def fit_gaussian_peak_step_background_2(x, y):
# create data from broadened step
npts = 201
x = np.linspace(0, 10, npts)
y = step(x, amplitude=12.5, center=4.5, sigma=0.88, form='erf')
y = y + np.random.normal(size=npts, scale=0.35)
# create Composite Model using the custom convolution operator
mod = CompositeModel(Model(jump), Model(gaussian), convolve)
pars = mod.make_params(amplitude=1, center=3.5, sigma=1.5, mid=5.0)
# 'mid' and 'center' should be completely correlated, and 'mid' is
# used as an integer index, so a very poor fit variable:
pars['mid'].vary = False
# fit this model to data array y
result = mod.fit(y, params=pars, x=x)
print(result.fit_report())
plot_components = True
# plot results
plt.plot(x, y, 'bo')
if plot_components:
# generate components
comps = result.eval_components(x=x)
plt.plot(x, 10 * comps['jump'], 'k--')
plt.plot(x, 10 * comps['gaussian'], 'r-')
else:
plt.plot(x, result.init_fit, 'k--')
plt.plot(x, result.best_fit, 'r-')
plt.show()
# #<end examples/model_doc3.py>
return fit_fwhm, fit_center, fwhm_err
def fit_composit(seq, *params, report=False):
x = np.arange(len(seq))
y = seq
amp, cen, wid = params
cmodel = CompositeModel(Model(gaussian), Model(LognormalModel),
ExponentialGaussianModel)
pars = cmodel.make_params(amplitude=amp, center=cen, sigma=wid, mid=cen)
# 'mid' and 'center' should be completely correlated, and 'mid' is
# used as an integer index, so a very poor fit variable:
pars['mid'].vary = False
# fit this model to data array y
result = cmodel.fit(y, params=pars, x=x)
# limit the amplitude to be in 0-256
cmodel.set_param_hint('amp', min=0)
cmodel.set_param_hint('amp', max=256)
result = gmodel.fit(y, x=x, amp=amp, cen=cen, wid=wid)
if result.redchi >= 1e3:
# if report:
plt.figure()
plt.plot(x, y, 'bo')
# plt.plot(x, result.init_fit, 'k--')
plt.plot(x, np.ceil(result.best_fit), 'r-')
plt.title('chi2: {0:.2e} - red_chi2: {0:.2e}'.format(
result.chisqr, result.redchi))
plt.show()
return result
def get_equivalent_circuit_model(modelname, logscale=False, diel=False):
"""Get LMFIT CompositeModel.
Parameters
----------
modelname: str
String representation of the equivalent circuit.
logscale: bool
Convert to logscale.
diel: bool
Convert to complex permittivity and fit this instead of impedance.
Returns
-------
:py:class:`lmfit.model.CompositeModel` or :class:`lmfit.model.Model`
the final model of the entire circuit
Notes
-----
The parser is based on Pyparsing.
It is sensitive towards extra `(` or `)` or `+`.
Thus, keep the circuit simple.
"""
circuit = []
assert isinstance(modelname, str), "Pass the model as a string"
str2parse = modelname.replace("parallel", "")
circuit_elements = pp.Word(pp.srange("[a-zA-Z_0-9]"))
plusop = pp.Literal('+')
commaop = pp.Literal(',')
expr = pp.infixNotation(circuit_elements, [(plusop, 2, pp.opAssoc.LEFT),
(commaop, 2, pp.opAssoc.LEFT)])
try:
circuitstr = expr.parseString(str2parse)
except pp.ParseException:
raise ("You must provide a correct string!")
