MATLAB: Extrapolation gives wrong values when using interp1

extrapolationinterpolationlinear

I have two different arrays and want to do interpolation and extrapolation.

X-value = [0 386.5 446.1 526.6 621.5 660.6 711.4 734.9 792.8 810.2 817.9 893.7 1136.8 1317 1420.2 1426.2]

Y-value = [1.225 1.216 1.203 1.194 1.182 1.178 1.171 1.169 1.161 1.160 1.160 1.151 1.122 1.101 1.091 1.091]

The y-value have a linear decrease with larger x-values. I want to do interpolation and extrapolation so I can find the y-value of any x-values. I have tried this code when I want to find the y-value when x- value is f.eks 2000:

interp1(Height,Density,2000,'linear','extrap');

When I try to extrapolation for x-values higher than the largest x-value value which is 1426.2, the y-value is not decreasing. Instead y-value stays nearly flat and even slightly increasing when x-value is increasing. The original curve is clearly decreasing linearly. I have no idea whats the problem. Hope someone can help.

Best Answer

"Extrapolation gives wrong values when using interp1"

interp1 is giving the right value.

The problem is simple: the last two points have the same Y value, so any linear extrapolation will simply continue with that value. Linear interpolation/extrapolation of a new point takes into account (at most) only two data points, which means that the overall downward trend of your data is irrelevant, because the last two points are these:

X = [... 1420.2 1426.2];
Y = [...  1.091 1.091];

So all larger X values will simply return Y = 1.091, no matter how large you make X.

To resolve this you might want to add some smoothing, or do some subsampling, or fit a line (e.g. using least squares), or merge points that are close together, or ... whatever makes sense for your data.

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MATLAB: Way to extend and interpolate the matrix by using thin plate spline

It is not clear in my opinion what you are asking.

If your question is how should one simply resample the domain by interpolation, so the new array will be more finely sampled over the same domain, then just use interp2. You have a choice of methods there.

If your question is how does one explicitly extrapolate a matrix out a significant distance, and you want to use a thin plate spline?

Mark Twain answered that question better than anyone else I know of:

“In the space of one hundred and seventy six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over a mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oölitic Silurian Period, just a million years ago next November, the Lower Mississippi was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-pole. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo [Illinois] and New Orleans will have joined their streets together and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”

Life on the Mississippi (1884)

Using a spline in any form to do significant extrapolation is asking for trouble and silly results, much like the quote above. The fact is, one of the most common interpolation problems I see is when people try to use an interpolant to extrapolate. Expect random crap as a result, or at least don't be surprised at that event.

You might decide to try my gridfit or inpaint_nans tools, both found on the file exchange. Either could be used here. In the default mode, both will aim to extrapolate as linearly as possible, so they are not too poorly behaved. Both tools also have an option that attempts to extrapolate as a constant, to the extent that is possible.

MATLAB: How to predict course of a graph

Hi,

Statistics and Machine Learning Toolbox and Curve Fitting Toolbox provide apps and functions for fitting curves and surfaces to data, and to describe, analyse and model the data. You could apply linear regression/nonlinear fitting, or you could extract features from data using supervised/unsupervised learning techniques by identifying a subset of features (if your data exhibits some common pattern) and applying machine learning models.

Also, the above told toolboxes provide you with apps as well, information for which can be found here (link1and link2).

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