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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function n = vectorNorm(v, varargin)
%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
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-21
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% extract the type of norm to compute
d = 2;
if ~isempty(varargin)
d = varargin{1};
end
if d==2
% euclidean norm: sum of squared coordinates, and take square root
n = sqrt(sum(v.*v, ndims(v)));
elseif d==1
% absolute norm: sum of absolute coordinates
n = sum(abs(v), ndims(v));
elseif d==inf
% infinite norm: uses the maximal corodinate
n = max(v, [], ndims(v));
else
% Other norms, use explicit but slower expression
n = power(sum(power(v, d), ndims(v)), 1/d);
end
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