Normalize to unit norm

I have a variable containing a probability distribution (just an one-dimensional array of values). How can I normalize a to unit norm?

Answer 1

[Wayne King]

If you want to normalize a vector to have unit L2 norm.

   x = randn(100,1);
   x = x./norm(x,2);
   norm(x,2)

[Nuchto]

Thanks, Wayne, for your quick reply :) However, I don't understand. My values in x should add up to 1, but I can't find the new array of elements in x with the new values that would add up to 1.

[Oleg Komarov]

They're in ans.

[Nuchto]

ANS is just a value (1), is not an array of values that add up to zero.

[Oleg Komarov]

My mistake, ans proves that the x values are normalized to a unit L2 norm.

[Nuchto]

when I sum(x) after the second line, the sum doesn't add up to 1.

[Nuchto]

Help!!!

[Oleg Komarov]

x./sum(x)

Now, this is not a unit norm normalization (as I understand it, thus nobody answered earlier).

[Nuchto]

What is a unit norm normalization as you understand it?

[Kye Taylor]

"Unit norm" itself is not well-defined without specifying the norm itself.

@Nuchto, it sounds like you are looking for the l1 norm, while the initial answer provided by @Wayne is using the l2 norm...

As @Oleg suggested, you can normalize by the sum to obtain the same as the following

normX = x/norm(x,1)

Be careful if simply normalizing by the sum because it doesn't account for negative values in the original vector. However, since you are working with a probability distribution, that isn't an issue.

[Oleg Komarov]

"same as the following

normX = x/norm(x,1)"

IF all x >0.

[Nuchto]

Thanks, it works now. What is in lay terms :) the difference between l1 and l2 norm?

[Oleg Komarov]

http://en.wikipedia.org/wiki/Norm_%28mathematics%29, Euclidean vs taxicab