function W = HWV(n,k,i,j,t)
% HWV1 two-dimensional Haar wavelet of type t
%
%   HWV1(n,k,i,j) is a 2^n-by-2^n matrix with all zeros except 
%   the 2^k x 2^k block W(i*2^k+1:(i+1)*2^k,j*2^k+1:(j+1)*2^k).
%   The entries of this block depend on the type t:
%   if type t = 1, then w=[ 1, 1; 1, 1]  (default)
%   if type t = 2, then w=[ 1, 1;-1,-1]  -- horizontal --  
%   if type t = 3, then w=[ 1,-1; 1,-1]  -- vertical   --
%   if type t = 4, then w=[ 1,-1;-1, 1]  -- diagonal   --
%   where in each case 1 stands for a ones(2^(k-1),2^(k-1)).
%
%   Main use is in conjunction with fasthaar2 and fastinvhaar
%   to illustrate one approach to image compression / coding.
%   To plot the wavelet, use e.g.
%       colormap(gray)
%       n=6; k=2;
%       for i=0:2^(n-k)-1, for j=0:2^(n-k)-1
%       image(32*(1+hwv(n,k,i,j,4))); pause(0.05), end, end
%
%   Matt Kawski 8-8-2008
%   http://math.asu.edu/~kawski
%   kawski@asu.edu
%
if nargin < 5; t=4; end
if nargin < 1; n=4; k=2; i=2; j=3; t=4; end
if k<1, disp('the second parameter must be positive integer'), end
if k>n, disp('the second parameter must be smaller than the first'), end
if i>2^(n-k)-1, disp('the third parameter i must be less than 2^(n-k)-1'), end
if j>2^(n-k)-1, disp('the fourth parameter j must be less than 2^(n-k)-1'), end


N=2^n;
W=zeros(N,N);
Z=ones(2^(k-1),2^(k-1));%%  /2^(k-1); %% /2^(n-k+1); %%  normalization???

a=1;
if t>2, b=-1; else b=1; end
if mod(t,2)>0, c=1; else c=-1; end
if (t-1)*(4-t)>0, d=-1; else d=1; end


W(i*2^k+1:(2*i+1)*2^(k-1),j*2^k+1:(2*j+1)*2^(k-1))=a*Z;
W((2*i+1)*2^(k-1)+1:(i+1)*2^k,j*2^k+1:(2*j+1)*2^(k-1))=b*Z;
W(i*2^k+1:(2*i+1)*2^(k-1),(2*j+1)*2^(k-1)+1:(j+1)*2^k)=c*Z;
W((2*i+1)*2^(k-1)+1:(i+1)*2^k,(2*j+1)*2^(k-1)+1:(j+1)*2^k)=d*Z;

% colormap(gray)
% image(32*(1+W))

end