Vectorize for loop - matlab

Question

The loop is as follows:
for j = 1:20
sigma = (y<0) - (y>=0);
x0 = x;
out_angle = out_angle - sigma*lut(j);
x = x-(y.*sigma)*poweroftwo;
y = y+(x0.*sigma)*poweroftwo;
poweroftwo = poweroftwo/2;
end
out_angle, x,y and sigma are matrices of dim m*n. lut is an array of size 20. poweroftwo is a scalar with initial value 1. Is it possible to vectorize this code and avoid the for loop?

Answer 1

A lot of informaiton is missing for the vectorization of this loop. Just have a look at the line
out_angle = out_angle - sigma*lut(j);
After vectorization you would like to have an expression similar to
out_angle(j) = out_angle(j-1) - sigma*lut(j);
You immediately see that the current out_angle depends on the previously computed value. This also means that out_angle can only be computed sequentially except if you can
come up with an explicit representation of out_angle.
out_angle(j) = out_angle(j-1) - sigma*lut(j)
= out_angle(j-2) - sigma*lut(j-1) - sigma*lut(j)
= out_angle(j-3) - sigma*lut(j-2) - sigma*lut(j-1) - sigma*lut(j)
= ...
= out_angle(0) - sum_{k = 0}^j (sigma*lut(k))
The thing gets more complicated as sigma also depends on j, i.e. actually you have
sigma(j) and thus
out_angle(j) = out_angle(0) - sum_{k = 0}^j (sigma(k)*lut(k))
Unfortunately you also have only an implicit expression for sigma which you have to
resolve in the same manner. You can probably think a bit about the structure behind sigma. This is a variable, which is 1, where y is negative and -1 where y is positive
or zero, i.e. it is something like
sigma = -mySign(y)
where mySign acts like the sign function but gives 1 for a zero argument.
If you can find an explicit representation for sigma, you can insert it into the explicit representation of out_angle above. After that you can (most likely) vectorize the code.