s2let_demo_curvelet_evaluate_performance

 s2let_demo_curvelet_evaluate_performance

 Evaluate timing and error of (spin) curvelet transform.

 -----------------------------------------------------------
 S2LET package to perform Wavelet Transform on the Sphere.
 Copyright (C) 2012-2016  Boris Leistedt, Jennifer Chan & Jason McEwen
 See LICENSE.txt for license details
 -----------------------------------------------------------

0001 % s2let_demo_curvelet_evaluate_performance
0002 %
0003 % Evaluate timing and error of (spin) curvelet transform.
0004 %
0005 % -----------------------------------------------------------
0006 % S2LET package to perform Wavelet Transform on the Sphere.
0007 % Copyright (C) 2012-2016  Boris Leistedt, Jennifer Chan & Jason McEwen
0008 % See LICENSE.txt for license details
0009 % -----------------------------------------------------------
0010 
0011 clear;
0012 
0013 N_test = 3
0014 
0015 B = 2;
0016 J_min = 1;  %rather than 0
0017 spin = 0;
0018 reality = false;
0019 sampling_method = 'MW';
0020 upsample= false;   % Multi-resolution On
0021 save_plots = true;
0022 
0023 Ls = [4 8 16 32 64]  
0024 
0025 err = zeros(N_test, length(Ls));
0026 time_analysis = zeros(N_test, length(Ls));
0027 time_synthesis = zeros(N_test, length(Ls));
0028 
0029 el_ind = 0;
0030 for L = Ls
0031    el_ind = el_ind + 1
0032    L
0033 
0034    for n = 1:N_test
0035    
0036       n
0037       
0038       %disp('Generate band-limited function in harmonic space')
0039       flm = zeros(L^2,1);
0040       flm = rand(size(flm)) + sqrt(-1)*rand(size(flm));
0041       flm = 2.*(flm - (1+sqrt(-1))./2);
0042 
0043       %disp('Construct the corresponding signal on the sphere')
0044       f = ssht_inverse(flm, L, 'Method', sampling_method);
0045       
0046       tstart = tic;
0047       [f_cur, f_scal] = s2let_transform_curvelet_analysis_px2cur(f, ...
0048          'B', B, 'L', L, 'J_min', J_min, ...
0049          'Upsample', upsample, 'Spin', spin, 'Reality', reality, ...
0050          'Sampling', sampling_method);
0051       time_analysis(n, el_ind) = toc(tstart);
0052       
0053       tstart = tic;
0054       f_recov = s2let_transform_curvelet_synthesis_cur2px(f_cur, f_scal, ...
0055          'L', L, 'B', B, 'J_min', J_min, ...
0056          'Upsample', upsample, 'Spin', spin, 'Reality', reality, ...
0057          'Sampling', sampling_method);
0058 
0059 
0060       time_synthesis(n, el_ind) = toc(tstart);
0061 
0062       err(n, el_ind) = max(abs(f(:) - f_recov(:)));
0063 
0064    end
0065 
0066 end
0067 
0068 err_mean = mean(err);
0069 err_std = std(err);
0070 err_std_log = std(log10(err));
0071 
0072 time_analysis_mean = mean(time_analysis);
0073 time_analysis_std = std(time_analysis);
0074 
0075 
0076 time_synthesis_mean = mean(time_synthesis);
0077 time_synthesis_std = std(time_synthesis);
0078 
0079 
0080 time_total = time_analysis + time_synthesis;
0081 time_total_mean = mean(time_total);
0082 time_total_std = std(time_total);
0083 time_total_std_log = std(log10(time_total));
0084 
0085 
0086 %% Define saved figure location
0087 pltroot = '../../../figs/' ;
0088 
0089 %% Define plotting parameters.
0090 
0091 istart = 1;
0092 iend = length(Ls);
0093 
0094 line_width = 1.8;
0095 line_width_thick = 2.5;
0096 marker_size = 7;
0097 marker_type = 'o';
0098 green_light = [0.2 0.6 0.4];% x339966
0099 green_dark = [0 0.4 0.2];   % x006633
0100 blue_light = [0.2 0.4 0.8]; % x3366CC
0101 blue_dark = [0 0 1];        % x0000FF
0102 red_light = [1 0.4 0.2];    % xFF6633
0103 red_dark = [0.8 0.2 0];     % xCC3300
0104 % -----------
0105 % Plot error
0106 % -----------
0107 figure;
0108    
0109 plot(log2(Ls(istart:iend)), ...
0110    log10(err_mean(istart:iend)), ...
0111    'Color', green_dark, ...
0112    'Marker', marker_type, ...
0113    'MarkerSize', marker_size, ...
0114    'MarkerFaceColor', green_light, ...
0115    'MarkerEdgeColor', green_dark, ...
0116    'LineStyle', '--', ...
0117    'LineWidth', line_width);
0118 
0119 hold on;
0120 
