Fitting of one set of data to another

I have some experimental data measured and I have a theoretical calculation to fit to the data.

How do I fit the theoretical model to the experimental data? If I try and read about MATLAB fitting, it's all about fitting functions to data - what if want to fit an already calculated model to data?

just to add, both data sets have been interpolated to share the same x axis - which is what allows me to do this when I use software such as Originpro

Thank you

Answer 1

[Star Strider]

Your model is the function you want to fit to your data (this is know as parameter estimation). There are several ways to do this in MATLAB. If you have the Statistics Toolbox, use the nlinfit function (and its friends, to get related statistics), if you have the Optimization Toolbox, use lsqcurvefit, and if you have none of these, you can use fminsearch, with an extra line to define your cost function, to do the parameter estimation.

[Crosshash]

Thank you for the response Star Strider. I'm struggling to get my head around using nlinfit. The third argument from the documentation looks like it specifically takes a function as an argument. I don't have a function to describe the data, just X and corresponding Y values. How exactly do I parse this data set as an argument to nlinfit?

Thank you

[Star Strider]

My pleasure.

‘I have a theoretical calculation to fit to the data’

How did you fit your original data? What relation or equation did you use? How did you estimate your parameters?

[Crosshash]

The model is generated using an Electronic Structure code. The curve generated is not created by specifying a function with parameters.

If I were to manually fit this data, I would be finding the least squares by scaling the y values to the experimental data.

Does this make sense?

[Star Strider]

I never heard of an Electronic Structure Code, at least by that name. The only sort of scaling I’m familiar with is, for instance, logarithmic scaling, plotting log(y) against x, and doing a log-linear least squares regression.

What sort of function are you using to scale the y values to your experimental data?

[Crosshash]

It'd be a very simple function of the form y=mx. y being the experimental data and x being the theoretical data. The software Originpro for example uses nonlinear-curve fitting to find the appropriate value for m such that the theoretical curve best describes the experimental data. I was hoping matlab had a similar feature.

[Star Strider]

The closest MATLAB can get to what you want (assuming I understand you correctly) are the polyfit and polyval functions. They do a polynomial fit to data. You would have to choose the appropriate polynomial order, 1 is a linear fit, 2 quadratic, etc. As a general rule, a 5th-order polynomial is likely the highest you can reasonably go, although the function itself will fit up to a 99th-order polynomial.

If you can describe what Originpro does in its scaling-and-fitting, it might be possible to approximate what it does in MATLAB. I’m not familiar with Originpro.

[Crosshash]

Thank you Star Strider. Those are exactly what I'm after.

[Star Strider]

My pleasure!

Answer 2

[Image Analyst]

If you want to fit the data to a polynomial, such as a line, you can use polyfit() and polyval() functions. I've attached a demo for you to look at and run.