Skip to content

Latest commit

 

History

History
185 lines (132 loc) · 7.66 KB

how_to_use_fitting.md

File metadata and controls

185 lines (132 loc) · 7.66 KB
Raw

How to use fitting in Qudi {#fit_logic}

First of all it is important to mention that the naming convention of methods is very important! Only if the methods are named right the automated import works properly!

General procedure to create new fitting routines:

A fitting routine consists of three major parts:

  1. a (mathematical) model make_<custom>_model()
    • Here we use the lmfit package, which has a couple of standard models like ConstantModel, LorentzianModel or GaussianModel. These models can be used straight away and also can be added, like: new_model = ConstantModel()+GaussianModel(), which yields a Gaussian model with an offset.
    • If there is no standard model one can define a customized model, see make_sinewithoutoffset_model()
    • With model.make_params() one can create a set of parameters with a value, min, max, vary and an expression. These parameters are returned as a Parameters object which contains all variables in a dictionary.
    • The make_""_model method returns, the model and a corresponding parameter dictionary
  2. an estimator, which can extract initial values for the fitting routine from the passed data. estimate_<custom>()
    • Here values have to be estimated from the raw data
    • In many cases a clever convolution helps a lot
    • Offsets can be retrieved from find_offset_parameter method
    • All parameters are given via a Parameters object
    • The estimated values are returned inside a Parameters object
  3. The actual fit method make_<custom>_fit()
    • First the model and parameters are created with the make_model method.
    • The initial values are returned by the estimator method
    • Constraints are set, e.g. param['offset'].min=0 param['offset'].max=data.max()
    • Additional parameters given by inputs can be overwritten by substitute_params method
    • Finally fit is done via model.fit(data, x=axis,params=params)
    • The fit routine from lmfit returns a dictionary with many parameters like: results with errors and correlations, best_values, initial_values, success flag, an error message.
    • With model.eval(...) one can generate high resolution data by setting an x-axis with maby points

The power of that general splitting is that you can write pretty independent fit algorithms, but their efficiency will (very often) rely on the quality of the estimator.

Naming convention:

  1. fit method: make_<custom>_fit() it is important to have no extra underscores, and that it starts with make_ and ends with _fit. In order to distinguish between oneD and twoD models, every twoD model has to include the string twoD e.g.

     def make_gaussian_fit() and def make_twoDgaussian_fit()

  2. estimate function: estimate_<custom>() e.g. estimate_gaussian() if you only have one estimator, if there are different estimators estimate_<custom>_<estimator name>. it is important to have no extra underscores, and that it starts with estimate_, e.g.

     def estimate_gaussian_dip() and def estimate_gaussian_peak()

  3. model function: make_<custom>_model(), if one wants to construct the model from a custom (not built-in) function one can do that within the `make__model()`` method e.g.

         def make_sinewithoutoffset_model(self):
         """ This method creates a model of sine.

         @return tuple: (object model, object params)
         """
         def sine_function(x, amplitude, frequency,phase):
             """
             Function of a sine.
             @param x: variable variable - e.g. time
             @param amplitude: amplitude
             @param frequency: frequency
             @param phase: phase

             @return: sine function: in order to use it as a model
             """

             return amplitude*np.sin(2*np.pi*frequency*x+phase)

         model = Model(sine_function, prefix='s0')

         params = model.make_params()

         return model, params

The model

Useful methods usable from the model are:

model.eval(x=x_axis, parameters)

or

linear_model.eval(x=np.linspace(0,10,100), slope=2., offset=10.)

One can retrieve the independent and variable variables from a model with:

 model.param_names and model.independent_vars

More information here: https://lmfit.github.io/lmfit-py/model.html

The returned object of the fit method

In the object returned from the fit method many parameters are saved. Some useful values are listed here:

  • a well readable fit_report result.fit_report()
  • an array of the fit corresponding to the x axis: result.best_fit
  • an array of the initial parameters corresponding to the x axis: result.init_fit
  • a parameters dictionary of the fitted values: result.best_values
  • a parameters dictionary of the initial values: result.init_values
  • information about the fit: result.message
  • a boolean which tells if the fit worked: result.success

More information at https://lmfit.github.io/lmfit-py/model.html

Parameters object

The parameter object can be created from a model:

    parameters = model.make_param()

It is also given back from the make_<custom>_model() method:

    model, parameters = make_<custom>_model()

Useful methods of the Parameters class are:

  • add, e.g. parameters.add('frequency', value=1, vary=True, min=0, max=10,expr=None)

  • add_many

                         #(Name,       Value,      Vary,           Min,                             Max,                       Expr)
  params.add_many(('amplitude',   amplitude,  True,        100,                               1e7,                           None),
                 (  'sigma_x',    sigma_x,    True,        1*(stepsize_x) ,              3*(x_axis[-1]-x_axis[0]),          None),
                 (  'sigma_y',  sigma_y,      True,   1*(stepsize_y) ,                        3*(y_axis[-1]-y_axis[0]) ,   None),
                 (  'x_zero',    x_zero,      True,     (x_axis[0])-n_steps_x*stepsize_x ,         x_axis[-1]+n_steps_x*stepsize_x,               None),
                 (  'y_zero',     y_zero,     True,    (y_axis[0])-n_steps_y*stepsize_y ,         (y_axis[-1])+n_steps_y*stepsize_y,         None),
                 (  'theta',       0.,        True,           0. ,                             np.pi,               None),
                 (  'offset',      offset,    True,           0,                              1e7,                       None))

Single changes can be set in the following way:

    params['amplitude'].min = 0.0
    params['amplitude'].max = 10.0
    params['lorentz1'].expr='lorentz0_center+2.15'
    params['amplitude'].vary = True
    params['amplitude'].value = 0.12

See very detailed description: https://lmfit.github.io/lmfit-py/parameters.html

General functions

  • Searching a double dip in data:

    _search_double_dip()

  • Search the end of a dip. This can be used to exclude a dip from data in order to find second dip, or one can estimate with this method the width of a dip/peak

     _search_end_of_dip()

  • Find offset from peaklike data, here first a lorentzian filter is applied on the data and the a histogram is made. The most frequent value is supposed to be the offset value:

     find_offset_parameter()

  • Smooth data with a gaussian filter, the filter is adjusted in size depending on the length of the input data:

      gaussian_smoothing()

List of fit functions

This list can be read out in the manager console:

    fitlogic.oneD_fit_methods and fitlogic.twoD_fit_methods