Damian Eads wrote: > Emanuele Olivetti wrote: >> ... >> [*] : ||x - x'||_w = (\sum_{i=1...N} (w_i*|x_i - x'_i|)**p)**(1/p) > > This feature could be implemented easily. However, I must admit I'm not > very familiar with weighted p-norms. What is the reason for raising w > to the p instead of w_i*(|x_i-x'_i|)**p? >
I believe that it is just a choice, that should be clearly expressed since the two formulations lead to different results. I think the expression I wrote is more convenient, since it gives what it is expected even in limit cases. 2 examples: 1) if |x-x'|=N.ones(n) , then ||x-x'||_w,p = ||w||_p in your case: ||x-x'||_w,p = (\sum(w_i))**(1/p) breaking this symmetry 2) when p goes to inifinity in my case: ||x-x'||_w,inf = max(w_i*|x_i-x'_i|_{i=1,...,n}) in your case: ||x-x'||_w,inf = max(|x_i-x'_i|_{i=1,...,n}) = ||x-x'||_1,inf But I welcome any comment on this topic! Emanuele _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion