easy indexing lon-loop versus loop

Hello, I have what I think is an easy indexing question, that has me scratching my head. I set up a simple moving average as such:

% the MA depth
Ml=16;

% the input data
x=[ zeros(1,Ml) 1:10 9:-1:7 8:10 9:-1:7 8:10 9:-1:7 8:10 9:-1:7]; % sequence to average out

% storage for output
y= zeros(1,length(x)+Ml);
%index
n= [Ml+1:length(x)];
%moving average
y(n)= y(n-1) + x(n)/Ml - x(n-Ml)/Ml;  

which gives the wrong value for y(n). If I implement as a loop, it works fine.

% storage for output
yl= zeros(1,length(x)+Ml);  
for n= Ml+1:length(x)
  yl(n)= yl(n-1) + x(n)/Ml - x(n-Ml)/Ml
end

what is wrong with the non-loop version?

[stephen williams]

This is a general indexing question. I thought if you preallocated the y(n) locations, I could calculate y(n) based on y(n-1) but that is not working right.

I could have made up some other difference equation.

Answer 1

[Bob Thompson]

I think the issue is with your loop definition. You define y1 to be length(x)+M1 long, but n is defined from M1+1 to length(x). I assume you were intending to do 1+M1 to length(x)+M1, but you will need to add the M1 to both sides of the colon.

% storage for output
yl= zeros(1,length(x)+Ml);  
for n= Ml+1:length(x)
  yl(n)= yl(n-1) + x(n)/Ml - x(n-Ml)/Ml
end

[stephen williams]

OK thanks. The issue I am trying to understand is with indexing in the non-loop equation.

%moving average
y(n)= y(n-1) + x(n)/Ml - x(n-Ml)/Ml;

If I add a line after to display each term, like this

[y(n-1)' (x(n)/Ml)' (-x(n-Ml)/Ml)'  (y(n-1)+x(n)/Ml-x(n-Ml)/Ml)'  y(n)']

you see this displayed

ans =

0 0.0625 0 0.0625 0.0625

0.0625 0.1250 0 0.1875 0.1250

0.1250 0.1875 0 0.3125 0.1875

0.1875 0.2500 0 0.4375 0.2500

.

.

.

stepping through line-by-line,

y(n-1)=0 looks right

x(n)/Ml= 0.0625 looks right

- x(n-Ml)/Ml=0 looks right

y(n-1)+x(n)/Ml-x(n-Ml)/Ml= 0.0625 looks right

y(n)= 0.0625 looks right

in the next line, n has incremented by 1

y(n-1)=0.0625 looks right

x(n)/Ml= 0.1250 looks right

- x(n-Ml)/Ml=0 looks right

y(n-1)+x(n)/Ml-x(n-Ml)/Ml= 0.1875 looks right

y(n)= 0.1250 ERROR- should have been 0.1875

in the next line, n has incremented by 1

y(n-1)=0.1250 ERROR- should have been 0.1875

x(n)/Ml= 0.1875 looks right

- x(n-Ml)/Ml=0 looks right

y(n-1)+x(n)/Ml-x(n-Ml)/Ml= 0.3125 looks right

y(n)= 0.1875 ERROR- should have been 0.3125

and so on.

This issue seems to have happened in the second iteration when the expression results were not saved in y(n) ? It looks like y(n) is in fact getting values from the 2nd term x(n)/Ml. How can that be?

[Bob Thompson]

Oh, the issue is because you're trying to do all the calculations at once, so as far as the outside the loop calculations are concerned, the y(n-1) = 0 no matter what you want y(n-1) to be. To write it out a bit more orderly:

1) Define initial values of everything, M1, x(an array of values), y(zeros), n(an array of values).

2) Calculate y using [M1, x(an array of values), y(zeros), n(an array of values)].

The loop wouldn't run into this issue, because you're sequentially calculating each of the values of y, so y(n-1) will have a chance to be defined before y(n) gets calculated.

[stephen williams]

thanks Bob.

Yes this issue is beucase I am trying to do the calculations all at once, and that is the question. I have aalternative ways to solve. I am trying to understand why this way does not work.

--Steve

[stephen williams]

thanks Bob.

Yes this issue is beucase I am trying to do the calculations all at once, and that is the question. I have alternative ways to solve. I am trying to understand why this way does not work.

--Steve