Hopfield network

h1.m

net = newhop(stimul);
Ai = stimul;
[Y,Pf,Af] = sim(net,360,[],Ai);
W= net.LW{1,1};
norm(stimul-Y)

otv=[];
ot=Y(:,2);
for n=1:96
otv(mod(n-1,8)+1,floor((n-1)/8)+1)=ot(n);
end
otv=otv';
pcolor(otv);figure(gcf);

a={stimul(:,38)};
[y,Pf,Af] = sim(net,{1 20},{},a);
ot=cell2mat(y(:,20));otv=[];
for n=1:96
otv(mod(n-1,8)+1,floor((n-1)/8)+1)=ot(n);
end
otv=otv';
pcolor(otv);figure(gcf);

a={rand(96,1)};
[y,Pf,Af] = sim(net,{1 20},{},a);
ot=cell2mat(y(:,20));otv=[];
for n=1:96
otv(mod(n-1,8)+1,floor((n-1)/8)+1)=ot(n);
end
otv=otv';
pcolor(otv);figure(gcf);



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
t=stimul;
[S,Q] = size(t);
Y = t(:,1:Q-1)-t(:,Q)*ones(1,Q-1);
[U,SS,V] = svd(Y);
K = rank(SS);

TP = zeros(S,S);
for k=1:K
  TP = TP + U(:,k)*U(:,k)';
  end

TM = zeros(S,S);
for k=K+1:S
  TM = TM + U(:,k)*U(:,k)';
  end

tau = 10;
Ttau = TP - tau*TM;
Itau = t(:,Q) - Ttau*t(:,Q);

h = 0.15;
C1 = exp(h)-1;
C2 = -(exp(-tau*h)-1)/tau;

w = expm(h*Ttau);
b = U * [  C1*eye(K)         zeros(K,S-K);
         zeros(S-K,K)  C2*eye(S-K)] * U' * Itau;
		 
%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% BASIC hopf		 
%%%%%%%%%%%%%%%%%%%%%%%%%%
correct=0;
error=0;

for k=1:Q
	x=t(:,k);
	while( norm(satlins(W*x)-x)>0 )
	x=satlins(W*x);
	end
	if( norm(x-t(:,k))>0 )
	error=error+1;
	else
	correct=correct+1;
	end
end

%%%%%%%%%%%%%%
%%%%%%%%%%%%% CHop
t=data;
[S,Q] = size(t);
W=zeros(S);
for k=1:Q
W = W + (1/Q)*t(:,k)*t(:,k)';
end
for k=1:S
W(k,k)=0;
end

CHD=[];CY=[];
for k=1:Q
	u=t(:,k);
	while( norm(satlins(W*u)-u)>0 )
	u=satlins(W*u);
	end
	CY=[CY u];x=idealo(:,k)-u;
	hd=0;
	for l=1:S
		if( x(l)~=0 )
		hd=hd+1;
		end
	end
	if(hd==0)
	disp(k)
	end
	CHD=[CHD hd];
end
CHOP=zeros(12,1);
for s=1:Q
CHOP(floor((s-1)/30)+1)=CHOP(floor((s-1)/30)+1)+CHD(s);
end
CHOP=CHOP/30;


%%%%%%%%%%%%% Hop
HD=[];
for k=1:Q
	x=idealo(:,k)-Y(:,k);
	hd=0;
	for l=1:S
		if( x(l)~=0 )
		hd=hd+1;
		end
	end
	if(hd==0)
	disp(k)
	end
	HD=[HD hd];
end
HOP=zeros(12,1);
for s=1:Q
HOP(floor((s-1)/30)+1)=HOP(floor((s-1)/30)+1)+HD(s);
end
HOP=HOP/30;
%%%%%%%%%%%%% SD
SD=[];
for k=1:Q
	x=idealo(:,k)-rsd(:,k);
	hd=0;
	for l=1:S
		if( x(l)~=0 )
		hd=hd+1;
		end
	end

	SD=[SD hd];
end
HSD=zeros(12,1);
for s=1:360
HSD(floor((s-1)/30)+1)=HSD(floor((s-1)/30)+1)+SD(s);
end
HSD=HSD/30;

