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

[Christoph Mayer]

Hi Laura, Marcus,

for small processors (e.g. the beaglebone, used for KiwiSDR GPS
position solutions) I have adapted an old library originally developed
by NIST,
https://github.com/hcab14/TNT_JAMA

Best regards

Christoph

On Thu, Jan 16, 2020 at 10:32 PM Müller, Marcus (CEL) <address@hidden> wrote:
>
> 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
> >