Equation of nonlinear data

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Rick 2014-9-16

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回答： Alex Sha 2019-6-4

采纳的回答： Stephen23

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Hello,

If I have data

rA = [-0.2 -0.0167 -0.00488 -0.00286 -0.00204];
X = [0 0.1 0.4 0.7 0.9];

and I plot

plot(X,-FA0./(rA/60))
xlabel('X')
ylabel('-FA0/rA')
title('FA0/-rA vs. Conversion')

How would I be able to find an equation that represents this non-linear plot? Thanks

I want rA as a function of X

perhaps it would be better visually to see plot(X,rA/60)

which is very nonlinear, but how would I represent this as an equation?

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Star Strider 2014-9-16

Looks almost perfectly linear to me (with a scalar ‘FA0’), but we’re missing ‘FA0’. Is it a scalar or vector?

Is there a specific process that generated these data that you want to estimate the parameters for? If so, what is it?

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Stephen23 2014-9-16

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You want to determine a function that matches your data. Doing this really depends on what you know about the data:

If you know the underlying function, then use this and fit it using least squares , or some tool from the curve fitting toolbox .
If you do not know the function, then model it using a spline or pchip function, using the polynomial output together with unmkpp .

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Rick 2014-9-16

编辑：Rick 2014-9-16

在 MATLAB Online 中打开

I don't have the curve fitting toolbox.

I don't know any underlying information that will tell me how this function will behave. I just have data and plotted it, which is in my first post.

Is there some way to fit other types of curves, other than polynomials? Maybe exponential fit, square root fit, etc?

This is all I have to go on

rA = [-0.2 -0.0167 -0.00488 -0.00286 -0.00204];
X = [0 0.1 0.4 0.7 0.9];
plot(X,rA/60)

the division by 60 is to make the units from minutes to seconds. Now I just need some function that will fit the data given.

Also, there is no need to repeat yourself regarding the magic tool. As I respond you are editing your old posts, I know I wont get something that will exactly fit the data, but I'm trying to find something as close as I can get. This is not a well defined function of X, as you may have guessed.

I just noticed that it seems to asymptote towards 0, if you just look at the data you will see what I mean. How would I fit an asymptotic curve with least squares?

Stephen23 2014-9-16

"Also, there is no need to repeat yourself regarding the magic tool"... except that no one else knows what criteria are required for "an equation that represents this non-linear plot", how complicated it needs to be, or how it should behave with data points outside those you have given. I cannot know this, no one else on the forum can know this, and MATLAB also cannot know this. MATLAB is a great numeric tool, and it is up to the user to know their own problem, and know the kind of solution that they require.

I understand that you are trying to figure out a way to parametrize some curve, but essentially it is a problem of inventing data... which, in appropriate circumstances (such as when the underlying model is well understood), can produce useful results.

Your original question was "How would I be able to find an equation that represents this non-linear plot,", to which I gave several suggestions of how you can find functions that represent this data, such as with splines, polyfit, etc.

It seems that perhaps you are actually trying to do something else: identify the most suitable mathematical function (i.e. identify the underlying process) for your data. Is this correct?

Rick 2014-9-20

编辑：Rick 2014-9-20

Well, I don't see how they are not one of the same animal. Of course the most suitable mathematical function should best fit the data. This data is monotonic, so a polynomial is not going to be a correct fit. I think a logarithm will better fit the data.

Is there something like logfit, analogous to polyfit??

Stephen23 2015-2-7

They are a completely different kind of animal. Just like analytic and numeric calculations, they only bear a passing relation to one another.

"Of course the most suitable mathematical function should best fit the data" sounds nice, but in the real world this is hardly guaranteed. It really depends what you mean by "fit": all data measurements are subject to errors, as are the calculations based on them. For any finite set of data values there are going to be precisely an infinite number of functions that could fit it. How on earth should any program "know" that your data is exponential, or linear, or any other convenient function?

"Also, there is no need to repeat yourself regarding the magic tool", sorry, but there is NO magic tool that can identify what function exactly describes the underlying system of behavior of some set of data.

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