BAR(:,1)=HSD;
BAR(:,2)=HOP;
BAR(:,3)=CHOP;
%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% how many classes do you have?	 
%%%%%%%%%%%%%%%%%%%%%%%%%%
t=Y;
class=360;
for n1=1:360
for n2=n1+1:360
if(norm(t(:,n1)-t(:,n2))==0) 
disp([n1 n2])
class=class-1;
break
end
end
end

   
  ideal=flipud(ideal);
  
otv=[];
ot=ideal(:,71);
for n=1:96
otv(floor((n-1)/8)+1,mod(n-1,8)+1)=ot(n);
end

% Create figure
figure1 = figure('PaperSize',[20.98404194812 29.67743169791],...
    'Colormap',[1 1 1;1 1 0.857142865657806;1 1 0.714285731315613;1 1 0.571428596973419;1 1 0.428571432828903;1 1 0.28571429848671;1 1 0.142857149243355;1 1 0;0.991911768913269 0.968137264251709 0;0.983823537826538 0.936274528503418 0;0.975735306739807 0.904411792755127 0;0.967647075653076 0.872548997402191 0;0.959558844566345 0.8406862616539 0;0.951470613479614 0.808823525905609 0;0.943382382392883 0.776960790157318 0;0.935294151306152 0.745098054409027 0;0.927205860614777 0.713235318660736 0;0.919117629528046 0.6813725233078 0;0.911029398441315 0.649509787559509 0;0.902941167354584 0.617647051811218 0;0.894852936267853 0.585784316062927 0;0.886764705181122 0.553921580314636 0;0.878676474094391 0.522058844566345 0;0.87058824300766 0.490196079015732 0;0.858823537826538 0.488725483417511 0;0.847058832645416 0.487254917621613 0;0.835294127464294 0.485784322023392 0;0.823529422283173 0.484313726425171 0;0.811764717102051 0.48284313082695 0;0.800000011920929 0.481372535228729 0;0.788235306739807 0.479901969432831 0;0.776470601558685 0.47843137383461 0;0.764705896377563 0.476960778236389 0;0.752941191196442 0.475490212440491 0;0.74117648601532 0.47401961684227 0;0.729411780834198 0.472549021244049 0;0.717647075653076 0.471078425645828 0;0.705882370471954 0.469607830047607 0;0.694117665290833 0.468137264251709 0;0.682352960109711 0.466666668653488 0;0.671078443527222 0.468872547149658 0.0313725508749485;0.659803926944733 0.471078425645828 0.062745101749897;0.648529410362244 0.473284333944321 0.0941176563501358;0.637254953384399 0.475490212440491 0.125490203499794;0.62598043680191 0.477696090936661 0.156862750649452;0.614705920219421 0.479901969432831 0.188235312700272;0.603431403636932 0.482107847929001 0.21960785984993;0.592156887054443 0.484313726425171 0.250980406999588;0.580882370471954 0.486519634723663 0.282352954149246;0.569607853889465 0.488725513219833 0.313725501298904;0.558333337306976 0.490931391716003 0.345098048448563;0.547058820724487 0.493137270212173 0.376470625400543;0.535784363746643 0.495343148708344 0.407843172550201;0.524509847164154 0.497549057006836 0.43921571969986;0.513235330581665 0.499754935503006 0.470588266849518;0.501960813999176 0.501960813999176 0.501960813999176;0.43921571969986 0.43921571969986 0.43921571969986;0.376470625400543 0.376470625400543 0.376470625400543;0.313725501298904 0.313725501298904 0.313725501298904;0.250980406999588 0.250980406999588 0.250980406999588;0.188235312700272 0.188235312700272 0.188235312700272;0.125490203499794 0.125490203499794 0.125490203499794;0.062745101749897 0.062745101749897 0.062745101749897;0 0 0]);

