daniele@160: classdef dictionary
daniele@160:     %% Dictionary for sparse representation
daniele@160:     properties
daniele@160:         phi         %Matrix containing the dictionary
daniele@160:         len         %Length of basis functions
daniele@160:         nAtoms      %Number of basis function
daniele@160:         name        %String containing the matrix ensemble from which the dictionary is drawn
daniele@160:     end
daniele@160:     properties (Dependent = true)
daniele@160:         redundancy      %Redundancy of the dictionary: nAtoms/len
daniele@160:         coherence       %Maximum inner product of different basis
daniele@160:         isNormalised    %True if the atoms have unit norm
daniele@160:         rank            %rank of the dictionary
daniele@160:     end
daniele@160:     
daniele@160:     methods
daniele@160:         %% Constructor
daniele@160:         function obj = dictionary(phi,len,nAtoms)
daniele@160:             % obj = dictionary(phi,len,nAtoms)
daniele@160:             % INPUTS:
daniele@160:             % - phi: either a string specifying a matrix ensamble or a
daniele@160:             % matrix defining an explicit dictionary
daniele@160:             % - len: length of the atoms (only for implicit dictionaries)
daniele@160:             % - nAtoms: number of atoms (only for implicit dictionaries)
daniele@160:             if nargin
daniele@160:                 if ~ischar(phi)
daniele@160:                     [obj.len obj.nAtoms] = size(phi);
daniele@160:                     obj.phi              = phi;
daniele@160:                     obj.name             = 'explicit';
daniele@160:                 else
daniele@160:                     switch lower(phi)
daniele@160:                         case 'dct'
daniele@160:                             obj.phi = dctmatrix(len,nAtoms);
daniele@184:                         case 'grassmannian'
daniele@160:                             obj.phi = grassmanian(len,nAtoms);
daniele@160:                         otherwise
daniele@160:                             obj.phi = MatrixEnsemble(len,nAtoms,phi);
daniele@160:                     end
daniele@160:                     obj.len    = len;
daniele@160:                     obj.nAtoms = nAtoms;
daniele@160:                     obj.name   = lower(phi);
daniele@160:                 end
daniele@160:             end
daniele@184: 		end
daniele@160:         %% Dependent properties
daniele@160:         function redundancy = get.redundancy(obj)
daniele@160:             redundancy = obj.nAtoms/obj.len;
daniele@160:         end
daniele@160:         function coherence = get.coherence(obj)
daniele@160:             obj.phi = normcol(obj.phi);
daniele@160:             G = obj.phi'*obj.phi;
daniele@160:             G = G - eye(size(G));
daniele@160:             coherence = max(abs(G(:)));
daniele@160:         end
daniele@160:         function isNormalised = get.isNormalised(obj)
daniele@160:             isNormalised = norm(sum(conj(obj.phi).*obj.phi) - ...
daniele@160:                 ones(1,obj.nAtoms))<1e-9;
daniele@160:         end
daniele@160:         function r = get.rank(obj)
daniele@160:             r = rank(obj.phi);
daniele@160:         end
daniele@160:         %% Operations
daniele@160:         function obj = normalize(obj)
daniele@160:             obj.phi = normcol(obj.phi);
daniele@184: 		end
daniele@160:         %% Visualization
daniele@160:         function image(obj)
daniele@160:             %Image of the dictionary
daniele@160:             if isreal(obj.phi)
daniele@160:                 imagesc(obj.phi);
daniele@160:                 title('Dictionary');
daniele@160:                 xlabel('Atom number');
daniele@160:             else
daniele@160:                 subplot(2,1,1)
daniele@160:                 imagesc(real(obj.phi));
daniele@160:                 title('Real');
daniele@160:                 xlabel('Atom number');
daniele@160:                 subplot(2,1,2)
daniele@160:                 imagesc(imag(obj.phi));
daniele@160:                 title('Imaginary');
daniele@160:                 xlabel('Atom number');
daniele@160:             end
daniele@160:         end
daniele@160:         function imagegram(obj)
daniele@160:             G = obj.phi'*obj.phi;
daniele@160:             imagesc(G);
daniele@160:             title('Gram Matrix')
daniele@160:         end
daniele@160:         function plot(obj,n)
daniele@160:             %Plot of the n-th basis
daniele@160:             if isreal(obj.phi)
daniele@160:                 plot(obj.phi(:,n));
daniele@160:                 title(['Atom number ' num2str(n) '/' num2str(size(obj.phi,2))]);
daniele@160:             else
daniele@160:                 subplot(2,1,1)
daniele@160:                 plot(real(obj.phi(:,n)));
daniele@160:                 title(['Atom number ' num2str(n) '/' num2str(size(obj.phi,2)) ' - Real']);
daniele@160:                 subplot(2,1,2)
daniele@160:                 plot(imag(obj.phi(:,n)));
daniele@160:                 title(['Atom number ' num2str(n) '/' num2str(size(obj.phi,2)) ' - Imaginary']);
daniele@160:             end
daniele@184: 		end
daniele@160:         function movie(obj)
daniele@160:             %Movie of the basis
daniele@160:             for i=1:size(obj.phi,2)
daniele@160:                 obj.plot(i);
daniele@160:                 pause(1/25);
daniele@160:             end
daniele@160:         end
daniele@160:     end
daniele@160: end