How does function std process complex numbers

In function S = std(A), there are complex numbers in matrix A. How does std calculate on complex numbers?

Thanks

Answer 1

[David Goodmanson]

Hi JFz,

First of all, for a matrix the std is calculated independently for each column, as is true of many Matlab functions. For each column, std subtracts off the mean value as a complex calculation, then takes the absolute values of deviations from the mean and does the standard std calculation on those. For a vector of length N,

stand_dev  = sqrt(sum(abs(r-mean(r)).^2)/(N-1))

[JFz]

Thank you so much!

[Walter Roberson]

Which is to say that it does not do anything special for complex numbers.

Answer 2

[John D'Errico]

std uses the formula that is given by David, which is just the standard fornula, with no difference for complex inputs. But just to add a couple of useful formulas that apply for complex arguments:

var(V) = var(real(V)) + var(imag(V))

std(V) = sqrt(std(real(V))^2 + std(imag(V))^2 )

For example:

V = rand(1,5) + rand(1,5)*i;

var(V)
ans =
      0.20393
      
var(real(V)) + var(imag(V))
ans =
      0.20393
      
std(V)
ans =
      0.45159
      
sqrt(std(real(V))^2 + std(imag(V))^2 )
ans =
      0.45159

[Rik]

Comment posted as flag by @Paramonte:

Nice!!