% Create axes
axes1 = axes('Parent',figure1,'YTickLabel',{'2','4','6','8','10','12'},...
    'YTick',[2.5 4.5 6.5 8.5 10.5 12.5],...
    'YGrid','on',...
    'YDir','reverse',...
    'XTickLabel',{'2','4','6','8'},...
    'XTick',[2.5 4.5 6.5 8.5],...
    'XGrid','on',...
    'Position',[0.0954107520333119 0.0668345743049818 0.883942766295707 0.920469361147327],...
    'Layer','top',...
    'FontSize',16,...
    'FontName','DejaVu Sans Mono');
% preserve the X-limits of the axes
xlim(axes1,[0.5 8.5]);
% preserve the Y-limits of the axes
ylim(axes1,[0.5 12.5]);
box(axes1,'on');
hold(axes1,'all');

% Create image
image(otv,'Parent',axes1,'CDataMapping','scaled');

data=[];
for k=1:360
	t=k-1;
	id=mod(floor(t/10),3)*120+floor(t/30)*10+mod(t,10)+1;
	data(:,k)=data0(:,id);
end

alld=[];
space=2;
for p=1:360
otv=[];
ot=data(:,p);
	for n=1:96
	otv(floor((n-1)/8)+1,mod(n-1,8)+1)=ot(n);
	end
	x=mod(p-1,30)*space;
	y=floor((p-1)/30)*space;
	a=floor((p-1)/30)*12+1+y:(floor((p-1)/30)+1)*12+y;
	b=x+mod(p-1,30)*8+1:x+(mod(p-1,30)+1)*8;
alld(a, b)=otv;
end
% Create figure
figure1 = figure('PaperSize',[20.98404194812 29.67743169791],...
    'Colormap',[1 1 1;1 1 0.857142865657806;1 1 0.714285731315613;1 1 0.571428596973419;1 1 0.428571432828903;1 1 0.28571429848671;1 1 0.142857149243355;1 1 0;0.991911768913269 0.968137264251709 0;0.983823537826538 0.936274528503418 0;0.975735306739807 0.904411792755127 0;0.967647075653076 0.872548997402191 0;0.959558844566345 0.8406862616539 0;0.951470613479614 0.808823525905609 0;0.943382382392883 0.776960790157318 0;0.935294151306152 0.745098054409027 0;0.927205860614777 0.713235318660736 0;0.919117629528046 0.6813725233078 0;0.911029398441315 0.649509787559509 0;0.902941167354584 0.617647051811218 0;0.894852936267853 0.585784316062927 0;0.886764705181122 0.553921580314636 0;0.878676474094391 0.522058844566345 0;0.87058824300766 0.490196079015732 0;0.858823537826538 0.488725483417511 0;0.847058832645416 0.487254917621613 0;0.835294127464294 0.485784322023392 0;0.823529422283173 0.484313726425171 0;0.811764717102051 0.48284313082695 0;0.800000011920929 0.481372535228729 0;0.788235306739807 0.479901969432831 0;0.776470601558685 0.47843137383461 0;0.764705896377563 0.476960778236389 0;0.752941191196442 0.475490212440491 0;0.74117648601532 0.47401961684227 0;0.729411780834198 0.472549021244049 0;0.717647075653076 0.471078425645828 0;0.705882370471954 0.469607830047607 0;0.694117665290833 0.468137264251709 0;0.682352960109711 0.466666668653488 0;0.671078443527222 0.468872547149658 0.0313725508749485;0.659803926944733 0.471078425645828 0.062745101749897;0.648529410362244 0.473284333944321 0.0941176563501358;0.637254953384399 0.475490212440491 0.125490203499794;0.62598043680191 0.477696090936661 0.156862750649452;0.614705920219421 0.479901969432831 0.188235312700272;0.603431403636932 0.482107847929001 0.21960785984993;0.592156887054443 0.484313726425171 0.250980406999588;0.580882370471954 0.486519634723663 0.282352954149246;0.569607853889465 0.488725513219833 0.313725501298904;0.558333337306976 0.490931391716003 0.345098048448563;0.547058820724487 0.493137270212173 0.376470625400543;0.535784363746643 0.495343148708344 0.407843172550201;0.524509847164154 0.497549057006836 0.43921571969986;0.513235330581665 0.499754935503006 0.470588266849518;0.501960813999176 0.501960813999176 0.501960813999176;0.43921571969986 0.43921571969986 0.43921571969986;0.376470625400543 0.376470625400543 0.376470625400543;0.313725501298904 0.313725501298904 0.313725501298904;0.250980406999588 0.250980406999588 0.250980406999588;0.188235312700272 0.188235312700272 0.188235312700272;0.125490203499794 0.125490203499794 0.125490203499794;0.062745101749897 0.062745101749897 0.062745101749897;0 0 0]);

