def test_custom_independentvar():
"""Tests using a non-trivial object as an independent variable."""
npts = 501
xmin = 1
xmax = 21
cen = 8
obj = Stepper(xmin, xmax, npts)
y = gaussian(obj.get_x(), amplitude=3.0, center=cen, sigma=2.5)
y += np.random.normal(scale=0.2, size=npts)
gmod = Model(gaussian_mod)
params = gmod.make_params(amplitude=2, center=5, sigma=8)
out = gmod.fit(y, params, obj=obj)
assert(out.nvarys == 3)
assert(out.nfev > 10)
assert(out.chisqr > 1)
assert(out.chisqr < 100)
assert(out.params['sigma'].value < 3)
assert(out.params['sigma'].value > 2)
assert(out.params['center'].value > xmin)
assert(out.params['center'].value < xmax)
assert(out.params['amplitude'].value > 1)
assert(out.params['amplitude'].value < 5)
def fitGompertz(x, y, dias): # fit a logistic function~
def Gompertz(a, b, c, x):
return a * np.exp(-1 * np.exp(-b * (x - c)))
model = Model(Gompertz, independent_vars=["x"])
params = model.make_params()
params["a"].value = 10000
params["b"].value = 0.05
params["c"].value = 100
output = model.fit(y, params, x=x)
amplitude = output.params["a"].value
amplitude = math.floor(amplitude)
center = output.params["c"].value
sigma = output.params["b"].value
fit = []
xfit = []
cumulative = []
for i in range(61, dias):
if i == 61:
xfit.append(i)
value = amplitude * np.exp(-1 * np.exp(-sigma * (i - center)))
fit.append(value)
cumulative.append(0)
else:
xfit.append(i)
value = amplitude * np.exp(-1 * np.exp(-sigma * (i - center)))
fit.append(value)
c = value - fit[i - 62]
cumulative.append(c)
return amplitude, center, sigma, xfit, fit, cumulative, output.fit_report()
def make_bareexponentialdecay_model(self):
"""
This method creates a model of bare exponential decay.
@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.
"""
def bareexponentialdecay_function(x, lifetime):
"""
Function of a bare exponential decay.
@param x: variable variable - e.g. time
@param lifetime: lifetime
@return: bare exponential decay function: in order to use it as a model
"""
return np.exp(-x / lifetime)
model = Model(bareexponentialdecay_function)
params = model.make_params()
return model, params
def make_twoDgaussian_model(self):
""" This method creates a model of the 2D gaussian function.
The parameters are: 'amplitude', 'center', 'sigm, 'fwhm' and offset
'c'. For function see:
@return lmfit.model.CompositeModel model: Returns an object of the
class CompositeModel
@return lmfit.parameter.Parameters params: Returns an object of the
class Parameters with all
parameters for the
gaussian model.
"""
def twoDgaussian_function(x, amplitude, x_zero, y_zero, sigma_x, sigma_y,
theta, offset):
# FIXME: x_data_tuple: dimension of arrays
""" This method provides a two dimensional gaussian function.
Function taken from:
http://stackoverflow.com/questions/21566379/fitting-a-2d-gaussian-function-using-scipy-optimize-curve-fit-valueerror-and-m/21566831
Question from: http://stackoverflow.com/users/2097737/bland & http://stackoverflow.com/users/3273102/kokomoking
& http://stackoverflow.com/users/2767207/jojodmo
Answer: http://stackoverflow.com/users/1461210/ali-m & http://stackoverflow.com/users/5234/mrjrdnthms
@param array[k][M] x_data_tuple: array which is (k,M)-shaped, x and y
values
@param float or int amplitude: Amplitude of gaussian
@param float or int x_zero: x value of maximum
@param float or int y_zero: y value of maximum
@param float or int sigma_x: standard deviation in x direction
@param float or int sigma_y: standard deviation in y direction
@param float or int theta: angle for eliptical gaussians
@param float or int offset: offset
@return callable function: returns the function
"""
(u, v) = x
x_zero = float(x_zero)
y_zero = float(y_zero)
a = (np.cos(theta) ** 2) / (2 * sigma_x ** 2) \
+ (np.sin(theta) ** 2) / (2 * sigma_y ** 2)
b = -(np.sin(2 * theta)) / (4 * sigma_x ** 2) \
+ (np.sin(2 * theta)) / (4 * sigma_y ** 2)
c = (np.sin(theta) ** 2) / (2 * sigma_x ** 2) \
+ (np.cos(theta) ** 2) / (2 * sigma_y ** 2)
g = offset + amplitude * np.exp(- (a * ((u - x_zero) ** 2) \
+ 2 * b * (u - x_zero) * (v - y_zero) \
+ c * ((v - y_zero) ** 2)))
return g.ravel()
model = Model(twoDgaussian_function)
params = model.make_params()
return model, params
def make_slope_model(self):
""" This method creates a model of a slope model.
@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. 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.
For further information have a look in:
http://cars9.uchicago.edu/software/python/lmfit/builtin_models.html#models.GaussianModel
"""
def slope_function(x, slope):
"""
Function of a constant value.
