nt_normcol

 [y,norm]=nt_normcol(x,w) - normalize each column so its weighted msq is 1
 
   y: normalized data
   norm: vector of norms

   x: data to normalize
   w: weight
 
 If x is 3D, pages are concatenated vertically before calculating the
 norm. If x is 4D, apply normcol to each book.
 
 Weight should be either a column vector, or a matrix (2D or 3D) of same
 size as data.

 See nt_normrow.

 NoiseTools

0001 function [y,norm]=nt_normcol(x,w)
0002 % [y,norm]=nt_normcol(x,w) - normalize each column so its weighted msq is 1
0003 %
0004 %   y: normalized data
0005 %   norm: vector of norms
0006 %
0007 %   x: data to normalize
0008 %   w: weight
0009 %
0010 % If x is 3D, pages are concatenated vertically before calculating the
0011 % norm. If x is 4D, apply normcol to each book.
0012 %
0013 % Weight should be either a column vector, or a matrix (2D or 3D) of same
0014 % size as data.
0015 %
0016 % See nt_normrow.
0017 %
0018 % NoiseTools
0019 
0020 if nargin<2; w=[]; end
0021 
0022 if isempty(x); error('empty x'); end
0023 
0024 if iscell(x)
0025     if nargin>1; error('weights not supported for cell array'); end
0026     disp('warning: normalizing each cell individually');
0027     y={};
0028     for iCell=1:numel(x);
0029         y{iCell}=nt_normcol(x{iCell});
0030     end
0031     return
0032 end
0033 
0034 if ndims(x)==4;
0035     if nargin>1; error('weights not supported for 4D data'); end
0036     [m,n,o,p]=size(x);
0037     y=zeros(size(x));
0038     N=zeros(1,n);
0039     for k=1:p
0040         [y(:,:,:,k),NN]=nt_normcol(x(:,:,:,k));
0041         N=N+NN.^2;
0042     end
0043     return
0044 end
0045 
0046 if ndims(x)==3;
0047     
0048     % 3D: unfold, apply normcol on 2D, fold
0049     [m,n,o]=size(x);
0050     x=nt_unfold(x);
0051     if isempty(w);
0052         % no weight
0053         [y,NN]=nt_normcol(x);
0054         N=NN.^2;
0055         y=nt_fold(y,m);
0056     else
0057         % weight
0058         if size(w,1)~=m; error('weight matrix should have same nrows as data'); end 
0059         if ndims(w)==2 && size(w,2)==1; 
0060             w=repmat(w,[1,m,o]);
0061         end
0062         if size(w)~=size(w); error('weight should have same size as data'); end
0063         w=nt_unfold(w);
0064         [y,NN]=nt_normcol(x,w);
0065         N=NN.^2;
0066         y=nt_fold(y,m);
0067     end
0068 
0069 else
0070     
0071     % 2D
0072     [m,n]=size(x);
0073     if isempty(w)
0074 
0075         % no weight
0076         %N=sqrt(sum(x.^2)/m);
0077         %y=vecmult(x,1./N);
0078         N=(sum(x.^2)/m);
0079         NN=N.^-0.5;
0080         NN(find(N==0))=0;
0081         y=nt_vecmult(x,NN);
0082        
0083     else
0084 
0085         % weight
0086         if size(w,1)~=size(x,1); error('weight matrix should have same ncols as data'); end 
0087         if ndims(w)==2 && size(w,2)==1; 
0088             w=repmat(w,1,n);
0089         end
0090         if size(w)~=size(w); error('weight should have same size as data'); end
0091         if size(w,2)==1; w=repmat(w,1,n);end
0092         %N=sqrt(sum((x.^2).*w)./sum(w));
0093         %y=vecmult(x,1./N);
0094         N=(sum((x.^2).*w)./sum(w));
0095         NN=N.^-0.5;
0096         NN(find(N==0))=0;
0097         y=nt_vecmult(x, NN);
0098         
0099     end
0100 end
0101 
0102 norm=N.^0.5;
0103