Re: Applying function to vector by index

[Schloegl Alois]

Zitiere Andy Adler <address@hidden>:

> I've got most of a patch in place, but there's all
> sorts of weird side cases.
> 
> For example, what should sparse(eye(2)).^(1+1i) give?
> 
> Matlab gives:
> >> full(sparse(eye(2)).^(1+1i))
> 
> ans =
> 
>      1     0
>      0     1
> 
> >> full(full(eye(2)).^(1+1i))
> 
> ans =
> 
>    1.0000             NaN +    NaNi
>       NaN +    NaNi   1.0000
> 
> 
> That's because a^(b+ci) = e^(ln(a))*(b+ci)
> and ln(a) is NaN


It should be 
   a^(b+ci) = e^(ln(a)*(b+ci))
            = e^(ln(a)*b + ln(a)*ci)
            = e^(ln(a)*b)*e^(ln(a)*ci)

ln(a) = [0,-inf;-inf,0]

Because e^(ln(a)*i) is limited (abs(e^(ln(a)*i)<=1) and b>0, the result 
converges. Hence, the result [1,0;0,1] is correct. 


   Alois 



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