@param x: variable variable
@param slope: independent variable - slope
@return: slope function: in order to use it as a model
"""
return slope + 0.0 * x
model = Model(slope_function)
params = model.make_params()
return model, params
def test_custom_independentvar():
"""Tests using a non-trivial object as an independent variable."""
npts = 501
xmin = 1
xmax = 21
cen = 8
obj = Stepper(xmin, xmax, npts)
y = gaussian(obj.get_x(), amplitude=3.0, center=cen, sigma=2.5)
y += np.random.normal(scale=0.2, size=npts)
gmod = Model(gaussian_mod)
params = gmod.make_params(amplitude=2, center=5, sigma=8)
out = gmod.fit(y, params, obj=obj)
assert (out.nvarys == 3)
assert (out.nfev > 10)
assert (out.chisqr > 1)
assert (out.chisqr < 100)
assert (out.params['sigma'].value < 3)
assert (out.params['sigma'].value > 2)
assert (out.params['center'].value > xmin)
assert (out.params['center'].value < xmax)
assert (out.params['amplitude'].value > 1)
assert (out.params['amplitude'].value < 5)
def make_amplitude_model(self, prefix=None):
""" Create a constant model.
@param str prefix: optional string, which serves as a prefix for all
parameters used in this model. That will prevent
name collisions if this model is used in a composite
way.
@return tuple: (object model, object params), for more description see in
the method make_constant_model.
"""
def amplitude_function(x, amplitude):
""" Function of a constant value.
@param numpy.array x: 1D array as the independent variable - e.g. time
@param float amplitude: constant offset
@return: constant function, in order to use it as a model
"""
return amplitude
if not isinstance(prefix, str) and prefix is not None:
self.log.error(
'The passed prefix <{0}> of type {1} is not a string and cannot be used as '
'a prefix and will be ignored for now. Correct that!'.format(
prefix, type(prefix)))
model = Model(amplitude_function, independent_vars='x')
else:
model = Model(amplitude_function, independent_vars='x', prefix=prefix)
params = model.make_params()
return model, params
def make_amplitude_model(self, prefix=None):
""" Create a constant model.
@param str prefix: optional string, which serves as a prefix for all
parameters used in this model. That will prevent
name collisions if this model is used in a composite
way.
@return tuple: (object model, object params), for more description see in
the method make_constant_model.
"""
def amplitude_function(x, amplitude):
""" Function of a constant value.
@param numpy.array x: 1D array as the independent variable - e.g. time
@param float amplitude: constant offset
@return: constant function, in order to use it as a model
"""
return amplitude
if not isinstance(prefix, str) and prefix is not None:
self.log.error('The passed prefix <{0}> of type {1} is not a string and cannot be used as '
'a prefix and will be ignored for now. Correct that!'.format(prefix,
type(prefix)))
model = Model(amplitude_function, independent_vars='x')
else:
model = Model(amplitude_function, independent_vars='x', prefix=prefix)
params = model.make_params()
return model, params
def make_gaussianwithoutoffset_model(self, prefix=None):
""" Create a model of a gaussian with specified amplitude.
@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.
For further information have a look in:
http://cars9.uchicago.edu/software/python/lmfit/builtin_models.html
"""
def physical_gauss(x, center, sigma):
""" Function of a bare Gaussian with unit height at center.
@param numpy.array x: independent variable - e.g. frequency
@param float center: center around which the distributions (expectation
value).
@param float sigma: standard deviation of the gaussian
@return: numpy.array with length equals to input x and with the values
of a bare Gaussian.
"""
return np.exp(-np.power((center - x), 2) / (2 * np.power(sigma, 2)))
amplitude_model, params = self.make_amplitude_model(prefix=prefix)
if not isinstance(prefix, str) and prefix is not None:
self.log.error(
'The passed prefix <{0}> of type {1} is not a string and'
'cannot be used as a prefix and will be ignored for now.'
'Correct that!'.format(prefix, type(prefix)))
gaussian_model = Model(physical_gauss, independent_vars='x')
else:
gaussian_model = Model(physical_gauss,
independent_vars='x',
prefix=prefix)
full_gaussian_model = amplitude_model * gaussian_model
if prefix is None:
prefix = ''
full_gaussian_model.set_param_hint(
'{0!s}fwhm'.format(prefix),
expr="2.3548200450309493*{0}sigma".format(prefix))
params = full_gaussian_model.make_params()
return full_gaussian_model, params
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 _fit_echo(self):
fit_start, fit_end = self._get_region()
df = self.data_in_range[(self.data_in_range.index > fit_start)
& (self.data_in_range.index < fit_end)]
# Fit arrays
fit_variable = self._graph_select.currentText() + '_mean'
x = np.array(df.index.get_values())
if self._fit_res_checkbox.isChecked():
y = df['peak_fit_res'] + self.c.best_val
else:
y = df[fit_variable]
params = Parameters()
params.add_many(
('y0', self.y0.param.value, self.y0.param.vary, self.y0.param.min,
self.y0.param.max),
('A', self.A.param.value, self.A.param.vary, self.A.param.min,
self.center.param.max),
('t2', self.t2.param.value, self.t2.param.vary, self.t2.param.min,
self.t2.param.max),
)
model = Model(echo_decay_curve, independent_vars=['x'])
result = model.fit(y, x=x, params=params)
all_time = np.linspace(0.1,
self.data_in_range.index.get_values().max(),
2000)
# plot data
self.echo_fit_line.set_data(x, echo_decay_curve(x=x, **result.values))
self.echo_fit_extended_line.set_data(
all_time, echo_decay_curve(x=all_time, **result.values))
# Подсчитываем данные
t2 = result.values['t2']
t2_stderr = result.params.get('t2').stderr
# Ширина линии в MHz
delta_f = 10**6 / (np.pi * result.values['t2'])
delta_f_stderr = delta_f * t2_stderr / t2
self._ax.set_title(
"$T_2$: {:0.2f} $\pm$ {:0.2f} $ps$ ({:0.2f} $\pm$ {:0.2f} $MHz$ )".
