Interpolating the y values of a dataset A to correspond to the x values of dataset B.

Hi,

I have 2 datasets containing the numerical (x1,y1) and experimental (x2,y2) results of a problem that lie within the same limits. I have to obtain the root-mean-square error to show the deviation of the numerical results from the experimental data, but the numerical data points (y1) are recorded on different locations (x1) from those of the experimental data points (x2) due to which the error calculation is not possible.

I'd like to know if there is a precise method to interpolate the y1 values for the locations prescribed in x2.

Answer 1

[Torsten]

The easiest way I can think of is

y1_at_x2 = interp1(x1,y1,x2)

If it's precise ? Define precise. At least you have the choice between different methods of interpolation. Read the documentation of "interp1" for more details.

If the (x1,y1) were obtained by a numerical method, you usually have the choice to define the output points x. Why didn't you choose x2 instead of x1 ?

[Shadab]

Thanks for your response, I'll look interp1 up further.

I'm actually reverse engineering the data from previous numerical studies (generating csv files using available graphical data and then calculating the error between numerical and experimental data) using an online tool, which doesn't let you obtain both datasets for the same locations. I have interpolated similar datasets using excel by combining the lookup functions with the linear forecast function but it's proving a bit tedious due to which I wanted to shift on Matlab.

By precise I meant to ask if it's possible to perform such interpolation using one command, or whether it will require a set of commands to be achieved.

[John D'Errico]

Exactly. Why not generate the numerical solutions at the desired points, instead of using interpolation at all? This eliminates the issue of interpolation errors. And since interpolation is ALWAYS an apprximation, that can be significant.

As far as precision goes, there is no good way to intelligently know which method of interpolation will be more "precise". You might decide to use higher order methods, but they are not always correct.

For example, a cubic spline is a higher order interpolant. Or you could even use higher order splines yet. But a spline can also introduce artifacts, known as ringing on some problems. And this is why it is important to understand the various methods available to you for interpolation. For example, PCHIP is a "lower order" interpolant than a spline. But if the spline causes ringing artifacts, you need a tool like PCHIP.

Another case where the interpolation method matters is when your data has noise in it. I showed many years ago (in an internal report for my employer, though externally unpublished work) that under noisy conditions, a piecewise linear interpolant is often the correct choice, as it minimizes the variance of the prediction. Of course, if you are interpolating the set (x1,y1), there is presumed to be no noise, so this is not an issue.

Anyway, best is to just avoid the interpolation completely.

[Shadab]

I have clarified the issue in response to the previous comment. I realize "precise" wasn't the right term to use for what I wanted to ask, for which I apologize. I wanted to ask if such interpolation could be achieved consicely or would it be possible using a series of commands.

[Torsten]

You need one command

y1_at_x2 = interp1(x1,y1,x2,method)

in which you should test for different interpolation methods available.