fitpy.analysis module
Actual fitting in form of analysis steps derived from the ASpecD framework.
Fitting of a model to (experimental) data can always be seen as an analysis step in context of the ASpecD framework, resulting in a calculated dataset.
Introduction
Fitting in context of the FitPy framework is always a twostep process:
define the model, and
define the fitting task.
The model is an instance of aspecd.model.Model
, and the fitting
task one of the analysis steps contained in this module. They are, in turn,
instances of aspecd.analysis.AnalysisStep
.
A first, simple but complete example of a recipe performing a fit on experimental data, is given below.
1format:
2 type: ASpecD recipe
3 version: '0.2'
4
5datasets:
6  /path/to/dataset
7
8tasks:
9  kind: model
10 type: Gaussian
11 properties:
12 parameters:
13 position: 1.5
14 width: 0.5
15 from_dataset: /path/to/dataset
16 output: model
17 result: gaussian_model
18
19  kind: fitpy.singleanalysis
20 type: SimpleFit
21 properties:
22 model: gaussian_model
23 parameters:
24 fit:
25 amplitude:
26 start: 5
27 range: [3, 7]
28 result: fitted_gaussian
In this case, a Gaussian model is created, with values for two parameters
set explicitly and not varied during the fit. The third parameter is varied
during the fit, within a given range. Furthermore, using
SimpleFit
here without further parameters, a leastsquares fit
using the LevenbergMarquardt method is carried out.
Note
Usually, you will have set another ASpecDderived package as
default package in your recipe for processing and analysing your data.
Hence, you need to provide the package name (fitpy) in the kind
property, as shown in the examples.
This seamless integration of FitPy into all packages derived from the ASpecD
framework ensures full reproducibility and allows to easily pre and
postprocess the data accordingly. Particularly for analysing the results of
fits, have a look at the dedicated plotters in the fitpy.plotting
module and the reporters in the fitpy.report
module.
Fitting strategies
Fitting models to data is generally a complex endeavour, and FitPy will not take any decisions for you. However, it provides powerful abstractions and a simple user interface, letting you automate as much as possible, while retaining full reproducibility. Thus, it is possible to create entire pipelines spanning a series of different fitting strategies, analyse the results, and making an informed decision for each individual question.
The following list provides an overview of the different fitting strategies supported by FitPy (currently, as of January 2022, only a subset of these strategies is implemented).
Simple fitting of single datasets
Make informed guesses for the initial values of the variable parameters of a model and fit the model to the data. The most straightforward strategy. Still, different optimisation algorithms can be chosen.
If the fitness landscape is rough and contains local minima, the fit may not converge or get stuck in local minima.
Robust fitting via sampling of initial conditions (LHS)
Instead of informed guesses for the initial values of the variable parameters of a model, these initial values are randomly chosen using a Latin Hypercube. For each of the resulting grid points, an optimisation is performed, analogous to what has been described above.
Generally, this approach will take much longer, with the computing time scaling with the number of grid points, but it is much more robust, particularly with complicated fitness landscapes containing many local minima.
Fitting multiple species to one dataset
Basically the same as fitting a simple model to the data of a dataset, but this time providing a
aspecd.model.CompositeModel
.Given the usually larger number of variable parameters, robust fitting strategies (LHS) should be used.
Global fitting of several datasets at once
Fit models with a joint set of parameters to a series of independent datasets. Can become arbitrarily complex given that some parameters may be allowed to independently vary for each dataset, while others are constrained, while still others (typically the majority) will be identical for each dataset.
Common to all these different fitting strategies is the need to sometimes omit parts of a dataset from fitting.
Concrete fitting tasks implemented
Currently (as of January 2022), only fitting tasks are implemented that operate on single datasets.

Perform basic fit of a model to data of a dataset.
The result is stored as calculated dataset and can be investigated graphically using dedicated plotters from the
fitpy.plotting
module as well as reporters from thefitpy.report
module.With default settings, a leastSquares minimization using the LevenbergMarquardt method is carried out. Initial values and ranges for each variable parameter of the model can be specified, as well as details for the algorithm.

Fit of a model to data of a dataset using LHS of starting conditions.
In case of more complicated fits, e.g. many variable parameters or a rough fitness landscape of the optimisation including several local minima, obtaining a robust fit and finding the global minimum requires to sample initial conditions and to perform fits for all these conditions.
