The easiest and probably fastest way to achieve that is to use histc respectively histcounts.
Code example:
% create some example data
x=linspace(0,10,100);
y=sin(x);
% those are the query points
xi=linspace(1,9,50);
% use histcounts to get the locations
% of the nearest left neighbours
[~,~,bin]=histcounts(xi,x);
plot(x,y,'b*')
hold on
plot(xi,y(bin),'r*')
Note that you would have to add some guard when interpolating data points outside the range of x.
