# How does function std process complex numbers

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JFz on 12 Jul 2019
Edited: John D'Errico on 15 Jul 2019
In function S = std(A), there are complex numbers in matrix A. How does std calculate on complex numbers?
Thanks

David Goodmanson on 12 Jul 2019
Edited: David Goodmanson on 12 Jul 2019
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 on 15 Jul 2019
Thank you so much!
Walter Roberson on 15 Jul 2019
Which is to say that it does not do anything special for complex numbers.

John D'Errico on 15 Jul 2019
Edited: John D'Errico on 15 Jul 2019
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