format(t2, t2_stderr, delta_f, delta_f_stderr))
# refresh canvas and rescale
self._ax.relim()
self._ax.autoscale_view()
# update plot
self._fitting_figure.canvas.draw()
self._fitting_figure.canvas.flush_events()
# Populating report
self.fit_report_text.append(result.fit_report())
# Populating spinboxes
self.y0.from_res(result)
self.A.from_res(result)
self.t2.from_res(result)
def poly_lorentzian(number_unique_lorentzians=None):
model = Model(lorentzian, independent_vars=['x'], prefix='lorentzian1_')
model += LinearModel(independent_vars=['x'], prefix='linear1_')
if number_unique_lorentzians is None:
raise UserWarning('number_unique_lorentzians need to be given')
for i in range(2, number_unique_lorentzians + 1):
model += Model(lorentzian,
independent_vars=['x'],
prefix='lorentzian{}_'.format(i))
return model
def make_poissonian_model(self, prefix=None):
""" Create a model of a single poissonian with an offset.
param str prefix: optional string, which serves as a prefix for all
parameters used in this model. That will prevent
name collisions if this model is used in a composite
way.
@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.
"""
def poisson_function(x, mu):
""" Function of a poisson distribution.
@param numpy.array x: 1D array as the independent variable - e.g. occurences
@param float mu: expectation value
@return: poisson function: in order to use it as a model
"""
return self.poisson(x, mu)
amplitude_model, params = self.make_amplitude_model(prefix=prefix)
if not isinstance(prefix, str) and prefix is not None:
self.log.error(
'The passed prefix <{0}> of type {1} is not a string and'
'cannot be used as a prefix and will be ignored for now.'
'Correct that!'.format(prefix, type(prefix)))
poissonian_model = Model(poisson_function, independent_vars='x')
else:
poissonian_model = Model(poisson_function,
independent_vars='x',
prefix=prefix)
poissonian_ampl_model = amplitude_model * poissonian_model
params = poissonian_ampl_model.make_params()
return poissonian_ampl_model, params
def make_barestretchedexponentialdecay_model(self, prefix=None):
""" Create a general bare exponential decay model.
@param str prefix: optional string, which serves as a prefix for all
parameters used in this model. That will prevent
name collisions if this model is used in a composite
way.
@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.
"""
def barestretchedexponentialdecay_function(x, beta, lifetime):
""" Function of a bare exponential decay.
@param numpy.array x: 1D array as the independent variable - e.g. time
@param float lifetime: constant lifetime
@return: bare exponential decay function: in order to use it as a model
"""
return np.exp(-np.power(x / lifetime, beta))
if not isinstance(prefix, str) and prefix is not None:
self.log.error(
'The passed prefix <{0}> of type {1} is not a string and'
'cannot be used as a prefix and will be ignored for now.'
'Correct that!'.format(prefix, type(prefix)))
model = Model(barestretchedexponentialdecay_function,
independent_vars='x')
else:
model = Model(barestretchedexponentialdecay_function,
independent_vars='x',
prefix=prefix)
params = model.make_params()
return model, params
def make_hyperbolicsaturation_model(self, prefix=None):
""" Create a model of the fluorescence depending on excitation power with
linear 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.
"""
def hyperbolicsaturation_function(x, I_sat, P_sat):
""" Fluorescence depending excitation power function
@param numpy.array x: 1D array as the independent variable e.g. power
@param float I_sat: Saturation Intensity
@param float P_sat: Saturation power
@return: hyperbolicsaturation function: for using it as a model
"""
return I_sat * (x / (x + P_sat))
if not isinstance(prefix, str) and prefix is not None:
self.log.error(
'The passed prefix <{0}> of type {1} is not a string and'
'cannot be used as a prefix and will be ignored for now.'