Here, a Latin Hypercube gets used to sample the initial conditions. For each of these, a fit is performed in the same way as in
SimpleFit
. The best fit is stored in the result as usual, and additionally, the sample grid, the discrepancy as measure for the quality of the grid, as well as all results from the individual fits are stored in thelhs
property of the metadata of the resulting dataset. This allows for both, handling this resulting dataset as usual and evaluating the robustness of the fit.
Helper classes
Additionally to the fitting tasks described above, helper classes exist for specific tasks.

Extract statistical criterion from LHS results for evaluating robustness.
When performing a robust fitting, e.g. by employing
LHSFit
, evaluating the robustness of the obtained results is a crucial step. Therefore, the results from each individual fit starting with a grid point of the Latin Hypercube are contained in the resulting dataset. This analysis step extracts the given criterion from the calculated dataset and returns itself a calculated dataset with the values of the criterion sorted in ascending order as its data. The result can be graphically represented using aaspecd.plotting.SinglePlotter1D
.
Module documentation
 class fitpy.analysis.SimpleFit[source]
Bases:
aspecd.analysis.SingleAnalysisStep
Perform basic fit of a model to data of a dataset.
The result is stored as calculated dataset and can be investigated graphically using dedicated plotters from the
fitpy.plotting
module as well as reporters from thefitpy.report
module.With default settings, a leastSquares minimization using the LevenbergMarquardt method is carried out. Initial values and ranges for each variable parameter of the model can be specified, as well as details for the algorithm.
 result
Calculated dataset containing the result of the fit.
 model
Model to fit to the data of a dataset
 Type
 parameters
All parameters necessary to perform the fit.
These parameters will be available from the calculation metadata of the resulting
fitpy.dataset.CalculatedDataset
. fit
dict
All model parameters that should be fitted.
The keys of the dictionary need to correspond to the parameter names of the model that should be fitted. The values are dicts themselves, at least with the key
start
for the initial parameter value. Additionally, you may supply arange
with a list as value defining the interval within the the parameter is allowed to vary during fitting. algorithm
dict
Settings of the algorithm used to fit the model to the data.
The key
method
needs to correspond to the methods supported bylmfit.minimizer.Minimizer
.To provide more information independent on the naming of the respective methods in
lmfit.minimizer
and the correspondingscipy.optimize
module, the keydescription
contains a short description of the respective method.To pass additional parameters to the solver, use the
parameters
dict. Which parameters can be set depends on the actual solver. For details, see thescipy.optimize
documentation.
 Type
 fit
 Raises
ValueError – Raised if the method provided in
parameters['algorithm'][ 'method']
is not supported or invalid.
Examples
For convenience, a series of examples in recipe style (for details of the recipedriven data analysis, see
aspecd.tasks
) is given below for how to make use of this class. The examples focus each on a single aspect.Fitting is always a twostep process: (i) define the model, and (ii) define the fitting task. Here and in the following examples we assume a dataset to be imported as
dataset
, and the model is initially evaluated for this dataset (to get the same data dimensions and alike, seeaspecd.model
for details).Note
Usually, you will have set another ASpecDderived package as default package in your recipe for processing and analysing your data. Hence, you need to provide the package name (fitpy) in the
kind
property, as shown in the examples.Suppose you have a dataset and want to fit a Gaussian to its data, in this case only varying the amplitude, but keeping position and width fixed to the values specified in the model:
 kind: model type: Gaussian properties: parameters: position: 1.5 width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: SimpleFit properties: model: gaussian_model parameters: fit: amplitude: start: 5 result: fitted_gaussian
In this particular case, you define your model specifying position and width, and fit this to the data allowing only the parameter amplitude to vary, keeping position and width fixed at the given values. Furthermore, no range is provided for the values the amplitude can be varied.
To provide a range (boundaries, interval) for the allowed values of a fit parameter, simply add the key
range
: kind: model type: Gaussian properties: parameters: position: 1.5 width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: SimpleFit properties: model: gaussian_model parameters: fit: amplitude: start: 5 range: [3, 7] result: fitted_gaussian
Note that models usually will have standard values for all parameters. Therefore, you only need to define those parameters in the model task that shall not change during fitting and should have values different from the standard.
