Forming a large matrix out of 2 separate column matrix.

Im having trouble trying to create a matrix that creates a graph like the one attached. I have managed to get half way but cant figure out how to create the final matrix. I want to get it so the first column repeats after a certain number of times. The second column would be 100 equally spaced numbers ranging from 0 to 100. Ive also attached my script to help.

Answer 1

[dpb]

I presumed you could see how to get from the simpler "Matlab way" of computing the power series to the scaled version, sorry...

refine = 1.02;          % Refinement Parameter
L=100;                  % length desired
x=refine.^(0:L-1).';    % the power series
x = cumsum(x)/sum(x);   % Cumulative Sum scaled

Try

all(x)==all(cumsum(dx_scaled))

to prove it works numerically or write the algebra from your loops to see it analytically.

Now to see if I can finally understand what you're after for the other column...I seem to be dense here. :( ... Oh, ok, I see--not sure why it took so long; perhaps because I was too focused on the code and the other numbers instead of the above verbiage that is clear. OK, try the following --

You've got the base case; since it's a tiling you want repmat is your friend.

 N=1000;        % The total length desired
 n=fix(N/L);    % Number of tilings of L to hit N w/o going over if not even
 y=linspace(0,1,100).';
 grid=repmat([x y],n,1);

doc repmat

for more detail on the last step. Work thru the examples in Getting Started on array operations and the colon and so on to get a feel for how Matlab vectorized operations work to eliminate the explicit loops.

[Dipesh]

Thanks this worked great with a few tweaks.

[dpb]

OK, good...I cleaned up the divergent portions of the thread for posterity.