'Correct that!'.format(prefix, type(prefix)))
mod_sat = Model(hyperbolicsaturation_function, independent_vars='x')
else:
mod_sat = Model(hyperbolicsaturation_function,
independent_vars='x',
prefix=prefix)
linear_model, params = self.make_linear_model(prefix=prefix)
complete_model = mod_sat + linear_model
params = complete_model.make_params()
return complete_model, params
def fitgaussian_lmfit(x,
y,
weights,
return_fit=True,
return_uncertainties=False):
try:
# noinspection PyUnresolvedReferences
from lmfit.models import Model, GaussianModel
except ImportError:
print(' Need module lmfit to use fitgauss_lmfit')
# calculate guess
mod = GaussianModel()
params = mod.guess(y, x=x)
guess = np.array([
params['height'].value, params['center'].value, params['sigma'].value,
0.0
])
# set up model fit
gmodel = Model(gauss_function)
# run model fit
out = gmodel.fit(y,
x=x,
a=guess[0],
x0=guess[1],
sigma=guess[2],
dc=guess[3],
params=None,
weights=weights)
# extract out parameters
pfit = [
out.values['a'], out.values['x0'], out.values['sigma'],
out.values['dc']
]
# extract out standard errors
siga = [
out.params['a'].stderr, out.params['x0'].stderr,
out.params['sigma'].stderr, out.params['dc'].stderr
]
# return
if return_fit and return_uncertainties:
return np.array(pfit), np.array(siga), out.best_fit
elif return_uncertainties:
return np.array(pfit), np.array(siga)
elif return_fit:
return np.array(pfit), out.best_fit
else:
return np.array(pfit)
def make_barestretchedexponentialdecay_model(self, prefix=None):
""" Create a general bare exponential decay model.
@param str prefix: optional string, which serves as a prefix for all
parameters used in this model. That will prevent
name collisions if this model is used in a composite
way.
@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.
"""
def barestretchedexponentialdecay_function(x, beta, lifetime):
""" Function of a bare exponential decay.
@param numpy.array x: 1D array as the independent variable - e.g. time
@param float lifetime: constant lifetime
@return: bare exponential decay function: in order to use it as a model
"""
return np.exp(-np.power(x/lifetime, beta))
if not isinstance(prefix, str) and prefix is not None:
self.log.error('The passed prefix <{0}> of type {1} is not a string and'
'cannot be used as a prefix and will be ignored for now.'
'Correct that!'.format(prefix, type(prefix)))
model = Model(barestretchedexponentialdecay_function,
independent_vars='x')
else:
model = Model(barestretchedexponentialdecay_function,
independent_vars='x', prefix=prefix)
params = model.make_params()
return model, params
def make_constant_model(self, prefix=None):
""" Create constant model.
@param str prefix: optional string, which serves as a prefix for all
parameters used in this model. That will prevent
name collisions if this model is used in a composite
way.
@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. 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.
For further information have a look in:
http://cars9.uchicago.edu/software/python/lmfit/builtin_models.html#models.GaussianModel
"""
def constant_function(x, offset):
""" Function of a constant value.
@param numpy.array x: 1D array as the independent variable - e.g. time
@param float offset: constant offset
@return: constant function, in order to use it as a model
"""
return offset
if not isinstance(prefix, str) and prefix is not None:
self.log.error(
'The passed prefix <{0}> of type {1} is not a string and cannot be used as '
'a prefix and will be ignored for now. Correct that!'.format(
prefix, type(prefix)))
model = Model(constant_function, independent_vars='x')
else:
model = Model(constant_function, independent_vars='x', prefix=prefix)
params = model.make_params()
return model, params
def make_constant_model(self, prefix=None):
""" Create constant model.
@param str prefix: optional string, which serves as a prefix for all
parameters used in this model. That will prevent
name collisions if this model is used in a composite
way.
@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. 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.
For further information have a look in:
http://cars9.uchicago.edu/software/python/lmfit/builtin_models.html#models.GaussianModel
"""
def constant_function(x, offset):
""" Function of a constant value.
@param numpy.array x: 1D array as the independent variable - e.g. time
@param float offset: constant offset
@return: constant function, in order to use it as a model
"""
return offset
if not isinstance(prefix, str) and prefix is not None:
self.log.error('The passed prefix <{0}> of type {1} is not a string and cannot be used as '
'a prefix and will be ignored for now. Correct that!'.format(prefix,
type(prefix)))
model = Model(constant_function, independent_vars='x')
else:
model = Model(constant_function, independent_vars='x', prefix=prefix)
params = model.make_params()
return model, params
def _calc_fit_start_dep_curve(self):
t2_array = []
t2_var_array = []
x_array = []
# Fit value
fit_variable_name = self._graph_select.currentText()
for start_fit_from in self.means[DELAY_TITLE]:
start_fit_from = float(start_fit_from)
fit_means = self.means[start_fit_from < self.means[DELAY_TITLE]]
fit_std = self.std[start_fit_from < self.std[DELAY_TITLE]]
params = self._init_params()
model = Model(echo_decay_curve, independent_vars=['x'])
try:
result = model.fit(fit_means[fit_variable_name],
x=fit_means[DELAY_TITLE],
params=params,
weights=1 / fit_std[LASER_TITLE]**2)
t2_array.append(result.params.get('t2').value)
t2_var_array.append(result.params.get('t2').stderr)