_check_circuit(circuitstr.asList()[0],
startpar=modelname.startswith("parallel"))
circuit = _process_circuit(circuitstr.asList()[0])
if logscale:
circuit = CompositeModel(circuit, Model(dummy), log)
elif diel:
circuit = CompositeModel(circuit, Model(make_eps), eps)
if logscale and diel:
raise RuntimeError(
"You must chose the representation of the impedance value")
_check_models_suffix(circuit)
logger.debug("Created composite model {}".format(circuit))
return circuit
def __init__(self, q, nLor=2, **kwargs):
prefix = ""
if "prefix" in kwargs.keys():
prefix = kwargs.pop("prefix")
left = delta(q, prefix="%sdelta_" % prefix, **kwargs)
right = lorentzian(q, prefix="%sl0_" % prefix, **kwargs)
for i in range(1, nLor):
right = CompositeModel(
right,
lorentzian(q, prefix="%sl%i_" % (prefix, i), **kwargs),
operator.add,
)
super().__init__(left, right, operator.add)
def _process_parallel(model):
"""Process parallel circuit.
Parameters
----------
model: list
Contains the parallel circuit as a nested list.
Returns
-------
:py:class:`lmfit.model.CompositeModel`
The CompositeModel of the parallel circuit.
"""
assert len(model) == 3, "The model must be [model1, ',' , model2]"
first_model = model[0]
second_model = model[2]
first = _process_element(first_model)
second = _process_element(second_model)
return CompositeModel(first, second, parallel)
# code from https://lmfit.github.io/lmfit-py/model.html
def convolve(arr, kernel):
# simple convolution of two arrays
npts = min(len(arr), len(kernel))
pad = np.ones(npts)
tmp = np.concatenate((pad * arr[0], arr, pad * arr[-1]))
out = np.convolve(tmp, kernel, mode='valid')
noff = int((len(out) - npts) / 2)
return out[noff:noff + npts]
# Create model for the fit
gmodel = CompositeModel(Model(irf_gate), Model(model_2lorentzians), convolve)
print('Names of parameters:', gmodel.param_names)
print('Independent variable(s):', gmodel.independent_vars)
# Load reference data - extract x and y values
two_lorentzians_iris = np.loadtxt(path_to_data + 'data_2lorentzians.dat')
xx = two_lorentzians_iris[:, 0]
yy = two_lorentzians_iris[:, 1]
# Fit
result = gmodel.fit(yy,
x=xx,
scale1=1.,
center1=0.,
hwhm1=0.25,
o = np.zeros(len(x))
imid = max(np.where(x<=mid)[0])
o[imid:] = 1.0
return o
def convolve(arr, kernel):
# simple convolution of two arrays
npts = min(len(arr), len(kernel))
pad = np.ones(npts)
tmp = np.concatenate((pad*arr[0], arr, pad*arr[-1]))
out = np.convolve(tmp, kernel, mode='valid')
noff = int((len(out) - npts)/2)
return out[noff:noff+npts]
#
# create Composite Model using the custom convolution operator
mod = CompositeModel(Model(jump), Model(gaussian), convolve)
pars = mod.make_params(amplitude=1, center=3.5, sigma=1.5, mid=5.0)
# 'mid' and 'center' should be completely correlated, and 'mid' is
# used as an integer index, so a very poor fit variable:
pars['mid'].vary = False
# fit this model to data array y
result = mod.fit(y, params=pars, x=x)
print(result.fit_report())
plot_components = False
# plot results
# Create convolution function
# code from https://lmfit.github.io/lmfit-py/model.html
def convolve(arr, kernel):
# simple convolution of two arrays
npts = min(len(arr), len(kernel))
pad = np.ones(npts)
tmp = np.concatenate((pad * arr[0], arr, pad * arr[-1]))
out = np.convolve(tmp, kernel, mode='valid')
noff = int((len(out) - npts) / 2)
return out[noff:noff + npts]
model = CompositeModel(Model(irf_gate), Model(QENSmodels.sqwWaterTeixeira),
convolve)
print('Names of parameters:', model.param_names)
print('Independent variable(s):', model.independent_vars)
# Define boundaries for parameters to be refined
model.set_param_hint('scale', min=0, max=100)
model.set_param_hint('center', min=-0.1, max=0.1)
model.set_param_hint('D', min=0.05, max=0.25)
model.set_param_hint('resTime', min=0, max=1)
model.set_param_hint('radius', min=0.9, max=1.1)
model.set_param_hint('DR', min=0, max=1)
# Fix some of the parameters
model.set_param_hint('q', vary=False)
model.set_param_hint('spectrum_nb', vary=False)
def _convolve(
self, left, right, params=None, returnComponents=None, **kwargs
):
r"""Perform a convolution between `left` and `right`.
