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

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##### 5 Comments

Star Strider
on 28 Mar 2021

### Accepted Answer

dpb
on 28 Mar 2021

Edited: dpb
on 28 Mar 2021

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?

##### 4 Comments

dpb
on 28 Mar 2021

"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.

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