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Apophenia is an open statistical library for working with data sets and statistical models. It provides functions on the same level as those of the typical stats package (such as OLS, probit, or singular value decomposition) but gives the user more flexibility to be creative in model-building. The core functions are written in C, but bindings exist for Python (and they should be easy to bind to in Perl/Ruby/&c.)
It is written to scale well, to comfortably work with gigabyte data sets or computationally-intensive agent-based models. If you have tried using other open source tools for computationally demanding work and found that those tools weren't up to the task, then Apophenia is the library for you.
To date, the library has over two hundred functions to facilitate scientific computing, such as:
For the full list, click the index link from the header.
Most users will just want to download the packaged version using the giant green button at the SourceForge page linked from the Download Apophenia here header.
Those who would like to work on a cutting-edge copy of the source code can get the latest version (and five years of project history) by cutting and pasting the following onto the command line. If you follow this route, be sure to read the development README in the apophenia directory this command will create.
git clone git://apophenia.git.sourceforge.net/gitroot/apophenia/apophenia
To start off, have a look at this Gentle Introduction to the library.
The outline gives a more detailed narrative.
The index lists every function in the library, with detailed reference information. Notice that the header to every page has a link to the outline and the index.
To really go in depth, download or pick up a copy of Modeling with Data, which discusses general methods for doing statistics in C with the GSL and SQLite, as well as Apophenia itself.
If you're interested, write to the maintainer (Ben Klemens), or join the SourceForge project.