If you were to fit multiple parameters of a model (as is usually the case), provide all these parameters in the fit section of the parameters of the fitting task:
 kind: model type: Gaussian properties: parameters: width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: SimpleFit properties: model: gaussian_model parameters: fit: amplitude: start: 5 range: [3, 7] position: start: 2 range: [0, 4] result: fitted_gaussian
While the default algorithm settings are quite sensible as a starting point, you can explicitly set the method and its parameters. Which parameters can be set depends on the method chosen, for details refer to the documentation of the underlying
scipy.optimize
module. The following example shows how to change the algorithm toleast_squares
(using a Trust Region Reflective method) and to set the tolerance for termination by the change of the independent variables (xtol
parameter): kind: model type: Gaussian properties: parameters: position: 1.5 width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: SimpleFit properties: model: gaussian_model parameters: fit: amplitude: start: 5 algorithm: method: least_squares parameters: xtol: 1e6 result: fitted_gaussian
 class fitpy.analysis.LHSFit[source]
Bases:
aspecd.analysis.SingleAnalysisStep
Fit of a model to data of a dataset using LHS of starting conditions.
In case of more complicated fits, e.g. many variable parameters or a rough fitness landscape of the optimisation including several local minima, obtaining a robust fit and finding the global minimum requires to sample initial conditions and to perform fits for all these conditions.
Here, a Latin Hypercube gets used to sample the initial conditions. For each of these, a fit is performed in the same way as in
SimpleFit
. The best fit is stored in the result as usual, and additionally, the sample grid, the discrepancy as measure for the quality of the grid, as well as all results from the individual fits are stored in thelhs
property of the metadata of the resulting dataset. This allows for both, handling this resulting dataset as usual and evaluating the robustness of the fit. result
Calculated dataset containing the result of the fit.
 model
Model to fit to the data of a dataset
 Type
 parameters
All parameters necessary to perform the fit.
These parameters will be available from the calculation metadata of the resulting
fitpy.dataset.CalculatedDatasetLHS
. fit
dict
All model parameters that should be fitted.
The keys of the dictionary need to correspond to the parameter names of the model that should be fitted. The values are dicts themselves, at least with the key
start
for the initial parameter value. Additionally, you may supply arange
with a list as value defining the interval within the the parameter is allowed to vary during fitting. algorithm
dict
Settings of the algorithm used to fit the model to the data.
The key
method
needs to correspond to the methods supported bylmfit.minimizer.Minimizer
.To provide more information independent on the naming of the respective methods in
lmfit.minimizer
and the correspondingscipy.optimize
module, the keydescription
contains a short description of the respective method.To pass additional parameters to the solver, use the
parameters
dict. Which parameters can be set depends on the actual solver. For details, see thescipy.optimize
documentation. lhs
dict
Settings for the Latin Hypercube used to sample initial conditions.
The most important parameter is
points
, defining the points in each direction of the Latin Hypercube.Additionally, all attributes of
scipy.stats.qmc.LatinHypercube
can be set. Currently, the relevant parameters arecentered
(to center the point within the multidimensional grid) andrng_seed
to allow for reproducible results.In case
rng_seed
is provided, the random number generator is reset and seeded with this value, ensuring reproducible creation of the grid.
 Type
 fit
 Raises
ValueError – Raised if the method provided in
parameters['algorithm'][ 'method']
is not supported or invalid.
Examples
For convenience, a series of examples in recipe style (for details of the recipedriven data analysis, see
aspecd.tasks
) is given below for how to make use of this class. The examples focus each on a single aspect.Fitting is always a twostep process: (i) define the model, and (ii) define the fitting task. Here and in the following examples we assume a dataset to be imported as
dataset
, and the model is initially evaluated for this dataset (to get the same data dimensions and alike, seeaspecd.model
for details).Note
Usually, you will have set another ASpecDderived package as default package in your recipe for processing and analysing your data. Hence, you need to provide the package name (fitpy) in the
kind
property, as shown in the examples.Suppose you have a dataset and want to fit a Gaussian to its data, in this case only varying the amplitude, but keeping position and width fixed to the values specified in the model:
 kind: model type: Gaussian properties: parameters: position: 1.5 width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: LHSFit properties: model: gaussian_model parameters: fit: amplitude: lhs_range: [2, 8] lhs: points: 7 result: fitted_gaussian
In this particular case, you define your model specifying position and width, and fit this to the data allowing only the parameter amplitude to vary, keeping position and width fixed at the given values. Furthermore, a range for the LHS for this parameter is provided, as well as the number of points sampled per dimension of the Latin Hypercube.
