Creating one big loop from smaller ones

Hi, I'm trying to come up with a loop for the following:

SP = 2778x1 array

w = 1x252 array

alpha = 1x252 array

beta = 1x252 array

ss = zeros(2527,252);

ss(1,:) = 0;

I need to create one loop which would produce a 2527x252 array for the results for the following 252 smaller loops:

for i = 1:2526
  ss(i+1) = w(1,1) + alpha(1,1).*SP(i) + beta(1,1).*ss(i);
end

for i = 2:2527
  ss(i+1) = w(1,2) + alpha(1,2).*SP(i) + beta(1,2).*ss(i);
end

..........

for i = 252:2577
  ss(i+1) = w(1,252) + alpha(1,252).*SP(i) + beta(1,252).*ss(i);
end

The code I've used is as follows:

for j = 1:252
  for i = j:2526+j-1
    ss(i+1,j) = w(1,j) + alpha(1,j).*SP(i) + beta(1,j).*ss(i);
end

This code works but it doesn't present the results the way I want i.e. it produces not 2527x252 array but a 2778x252 array and it looks like this:

1)    0  0  0  ...  0
2)    #  0  0  ...  0
3)    #  #  0  ...  0
4)    #  #  #  ...  0
...    ...  ...  ...  ...  ...
2527)    #  #  #  ...  #
2528)    0  #  #  ...  #
2529)    0  0  #  ...  #
...    ...  ...  ...  ...  ...
2778)    0  0  0  ...  #

What I need is for this array to have only one initial zero on top of every column. First column was perfect up to observation 2527. I need column two, three and so on to be pulled up, so that each has one zero on top and then another 2526 observations (that makes it 2527 in total). I would appreciate any help I can get on this one.

Answer 1

[Jan]

Before I give an advice about a much faster vectorized approach - does this create the wanted output:

EDITED: Index of ss adjusted to Julia's comments:

for j = 1:252
  for i = j:2526+j-1
    ss(i-j+2, j) = w(j) + alpha(j) * SP(i) + beta(j) * ss(i-j+1, j);
  end
end

This takes 0.06 sec on my old 1.5GHz Pentium-M. A vectorization would be useful only if you run this funciton thousands of times. Do you?

[Andrew Newell]

I think that ss(i) should be replaced by ss(i,j).

[Julia]

Thanks Jan, this is exactly what I was looking for.

[Andrew Newell]

Hey, wait, he was going to vectorize it for you!

[Julia]

I know that, that's why I'm checking this page every 15 mins or so.

[Jan]

And is it really ss(i), which is equivalent to ss(i,1), or do you want ss(i,j) as Andrew guessed?

[Julia]

ss(i) was fine. I tried ss(i,j) but it didn't work even though it seems like it should be more appropriate.

[Julia]

Actually, now that I think about it, it's not i, it's going to be (i-j+2-1) = (i-j+1). It's the previous observation.

[Julia]

Basically, if we're looking to find ss(5,6) for example, then we use the previous observation in the same column i.e. ss(4,6).

[Julia]

I made an adjustment. I used ss(i-j+1,j) and it worked and it also gave me values which I would expect based on theory and data.

[Jan]

@Julia: It seems to me, like you perform a stochastic index permutation. See: http://en.wikipedia.org/wiki/Programming_by_permutation

Therefore I will wait some time with further improvements of my code until your indices reach a stable level ;-)

[Julia]

This programming by permutation is exactly what I was doing. I'm not a programmer, I have started using MATLAB on and off about 3 months ago. I'm hopeless with code. But I do know theory behind what I'm doing (well, at least I think I do) and when I ran the code the first time I got results which seemed ok at first, but then I used those results to compute something else and I was surprised at what I got. It didn't seem right. When I re-run the code as per my adjustment, I got exactly what I needed. So my indices have reached a stable level :).

By the way, I'm going to post another loop question in about 5 minutes. This one is going to be more tricky. I don't even know if it's possible to do what I want to do with a loop.

[Jan]

@Julia: With the joined power of Matlab and Walter anything is possible - if it is at least deterministic and can be defined by a primitive recursive function.

[Julia]

@ Jan: I don't run it thousands of times. I have 3GHz Pentium 4 as far as I can remeber, so the speed would improve. But really, even 0.06 sec is nothing. I was using garchfit function to estimate beta, alpha and w above and it took me about 2 mins 40 secs to do it (I had enough time to go downstairs and make myself some tea :) ), so 0.06 sec is nothing.