opToepSign.m

%opToepSign  Toeplitz matrix with random sign entries
%
%   OP = opToepSign(M,N,TYPE,NORMALIZED) creates an M by N Toeplitz
%   matrix with random +1 and -1 entries. TYPE can either be
%   'toeplitz' or 'circular'. For the 'toeplitz' type matrix, m+n-1
%   different generating entries are generated at random, whereas for
%   the 'circular' matrix, only max(m,n) are needed. When the TYPE
%   field is empty [], or not specified 'toeplitz' is chosen by
%   default. Setting the NORMALIZED flag scales the columns of the
%   Toeplitz matrix to unit norm.  Multiplication is implemented using
%   the fast Fourier transform. The use of such matrices in compressed
%   sensing was suggested by:
%
%   [1] W. U. Bajwa, J. D. Haupt, G. M. Raz, S. J. Wright, and
%       R. D. Nowak, Toeplitz-Structured Compressed Sensing Matrices,
%       IEEE/SP 14th Workshop on Statistical Signal Processing,
%       pp. 294-298, August 2007.
%
%   See also opToepGauss, opToeplitz.

%   Copyright 2009, Ewout van den Berg and Michael P. Friedlander
%   http://www.cs.ubc.ca/labs/scl/sparco
%   $Id$

classdef opToepSign < opToeplitz

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % Methods - Public
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    methods
        
        % Constructor
        function op = opToepSign(m,n,type,normalized)

           if nargin < 3 || isempty(type)
              type = 'Toeplitz';
           end
           if nargin < 4
              normalized = 0;
           end
           
           switch lower(type)
              case 'circular'
                 % Generate the entries of the matrix
                 if m < n
                    r = 2*double(randn(n,1) >= 0) - 1;
                    c = [r(1); r(end:-1:end-m+2)];
                 else
                    c = 2 * double(randn(m,1) >= 0) - 1;
                    r = [c(1); c(end:-1:end-n+2)];
                 end

              case 'toeplitz'
                 % Generate the entries of the matrix
                 c = 2*double(randn(m,1) >= 0) - 1;
                 r = [c(1); 2*double(randn(n-1,1) >= 0)-1];

              otherwise
                 error('Unrecognized type parameter.');
           end

           % Construct operator
           op = op@opToeplitz(c,r,normalized);
           op.type = 'ToepSign';
        end % Constructor
        
    end % Methods
        
end % Classdef