localmoran_orig

 PURPOSE: calculate local Moran's I for a local grid using a weight matrix.
 -------------------------------------------------------------------
 USAGE: m = localmoran_orig(raster, W, s);
 where: [raster] is the grid to analyse
        [W] is the normalized weight matrix of same size as [raster]
        [s] is an optional flag to use zscores of input values for
        calculation. Set to 'true' if zscores of local grid should be
        calculated. Leave blank if not desired or input values are already
        standardized. 
 -------------------------------------------------------------------------
 OUTPUTS:
        [m] local Moran's I 
 -------------------------------------------------------------------
 Version: Original version true to Jo Woods code for edge effects, see
          code line 63.
          Based on code from Jo Woods dissertation
          http://www.soi.city.ac.uk/~jwo/phd/04param.php

 NOTES: Weight matrix needs to be 'moving window' style, not contiguity
        matrix: Moran's I is calculated and weighted for neighbours to center cell.
        Matrix needs to be normalized (weights sum to 1) and center cell weight 
        will be set to 0 if not already. 
        Use euklid_W() or euklid_invW() to construct weight matrices with
        euklidean distances.

 See Anselin (1995, 'LISA.', Geogr. Analysis 27(2),p.93f) for details on standardized variables in 
 calculation of local Moran's I. 

 Felix Hebeler, Geography Dept., University Zurich, March 2006.

0001 function m = localmoran_orig(raster, W);
0002 
0003 % PURPOSE: calculate local Moran's I for a local grid using a weight matrix.
0004 % -------------------------------------------------------------------
0005 % USAGE: m = localmoran_orig(raster, W, s);
0006 % where: [raster] is the grid to analyse
0007 %        [W] is the normalized weight matrix of same size as [raster]
0008 %        [s] is an optional flag to use zscores of input values for
0009 %        calculation. Set to 'true' if zscores of local grid should be
0010 %        calculated. Leave blank if not desired or input values are already
0011 %        standardized.
0012 % -------------------------------------------------------------------------
0013 % OUTPUTS:
0014 %        [m] local Moran's I
0015 % -------------------------------------------------------------------
0016 % Version: Original version true to Jo Woods code for edge effects, see
0017 %          code line 63.
0018 %          Based on code from Jo Woods dissertation
0019 %          http://www.soi.city.ac.uk/~jwo/phd/04param.php
0020 %
0021 % NOTES: Weight matrix needs to be 'moving window' style, not contiguity
0022 %        matrix: Moran's I is calculated and weighted for neighbours to center cell.
0023 %        Matrix needs to be normalized (weights sum to 1) and center cell weight
0024 %        will be set to 0 if not already.
0025 %        Use euklid_W() or euklid_invW() to construct weight matrices with
0026 %        euklidean distances.
0027 %
0028 % See Anselin (1995, 'LISA.', Geogr. Analysis 27(2),p.93f) for details on standardized variables in
0029 % calculation of local Moran's I.
0030 %
0031 % Felix Hebeler, Geography Dept., University Zurich, March 2006.
0032 
0033 
0034 %initialise variables
0035 covar=0; 
0036 
0037 %if exist('W')
0038     %if (W==1) W=ones(size(raster,1),size(raster,2)); end
0039 %else W=ones(size(raster,1),size(raster,2));end
0040 
0041 ncols= size(raster,2);
0042 nrows= size(raster,1);
0043 %n= ncols*nrows-1; %number of neighbours for center cell
0044 w=0;   %-W(ceil(nrows/2),ceil(ncols/2)); % set counter to ignore center weight
0045 
0046 % calculate mean for raster
0047 zbar = mean(nanmean(raster(:))); 
0048 
0049 zi = raster(ceil(nrows/2),ceil(ncols/2))*W(ceil(nrows/2),ceil(ncols/2)); % value at center of raster
0050 if (isnan(zi)) m=NaN; return; end;
0051 
0052 vari = (zi - zbar) * (zi - zbar); %variance of center cell i
0053 var = mean(nanmean((raster-zbar)*(raster-zbar))); % mean variance over window
0054 
0055 for row=1:1:nrows;
0056     for col=1:1:ncols;
0057           zj = raster(row,col);
0058           if (isnan(zj)) break; end; %don't include NaNs
0059           covar = covar + (W(row,col)*((zi - zbar) * (zj - zbar)));
0060           w = w+ W(row,col);
0061      end
0062 end
0063 covar = covar - (W(ceil(nrows/2),ceil(ncols/2))*vari); % subtract 'covar'=vari of center cell with itself from sum of covariances
0064 if (vari~=0.0)
0065     m = covar/(vari*w); 
0066 else
0067     m = 1.0;
0068 end