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exp2.m
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exp2.m
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clc
clear all
close all
warning off
%% graph settings
N=5;
% G=gen_graph(N);
G=[0 1 0 0 1;
1 0 1 0 0;
0 1 0 1 0;
0 0 1 0 1;
1 0 0 1 0];%circle 50 100
% N=10;
% G=[ 0 1 0 0 0 0 0 0 0 1
% 1 0 1 0 0 0 0 0 0 0
% 0 1 0 1 0 0 0 0 0 0
% 0 0 1 0 1 0 0 0 0 0
% 0 0 0 1 0 1 0 0 0 0
% 0 0 0 0 1 0 1 0 0 0
% 0 0 0 0 0 1 0 1 0 0
% 0 0 0 0 0 0 1 0 1 0
% 0 0 0 0 0 0 0 1 0 1
% 1 0 0 0 0 0 0 0 1 0
% ]; %20 20
% N=15;
% G=[
% 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
% 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
% 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0
% 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
% 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0
% 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
% 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0
% 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0
% 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0
% 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0
% 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0
% 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0
% 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
% 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
% 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
% ];%20 20
% N=20;
% G=[
% 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
% 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
% 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
% 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
% 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
% 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
% 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
% 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0
% 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
% 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0
% 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
% 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0
% 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0
% 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0
% 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0
% 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0
% 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0
% 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
% 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
% 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
% ];
G_=triu(G);
index=find(G_(:));
for i=1:N
n(:,i)=sum(G(:,i));% number of neighbor
end
%% sample distributed
d=200;
% [A,B] = gen_fix_data(d);
% chol(A);
% chol(B);
% sumA=A;
% sumB=B;
load('data2.mat');
sumA=A*N;
sumB=B*N;
clear A B
%% ground truth
[V,D]=eig(sumA,sumB);%AV=BVD norm(sumA*V-sumB*V*D)
global VV
VV=V(:,1)/sqrt(norm(V(:,1)'*sumB*V(:,1)));% constraint norm(VV(:,1)'*sumA*VV(:,1)),norm(VV(:,1)'*sumB*VV(:,1))
F_true=-norm(VV(:,1)'*sumA*VV(:,1));
% VV=V/sqrt(V(1,:)*sumB*V(1,:)');% constraint norm(VV(:,1)'*sumA*VV(:,1)),norm(VV(:,1)'*sumB*VV(:,1))
