scripts for reproduce figure 1 and 2

matlab/tfgm/scripts/exp_gabmul_eigs_properties.m

+clc; clear; close all;
+%%
+% This script generates figures 1 and 2 of the paper.
+% The mask used for figure 1 is the one that has been computed with
+% the time-frequency parameters generated with a Gauss window of 256 time samples.
+
+%%  Load time-frequency mask from .mat file
+mask_gauss = load('mask_with_gauss256_win.mat');
+mask_hann = load('mask_with_hann512_win.mat');
+
+%save masks in a structure
+mask_dict.('Gauss256') = mask_gauss;
+mask_dict.('Hann512') = mask_hann;
+
+%% directory for figures
+
+fig_dir ='fig_localisation_properties_of_gabmul_eigs';
+if ~exist(fig_dir,'dir')
+    mkdir(fig_dir);
+end
+addpath(fig_dir)
+
+%% structure containing the parameters for each of the windows
+
+param_dict = struct('Gauss256', struct('win_type', 'gauss', 'win_dur',256/8000,...
+    'hop_ratio', 1/4, 'nbins_ratio',4),...
+    'Hann512', struct('win_type','hann', 'win_dur',512/8000,...,
+    'hop_ratio',1/8, 'nbins_ratio',2));
+
+
+
+%% structure of signals parameters
+signal_params = struct('fs',8000,'sig_len', 16384);
+
+%%
+for k_param= 1 :length(fieldnames(param_dict))
+    keys = fieldnames(param_dict);
+    param = param_dict.(keys{k_param});
+    
+    win_type=param.('win_type');
+    win_dur=param.('win_dur');
+    fs = signal_params.fs;
+    hop_ratio=param.('hop_ratio');
+    nbins_ratio=param.('nbins_ratio');
+    
+    approx_win_len = 2.^round(log2(win_dur*fs));
+    hop =  approx_win_len* hop_ratio;
+    nbins = approx_win_len * nbins_ratio;
+    
+    sig_len = signal_params.sig_len;
+    
+    dgt_params = generate_dgt_parameters(win_type, approx_win_len, hop,...,
+        nbins, sig_len);
+    
+    [dgt, idgt] = get_stft_operators(dgt_params, signal_params);
+    
+    
+    param_dict.(keys{k_param}).('signal_params') = signal_params;
+    param_dict.(keys{k_param}).('dgt_params') = dgt_params;
+    param_dict.(keys{k_param}).('dgt') = dgt;
+    param_dict.(keys{k_param}).('idgt') = idgt;
+    
+end
+
+
+%% Compute the evd of the multiplier by using the DGT and IDGT
+% generated from the Gauss window. The calculation of the evd is
+% done for each of the two Gauss and Hann masks.
+
+%%
+
+nb_eigvalues=4000;
+masks = fieldnames(mask_dict);
+evdn_gauss ={};
+
+sig_len = param_dict.Gauss256.signal_params.sig_len;
+for k=1: length(masks)
+    
+    disp(k);
+    gab_mul = gen_gabmul_operator(param_dict.('Gauss256').dgt, ...,
+        param_dict.('Gauss256').idgt, mask_dict.(masks{k}).mask);
+    tic;
+    q_mat = randomized_range_finder(gab_mul, sig_len, nb_eigvalues);
+    t1= toc;
+    fprintf(" runtimes for Q: %f\n", t1);
+    
+    tic;
+    evdn = EVD_nystrom(gab_mul, q_mat);
+    t2 = toc;
+    evdn_gauss.(masks{k}) = evdn;
+    fprintf(" runtimes for nystrom - gauss: %f\n", t2);
+end
+
+%% Compute the evd of the multiplier by using the DGT and IDGT
+% generated from the Hanns window. The calculation of the evd is
+% done for each of the two Gauss and Hann masks.
