Gitlab repository https://gitlab.u-angers.fr/cours/interval_analysis_student

INTERVAL ANALYSIS - Master SDS course

Planning of the course

TD0 : Intervals and interval arythmetics

• What is an interval : https://youtu.be/v72MPKvh6iA
• Operators : https://youtu.be/0HXLAcqmPOs
• Examples : https://youtu.be/gQ4VZkf7BE4

Complete the Interval class (interval/interval.py)

• Elementary functions: https://youtu.be/V5gTFTNh3Go
• Elementary functions examples : https://youtu.be/KDJQX2CyGXc

Implements the interval functions (interval/ifunctions.py).

Note that the files interval.py and ifunctions.py will be used for all the other exercises and completed step by step. No need to implements all the functions at once.

TD1 : Function evaluation

• Boxes : https://youtu.be/ZJPl1d5wnPY
• Width : https://youtu.be/V2BjOnylhoI
• Subpaving : https://youtu.be/R-iHsOh6Dv8
• Inclusion functions : https://youtu.be/dt5Zg9Sp1K8
• Monotonicity : https://youtu.be/C5BwfXP0lns
• Convergence : https://youtu.be/cBcBh8cayx0
• Natural inclusion function : https://youtu.be/IEzCgW2z7Es
• Minimal inclusion function : https://youtu.be/uX-80OCICTk

Complete the file TD1/work2do.py

Here is the expected result :

TD2 : SIVIA

• What is set inversion : https://youtu.be/NI370RrYNYI
• Example : https://youtu.be/OFxbGN7hzZI
• Inclusion tests : https://youtu.be/kNbIPn64WKM
• SIVIA : https://youtu.be/ZrjiYjgCYMs
• Parameter estimation : https://youtu.be/Uq3VGMmRSXk

Complete the file TD2/work2do.py

Here is the expected result :

TD3 : Contractors

• Motivations : https://youtu.be/-sAUCuUx36Q
• What is a contractor : https://youtu.be/e6NYzopRi8o
• Properties : https://youtu.be/dbdwTzEPgs0
• Example : https://youtu.be/SXlIMIYI2Hs
• Contractor for z=x+y : https://youtu.be/FkzKoQ0vEGI
• For primitive equations : https://youtu.be/qRjOYqJOIXA
• Decomposition : https://youtu.be/sDEjmM3-2cU
• Forward/Backward : https://youtu.be/aZpPD1Wbmv8

Complete the file TD3/work2do.py

Here is the expected result :

TD4 : Distance contractor

Complete the file TD4/work2do.py

Here is the expected result :

TD5 : SIVIA + Contractors

Complete the file TD5/work2do.py

Here is the expected result :

TD6 : Mobile robot localization

The introduction to that TD is in TD6_documents/localization.pdf

Complete the file TD6/work2do.py