MATLAB: How to find data values that falls on line connecting loglog plot in matlab

Question

I tried 'interp1' with 'linear' and 'pchip' to tried to pull more data values out of the line that matlab connected my data points. Neither of them look correct when i go to plot the new data values on a loglog plot.

The problem is obvious when using the example from the Matlab Help for 'loglog'

x = logspace(-1,2);

y = exp(x);

loglog(x,y,'-s');

Then find the interpolation to get more data points in the middle, the line isn't smooth:

xq = logspace(-1,2,500);

yq = interp1(x,y,xq,'linear'); %OR% yq = interp1(x,y,xq,'pchip');

figure; loglog(xq,yq);

I must be missing something easy. Thanks.

Answer 1

To get a smooth interpolation, it is necessary to do two transformations on it. First, interpolate log(y), and then take the exponential of the interpolated result:

yq = exp(interp1(x,log(y),xq,'linear'));