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JNumeric provides the functionality for Jython that Numerical Python does for Python (CPython). As the Numerical Python documentation states, it is "...a collection of extension modules to provide high-performance multidimensional numeric arrays to the Python programming language." JNumeric provides the same functionality as the core of Numeric module and aims to provide all of the standard extensions to Numeric module (FFT, LinearAlgebra, RandomArray).
In effect, Numerical Python is a free alternative to commercial solutions such as Matlab with the added bonus of the Python language which can be argue to be much better than what can be found in most commercial solution. You have to try Python to understand!
Why Java? Using Python inside a JVM has advantages because you can embed Python programs inside Java software or vice versa. Whereas mixing C and Python must be done with care by people wide awake, mixing Java and Jython is a no brainer. As far as performances are concerned, expect Jython to be as fast or faster than Python.
One nice application of Jython is to run it inside jEdit, the text editor! Together with JNumeric, this allows you to run sophisticated mathematical scripts in a very convenient setting while remaining portable.
Of course, JNumeric is free software (Python license) and we owe the original codebase to Tim Hochberg.