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optimization_of_discrete_design_freedoms.m

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+clear all; close all; clc
+
+T=16; Lh=2*T; Lg=Lh; eta=1e4; lambda=0.0;
+figure;
+
+%% first with SAME symmetry constraint
+subplot(1,2,1)
+for B = 7:9
+ Costs = zeros(Lh+Lg, 1);
+ for tau = 1 : length(Costs)
+ try
+ fb = FilterBankStruct( );
+ fb.T = T;
+ fb.B = B;
+ fb.tau0 = tau - 1;
+ fb.symmetry = [-1;0;0];
+
+ best_cost = inf;
+ best_fb = fb;
+ for num_trial = 1 : 20
+ [h, g] = fbd_random_initial_guess(Lh, Lg, fb.B, fb.tau0);
+ fb.h = h; fb.g = g;
+ [fb, cost, recon_err, iter] = FilterBankDesign(fb, eta, lambda, 100);
+ fprintf('Trial: %g; cost: %g; reconstruction error: %g; iterations %g\n', num_trial, cost, recon_err, iter)
+ if cost < best_cost
+ best_cost = cost;
+ best_fb = fb;
+ end
+ end
+ [fb, cost, recon_err, iter] = FilterBankDesign(best_fb, eta, lambda, 1000);
+ fprintf('Refinement. Cost: %g; reconstruction error: %g; iterations %g\n', cost, recon_err, iter)
+ Costs(tau) = cost;
+ catch
+ % infeasible
+ Costs(tau) = inf;
+ end
+ end
+ hold on; semilogy((0:length(Costs)-1), log(Costs))
+end
+box on;
+xlabel('Latency')
+ylabel('$\log({\rm Design \; loss})$', 'Interpreter','latex')
+legend('$T=16,\, B=7$', '$T=16,\, B=8$', '$T=16,\, B=9$', 'Interpreter','latex')
+title('(a) SAME symmetry')
+
+%% then free designs
+subplot(1,2,2)
+for B = 7:9
+ Costs = zeros(Lh+Lg, 1);
+ for tau = 1 : length(Costs)
+ try
+ fb = FilterBankStruct( );
+ fb.T = T;
+ fb.B = B;
+ fb.tau0 = tau - 1;
+
+ best_cost = inf;
+ best_fb = fb;
+ for num_trial = 1 : 20
+ [h, g] = fbd_random_initial_guess(Lh, Lg, fb.B, fb.tau0);
+ fb.h = h; fb.g = g;
+ [fb, cost, recon_err, iter] = FilterBankDesign(fb, eta, lambda, 100);
+ fprintf('Trial: %g; cost: %g; reconstruction error: %g; iterations %g\n', num_trial, cost, recon_err, iter)
+ if cost < best_cost
+ best_cost = cost;
+ best_fb = fb;
+ end
+ end
+ [fb, cost, recon_err, iter] = FilterBankDesign(best_fb, eta, lambda, 1000);
+ fprintf('Refinement. Cost: %g; reconstruction error: %g; iterations %g\n', cost, recon_err, iter)
+ Costs(tau) = cost;
+ catch
+ Costs(tau) = inf;
+ end
+ end
+ hold on; semilogy((0:length(Costs)-1), log(Costs))
+end
+box on;
+xlabel('Latency')
+ylabel('$\log({\rm Design \; loss})$', 'Interpreter','latex')
+legend('$T=16,\, B=7$', '$T=16,\, B=8$', '$T=16,\, B=9$', 'Interpreter','latex')
+title('(b) Free design')