frs[i_dim].mcmc.flatchain["center"])
scatter[i_dim] = np.median(frs[i_dim].mcmc.flatchain["sigma"])
params = [fr.mcmc.params for fr in frs]
histdata = []
if plot:
gm = GaussianModel()
fig = plt.figure(figsize=(3 * n_dim, 4))
for i_dim in range(n_dim):
ax = fig.add_subplot(1, n_dim, i_dim + 1)
data = label2[:, i_dim] - label1[:, i_dim]
# binned statistics
if bins == 'robust':
bins = np.arange(np.min(data), np.max(data),
np.std(data) / bin_std)
hist, bin_edges = np.histogram(data, bins=bins)
histdata.append((hist, bin_edges, data))
# bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2
# bin_xx = np.linspace(bin_edges[0], bin_edges[-1], 100)
ax.hist(data, bins=bin_edges, histtype='step')
ax.plot(bin_edges, gm.eval(params[i_dim], x=bin_edges))
ax.set_title("{:5f}+-{:5f}".format(bias[i_dim], scatter[i_dim]))
else:
for i_dim in range(n_dim):
data = label2[:, i_dim] - label1[:, i_dim]
hist, bin_edges = np.histogram(data, bins=bins)
histdata.append((hist, bin_edges, data))
return bias, scatter, frs, histdata
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 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 xrf_calib_init_roi(mca, roiname):
"""initial calibration step for MCA:
find energy locations for one ROI
"""
if not isLarchMCAGroup(mca):
print('Not a valid MCA')
return
energy = 1.0 * mca.energy
chans = 1.0 * np.arange(len(energy))
counts = mca.counts
bgr = getattr(mca, 'bgr', None)
if bgr is not None:
counts = counts - bgr
if not hasattr(mca, 'init_calib'):
mca.init_calib = OrderedDict()
roi = None
for xroi in mca.rois:
if xroi.name == roiname:
roi = xroi
break
if roi is None:
return
words = roiname.split()
elem = words[0].title()
family = 'Ka'
if len(words) > 1:
family = words[1].title()
if family == 'Lb':
family = 'Lb1'
try:
eknown = xray_line(elem, family).energy / 1000.0
except:
eknown = 0.001
llim = max(0, roi.left - roi.bgr_width)
hlim = min(len(chans) - 1, roi.right + roi.bgr_width)
segcounts = counts[llim:hlim]
maxcounts = max(segcounts)
ccen = llim + np.where(segcounts == maxcounts)[0][0]
ecen = ccen * mca.slope + mca.offset
bkgcounts = counts[llim] + counts[hlim]
if maxcounts < 2 * bkgcounts:
mca.init_calib[roiname] = (eknown, ecen, 0.0, ccen, None)
else:
model = GaussianModel() + ConstantModel()
params = model.make_params(amplitude=maxcounts,
sigma=(chans[hlim] - chans[llim]) / 2.0,
center=ccen - llim,
c=0.00)
params['center'].min = -10
params['center'].max = hlim - llim + 10
params['c'].min = -10
out = model.fit(counts[llim:hlim], params, x=chans[llim:hlim])
ccen = llim + out.params['center'].value
ecen = ccen * mca.slope + mca.offset
fwhm = out.params['fwhm'].value * mca.slope
mca.init_calib[roiname] = (eknown, ecen, fwhm, ccen, out)
def test_report_modelpars(fitresult):
"""Verify that model_values are shown when modelpars are given."""
