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test2.m
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%% Comparing Sara
close all
clear;
clc;
%nrange = [100, 300, 600, 1000, 2000];
%mrange = [100, 150, 200, 300, 400, 500, 600];
mrange = [200];
nrange = 200;
Params.Tmont = 1; % Number of Monte-Carlo repeats
Err_SE_theory = zeros(length(nrange), Params.Tmont);
Err_SE_prac = zeros(length(nrange), Params.Tmont);
Err_SE_AltMin = zeros(length(nrange), Params.Tmont);
Err_SE_RWF = zeros(length(nrange), Params.Tmont);
for nn = mrange
fprintf('m = %d', nn);
Params.n = nn; % Number of rows of the low rank matrix
Params.q = 400; % Number of columns of the matrix for LRPR
Params.r = 4; % Rank
Params.m = 80; % Number of measurements
Params.tnew = 10; % Total number of main loops of new LRPR
Params.told = 10; % Total number of main loops of Old LRPR
m_b = Params.m; %Number of measuremnets for coefficient estimate
m_u = Params.m; % Number of measuremnets for subspace estimate
Params.m_init = Params.m;
m_init = Params.m;
Params.rank_est_flag = 1; % Number of measuremnets for init of subspace
Params.m_b = Params.m;
Params.m_u = Params.m;
%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 = 50;% Number of loops for initialization of TWF with power method
Paramsrwf.mu = 0.2;% Parameter for gradient
Params.Tb_LRPRnew = 85 * ones(1, Params.tnew);
Paramsrwf.TRWF = 25;% Number of loops for b_k with simple PR
Paramsrwf.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';
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
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 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);
TmpExTLRPROld = zeros(Params.told,Params.Tmont);
TmpErXLRPRnew = zeros(Params.tnew,Params.Tmont);
TmpErULRPRnew = zeros(Params.tnew,Params.Tmont);
TmpExTLRPEnew = zeros(Params.tnew,Params.Tmont);
% TmpErXLRPRmes = zeros(Params.tot,Params.Tmont);
% TmpErULRPRmes = zeros(Params.tot,Params.Tmont);
% TmpExTLRPRmes = zeros(Params.tot,Params.Tmont);
%
TmpErXLRPRqr = zeros(Params.tnew,Params.Tmont);
TmpErULRPRqr = zeros(Params.tnew,Params.Tmont);
TmpExTLRPRqr = zeros(Params.tnew,Params.Tmont);
flag_lrpr_new = 0;
for t = 1 : Params.Tmont
fprintf('=============== Monte Carlo = %d ====================\n', t);
[Ysqrt,Y,A] = Generate_Mes(X,Params,Params.m);
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% LRPR_new
%%%%%%%%%%%%%
if(flag_lrpr_new)
tic;
[B_new, U_new] = LRPRnew(Params, Paramsrwf, Y, Ysqrt, A);
TmpTLRPRnew(t) = toc;
ERULRPRnew(t) = abs(sin(subspace(U_new, U)));
fprintf('LRPR new error U:\t %2.2e\t\t Time:\t %2.2e\n', ERULRPRnew(t), TmpTLRPRnew(t));
end
% ERRXLRPRnew= 0;
% for ni = 1 : Params.q
% ERRXLRPRnew = ERRXLRPRnew + min(norm(X(:,ni)-X_hat(:,ni))^2, norm(X(:,ni)+X_hat(:,ni))^2);
% end
% ERRXLRPRnew = ERRXLRPRnew / normX;
% fprintf('LRPRnew subspace error U:\t\t %2.2e\n', ERULRPRnew );
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% LRPR_QR
%%%%%%%%%%%%%
tic;
[B_QR, U_QR, X_hat_QR] = LRPRQR(Params, Paramsrwf, Y, Ysqrt, A);
TmpTLRPQR(t) = toc;
ERULRPRQR(t) = abs(sin(subspace(U_QR, U)));
Err_SE_prac(find(nn == nrange), t) = ERULRPRQR(t);
fprintf('LRPRQR error U:\t %2.2e\t\t Time:\t %2.2e\n', ERULRPRQR(t), TmpTLRPQR(t));
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% LRPR_Newmes
%%%%%%%%%%%%%
tic;
[B_new_sample, U_new_sample, X_new_sample] = LRPRNewmes(Params, Paramsrwf, Y, Ysqrt, A, X);
TmpTLRPmes(t) = toc;
ERULRPRmes(t) = abs(sin(subspace(U_new_sample, U)));
Err_SE_theory(find(nn == nrange), t) = ERULRPRmes(t);
fprintf('LRPR new sample error U:\t %2.2e\t\t Time:\t %2.2e\n', ERULRPRmes(t), TmpTLRPmes(t));
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% LRPROLD
%%%%%%%%%%%%%
tic;
[X_old, U_old]= LRPR_AltMin(Y, A, Params);
TmpExTLRPROld(t) = toc;
TmpErULRPROld(t) = abs(sin(subspace(U_old, U)));
Err_SE_AltMin(find(nn == nrange), t) = TmpErULRPROld(t);
fprintf('LRPR error U:\t %2.2e\t\t Time:\t %2.2e\n', TmpErULRPROld(t), TmpExTLRPROld(t));
% fprintf('LRTWF started!\n');
%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% 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] = RWFsimple2(Ysqrt(:,nk), Paramsrwf, A1, At, X(:, nk));
X_rwf(:,nk) = x_rwf;
end
[Ur,~,~] = svd(X_rwf);
U_rwf = Ur(:,1:Params.r);
TmpExTrwf(t) = toc;
TmpErUrwf(t) = abs(sin(subspace(U_rwf, U)));
Err_SE_RWF(find(nn == nrange), t) = TmpErUrwf(t);
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 NEW
if(flag_lrpr_new);
x_hat = U_new * B_new(:, nk);
Error_X_LRPR_new = Error_X_LRPR_new + min(norm(x_opt-x_hat)^2, norm(x_opt+x_hat)^2);
end
% LRPR QP
%x_hat = U_QR * B_QR(:, nk);
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 new sample
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
if(flag_lrpr_new)
tmpEr_X_LRPR_new(t) = Error_X_LRPR_new / normX;
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;
end
if(flag_lrpr_new)
mean_Error_X_LRPR_new = mean(tmpEr_X_LRPR_new);
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);
if(flag_lrpr_new)
mean_Error_U_LRPR_new = mean(ERULRPRnew);
end
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);
if(flag_lrpr_new)
mean_Time_LRPR_new = mean(TmpTLRPRnew);
end
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 new:\t\t%2.2e\n', mean_Error_X_LRPR_new);
fprintf('LRPR QR:\t\t%2.2e\n', mean_Error_X_LRPR_QR);
fprintf('LRPR new samples:\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 new:\t\t%2.2e\n', mean_Error_U_LRPR_new);
fprintf('LRPR QR:\t\t%2.2e\n', mean_Error_U_LRPR_QR);
fprintf('LRPR new samples:\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 new:\t\t%2.2e\n', mean_Time_LRPR_new);
fprintf('LRPR QR:\t\t%2.2e\n', mean_Time_LRPR_QR);
fprintf('LRPR new samples:\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);
end
%data_m200 = [mean_Error_U_LRPR_Newmes, mean_Error_U_LRPR_QR, mean_Error_U_LRPR_OLD, mean_Error_U_RWF];
%save('temp4.mat', 'data_m300')
%save('data_nvarying.mat');