(Note: this is not for the course it itself since i have already completed it, i just though this wpuld be the most fitting category)

Hello, so i am trying to implement the multivariate gaussian in java. But it seems like i got something wrong in the formula and i am not sure.

My implemention:
double value = (1/2*PI) * Math.abs(sigma) - 1/2 * Math.exp(-1/2 (x - mu) * 1/sigma1/2 * (x- mu)

x = 2d array
mu & sigma = 1d array

I am probably thinking its likely an error in the the converstion i have written in java. But i am actually not really sure what part i have written wrong.

I have seen a thread that gives the python wih numpy implemention. But that really doesnt make me understand what i have done wrong in the implemention of the raw formula, since i would like to understand math aspect more.

I don’t use Java but we can talk about the meaning of the symbol so you can find the right Java library/function yourself.

|\Sigma| is the determinant of the covariance matrix \Sigma, instead of absolute value of something.

\Sigma^{-1} is the inverse of the covariance matrix \Sigma. This is a matrix inverse operation instead of taking reciprocal of something.

Lastly, the 3 terms inside the exponential are matrix-multiplicated instead of simple multiplication.

When you search for the right Java function yourself, please be reminded that you are working with matrices here, so the algebra is matrix algebra. I suggest you to verify you have the right function by initializing the variables into some small arrays such as a 2x2 array for x. With these sample variables you can cross check the result from the function you find with the result you calculated using pencil and paper.

Thank you, this was absolutely what i was looking for, i was pretty sure i had misunerstood some of the symbols myself. The implementation itself should be easy now.