% Create axes
axes1 = axes('Parent',figure1,'YTickLabel',{'2','4','6','8','10','12'},...
    'YTick',[2.5 4.5 6.5 8.5 10.5 12.5],...
    'YGrid','on',...
    'YDir','reverse',...
    'XTickLabel',{'2','4','6','8'},...
    'XTick',[2.5 4.5 6.5 8.5],...
    'XGrid','on',...
    'Position',[0.0954107520333119 0.0668345743049818 0.883942766295707 0.920469361147327],...
    'Layer','top',...
    'FontSize',16,...
    'FontName','DejaVu Sans Mono');
% preserve the X-limits of the axes
xlim(axes1,[0.5 8.5]);
% preserve the Y-limits of the axes
ylim(axes1,[0.5 12.5]);
box(axes1,'on');
hold(axes1,'all');

% Create image
image(otv,'Parent',axes1,'CDataMapping','scaled');

h2.m

t=hardlims(rand(40,4)*2-1);
[S,Q] = size(t);
CW=zeros(S);
for k=1:Q
CW = CW + (1/Q)*t(:,k)*t(:,k)';
end
CW=CW-eye(S);
CY=[];
for k=1:Q
	u=t(:,k);
while( norm(hardlims(CW*u)-u)>0 )
	u=hardlims(CW*u);
	end
	CY=[CY u];
end
CY

%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% BASIC hopf		 
%%%%%%%%%%%%%%%%%%%%%%%%%%

data0=data0';
data=[];
for k=1:360
	t=k-1;
	id=mod(floor(t/10),3)*120+floor(t/30)*10+mod(t,10)+1;
	data(:,k)=data0(:,id);
end

g=2;
d=1/(Q*g);
t=data(:,1:360);
[S,Q] = size(t);
CW=zeros(S);
for k=1:Q
CW = CW + (1-k*d)*t(:,k)*t(:,k)';%%CW = CW + (1/(k+2))*t(:,k)*t(:,k)';
end
CW=CW-eye(S);
CW=normr(CW);

