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Math Utilities.md

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Math Utilities

In order to cope with lack of NumPy on Jython, PShell includes Apache's Commons Math library (http://commons.apache.org/proper/commons-math/).

All functionality available in org.apache.commons.math3 can be accessed from the scripts. The direct access to this library is not straightforward in Python though. The module mathutils.py implements a facade to this library, in order to facilitate the use of its most common features.

The functions in mathutils.py are not built-in functions: the module must be imported such as:

from mathutils import *

The tutorial provides examples on the use of mathutils.

The main functions available are:

  • Derivative and interpolation:

    • deriv: Calculate derivative of UnivariateFunction, array or list.
    • integrate: Integrate UnivariateFunction, array or list.
    • trapz: Integrate an array or list using the composite trapezoidal rule.
    • interpolate: Interpolate data array or list to a UnivariateFunction.

  • Fitting and peak search:

    • fit_polynomial: Fits data vector as a polynomial.
    • fit_gaussian: Fits data vector as a gaussian.
    • fit_gaussian_offset:Fits data vector as a gaussian with constant background.
    • fit_gaussian_linear:Fits data vector as a gaussian with linear background.
    • fit_harmonic: Fits data vector as an harmonic.
    • estimate_peak_indexes: Estimation of peaks in an array by ordering local maxima according to given criteria.
    • fit_gaussians: Fits data on multiple gaussians on the given peak indexes.
    • calculate_peaks: Calculate peaks of a DifferentiableUnivariateFunction in a given range by finding the roots of the derivative.

  • Least squares problem:

    • optimize_least_squares: Fits a parametric model to a set of observed values by minimizing a cost function.

  • Transforms:

    • fft: Calculate the FFT of a vector, padding to the next power of 2 elements.
    • ffti: Calculates the Inverse FFT of a vector, padding to the next power of 2 elements.
    • get_real: Calculate real part of a complex vector.
    • get_imag: Calculate imaginary part of a complex vector.
    • get_modulus: Calculate modulus of a complex vector.
    • get_phase: Calculate phase of a complex vector.

  • Tools:

    • get_values: Computes list of values of a UnivariateFunction

Note: Check the PyDocs of the methods for parameters and return types:

        help(function_name)