
Ublas : 
From: Karl Meerbergen (Karl.Meerbergen_at_[hidden])
Date: 20050930 09:11:09
Hi all,
I have a question about norms for complex values.
I have the impression that norm_1 and norm_inf are not correctly
computed for complex vectors.
It looks like norm_1 makes the sum of the absolute values of the real
and imaginary parts, and norm_inf is the maximum of the absolute values
of the real and the imaginary parts.
Most textbooks only talk about real valued vectors. I would expect that
norm_1 is the sum of the moduli of the vector's elements. Norm_inf is
the maximum modulus. One of the definitions of norm is that for any
scalar a and vector v, we have
norm_1(a*v) = a * norm_1(v)
What is a for a complex value? If it is std::abs(), norm_1 and
norm_inf are definitely not correct.
If a = std::abs(a.real())+std::abs(a.imag)), this is not correct
either, I think. Correct me if I am wrong.
Karl