function ani_opt_pnorm_fitting_all()
nx=60;
ny=1;
nz=20;
volfrac=0.535;
rmin=1.5;
[Hs,H]=filter_coef_3D(nx,ny,nz,rmin);

a(1:nz,1:ny,1:nx) = 1.0;
b(1:nz,1:ny,1:nx) = 1.0;
c(1:nz,1:ny,1:nx) = 0.0;
aPhys = a;
bPhys = b;
cPhys = c;
% -1+a+b-c>=0
%  1-a+b-c>=0
%  1+a-b-c>=0

%OPTIMIZE a
% a>=max(1-b+c,-1+b+c)
% a<=1+b-c
%OPTIMIZE b
% b>=max(1-a+c,-1+a+c)
% b<=1+a-c
%OPTIMIZE c
% c<=min(-1+a+b,1-a+b,1+a-b)
nele  = nx * ny * nz;  

m     = 4 + 1;                % The number of general constraints.
n     = 3 * nx * ny * nz; % The number of design variables x_j.
         
xmin  = [ones(nele,1).*0.52;...
         ones(nele,1).*0.52;...
         ones(nele,1).*(-4.98)];
    % Column vector with the lower bounds for the variables x_j.
xmax  = [ones(nele,1).*1.98;...
         ones(nele,1).*1.98;...
         ones(nele,1).*0.98];
xold1 = [ a(:); b(:);c(:)]; % xval, one iteration ago (provided that iter>1).
xold2 = [ a(:); b(:);c(:)]; % xval, two iterations ago (provided that iter>2).
low   = ones(n,1);        % Column vector with the lower asymptotes from the previous iteration (provided that iter>1).
upp   = ones(n,1);        % Column vector with the upper asymptotes from the previous iteration (provided that iter>1).
a0    = 1;                % The constants a_0 in the term a_0*z.
a1    = zeros(m,1);       % Column vector with the constants a_i in the terms a_i*z.
% c_MMA = 1e3.*ones(m,1);   % Column vector with the constants c_i in the terms c_i*y_i.
c_MMA = [1e3.*ones(m-1,1);1.1e3];   % Column vector with the constants c_i in the terms c_i*y_i.
d     = zeros(m,1);       % Column vector with the constants d_i in the terms 0.5*d_i*(y_i)^2.

maxloop = 200;
a_log = cell(maxloop,2);
b_log = cell(maxloop,2);
c_log = cell(maxloop,2);
tim=zeros(maxloop,1);
sumCompliance=zeros(maxloop,1);
volfraction = zeros(maxloop,1);
loop = 0;
change = 1.;
while change > 0.001 && loop < maxloop
    loop = loop + 1;
    tic
    
%     ch=interp_ch(aPhys,bPhys,cPhys);
    [ch,ch_da,ch_db,ch_dc]=fitting_val(aPhys,bPhys,cPhys);
ke_all=lk_all(ch);
U=FEM_Beam(nx,ny,nz,ke_all);
    
% [ch_da]=interp_ch_da(aPhys,bPhys,cPhys);
% [ch_db]=interp_ch_db(aPhys,bPhys,cPhys);
% [ch_dc]=interp_ch_dc(aPhys,bPhys,cPhys);
ke_da=lk_all(ch_da);
ke_db=lk_all(ch_db);
ke_dc=lk_all(ch_dc);
[~,~,dcdb] = COMP(U,ke_all,ke_db,nx,ny,nz);
[~,~,dcda] = COMP(U,ke_all,ke_da,nx,ny,nz);
[comp,compliance,dcdc] = COMP(U,ke_all,ke_dc,nx,ny,nz);

% [dvda]=interp_dvda(aPhys(:),bPhys(:),cPhys(:));
% [dvdb]=interp_dvdb(aPhys(:),bPhys(:),cPhys(:));
% [dvdc]=interp_dvdc(aPhys(:),bPhys(:),cPhys(:));

[vol,dvda,dvdb,dvdc]=fittingV_val(aPhys(:),bPhys(:),cPhys(:));

dv=[dvda;dvdb;dvdc];
xval=[aPhys(:);bPhys(:);cPhys(:)];
f0val = compliance;
df0dx = [dcda(:);dcdb(:);dcdc(:)];

