A Python library for parameter screening of computational models using Morris' method of Elementary Effects and its extension of Efficient or Sequential Elementary Effects by Cuntz, Mai et al. (Water Res Research, 2015).
pyeee is a Python library for performing parameter screening of computational models. It uses Morris' method of Elementary Effects and its extension, the 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).
The complete documentation for pyeee is available at Github Pages:
https://mcuntz.github.io/pyeee/
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 as:
from pyeee import screening
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 = screening(ishigami1, lb, ub, 10) # mu*, mu, sigma
print("{:.1f} {:.1f} {:.1f}".format(*out[:, 0]))
# gives: 173.1 0.6 61.7which gives the Elementary Effects mu*.
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]The function for the routines in 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.
We recommend to use our package partialwrap for external executables, which allows easy use of external programs and 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)The easiest way to install is via pip:
pip install pyeeeor via conda:
conda install -c conda-forge pyeeepyeee 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.