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General functions

General functions#

Functions used with Efficient/Sequential Elementary Effects

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:

Copyright 2015- Matthias Cuntz, see AUTHORS.rst for details.

license:

MIT License, see LICENSE for details.

Functions:

cost_square(p, func, x, y)

General cost function for optimising func(x, p) vs y with sum of square deviations.

curvature(x, dfunc, d2func, *args, **kwargs)

Curvature of a function f
History

  • 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

  • More consistent docstrings, Jan 2022, Matthias Cuntz

  • Transferred curvature and cost_square from pyjams to pyeee, Mar 2024, Matthias Cuntz

cost_square(p, func, x, y)[source]#

General cost function for optimising func(x, p) vs y with sum of square deviations.

Parameters:

  • p (iterable of floats) – parameters

  • func (callable) – fun(x,p) -> float

  • x (float or array_like of floats) – independent variable

  • y (float or array_like of floats) – dependent variable, observations

Returns:

sum of squared deviations

Return type:

float

curvature(x, dfunc, d2func, *args, **kwargs)[source]#

Curvature of a function f

\[f''/(1+f'^2)^{3/2}\]
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:

Curvature of function f at x

Return type:

float or ndarray

Examples

from pyjams.functions import dlogistic_offset, d2logistic_offset
curvature(1., dlogistic_offset, d2logistic_offset,
          [1., 2., 2., 1.])
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