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%% Copyright (c) 2011, INRA
%% 2007-2011, David Legland <david.legland@grignon.inra.fr>
%% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
%%
%% All rights reserved.
%% (simplified BSD License)
%%
%% 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 COPYRIGHT HOLDER 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 copyright holder.
%% -*- texinfo -*-
%% @deftypefn {Function File} {@var{nm} = } vectorNorm (@var{v})
%% @deftypefnx {Function File} {@var{nm} = } vectorNorm (@var{v},@var{n})
%% Compute norm of a vector, or of a set of vectors
%%
%% Without extra arguments, returns the euclidean norm of vector V.
%% Optional argument @var{n} specifies the norm to use. N can be any value
%% greater than 0.
%% @table @samp
%% @item N=1
%% City lock norm.
%% @item N=2
%% Euclidean norm.
%% @item N=inf
%% Compute max coord.
%% @end table
%%
%% When @var{v} is a MxN array, compute norm for each vector of the array.
%% Vector are given as rows. Result is then a Mx1 array.
%%
%% Example
%%
%% @example
%% n1 = vectorNorm([3 4])
%% n1 =
%% 5
%%
%% n2 = vectorNorm([1, 10], inf)
%% n2 =
%% 10
%% @end example
%%
%% @seealso{vectors2d, vectorAngle}
%% @end deftypefn
function n = vectorNorm(v, varargin)
% size of vector
dim = size(v);
% 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
if dim(1)==1 || dim(2)==1
n = sqrt(sum(v.*v));
else
n = sqrt(sum(v.*v, 2));
end
elseif d==1
% absolute norm: sum of absolute coordinates
if dim(1)==1 || dim(2)==1
n = sum(abs(v));
else
n = sum(abs(v), 2);
end
elseif d==inf
% infinite norm: uses the maximal corodinate
if dim(1)==1 || dim(2)==1
n = max(v);
else
n = max(v, [], 2);
end
else
% Other norms, use explicit but slower expression
if dim(1)==1 || dim(2)==1
n = power(sum(power(v, d)), 1/d);
else
n = power(sum(power(v, d), 2), 1/d);
end
end
endfunction
%!assert (5, vectorNorm ([3 4]))
%!assert(10, vectorNorm ([1, 10], inf))
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