[Math] Basic software libraries for numerical analysis using modern programming languages

Question

I'm looking for a software library with a scope similar to "numerical recipes", but implemented in a modern programming language. "Modern" in this context means to me: object oriented (not C or Fortran), running in a virtual machine with garbage collection (not C++), and with support for functional programming.
Examples therefore would be: F#, C# from the .NET framework, Scala and to a lesser extend Java (no functional programming yet).

"Scope" means that it should cover all algorithms that are taught in, say, a general, one or two year(s) long introduction to numerical analysis, starting with linear algebra, up to partial differential equations and stochastic processes.

In addition I am interested if any research group using high performance computing uses a language that fits the description, and if not, why not. It is "common knowledge" in the software industry that one should no longer worry about performance problems of languages running in a virtual machine compared to languages compiled directly to machine code, e.g. Java versus C++. Any experience from high performance computing that affirms or contradicts this would be interesting to me, too.

Addendum after reading the first three answers (rather than commenting them individually): My motivation for asking about these "modern" programming language is this: It takes some effort to learn a programming language, much commercial software is written in Java, often not because Java is designed for the kind of problem people have to solve, but because there are many programmers out there that know Java, there is a big open source community, and, finally, "nobody gets fired for choosing Java" (paraphrasing "nobody gets fired for buying IBM"). This outweighs the fact that Java is often clearly not the best choice from a pure language point of view.
A software library in a "modern" programming language could attract more people (maybe more contributors if it is open source), for this reason, than a library in a much better suited, but less known, programming language.

Edit: To a certain extend the Sage project and software is what I was looking for, although it employs Python as a higher level language which I don't think is a good choice. (http://www.sagemath.org/)

Answer 1

Try http://numpy.scipy.org/ (assuming you're fine with an interpreted language -- otherwise, there is a python compiler, but I know very little about it).

Why languages like Java are not widespread? Well, my view on the subject is the following. You have two kinds of people who do numerical mathematics:

• Some need to squeeze every instruction of performance out of their mission-critical software, and naturally they are worried about aliasing, garbage processing, cache misses. Thus they use plain C or even Fortran, and use all the voodoo they know to make it run faster.
• Some don't, as they develop algorithms for testing/research only, or where the sheer computing time is not the bottleneck. They generally use Matlab, since it is much easier to work with, and as long as you avoid (or recode in C) tight for loops has a reasonable performance.