Linear algebra methods in SciPy

SciPy offers a large range of methods from numerical linear algebra in its scipy.linalg module. Many of these methods are Python wrapping programs from LAPACK, a collection of well-approved FORTRAN subroutines used to solve linear equation systems and eigenvalue problems. Linear algebra methods are the core of any method in scientific computing, and the fact that SciPy uses wrappers instead of pure Python code makes these central methods extremely fast. We present in detail here how two linear algebra problems are solved with SciPy to give you a flavour of this module.

Solving several linear equation systems with LU

Let A be an n × n matrix and b₁ , b₂ , ..., b_k  be a sequence of n-vectors. We consider the problem to find n vectors x_i such that:

We assume that the vectors b_i are not known simultaneously. In particular, it is quite a common situation that the i^th problem has to be solved before b_i+1 becomes available.

LU factorization is a way to organize...