vnorm.m

实现地震勘探中

function y=vnorm(A,varargin)
% VNORM - Return the vector norm along specified dimension of A
%
%   VNORM(A) returns the 2-norm along the first non-singleton dimension of A
%   VNORM(A,dim) return the 2-norm along the dimension 'dim'
%   VNORM(A,dim,normtype) returns the norm specified by normtype along the 
%   dimension 'dim'
%   VNORM(A,[],normtype) returns the norm specified by normtype along the 
%   first non-singleton dimension of A
% 
%   normtype may be one of {inf,-inf,positive integer}.
%   For a given vector, v, these norms are defined as
%    inf: max(abs(v))
%   -inf: min(abs(v))
%   p (where p is a positive integer): sum(abs(v).^p)^(1/p)
% 
%   Matlab File Exchange, File 10708, by Winston Smith
%
%   Examples:
%       A= [8 1 6; 3 5 7; 4 -9 2];
%
%       % Columnwise 2-norm (Euclidean norm)
%       vnorm(A,1)=[9.4340 10.3441 9.4340];
%       vnorm(A,[],2) % Same as above (since first non-singleton dimensions
%                     % is columnwise and default norm is 2-norm.
%       vnorm(A,[],[])% Again, same as above
%
%       % Row-wise maximum of absolute values
%       vnorm(A,2,inf)=[8 7 9]'; 
%
%       % Columnwise minimum of absolute values
%       vnorm(A,[],-inf)=[3 1 2];
%       
%       % Error: Use the inf type and not the string 'inf'
%       vnorm(A,[],'inf')   % Wrong
%       vnorm(A,[],inf)     % Correct

dim=[];
ntype=[];

if nargin>1
   dim=varargin{1};
   if isempty(dim)
      idx=find(size(A)~=1);
      dim=idx(1);
   elseif dim ~= floor(dim) || dim < 1
      error('Dimension must be a positive integer.');
   end
   if nargin > 2
      ntype=varargin{2};
   end
else
   dim=1;
end


if isempty(ntype)
   y=sqrt(sum( abs(A).^2,dim) );

elseif ntype == 1
   y=sum( abs(A),dim );
   
elseif isinf(ntype)
   if ntype > 0
      y=max(abs(A),[],dim);
   else
      y=min(abs(A),[],dim);
   end

elseif ntype~=floor(ntype) || ntype<1
   error('Norm type must be one of inf,-inf or a positive integer.');

else 
   y=(sum( abs(A).^ntype , dim) ).^(1/ntype);

end