A Python package for smoothing data and estimating first- and second-order derivatives and their errors.
Covariance functions can either be linear, squared exponential, neural network-like, or squared exponential with a linear trend.
An example workflow to smooth data (x, y), where the columns of y are replicates, is
>>> import gaussian process as gp
>>> g= gp.maternGP({0: (-4, 4), 1: (-4, 4), 2: (-4, -2)}, x, y)
The dictionary sets bounds on the hyperparameters, so that 0: (-4, 4) means that the bounds on the first hyperparameter are 1e-4 and 1e4.
>>> g.info()
explains what each hyperparameter does.
Once g is instantiated,
>>> g.findhyperparameters()
>>> g.results()
>>> g.predict(x, derivs= 2)
optimises the hyperparameters and determines a smoothed version of the data and estimates the derivatives.
The results can be visualised by
>>> import matplotlib.pylab as plt
>>> plt.figure()
>>> plt.subplot(2,1,1)
>>> g.sketch('.')
>>> plt.subplot(2,1,2)
>>> g.sketch('.', derivs= 1)
>>> plt.show()
and are available as g.f and g.fvar (smoothed data and error), g.df and g.dfvar (estimate of dy/dx), and g.ddf and g.ddfvar (estimate of d2y/dx2).
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