pyeee 4.1

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)