CODEWITHSUNDEEP
matlabinteger
hbaderts
hbaderts

Reputation: 14316

Calculate the variance of an integer vector in MATLAB

I need to calculate the variance of a large vector which is stored as uint8. The MATLAB var function however only accepts double and single types as input. The easiest way to calculate the variance would therefore be

vec = randi(255,1,100,'uint8');
var(single(vec))

This of course gives the correct result. However using single datatype increses the memory usage by a factor of 4. For large vectors (~ 1 million elements) this will quickly fill up the memory.

What I tried: The definition of the variance for a discrete random variable X is

Definition (Source: Wikipedia)

I estimated the p's using the histogram, but then got stuck: To calculate the variance in a vectorized fashion, I would need to convert the x_i's to single or double.

Is there any possibility to calculate the variance without converting the whole vector to single or double?

Upvotes: 2

Views: 850

Answers (2)

Ander Biguri
Ander Biguri

Reputation: 35525

No. The value of the variance is going to be a floating point value most likely, so you need to perform floating point operations.

p_i itself is the Probability mass function, so sum(p_i) should be one, therefore each p_i is a floating point number.

In addition, nu, the mean, will probably not be integer neither

Upvotes: 1

yoh.lej
yoh.lej

Reputation: 1104

If you're willing to work with uint16, you can do this, it creates only 3 floating point numbers (var and the 2 means), use Var(X)=Mean(X^2)-Mean(X)^2:

uivec=uint16(vec);
mean(uivec.^2)-mean(uivec)^2

So, not as good as keeping uint8 but still twice better than converting to single. It should work with uint16 because your input is uint8 and (2^8)^2=2^16.

If you want the exact same answer as var, you need to remember that MATLAB uses the unbiased estimator for var (it divides the sum by n-1 instead of n, where n is your number of samples) so you need to do:

n=length(vec);
v=mean(uivec.^2)-mean(uivec)^2*(n/(n-1))

then your v will be exactly equal to var(single(vec)).

Upvotes: 3

Related Questions