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tmp1.m
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%% Attempts to speed up LRPR new algorithm
%close all
% clear;
% clc;
tt1 = tic;
Params.Tmont = 100;
Params.n = 600; % Number of rows of the low rank matrix
Params.q = 1000; % Number of columns of the matrix for LRPR
Params.r = 4; % Rank
%Params.m = ceil(4 * Params.n); % Number of measurements
Params.m = ceil(4 * Params.n);
Params.tnew = 10; % Total number of main loops of new LRPR
Params.told = 10; % Total number of main loops of Old LRPR
Params.m_b = Params.m; %Number of measuremnets for coefficient estimate
Params.m_u = Params.m; % Number of measuremnets for subspace estimate
Params.m_init = Params.m; % Number of measuremnets for init of subspace
%m_init = 50;
Params.rank_est_flag = 1;
Paramsrwf.r = Params.r;
Paramsrwf.proj =0;
%Params.m = m_init + (m_b+m_u)*Params.tot;% Number of measurements
%%~PN editing m, n, r so that the variables are globally same
% TWF Parameters
Paramsrwf.m = Params.m;% Number of measurements
Paramsrwf.n = Params.n;% size of columns of coefficient matrix or x_k
Paramsrwf.r = Params.r;% size of columns of coefficient matrix or b_k
Paramsrwf.npower_iter = 300;% Number of loops for initialization of TWF with power method
Paramsrwf.mu = 0.2;% Parameter for gradient
Params.Tb_LRPRnew = unique(ceil(linspace(5, 20, Params.tnew)));% Number of loops for b_k with simple PR
%Params.Tb_LRPRnew = 85 * ones(1, Params.tnew);
% Paramsrwf.Tb_LRPRnew = 85;% Number of loops for b_k with simple PR
Paramsrwf.TRWF = 300;% Number of loops for b_k with simple PR
err_rwf = zeros(Paramsrwf.TRWF + 1, Params.q);
Paramsrwf.cplx_flag = 0;
Paramstwf.cplx_flag = 0;
Paramstwf.alpha_y = 3;
Paramstwf.alpha_h = 5;
Paramstwf.alpha_ub = 5;
Paramstwf.alpha_lb = 0.3;
Paramstwf.grad_type = 'TWF_Poiss';
Paramstwf.npower_iter = 300;
Paramstwf.n = Params.n;
Paramstwf.mu = 0.2;
Paramstwf.T = 300;
Paramstwf.m = Params.m;
%err_rwf = zeros(Paramstwf.T, Params.q);
%%Params.seed = rng;
err_SE_iter = zeros(2, Params.tnew, Params.Tmont);
err_X_iter = zeros(2, Params.tnew, Params.Tmont);
err_X_rwf_iter = zeros(Paramsrwf.TRWF+1, Params.Tmont);
%err_X_rwf_iter = zeros(Paramstwf.T, Params.Tmont);
file_name = strcat(['Copmare_n', num2str(Params.n), 'm', num2str(Params.m), 'r', num2str(Params.r), 'q', num2str(Params.q)]);
file_name_txt = strcat(file_name,'.txt');
file_name_mat = strcat(file_name,'.mat');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%Generating U and B and X
%rng('shuffle')
U = orth(randn(Params.n, Params.r));
B = randn(Params.r, Params.q);
X = U * B;
normX = norm(X,'fro')^2; % Computing Frobenius norm of the low rank matrix
Params.sig_star = svds(X, Params.r);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Compare
TmpErXRWF = zeros(Paramsrwf.TRWF,Params.Tmont);
TmpErURWF = zeros(Paramsrwf.TRWF,Params.Tmont);
TmpExTRWF = zeros(Paramsrwf.TRWF,Params.Tmont);
TmpErXLRPROld = zeros(Params.told,Params.Tmont);
TmpErULRPRoLd = zeros(Params.told,Params.Tmont);
TmpErXLRPRnew = zeros(Params.tnew,Params.Tmont);
TmpErULRPRnew = zeros(Params.tnew,Params.Tmont);
TmpExTLRPEnew = zeros(Params.tnew,Params.Tmont);
TmpErXLRPRqr = zeros(Params.tnew,Params.Tmont);
TmpErULRPRqr = zeros(Params.tnew,Params.Tmont);
TmpExTLRPRqr = zeros(Params.tnew,Params.Tmont);
time_QR = zeros(Params.tnew, Params.Tmont);
time_OLD = zeros(Params.told, Params.Tmont);
%time_RWF = zeros(Paramsrwf.TRWF, Params.Tmont);
time_RWF = zeros(Paramstwf.T, Params.Tmont);
for t = 1 : Params.Tmont
[Ysqrt,Y,A] = Generate_Mes(X,Params,Params.m);
fprintf('=============== Monte Carlo = %d ====================\n', t);
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% LRPR - practice
%%%%%%%%%%%%%
% tic;
% [B_QR, U_QR, X_hat_QR, U_track_QR, X_track_QR, time_QR(:, t)] = LRPRQR(Params, Paramsrwf, Y, Ysqrt, A);
% TmpTLRPQR(t) = toc;
% ERULRPRQR(t) = abs(sin(subspace(U_QR, U)));
% fprintf('LRPR-practice error U:\t %2.2e\t\t Time:\t %2.2e\n', ERULRPRQR(t), TmpTLRPQR(t));
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% LRPR - theory
%%%%%%%%%%%%%
% tic;
% [B_new_sample, U_new_sample, X_new_sample, U_track_new] = ...
