function [out] = idv2idv(n)
% Outputs a transformation matrix for changing from forward to reverse order.
%
% order 1 (Jennie's)
%
% 000, 001, 010, 011, 100, 101, 110, 111
%
% order 2 (mine)
%
% 000, 100, 010, 110, 001, 101, 011, 111
%
% USAGE:
%
%    [out] = idv2idv(n)
%
% INPUT:
%    n:      matrix, size of matrix `(2^n x 2^n)`
%
% OUTPUT:
%    out:    transforamtion matrix

warning('are you sure you want to call this function?');

if n <= 0
    out = 1;
    return;
end

out = sparse(2^n,2^n);
for i = 0:(2^n-1)
    t = dec2bin(i,n);
    t2 = t(end:-1:1);
    i2 = bin2dec(t2);
    out(i+1,i2+1) = 1;
end
