Quickstart#

pyeee: 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).

About pyeee#

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) mpi4py.

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 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 61.7

which 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]

Python function with extra parameters#

The function for 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.

Function wrappers#

We recommend to use our package partialwrap for external executables, which allows easy use of external programs and their parallel execution. See the User Guide 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#

License#

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

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

Quickstart

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