% LRPRNewmes(Params, Paramsrwf, Y, Ysqrt, A, X);
% TmpTLRPmes(t) = toc;
% ERULRPRmes(t) = abs(sin(subspace(U_new_sample, U)));
% fprintf('LRPR theory error U:\t %2.2e\t\t Time:\t %2.2e\n', ERULRPRmes(t), TmpTLRPmes(t));
% TmpTLRPmes(t) = 0;
% ERULRPRmes(t) = eps;
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% LRPR Alt Min
%%%%%%%%%%%%%
% tic;
% [X_old, U_old, U_track_old, X_track_OLD, time_OLD(:, t)]= LRPR_AltMin(Y, A, Params);
% TmpExTLRPROld(t) = toc;
% TmpErULRPROld(t) = abs(sin(subspace(U_old, U)));
% fprintf('LRPR error U:\t %2.2e\t\t Time:\t %2.2e\n', TmpErULRPROld(t), TmpExTLRPROld(t));
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% RWF
%%%%%%%%%%%%
X_rwf = zeros(Params.n, Params.q);
tic;
for nk = 1: Params.q
Amatrix = A(:,:,nk)';
A1 = @(I) Amatrix * I;
At = @(Y) Amatrix' * Y;
[x_rwf, err_rwf(:, nk), time_temp] = RWFsimple2(Ysqrt(:,nk), Paramsrwf, A1, At, X(:, nk));
time_RWF(:, t) = time_RWF(:, t) + time_temp;
% [x_rwf, err_rwf(:, nk), time_temp] = TWF(Y(:,nk), Paramstwf, A1, At, X(:,nk));
% time_RWF(:, t) = time_RWF(:, t) + time_temp';
X_rwf(:,nk) = x_rwf;
end
err_X_rwf_iter(:, t) = sum(err_rwf, 2)/normX;
[Ur,~,~] = svd(X_rwf);
U_rwf = Ur(:,1:Params.r);
TmpExTrwf(t) = toc;
TmpErUrwf(t) = abs(sin(subspace(U_rwf, U)));
fprintf('RWF subspace error:\t%2.2e\t\tTime: %2.2e\n', TmpErUrwf(t), TmpExTrwf(t));
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% Error X
%%%%%%%%%%%%
Error_X_LRPR_new = 0;
Error_X_LRPR_QR = 0;
Error_X_LRPR_Newmes = 0;
Error_X_LRPROLD = 0;
Error_X_RWF = 0;
for nk = 1 : Params.q
x_opt = X(:, nk);
% LRPR practical
% x_hat = X_hat_QR(:, nk);
% Error_X_LRPR_QR = Error_X_LRPR_QR + min(norm(x_opt-x_hat)^2, norm(x_opt+x_hat)^2);
% LRPR theory
% x_hat = X_new_sample(:, nk);
% Error_X_LRPR_Newmes = Error_X_LRPR_Newmes + min(norm(x_opt-x_hat)^2, norm(x_opt+x_hat)^2);
% LRPR old
% x_hat = X_old(:, nk);
% Error_X_LRPROLD = Error_X_LRPROLD + min(norm(x_opt-x_hat)^2, norm(x_opt+x_hat)^2);
%RWF
x_hat = U_rwf*U_rwf'*X_rwf(:, nk);
Error_X_RWF = Error_X_RWF + min(norm(x_opt-x_hat)^2, norm(x_opt+x_hat)^2);
end
tmpEr_X_LRPR_QR(t) = Error_X_LRPR_QR / normX;
% tmpEr_X_LRPR_Newmes(t) = Error_X_LRPR_Newmes / normX;
tmpEr_X_LRPROLD(t) = Error_X_LRPROLD / normX;
tmpEr_X_RWF(t) = Error_X_RWF / normX;
% for ii = 1 : Params.tnew
% err_SE_iter(:, ii, t) = [abs(sin(subspace(U_track_QR{ii}, U))); ...
