Re: Library for matrix operations? (eigenvalues, pseudoinverse)

[CEL]

So, that depends a bit on what you want to do:

These operations are classically implemented in a library called
LAPACK, which is really mature (and, it's written in Fortran90). You
use it through C++ wrappers like "IT++" or "Armadillo".

Be a bit careful though. The usual way of defining the pseudoinverse of
a martrix with lin. indep. columns is 

A⁺ = (A* A)⁻¹ A*

(with * being hermitian transposition).

One of the relatively eternal laws of numerical math seems to be

"you DON'T want to calculate that matrix inverse; it's way more work
than finding the solution to a system of linear equations directly (and
potentially much worse in terms of accuracy[2, (1.2) on p.2])"

even for relatively small (A'A). Therefore, other methods exist, which
tend to be faster, and can, under some assumptions, be more stable[1];
one is based on the singular value decomposition

       A = U𝛴V*

TL;DR: LAPACK wrapped for your language of choice, e.g. IT++ has
eigenvalue, and singular value decompositions. You should find the
Pseudoinverse through the singular value decomposition.

Best regards,
Marcus

[1]https://www.johndcook.com/blog/2018/05/05/svd/
[2] S. Rump: "Inversion of Extremely Ill-Conditioned Matrices
in Floating-Point" http://www.ti3.tuhh.de/paper/rump/Ru08a.pdf

On Thu, 2020-01-16 at 20:57 -0800, Laura Arjona wrote:
> Hi all,
> 
> Is there any library to use in gnuradio for algebra operations, such as 
> matrix eigenvalues, and pseudoinverse? Or I'd need to code them myself in C++?
> 
> I need to integrate those operations into my OOT C++ blocks.
> 
> Thanks for your time
> 
> Best
>

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