How to create array with unequal spacing?

I want to create an array with unequal spacing. I have h = 1 1/2 1/4 1/8 ..... 2^-60.

Every second entry in this array is 1/2 of the last one. I only know, how to make arrays with equal spacing.

a = 1:5:40

But how do I create array that gets halved with every entry?

[Stephen23]

For the special case of binary powers it may be more efficient to use pow2:

h = pow2(0:-1:-60)

[Walter Roberson]

timeit() disagrees:

>> timeit(@() pow2(0:-1:-60),0)
ans =
      3.45591429508197e-06
>> timeit(@() 2.^-(0:60),0)
Warning: The measured time for F may be inaccurate because it is running too fast. Try measuring something that takes longer. 
> In timeit (line 158) 
ans =
     0

And if you

>> tic;for K = 1 : 1000; h = 2.^-(0:60); end; toc
Elapsed time is 0.000007 seconds.

-- not the first time, at least not from the command line, but after a few times repeating the same line, the JIT fully kicks in.

By way of contrast,

>> tic;for K = 1 : 1000; h = pow2(0:-1:-60); end; toc
Elapsed time is 0.004652 seconds.

was the best I could do.

[Ahmad Hasnain]

Thanks

[Stephen23]

@Walter Roberson: Interesting. So what is the usecase for pow2(n) then?

[Walter Roberson]

In 2.^-(0:60) the JIT is detecting that the expression is constant and optimizes it, at least in the case of re-use. If you use B = 2; B.^-(0:60) or if you use V = -(0:60); 2.^B then JIT optimization is not as good and pow2 can have better performance than those.

Answer 1

[Walter Roberson]

h = 2.^-(0:60);