Curve fitting ************* HyperSpy can perform curve fitting in n-dimensional data sets. It can create a model from a linear combinantion of predefined components and can use multiple optimisation algorithms to fit the model to experimental data. It supports bounds and weights. .. versionadded:: 0.7 Before creating a model verify that the ``Signal.binned`` metadata attribute of the signal is set to the correct value because the resulting model depends on this parameter. See :ref:`signal.binned` for more details. Creating a model ^^^^^^^^^^^^^^^^ A :py:class:`~.model.Model` can be created using the :py:meth:`~._signals.signal1d.Signal1D.create_model` method: .. code-block:: python >>> s = hs.load('YourDataFilenameHere') # Load the data from a file >>> m = s.create_model() # Create the model and asign it to the variable m At this point you may be prompted to provide any necessary information not already included in the datafile, e.g.if s is EELS data, you may be asked for the accelerating voltage, convergence and collection semi-angles etc. Adding components to the model ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In HyperSpy a model consists of a linear combination of :py:mod:`~.components`. These are some of the components which are currently available: * :py:class:`~._components.eels_cl_edge.EELSCLEdge` * :py:class:`~._components.volume_plasmon_drude.VolumePlasmonDrude` * :py:class:`~._components.power_law.PowerLaw` * :py:class:`~._components.offset.Offset` * :py:class:`~._components.exponential.Exponential` * :py:class:`~._components.scalable_fixed_pattern.ScalableFixedPattern` * :py:class:`~._components.gaussian.Gaussian` * :py:class:`~._components.lorentzian.Lorentzian` * :py:class:`~._components.voigt.Voigt` * :py:class:`~._components.polynomial.Polynomial` * :py:class:`~._components.logistic.Logistic` * :py:class:`~._components.bleasdale.Bleasdale` * :py:class:`~._components.error_function.Erf` * :py:class:`~._components.pes_see.SEE` * :py:class:`~._components.arctan.Arctan` * :py:class:`~._components.heaviside.HeavisideStep` However, this doesn't mean that you have to limit yourself to this meagre list of function. .. _expression_component-label: .. versionadded:: 0.8.1 :py:class:`~._components.expression.Expression` component The easiest way to turn a mathematical expression into a component is using the :py:class:`~._components.expression.Expression` component. For example, the following is all you need to create a`Gaussian` component with more sensible parameters for spectroscopy than the one that ships with HyperSpy: .. code-block:: python >>> g = hs.model.components.Expression( ... expression="height * exp(-(x - x0) ** 2 * 4 * log(2)/ fwhm ** 2)", ... name="Gaussian", ... position="x0", ... height=1, ... fwhm=1, ... centre=0, ... module="numpy") :py:class:`~._components.expression.Expression` uses `Sympy `_ internally to turn the string into a funtion. By default it "translates" the expression using numpy, but often it is possible to boost performance by using `numexpr `_ instead. :py:class:`~._components.expression.Expression` is only useful for analytical functions. If you know how to write the function with Python, turning it into a component is very easy modifying the following template: .. code-block:: python from hyperspy.component import Component class My_Component(Component): """ """ def __init__(self, parameter_1=1, parameter_2=2): # Define the parameters Component.__init__(self, ('parameter_1', 'parameter_2')) # Optionally we can set the initial values self.parameter_1.value = parameter_1 self.parameter_1.value = parameter_1 # The units (optional) self.parameter_1.units = 'Tesla' self.parameter_2.units = 'Kociak' # Once defined we can give default values to the attribute is we want # For example we fix the attribure_1 (optional) self.parameter_1.attribute_1.free = False # And we set the boundaries (optional) self.parameter_1.bmin = 0. self.parameter_1.bmax = None # Optionally, to boost the optimization speed we can define also define # the gradients of the function we the syntax: # self.parameter.grad = function self.parameter_1.grad = self.grad_parameter_1 self.parameter_2.grad = self.grad_parameter_2 # Define the function as a function of the already defined parameters, x # being the independent variable value def function(self, x): p1 = self.parameter_1.value