2 unknowns in matching datasets

Hello everyone.

I have 3 sets of data and need to find "a" and "b":

Y1=a*Y2+b*Y3;

there are 2 unknowns so I would need 2 equations to solve this but maybe there is a way to solve this as is? Help please.

Thank you

Answer 1

[DGM]

I'm sure there are other ways, but:

load datasett.mat

% omit nans
nanmask = ~(isnan(Y1) | isnan(Y2) | isnan(Y3));
Y1 = Y1(nanmask);
Y2 = Y2(nanmask);
Y3 = Y3(nanmask);

% when overdefined, mldivide returns the least-squares solution
ab = [Y2 Y3]\Y1

ab = 2×1

0.7007 0.2259

That said, I'm not sure it's going to be good enough to just blindly process the data. Y1 doesn't look like the linear combination of Y2 and Y3 (at least it doesn't respond events in Y2).

Y1est = [Y2 Y3]*ab; % assume that Y1 is a linear combination

subplot(2,1,1)
plot(Y2); hold on
plot(Y3)

subplot(2,1,2)
plot(Y1); hold on
plot(Y1est)

Some sort of preprocessing is probably warranted here.

[Asliddin Komilov]

looks nice, thank you.

I have calculated the deviation:

ddif=(trapz(X,Y1)-trapz(X,Y1est))/trapz(X,Y1est);

that is around 8%, how do I make it smaller? Thanks

[DGM]

If the data is taken at face value, Y1 isn't a linear combination of Y2 and Y3. That should be visually apparent just by looking at the graphs.

If the underlying system is expected to be linear, then you'll have to find an appropriate way to deal with the noise events in Y1 and Y2. I'm not sure what would be appropriate. You might try omitting outliers, filling them, or smoothing them.

[Asliddin Komilov]

Sorry if I misled you anyhow.

It is not supposed to be linear, these are spectral distribution of light sources. The code should add the values for each wavelength (x-axis). And the power (integrals) of combined sources must me as close as possibe to the single one.

Later I may look for other light sources those's shapes also match better, but the main thing is that the code gives the correlation coeffients to match the combination of multiple sources with the etalon source.

Thanks