The Eigen C++ template library is a great environment for matrix computing; it is fast, reliable, extensive, and well-documented. It is also completely free, and does not rely on any external dependencies. Unfortunately for AutoIt users, the term “template library” implies that any functions you call are only instantiated upon compilation (in C++). That means there's nothing to hook into.
To make Eigen ’s most important functionality directly accessible from within AutoIt scripts (version 3.3.12+, download it here), I developed the Eigen4AutoIt environment. It runs on Windows and under Wine also on Linux.
>Download the latest version
It consists of:
an AutoIt library of wrapper functions that contain extensive bounds checks, matrix management, file I/O, type conversion, precision and debugging control, and two-way data exchange with files and native AutoIt arrays;
2) Eigen-wrapper dlls (EigenDense.dll, EigenDense_Debug.dll)
re-maps matrices created in AutoIt as Eigen Matrix objects, then calls Eigen’s powerful core functions; the single-precision part of the C++ source code I wrote is included in the bundle (the double-precision alternative just duplicates this with different memory mappings and variable types). The basic functions consist of a single Eigen call; decompositions and statistics are more involved.
3) Additional materials:
the user-interactive, animated Function Selector tool
three libraries of scientific and mathematical constants
Large (.chm) Help file
Quickstart Manual (11-page pdf, updated)
Tutorials (Basics, Slicing & Dicing, regression, PCA, multi-processing)
none of this is part of Eigen's own distribution
you only need this bundle; you do not need to install Eigen.
How it works:
No matrix content is ever transferred, only memory pointers, meaning computations in AutoIt are virtually as fast as in Eigen’s native environment, with the added advantage of not having to be compiled first. The drawback is that Eigen's native ad-hoc expression templates (and their internal optimisations) cannot be exploited here; you have to construct your operations with the basic building blocks. These provide matrix creation, I/O, cellwise operations, reduction, multiplication, transformation, decomposition (LU, Householder, Choleski, and Jacobi SVD; these include general linear solvers) and a small statistics module by yours truly.
Possible future expansions:
I haven't added support for Eigen's Geometry module (useful in 3D game engines, CAD, etc), and will consider this only if the community expresses sufficient interest and support for these additions. (I don't use this myself at the moment.) I have no intention of ever implementing support for sparse matrices (their memory management is a total buttsore I can do without, and anything you compute sparse can also be obtained by dense computation, it just takes longer). GPU parallelisation is still an open question I need to look into at some point. At least the Help file is already done:
IMPORTANT: Posting Rules for this thread:
1) Do not post or PM me any matrix-, maths-, or Eigen-related questions. Eigen has its own User Forum for that (or try math.stackExchange.com). I am not your maths guru! If you post such questions, I will either ignore your post or remind you of this rule.
2) Do not post or PM me your data sets and/or non-working Eigen4AutoIt scripts; I will not analyse your data or fix your scripts for you! There are many reasons why a linear algebra procedure might fail to produce the answer you expect. You are wielding great mathematical power here, so exploit the fantastic internet resources at your fingertips and learn how to use it. To get you started, I've listed a few video tutorials and other helpful materials in the header remarks of Eigen4AutoIt.au3. Also check out the test scripts, the Tutorials, and the Help file.
3) I do warmly welcome all of the following:
remarks, advice, suggestions for improvements, encouragement, cash;
bug reports re. the Eigen4AutoIt interface (individual functions that don't work the way they should) and/or the associated dll code (ditto);
your own working Eigen4AutoIt templates of general use that you'd like to see implemented in a future release.
Regarding that last item, have a look at my PCA tutorial. After the step-by-step stage I summarise the entire procedure in a "mini script" of Eigen4AutoIt calls. Then I introduce the two internal PCA functions I developed, which replace that script with two simple calls. You can do the same thing, and submit your own functional Eigen4AutoIt script in this thread. If I consider it of general use and can implement it, it may become a new Eigen4AutoIt function in the next release (with source acknowledgement, of course). This means that you'd get a precompiled dll version of your script that will likely run faster and be simpler to call. Thereby this thread would become an Eigen4AutoIt Example Scripts mini forum. It's just a thought.
>Download the latest version (uncompressed size: 34.2 MB)
How to Install
You need AutoIt version 3.3.12 or later. Extraction (with 7-zip) creates subdirectory Eigen4AutoIt, where you'll find Eigen4AutoIt.au3. Open it, navigate to the top of #region Globals, find global variable $EIGEN_DLLPATH, and copy/paste the full absolute path (without trailing backslash) where the Eigen4AutoIt dlls are located on your machine. Save the script, open the first tutorial ("intro"), and start it. This shows basic matrix I/O and mode switching (single versus double precision, debugging versus computing mode). If that runs, you're in business.