Currently, v.lpNorm<Infinity>() is implemented as v.cwiseAbs().maxCoeff(), which fails for the corner case of an empty vector. In many occasions, a result of 0 would be more convenient (and also consistent with other p-norms). Also, both Matlab's and Octave's norm([], inf) return 0 (although via interpreting [] as a matrix instead of a vector and applying the matrix inf-norm definition). Of course, one could always check for v.size() > 0 before invoking v.lpNorm<Infinity>(), but this looks inconvenient, especially in templated code where the norm type is a parameter. Moving the check to src/Core/Dot.h, lpNorm_selector<..., Infinity> (line 233 in current dev branch) seems more appropriate. Btw. Are there any plans of adding more specializations to lpNorm, e.g. - v.lpNorm<0> ==> v.array().count() - v.lpNorm<NegativeInfinity> ==> v.cwiseAbs().minCoeff() (with a new constant Eigen::NegativeInfinity)

Fixed: https://bitbucket.org/eigen/eigen/commits/677c9f157781/ Regarding L_0, v.array().count() does not define a proper norm, and L_0 refers to another definition for mathematicians, i.e.: (v.abs()/(1+v.abs())).sum()/2^n Regarding minus infinity, are there any use cases?

Using \ell_0 as "counting norm" is not completely uncommon: https://en.wikipedia.org/wiki/Lp_space#When_p_.3D_0 But, I guess using v.array().count() would definitely be less confusing here. The same goes for v.cwiseAbs().minCoeff() instead of lpNorm<NegativeInfinity>(); We could also consider providing a v.lpNorm(const RealScalar& p) function (allowing non-integer p), which for for p<1 returns the corresponding pseudo norm (however, for p-->0 the natural limit for anything with more than one non-zero would be infinity instead of .array().count() -- and for floating point values checking != 0.0 actually is often meaningless ...)

yes, I perfectly agree that using L_0 as v.array().count() is extremely common! I just wanted to point out that there do exist a risk of ambiguity. Ok for v.lpNorm(const RealScalar& p).

Thanks for the fix! Regarding the 0-case: After checking the Wikipedia article, I also agree that v.array().count() is less ambiguous and should be preferred. The variant with a runtime norm type is a good idea, though. For performance reasons, I would also propose an integer overload that behaves exactly as the templated version for the special argument values 1, 2 and Eigen::Infinity. Regarding minus infinity: I had no particular use case in mind. It was just a consideration for bringing the API on par with Matlab/Octave.

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