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Description:

pyeee 4.1.12

A Python library for parameter screening of computational models using
the extension of Morris’ method of Elementary Effects called Efficient
or 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 the extension of Morris’ method of
Elementary Effects of so-called Efficient or Sequential Elementary
Effects published by
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.
pyeee can be used with Python functions but also with external
programs, using for example the library partialwrap. Function
evaluation can be distributed with Python’s multiprocessing module
or via the Message Passing Interface (MPI).

Documentation
The complete documentation for pyeee is available at Github Pages:

https://mcuntz.github.io/pyeee/

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 using, for example,
the Python library pyjams, giving the Elementary Effects (mu*):
from pyjams import ee

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(ishigami1, lb, ub, 10) # 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, returning a logical ndarray with True for the informative
parameters and False for the uninformative parameters:
from pyeee import eee

# screen
np.random.seed(seed=1023) # for reproducibility of examples
out = eee(ishigami1, lb, ub, ntfirst=10)
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 eee
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_ishigami(func, a, b, x):
return func(x, a, b)

# Partialise function with fixed parameters
a = 0.5
b = 2.0
func = partial(call_ishigami, 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 = eee(func, lb, ub, ntfirst=10)
Figuratively speaking, partial passes a and b to the
function call_ishigami already during definition so that eee
can then simply call it as func(x), where x is passed to
call_ishigami then as well.

Function wrappers
We recommend to use our package partialwrap for external
executables, which allows easy use of external programs and also their
parallel execution. See the userguide for details. A trivial
example is the use of partialwrap for the above function wrapping:
from partialwrap import function_wrapper

args = [a, b]
kwargs = {}
func = partial(func_wrapper, ishigami, args, kwargs)
# screen
out = eee(func, lb, ub, ntfirst=10)

Installation
The easiest way to install is via pip:
pip install pyeee
or via conda:
conda install -c conda-forge pyeee

Requirements

NumPy
SciPy
schwimmbad
pyjams

License
pyeee is distributed under the MIT License. See the
LICENSE file for details.
Copyright (c) 2019-2024 Matthias Cuntz, Juliane Mai
The project structure is based on a template provided by Sebastian Müller.