+%%
+evdn_hann = {};
+%%
+for k=1: length(masks)
+    gab_mul = gen_gabmul_operator(param_dict.('Hann512').dgt, ...,
+        param_dict.('Hann512').idgt,  mask_dict.(masks{k}).mask);
+    tic;
+    q_mat = randomized_range_finder(gab_mul, sig_len, nb_eigvalues);
+    t1= toc;
+    fprintf(" runtimes for Q: %f\n", t1);
+    tic;
+    evdn = EVD_nystrom(gab_mul, q_mat);
+    t2 = toc;
+    
+    evdn_hann.((masks{k})) = evdn;
+    fprintf(" runtimes for nystrom-hann: %f\n", t2);
+end
+
+
+%% eigenvalues
+
+%%
+figure; 
+D1 = diag(evdn_hann.Gauss256.D);
+D4= diag(evdn_gauss.Gauss256.D);
+
+semilogy(D4,'b', 'Linewidth',4);
+hold on; 
+semilogy(D1, 'r','Linewidth',4);
+semilogy(D4(1),'bo', 'Linewidth', 15,'MarkerSize',10)
+semilogy(D1(1),'r^','Linewidth', 15,'MarkerSize',10)
+semilogy(3539,D4(3539),'bo','Linewidth', 15,'MarkerSize',10)
+semilogy(3408,D1(3408),'r^','Linewidth', 15,'MarkerSize',10)
+grid on;
+
+
+xlabel({'index = $k$'},'Interpreter','latex');
+ylabel({' Eigenvalues $\sigma[k]$'},'Interpreter','latex');
+
+set(gca, 'FontSize', 20, 'fontName','Times');
+
+l = legend('Gauss','Hann',...,
+    '$\sigma[1]$ = 1, $\sigma[3539] = 2.699 \times 10^{-4}$',...,
+    '$\sigma[1]$ =1, $\sigma[3408] = 1.258 \times 10^{-4}$',...,
+    'Location','southwest');
+
+set(l, 'interpreter', 'latex')
+saveas(gcf,fullfile(fig_dir, 'eigenvalues_gauss_hann.fig'));
+saveas(gcf,fullfile(fig_dir, 'eigenvalues_gauss_hann.png'));
+%% eigenvectors
+figure; 
+set(gcf,'position',[1, 1 1000 800]);
+subplot(221);
+plot_spectrogram(eigs_gauss(:,147), param_dict.('Gauss256').dgt_params,...,
+    param_dict.('Gauss256').signal_params, param_dict.('Gauss256').dgt);
+yticks([0,1000,2000,3000,4000]);
+yticklabels([0,1,2,3,4]);
+ylabel('Frequency (kHz)')
+set(gca, 'FontSize', 20, 'fontName','Times');
+subplot(222);
+plot_spectrogram(eigs_gauss(:,86), param_dict.('Gauss256').dgt_params,...,
+    param_dict.('Gauss256').signal_params, param_dict.('Gauss256').dgt);
+yticks([0,1000,2000,3000,4000]);
+yticklabels([0,1,2,3,4]);
+ylabel('Frequency (kHz)')
+set(gca, 'FontSize', 20, 'fontName','Times');
+    subplot(223);
+plot_spectrogram(eigs_gauss(:,3039), param_dict.('Gauss256').dgt_params,...,
+    param_dict.('Gauss256').signal_params, param_dict.('Gauss256').dgt);
+yticks([0,1000,2000,3000,4000]);
+yticklabels([0,1,2,3,4]);
+ylabel('Frequency (kHz)')
+set(gca, 'FontSize', 20, 'fontName','Times');
+subplot(224);
+plot_spectrogram(eigs_gauss(:,3046), param_dict.('Gauss256').dgt_params,...,
+    param_dict.('Gauss256').signal_params, param_dict.('Gauss256').dgt);
+ylabel('Frequency (kHz)')
+yticks([0,1000,2000,3000,4000]);
+yticklabels([0,1,2,3,4]);
+set(gca, 'FontSize', 20, 'fontName','Times');
+saveas(gcf,fullfile(fig_dir, 'eigvectors_prop_illustration.png'));
+saveas(gcf,fullfile(fig_dir, 'eigvectors_prop_illustration.fig'));
+
+%% mask
+figure;
+plot_spectrogram(mask_gauss.mask, param_dict.('Gauss256').dgt_params,...,
+    param_dict.('Gauss256').signal_params, param_dict.('Gauss256').dgt);
+ylabel('Frequency (kHz)')
+yticks([0,1000,2000,3000,4000]);
+yticklabels([0,1,2,3,4]);
+set(gca, 'FontSize', 20, 'fontName','Times');
+saveas(gcf,fullfile(fig_dir, 'mask_gauss.pdf'));
+
+
+%%
+save('evdn_gauss_hann.mat','evdn_hann','evdn_gauss','param_dict','mask_dict');
+
+
+
+
+