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****************
Useful Utilities
****************
Using PyCogent's optimisers for your own functions
==================================================
You have a function that you want to maximise/minimise. The parameters in your function may be bounded (must lie in a specific interval) or not. The cogent optimisers can be applied to these cases. The ``Powell`` (a local optimiser) and ``SimulatedAnnealing`` (a global optimiser) classes in particular have had their interfaces standardised for such use cases. We demonstrate for a very simple function below.
We write a simple factory function that uses a provided value for omega to compute the squared deviation from an estimate.
.. doctest::
>>> import numpy
>>> def DiffOmega(omega):
... def omega_from_S(S):
... omega_est = S/(1-numpy.e**(-1*S))
... return abs(omega-omega_est)**2
... return omega_from_S
We then import the ``Powell`` optimiser, create our optimisable function with a value of omega to solve for S and instantiate an optimiser instance. Note that we provide lower and upper bounds and an initial guess for our parameter of interest (``S``).
.. doctest::
>>> from cogent.maths.optimisers import Powell
>>> omega = 0.1
>>> opt = Powell(DiffOmega(omega),
... xinit=[1.0], # the vector of initial values
... bounds=([-100], [100]), # [(lower),(upper)] bounds for the params
... direction=-1) # -1 is minimise func, 1 is maximise
We then optimise the function, obtaining the fit statistic and the associated estimate of S.
.. doctest::
>>> fit, vec = opt.run(show_progress=False)
>>> assert 0.0 <= fit < 1e-6
>>> print 'S=%.4f' % vec[0]
S=-3.6150
Cartesian products
==================
*To be written.*
.. cogent.util.transform
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