Find Fitting Function for Plot Without Data Points

In summary, the person is trying to find a fitting function for a plot they obtained from a journal paper. They want to parameterize the curve with two variables and use a functional form to change the shape of the curve. They are not sure where to start and are considering using a least squares solution or an n-1 power polynomial. The figure shows different curves with varying amounts of energy injected at different times. The person wants to be able to manipulate the variables and cycle between the curves. They mention that the function in the paper is a complicated one that was numerically integrated. They are considering using interpolation or least squares fitting, but are unsure if it is the right approach. They also mention that the curves resemble an arctan function
  • #1
Dathascome
55
0
Hi there,
This might be a sort of vague question, but if I have a plot say that I don't know the data points for, how can I go about trying to find a fitting function (basically a functional form) for the curves I'm looking at?
Basically I have a figure I got from a journal paper that I want to parameterize with two variables of interest, come up with some sort of functional form for it whose parameters I can tune to change what the curve looks like and then put this into some code that I have.

I'm not really sure where to start with this. I know that there fitting procedure I can use if I have a guess at the functional form but maybe want to tweak the exponents or coefficients say, but I'm not really sure if this applies in this situation.

Sorry if this is to general and vague.

Thanks much.
 
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  • #2
It's not clear what you want. If you want a function that is close to the given points, then a "least squares" solution is the best to use. You will need to decide, from the given points, if least squares plane, or quadratic, or cubic, etc. is what you need. If you want a function that passes exactly through the points, then you will need an n-1 power polynomial in both parameters. That, typically, is far more complicated than a least squares approximation.
 
  • #3
I think part of the reason that it's not so clear what I'm trying to do is that I'm not 100% sure what I need to be doing and I'm trying to figure that out.

Here's the figure (since I got it from a journal article I thought it best to leave it unlabled).

screen-capture.jpg


The solid line is say f(x,y=const). At some specific x I change y to some other value and get the dashed line and at the same x if i change y to another value I get the dotted line. At some different x I change y again and get the thin solid line. Basically x is time and y is energy. The solid line is no extra energy injected, dashed and dotted lines are differing amounts of energy injected at the same time, and the thin line is injecting energy at a different time.

I know the amounts of energy injected and at what times but I want to come up with some sort of functional form for f(x,y) where I can basically tweak x and or y and sort of cycle between the curves.

From the paper that contained this figure I know that f(x,y) is some complicated function that was numerically integrated.

Does that make more sense that what I initially said?

I've been reading a bit about interpolation and least squares fitting which sound promising but I'm not totally sure this is what I'm looking to do.

If I'm understanding them right, I need to have some function in mind that the ones I'm looking at could fit to and then do the least squares say and see how well it does fit? The curves look vaguely arctan-esque to me, so would I start with that or would I want to try to fit it to some polynomial?

Sorry if this is still confusing, it is to me to :smile:
Thanks much for the help.
 

1. What is the purpose of finding a fitting function for a plot without data points?

The purpose of finding a fitting function for a plot without data points is to mathematically describe the relationship between the variables in the plot. This function can then be used to predict the behavior of the variables and make informed decisions based on the data.

2. What methods can be used to find a fitting function for a plot without data points?

There are several methods that can be used, such as linear regression, polynomial regression, and exponential regression. Other methods include interpolation and curve fitting.

3. How do I choose the best fitting function for my plot without data points?

The best fitting function will depend on the type of data and the nature of the relationship between the variables. It is important to consider the accuracy and simplicity of the function when choosing the best fit for your plot. It may also be helpful to consult with a statistician or use statistical software to determine the best fit.

4. Can a fitting function be used to make predictions for data outside of the plotted range?

Yes, a fitting function can be used to make predictions for data outside of the plotted range. However, it is important to note that the accuracy of these predictions may decrease as the data moves further away from the plotted range.

5. What are the limitations of using a fitting function for a plot without data points?

Using a fitting function for a plot without data points can be limited by the assumptions made about the data and the function itself. It is important to consider the accuracy and reliability of the data before using a fitting function. Additionally, the function may not accurately capture the true relationship between the variables and may not be suitable for making predictions in all cases.

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