% abs(sin(subspace(U_track_new{ii}, U))); ...
% abs(sin(subspace(U_track_old{ii}, U)));];
% end
%
err_track_X_QR = zeros(Params.tnew,1);
err_track_X_OLD = zeros(Params.tnew,1);
for ii = 1 : Params.tnew
% err_SE_iter(:, ii, t) = [abs(sin(subspace(U_track_QR{ii}, U))); ...
% abs(sin(subspace(U_track_old{ii}, U)));];
for jj = 1 : Params.q
% x_opt = X(:, nk);
%
% XhatQR = X_track_QR{ii};
% x_hat = XhatQR(:, nk);
% err_track_X_QR(ii) = err_track_X_QR(ii) + min(norm(x_opt-x_hat)^2, norm(x_opt+x_hat)^2);
%
% XhatOLD = X_track_OLD{ii};
% x_hat = XhatOLD(:, nk);
% err_track_X_OLD(ii) = err_track_X_OLD(ii) + min(norm(x_opt-x_hat)^2, norm(x_opt+x_hat)^2);
end
err_track_X_OLD(ii) = err_track_X_OLD(ii)/Params.q;
err_track_X_QR(ii) = err_track_X_QR(ii)/Params.q;
err_X_iter(:, ii, t) = [err_track_X_QR(ii)/normX; err_track_X_OLD(ii)/normX;];
end
end
mean_Error_X_LRPR_QR = mean(tmpEr_X_LRPR_QR);
% mean_Error_X_LRPR_Newmes = mean(tmpEr_X_LRPR_Newmes);
mean_Error_X_LRPR_OLD = mean(tmpEr_X_LRPROLD);
mean_Error_X_RWF = mean(tmpEr_X_RWF);
% mean_Error_U_LRPR_QR = mean(ERULRPRQR);
% mean_Error_U_LRPR_Newmes = mean(ERULRPRmes);
% mean_Error_U_LRPR_OLD = mean(TmpErULRPROld);
mean_Error_U_RWF = mean(TmpErUrwf);
% mean_Time_LRPR_QR = mean(TmpTLRPQR);
% mean_Time_LRPR_Newmes = mean(TmpTLRPmes);
% mean_Time_LRPR_OLD = mean(TmpExTLRPROld);
mean_Time_RWF = mean(TmpExTrwf);
% fprintf('**************************************\n');
% fprintf('Error X: ...\n');
% fprintf('LRPR practical:\t\t%2.2e\n', mean_Error_X_LRPR_QR);
% % fprintf('LRPR theory:\t%2.2e\n', mean_Error_X_LRPR_Newmes);
% fprintf('LRPR OLD:\t\t%2.2e\n', mean_Error_X_LRPR_OLD);
% % fprintf('RWF:\t\t\t%2.2e\n', mean_Error_X_RWF);
% fprintf('**************************************\n');
%
% fprintf('Error U: ... \n');
% fprintf('LRPR practical:\t\t%2.2e\n', mean_Error_U_LRPR_QR);
% % fprintf('LRPR theory:\t%2.2e\n', mean_Error_U_LRPR_Newmes);
% fprintf('LRPR OLD:\t\t%2.2e\n', mean_Error_U_LRPR_OLD);
% % fprintf('RWF:\t\t\t%2.2e\n', mean_Error_U_RWF);
% fprintf('**************************************\n');
% fprintf('Exe Time: ... \n');
% fprintf('LRPR practical:\t\t%2.2e\n', mean_Time_LRPR_QR);
% % fprintf('LRPR theory:\t%2.2e\n', mean_Time_LRPR_Newmes);
