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https://github.com/leftaroundabout/linearmap-family

Purely-functional, coordinate-free linear algebra
https://github.com/leftaroundabout/linearmap-family

functional-analysis haskell linear-algebra

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Purely-functional, coordinate-free linear algebra

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README 

        
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This project has two goals:



### To give Haskell a competitive, _native_ linear algebra library



That is, a library that supports:



1. Basic vector operations ✓

2. Efficient linear maps ✓

3. Solving linear equations

  1. Inversion of finite-dimensional, linear isomorphisms (full-rank matrices) ✓

  2. Least-squares solution to under/overdetermined problems (?)

  3. Fast iterative methods (for large sparse systems, e.g. conjugate gradient) ✗

4. Eigenvalue problems ✓

5. Singular value decomposition ✗



At the moment, the only Haskell libraries that offer all of that appear to be

[hmatrix](http://hackage.haskell.org/package/hmatrix) and [eigen](http://hackage.haskell.org/package/eigen),

which use bindings to the [GSL](https://www.gnu.org/software/gsl/) (C)

and [Eigen](http://eigen.tuxfamily.org/index.php?title=Main_Page) (C++) libraries.



- Eigen is a great project that uses the C++ template system for both an elegant interface and nice optimisations.

  However, this interface doesn't really translate that nicely over to Haskell. The C interface layer necessary

  forgets much of the template niceties.

- GSL is extremely comprehensive and well-suited for binding to other languages, in particular dynamic languages.

  However, it's a bit of a messy _big collection of all kind of algorithms_, and not exactly the fastest library,

  which adds to the general overhead of calling to external code with C-marshalled memory.



### To get rid of those pesky matrices



Linear algebra isn't really about matrices. Vectors aren't _really_ arrays of numbers.



What LA is really about are _points in vector spaces_, and ultimately geometric relations between them.

And many interesting spaces aren't even finite-dimensional.



Regardless of whether matrices are used for the internal operations – and in fact, it's not so clear if

this is always a good idea! – matrices shouldn't dominate the API of a linear algebra library.

Haskell has managed to bring a lot innovation to the world of programming languages.

It can nicely work with infinite, lazy data structures.

Hopefully it can also make a bit of a revolution in the field of linear algebra!