8 posts in this topic
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 and Mac (Ubuntu, Debian, Fedora, and MacOS supported by WineHQ), and SUSE, Slackware, and FreeBSD supported by the distros).
>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, and precision control, and two-way data exchange with files and native AutoIt arrays;
2) Eigen-wrapper dlls (EigenDense.dll, EigenDense_x64.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,, integer, and complex alternatives just duplicate 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 and MatrixViewer tools the MatrixFileConverter to read/write E4A matrices from/to .csv ASCII, Excel, and Xbase files. three libraries of scientific and mathematical constants online Help Large (.chm) Help file Quickstart Manual (11-page pdf, updated) Test suite Tutorials from Basics to Advanced Please note:
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.
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: 29 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.ini. Open it, 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 ini file, open the first tutorial ("intro") in Scite, and start it. This shows basic matrix I/O and mode switching (single versus double precision). If that runs, you're in business.
The Eigen4AutoIt environment (thread is here:
online Help is here) allows you to do matrix I/O (memory & files), matrix arithmetic, transformation, and decomposition, solve systems of linear equations, and perform advanced statistics, all at either single or double precision. Most functions can act on real or complex matrices (or the latter's real/imaginary parts separately). Much of the actual complexity of using Eigen in its native C++ environment has been hidden for AutoIt users, through extensive bounds and error checks, an intuitive function-naming convention, a large help file, and detailed tutorials and test examples.
This library allows you to perform fast matrix operations on large numerical data sets, using special matrix variables and simple AutoIt wrapper functions. These wrappers call C++ wrappers in the dlls (also written by RTFC, source included). The dlls in turn re-map AutoIt memory and call one or more Eigen functions. All operations are memory pointer-based and act directly on the matrices created in your AutoIt script, obviating the need for data transfers. Both 32-bit and 64-bit environments are supported; in x64, matrices can be any size that fits into virtual memory.
RunningStats calculates running (moving) statistics: Standard Deviation, Variance, and Mean . The single function _RunningStats(), queries, clears, restores, or adds to the running statistics.
Example.au3 adds 7 samples of data to running statistics and displays the results using _ArrayDisplay().
Example-Persistent-Storage.au3 adds the first 6 samples to the running statistics and stores the results in an INI file. The data is read from the INI file and restored to the running statistics. The 7th sample is added and the results displayed, matching the results from Example.au3.
Credits: John D. Cook for his article "Accurately computing running variance" at http://www.johndcook.com/blog/standard_deviation/
I started writing this UDF a while ago, so I decided to share it here.
This is an UDF full of advanced mathematical functions. It allows to work with primes, create number sequences, interpolate, calculate values of functions like Riemann zeta.
Full list of functions:
Hello friends! I have been working on an encryption algorithm in autoit as a proof of concept for some time now. Basically the algorithm uses a progressive recursion to encode data inside a matrix using a key that changes according to the date-time of the system, which is extracted from a larger key array. Recently after a drive failure, I lost the source and had to start from scratch, now I can't quite get it working the way it was before, and I can't see what I'm doing wrong, if anyone who understands matrix math or encryption could help I would much appreciate it. The problem is that the values returned by the decryption (extraction) process are way too big.
I have figured out the solution to my problem, it was a typo, please disregard this thread.
I will post my project into example scripts when it's ready.