Create a Python function

In this basic example we are going to create a Function object (ie usable in the OpenTURNS context) from a pure Python function.

The pure Python function to wrap must accept a sequence of floats and return a sequence of float.

f(x) = [x_0+x_1+x_2, (x_1-1)*e^{x_0} * x_2]

In [1]:
from __future__ import print_function
import openturns as ot
import math as m
In [2]:
# define a pure Python function from R^3 to R^2
def regularFunc(X):
    x0, x1, x2 = X
    y0 = x0 + x1 + x2
    y1 = (x1 - 1.0) * m.exp(x0) * x2
    return [y0, y1]
In [3]:
# create a Function object from a regular Python function
function = ot.PythonFunction(3, 2, regularFunc)
In [4]:
# evaluate the function on a Point
x = [1.0, 2.0, 3.0]
print('x=', x, 'f(x)=', function(x))
x= [1.0, 2.0, 3.0] f(x)= [6,8.15485]
In [5]:
# evaluate the function on a Sample
xs = [[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]
print('xs=', xs, '\nf(xs)=', function(xs))
xs= [[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]
f(xs)=     [ y0         y1         ]
0 : [    6          8.15485 ]
1 : [   15       1310.36    ]
In [6]:
# now we can use the Function object services such as the gradient
function.gradient(x)
Out[6]:

[[ 1 8.15485 ]
[ 1 8.15485 ]
[ 1 2.71828 ]]

Performance issues

When this function is used internally to evaluate a Sample, it loops over its points. This requires many memory allocations; moreover this loop is done in Python, it may thus be slow if Sample is large. We can define a function to operate on a Sample, and return a Sample.

For maximum performance, argument is in fact not a Sample, but a wrapper object which contains a pointer to data. When using Numpy arrays without copies and loops, performance is similar to C code, but Python definition is somewhat convoluted; please refer to Numpy documentation to learn how to efficiently define such functions.

In [7]:
# define the same function on a Sample
import numpy as np
def regularFuncSample(X):
    # Create a numpy array with the contents of X without copy
    xarray = np.array(X, copy=False)
    # Get columns as vectors, there is also no copy
    x0, x1, x2 = xarray.T
    # Allocate a numpy array to store result
    y = np.zeros((len(X), 2))
    y[:,0] = x0 + x1 + x2
    y[:,1] = (x1 - 1.0) * np.exp(x0) * x2
    return y
In [8]:
# create a Function object from a regular Python function
functionSample = ot.PythonFunction(3, 2, func_sample=regularFuncSample)
In [9]:
# evaluate the function on a Sample
print('xs=', xs, '\nf(xs)=', functionSample(xs))
xs= [[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]
f(xs)=     [ y0         y1         ]
0 : [    6          8.15485 ]
1 : [   15       1310.36    ]
In [10]:
# evaluate the function on a Point
print('x=', x, 'f(x)=', functionSample(x))
x= [1.0, 2.0, 3.0] f(x)= [6,8.15485]

The most efficient solution is to provide evaluations both on Point and Sample. This requires two Python function definitions, but if your code takes a lot of time, you should consider this option.

In [11]:
functionFast = ot.PythonFunction(3, 2, func=regularFunc, func_sample=regularFuncSample)