x_array.append(start_fit_from)
except TypeError:
break
ax = self._fitting_stats_figure.add_subplot(111)
ax.errorbar(x_array,
t2_array,
yerr=t2_var_array,
fmt='--bo',
capthick=2,
ecolor='b',
alpha=0.9)
ax.set_xlim([-10, 100])
ax.set_ylim([0, 2000])
ax.set_title("Зависимость $T_2$ от точки старта фитирования")
# refresh canvas and tight layout
self._fitting_stats_canvas.draw()
self._fitting_stats_figure.tight_layout()
self._fit_stats = True
# Adding to fit report
self.fit_report_text.append(
"Зависимость t2 от точки старта фитирования:\n")
self.fit_report_text.append(" ".join(
"{:.4f}: {:.2f}".format(x, y) for x, y in zip(x_array, t2_array)))
self.fit_report_text.append("\n")
def _make_model(fct, number_unique_lorentzians=None):
if not fct == poly_gaussian and not fct == double_gaussian and not fct == poly_lorentzian:
return Model(fct, independent_vars=['x'])
elif not fct == poly_lorentzian:
return fct()
else:
return poly_lorentzian(
number_unique_lorentzians=number_unique_lorentzians)
def fit_signal(signal,l):
x1=np.linspace(0,1,len(signal))
piecewiseModel=Model(piecewise_prob)
piecewiseModel.set_param_hint('l', value=1,vary=False)
piecewiseModel.set_param_hint('C', vary=True, value=.1,min=0,max=1)
piecewiseModel.make_params()
res=piecewiseModel.fit(signal,x=x1,weights=np.sin(1.5*x1)+1.5)
return res
def fit_residuals(df, start_fit_from=0.4, fit_field='fit_lorenz_res', init_params=None):
"""
Fits residuals with EchoDecay curve
"""
x = np.array(df[df.index > start_fit_from].index.get_values())
y = np.array(df[df.index > start_fit_from][fit_field].values)
echo_model = Model(echo_decay_curve, independent_vars=['x'])
if init_params:
params = init_params
else:
params = _init_echo_params(0, 500, 50)
result = echo_model.fit(y, x=x, params=params)
full_x = np.array(df.index.get_values())
res_fit_eval = result.eval(x=full_x)
df['res_echo_fit'] = pd.Series(res_fit_eval, index=df.index)
return df, result
def make_baresine_model(self, prefix=None):
""" This method creates a model of bare sine without amplitude and
offset.
@param string prefix: variable prefix
@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.
For further information have a look in:
http://cars9.uchicago.edu/software/python/lmfit/builtin_models.html#models.GaussianModel
"""
def sine_function(x, frequency, phase):
"""
Function of a sine.
@param x: variable variable - e.g. time
@param frequency: frequency
@param phase: phase
@return: sine function: in order to use it as a model
"""
return np.sin(2 * np.pi * frequency * x + phase)
if prefix is not None:
model = Model(sine_function, prefix=prefix)
else:
model = Model(sine_function)
params = model.make_params()
return model, params
def make_linear_model(self, prefix=None):
""" Create linear model.
@param str prefix: optional string, which serves as a prefix for all
parameters used in this model. That will prevent
name collisions if this model is used in a composite
way.
@return tuple: (object model, object params), for more description see in
the method make_constant_model.
"""
def linear_function(x):
""" Function of a linear model.
@param numpy.array x: 1D array as the independent variable - e.g. time
@return: linear function, in order to use it as a model
"""
return x
if not isinstance(prefix, str) and prefix is not None:
self.log.error(
'The passed prefix <{0}> of type {1} is not a string and cannot be used as '
'a prefix and will be ignored for now. Correct that!'.format(
prefix, type(prefix)))
linear_mod = Model(linear_function, independent_vars='x')
else:
linear_mod = Model(linear_function,
independent_vars='x',
prefix=prefix)
slope, slope_param = self.make_slope_model(prefix=prefix)
constant, constant_param = self.make_constant_model(prefix=prefix)
model = slope * linear_mod + constant
params = model.make_params()
return model, params
def make_poissonian_model(self, no_of_functions=None):
""" This method creates a model of a poissonian with an offset.
@param no_of_functions: if None or 1 there is one poissonian, else
more functions are added
@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:
'mu' : expected value mu
"""
def poisson_function(x, mu):
"""
Function of a poisson distribution.
@param x: occurences
@param mu: expected value
@return: poisson function: in order to use it as a model
"""
return self.poisson(x, mu)
def amplitude_function(x, amplitude):
"""
Function of a amplitude value.
@param x: variable variable
@param offset: independent variable - amplitude
@return: amplitude function: in order to use it as a model
"""
return amplitude + 0.0 * x
if no_of_functions is None or no_of_functions == 1:
model = (Model(poisson_function, prefix='poissonian_') *
Model(amplitude_function, prefix='poissonian_'))
else:
model = (
Model(poisson_function, prefix='poissonian{0}_'.format('0')) *
Model(amplitude_function, prefix='poissonian{0}_'.format('0')))
for ii in range(no_of_functions - 1):
model += (Model(poisson_function,
prefix='poissonian{0}_'.format(ii + 1)) *
Model(amplitude_function,
prefix='poissonian{0}_'.format(ii + 1)))
params = model.make_params()
return model, params
def make_amplitude_model(self, prefix=None):
""" This method creates a model of a constant model.
@param string prefix: variable prefix
@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. 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.
For further information have a look in:
http://cars9.uchicago.edu/software/python/lmfit/builtin_models.html#models.GaussianModel
"""
def amplitude_function(x, amplitude):
"""
Function of a constant value.