0121 plot(log2(Ls(istart:iend)), ...
0122    log10(Ls(istart:iend).^2)-15, ...
0123    'r', ...
0124    'LineWidth', line_width_thick);
0125 
0126 a = axis;
0127 set(gca,'XTick',a(1):1:a(2));
0128 set(gca,'XTickLabel', 2.^[a(1):1:a(2)]);
0129 set(gca,'YTick',floor(a(3)):1:ceil(a(4)));
0130 set(gca,'YTickLabel',{10.^[floor(a(3)):ceil(a(4))]});
0131 xlabel('$L$','Interpreter','LaTex');
0132 ylabel('Maximum error');
0133 
0134 set(gca, 'LineWidth', 3)
0135 set(gca, 'FontSize', 20)
0136 xt =get(gca,'XTick');
0137 set(gca, 'FontSize', 18); 
0138 
0139 fname = [pltroot,'curvelet_error.png']
0140 print('-r200', '-dpng', fname);
0141 
0142 % ----------------------------
0143 % Plot error with error bars
0144 %-----------------------------
0145 figure
0146   
0147 errorbar(log2(Ls(istart:iend)), ...
0148    log10(err_mean(istart:iend)), ...
0149    err_std_log(istart:iend), ...
0150    'Color', green_dark, ...
0151    'Marker', marker_type, ...
0152    'MarkerSize', marker_size, ...
0153    'MarkerFaceColor', green_light, ...
0154    'MarkerEdgeColor', green_dark, ...
0155    'LineStyle', '--', ...
0156    'LineWidth', line_width);
0157 
0158 hold on;
0159 
0160 plot(log2(Ls(istart:iend)), ...
0161    log10(Ls(istart:iend).^2)-15, ...
0162    'r', ...
0163    'LineWidth', line_width_thick);
0164 
0165 a = axis;
0166 set(gca,'XTick',a(1):1:a(2));
0167 set(gca,'XTickLabel', 2.^[a(1):1:a(2)]);
0168 set(gca,'YTick',floor(a(3)):1:ceil(a(4)));
0169 set(gca,'YTickLabel',{10.^[floor(a(3)):ceil(a(4))]});
0170 xlabel('$L$','Interpreter','LaTex');
0171 ylabel('Maximum error','Interpreter','LaTex');
0172 
0173 
0174 set(gca, 'LineWidth', 3)
0175 set(gca, 'FontSize', 20)
0176 
0177 fname = [pltroot,'curvelet_errorbar.png']
0178 print('-r200', '-dpng', fname);
0179 
0180 % -----------------
0181 % Plot timing
0182 % ------------------
0183 figure;
0184    
0185 plot(log2(Ls(istart:iend)), ...
0186    log10(time_total_mean(istart:iend)), ...
0187    'Color', green_dark, ...
0188    'Marker', marker_type, ...
0189    'MarkerSize', marker_size, ...
0190    'MarkerFaceColor', green_light, ...
0191    'MarkerEdgeColor', green_dark, ...
0192    'LineStyle', '--', ...
0193    'LineWidth', line_width);
0194 
0195 hold on;
0196 
0197 % theoretical scaling : L^3log_2{L}
0198 plot(log2(Ls(istart:iend)), ...
0199    log10((Ls(istart:iend).^3).*log2(Ls(istart:iend)))-2,...  
0200    'r', ...
0201    'LineWidth', line_width_thick);
0202 a = axis;
0203 set(gca,'XTick',a(1):1:a(2));
0204 set(gca,'XTickLabel', 2.^[a(1):1:a(2)]);
0205 set(gca,'YTick',floor(a(3)):1:ceil(a(4)));
0206 set(gca,'YTickLabel',{10.^[floor(a(3)):ceil(a(4))]});
0207 xlabel('$L$','Interpreter','LaTex');
0208 ylabel('Computation time (s)');
0209 
0210 set(gca, 'LineWidth', 3)
0211 set(gca,'FontSize', 20)
0212 
0213 fname = [pltroot,'curvelet_timing.png']
0214 print('-r200', '-dpng', fname);
0215 
0216 % Plot timing with error bars
0217 figure;
0218    
0219 errorbar(log2(Ls(istart:iend)), ...
0220    log10(time_total_mean(istart:iend)), ...
0221    time_total_std_log(istart:iend), ...
0222    'Color', green_dark, ...
0223    'Marker', marker_type, ...
0224    'MarkerSize', marker_size, ...
0225    'MarkerFaceColor', green_light, ...
0226    'MarkerEdgeColor', green_dark, ...
0227    'LineStyle', '--', ...
0228    'LineWidth', line_width);
0229 
0230 hold on;
0231 
0232 % theoretical scaling: L^3log_2{L}
0233 plot(log2(Ls(istart:iend)), ...
0234     log10((Ls(istart:iend).^3).*log2(Ls(istart:iend)))-2,...  
0235    'r', ...
0236    'LineWidth', line_width_thick);
0237 a = axis;
0238 set(gca,'XTick',a(1):1:a(2));
0239 set(gca,'XTickLabel', 2.^[a(1):1:a(2)]);
0240 set(gca,'YTick',floor(a(3)):1:ceil(a(4)));
0241 set(gca,'YTickLabel',{10.^[floor(a(3)):ceil(a(4))]});
0242 xlabel('$L$','Interpreter','LaTex');
0243 ylabel('Computation time (s)','Interpreter','LaTex');
0244 
0245 set(gca, 'LineWidth', 3)
0246 set(gca,'FontSize', 20)
0247 
0248 fname = [pltroot,'curvelet_timing_errorbar.png']
0249 print('-r200', '-dpng', fname);
0250