%?Comparison?of?different?linearized?Bregman?approaches?on?recovering?a?sparse?solution?x?from?Ax?=?b?
%?The?nonzero?entries?of?x?have?iid?Gaussian?random?values
%?The?entries?of?A?are?+/-?1?randomly

clear

%%?Generate?problem?data
rand（‘seed‘?0）;?randn（‘seed‘?0）;

m?=?250;?n?=?500;?%?matrix?dimension?m-by-n
k?=?25;?%?sparsity

A?=?sign（randn（mn））;?%?random?matrix
x_ref?=?zeros（n1）;?%?true?vector
x_ref（randsample（nk））?=?randn（k1）;?%?Gaussian?random?values
b?=?A*x_ref;?%?finish?generating?equations?Ax?=?b

%%?set?parameters
alpha?=?5*norm（x_refinf）;?%?don‘t?need?to?be?exact?roughly?1?-?10?times?norm（x_refinf）?is?fine
opts.tol?=?1e-6;???%?stop?once?norm（Ax-b）opts.maxit?=?2000;?%?run?maximally?1000?iterations
opts.x_ref?=?x_ref;

%%?LBreg:?fixed?stepsize?---
opts.stepsize?=?2/alpha/normest（A*A.‘1e-2）;?%?roughly?2/alpha/norm（A）^2
t0?=?tic;
[xout]?=?lbreg_fixedstep（Abalphaopts）;
time?=?toc（t0）;
fprintf（‘iter?=?%d?time?=?%4.2e?‘?out.iter?time）;
fprintf（‘solution?relative?error?=?%4.2e\n‘?norm（x?-?x_ref）/norm（x_ref））;
opts?=?rmfield（opts?‘stepsize‘）;

%%?LBreg:?Barzilai-Borwein?and?non-montone?line?search?---
opts.stepsize?=?2/alpha/normest（A*A.‘1e-2）;?%?roughly?2/alpha/norm（A）^2
t0?=?tic;
[x1out1]?=?lbreg_bbls（Abalphaopts）;
time?=?toc（t0）;
fprintf（‘iter?=?%d?time?=?%4.2e?‘?out1.iter?time）;
fprintf（‘solution?relative?error?=?%4.2e\n‘?norm（x1?-?x_ref）/norm（x_ref））;
opts?=?rmfield（opts?‘stepsize‘）;

%%?LBreg:?accelerated?no?restart?---
t0?=?tic;
[x2out2]?=?lbreg_accelerated（Abalphaopts）;
time?=?toc（t0）;
fprintf（‘iter?=?%d?time?=?%4.2e?‘?out2.iter?time）;
fprintf（‘solution?relative?error?=?%4.2e\n‘?norm（x2?-?x_ref）/norm（x_ref））;

%%?LBreg:?skip:?monotonic?gradient?scheme?---
opts.reset?=?6;
t0?=?tic;
[x3out3]?=?lbreg_accel_w_reset（Abalphaopts）;?%?no?restart
time?=?toc（t0）;
fprintf（‘iter?=?%d?time?=?%4.2e?‘?out3.iter?time）;
fprintf（‘solution?relative?error?=?%4.2e\n‘?norm（x3?-?x_ref）/norm（x_ref））;
opts?=?rmfield（opts?‘reset‘）;

%%?Reporting
figure;
plot（1:out.iter??out.hist_obj??‘k-‘?...
?????1:out1.iter?out1.hist_obj?‘b--‘?...
?????1:out2.iter?out2.hist_obj?‘g--‘?...
?????1:out3.iter?out3.hist_obj?‘r--‘?...
?????‘LineWidth‘?2）;
legend（‘fixed?stepsize‘?‘BB+line?search‘?‘Nesterov?accel‘?‘Nesterov+skip‘‘Location‘‘SouthEast‘）;
title（‘Dual?objective‘）
xlabel（‘iteration‘）;?ylabel（‘dual?objective‘）;

figure;
semilogy（1:out.iter??out.hist_err/norm（x_ref）??‘k-‘?...
?????????1:out1.iter?out1.hist_err/norm（x_ref）?‘b--‘?...
?????????1:out2.iter?out2.hist_err/norm（x_ref）?‘g--‘?...
?????????1:out3.iter?out3.hist_err/norm（x_ref）?‘r--‘?...
?????????‘LineWidth‘?2）;
legend（‘fixed?stepsize‘?‘BB+line?search‘?‘Nesterov?accel‘?‘Nesterov+skip‘‘Location‘‘NorthEast‘）;
title（‘Primal?solution?relative?error‘）
xlabel（‘iteration‘）;?ylabel（‘||x?-?x_{ref}||_2/||x_{ref}||_2‘）;

%%?