% F_true=-norm(VV(1,:)*sumA*VV(1,:)');
%% parameter initialization
rho1=50;%Íâ 20
rho2=50;%ÄÚ 20
w_init=randn(d,1);
w_init=w_init/sqrt(w_init'*sumB*w_init);%must
% load('wronginit.mat');
l_init=zeros(d,1);
% z_init=w_init+l_init/rho2;
E_list=[];
L_list=[];
%% local data preparation
w_b=0;
for i=1:N
A(:,:,i)=sumA/N;
B(:,:,i)=sumB/N;
l(:,:,i)=l_init;
w(:,:,i)=w_init;%randn(d,1);
w_b=w_b+w(:,:,i);
c(:,i)=w(:,:,i)'*B(:,:,i)*w(:,:,i);
end
if w_b'*VV<0
w_b=-w_b;
end
w_b=w_b/N;
iter=0;
L=0;
%% outer ADMM
tic;
while 1
%% w_i update: select edge and inner loop
L_old=L;
w_b_old=w_b;
iter=iter+1;
flag=zeros(N,1);
%% z update in the FC
w_m=0;
l_m=0;
for i=1:N
w_m=w_m+w(:,:,i);
l_m=l_m+l(:,:,i);
end
w_m=w_m/N;
l_m=l_m/N;
z=w_m+l_m/rho1;
fprintf('outerL after z: %0.5f\n',outerL(N,w,A,l,z,rho1));
%% w-update
while 1
r=randperm(size(index,1));
s_rp=r(1:size(r,2)/2);%
% resz=0;
% zm=0;
for k=1:size(s_rp,2)%3N
ii=floor((index(s_rp(k))-1)/N)+1;
jj=index(s_rp(k))-(ii-1)*N;
sumc=cal_globalc(c,N);%(k)
fprintf('!! Node %d and Node %d are updating!\n',ii,jj);
[w(:,:,ii),w(:,:,jj),c(:,ii),c(:,jj)]=inner_loop(ii,jj,A,B,rho1,d,sumc,w(:,:,ii),w(:,:,jj),l(:,:,ii),l(:,:,jj),z,rho2);
flag(ii)=1;
flag(jj)=1;
[w(:,:,ii),w(:,:,jj)]=check_allign(VV,w(:,:,ii),w(:,:,jj));
end
if isempty(find(~flag))%&& resz<1e-3
break;
% else
% flag=zeros(N,1);
end
end
L=outerL(N,w,A,l,z,rho2);
fprintf('outerL after w_i: %0.5f\n',L);
L_list=[L_list L];
%% lambda update
for i=1:N
temp=l(:,:,i)+rho2*(w(:,:,i)-z);
if iter==1||norm(temp)>1e-3
l(:,:,i)=temp;
end
end
fprintf('outerL after l_i: %0.5f\n',outerL(N,w,A,l,z,rho2));
%% stop criteria
w_b=0;
for i=1:N
w_b=w_b+w(:,:,i);
end
w_b=w_b/N; %output
% if norm(L-L_old)<1e-5
% fprintf('#complete outer iter=%d, res=%0.5f\n',iter,norm(L-L_old));%
% sin(subspace(VV,w_b))
% norm(w_b-VV)
% fprintf('\n')
% break;
% else
% fprintf('#complete outer iter=%d, res=%0.5f\n',iter,norm(L-L_old));%
% end
res1=0; %
for i=1:N
res1=res1+norm(w(:,:,i)-w_b);
end
res2=norm(w_b-w_b_old);%z-residual
if res1<1e-04 &&res2<1e-02%iter>300
fprintf('#complete outer iter=%d, res1=%0.5f, res2=%0.5f\n',iter,res1,res2);%
sin(subspace(VV,w_b))
fprintf('\n')
break;
else
fprintf('#complete outer iter=%d, res1=%0.5f, res2=%0.5f\n',iter,res1,res2);%
% fprintf('\n')
end
sin(subspace(VV,w_b))
E_list=[E_list sin(subspace(VV,w_b))];
end
t=toc;
%%
figure; yyaxis left;
plot(E_list,'LineWidth',1);
title('Convergence performance of Alg.1','interpreter','latex', 'FontSize', 18);
xlabel('iterations','interpreter','latex', 'FontSize', 18);
ylabel('distance of subspaces','interpreter','latex', 'FontSize', 18);
yyaxis right;
plot(L_list,'LineWidth',1);
ylabel('The Lagrangian fuction value');
%% functions
function [wi,wj]=check_allign(w_b,wi,wj)
if w_b'*wi<0
wi=-wi;
end
if w_b'*wj<0
wj=-wj;
end
end
function [L]=outerL(N,w,A,l,z,rho2)%,F
L=0;
% F=0;
for i=1:N
L=L-w(:,:,i)'*A(:,:,i)*w(:,:,i)+l(:,:,i)'*(w(:,:,i)-z)+rho2/2*(norm(w(:,:,i)-z)^2);
% F=F-w(:,:,i)'*A(:,:,i)*w(:,:,i)
end
end
function sumc=cal_globalc(c,N)
sumc=0;
for i=1:N
sumc=sumc+c(:,i);
end
end
function L=innerLGD(wi,wj,Ai,Aj,Bi,Bj,ai,li,lj,rho1,c,z,rho2)
