Skip to content

sim_fit.rst

Latest commit

 

History

History
123 lines (92 loc) · 4.44 KB

sim_fit.rst

File metadata and controls

123 lines (92 loc) · 4.44 KB

Simulation and Fitting

PyPWA defines both the monte carlo simulation method as well as the several likelihoods. To use these, the cost function or amplitude needs to be defined in a support object.

Defining an Amplitude

Amplitudes or cost functions can be defined for using either an Object Oriented approach, or a Functional programming approach. If using pure functions for the function, wrap the calculation function and optional setup function in PyPWA.FunctionalAmplitude, if using the OOP approach, extend the PyPWA.NestedFunction abstract class when defining the amplitude.

It is assumed by both the Likelihoods and Monte Carlo that the calculate functions of either methods will return a standard numpy array of final values.

.. autoclass:: PyPWA.NestedFunction
   :members:


.. autoclass:: PyPWA.FunctionAmplitude
   :members:

Simulating

There are two choices when using the Monte Carlo Simulation method defined in PyPWA: Simulation in one pass producing the rejection list, or simulation in two passes to produce the intensities and finally the rejection list. Both methods will take advantage of SMP where available.

  • If doing a single pass, just use the PyPWA.monte_carlo_simulation function. This will take the fitting function defined from :ref:`Defining an Amplitude<amplitude>` along with the data, and return a single rejection list.
  • If doing two passes for more control over when the intensities and rejection list, use both PyPWA.simulate.process_user_function to calculate the intensity and local max value, and PyPWA.simulate.make_rejection_list to take the global max value and local intensity to produce the local rejection list.
.. autofunction:: PyPWA.monte_carlo_simulation

.. autofunction:: PyPWA.simulate.process_user_function

.. autofunction:: PyPWA.simulate.make_rejection_list

Likelihoods

PyPWA supports 3 unique likelihood types for use with either the Minuit wrapper or any optimizer that expects a function. All likelihoods have built in support for SMP when they're called, and require to be closed when no longer needed.

  • PyPWA.LogLikelihood defines the likelihood, and works with either the standard log likelihood, the binned log likelihood, or the extended log likelihood.
  • PyPWA.ChiSquared defines the ChiSquared method, supporting both the binned and standard ChiSquare.
  • PyPWA.EmptyLikelihood does no post operation on the final values except sum the array and return the final sum. This allows for defining unique likelihoods that have not already been defined, fitting functions that do not require a likelihood, or using the builtin multi processing without the weight of a standard likelihood.
.. autoclass:: PyPWA.LogLikelihood
   :members:


.. autoclass:: PyPWA.ChiSquared
   :members:


.. autoclass:: PyPWA.EmptyLikelihood
   :members:

Fitting

PyPWA supplies a single wrapper around iMinuit's module. This is a convenience function to make working with Minuit's parameters easier. However, if wanting to use a different fitting function, like Scikit or Scipy, the likelihoods should work natively with them. In addition, PyPWA also supplies a wrapper around the MCMC package emcee.

Most optimizers built in Python assume the data is some sort of global variable, and the function passed to them is just accepting parameters to fit against. The Likelihoods take advantage of this by wrapping the data and the defined functions a wrapper that attempts to scale the function to several processors, while providing function-like capabilities by taking advantage of Python's builtin __call__ magic function.

This should allow the likelihoods to work with any optimizer, as long as they're expecting a function or callable object, and as long as the parameters they pass are pickle-able.

.. autofunction:: PyPWA.minuit


.. autofunction:: PyPWA.mcmc