How do I compare two graphs for X value at a specific point?

I have two dataset that gives plots as below. My goal is to match them and get the x value at a certain point. I have been trying interpolation but isn't getting the result I want. Your help is appreciated.

[darova]

What is wrong with interpolation? Why didn't it work?

[dpb]

" My goal is to match them and get the x value at a certain point."

What does this mean, specifically? Match what? The range of neither variable in the two is anything at all like that in the other so what does one have to do with the other at all?

[Ashik Rahman]

One is the standard curve and another is a portion of experimental data. You may see the curve pattern is similar. I want to find the value of Y of the other curve at a certain point of the standard curve. I will be using that Y value for further calculation.

[dpb]

Well, you'll have to define what is the end point of the experimental data -- is the last measured point a normalized value of 1.0 or something less since your other figure only goes to 0.9?

Then, you've got a problem in that 7.1/7.8 --> 0.91 for the relative range of your observations whereas the other variable range i covers nearly the full range, so it certainly isn't just a relative ratio.

Tell us exactly what you think your expected result should be here.

Then attach the data for the curves as a .mat file would help immensely for anybody to do anything; otherwise have to try to make up data besides...

[Star Strider]

The plots in the two images not only appear to have no independent or dependent variable values in common, they actually appear to orders-of-magnitude different.

Answer 1

[dpb]

Well, as Star Strider says, the disparity in orders of magnitude between the two makes one truly wonder just how they're supposed to have been related to each other somehow -- but, presuming there is some reason it might make sense, here's the simplest stab at it --

[b,S,mu]=polyfit(ind,refVt5,9);     % NB: badly scaled, a 9th deg polynomial is very sensitive
tiledlayout(2,1),hAx=nexttile,plot(ind,refVt5)  % plot raw data first
hAx.YDir="reverse";
ylim([2.2 2.7])
Vhat=polyval(b,ind,S,mu);           % evaluate the polynomial on refV
hold(hAx,'on');hL=plot(hAx,ind,Vhat,'.r'); % add to the plot

hAx(2)=nexttile;
plot(XX,YY)

% the engine
Xhat=interp1([XX(1);XX(end)],[ind(1);ind(end)],XX);     % scale standard curve ranges to
Yhat=interp1([YY(1);YY(end)],[Vhat(1);Vhat(end)],YY);   % those of experimental data
hL(2)=plot(hAx(1),Xhat,Yhat,'.k-');                     % plot on top of experimental data
legend(hAx(1),'refVt5','fitVt5','Scaled STD')

results in

There a little similarity in that both are concave, but that's about as much as can be said for a linear scaling.

Is there any physical model that could be used to predict some functional form that could aid in justifying some nonlinear scaling operation?

[Ashik Rahman]

what is hT here?

getting "Unrecognized function or variable 'hT'."

[dpb]

Oh. It's the handle of the nexttile object that contains the two axes handles to use to plot into...I had forgotten to save the axes handles in the initial test coding and pulled them out later and missed fixing up the code pasted above.

Use the revised code above instead to duplicate the figures. It's immaterial to solving the problem other than displaying the graphics.

The far more interesting/important questions are those raised about what the data represent and whether there's any better way to normalize.

[dpb]

That would just be interpolating the other direction from ind to XX instead of XX to ind on abscissa and, apparently, not scaling the ordinate (y) values.

And, of course, that the actual experimental curve data is concave downward rather than upward as is the STD curve complicates matters -- the scaling operation above does the implicit change in axes direction internally with the transformation/scaling of the data.

Some idea of why that is so might make for more satisfying way to approach the problem.

[dpb]

"the actual experimental curve data is concave downward rather than upward"

One way one might deal with that would be something like --

refVt5Flip=refVt5-refVt5(1);            % difference from first point of curve
refVt5Flip=refVt5(1)-refVt5Flip;        % switch sign difference relative first point

will give the reflection of the original curve about the initial point in the y direction. Then can plot both curves on same axes with same curvature.

Again, it is totally unknown as to whether any of this makes any sense to do or not with no klew about what these data might represent and, therefore, why such a reflection might be expected as well as the tremendous scale factor differences.

If I do that on the lower of the two previous plots, the result is\

which makes the two look more similar in shape on the larger scale y axes. One might then try simply computing the mean difference between the two and using that to adjust one or the other.

This again, of course, still uses the linear transformation/scaling of the x axis to get the two on the same scale with all the assumptions that implies.