CY=[];
for k=1:Q
	u=t(:,k);
	while( norm(satlins(CW*u)-u)>0 )
	u=satlins(CW*u);
	end
	CY=[CY u];
end
calld=[];
space=2;
for p=1:Q
otv=[];
ot=CY(:,p);
	for n=1:96
	otv(floor((n-1)/8)+1,mod(n-1,8)+1)=ot(n);
	end
	x=mod(p-1,30)*space;
	y=floor((p-1)/30)*space;
	a=floor((p-1)/30)*12+1+y:(floor((p-1)/30)+1)*12+y;
	b=x+mod(p-1,30)*8+1:x+(mod(p-1,30)+1)*8;
calld(a, b)=otv;
end
% Create figure
figure1 = figure('PaperSize',[20.98404194812 29.67743169791],...
    'Colormap',[1 1 1;1 1 0.857142865657806;1 1 0.714285731315613;1 1 0.571428596973419;1 1 0.428571432828903;1 1 0.28571429848671;1 1 0.142857149243355;1 1 0;0.991911768913269 0.968137264251709 0;0.983823537826538 0.936274528503418 0;0.975735306739807 0.904411792755127 0;0.967647075653076 0.872548997402191 0;0.959558844566345 0.8406862616539 0;0.951470613479614 0.808823525905609 0;0.943382382392883 0.776960790157318 0;0.935294151306152 0.745098054409027 0;0.927205860614777 0.713235318660736 0;0.919117629528046 0.6813725233078 0;0.911029398441315 0.649509787559509 0;0.902941167354584 0.617647051811218 0;0.894852936267853 0.585784316062927 0;0.886764705181122 0.553921580314636 0;0.878676474094391 0.522058844566345 0;0.87058824300766 0.490196079015732 0;0.858823537826538 0.488725483417511 0;0.847058832645416 0.487254917621613 0;0.835294127464294 0.485784322023392 0;0.823529422283173 0.484313726425171 0;0.811764717102051 0.48284313082695 0;0.800000011920929 0.481372535228729 0;0.788235306739807 0.479901969432831 0;0.776470601558685 0.47843137383461 0;0.764705896377563 0.476960778236389 0;0.752941191196442 0.475490212440491 0;0.74117648601532 0.47401961684227 0;0.729411780834198 0.472549021244049 0;0.717647075653076 0.471078425645828 0;0.705882370471954 0.469607830047607 0;0.694117665290833 0.468137264251709 0;0.682352960109711 0.466666668653488 0;0.671078443527222 0.468872547149658 0.0313725508749485;0.659803926944733 0.471078425645828 0.062745101749897;0.648529410362244 0.473284333944321 0.0941176563501358;0.637254953384399 0.475490212440491 0.125490203499794;0.62598043680191 0.477696090936661 0.156862750649452;0.614705920219421 0.479901969432831 0.188235312700272;0.603431403636932 0.482107847929001 0.21960785984993;0.592156887054443 0.484313726425171 0.250980406999588;0.580882370471954 0.486519634723663 0.282352954149246;0.569607853889465 0.488725513219833 0.313725501298904;0.558333337306976 0.490931391716003 0.345098048448563;0.547058820724487 0.493137270212173 0.376470625400543;0.535784363746643 0.495343148708344 0.407843172550201;0.524509847164154 0.497549057006836 0.43921571969986;0.513235330581665 0.499754935503006 0.470588266849518;0.501960813999176 0.501960813999176 0.501960813999176;0.43921571969986 0.43921571969986 0.43921571969986;0.376470625400543 0.376470625400543 0.376470625400543;0.313725501298904 0.313725501298904 0.313725501298904;0.250980406999588 0.250980406999588 0.250980406999588;0.188235312700272 0.188235312700272 0.188235312700272;0.125490203499794 0.125490203499794 0.125490203499794;0.062745101749897 0.062745101749897 0.062745101749897;0 0 0]);

% Create axes
axes1 = axes('Parent',figure1,'YTick',zeros(1,0),'YDir','reverse',...
    'XTick',zeros(1,0),......
    'Position',[0.0954107520333119 0.0668345743049818 0.883942766295707 0.920469361147327],...
    'Layer','top',...
    'FontSize',16,...
    'FontName','DejaVu Sans Mono');
% preserve the X-limits of the axes
%xlim(axes1,[0.5 8.5]);
% preserve the Y-limits of the axes
%ylim(axes1,[0.5 12.5]);
hold(axes1,'all');

% Create image
image(calld,'Parent',axes1,'CDataMapping','scaled');













%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Matlab hopf		 
%%%%%%%%%%%%%%%%%%%%%%%%%%