% fprintf('LRPR OLD:\t\t%2.2e\n', mean_Time_LRPR_OLD);
% fprintf('RWF:\t\t\t%2.2e\n', mean_Time_RWF);
toc(tt1)
%save('data/rank_est_yes_large_mc100.mat')
%
% final_err_SE = mean(err_SE_iter, 3);
% final_err_SE_med = median(err_SE_iter, 3);
% final_err_SE_std = std(err_SE_iter, 0, 3);
% figure;
% %subplot(211)
% plot(log10(final_err_SE(1, :)), 'rs--', 'LineWidth', 2);
% hold
% % plot(log10(final_err_SE(2, :)), 'gs-.', 'LineWidth', 2);
% plot(log10(final_err_SE(2, :)), 'bo-', 'LineWidth', 2);
% axis tight
% stry = '$$\log(SE(\hat{U}^t, U))$$';
% xlabel('outer loop iteration (t)', 'Fontsize', 15)
% ylabel(stry, 'Interpreter', 'latex', 'Fontsize', 15)
% l1 = legend('LRPR-prac', 'LRPR-AltMin');
% set(l1, 'Fontsize', 15)
% t1 = title('m = 80, n200, q = 400, r=4');
% set(t1, 'Fontsize', 15)
time_RWF1 = time_RWF;
final_err_X = median(err_X_iter, 3);
final_err_X_rwf1 = mean(err_X_rwf_iter, 2);
final_err_X_rwf1 = min(err_X_rwf_iter(:,1)) * ones(301,1);
final_err_X_rwf1 = median(err_X_rwf_iter, 2);
final_err_X_rwf_std = median(err_X_rwf_iter, 2);
figure
% semilogy(mean(time_RWF1, 2), final_err_X_rwf1, 'ko--', 'LineWidth', 2)
semilogy(mean(time_RWF1, 2), final_err_X_rwf1(1:end-1), 'ko--', 'LineWidth', 2)
figure
% t1 =mean(time_QR, 2);
% t2 = mean(time_OLD, 2);
semilogy(mean(time_QR, 2), final_err_X(1, :), 'rs--', 'LineWidth', 2)
hold
semilogy(mean(time_OLD, 2), final_err_X(2, :), 'b>--', 'LineWidth', 2)
semilogy(time_RWF2, final_err_X_rwf2, 'gd--', 'LineWidth', 2)
semilogy(mean(time_RWF1, 2), final_err_X_rwf1(1, :), 'ko--', 'LineWidth', 2)
axis tight
stry = ['mat-dist', '$$(\hat{X}^t, X)$$'];
xlabel('time', 'Fontsize', 15)
ylabel(stry, 'Interpreter', 'latex', 'Fontsize', 15)
l1 = legend('AltminLowRap', 'LRPR2', 'Proj-RWF', 'RWF');
set(l1, 'Fontsize', 15)
t1 = title('m = 150, n = 600, q = 1000');
set(t1, 'Fontsize', 15)
figure
errorbar(mean(time_QR, 2), log10(final_err_X(1, :)), log10(final_err_X_std(1, :)),...
'rs--', 'LineWidth', 2);
hold
errorbar(mean(time_OLD, 2), log10(final_err_X(2, :)), final_err_X_std(2, :),...
'b>--', 'LineWidth', 2);
errorbar(mean(time_RWF1, 2), log10(min(final_err_X_rwf1(1:end-1)) * ones(300,1)), eps * ones(300,1), ...
