# 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

* 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
```