MATLAB: Identifying x value at y on an xy plot

interpolationplot

I have a fairly simple problem that I imagine has a simple solution. I have a plot in which the x-axis represents a location (0-8) and the y-axis is the probability of a certain action occuring at that location. I need to identify the x value when there is a 50% chance of the action happening. Example data below.
x = [0,1,2,3,4,5,6,7,8];
y = [0,0,0,.25,.25,.25,.75,1,1];
plot(x,y);
line([0,8],[.5,.5]);
I just need to identify the x value when y is 0.5. Is there a simple solution I am missing here? Thank you!

Best Answer

A common problem interpolating y-values that are not unique is how to make them appropriate for interpolation. One way is to simply choose a small range of data in the vicinity of the desired interpolation point.
Try this: 
x = [0,1,2,3,4,5,6,7,8];
y = [0,0,0,.25,.25,.25,.75,1,1];
idx = find(y <= 0.5, 1, 'last');                        % Select Small Range Of Data Based On Desired Interpolation Point
idxrng = [0 1]+idx;
Lxq = interp1(y(idxrng), x(idxrng), 0.5, 'linear');     % Interpolate Over Small Range Of Data

Pxq = interp1(y(idxrng), x(idxrng), 0.5, 'spline');     % Interpolate Over Small Range Of Data
figure
plot(x,y)
hold on
plot(Lxq, 0.5, 'p')
hold off
line([0,8],[.5,.5]);
Here the two interpolation menthods give the same result. That may not always be the situation, so specify an appropriate method.
Experiment to get different results.
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