L=-wi'*Ai*wi-wj'*Aj*wj+ai*(wi'*Bi*wi+wj'*Bj*wj-c)+li'*(wi-z)+lj'*(wj-z)+rho1/2*(norm(wi-z)^2+norm(wj-z)^2)+rho2/2*norm(wi'*Bi*wi+wj'*Bj*wj-c)^2;
end
% function L=innerL(wi,wj,Ai,Aj,Bi,Bj,ai,li,lj,rho1,c,z)
% L=-wi'*Ai*wi-wj'*Aj*wj+ai*(wi'*Bi*wi+wj'*Bj*wj-c)+li'*(wi-z)+lj'*(wj-z)+rho1/2*(norm(wi-z)^2+norm(wj-z)^2);
% end
function p=inv_ill(A)
[u,d,v]=svd(A);%A=udv'
dd=size(d,1);
for i=1:dd
if d(i,i)<=1e-3
s(i)=0;
else
s(i)=1/d(i,i);
end
end
S=diag(s);
p=v*S*u';
end
function [wi,wj,ci,cj]=inner_loop(i,j,A,B,rho1,d,sumc,wi,wj,li,lj,z,rho2)
%% initialization
global VV
a=0;
Ai=A(:,:,i);
Aj=A(:,:,j);
Bi=B(:,:,i);
Bj=B(:,:,j);
cj=wj'*Bj*wj;
ci=wi'*Bi*wi;
sumk=sumc-ci-cj;
c=1-sumk; %c=ci+cj
clear A B
iter=0;
% a_old=a;
% fprintf('init_L: %0.5f\n',innerLGD(wi,wj,Ai,Aj,Bi,Bj,a,li,lj,rho1,c,z,rho2));
% fprintf('init_L: %0.5f\n',innerL(wi,wj,Ai,Aj,Bi,Bj,a,li,lj,rho1,c,z));
while 1
iter=iter+1;
wi_old=wi;
wj_old=wj;
% cj+ci-c
% flag=0;
% wi=inv_ill(2*(a*Bi-Ai+rho1/2*eye(d)))*(rho1*z-li); %pinv
wi=w_GD(wi,Ai,Bi,rho1,rho2,z,a,li,cj,c);
% fprintf('L after wi: %0.5f\n',innerLGD(wi,wj,Ai,Aj,Bi,Bj,a,li,lj,rho1,c,z,rho2));
% fprintf('L after wi: %0.5f\n',innerL(wi,wj,Ai,Aj,Bi,Bj,a,li,lj,rho1,c,z));
ci= wi'*Bi*wi;
wj=w_GD(wj,Ai,Bi,rho1,rho2,z,a,lj,ci,c);
% wj=inv_ill(2*(a*Bj-Aj+rho1/2*eye(d)))*(rho1*z-lj);
% fprintf('L after wj: %0.5f\n',innerLGD(wi,wj,Ai,Aj,Bi,Bj,a,li,lj,rho1,c,z,rho2));
% fprintf('L after wj: %0.5f\n',innerL(wi,wj,Ai,Aj,Bi,Bj,a,li,lj,rho1,c,z));
cj= wj'*Bj*wj;
% aj=aj+rho1*(ci+cj-c);
if norm(wi_old-wi)<1e-3&&norm(wj_old-wj)<1e-3
a=a+rho1*(cj+ci-c);%
% fprintf('L after a: %0.5f\n',innerL(wi,wj,Ai,Aj,Bi,Bj,a,li,lj,rho1,c,z));
% fprintf('L after a: %0.5f\n',innerLGD(wi,wj,Ai,Aj,Bi,Bj,a,li,lj,rho1,c,z,rho2));
% flag=1;
end
% if iter==1||temp>1e-3
% a=temp;
% else
% a=0;
% end
% fprintf('L after a: %0.5f\n',innerL(wi,wj,Ai,Aj,Bi,Bj,a,li,lj,rho1,c,z,rho1));
res1=norm(wi_old-wi);
res2=norm(wj_old-wj);
%% stop criteria
if res1<1e-03 && res2<1e-03 %(ci+cj-c)<1e-3&&norm(a_old-a)<1e-3&&flag==1
% fprintf('#complete inner iter=%d, res_wi=%0.5f, res_wj=%0.5f\n',iter,res1,res2);
break;
else
% fprintf('#complete inner iter=%d, res_wi=%0.5f, res_wj=%0.5f\n',iter,res1,res2);
% fprintf('\n')
end
% a_old=a;
end
end
function [w]=w_GD(w,A,B,rho1,rho2,z,a,l,ci,c)
iter=0;
r=0.001;
w=w/norm(w);
L_old=wL_func(w,A,B,a,l,z,rho1,rho2,ci,c);
while 1
iter=iter+1;
g=2*(a*B-A)*w+l+rho1*w-rho1*z+2*rho2*w'*B*w*B*w+2*rho2*(ci-c)*B*w;
g=g/norm(g);
w=w-r*g;
L=wL_func(w,A,B,a,l,z,rho1,rho2,ci,c);
% if norm(w_old-w)<1e-3
% break;
% end
if norm(L_old-L)<1e-3
break;
else
% fprintf('#iter=%d,norm_gradient:%f\n',iter,norm(g))
end
L_old=L;
end
end
function [L]=wL_func(wi,Ai,Bi,ai,li,z,rho1,rho2,cj,c)
L=-wi'*Ai*wi+ai*(wi'*Bi*wi+cj-c)+li'*wi+rho1/2*wi'*wi-rho1*wi'*z+rho2/2*norm(wi'*Bi*wi+cj-c)^2;
end
function [A,B] = gen_fix_data(d)
sigma=[];
% for i=1:d
% sigma=[sigma k/i];
% end
A=randn(d,d);%N*
sumA=A+A';%symmetric
sigma=[200,100, 50*ones(1,d-2)];% (sort((1:99),'descend'))];
% v1=orth(randn(d,d));
v2=orth(randn(d,d));
% A=v1*(diag(sigma)+eye(d))*v1';
B=v2*(diag(sigma)+eye(d))*v2';
save data2.mat A B
% B=N*randn(d,d);
% sumB=B+B';%symmetric
end