Creating a function in MATLAB

I need to create a function with input i and outputs j and k. So i varies from 1,2,3... and i,j and k are related as , where j =0,1,2,... and k=0,1,2,...,. So,

for input i=1, outputs should be j=0,k=0;

i=2 ⇒ j=1,k=0;

i=3 ⇒ j=1,k=1;

i=4 ⇒ j=2,k=0;

i=5 ⇒ j=2,k=1;

i=6 ⇒ j=2,k=2;

i=7 ⇒ j=2,k=3;

and so on. How do I create such a function?

Answer 1

[Walter Roberson]

for I = 1 : 10
   [J, K] = decode(I);
   fprintf('i = %d, j = %d, k = %d\n', I, J, K);
end

i = 1, j = 0, k = 0
i = 2, j = 1, k = 0
i = 3, j = 1, k = 1
i = 4, j = 2, k = 0
i = 5, j = 2, k = 1
i = 6, j = 2, k = 2
i = 7, j = 2, k = 3
i = 8, j = 3, k = 0
i = 9, j = 3, k = 1
i = 10, j = 3, k = 2

function [j, k] = decode(i)
   L2 = nextpow2(i);
   if 2.^L2 == i
       j = L2;
       k = 0;
   else
       j = L2 - 1;
       k = i - 2.^j;
   end
end

[Saurabh Madankar]

Thanks a lot, I didn't know about the built in function nextpow2. I went through the documentation and now have understood how this code works.

[Walter Roberson]

j = floor(log2(i)) ;
k = i - 2.^j;

... a vectorized version