clean up

examples/example3_5.m → examples/example5_1.m

@@ -1,5 +1,5 @@
 % =================================================================
-% Code for Example 3.5 in the paper:
+% Code for Example 5.1 in the paper:
 % Y. Zheng, G. Fantuzzi, Sum-of-squares chordal decomposition of polynomial 
 % matrix inequalities
 %

examples/example3_5b.m → examples/example5_1b.m

@@ -1,9 +1,11 @@
 % =================================================================
-% Code for Example 3.5 in the paper:
+% Code for Example 5.1 in the paper:
 % Y. Zheng, G. Fantuzzi, Sum-of-squares chordal decomposition of polynomial 
 % matrix inequalities
 %
-% NOTE: Assume the option sos.csp in Yalmip has been modified
+% NOTE: Assume the option sos.csp in Yalmip has been modified or
+%          install the following fork of YALMIP:
+% https://github.com/aeroimperial-optimization/aeroimperial-yalmip
 % =================================================================
 clc
 clear
@@ -15,9 +17,9 @@
 opts.verbose = 0;
 
 % Parameters
-Dim = 2:2:6;     % Dimension of the polynomial matrix
+Dim = 5:5:40;     % Dimension of the polynomial matrix
                  % the range of 5:5:40 was used in the paper                  
-nu = 1;          % degree of SOS multipler  
+nu = 0:1:3;          % degree of SOS multipler  
                  % the range of 1:4 was used in the paper            
 
 % Initalize containers
@@ -83,6 +85,6 @@
             end
         end
 
-        fprintf('m = %d,  time %5.3f  %5.3f \n ',m, TimeSolver{dind}(index,1),TimeSolver{dind}(index,2));
+        fprintf('m = %d,  time %5.3f  %5.3f \n',m, TimeSolver{dind}(index,1),TimeSolver{dind}(index,2));
     end
 end

examples/example5_2_dense.m

@@ -25,7 +25,7 @@
 objStandard  = zeros(length(Deg),length(Gsize));
 timeStandard = zeros(length(Deg),length(Gsize));
 
-for indm = 1%:length(Gsize)
+for indm = 1:length(Gsize)
     m         = Gsize(indm);
     fprintf('Graph size: %d \n\n',m);
     memFlag = 0;  % out of memory for Standard SOS?
@@ -66,12 +66,12 @@
 
         % Solve without sparsity exploitation
         opts = sdpsettings('sos.csp',0);
-        if m >= 30 && Deg(indx) == 4  % these choices --> out of memory on our computer
-            memFlag = 1;
-        end
-        if m >= 35 && Deg(indx) >= 3 % these choices --> out of memory on our computer
-            memFlag = 1;
-        end
+%         if m >= 30 && Deg(indx) == 4  % these choices --> out of memory on our computer
+%             memFlag = 1;
+%         end
+%         if m >= 35 && Deg(indx) >= 3 % these choices --> out of memory on our computer
+%             memFlag = 1;
+%         end
         if memFlag == 0
             try
                 sol =  solvesos(F,-cost,opts,[s1c; gc]);

examples/example5_2_graphs.m

@@ -5,7 +5,7 @@
 %
 % =================================================================
 
-Gsize = 10:5:40;
+Gsize = 5:2:10;  % 10:5:40 was used in the paper
 maxClique = 5;   % bound on the largest maximal cliques
 G = [];
 A = [];
@@ -23,4 +23,4 @@
     B{indm} = (spones(G{indm}) - eye(m)).*tmp;   % zeros on its diagonal
 end
 
-%save('example5_2_graphs.mat','G','A','B','Gsize');
+%save('data/example5_2_graphs_new.mat','G','A','B','Gsize');

examples/example5_2_integral.m

@@ -6,20 +6,20 @@
 %
 % =================================================================
 
-function example5_2_integral
-    load('data/example5_2_graphs.mat','A','B','Gsize')
+%function example5_2_integral
+load('data/example5_2_graphs.mat','A','B','Gsize')
 
