R help - Mar 2010 - Calculate variance/covariance with complex numbers

Anybody knows what functions can be used to calculate
variance/covariance with complex numbers? var and cov don't seem to
work:
> a
                        1
V1 0.00810014+0.00169366i
V2 0.00813054+0.00158251i
V3 0.00805489+0.00163295i
V4 0.00809141+0.00159533i
V5 0.00813976+0.00161850i
> var(a)
             1
1 1.141556e-09
Warning message:
In var(a) : imaginary parts discarded in coercion
> cov(a)
             1
1 1.141556e-09
Warning message:
In cov(a) : imaginary parts discarded in coercion

Thanks in advance,
Gang

Gang Chen <gangchen6 <at> gmail.com> writes:
> 
> Anybody knows what functions can be used to calculate
> variance/covariance with complex numbers? var and cov don't seem to
> work:
How about:

y <- complex(real=5:1,imag=2:6)
z <- complex(real=1:5,imag=6:10)

complex.var <- function(x) {
  mx <- mean(x)
  n <- length(x)
  mean((x-mx)^2)*n/(n-1)
}

complex.cov <- function(x,y) {
  mx <- mean(x)
  my <- mean(y)
  n <- length(x)
  mean((x-mx)*(y-my))*n/(n-1)
}

complex.var(z)
complex.cov(y,z)

## check that they agree with the usual defs for y,z real:

z <- 1:5
var(z)-complex.var(z)
y <- c(6,5,4,2,3)
cov(y,z)-complex.cov(y,z)

On Sat, 27 Mar 2010, Gang Chen wrote:
> Anybody knows what functions can be used to calculate
> variance/covariance with complex numbers? var and cov don't seem to
> work:
How about?
> xri <- matrix(rnorm(10000)+1i*rnorm(10000),nc=2)
> crossprod(xri-colMeans(xri))/(nrow(xri)-1)
HTH,

Chuck
>
>> a
>                        1
> V1 0.00810014+0.00169366i
> V2 0.00813054+0.00158251i
> V3 0.00805489+0.00163295i
> V4 0.00809141+0.00159533i
> V5 0.00813976+0.00161850i
>
>> var(a)
>             1
> 1 1.141556e-09
> Warning message:
> In var(a) : imaginary parts discarded in coercion
>
>> cov(a)
>             1
> 1 1.141556e-09
> Warning message:
> In cov(a) : imaginary parts discarded in coercion
>
> Thanks in advance,
> Gang
>
> ______________________________________________
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>
Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901

Rolf Turner wrote:
> On 28/03/2010, at 11:50 AM, Ben Bolker wrote:
> 
>> Gang Chen <gangchen6 <at> gmail.com> writes:
>>
>>> Anybody knows what functions can be used to calculate
>>> variance/covariance with complex numbers? var and cov don't
seem to
>>> work:
>> How about:
>>
>> y <- complex(real=5:1,imag=2:6)
>> z <- complex(real=1:5,imag=6:10)
>>
>> complex.var <- function(x) {
>>  mx <- mean(x)
>>  n <- length(x)
>>  mean((x-mx)^2)*n/(n-1)
>> }
> 
> 	<SNIP>
> 
> Don't you want variances to be positive (non-negative) reals?
> 
> IIRC the population variance of a complex random variable is
> 
> 	E(|X - mu|^2) not E((X - mu)^2)
> 
> So shouldn't your complex.var function have Mod(x-mx)^2 where
> you currently have (x-mx)^2 ???
> 
> 	cheers,
> 
> 		Rolf
  Probably.  To be honest, I wasn't thinking about it that carefully.
It crossed my mind to wonder what the appropriate definition was of the
variance for complex numbers, but I didn't bother to go find out.
   I guess it goes to show (yet again) that advice may be worth what you
pay for it ...


  cheers
    Ben

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