% BOXCARFILTER   Rectangular filtering of data series
%
%    A rectangular filtering is performed. For each abscissa point, the 
%    filtered value is based on all data inside +-xw/2.
%
%    The distance between the abscissa points is considered when calculating
%    filtered values. Data are weighted with data range they represent.
%    The filter is throughout applied symmetrically. Parts of the filter
%    extending outside the complete data range is neglected.
%
% FORMAT   yf = boxcarfilter(x,y,xw)
%        
% OUT   yf   Filtered data.
% IN    x    Data abscissa.
%       y    Data values. Must be given as a column vector or a matrix.
%       xw   Width (total) of the filter. 

% 2006-04-05   Created by Patrick Eriksson.


function yf = boxcarfilter(x,y,xw)

if size(y,1) ~= length(x)
  error('Size of *y* does not match size of *x*.');
end
%
if ~issorted(x)
  error('The vector *x* must be sorted.');
end


%= Set-up output variable
%
yf = y;


%= Length of each data range
%
l  = diff( grid2edges(x) );


x = vec2col(x);
l = vec2col(l);


for i = 1:length(x)

  % Calculate distance to closest edge of data ranges
  d       = abs( x - x(i) ) - l/2;
  d(i)    = 0;

  % What data points to consider  
  ind     = find( d < xw/2 );

  % Calculate effective length 
  leff      = l(ind);
  if d(ind(1)) + l(ind(1)) > xw/2
    leff(1)   = d(ind(1)) + l(ind(1)) - xw/2;
  end
  if d(ind(end)) + l(ind(end)) > xw/2;
    leff(end) = d(ind(end)) + l(ind(end)) - xw/2;
  end

  % Filter
  yf(i,:) = sum(y(ind,:).*repmat(leff,1,size(y,2))) / sum(leff);

end