pyeee - Parameter screening of computational models

A Python library for parameter screening of computational models using Morris' method of Elementary Effects or its extension of Efficient/Sequential Elementary Effects by Cuntz, Mai et al. (Water Res Research, 2015).

About pyeee

pyeee is a Python library for performing parameter screening of computational models. It uses Morris' method of Elementary Effects and also its extension of Efficient or Sequential Elementary Effects published of

Cuntz, Mai et al. (2015)
Computationally inexpensive identification of noninformative model parameters by sequential screening
Water Resources Research 51, 6417-6441, doi:10.1002/2015WR016907.

The package uses several functions of the JAMS Python package https://github.com/mcuntz/jams_python
The JAMS package and hesseflux are synchronised irregularly.

pyeee can be used with Python functions but also with external programs, using for example partialwrap. Function evaluation can be distributed with Python's multiprocessing or via MPI.

Documentation

The complete documentation for pyeee is available from Read The Docs.

http://pyeee.readthedocs.org/en/latest/

Quick usage guide

Simple Python function

Consider the Ishigami-Homma function: y = sin(x_0) + a*sin(x_1)^2 + b*x_2^4*sin(x_0).

Taking a = b = 1 gives:

    import numpy as np
    def ishigami1(x):
       return np.sin(x[0]) + np.sin(x[1])**2 + x[2]**4 * np.sin(x[0])

The three paramters x_0, x_1, x_2 follow uniform distributions between -pi and +pi.

Morris' Elementary Effects can then be calculated like:

    npars = 3
    # lower boundaries
    lb = np.ones(npars) * (-np.pi)
    # upper boundaries
    ub = np.ones(npars) * np.pi

    # Elementary Effects
    from pyeee import ee
    np.random.seed(seed=1023) # for reproducibility of examples
    out = ee(ishigami1, lb, ub, 10)

which gives the Elementary Effects ($\mu*$):

    # mu*
    print("{:.1f} {:.1f} {:.1f}".format(*out[:,0]))
    # gives: 173.1 0.6 61.7

Sequential Elementary Effects distinguish between informative and uninformative parameters using several times Morris' Elementary Effects:

    # screen
    from pyeee import eee
    np.random.seed(seed=1023) # for reproducibility of examples
    out = eee(ishigami1, lb, ub, ntfirst=10)

which returns a logical ndarray with True for the informative parameters and False for the uninformative parameters:

    print(out)
    [ True False  True]

Python function with extra parameters

The function for pyeee must be of the form func(x). Use Python's partial from the functools module to pass other function parameters.

For example pass the parameters $a$ and $b$ to the Ishigami-Homma function.

    import numpy as np
    from pyeee import ee
    from functools import partial

    def ishigami(x, a, b):
       return np.sin(x[0]) + a * np.sin(x[1])**2 + b * x[2]**4 * np.sin(x[0])

    def call_func_ab(func, a, b, x):
       return func(x, a, b)

    # Partialise function with fixed parameters
    a = 0.5
    b = 2.0
    func  = partial(call_func_ab, ishigami, a, b)
    npars = 3

    # lower boundaries
    lb = np.ones(npars) * (-np.pi)
    # upper boundaries
    ub = np.ones(npars) * np.pi

    # Elementary Effects
    np.random.seed(seed=1023) # for reproducibility of examples
    out = ee(func, lb, ub, 10)

Figuratively speaking, partial passes a and b to the function call_func_ab already during definition so that pyeee can then simply call it as func(x), so that x is passed to call_func_ab as well.

Function wrappers

We recommend to use the package partialwrap, which provides wrappers to use with partial.

    from pyeee.utils import func_wrapper
    args = [a, b]
    kwargs = {}
    func = partial(func_wrapper, ishigami, args, kwargs)

    # screen
    out = eee(func, lb, ub)

There are wrappers to use with Python functions with or without masking parameters, as well as wrappers for external programs.

See the documentation for details:

http://pyeee.readthedocs.org/en/latest/

Installation

The easiest way to install is via pip::

pip install pyeee

See the installation instructions in the documentation for more information.

Requirements:

• NumPy
• SciPy
• schwimmbad
• pyjams

License

pyeee is distributed under the MIT License.
See the LICENSE file for details.

Copyright (c) 2013-2021 Matthias Cuntz, Juliane Mai

The project structure is based on a template provided by Sebastian Müller.

Contributing to pyeee

Users are welcome to submit bug reports, feature requests, and code contributions to this project through GitHub.

More information is available in the Contributing guidelines.