model = GaussianModel()
params = model.make_params(amplitude=35, center=7, sigma=0.9)
report_split = fitresult.fit_report(modelpars=params).split('\n')
indices = [i for i, val in enumerate(report_split) if
('sigma:' in val or 'center:' in val or 'amplitude:' in val)]
for indx in indices:
assert 'model_value' in report_split[indx]
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 gauss_shoulder(self, fitv, par_g: list, bounds_g: list, Ng: int = 1):
gauss2 = GaussianModel(prefix='g' + str(Ng) + '_')
pars = fitv.params
pars.update(gauss2.make_params())
for k, p, b in zip(gauss2.param_names, par_g, bounds_g):
pars[k].set(value=p, min=b[0], max=b[1])
mod = fitv.model + gauss2
return self.finish_fit(self, mod, pars)
def gauss_mod(N):
'''
Returns a model consisting of N gaussian curves
'''
# initialize model
model = GaussianModel(prefix='gau1_')
# Add N-1 gaussians
for i in range(N - 1):
model += GaussianModel(prefix='gau' + str(i + 2) + '_')
return model
def SPErough(data, n_channel_s):
fit_input, bins, check = SPE_input(data)
amplitude = get_amp(data)
gauss = GaussianModel(prefix='g_')
s, bins = np.histogram(amplitude, bins=bins)
topnoise = fit_input[0]
valley = fit_input[1]
endvalley = fit_input[2]
spebump = fit_input[3]
endbin = fit_input[4]
idx_1 = endvalley
idx_2 = spebump + (spebump-endvalley)
if idx_1 < endvalley:
idx_1 = endvalley
if idx_2 > endbin:
idx_2 = endbin
if check == 1:
gauss.set_param_hint('g_height', value=s[spebump], min=s[spebump]-30, max=s[spebump]+30)
gauss.set_param_hint('g_center', value=bins[spebump], min=bins[spebump]-30, max=bins[spebump]+30)
gauss.set_param_hint('g_sigma', value=idx_2-idx_1, max=(idx_2-idx_1)+30)
result = gauss.fit(s[idx_1:idx_2], x=bins[idx_1:idx_2], weights=1.0/np.sqrt(s[idx_1:idx_2]))
else:
gauss = 0
result = 0
return gauss, result
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 get_gaussianmodel(amplitude=1.0, center=5.0, sigma=1.0, noise=0.1):
# create data to be fitted
np.random.seed(7392)
x = np.linspace(-20, 20, 201)
y = gaussian(x, amplitude, center=center, sigma=sigma)
y = y + np.random.normal(size=len(x), scale=noise)
model = GaussianModel()
params = model.make_params(amplitude=amplitude/5.0,
center=center-1.0,
sigma=sigma*2.0)
return x, y, model, params
def xrf_calib_init_roi(mca, roiname):
"""initial calibration step for MCA:
find energy locations for one ROI
"""
if not isLarchMCAGroup(mca):
print( 'Not a valid MCA')
return
energy = 1.0*mca.energy
chans = 1.0*np.arange(len(energy))
counts = mca.counts
bgr = getattr(mca, 'bgr', None)
if bgr is not None:
counts = counts - bgr
if not hasattr(mca, 'init_calib'):
mca.init_calib = OrderedDict()
roi = None
for xroi in mca.rois:
if xroi.name == roiname:
roi = xroi
break
if roi is None:
return
words = roiname.split()
elem = words[0].title()
family = 'Ka'
if len(words) > 1:
family = words[1].title()
if family == 'Lb':
family = 'Lb1'
eknown = xray_line(elem, family)[0]/1000.0
llim = max(0, roi.left - roi.bgr_width)
hlim = min(len(chans)-1, roi.right + roi.bgr_width)
segcounts = counts[llim:hlim]
maxcounts = max(segcounts)
ccen = llim + np.where(segcounts==maxcounts)[0]
ecen = ccen * mca.slope + mca.offset
bkgcounts = counts[llim] + counts[hlim]
if maxcounts < 2*bkgcounts:
mca.init_calib[roiname] = (eknown, ecen, 0.0, ccen, None)
else:
model = GaussianModel() + ConstantModel()
params = model.make_params(amplitude=maxcounts,
sigma=(chans[hlim]-chans[llim])/2.0,
center=ccen-llim, c=0.00)
params['center'].min = -10
params['center'].max = hlim - llim + 10
params['c'].min = -10
out = model.fit(counts[llim:hlim], params, x=chans[llim:hlim])
ccen = llim + out.params['center'].value
ecen = ccen * mca.slope + mca.offset
fwhm = out.params['fwhm'].value * mca.slope
mca.init_calib[roiname] = (eknown, ecen, fwhm, ccen, out)
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 test_default_inputs_gauss():
area = 1
cen = 0
std = 0.2
x = np.arange(-3, 3, 0.01)
y = gaussian(x, area, cen, std)
g = GaussianModel()
fit_option1 = {'maxfev': 5000, 'xtol': 1e-2}
result1 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option1)
fit_option2 = {'maxfev': 5000, 'xtol': 1e-6}
result2 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option2)
assert_true(result1.values!=result2.values)
return
def test_itercb():
x = np.linspace(0, 20, 401)
y = gaussian(x, amplitude=24.56, center=7.6543, sigma=1.23)
y = y - .20*x + 3.333 + np.random.normal(scale=0.23, size=len(x))
mod = GaussianModel(prefix='peak_') + LinearModel(prefix='bkg_')
pars = mod.make_params(peak_amplitude=21.0,
peak_center=7.0,
peak_sigma=2.0,
bkg_intercept=2,
bkg_slope=0.0)
out = mod.fit(y, pars, x=x, iter_cb=per_iteration)
assert(out.nfev == 23)
assert(out.aborted)
assert(not out.errorbars)
assert(not out.success)
def create_model_params(x, y):
"""Create the model and parameters."""
