Main_Example3.m

%{
        This is an example to show how to use the dimension-reduction algorithm function.
        At the same time, the computational efficiency of blocking-stacking algorithm  and
        dimension-reduction algorithm are compared.

        At first, assume that the number q of nuisance parameters is fixed to be  q = 20, and the number 
        of each set of observations gradually increase from 20 to 200 to test the proposed 
        algorithm performance.
%}

clc; clear all; close all;

m      = 3;    % Number of main parameters
q      = 2;   % Number of nuisance parameters 
Loop   = 0;    % Recording the iteration times

for ObsNum = 50:50  % is the number of each set of observations
    
    Loop = Loop + 1; 
    ks   = ones(1,q) * ObsNum;                    % Numbers of block observations

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %        +++++++++++ test data simulation  +++++++++++            %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    x = [1 1 1]';                                       % main parameter
    b = 0.1;                                            % nusaince parameter
    for i=1:length(ks)
        As{i} = rand(ks(i),m);                          % productiong design martix
        Zs{i} = rand(ks(i),1);                        % coefficients of the nusaince parameter 
        Ls{i} = As{i} * x + Zs{i} * b + randn(ks(i),1) * 1;     % productiong Observations
        ps{i} = ones(ks(i),1);                          % productiong weighted
    end
    
    A = [As{1} Zs{1} zeros(50,1);
        As{2}  zeros(50,1) Zs{2}];
    Ps = diag([ps{1};ps{2}]);
    x = inv(A'*Ps*A)* A' * Ps * [Ls{1};Ls{2}]
    
    
    [As Ls ps] = IsotropyTrans(Zs,As,Ls,ps);
% 
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     % +++++++++++ performance test for equal-weight case +++++++++++  %
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     % Dimension-reduction algorithm
%     StartTime_Dim1 = tic;                         % Record running time(Dimension-reduction algorithm)
%     xd1             = FastDiffSolEW(As,Ls);        % Equal-weight
%     RunTime_Dim1   = toc(StartTime_Dim1);
%     
%     % Blocking-stacking algorithm
%     StartTime_Blo1 = tic;                         % Record running time(Blocking-stacking algorithm)
%     xu1            = UnDiffSolEW(As,Ls);          % Equal-weight
%     RunTime_Blo1   = toc(StartTime_Blo1);
%     
%     % RunningTime = [Dimension-reduction , Blocking-stacking]
%     RunTime_Case1(Loop,:) = [RunTime_Dim1   ,  RunTime_Blo1];
    
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % +++++++++++ performance test for unequal-weight case +++++++++++%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % Dimension-reduction algorithm                   
    StartTime_Dim2 = tic;                           % Record running time
    xd             = FastDiffSolUEW(As,Ls,ps);      
    RunTime_Dim2   = toc(StartTime_Dim2);
    
    % Blocking-stacking algorithm                
    StartTime_Blo2 = tic;                           % Record running time
    xu             = UnDiffSolUEW(As,Ls,ps);                 
    RunTime_Blo2   = toc(StartTime_Blo2);
    RunTime_Case2(Loop,:) = [RunTime_Dim2   ,  RunTime_Blo2];
end

% Drawing results (Equal-weight case)
FigOutput(RunTime_Case1(:,1) ,RunTime_Case1(:,2))
title({'Running time increasing with the number of observations(Euqal-weight)'});

% Drawing results( Unequal-weight case)
FigOutput(RunTime_Case2(:,1) ,RunTime_Case2(:,2))
title({'Running time increasing with the number of observations(Uneuqal-weight)'});