Fit Reference plot to data

Hi,

I have data from the experiment and I want to fit my data to the Reference plot. I do not want to fit specific equation to my data. I want to get the percentage of my element by fitting data with the plot from Reference. I do not know how to do that. I would highly appreciate if you could help me. Thanks

[dpb]

Well, I don't know how to do that, either, at least in part because I have no idea what you mean. What is "the Reference plot" for starters?

[Zahra Shaf]

Hi, for example in this image, the reference plots are shown in green and blue and the plot from the experiment is in black. I want to fit plot from experiment to each reference plot. Thank you for your time.

[Rik]

You mean you want to calculate the relative contributions? Do you have correlating data? (i.e. do you have 3 y-values for each x-value?)

[Zahra Shaf]

I have 3 X values and 3 Y values. The X values are so close to each other. Thank you for your time.

[John D'Errico]

@Elias - It is only annoying for people who have no idea how to use MATLAB. Why not learn how, and you might find it useful?

[Elias Ghechi]

Well then you could have not closed my question, John. You could have helped me. Thanks though.

Answer 1

[Star Strider]

If you have the data that created the ‘Ti3+’ and ‘Ti4+’ curves, do a simple linear fit to each of those with your data at the same values of ‘Energy Loss’.

[Zahra Shaf]

I have data that created ‘Ti3+’ and ‘Ti4+’ curves. In other papers, it was mentioned that they fit their own data with reference Ti3+ and Ti4+ and find that their curve has 20% Ti3+. I do not know how they do that. Thank you for your time.

[Star Strider]

If other authors are reporting percentages of ‘T13+’, and did not state in the ‘Methods’ section how they arrived at that (and did not cite other sources for that calculation that you could use, a genuine oversight), you have to create your own method.

One option is to divide your data point-by-point by ‘Ti3+’ and report that mean percentage.

Keep searching the literature to see if you can find the accepted way to report your results with respect to the published values for ‘Ti3+’. It has to be available somewhere.

EDIT —

I am not sure what you are doing, so I did a short search. These authors (see Electron energy loss spectroscopy determination of Ti oxidation state at the (001) LaAlO3/SrTiO3 interface as a function of LaAlO3 growth conditions (link) did a least-squares fit.

[Zahra Shaf]

Thank you for your time and help. Thank you very much for Edit and paper.

[Star Strider]

My pleasure.

Answer 2

[John D'Errico]

This seems to be a fairly classic calibration problem. Are the two curves sampled at the same values for EV? If so, then this is simple. If not, then you would need to use interpolation to bring them to the same locations.

Next, I assume that you just want to find the fractional coefficient, such that

T14 = f14*layer16
T13 = f13*layer16

I'll assume that each is stored as a vector.

f14 = layer16(:)\T14(:);
f13 = layer16(:)\T13(:);

That presumes there is no constant (vertical offset) term in the calibration.

Or, are you asking to find a model like this, perhaps something of the form:

layer16 = f14*T14 + f13*T13

It is unclear what you are asking to do.

[Zahra Shaf]

Hi, Thank you for your response. I do not have same X values but I have to make them the same. I want to compare Y values of my data with Y values of Reference plots Ti3+ and Ti4+. I think I have to do

(Y of Ti3+)*a + (1-a)* Y of Ti4+

and then match this with Y values of my own data to obtain a.