exp_mod = ExponentialModel(prefix='exp_')
params = exp_mod.guess(y, x=x)
gauss1 = GaussianModel(prefix='g1_')
params.update(gauss1.make_params())
gauss2 = GaussianModel(prefix='g2_')
params.update(gauss2.make_params())
params['g1_center'].set(value=105, min=75, max=125)
params['g1_sigma'].set(value=15, min=3)
params['g1_amplitude'].set(value=2000, min=10)
params['g2_center'].set(value=155, min=125, max=175)
params['g2_sigma'].set(value=15, min=3)
params['g2_amplitude'].set(value=2000, min=10)
model = gauss1 + gauss2 + exp_mod
return model, params
def fitTwoGaussians(x,y):
background = PolynomialModel(2)
pars = background.make_params()
peak1 = GaussianModel(prefix='p1_')
pars.update( peak1.make_params())
peak2 = GaussianModel(prefix='p2_')
pars.update( peak2.make_params())
# Guess some parameters from data to help the fitting
span = max(x)-min(x)
c1Guess = (y[-1]-y[0])/(x[-1]-x[0])
c0Guess = y[0]-c1Guess*x[0]
bgGuess = background.func(x=x,c0=c0Guess,c1=c1Guess,c2=0.)
signalGuess=min(y-bgGuess)
sigmaGuess = span/30.
amplitudeGuess = signalGuess*(sigmaGuess*np.sqrt(2.0*np.pi))
# Fit variables initialization
# pars.add('splitting',0.0001,max=span)
pars['c2'].set(0.,min=-0.000001,max=0.001)
pars['c1'].set(c1Guess)
pars['c0'].set(c0Guess)
pars['p1_center'].set(min(x)+span*0.35,min=min(x),max=max(x))
pars['p2_center'].set(min(x)+span*0.55,min=min(x),max=max(x))
# pars['p2_center'].set(min(x)+span*0.65,expr='p1_center+splitting')
pars['p1_amplitude'].set(amplitudeGuess,max=amplitudeGuess/10000.)
pars['p2_amplitude'].set(amplitudeGuess,max=amplitudeGuess/10000.)
pars['p1_sigma'].set(sigmaGuess, min=sigmaGuess/100.,max=sigmaGuess*10000.)
pars['p2_sigma'].set(sigmaGuess, min=sigmaGuess/100.,max=sigmaGuess*10000.)
#Add some useful parameters to evaluate
pars.add('p1_signal', expr='p1_amplitude/(p1_sigma*sqrt(2.0*pi))')
pars.add('p2_signal', expr='p2_amplitude/(p2_sigma*sqrt(2.0*pi))')
pars.add('p1_contrast', expr='-p1_amplitude/(p1_sigma*sqrt(2.0*pi)*(c0+c1*p1_center+c2*p1_center**2))')
pars.add('p2_contrast', expr='-p2_amplitude/(p2_sigma*sqrt(2.0*pi)*(c0+c1*p2_center+c2*p2_center**2))')
pars.add('splitting',pars['p2_center']-pars['p1_center'],expr='p2_center-p1_center',min=0.00001)
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 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 GaussConst(signal, guess):
"""
Fits a Gaussian function
Plots fwhm and 2*sigma gap widths for comparison
with the analytically calculated one
"""
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 = gauss_mod.make_params(center=centre, sigma=stdev, amplitude=amp)
pars += const_mod.guess(Y, x=X)
pars['gauss_center'].min = centre - 5.
