1 %% Copyright (c) 2011, INRA
2 %% 2007-2011, David Legland <david.legland@grignon.inra.fr>
3 %% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
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35 %% @deftypefn {Function File} {@var{nm} = } vectorNorm (@var{v})
36 %% @deftypefnx {Function File} {@var{nm} = } vectorNorm (@var{v},@var{n})
37 %% Compute norm of a vector, or of a set of vectors
39 %% Without extra arguments, returns the euclidean norm of vector V.
40 %% Optional argument @var{n} specifies the norm to use. N can be any value
51 %% When @var{v} is a MxN array, compute norm for each vector of the array.
52 %% Vector are given as rows. Result is then a Mx1 array.
57 %% n1 = vectorNorm([3 4])
61 %% n2 = vectorNorm([1, 10], inf)
66 %% @seealso{vectors2d, vectorAngle}
69 function n = vectorNorm(v, varargin)
74 % extract the type of norm to compute
81 % euclidean norm: sum of squared coordinates, and take square root
82 if dim(1)==1 || dim(2)==1
85 n = sqrt(sum(v.*v, 2));
88 % absolute norm: sum of absolute coordinates
89 if dim(1)==1 || dim(2)==1
95 % infinite norm: uses the maximal corodinate
96 if dim(1)==1 || dim(2)==1
102 % Other norms, use explicit but slower expression
103 if dim(1)==1 || dim(2)==1
104 n = power(sum(power(v, d)), 1/d);
106 n = power(sum(power(v, d), 2), 1/d);
112 %!assert (5, vectorNorm ([3 4]))
113 %!assert(10, vectorNorm ([1, 10], inf))