Source code for hesseflux.functions.general_functions

#!/usr/bin/env python
"""
Module with general functions that are not specialised for fitting,
optimisation, sensitivity analysis, etc.

The current functions are:
    curvature   Curvature of function f: f''/(1+f'^2)^3/2

This module was written by Matthias Cuntz while at Department of
Computational Hydrosystems, Helmholtz Centre for Environmental
Research - UFZ, Leipzig, Germany, and continued while at Institut
National de Recherche pour l'Agriculture, l'Alimentation et
l'Environnement (INRAE), Nancy, France.

Copyright (c) 2015-2020 Matthias Cuntz - mc (at) macu (dot) de
Released under the MIT License; see LICENSE file for details.

* Written Mar 2015 by Matthias Cuntz (mc (at) macu (dot) de)
* Changed to Sphinx docstring and numpydoc, Dec 2019, Matthias Cuntz
* Split logistic and curvature into separate files, May 2020, Matthias Cuntz

.. moduleauthor:: Matthias Cuntz

The following functions are provided:

.. autosummary::
    curvature
"""
from __future__ import division, absolute_import, print_function
import numpy as np
import scipy.special as sp


__all__ = ['curvature']


# -----------------------------------------------------------
# curvature of function
[docs]def curvature(x, dfunc, d2func, *args, **kwargs): """ Curvature of function: `f''/(1+f'^2)^3/2` Parameters ---------- x : array_like Independent variable to evalute curvature dfunc : callable Function giving first derivative of function f: f', to be called `dfunc(x, *args, **kwargs)` d2func : callable Function giving second derivative of function f: f'', to be called `d2func(x, *args, **kwargs)` args : iterable Arguments passed to `dfunc` and `d2func` kwargs : dict Keyword arguments passed to `dfunc` and `d2func` Returns ------- float or ndarray Curvature of function f at `x` """ return ( d2func(x, *args, **kwargs) / (1. + dfunc(x, *args, **kwargs)**2)**1.5 )
# ----------------------------------------------------------- if __name__ == '__main__': import doctest doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE) # from logistic_function import dlogistic_offset, d2logistic_offset, dlogistic_offset_p, d2logistic_offset_p # print(np.around(curvature(1., dlogistic_offset, d2logistic_offset, 1., 2., 2., 1.),4)) # # 0.2998 # print(np.around(curvature(1., dlogistic_offset_p, d2logistic_offset_p, [1., 2., 2., 1.]),4)) # # 0.2998