Formula for setting Diagonals

Basically, I'm creating a very large matrix (1000000 x 1000000) in which I will do operations such as finding eigenvalues on. Only certain diagonals are used, and they all follow simple formulas.

The main diagonal is just A(i,i) = 2 * i

I figured that I need to use a sparse matrix, but I don't know how to set the diagonal efficiently. A while loop that iterates through the diagonals and sets each element takes an EXTREMELY long time

Is there something along the lines of diag(2*i) or some effective formulated way to this?

Answer 1

[Walter Roberson]

http://www.mathworks.com/help/matlab/ref/spdiags.html

"A = spdiags(B,d,A) replaces the diagonals specified by d with the columns of B. The output is sparse."

[Eric Fleming]

But in forming a matrix B (which is the main diagonal), I would still need 1000000 entries correct? I was thinking something along the lines of A = spdiags(2*i,d,A), where I wouldn't have to store a matrix B, unless I'm mistaken about something

[Walter Roberson]

You cannot give spdiags a formula or function handle: it would have to be the actual (full) vector of values

d = 0;
B = (1:size(A,1)-abs(d)).'*2;
A = spdiags(B, d, A);