net = newhop(data);
[Y,Pf,Af] = sim(net,360,[],data);
W= net.LW{1,1};
alld=[];
space=2;
for p=1:360
otv=[];
ot=Y(:,p);
	for n=1:96
	otv(floor((n-1)/8)+1,mod(n-1,8)+1)=ot(n);
	end
	x=mod(p-1,30)*space;
	y=floor((p-1)/30)*space;
	a=floor((p-1)/30)*12+1+y:(floor((p-1)/30)+1)*12+y;
	b=x+mod(p-1,30)*8+1:x+(mod(p-1,30)+1)*8;
alld(a, b)=otv;
end
% Create figure
figure1 = figure('PaperSize',[20.98404194812 29.67743169791],...
    'Colormap',[1 1 1;1 1 0.857142865657806;1 1 0.714285731315613;1 1 0.571428596973419;1 1 0.428571432828903;1 1 0.28571429848671;1 1 0.142857149243355;1 1 0;0.991911768913269 0.968137264251709 0;0.983823537826538 0.936274528503418 0;0.975735306739807 0.904411792755127 0;0.967647075653076 0.872548997402191 0;0.959558844566345 0.8406862616539 0;0.951470613479614 0.808823525905609 0;0.943382382392883 0.776960790157318 0;0.935294151306152 0.745098054409027 0;0.927205860614777 0.713235318660736 0;0.919117629528046 0.6813725233078 0;0.911029398441315 0.649509787559509 0;0.902941167354584 0.617647051811218 0;0.894852936267853 0.585784316062927 0;0.886764705181122 0.553921580314636 0;0.878676474094391 0.522058844566345 0;0.87058824300766 0.490196079015732 0;0.858823537826538 0.488725483417511 0;0.847058832645416 0.487254917621613 0;0.835294127464294 0.485784322023392 0;0.823529422283173 0.484313726425171 0;0.811764717102051 0.48284313082695 0;0.800000011920929 0.481372535228729 0;0.788235306739807 0.479901969432831 0;0.776470601558685 0.47843137383461 0;0.764705896377563 0.476960778236389 0;0.752941191196442 0.475490212440491 0;0.74117648601532 0.47401961684227 0;0.729411780834198 0.472549021244049 0;0.717647075653076 0.471078425645828 0;0.705882370471954 0.469607830047607 0;0.694117665290833 0.468137264251709 0;0.682352960109711 0.466666668653488 0;0.671078443527222 0.468872547149658 0.0313725508749485;0.659803926944733 0.471078425645828 0.062745101749897;0.648529410362244 0.473284333944321 0.0941176563501358;0.637254953384399 0.475490212440491 0.125490203499794;0.62598043680191 0.477696090936661 0.156862750649452;0.614705920219421 0.479901969432831 0.188235312700272;0.603431403636932 0.482107847929001 0.21960785984993;0.592156887054443 0.484313726425171 0.250980406999588;0.580882370471954 0.486519634723663 0.282352954149246;0.569607853889465 0.488725513219833 0.313725501298904;0.558333337306976 0.490931391716003 0.345098048448563;0.547058820724487 0.493137270212173 0.376470625400543;0.535784363746643 0.495343148708344 0.407843172550201;0.524509847164154 0.497549057006836 0.43921571969986;0.513235330581665 0.499754935503006 0.470588266849518;0.501960813999176 0.501960813999176 0.501960813999176;0.43921571969986 0.43921571969986 0.43921571969986;0.376470625400543 0.376470625400543 0.376470625400543;0.313725501298904 0.313725501298904 0.313725501298904;0.250980406999588 0.250980406999588 0.250980406999588;0.188235312700272 0.188235312700272 0.188235312700272;0.125490203499794 0.125490203499794 0.125490203499794;0.062745101749897 0.062745101749897 0.062745101749897;0 0 0]);

% Create axes
axes1 = axes('Parent',figure1,'YTickLabel',{'2','4','6','8','10','12'},...
    'YTick',[2.5 4.5 6.5 8.5 10.5 12.5],...
    'YGrid','on',...
    'YDir','reverse',...
    'XTickLabel',{'2','4','6','8'},...
    'XTick',[2.5 4.5 6.5 8.5],...
    'XGrid','on',...
    'Position',[0.0954107520333119 0.0668345743049818 0.883942766295707 0.920469361147327],...
    'Layer','top',...
    'FontSize',16,...
    'FontName','DejaVu Sans Mono');
% preserve the X-limits of the axes
xlim(axes1,[0.5 8.5]);
% preserve the Y-limits of the axes
ylim(axes1,[0.5 12.5]);
box(axes1,'on');
hold(axes1,'all');

% Create image
image(alld,'Parent',axes1,'CDataMapping','scaled');

h3.m

[S,Q] = size(t);
W=zeros(S);
W = W + (2/3)*t(:,1)*t(:,1)';
W = W + (1/6)*t(:,2)*t(:,2)';
W = W + (1/6)*t(:,3)*t(:,3)';
for k=1:S
W(k,k)=0;
end