@param x: variable variable
@param amplitude: independent variable - e.g. amplitude
@return: constant function: in order to use it as a model
"""
return amplitude + 0.0 * x
if prefix is None:
model = Model(amplitude_function)
else:
if not isinstance(prefix, str):
logger.error('Given prefix in constant model is no string. '
'Deleting prefix.')
try:
model = Model(amplitude_function, prefix=prefix)
except:
logger.error('Creating the constant model failed. '
'The prefix might not be a valid string. '
'The prefix was deleted.')
model = Model(amplitude_function)
params = model.make_params()
return model, params
def make_powerfluorescence_model(self):
""" This method creates a model of the fluorescence depending on excitation power with an linear 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.
For further information have a look in:
http://cars9.uchicago.edu/software/python/lmfit/builtin_models.html#models.GaussianModel
"""
def powerfluorescence_function(x, I_saturation, P_saturation):
"""
Function to describe the fluorescence depending on excitation power
@param x: variable variable - Excitation pwer
@param I_saturation: Saturation Intensity
@param P_saturation: Saturation power
@return: powerfluorescence function: for using it as a model
"""
return I_saturation * (x / (x + P_saturation))
mod_sat = Model(powerfluorescence_function)
model = mod_sat + LinearModel()
params = model.make_params()
return model, params
def make_stretchedexponentialdecay_model(self):
"""
This method creates a model of stretched exponential decay.
@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.
"""
def stretched_exponentialdecay_function(x, lifetime, beta):
"""
Function of a stretched exponential decay.
@param x: variable variable - e.g. time
@param amplitude: amplitude
@param beta: stretch exponent
@param offset: offset
@return: streched exponential decay function:
in order to use it as a model
"""
return np.exp(-np.power(x / lifetime, beta))
constant_model, params = self.make_constant_model()
amplitude_model, params = self.make_amplitude_model()
model = amplitude_model * Model(
stretched_exponentialdecay_function) + constant_model
params = model.make_params()
return model, params
def UserDefinedFunctionFit(self):
userDefinedFunctionList = [s for s in dir(UserDefinedFunction) if s[0].isupper()]
d = QtGui.QInputDialog()
func_name, ok = d.getItem(
self, 'User Defined Function', 'Choose a function',
userDefinedFunctionList)
if ok:
try:
fun = getattr(UserDefinedFunction, str(func_name))
# print fun
except AttributeError:
QtGui.QMessageBox.warning(
self, 'Warning',
'No such a function,\nplease check the name.')
return
else:
return
fun_model = Model(fun)
self.Fitting(False, fun_model)
y1=smooth_signal(y1,10**3)
y1=np.real(sharpen_filter(y1))
plt.clf()
plt.plot(y1,'b')
plt.savefig("".join([sys.argv[1],"blak"])+".png")
print(sys.argv[1]+": Coverage OK ("+str(coveragePercentage)+" x).")
x1=np.linspace(0,genomeLen-1,len(y1))
### Korem fit
# fit piecewise using least squares (LM)
piecewiseModel=Model(piecewiseLinear)
piecewiseModel.set_param_hint('Ol', value=0.5*genomeLen,vary=True,min=0,max=genomeLen)
#piecewiseModel.set_param_hint('Tl', value=0.6*genomeLen,vary=True,min=0,max=genomeLen)
piecewiseModel.set_param_hint('Tc', value = np.median(np.log2(y1)), vary=True)
piecewiseModel.set_param_hint('Oc', value = np.median(np.log2(y1)), vary=True)
piecewiseModel.set_param_hint('delta', value = 0.545*genomeLen, min=0.45*genomeLen, max=0.55*genomeLen, vary=True)#,expr='Tl-Ol if Tl-Ol > 0 else Ol-Tl')
#piecewiseModel.set_param_hint('Tl', value=0.6*genomeLen,vary=True,min=0,max=genomeLen,expr='mod(Ol+delta,genLen)')
piecewiseModel.set_param_hint('genLen', vary=False, value=genomeLen)
piecewiseModel.make_params()
result=piecewiseModel.fit(np.log2(y1),x=x1)
resR2=R2(result.best_fit,y1)
# var=np.var(abs(np.log2(y1)-result.best_fit), dtype=np.float64)
#med=np.median(np.log2(y1))
def make_twoDgaussian_model(self, prefix=None):
""" Creates a model of the 2D gaussian function.
@param str prefix: optional, if multiple models should be used in a
composite way and the parameters of each model should be
distinguished from each other to prevent name collisions.
@return tuple: (object model, object params), for more description see in
the method make_gaussianwithoutoffset_model.
"""
def twoDgaussian_function(x, amplitude, center_x, center_y, sigma_x, sigma_y,
theta, offset):
""" Provide a two dimensional gaussian function.