p2 = self.parameter_2.value return p1 + x * p2 # Optionally define the gradients of each parameter def grad_parameter_1(self, x): """ Returns d(function)/d(parameter_1) """ return 0 def grad_parameter_2(self, x): """ Returns d(function)/d(parameter_2) """ return x If you need help with the task please submit your question to the :ref:`users mailing list `. .. _model_components-label: .. versionchanged:: 0.8.1 printing current model components To print the current components in a model use :py:attr:`components` of the variable. A table with component number, attribute name, component name and component type will be printed: .. code-block:: python >>> m >>> m.components # an empty model # | Attribute Name | Component Name | Component Type ---- | ------------------------- | ------------------------- | ------------------------- In fact, components may be created automatically in some cases. For example, if the `Signal` is recognised as EELS data, a power-law background component will automatically be placed in the model. To add a component first we have to create an instance of the component. Once the instance has been created we can add the component to the model using the :py:meth:`append` method, e.g. for a type of data that can be modelled using gaussians we might proceed as follows: .. code-block:: python >>> gaussian = hs.model.components.Gaussian() # Create a Gaussian function component >>> m.append(gaussian) # Add it to the model >>> m.components # Print the model components # | Attribute Name | Component Name | Component Type ---- | ------------------------- | ------------------------- | ------------------------- 0 | Gaussian | Gaussian | Gaussian >>> gaussian2 = hs.components.Gaussian() # Create another gaussian components >>> gaussian3 = hs.components.Gaussian() # Create a third gaussian components We could use the append method two times to add the two gaussians, but when adding multiple components it is handier to use the extend method that enables adding a list of components at once. .. code-block:: python >>> m.extend((gaussian2, gaussian3)) # note the double brackets! >>> m.components # | Attribute Name | Component Name | Component Type ---- | ------------------------- | ------------------------- | ------------------------- 0 | Gaussian | Gaussian | Gaussian 1 | Gaussian_0 | Gaussian_0 | Gaussian 2 | Gaussian_1 | Gaussian_1 | Gaussian We can customise the name of the components. .. code-block:: python >>> gaussian.name = 'Carbon' >>> gaussian2.name = 'Long Hydrogen name' >>> gaussian3.name = 'Nitrogen' >>> m.components # | Attribute Name | Component Name | Component Type ---- | ------------------------- | ------------------------- | ------------------------- 0 | Carbon | Carbon | Gaussian 1 | Long_Hydrogen_name | Long Hydrogen name | Gaussian 2 | Nitrogen | Nitrogen | Gaussian Two components cannot have the same name. .. code-block:: python >>> gaussian2.name = 'Carbon' Traceback (most recent call last): File "", line 1, in g2.name = "Carbon" File "/home/fjd29/Python/hyperspy/hyperspy/component.py", line 466, in name "the name " + str(value)) ValueError: Another component already has the name Carbon It is possible to access the components in the model by their name or by the index in the model. .. code-block:: python >>> m # | Attribute Name | Component Name | Component Type ---- | ------------------------- | ------------------------- | ------------------------- 0 | Carbon | Carbon | Gaussian 1 | Long_Hydrogen_name | Long Hydrogen name | Gaussian 2 | Nitrogen | Nitrogen | Gaussian >>> m[0] >>> m["Long Hydrogen name"] .. versionadded:: 0.8.1 :py:attr:`components` attribute In addition, the components can be accessed in the :py:attr:`~.model.Model.components` `Model` attribute. This is specially useful when working in interactive data analysis with IPython because it enables tab completion. .. code-block:: python >>> m # | Attribute Name | Component Name | Component Type ---- | ------------------------- | ------------------------- | ------------------------- 0 | Carbon | Carbon | Gaussian 1 | Long_Hydrogen_name | Long Hydrogen name | Gaussian 2 | Nitrogen | Nitrogen | Gaussian >>> m.components.Long_Hydrogen_name It is possible to "switch off" a component by setting its :py:attr:`~.component.Component.active` to `False`. When a components is switched off, to all effects it is as