Examples

This is the list of the different examples that shows how to use the affapy library. The examples 1 to 5 are inspired by the libaffa library which is a C++ Affine Arithmetic library.

Affine example: Basic usage of Affine module

Interval example: Basic usage of Interval module

Conversion example: Conversion between IA and AA

Precision example 1: Use of precision module with affapy

Precision example 2: Use of precision module with decorators

Example 1

A simple example of using the lib

This example is a simply way to use the affapy library.

Example 2

Time performances between AA and IA model

This example shows the time performances between AA and IA. It permorms calculations on the following function:

\[x_1, x_2 \mapsto 1 + (x_1^2 - 2)x_2 + x_1x_2^2\]

The result of this example is that AA is slower than IA.

Usage:

python3 example5.py [lbound1] [ubound1] [lbound2] [ubound2] [boxn]

  • lbound1: lower bound of the interval 1 (default: 10)

  • ubound1: upper bound of the interval 1 (default: 100)

  • lbound2: lower bound of the interval 2 (default: 10)

  • ubound2: upper bound of the interval 2 (default: 100)

  • boxn: number of boxes (default: 1000)

Example 3

Underflow demonstration

This example shows that with a little uncertainty, the model of AA can return a huge interval after calculations.

Example 4

Comparison AA vs IA

We consider the function:

\[\frac{sin(x)^2 cos(x) - 4}{\sqrt{x}}\]

We consider the interval [lbound, ubound] (default: [1, 6]) and a subdivision of this interval containing n boxes (default: 12). The function is evaluated for each box with AA and IA. The result is plotted using matplotlib.

Usage:

python3 example4.py [lbound] [ubound] [boxn]

  • lbound: lower bound of the interval (default: 1)

  • ubound: upper bound of the interval (default: 6)

  • boxn: number of boxes (default: 12)

You need to install matplotlib and numpy to run this example.

_images/example4.png

Output of example 4:

  • in blue: the function

  • in yellow: IA

  • in orange: AA

Example 5

Comparison AA vs IA

We consider the function:

\[\frac{\sqrt{x^2 - x + \frac{1}{2}}}{\sqrt{x^2 + \frac{1}{2}}}\]

We consider the interval [lbound, ubound] (default: [0, 5]) and a subdivision of this interval containing n boxes (default: 60). The function is evaluated for each box with AA and IA. The result is plotted using matplotlib.

Usage:

python3 example5.py [lbound] [ubound] [boxn]

  • lbound: lower bound of the interval (default: 0)

  • ubound: upper bound of the interval (default: 5)

  • boxn: number of boxes (default: 60)

You need to install matplotlib and numpy to run this example.

_images/example5.png

Output of example 5:

  • in blue: the function

  • in yellow: IA

  • in orange: AA