How does function std process complex numbers

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

Accepted Answer

David Goodmanson
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))
  2 Comments
Walter Roberson
Walter Roberson on 15 Jul 2019
Which is to say that it does not do anything special for complex numbers.

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More Answers (1)

John D'Errico
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

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