pars['gauss_center'].max = centre + 5.
pars['gauss_sigma'].max = stdev + 5.
mod = gauss_mod + const_mod
result = mod.fit(Y, pars, x=X)
fwhm = result.best_values['gauss_sigma'] #* 2.3548
centr = result.best_values['gauss_center']
# Values within two stdevs i.e. 95%
pl.plot(np.repeat(centr - fwhm * 2, len(Y)),
np.arange(len(Y)), 'b-')
pl.plot(np.repeat(centr + fwhm * 2, len(Y)),
np.arange(len(Y)), 'b-', label="Sigma * 2")
pl.plot(np.repeat(centr - fwhm * 2.3548 / 2., len(Y)),
np.arange(len(Y)), 'y--')
pl.plot(np.repeat(centr + fwhm * 2.3548 / 2., len(Y)),
np.arange(len(Y)), 'y--', label="FWHM")
return X, result.best_fit, result.best_values['gauss_sigma'] * 4, centr
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 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 test_reports_created():
"""do a simple Model fit but with all the bells-and-whistles
and verify that the reports are created
"""
x = np.linspace(0, 12, 601)
data = gaussian(x, amplitude=36.4, center=6.70, sigma=0.88)
data = data + np.random.normal(size=len(x), scale=3.2)
model = GaussianModel()
params = model.make_params(amplitude=50, center=5, sigma=2)
params['amplitude'].min = 0
params['sigma'].min = 0
params['sigma'].brute_step = 0.001
result = model.fit(data, params, x=x)
report = result.fit_report()
assert(len(report) > 500)
html_params = result.params._repr_html_()
assert(len(html_params) > 500)
html_report = result._repr_html_()
assert(len(html_report) > 1000)
def test_example_2_Gaussians_1_exp():
dat = np.loadtxt('NIST_Gauss2.dat')
x = dat[:, 1]
y = dat[:, 0]
exp_mod = ExponentialModel(prefix='exp_')
pars = exp_mod.guess(y, x=x)
gauss1 = GaussianModel(prefix='g1_')
pars.update(gauss1.make_params())
pars['g1_center'].set(105, min=75, max=125)
pars['g1_sigma'].set(15, min=3)
pars['g1_amplitude'].set(2000, min=10)
gauss2 = GaussianModel(prefix='g2_')
pars.update(gauss2.make_params())
pars['g2_center'].set(155, min=125, max=175)
pars['g2_sigma'].set(15, min=3)
pars['g2_amplitude'].set(2000, min=10)
mod = gauss1 + gauss2 + exp_mod
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()
#!/usr/bin/env python
# <examples/doc_builtinmodels_nistgauss.py>
import matplotlib.pyplot as plt
import numpy as np
from lmfit.models import ExponentialModel, GaussianModel
dat = np.loadtxt('NIST_Gauss2.dat')
x = dat[:, 1]
y = dat[:, 0]
exp_mod = ExponentialModel(prefix='exp_')
pars = exp_mod.guess(y, x=x)
gauss1 = GaussianModel(prefix='g1_')
pars.update(gauss1.make_params())
pars['g1_center'].set(105, min=75, max=125)
pars['g1_sigma'].set(15, min=3)
pars['g1_amplitude'].set(2000, min=10)
gauss2 = GaussianModel(prefix='g2_')
pars.update(gauss2.make_params())
pars['g2_center'].set(155, min=125, max=175)
pars['g2_sigma'].set(15, min=3)
pars['g2_amplitude'].set(2000, min=10)
mod = gauss1 + gauss2 + exp_mod
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()
from lmfit.models import GaussianModel, LorentzianModel, VoigtModel
data = loadtxt('test_peak.dat')
x = data[:, 0]
y = data[:, 1]
gamma_free = False
MODEL = 'gauss'
# 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'