[Numpy-tickets] [NumPy] #638: var should take absolute value for complex numbers.

NumPy numpy-tickets@scipy....
Sun Dec 30 21:02:08 CST 2007


#638: var should take absolute value for complex numbers.
-------------------------+--------------------------------------------------
 Reporter:  akumar       |        Owner:  somebody
     Type:  defect       |       Status:  new     
 Priority:  normal       |    Milestone:  1.0.5   
Component:  numpy.core   |      Version:  none    
 Severity:  normal       |   Resolution:          
 Keywords:  var complex  |  
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Comment (by kumanna):

 Dear Robert,

 Replying to [comment:7 rkern]:
 > Note that the formula given in the Wikipedia article does not match the
 sentence following it. I think the sentence makes more sense than the
 formula. Complex numbers have two components. The appropriate (default)
 measure of spread of a distribution of complex numbers would be an ellipse
 (covariance matrix) rather than a circle (real scalar value). As far as
 statistical distributions are concerned, complex numbers are no different
 than 2-vectors. I need another reference to be convinced otherwise.

 Well, I do not wish to argue over this, since you have provided a
 workaround. However, I would still like you to see the following before
 closing this ticket:

 http://books.google.com/books?id=seoUuxiqG-
 oC&pg=PA408&dq=Variance+of+complex+random+variables&lr=&as_brr=0&sig=FTeiSD2WgxYYSg_F9vp5GiBMjAY
 http://books.google.com/books?id=CVJf2vHEF4cC&pg=PA32&dq=Variance+of+complex+random+variables&lr=&as_brr=0&sig=tt4_9H3Ko5KQrW_aDN7JQKC933o
 http://books.google.com/books?id=JKhw0jiqlckC&pg=PA194&dq=Variance+of+complex+random+variables&lr=&as_brr=0&sig=eumdxuzzpm1KtzMIbOY1KwAncDY

 and more from:
 http://books.google.com/books?as_q=Variance+of+complex+random+variables&num=10&btnG=Google+Search&as_epq=&as_oq=&as_eq=&as_libcat=0&as_brr=0&lr=&as_vt=&as_auth=&as_pub=&as_sub=&as_drrb=c&as_miny=&as_maxy=&as_isbn=

 Of course, if you feel that is for `random variables' and not relevant for
 a deterministic array, like in our case, you may close this ticket.

 > You can use {{{cov()}}} by separating the real and imaginary components.
 {{{cov([z.real, z.imag])}}}.

 Right, what you mean. But still, I would request you to give it one more
 thought before closing my request. :-)

 Thanks for the time!

 Kumar

-- 
Ticket URL: <http://scipy.org/scipy/numpy/ticket/638#comment:8>
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