If the convolutions between function in `left` and the
function in `right` is defined in `convolutions` attribute,
then use this corresponding function for analytical
convolution.
Else, the behavior is determined by the `on_undefined_conv`
parameter.
Parameters
----------
left : :class:`Model` or :class:`CompositeModel`
Model or CompositeModel to be used for convolution.
right : :class:`Model` or :class:`CompositeModel`
Model or CompositeModel to be used for convolution.
params : Parameters, optional
Parameters to be given to the model functions.
kwargs : dict
Additional keyword arguments to pass to the model functions.
Returns
-------
An array containing the result of the convolution.
Notes
-----
This composition of models works differently than for other operators,
as the operators is applied between each pair of components in left
and right components.
That is, for ``left = a1 + a2 - a3`` and ``right = b1 * b2``, where
a's and b's are instances of :class:`Model` class:
.. math::
left \otimes right = (a_1 \otimes b_1 * a_1 \otimes b_2)
+ (a_2 \otimes b_1 * a_2 \otimes b_2)
- (a_3 \otimes b_1 * a_3 \otimes b_2)
"""
if returnComponents == "right":
tmp = left
left = right
right = tmp
lcomponents = left.components
rcomponents = right.components
lops, rops = self._operators()
models = []
compPrefix = []
for lcomp in lcomponents:
tmpRes = []
for rcomp in rcomponents:
if lcomp.func.__name__ in self.convMap.keys():
funcName = rcomp.func.__name__
leftConvMap = self.convMap[lcomp.func.__name__]
if funcName in leftConvMap.keys():
if params is None:
params = self.make_params()
convFunc = leftConvMap[funcName]
tmpRes.append(convFunc(lcomp, rcomp, params, **kwargs))
else:
if self._on_undefined_conv == "numeric":
convFunc = lambda l, r: fftconvolve(
l, r, mode="same", axes=-1
)
tmpRes.append(
CompositeModel(lcomp, rcomp, convFunc).eval(
params, **kwargs
)
)
elif self._on_undefined_conv == "raise":
raise KeyError(
"Convolution function between %s and %s is "
"not defined."
% (lcomp.func.__name__, funcName)
)
else:
if self._on_undefined_conv == "numeric":
convFunc = lambda l, r: fftconvolve(
l, r, mode="same", axes=-1
)
tmpRes.append(
CompositeModel(lcomp, rcomp, convFunc).eval(
params, **kwargs
)
)
# apply operators from the right
if len(tmpRes) > 1:
for idx, rop in enumerate(rops):
tmpRes[0] = rop(tmpRes[idx], tmpRes[idx + 1])
models.append(tmpRes[0])
compPrefix.append(lcomp.prefix)
if returnComponents is None:
# finally apply operators from the left
if len(models) > 1:
for idx, lop in enumerate(lops):
models[0] = lop(models[idx], models[idx + 1])
return models[0]
else:
out = OrderedDict()
for val in zip(compPrefix, models):
out[val[0]] = val[1]
return out
return o
def convolve(arr, kernel):
# simple convolution of two arrays
npts = min(len(arr), len(kernel))
pad = np.ones(npts)
tmp = np.concatenate((pad * arr[0], arr, pad * arr[-1]))
out = np.convolve(tmp, kernel, mode='valid')
noff = int((len(out) - npts) / 2)
return out[noff:noff + npts]
#
# create Composite Model using the custom convolution operator
mod = CompositeModel(Model(jump), Model(gaussian), convolve)
pars = mod.make_params(amplitude=1, center=3.5, sigma=1.5, mid=5.0)
# 'mid' and 'center' should be completely correlated, and 'mid' is
# used as an integer index, so a very poor fit variable:
pars['mid'].vary = False
# fit this model to data array y
result = mod.fit(y, params=pars, x=x)
print(result.fit_report())
plot_components = False
# plot results