## How does function std process complex numbers

### JFz (view profile)

on 12 Jul 2019
Latest activity Edited by John D'Errico

on 15 Jul 2019

### David Goodmanson (view profile)

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

R2018b

### David Goodmanson (view profile)

on 12 Jul 2019
Edited by David Goodmanson

### David Goodmanson (view profile)

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

### JFz (view profile)

on 15 Jul 2019
Thank you so much!
Walter Roberson

### Walter Roberson (view profile)

on 15 Jul 2019
Which is to say that it does not do anything special for complex numbers. ### John D'Errico (view profile)

on 15 Jul 2019
Edited by John D'Errico

### John D'Errico (view profile)

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