@param float amplitude: Amplitude of gaussian
@param float center_x: x value of maximum
@param float center_y: y value of maximum
@param float sigma_x: standard deviation in x direction
@param float sigma_y: standard deviation in y direction
@param float theta: angle for eliptical gaussians
@param float offset: offset
@return callable function: returns the reference to the function
Function taken from:
http://stackoverflow.com/questions/21566379/fitting-a-2d-gaussian-function-using-scipy-optimize-curve-fit-valueerror-and-m/21566831
Question from: http://stackoverflow.com/users/2097737/bland
http://stackoverflow.com/users/3273102/kokomoking
http://stackoverflow.com/users/2767207/jojodmo
Answer: http://stackoverflow.com/users/1461210/ali-m
http://stackoverflow.com/users/5234/mrjrdnthms
"""
# FIXME: x_data_tuple: dimension of arrays
# @param np.arra[k][M] x_data_tuple: array which is (k,M)-shaped,
# x and y values
(u, v) = x
center_x = float(center_x)
center_y = float(center_y)
a = (np.cos(theta) ** 2) / (2 * sigma_x ** 2) \
+ (np.sin(theta) ** 2) / (2 * sigma_y ** 2)
b = -(np.sin(2 * theta)) / (4 * sigma_x ** 2) \
+ (np.sin(2 * theta)) / (4 * sigma_y ** 2)
c = (np.sin(theta) ** 2) / (2 * sigma_x ** 2) \
+ (np.cos(theta) ** 2) / (2 * sigma_y ** 2)
g = offset + amplitude * np.exp(- (a * ((u - center_x) ** 2)
+ 2 * b * (u - center_x) * (v - center_y)
+ c * ((v - center_y) ** 2)))
return g.ravel()
if not isinstance(prefix, str) and prefix is not None:
self.log.error('The passed prefix <{0}> of type {1} is not a string and'
'cannot be used as a prefix and will be ignored for now.'
'Correct that!'.format(prefix, type(prefix)))
gaussian_2d_model = Model(twoDgaussian_function, independent_vars='x')
else:
gaussian_2d_model = Model(twoDgaussian_function, independent_vars='x',
prefix=prefix)
params = gaussian_2d_model.make_params()
return gaussian_2d_model, params
# ----------------------- Observed frame
flux_voxel_norm = flux_voxel / norm_flux
err_voxel_norm = flux_err / norm_flux
obsLineWaves = wave_regions * (1 + z_objs[i])
idcsEmis, idcsCont = obsLm.define_masks(wave, flux_voxel_norm,
obsLineWaves)
emisWave, emisFlux = wave[idcsEmis], flux_voxel_norm[idcsEmis]
contWave, contFlux = wave[idcsCont], flux_voxel_norm[idcsCont]
obsLm.line_properties(emisWave,
emisFlux,
contWave,
contFlux,
bootstrap_size=5000)
fit_model = Model(linear_model, prefix=f'{lineLabel}_cont_')
fit_model.set_param_hint(f'{lineLabel}_cont_slope', **{
'value': obsLm.m_cont,
'vary': False
})
fit_model.set_param_hint(f'{lineLabel}_cont_intercept', **{
'value': obsLm.n_cont,
'vary': False
})
fit_model += Model(gaussian_model, prefix=f'{lineLabel}_')
fit_model.set_param_hint(f'{lineLabel}_amplitude',
value=obsLm.peak_flux - obsLm.cont)
fit_model.set_param_hint(f'{lineLabel}_center', value=obsLm.peak_wave)
fit_model.set_param_hint(f'{lineLabel}_sigma', value=1.0)
def lmfit_gaussian(x_array, y_array, err_array, x_boundarys):
# Find indeces for six points in spectrum
idcsW = np.searchsorted(x_array, x_boundarys)
# Emission region
idcsEmis = (x_array[idcsW[2]] <= x_array) & (x_array <= x_array[idcsW[3]])
# Return left and right continua merged in one array
idcsCont = (((x_array[idcsW[0]] <= x_array) &
(x_array <= x_array[idcsW[1]])) |
((x_array[idcsW[4]] <= x_array) &
(x_array <= x_array[idcsW[5]]))).squeeze()
emisWave, emisFlux = x_array[idcsEmis], y_array[idcsEmis]
contWave, contFlux = x_array[idcsCont], y_array[idcsCont]
idx_peak = np.argmax(emisFlux)
fit_model = Model(linear_model, prefix=f'{lineLabel}_cont_')
fit_model.set_param_hint(f'{lineLabel}_cont_slope', **{
'value': 0,
'vary': False
})
fit_model.set_param_hint(f'{lineLabel}_cont_intercept', **{
'value': contFlux.mean(),
'vary': False
})
fit_model += Model(gaussian_model, prefix=f'{lineLabel}_')
fit_model.set_param_hint(f'{lineLabel}_amp',
value=emisFlux[idx_peak] - contFlux.mean())
fit_model.set_param_hint(f'{lineLabel}_center', value=emisWave[idx_peak])
fit_model.set_param_hint(f'{lineLabel}_sigma', value=1.0)
x_fit = x_array[idcsEmis + idcsCont]
y_fit = y_array[idcsEmis + idcsCont]
w_fit = 1.0 / err_array[idcsEmis + idcsCont]
fit_params = fit_model.make_params()
obs_fit_output = fit_model.fit(y_fit, fit_params, x=x_fit, weights=w_fit)
# amp = obs_fit_output.params[f"{lineLabel}_amp"].value
mu = obs_fit_output.params[f"{lineLabel}_center"].value
sigma = obs_fit_output.params[f"{lineLabel}_sigma"].value
mu_err = obs_fit_output.params[f"{lineLabel}_center"].stderr
sigma_err = obs_fit_output.params[f"{lineLabel}_sigma"].stderr
x_obs, y_obs = obs_fit_output.userkws['x'], obs_fit_output.data
wave_obs = np.linspace(x_obs[0], x_obs[-1], 500)
flux_comps_obs = obs_fit_output.eval_components(x=wave_obs)
flux_obs = flux_comps_obs.get(f'{lineLabel}_cont_',
0.0) + flux_comps_obs[f'{lineLabel}_']
return x_fit, y_fit, wave_obs, flux_obs, mu, sigma, mu_err, sigma_err
def make_lorentzianwithoutoffset_model(self, prefix=None):
""" Create a model of a bare physical Lorentzian with an amplitude.