-    cost_integral = zeros(length(Gsize),1);
-    for indm = 2%:length(Gsize)   % Different matris sizes
-        m  = Gsize(indm);
-        Am = A{indm};
-        Bm = B{indm};
-        p = @(r,theta) mineigP(m,Am,Bm,r,theta) .* r;
-        tstart = tic;
-        cost_integral(indm) = integral2(p,0,1,0,2*pi,'AbsTol',1e-7,'RelTol',1e-8); 
-        tend = toc(tstart);
-        fprintf('%d   %4.2f   %4.5f\n',m,tend,cost_integral(indm));
-    end
-
-    %save('example5_2_graphs.mat','G','A','B','Gsize','cost_integral')
+cost_integral = zeros(length(Gsize),1);
+for indm = 2:length(Gsize)   % Different matris sizes
+    m  = Gsize(indm);
+    Am = A{indm};
+    Bm = B{indm};
+    p = @(r,theta) mineigP(m,Am,Bm,r,theta) .* r;
+    tstart = tic;
+    cost_integral(indm) = integral2(p,0,1,0,2*pi,'AbsTol',1e-7,'RelTol',1e-8); 
+    tend = toc(tstart);
+    fprintf('%d   %4.2f   %4.5f\n',m,tend,cost_integral(indm));
 end
+
+%save('example5_2_graphs.mat','G','A','B','Gsize','cost_integral')
+%end

examples/example5_2_plot_patterns.m

@@ -1,19 +1,17 @@
 % =================================================================
-% Plot chordal patterns, Example 5-2 in the paper:
+% Plot chordal patterns (Figure 5), Example 5-2 in the paper:
 % Y. Zheng, G. Fantuzzi, Sum-of-squares chordal decomposition of polynomial 
 % matrix inequalities
 %
 % =================================================================
 
-function example5_2_plot_patterns
-    close all
-    load('data/example5_2_results.mat','G','Gsize');  % Pre-generated chordal graphs
-    for indg = 2:7
-        figure;
-        spym(G{indg},'ks',5);               
-        set(gcf,'Position',[100 100 300 300])
-        fname = ['chordal',num2str(Gsize(indg))];
-        print(gcf,fname,'-painters','-depsc','-r600')
-    end
+close all
+load('data/example5_2_graphs.mat','G','Gsize');  % Pre-generated chordal graphs
+for indg = 2:7
+    figure;
+    spym(G{indg},'ks',5);               
+    set(gcf,'Position',[100 100 300 300])
+    fname = ['chordal',num2str(Gsize(indg))];
+    %print(gcf,fname,'-painters','-depsc','-r600')
 end
 

examples/example5_2_plots.m

@@ -1,5 +1,5 @@
 % =================================================================
-% Plot inner approximation, Example 5-2 in the paper:
+% Plot inner approximation (Figure 6), Example 5-2 in the paper:
 %
 % Y. Zheng, G. Fantuzzi, Sum-of-squares chordal decomposition of polynomial
 % matrix inequalities
@@ -123,6 +123,6 @@
 ff.PaperSize = FigSize;
 ff.PaperPosition = [0 0 FigSize];
 fname = ['gio_inner_approx'];
-print(gcf,fname,'-painters','-depsc','-r300')
+%print(gcf,fname,'-painters','-depsc','-r300')
 
 

examples/example5_2_sparse.m

@@ -1,4 +1,5 @@
-% =================================================================% Code for Example 5-2 in the paper:
+% =================================================================
+% Code for Example 5-2 in the paper:
 % Y. Zheng, G. Fantuzzi, Sum-of-squares chordal decomposition of polynomial
 % matrix inequalities
 %
@@ -16,15 +17,16 @@
 load('data/example5_2_graphs.mat','G','A','B','Gsize')
 
 % Parameters: half-degree of SOS multipliers
+% Deg = 2:4;
 Deg = 14;
 
 % Initalize containers for the results
 gSparse    = cell(length(Deg),length(Gsize));
-exponents    = cell(length(Deg),length(Gsize));
+exponents  = cell(length(Deg),length(Gsize));
 objSparse  = zeros(length(Deg),length(Gsize));
 timeSparse = zeros(length(Deg),length(Gsize));
 
-for indm = 2%length(Gsize)
+for indm = 2%:length(Gsize)
     m = Gsize(indm);
     clique = cliquesFromSpMatD(G{indm}); % cliques of graph
     fprintf('     Graph size: %d \n',m)