How to create nonlinear spaced vector in Matlab?

Question

I'm trying to create a contour plot with focus around a particular finite range from 1 to 1.05. At the same time, I need very high resolution closer to 1. I thought I could use something like the following but the spacing still looks linear

out=exp(linspace(log(1),log(1.05),100))
plot(diff(out))

What is the best way to enhance the nonlinearity of the spacing when the bounds are so tight? Again, I need to maintain high density near 1 with the resolution tapering off in a nonlinear way. I have a few ideas but I thought someone might have a quick 2 liner or something of the sort.

Answer 1

instead of applying the function f(x) = e^x, to get a 'steeper' non-linearity, rather apply f(x) = e^ax

n = 20;
a = 100;
lower = 1;
upper = 1.05;
temp = exp(linspace(log(1)*a,log(1.05)*a,n))
% re-scale to be between 0 and 1
temp_01 = temp/max(temp) - min(temp)/max(temp)
% re-scale to be between your limits (i.e. 1 and 1.05)
out = temp_01*(upper-lower) + lower

now plot(diff(out),diff(out),'o') produces

Note that you can use the exact same scaling scheme above with logspace so just use

temp = logspace(...)

and then the rest is the same

Answer 2

You can generate a logarithmic distribution between, for example, 1 and 1000 and then scale it back to [1, 1.05]:

out = logspace(0, 3, 100);
out = ( (out-min(out(:)))*(1.05-1) ) / ( max(out(:))-min(out(:)) ) + 1;

Result:

plot(diff(out));