generated C/C++ code from `pinv`-command gives different result than the command `pinv` itself

I am using Matlab Coder for my Arduino. Inside my Matlab function I use the Matlab-command `pinv`. This Matlab-function is then converted into C/C++ code (let's call it `pinvC`) using the Code Generator from Matlab.

However, I noticed the following. The result of Matlab-command `pinv` inside Matlab function is different to the result of `pinvC`. What is causing this? How can I solve it?

Answer 1

[James Tursa]

How much different? The MATLAB code is calling into BLAS and LAPACK library routines to accomplish this. But the Coder is not using that same library code to generate its results, hence the difference.

[Victor Lam]

The pseudo-inverses are a little different. But after some multiplications the small errors accumulate and the difference is about a factor of 5.

So I tried to compute the pinv beforehand and store it in .mat file and load it inside the function using `coder.load` but then some variables are blowing up to order of 1e3, while they should be below 10.

Could the C/C++ `pinv` version be different, for numerically stability reasons?

[Mike Hosea]

James is correct. Different stability properties induced by PINV per se does not seem likely, but different PINV implementations will issue different numerical perturbations, which might be magnified by how you use PINV.

You might try an experiment perturbing the output of PINV in MATLAB by some units in the last place to explore what your algorithm does with it in MATLAB, i.e. with no code generation involved. Something like:

X = pinv(A);
X = X + randi([-10,10],size(X)).*eps(X)