extrapolate the plot to the point out of the interval

I want to extrapolate the plot in the figure to the start point on x-axis, i tried with "interp1" but i could not do that, Please guide in this regard.

Answer 1

[John D'Errico]

You can't. Well, you can, but interp1 will give you meaningless garbage, as it should.

Extrapolation is a dangerous thing. And extrapolation without intelligence behind it? That equals dangerously meaningless garbage.

Think of it like this: How is any extrapolation to know that your function should behave outside of the interval? Should an extrapolant extrapolate linearly from that last point? Should it somehow be able to know that your curve seems to be an vaguely exponentially decreasing oscillating function? Should it somehow be able to model your function as such?

Computers are generally not intelligent things, unless you provide the intelligence, the knowledge of the process you have plotted. They cannot just look at some data and know how to extrapolate it.

So in order for MATLAB to somehow extrapolate, you must first decide on an appropriate model for that process. Then you would use a tool like the curve fitting toolbox, and estimate the parameters of that model. Finally, you would then evaluate that model at any set of points. Sadly, even having done all of that, your extrapolant need not be very accurately predictive. That is the nature of extrapolation. If we could do it truly well, then we could do things like predict the weather years in advance. Instead, we look outside, and say it looks like it might rain, maybe.

[John D'Errico]

Please learn to use COMMENTS. Your response was not an answer.

"Thank you Jhon, i add the picture of my plot but i am not seeing that in the question window, i think i didnot do it properly, i am adding again. This looks to be increase exponentially form the starting point. And if it is, then which matlab command should be used, please show with a small example."

[John D'Errico]

As I said in my answer, whoile this LOOKS to be a vaguely exponentially decreasing sinusoidally osscialling wave, it need not be exactly so.

There is NO code in MATLAB that will be able to look at your data, and somehow magically extrapolate it. Nor should there ever be any such code, as that is far too dangerous a thing to do. People might decide that such code was actually correct in its workings, and then use that prediction to make inferences upon. If in turn, that led them to terribly bad conclusions, this would be a really bad thing. And extrapolation would be something far too easily misused, because people would simply not understand what was happening.

Anyway, your statement that it "looks" to behave exponentially is clearly wrong. If you look at the amplitude of those maximuma as you go down the curve, they are not a smoothly decreasing series. It is actually a bit bumpy, and I can see that just from the picture. So while it looks to be a vaguely exponential decrease, it is clearly not so.

Next, I would point out that the period of that oscillation is NOT constant!!!!!!! The first few periods are clearly much wider than those at the end. So your suggestion that this "looks" to be anything is only a poor approximation.

Without the data in hand, I would not even hazard to guess at a valid model. Without knowledge of the system under study, I would also not even hazard a guess either. You are the only person who has that information.

How would I try to solve the problem, IF I had the data? I would probably take only a couple of periods of data at the end, then try to use the curve fitting toolbox. I would need to pose a model that allows an exponentially amplified sinusoidal curve, where the period is allowed to change with t.

[shahab ullah khan]

Thank you for your time jhon, my model needs the plot to be decraesed parabolically or may be exponentially to zero beyond the basic interval near the left end(specifically near

1. 4546*10^(-10) or 351.9 in the plot) of the t-axis. I am attaching my data in csv file. Thank you again

[John D'Errico]

You should realize that your data is useless for extrapolation as you have posted it?

By writing those numbers out to only 5 significant digits, you have created replicate data, thus duplicate values in x, with what seems to be smoothly varying y. Here is subset of the data from the ends:

1.4551e+10   6.9182e-18
1.4551e+10   7.0748e-18
1.4551e+10   7.2165e-18
1.4551e+10   7.3378e-18
1.4551e+10   7.4334e-18
1.4551e+10   7.4985e-18
1.4551e+10   7.5286e-18
1.4551e+10   7.5195e-18
1.4551e+10   7.4679e-18
1.4551e+10   7.3709e-18

...
    
1.5708e+10   3.7775e-19
1.5708e+10   6.7912e-19
1.5709e+10   1.1964e-19
1.5709e+10   8.7459e-19
1.5709e+10   2.2978e-19
1.5709e+10   3.8253e-20
1.5709e+10   2.1481e-19
1.5709e+10   8.0683e-20
1.5709e+10   8.3761e-19
1.5709e+10   3.8734e-19
1.5709e+10   2.2553e-19
1.5709e+10   1.2713e-18
1.5709e+10   3.2215e-19
1.5709e+10   2.7337e-19
1.571e+10    1.0491e-18
1.571e+10    2.3649e-19
1.571e+10    3.8928e-19

[shahab ullah khan]

Sorry for taking your time jhon, thanks for your kind comment, this time i saved the data in mat file, i plot the data from the mat file, it is working this time. Following code can be used to extract the data from the mat file.

load('myData.mat')
plot(myData.tf,myData.flux)