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Normalize to unit norm

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Nuchto 2012-5-27

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采纳的回答： Wayne King

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

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Wayne King 2012-5-27

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

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

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Nuchto 2012-5-27

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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 2012-5-27

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They're in ans.

Nuchto 2012-5-27

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

Oleg Komarov 2012-5-27

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

Nuchto 2012-5-27

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

Nuchto 2012-5-30

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Help!!!

Oleg Komarov 2012-5-30

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x./sum(x)

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

Nuchto 2012-6-1

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What is a unit norm normalization as you understand it?

Kye Taylor 2012-6-1

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"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.