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Working Wonders with ADPL Math – Ep 03: Data Reduction Fundamentals

What are we doing here?

This post may come as a surprise to many, as ANSYS APDL is at its core a tool aiming at simulating physical phenomena so that «data reduction», being more oriented to the data analysis community, might sound a bit out-of-place.

As a matter of fact, being a numerical tool, it does have ubiquitous applications and -as we shall shortly see- it can be also beneficial to down-to-earth, goal-oriented folks like say -engineers.

Browsing the APDL Math commands, I started being curious about the *COMPRESS command, which I had so far ignored: as it was, I had assumed that it merely was a functionality aimed at compressing sparse matrices, i.e. a lossless procedure, detecting and eliminating near-zero entries. And yes, that’s exactly what it can do, but there is more to it: it will also compress data using Singular Values Decomposition (SVD), which is probably one of the most important numerical tool there is. This is not the place to provide too much background on the topic, and for those interested there is a wealth of books and articles on the subject, one prominent contribution being the online videos by Steven Brunton and Nathan Kuntz, see [1] for an introduction.

Before discussing applications, I will briefly introduce the topic of SVD, how it relates to data compression, and which APDL Math capabilities we need to use.