@param str prefix: optional, if multiple models should be used in a
composite way and the parameters of each model should be
distinguished from each other to prevent name collisions.
@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.
For further information have a look in:
http://cars9.uchicago.edu/software/python/lmfit/builtin_models.html#models.LorentzianModel
"""
def physical_lorentzian(x, center, sigma):
""" Function of a Lorentzian with unit height at center.
@param numpy.array x: independent variable - e.g. frequency
@param float center: center around which the distributions will be
@param float sigma: half length at half maximum
@return: numpy.array with length equals to input x and with the values
of a lorentzian.
"""
return np.power(sigma, 2) / (np.power(
(center - x), 2) + np.power(sigma, 2))
amplitude_model, params = self.make_amplitude_model(prefix=prefix)
if not isinstance(prefix, str) and prefix is not None:
self.log.error(
'The passed prefix <{0}> of type {1} is not a string and'
'cannot be used as a prefix and will be ignored for now.'
'Correct that!'.format(prefix, type(prefix)))
lorentz_model = Model(physical_lorentzian, independent_vars='x')
else:
lorentz_model = Model(physical_lorentzian,
independent_vars='x',
prefix=prefix)
full_lorentz_model = amplitude_model * lorentz_model
params = full_lorentz_model.make_params()
# introduces a new parameter, which is solely depending on others and which
# will be not optimized:
if prefix is None:
prefix = ''
full_lorentz_model.set_param_hint('{0!s}fwhm'.format(prefix),
expr="2*{0!s}sigma".format(prefix))
# full_lorentz_model.set_param_hint('{0}contrast'.format(prefix),
# expr='(-100.0)')
# expr='({0!s}amplitude/offset)*100'.format(prefix))
# params.add('{0}contrast'.format(prefix), expr='({0!s}amplitude/offset)*100'.format(prefix))
return full_lorentz_model, params
def make_twoDgaussian_model(self, prefix=None):
""" Creates a model of the 2D gaussian function.
@param str prefix: optional, if multiple models should be used in a
composite way and the parameters of each model should be
distinguished from each other to prevent name collisions.
@return tuple: (object model, object params), for more description see in
the method make_gaussianwithoutoffset_model.
"""
def twoDgaussian_function(x, amplitude, center_x, center_y, sigma_x,
sigma_y, theta, offset):
""" Provide a two dimensional gaussian function.
@param float amplitude: Amplitude of gaussian
@param float center_x: x value of maximum
@param float center_y: y value of maximum
@param float sigma_x: standard deviation in x direction
@param float sigma_y: standard deviation in y direction
@param float theta: angle for eliptical gaussians
@param float offset: offset
@return callable function: returns the reference to the function
Function taken from:
http://stackoverflow.com/questions/21566379/fitting-a-2d-gaussian-function-using-scipy-optimize-curve-fit-valueerror-and-m/21566831
Question from: http://stackoverflow.com/users/2097737/bland
http://stackoverflow.com/users/3273102/kokomoking
http://stackoverflow.com/users/2767207/jojodmo
Answer: http://stackoverflow.com/users/1461210/ali-m
http://stackoverflow.com/users/5234/mrjrdnthms
"""
# FIXME: x_data_tuple: dimension of arrays
# @param np.arra[k][M] x_data_tuple: array which is (k,M)-shaped,
# x and y values
(u, v) = x
center_x = float(center_x)
center_y = float(center_y)
a = (np.cos(theta) ** 2) / (2 * sigma_x ** 2) \
+ (np.sin(theta) ** 2) / (2 * sigma_y ** 2)
b = -(np.sin(2 * theta)) / (4 * sigma_x ** 2) \
+ (np.sin(2 * theta)) / (4 * sigma_y ** 2)
c = (np.sin(theta) ** 2) / (2 * sigma_x ** 2) \
+ (np.cos(theta) ** 2) / (2 * sigma_y ** 2)
g = offset + amplitude * np.exp(-(a * ((u - center_x)**2) + 2 * b *
(u - center_x) * (v - center_y) + c *
((v - center_y)**2)))
return g.ravel()
if not isinstance(prefix, str) and prefix is not None:
self.log.error(
'The passed prefix <{0}> of type {1} is not a string and'
'cannot be used as a prefix and will be ignored for now.'
'Correct that!'.format(prefix, type(prefix)))
gaussian_2d_model = Model(twoDgaussian_function, independent_vars='x')
else:
gaussian_2d_model = Model(twoDgaussian_function,
independent_vars='x',
prefix=prefix)
params = gaussian_2d_model.make_params()
return gaussian_2d_model, params
def double_gaussian():
gauss1 = Model(gaussian, independent_vars=['x'], prefix='gauss1_')
gauss2 = Model(gaussian, independent_vars=['x'], prefix='gauss2_')
linear1 = LinearModel(independent_vars=['x'], prefix='linear1_')
model = gauss1 + linear1 + gauss2
return model
