function [I, IPx, IPy] = formPermutationMatricesScale1(nGridRow, nGridCol, nD)
% Version 0.1, Feb 2006.
% This code is copyrighted by Ashutosh Saxena, Stanford University
% It is available for non-commercial use only. For commericial use, please
% contact the authors.
% Any publication or report resulting from Use of this code, should cite:
% Learning Depth from Single Monocular Images, Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng, NIPS 2005.
% 3-D Depth Reconstruction from a Single Still Image, Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng, To appear in IJCV 2007.
% For more info and dataset, visit: http://ai.stanford.edu/~asaxena/learningdepth/
% For a better version of the algorithm, also visit: 
% http://ai.stanford.edu/~asaxena/reconstruction3d/

% This is from IJCAIR version of the code, so might differ.
% This function forms the "Q" matrices in the IJCV paper in Appendix for inference/learning.


tmp = nGridRow;
nGridRow = nGridCol;
nGridCol = tmp;
% HACK order of dimensions!!!!!#R^%E#%$#


if nargin < 3
    nD = 1;     %neighbor is by default the nearest
end

totalnDepths = nGridRow*nGridCol;
totalnDepth = totalnDepths;

%=======start forming permuation matrices====================
%disp('Making Permutation matrices for 2.5 scales........');

I = speye(totalnDepths);
appI = [I; zeros(1,totalnDepths)];
zR = totalnDepths+1;

ind0 = [];  ind2 = [];

%======= for Y direction ===========
for r = 0:(nGridRow-1-nD)
    c = r*nGridCol + (1:nGridCol);
    ind0 = [ind0, c];
    ind2 = [ind2, (c+nGridCol)];
end

IPy_short = (appI(ind0,:) - appI(ind2,:) );
IPy = [IPy_short; zeros(nD*nGridCol, totalnDepths) ];   


%==========for X-direction ===================
ind0 = [];  ind4 = [];

for r = 0:(nGridRow-1)
    c = r*nGridCol + (1:(nGridCol-nD) );
    ind0 = [ind0, c, repmat(zR,1,nD)];
    ind4 = [ind4, (c+1), repmat(zR,1,nD)];
end

IPx_short = (appI(ind0,:) - appI(ind4,:) );
IPx = IPx_short;