Only those fitting parameters having set the
lhs_range
parameter will be used for sampling. All other parameters will be used with their starting values as defined: kind: model type: Gaussian properties: parameters: position: 1.5 width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: LHSFit properties: model: gaussian_model parameters: fit: amplitude: lhs_range: [2, 8] position: start: 2 range: [0, 4] lhs: points: 7 result: fitted_gaussian
Here, only the
amplitude
parameter will be sampled (in this particular case resulting in a 1D Latin Hypercube), while for each of the grid points, theposition
parameter is set as given.Sometimes the grid created by the LHS should be reproducible. In this case, provide a seed for the random number generator used internally:
 kind: model type: Gaussian properties: parameters: position: 1.5 width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: LHSFit properties: model: gaussian_model parameters: fit: amplitude: lhs_range: [2, 8] lhs: points: 7 rng_seed: 42 result: fitted_gaussian
Similarly, if the points should be centred within the multidimensional grid, set the
centered
property accordingly: kind: model type: Gaussian properties: parameters: position: 1.5 width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: LHSFit properties: model: gaussian_model parameters: fit: amplitude: lhs_range: [2, 8] lhs: points: 7 centered: true result: fitted_gaussian
While the default algorithm settings are quite sensible as a starting point, you can explicitly set the method and its parameters. Which parameters can be set depends on the method chosen, for details refer to the documentation of the underlying
scipy.optimize
module. The following example shows how to change the algorithm toleast_squares
(using a Trust Region Reflective method) and to set the tolerance for termination by the change of the independent variables (xtol
parameter): kind: model type: Gaussian properties: parameters: position: 1.5 width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: LHSFit properties: model: gaussian_model parameters: fit: amplitude: lhs_range: [2, 8] lhs: points: 7 algorithm: method: least_squares parameters: xtol: 1e6 result: fitted_gaussian
 class fitpy.analysis.ExtractLHSStatistics[source]
Bases:
aspecd.analysis.SingleAnalysisStep
Extract statistical criterion from LHS results for evaluating robustness.
When performing a robust fitting, e.g. by employing
LHSFit
, evaluating the robustness of the obtained results is a crucial step. Therefore, the results from each individual fit starting with a grid point of the Latin Hypercube are contained in the resulting dataset. This analysis step extracts the given criterion from the calculated dataset and returns itself a calculated dataset with the values of the criterion sorted in ascending order as its data. The result can be graphically represented using aaspecd.plotting.SinglePlotter1D
. result
Calculated dataset containing the extracted statistical criterion.
 parameters
All parameters necessary to perform the fit.
These parameters will be available from the calculation metadata of the resulting
fitpy.dataset.CalculatedDatasetLHS
. criterion
str
Statistical criterion extracted from the LHS results
 Type
 criterion
Examples
For convenience, a series of examples in recipe style (for details of the recipedriven data analysis, see
aspecd.tasks
) is given below for how to make use of this class. The examples focus each on a single aspect.Suppose you have fitted a Gaussian to the data of a dataset, as shown in the example section of the
LHSFit
class. If you now want to extract the reduced chi square value and plot it, the whole procedure could look like this: kind: model type: Gaussian properties: parameters: position: 1.5 width: 0.5 from_dataset: dataset output: model result: gaussian_model  kind: fitpy.singleanalysis type: LHSFit properties: model: gaussian_model parameters: fit: amplitude: lhs_range: [2, 8] lhs: points: 7 result: fitted_gaussian  kind: fitpy.singleanalysis type: ExtractLHSStatistics properties: parameters: criterion: reduced_chi_square result: reduced_chi_squares apply_to: fitted_gaussian  kind: singleplot type: SinglePlotter1D properties: properties: drawing: marker: 'o' linestyle: 'none' filename: 'reduced_chi_squares.pdf' apply_to: reduced_chi_squares
This would plot the reduced chi square values in ascending order, showing the individual values as not connected dots.