if it was not part of the model. To switch it on simply set the :py:attr:`~.component.Component.active` attribute back to `True`. .. versionadded:: 0.7.1 :py:attr:`~.component.Component.active_is_multidimensional` In multidimensional signals it is possible to store the value of the :py:attr:`~.component.Component.active` attribute at each navigation index. To enable this feature for a given component set the :py:attr:`~.component.Component.active_is_multidimensional` attribute to `True`. .. code-block:: python >>> s = hs.signals.Signal1D(np.arange(100).reshape(10,10)) >>> m = s.create_model() >>> g1 = hs.components.Gaussian() >>> g2 = hs.components.Gaussian() >>> m.extend([g1,g2]) >>> g1.active_is_multidimensional = True >>> g1._active_array array([ True, True, True, True, True, True, True, True, True, True], dtype=bool) >>> g2._active_array is None True >>> m.set_component_active_value(False) >>> g1._active_array array([False, False, False, False, False, False, False, False, False, False], dtype=bool) >>> m.set_component_active_value(True, only_current=True) >>> g1._active_array array([ True, False, False, False, False, False, False, False, False, False], dtype=bool) >>> g1.active_is_multidimensional = False >>> g1._active_array is None True Getting and setting parameter values and attributes ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ :py:meth:`~.model.Model.print_current_values` prints the value of the parameters of the components in the current coordinates. :py:attr:`~.component.Component.parameters` contains a list of the parameters of a component and :py:attr:`~.component.Component.free_parameters` lists only the free parameters. The value of a particular parameter can be accessed in the :py:attr:`~.component.Parameter.value`. If a model contains several components with the same parameters, it is possible to change them all by using :py:meth:`~.model.Model.set_parameters_value`. Example: .. code-block:: python >>> s = hs.signals.Signal1D(np.arange(100).reshape(10,10)) >>> m = s.create_model() >>> g1 = hs.model.components.Gaussian() >>> g2 = hs.model.components.Gaussian() >>> m.extend([g1,g2]) >>> m.set_parameters_value('A', 20) >>> g1.A.map['values'] array([ 20., 20., 20., 20., 20., 20., 20., 20., 20., 20.]) >>> g2.A.map['values'] array([ 20., 20., 20., 20., 20., 20., 20., 20., 20., 20.]) >>> m.set_parameters_value('A', 40, only_current=True) >>> g1.A.map['values'] array([ 40., 20., 20., 20., 20., 20., 20., 20., 20., 20.]) >>> m.set_parameters_value('A',30, component_list=[g2]) >>> g2.A.map['values'] array([ 30., 30., 30., 30., 30., 30., 30., 30., 30., 30.]) >>> g1.A.map['values'] array([ 40., 20., 20., 20., 20., 20., 20., 20., 20., 20.]) To set the the `free` state of a parameter change the :py:attr:`~.component.Parameter.free` attribute. To change the `free` state of all parameters in a component to `True` use :py:meth:`~.component.Component.set_parameters_free`, and :py:meth:`~.component.Component.set_parameters_not_free` for setting them to `False`. Specific parameter-names can also be specified by using `parameter_name_list`, shown in the example: .. code-block:: python >>> g = hs.model.components.Gaussian() >>> g.free_parameters set([, , ]) >>> g.set_parameters_not_free() set([]) >>> g.set_parameters_free(parameter_name_list=['A','centre']) set([, ]) Similar functions exist for :py:class:`~.model.Model`: :py:meth:`~.model.Model.set_parameters_free` and :py:meth:`~.model.Model.set_parameters_not_free`. Which sets the :py:attr:`~.component.Parameter.free` states for the parameters in components in a model. Specific components and parameter-names can also be specified. For example: .. code-block:: python >>> g1 = hs.model.components.Gaussian() >>> g2 = hs.model.components.Gaussian() >>> m.extend([g1,g2]) >>> m.set_parameters_not_free() >>> g1.free_parameters set([]) >>> g2.free_parameters set([]) >>> m.set_parameters_free(parameter_name_list=['A']) >>> g1.free_parameters set([]) >>> g2.free_parameters set([]) >>> m.set_parameters_free([g1], parameter_name_list=['sigma']) >>> g1.free_parameters set([, ]) >>> g2.free_parameters set([]) The value of a parameter can be coupled to the value of another by setting the :py:attr:`~.component.Parameter.twin` attribute. For example: .. code-block:: python >>> gaussian.parameters # Print the parameters of the gaussian components (A, sigma, centre) >>> gaussian.centre.free = False # Fix the centre >>> gaussian.free_parameters # Print the free parameters set([A, sigma]) >>> m.print_current_values() # Print the current value of all the free parameters Components Parameter Value Normalized Gaussian A 1.000000 sigma 1.000000 Normalized Gaussian centre 0.000000 A 1.000000 sigma 1.000000 Normalized Gaussian A 1.000000 sigma 1.000000 centre 0.000000 >>> gaussian2.A.twin = gaussian3.A # Couple the A parameter of gaussian2 to the A parameter of gaussian 3 >>> gaussian2.A.value = 10 # Set the gaussian2 centre value to 10 >>> m.print_current_values() Components Parameter Value Carbon sigma 1.000000 A 1.000000 centre 0.000000 Hydrogen sigma 1.000000 A 10.000000 centre 10.000000 Nitrogen sigma 1.000000 A 10.000000 centre 0.000000 >>> gaussian3.A.value = 5 # Set the gaussian1 centre value to 5 >>> m.print_current_values() Components Parameter Value Carbon sigma 1.000000 A 1.000000 centre 0.000000 Hydrogen sigma 1.000000 A 5.000000 centre 10.000000 Nitrogen sigma 1.000000 A 5.000000 centre 0.000000 By default the coupling function is the identity function. However it is possible to set a different coupling function by setting the :py:attr:`~.component.Parameter.twin_function` and :py:attr:`~.component.Parameter.twin_inverse_function` attributes. For example: >>> gaussian2.A.twin_function = lambda x: x**2 >>> gaussian2.A.twin_inverse_function = lambda x: np.sqrt(np.abs(x)) >>> gaussian2.A.value = 4 >>> m.print_current_values() Components Parameter Value Carbon sigma 1.000000 A 1.000000 centre 0.000000 Hydrogen sigma 1.000000 A 4.000000 centre 10.000000 Nitrogen sigma 1.000000 A 2.000000 centre 0.000000 >>> gaussian3.A.value = 4 >>> m.print_current_values() Components Parameter Value Carbon sigma 1.000000 A 1.000000 centre 0.000000 Hydrogen sigma 1.000000 A 16.000000 centre 10.000000 Nitrogen sigma 1.000000 A 4.000000 centre 0.000000 .. _model.fitting: Fitting the model to the data ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ To fit the model to the data at the current coordinates (e.g. to fit one spectrum at a particular point in a spectrum-image) use :py:meth:`~.model.Model.fit`. The following table summarizes the features of the currently available optimizers: .. table:: Features of curve fitting optimizers. +-----------+--------+------------------+-----------------------------------+ | Optimizer | Bounds | Error estimation | Method | +===========+========+==================+===================================+ | "leastsq" | No | Yes | least squares | +-----------+--------+------------------+-----------------------------------+ | "mpfit" | Yes | Yes | least squares | +-----------+--------+------------------+-----------------------------------+ | "odr" | No | Yes | least squares | +-----------+--------+------------------+-----------------------------------+ | "fmin" | No | No | least squares, maximum likelihood | +-----------+--------+------------------+-----------------------------------+ The following example shows how to perfom least squares with error estimation. First we create data consisting of a line line ``y = a*x + b`` with ``a = 1`` and ``b = 100`` and we add white noise to it: .. code-block:: python >>> s = hs.signals.SpectrumSimulation( ... np.arange(100, 300)) >>> s.add_gaussian_noise(std=100) To fit it we create a model consisting of a :class:`~._components.polynomial.Polynomial` component of order 1 and fit it to the data. .. code-block:: python >>> m = s.create_model() >>> line = hs.model.components.Polynomial(order=1) >>> m.append(line) >>> m.fit() On fitting completion, the optimized value of the parameters and their estimated standard deviation are stored in the following line attributes: .. code-block:: python >>> line.coefficients.value (0.99246156488437653, 103.67507406125888) >>> line.coefficients.std (0.11771053738516088, 13.541061301257537) When the noise is heterocedastic, only if the ``metadata.Signal.Noise_properties.variance`` attribute of the :class:`~._signals.signal1d.Signal1D` instance is defined can the errors be estimated accurately. If the variance is not defined, the standard deviation of the parameters are still computed and stored in the :attr:`~.component.Parameter.std` attribute by setting variance equal 1. However, the value won't be correct unless an accurate value of the variance is