# How does function std process complex numbers

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JFz am 12 Jul. 2019
Kommentiert: Rik am 14 Feb. 2022
In function S = std(A), there are complex numbers in matrix A. How does std calculate on complex numbers?
Thanks
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### Akzeptierte Antwort

David Goodmanson am 12 Jul. 2019
Bearbeitet: David Goodmanson am 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))
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Walter Roberson am 15 Jul. 2019
Which is to say that it does not do anything special for complex numbers.

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### Weitere Antworten (1)

John D'Errico am 15 Jul. 2019
Bearbeitet: John D'Errico am 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
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Rik am 14 Feb. 2022
Comment posted as flag by @Paramonte:
Nice!!

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