A Python library providing parameter screening of computational models using the Morris method of Elementary Effects or its extension of Efficient Elementary Effects by Cuntz, Mai et al. (Water Res Research, 2015).
Project description
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:
License
pyeee is distributed under the MIT License.
See the LICENSE file for details.
Copyright (c) 2013-2020 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.
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