defined in ``metadata.Signal.Noise_properties.variance``. See :ref:`signal.noise_properties` for more information. In the following example, we add poissonian noise to the data instead of gaussian noise and proceed to fit as in the previous example. .. code-block:: python >>> s = hs.signals.SpectrumSimulation( ... np.arange(300)) >>> s.add_poissonian_noise() >>> m = s.create_model() >>> line = hs.model.components.Polynomial(order=1) >>> m.append(line) >>> m.fit() >>> line.coefficients.value (1.0052331707848698, -1.0723588390873573) >>> line.coefficients.std (0.0081710549764721901, 1.4117294994070277) Because the noise is heterocedastic, the least squares optimizer estimation is biased. A more accurate result can be obtained by using weighted least squares instead that, although still biased for poissonian noise, is a good approximation in most cases. .. code-block:: python >>> s.estimate_poissonian_noise_variance(expected_value=hs.signals.Signal1D(np.arange(300))) >>> m.fit() >>> line.coefficients.value (1.0004224896604759, -0.46982916592391377) >>> line.coefficients.std (0.0055752036447948173, 0.46950832982673557) We can use poissonian maximum likelihood estimation instead that is an unbiased estimator for poissonian noise. .. code-block:: python >>> m.fit(fitter="fmin", method="ml") >>> line.coefficients.value (1.0030718094185611, -0.63590210946134107) Problems of ill-conditioning and divergence can be ameliorated by using bounded optimization. Currently, only the "mpfit" optimizer supports bounds. In the following example a gaussian histogram is fitted using a :class:`~._components.gaussian.Gaussian` component using mpfit and bounds on the ``centre`` parameter. .. code-block:: python >>> s = hs.signals.Signal(np.random.normal(loc=10, scale=0.01, size=1e5)).get_histogram() >>> s.metadata.Signal.binned = True >>> m = s.create_model() >>> g1 = hs.model.components.Gaussian() >>> m.append(g1) >>> g1.centre.value = 7 >>> g1.centre.bmin = 7 >>> g1.centre.bmax = 14 >>> g1.centre.bounded = True >>> m.fit(fitter="mpfit", bounded=True) >>> m.print_current_values() Components Parameter Value Gaussian sigma 0.00996345 A 99918.7 centre 9.99976 .. versionadded:: 0.7 chi-squared and reduced chi-squared The chi-squared, reduced chi-squared and the degrees of freedom are computed automatically when fitting. They are stored as signals, in the :attr:`~.model.Model.chisq`, :attr:`~.model.Model.red_chisq` and :attr:`~.model.Model.dof` attributes of the model respectively. Note that, unless ``metadata.Signal.Noise_properties.variance`` contains an accurate estimation of the variance of the data, the chi-squared and reduced chi-squared cannot be computed correctly. This is also true for homocedastic noise. .. _model.visualization: Visualizing the model ^^^^^^^^^^^^^^^^^^^^^ To visualise the result use the :py:meth:`~.model.Model.plot` method: .. code-block:: python >>> m.plot() # Visualise the results .. versionadded:: 0.7 By default only the full model line is displayed in the plot. In addition, it is possible to display the individual components by calling :py:meth:`~.model.Model.enable_plot_components` or directly using :py:meth:`~.model.Model.plot`: .. code-block:: python >>> m.plot(plot_components=True) # Visualise the results To disable this feature call :py:meth:`~.model.Model.disable_plot_components`. .. versionadded:: 0.7.1 :py:meth:`~.model.Model.suspend_update` and :py:meth:`~.model.Model.resume_update` By default the model plot is automatically updated when any parameter value changes. It is possible to suspend this feature with :py:meth:`~.model.Model.suspend_update`. To resume it use :py:meth:`~.model.Model.resume_update`. .. _model.starting: Setting the initial parameters ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Non-linear regression often requires setting sensible starting parameters. This can be done by plotting the model and adjusting the parameters by hand. .. versionadded:: 0.7 In addition, it is possible to fit a given component independently using the :py:meth:`~.model.Model.fit_component` method. .. versionadded:: 0.8.5 :py:meth:`~.model.Model.notebook_interaction`, .. _notebook_interaction-label: If running in a Jupyter Notebook, interactive widgets can be used to conveniently adjust the parameter values by running :py:meth:`~.model.Model.notebook_interaction` for :py:class:`~.model.Model`, :py:class:`~.component.Component` and :py:class:`~.component.Parameter`. .. Warning:: :py:meth:`~.model.Model.notebook_interaction` functions require ``ipywidgets``, which is an optional dependency of HyperSpy. .. figure:: images/notebook_widgets.png :align: center :width: 985 Interactive widgets for the full model in a Jupyter notebook. Drag the sliders to adjust current parameter values. Typing different minimum and maximum values changes the boundaries of the slider. .. versionadded:: 0.6 :py:meth:`~.model.Model.enable_adjust_position` and :py:meth:`~.model.Model.disable_adjust_position` Also, :py:meth:`~.model.Model.enable_adjust_position` provides an interactive way of setting the position of the components with a well define position. :py:meth:`~.model.Model.disable_adjust_position` disables the tool. .. figure:: images/model_adjust_position.png :align: center :width: 500 Interactive component position adjustment tool.Drag the vertical lines to set the initial value of the position parameter. Exclude data from the fitting process ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The following :py:class:`~.model.Model` methods can be used to exclude undesired spectral channels from the fitting process: * :py:meth:`~.model.Model.set_signal_range` * :py:meth:`~.model.Model.remove_signal_range` * :py:meth:`~.model.Model.reset_signal_range` Fitting multidimensional datasets ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ To fit the model to all the elements of a multidimensional datataset use :py:meth:`~.model.Model.multifit`, e.g.: .. code-block:: python >>> m.multifit() # warning: this can be a lengthy process on large datasets :py:meth:`~.model.Model.multifit` fits the model at the first position, store the result of the fit internally and move to the next position until reaching the end of the dataset. Sometimes one may like to store and fetch the value of the parameters at a given position manually. This is possible using :py:meth:`~.model.Model.store_current_values` and :py:meth:`~.model.Model.fetch_stored_values`. Visualising the result of the fit ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The :py:class:`~.model.Model` :py:meth:`~.model.Model.plot_results`, :py:class:`~.component.Component` :py:meth:`~.component.Component.plot` and :py:class:`~.component.Parameter` :py:meth:`~.component.Parameter.plot` methods can be used to visualise the result of the fit **when fitting multidimensional datasets**. Saving and loading the result of the fit ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ As of HyperSpy 0.8, the following is the only way to save a model to a file and load it back. Note that this method is known to be brittle i.e. there is no guarantee that a version of HyperSpy different from the one used to save the model will be able to load it sucessfully. Also, it is advisable not to use this method in combination with functions that alter the value of the parameters interactively (e.g. `enable_adjust_position`) as the modifications made by this functions are normally not stored in the IPython notebook or Python script. To save a model: 1. Save the parameter arrays to a file using :py:meth:`~.model.Model.save_parameters2file`. 2. Save all the commands that used to create the model to a file. This can be done in the form of an IPython notebook or a Python script. 3. (Optional) Comment out or delete the fitting commangs (e.g. `multifit`). To recreate the model: 1. Execute the IPython notebook or Python script. 2. Use :py:meth:`~.model.Model.load_parameters_from_file` to load back the parameter values and arrays. Exporting the result of the fit ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The :py:class:`~.model.Model` :py:meth:`~.model.Model.export_results`, :py:class:`~.component.Component` :py:meth:`~.component.Component.export` and :py:class:`~.component.Parameter` :py:meth:`~.component.Parameter.export` methods can be used to export the result of the optimization in all supported formats. Batch setting of parameter attributes ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. versionadded:: 0.6 The following methods can be used to ease the task of setting some important parameter attributes: * :py:meth:`~.model.Model.set_parameters_not_free` * :py:meth:`~.model.Model.set_parameters_free` * :py:meth:`~.model.Model.set_parameters_value`