sparse-linear-algebra

Numerical computation in native Haskell

TravisCI :

This library provides common numerical analysis functionality, without requiring any external bindings. It is not optimized for performance (yet), but it serves as an experimental platform for scientific computation in a purely functional setting.

Algorithms :

• Iterative linear solvers

  • Conjugate Gradient Squared (CGS)

  • BiConjugate Gradient Stabilized (BiCGSTAB) (non-Hermitian systems)

• Matrix decompositions

  • QR factorization

• Eigenvalue algorithms

  • QR algorithm

  • Rayleigh quotient iteration

• Utilities : Vector and matrix norms, matrix condition number, Givens rotation, Householder reflection

• Predicates : Matrix orthogonality test (A^T A ~= I)

This is also an experiment in principled scientific programming :

• set the stage by declaring typeclasses and some useful generic operations (normed linear vector spaces, i.e. finite-dimensional spaces equipped with an inner product that induces a distance function),

• define appropriate data structures, and how they relate to those properties (sparse vectors and matrices, defined internally via Data.IntMap, are made instances of the VectorSpace and Additive classes respectively). This allows to decouple the algorithms from the actual implementation of the backend,

• implement the algorithms, following 1:1 the textbook [1]

License

GPL3, see LICENSE

Credits

Inspired by

• linear : https://hackage.haskell.org/package/linear
• sparse-lin-alg : https://github.com/laughedelic/sparse-lin-alg

References

[1] : Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., 2000