vectorNorm

VECTORNORM Compute norm of a vector, or of a set of vectors.

   N = vectorNorm(V);
   Returns the euclidean norm of vector V.

   N = vectorNorm(V, N);
   Specifies the norm to use. N can be any value greater than 0. 
   N=1 -> city lock norm
   N=2 -> euclidean norm
   N=inf -> compute max coord.

   When V is a MxN array, compute norm for each vector of the array.
   Vector are given as rows. Result is then a [M*1] array.

   Example
   n1 = vectorNorm([3 4])
   n1 =
       5

   n2 = vectorNorm([1, 10], inf)
   n2 =
       10

   See also
     vectors2d, vectorAngle

0001 function n = vectorNorm(v, varargin)
0002 %VECTORNORM Compute norm of a vector, or of a set of vectors.
0003 %
0004 %   N = vectorNorm(V);
0005 %   Returns the euclidean norm of vector V.
0006 %
0007 %   N = vectorNorm(V, N);
0008 %   Specifies the norm to use. N can be any value greater than 0.
0009 %   N=1 -> city lock norm
0010 %   N=2 -> euclidean norm
0011 %   N=inf -> compute max coord.
0012 %
0013 %   When V is a MxN array, compute norm for each vector of the array.
0014 %   Vector are given as rows. Result is then a [M*1] array.
0015 %
0016 %   Example
0017 %   n1 = vectorNorm([3 4])
0018 %   n1 =
0019 %       5
0020 %
0021 %   n2 = vectorNorm([1, 10], inf)
0022 %   n2 =
0023 %       10
0024 %
0025 %   See also
0026 %     vectors2d, vectorAngle
0027 %
0028 
0029 % ------
0030 % Author: David Legland
0031 % E-mail: david.legland@inrae.fr
0032 % Created: 2005-02-21
0033 % Copyright 2005-2024 INRA - TPV URPOI - BIA IMASTE
0034 
0035 % extract the type of norm to compute
0036 d = 2;
0037 if ~isempty(varargin)
0038     d = varargin{1};
0039 end
0040 
0041 if d==2
0042     % euclidean norm: sum of squared coordinates, and take square root
0043     n = sqrt(sum(v.*v, ndims(v)));
0044     
0045 elseif d==1 
0046     % absolute norm: sum of absolute coordinates
0047     n = sum(abs(v), ndims(v));
0048 
0049 elseif d==inf
0050     % infinite norm: uses the maximal corodinate
0051     n = max(v, [], ndims(v));
0052 
0053 else
0054     % Other norms, use explicit but slower expression
0055     n = power(sum(power(v, d), ndims(v)), 1/d);
0056     
0057 end