comparison util/classes/@dictionary/dictionary.m @ 160:e3035d45d014 danieleb

Added support classes

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