Merge pull request #34 from jasonmccampbell/add-math-page

Content for the Math stack page

index.html

@@ -83,7 +83,7 @@ <h4 class="first">Software stacks</h4>
     </p>
     <ul>
       <li><a href="webstacks/index.html">Web Stacks</a></li>
-      <li>Math Stacks</li>
+      <li><a href="math/index.html">Math Stacks</a></li>
       <li>Big Data Stacks</li>
       <li>Scalable Compute Stacks</li>
       <li><a href="games/index.html">Game and Visualisation stacks</a></li>

math/index.md

@@ -8,22 +8,94 @@ This page provides information about using F# for numerical computing.
 
 ### Why F#?
 
-Why is F# great for solving numerical problems...
+F# is particularly well suited to numerical programming, compared with many
+mainstream languages, because of its functional-first design. Functional programming
+is rooted in the development of lambda calculus and focuses on the definition
+of functions to transform data, as opposed to the manipulation of program state common
+with other popular paradigms such as object-oriented programming. 
+As such, the functional style is often a more natural translation of the underlying
+mathematics.
+
+Performance of the code and the developer are two big requirements for numerical computing. 
+The computing tasks are often CPU-intensive so the language must be efficient in this 
+regard. F# runs on the [Microsoft .NET Common Language Runtime (CLR)](http://msdn.microsoft.com/en-us/library/ddk909ch(v=vs.71).aspx)
+on Windows and on [Mono](http://www.mono-project.com/Main_Page) on Windows, Linux, and Mac OS. 
+Both of these environments include high-performance 
+[Just-In-Time compilers](http://en.wikipedia.org/wiki/Just-in-time_compilation), which means the 
+code is compiled to native code (high-performance) on-demand. The Mono environment additionally 
+provides easy access to the [x86 SIMD](http://www.counity.at/blog/2011/hardware-acceleration-in-net-part-1-1-mono-simd-introduction/)
+(Single Instruction, Multiple Data) commands which provide substantial speed-ups
+for certain types of processing.
+
+Being built on the .NET and Mono runtimes, integrating highly optimized, 
+native code libraries (C/C++, FORTRAN, etc) such as the Intel [Math Kernel Library (MKL)]
+(http://software.intel.com/en-us/intel-mkl) is straightforward. The [P/Invoke]
+(http://en.wikipedia.org/wiki/Platform_Invocation_Services) system allows managed code
+to call directly into native libraries and helps marshal data between environments.
+
+Performance of the developer is at least as critical as the performance of the resulting
+code. F# is a very expressive, concise language with ready access to libraries of common
+algorithms and data structures. The rest of this page surveys some of the most common
+numerical computing libraries available for F#.
+
 
 ### Open-source libraries
 
 Here are some open source libraries:
 
- * Math.NET
+ * [ILNumerics](http://ilnumerics.net/) - an open- or closed-source library offering high-
+   performance numerical algorithms as well as charting and plotting capabilities. The library
+   is based on efficient, general-purpose array classes implementing vectors, matrices, and
+   n-dimensional arrays. Provided algorithms include standard linear algebra transforms,
+   a high-performance Fast Fourier Transform (FFT) library, and a collection of sorting 
+   and machine learning algorithms. Plotting is based on OpenGL and supports both 2d and 3d
+   plots. ILNumerics supports .NET 4.0 as well as Mono (recommend 2.10 or above). Licensing 
+   is GPLv3 or commercial (paid) license.
+
+  * [Math.NET Numerics](https://github.com/mathnet/mathnet-numerics) Math.NET Numerics provides
+   a large collection of common algorithms needed in science and engineering, including
+   linear algebra, probability models, random numbers, interpolation, and FFT's. This package
+   also includes commonly used data structure such as sparse and dense vector and matrix
+   implementations. The libraries are managed code with wrappers available for optimized native 
+   implementations such as MKL and ATLAS. License: MIT/X11
 
 
 ### Commercial libraries
 
 Here are some commercial libraries:
 
- * StatFactory FCore
- * QuantAlea
- * Flying Frog
- * etc..
+ * [Extreme Optimization Numerical Libraries for .NET](http://www.extremeoptimization.com/) - 
+   a set of three libraries focused on vector and matrix processing, 
+   linear algebra methods, and statistics functions. The library includes a large selection of 
+   standard algorithms from matrix factorization, function optimization, numerical integration, 
+   K-means clustering, and PCA (principal component analysis). Options are provided to run  
+   using pure managed code for portability or to utilize highly tuned native code for 
+   additional performance. Extreme Optimization supports .NET 3.5 and 4.0 (2.0 version 
+   available) and execution on Mono.
+
+ * [Microsoft Solver Foundation (MSF)](http://msdn.microsoft.com/en-us/devlabs/hh145003.aspx) -
+   a .NET package for designing and optimizing mathematical models. MSF provides built-in
+   solvers for linear- and quadratic-programming, as well as non-linear models based on Nelder-Mead
+   or quasi-Newtonian algorithms. Models can be built using the Optimization Modeling Language
+   (OML) or using C# or F# and other .NET languages. MSF version 3.1 is available in a free
+   Express Edition or via an MSDN subscription.
+
+ * [StatFactory FCore](http://www.statfactory.co.uk/) - a high-performance numerical
+   library supporting both CPU and GPGPU computing. The library includes multi-dimensional
+   dense matrix and 2d sparse matrix support, standard linear algebra routines, and summary
+   statistics. The library provides options to run both 100% managed code or to use optimized 
+   native libraries such as MKL.
+
+ * [F# for Numerics](http://www.ffconsultancy.com/products/fsharp_for_numerics/) - 
+   a collection of numeric algorithms including matrix operations, optimization and 
+   interpolation functions, 1d and 2d FFTs, and pseudo-random number generation. The library uses 
+   the standard F# PowerPack Matrix for compatibility. F# for Numerics supports .NET. 
+   The library is available from [Flying Frog Consultancy](http://www.ffconsultancy.com/).
+
+ * [F# for Visualization](http://www.ffconsultancy.com/products/fsharp_for_visualization/index.html) -
+   a 2d and 3d vector graphics library with a native F# interface.  The
+   package provides interactive plotting from within Visual Studio and support for generating
+   animations. F# for Visualization supports .NET. The library is
+   available from [Flying Frog Consultancy](http://www.ffconsultancy.com/).