Matrix Inversion and Lapack

General Discussion
1

Hello FreeFem Community,

I’m looking to invert a square matrix A in order to solve the problem Ax=b. The problem is, this matrix A, has no reason to be invertible, so when it’s the case, I would like to compute the more-penrose pseudoinverse solution to the problem : min_{Y\in R^{n\times n} ||AY-I_n||.
I was going through the lapack FreeFem sources on Github (FreeFem-sources/lapack.cpp at 897a6ed0606d497b043b593e0d7db86448731889 · FreeFem/FreeFem-sources · GitHub) and found that we can call on the lapack function dgelsy from Freefem, which would take care of this.
I can’t seem to make it work though, as the following example returns an error message :
" Intel MKL ERROR: Parameter 5 was incorrect on entry to DGELSY."

load “lapack”

real[int,int] A=[[1,1,1],[0,2,0],[1,1,1]];
real[int,int] B=[[1,0,0],[0,1,0],[0,0,1]];

dgelsy(A,B);

Can anyone please confirm if my calling of the function is correct? and in case dgelsy is not the way to go, are there other ways to compute pseudo-inverses?

Thank you so much for your time and help,

Salah

2

This is a bug, thank you for your report. It is fixed here: Wrong LDA in call to dgelsy. · FreeFem/FreeFem-sources@c508630 · GitHub. Now, you’ll get the proper B:

3 3
	 0.25 -0.25 0.25
	 4.394057034e-17 0.5 1.259510683e-16
	 0.25 -0.25 0.25
3

Thank you so much for your quick reply,

I am not familiar with how Github works, but my feeling is that I would have to rebuild FreeFem (installed initially through the dmg image) to get the changes, and inform the university to rebuild it on the cluster. I wanted to ask before I mess with my installation files if just correcting my source file would do the trick?

Salah,

4

If you are using the .dmg, then yes, you’d need to rebuild FreeFEM from the sources (there is probably a release coming up soon though if you are not in a rush).
For the installation on the cluster, the admin can just fetch the file on GitHub, and then recompile only the plugin.

$ cd FreeFem-sources/plugin/seq
$ ./ff-c++ -auto lapack.cpp

Assuming lapack.cpp as been overwritten by the latest version from GitHub. Then, the corresponding library (lapack.so) must be copied in the installation directory.

5

Thanks again! Have a good day.

Salah