How to calculate response function from measurements - Overdetermined equitation

Hi there,

my problem is finding a solution for a (complicated) A*X = B matrix problem.

However, as all values are derived from measurements multiplying with the inverse Matrix does not produce any useful results:

I got an input function a, the shape defined by 41 measured (so not totally exact) x,y pairs (all y creating a vector a) and an - unknown - response function (41 x,y' pairs, y' creating vector x).

A further measurement then creates a single value a*x = b0 (the response of the system).

I now do have measurements of 252 different input functions/vectors, creating an overdetermined system A*x = B with A being a 252*41 matrix and B being a 252*1 vector of measurement results. This theoretically should give me a solution vector x (1*41), which would be my response function.

Unfortunately putting this values into a standard linear least squares calculator produces just nonsense and I was hoping Matlab could come up with something more sophisticated, however I'm not sure what would be the best approach (new to Matlab).

The response function isn't a simple logarithmic function or so, the only help is possibly(?) that all numbers are >0.

Any help with this would be greatly appreciated! :)

Answer 1

[Star Strider]

Taking the inverse is rarely the best approach. Use the mldivide,\ function or operator for best results. If your matrices are sparse, use the lsqr function.

[MLUGCC]

Hi there,

Thanks a lot for your reply - I tried this, however the results are unfortunately very similar to using a standard linear least squares calculator. I think the problem is that I cannot define that all the solutions for x should be values > 0. It;s an overdetermined equitation, so there is no exact solution and once it's using a negative value for one part of x, all subsequent values are wrong, too.

Is there a way to limit the possibles values within x?

Thanks a lot for your help again!

[Star Strider]

My pleasure.

If ‘x’ is constrained to be >0, use the lsqnonneg function. This is part of MATLAB and does not require any Toolboxes.

[MLUGCC]

Thanks a lot again - yes, that was what I was looking for (new to Matlab)!

[Star Strider]

My pleasure!

If my Answer solves your problem, please Accept it!

[MLUGCC]

Hi there and sorry - new here, so I didn't realize how that works... done! :)

[Star Strider]

Thank you!