CY=[];
for k=1:Q
	u=t(:,k);
	while( norm(satlins(W*u)-u)>0 )
	u=satlins(W*u);
	end
	CY=[CY u];
end
	
alld=[];
space=2;
for p=1:Q
	otv=[];
	ot=CY(:,p);
	for n=1:S
		otv(floor((n-1)/8)+1,mod(n-1,8)+1)=ot(n);
	end
	x=mod(p-1,30)*space;
	y=floor((p-1)/30)*space;
	a=floor((p-1)/30)*6+1+y:(floor((p-1)/30)+1)*6+y;
	b=x+mod(p-1,30)*8+1:x+(mod(p-1,30)+1)*8;
	alld(a, b)=otv;
end
% Create figure
figure1 = figure('PaperSize',[20.98404194812 29.67743169791],...
    'Colormap',[1 1 1;1 1 0.857142865657806;1 1 0.714285731315613;1 1 0.571428596973419;1 1 0.428571432828903;1 1 0.28571429848671;1 1 0.142857149243355;1 1 0;0.991911768913269 0.968137264251709 0;0.983823537826538 0.936274528503418 0;0.975735306739807 0.904411792755127 0;0.967647075653076 0.872548997402191 0;0.959558844566345 0.8406862616539 0;0.951470613479614 0.808823525905609 0;0.943382382392883 0.776960790157318 0;0.935294151306152 0.745098054409027 0;0.927205860614777 0.713235318660736 0;0.919117629528046 0.6813725233078 0;0.911029398441315 0.649509787559509 0;0.902941167354584 0.617647051811218 0;0.894852936267853 0.585784316062927 0;0.886764705181122 0.553921580314636 0;0.878676474094391 0.522058844566345 0;0.87058824300766 0.490196079015732 0;0.858823537826538 0.488725483417511 0;0.847058832645416 0.487254917621613 0;0.835294127464294 0.485784322023392 0;0.823529422283173 0.484313726425171 0;0.811764717102051 0.48284313082695 0;0.800000011920929 0.481372535228729 0;0.788235306739807 0.479901969432831 0;0.776470601558685 0.47843137383461 0;0.764705896377563 0.476960778236389 0;0.752941191196442 0.475490212440491 0;0.74117648601532 0.47401961684227 0;0.729411780834198 0.472549021244049 0;0.717647075653076 0.471078425645828 0;0.705882370471954 0.469607830047607 0;0.694117665290833 0.468137264251709 0;0.682352960109711 0.466666668653488 0;0.671078443527222 0.468872547149658 0.0313725508749485;0.659803926944733 0.471078425645828 0.062745101749897;0.648529410362244 0.473284333944321 0.0941176563501358;0.637254953384399 0.475490212440491 0.125490203499794;0.62598043680191 0.477696090936661 0.156862750649452;0.614705920219421 0.479901969432831 0.188235312700272;0.603431403636932 0.482107847929001 0.21960785984993;0.592156887054443 0.484313726425171 0.250980406999588;0.580882370471954 0.486519634723663 0.282352954149246;0.569607853889465 0.488725513219833 0.313725501298904;0.558333337306976 0.490931391716003 0.345098048448563;0.547058820724487 0.493137270212173 0.376470625400543;0.535784363746643 0.495343148708344 0.407843172550201;0.524509847164154 0.497549057006836 0.43921571969986;0.513235330581665 0.499754935503006 0.470588266849518;0.501960813999176 0.501960813999176 0.501960813999176;0.43921571969986 0.43921571969986 0.43921571969986;0.376470625400543 0.376470625400543 0.376470625400543;0.313725501298904 0.313725501298904 0.313725501298904;0.250980406999588 0.250980406999588 0.250980406999588;0.188235312700272 0.188235312700272 0.188235312700272;0.125490203499794 0.125490203499794 0.125490203499794;0.062745101749897 0.062745101749897 0.062745101749897;0 0 0]);
% Create axes
axes1 = axes('Parent',figure1,'YTickLabel',{'2','4','6','8','10','12'},...
    'YTick',[2.5 4.5 6.5 8.5 10.5 12.5],...
    'YGrid','on',...
    'YDir','reverse',...
    'XTickLabel',{'2','4','6','8'},...
    'XTick',[2.5 4.5 6.5 8.5],...
    'XGrid','on',...
    'Position',[0.0954107520333119 0.0668345743049818 0.883942766295707 0.920469361147327],...
    'Layer','top',...
    'FontSize',16,...
    'FontName','DejaVu Sans Mono');

box(axes1,'on');
hold(axes1,'all');

% Create image
image(alld,'Parent',axes1,'CDataMapping','scaled');