How does function std process complex numbers

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JFz
JFz el 12 de Jul. de 2019
Comentada: Rik el 14 de Feb. de 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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David Goodmanson
David Goodmanson el 12 de Jul. de 2019
Editada: David Goodmanson el 12 de Jul. de 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 comentarios
JFz
JFz el 15 de Jul. de 2019
Thank you so much!
Walter Roberson
Walter Roberson el 15 de Jul. de 2019
Which is to say that it does not do anything special for complex numbers.

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John D'Errico
John D'Errico el 15 de Jul. de 2019
Editada: John D'Errico el 15 de Jul. de 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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