How does function std process complex numbers

Question

JFz 2019-7-12

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https://ww2.mathworks.cn/matlabcentral/answers/471509-how-does-function-std-process-complex-numbers

评论： Rik 2022-2-14

采纳的回答： David Goodmanson

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

Thanks

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Answer 1

David Goodmanson 2019-7-12

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编辑：David Goodmanson 2019-7-12

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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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JFz 2019-7-15

Thank you so much!

Walter Roberson 2019-7-15

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

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Answer 2

John D'Errico 2019-7-15

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编辑：John D'Errico 2019-7-15

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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