'ko--', 'LineWidth', 2)
axis tight
stry = ['log(mat-dist', '$$(\hat{X}^t, X))$$'];
xlabel('time', 'Fontsize', 15)
ylabel(stry, 'Interpreter', 'latex', 'Fontsize', 15)
% l1 = legend('LRPR-prac', 'LRPR-AltMin', 'RWF');
l1 = legend('AltMin-PhaPCA', 'LRPR2', 'RWF');
set(l1, 'Fontsize', 15)
t1 = title('m = 80, n = 200, q = 400, r=4');
set(t1, 'Fontsize', 15)
%save('data/rank_est_yes_mc30.mat')
% subplot(212)
% plot(log10(final_err_SE_med(1, :)), 'rs--', 'LineWidth', 2);
% hold
% plot(log10(final_err_SE_med(2, :)), 'gs-.', 'LineWidth', 2);
% plot(log10(final_err_SE_med(3, :)), 'bo-', 'LineWidth', 2);
% axis tight
% stry = '$$\log(SE(\hat{U}^t, U))$$';
% xlabel('outer loop iteration (t)', 'Fontsize', 15)
% ylabel(stry, 'Interpreter', 'latex', 'Fontsize', 15)
% l1 = legend('LRPR-prac', 'LRPR-theory', 'LRPR-AltMin');
% set(l1, 'Fontsize', 15)
% t1 = title('m = 80, n=q=200, r=2');
% set(t1, 'Fontsize', 15)
% subplot(212)
% errorbar([1:10], log10(final_err_SE_med(1, :)), final_err_SE_std(1, :),...
% 'rs--', 'LineWidth', 2);
% hold
% errorbar([1:10], log10(final_err_SE_med(2, :)), final_err_SE_std(2, :),...
% 'gs-.', 'LineWidth', 2);
% errorbar([1:10], log10(final_err_SE_med(3, :)), final_err_SE_std(3, :),...
% 'bo-', 'LineWidth', 2);
% axis tight
% stry = '$$\log(SE(\hat{U}^t, U))$$';
% xlabel('outer loop iteration (t)', 'Fontsize', 15)
% ylabel(stry, 'Interpreter', 'latex', 'Fontsize', 15)
% l1 = legend('LRPR-prac', 'LRPR-theory', 'LRPR-AltMin');
% set(l1, 'Fontsize', 15)
% t1 = title('m = 80, n=q=200, r=2');
% set(t1, 'Fontsize', 15)
figure
% t1 =mean(time_QR, 2);
% t2 = mean(time_OLD, 2);
% loglog(lrpr_suc_time2(1:4), lrpr_suc_err2(1:4), 'rs--', 'LineWidth', 2)
loglog(lrpr_suc_time4(1:end-2), lrpr_suc_err4(1:end-2), 'rs--', 'LineWidth', 2)
hold
loglog(rwf_suc_time1(1:37), rwf_suc_err1(1:37), 'b>--', 'LineWidth', 2)
loglog(rwf_fail_time1, rwf_fail_err1, 'md--', 'LineWidth', 2)
loglog(twf_suc_time1(1:80), twf_suc_err1(1:80), 'ko--', 'LineWidth', 2)
axis tight
stry = ['mat-dist', '$$(\hat{X}^t, X)$$'];
xlabel('time', 'Fontsize', 15)
ylabel(stry, 'Interpreter', 'latex', 'Fontsize', 15)
l1 = legend('AltminLowRap m = n/4', 'RWF m = 5n', 'RWF m=4n', 'TWF m=5n');
set(l1, 'Fontsize', 12)
t1 = title('n = 200, q = 150, r=2');
set(t1, 'Fontsize', 15)
figure
% t1 =mean(time_QR, 2);
% t2 = mean(time_OLD, 2);
% loglog(lrpr_suc_time2(1:4), lrpr_suc_err2(1:4), 'rs--', 'LineWidth', 2)
semilogy(lrpr_suc_time4(1:end-2), lrpr_suc_err4(1:end-2), 'rs--', 'LineWidth', 2)
hold
semilogy(rwf_suc_time1(1:37), rwf_suc_err1(1:37), 'b>--', 'LineWidth', 2)
semilogy(rwf_fail_time1, rwf_fail_err1, 'gd--', 'LineWidth', 2)
semilogy(twf_suc_time1(1:80), twf_suc_err1(1:80), 'ko--', 'LineWidth', 2)
axis tight
stry = ['mat-dist', '$$(\hat{X}^t, X)$$'];
xlabel('time', 'Fontsize', 15)
ylabel(stry, 'Interpreter', 'latex', 'Fontsize', 15)
l1 = legend('AltminLowRap m = n/4', 'RWF m = 5n', 'RWF m=4n', 'TWF m=5n');
set(l1, 'Fontsize', 13)
t1 = title('n = 200, q = 150, r=2');
% set(t1, 'Fontsize', 15)