% vol=interp_v(aPhys(:),bPhys(:),cPhys(:));

%     cnstrt1 = -1-a(:)-b(:)-c(:);
%     cnstrt2 = -(-1+a(:)+b(:)-c(:));
%     cnstrt3 = -(1-a(:)+b(:)-c(:));
%     cnstrt4 = -(1+a(:)-b(:)-c(:));
%     cnstrt1 = -1-aPhys(:)-bPhys(:)-cPhys(:);
%     cnstrt2 = -(-1+aPhys(:)+bPhys(:)-cPhys(:));
%     cnstrt3 = -(1-aPhys(:)+bPhys(:)-cPhys(:));
%     cnstrt4 = -(1+aPhys(:)-bPhys(:)-cPhys(:));
%     cnstrt1 =cnstrt1./6;
%     cnstrt2 =cnstrt2./8;
%     cnstrt3 =cnstrt3./6;
%     cnstrt4 =cnstrt4./6;
p=400;
cnstrt1 = mean((5-aPhys(:)-bPhys(:)-cPhys(:)).^p).^(1/p)-6;
cnstrt2 = mean((9-aPhys(:)-bPhys(:)+cPhys(:)).^p).^(1/p)-8;
cnstrt3 = mean((5+aPhys(:)-bPhys(:)+cPhys(:)).^p).^(1/p)-6;
cnstrt4 = mean((5-aPhys(:)+bPhys(:)+cPhys(:)).^p).^(1/p)-6;
    
    cnstrt1 =cnstrt1./6;
    cnstrt2 =cnstrt2./8+0.015;
    cnstrt3 =cnstrt3./6+0.035;
    cnstrt4 =cnstrt4./6+0.040;
    
fval = [cnstrt1;cnstrt2;cnstrt3;cnstrt4;...
            sum(vol)/(volfrac*nele)-1]; 
disp('fval: ')
disp(fval.')

disp('connect_check: ')
% disp([sum(cnstrt1),sum(cnstrt2),sum(cnstrt3),sum(cnstrt4)])
% [num_unconnect,cnstrt1,cnstrt2,cnstrt3,cnstrt4]=connect_check(a,b,c);
[num_unconnect,cnstrt1,cnstrt2,cnstrt3,cnstrt4]=connect_check(aPhys,bPhys,cPhys);
disp(num_unconnect.')

dc1da=-sum((5-aPhys(:)-bPhys(:)-cPhys(:)).^p).^(1/p-1).*((5-aPhys(:)-bPhys(:)-cPhys(:)).^(p-1));

dc2da=-sum((9-aPhys(:)-bPhys(:)+cPhys(:)).^p).^(1/p-1).*(9-aPhys(:)-bPhys(:)+cPhys(:)).^(p-1);
dc2dc= -dc2da;

dc3da= sum((5+aPhys(:)-bPhys(:)+cPhys(:)).^p).^(1/p-1).*(5+aPhys(:)-bPhys(:)+cPhys(:)).^(p-1);
dc3db=-dc3da;

dc4da=-sum((5-aPhys(:)+bPhys(:)+cPhys(:)).^p).^(1/p-1).*(5-aPhys(:)+bPhys(:)+cPhys(:)).^(p-1);
dc4db= -dc4da;

dc1da = dc1da./6;
dc2da = dc2da./8; dc2dc=dc2dc./8;
dc3da = dc3da./6; dc3db=dc3db./6;
dc4da = dc4da./6; dc4db=dc4db./6;

% EYES=eye(nele);
dfdx  = [dc1da.',dc1da.',dc1da.';
         dc2da.',dc2da.',dc2dc.';
         dc3da.',dc3db.',dc3da.';
         dc4da.',dc4db.',dc4db.';
         dv(:)' / (volfrac*nele)]; % m X n

% fval = sum(vol)/(volfrac*nele)-1;
% EYES=eye(nele);
% dfdx  = [EYES.*(-1)./6,EYES.*(-1)./6,EYES.*(-1)./6;
%              EYES.*(-1)./8,EYES.*(-1)./8,EYES.*( 1)./8;
%              EYES.*( 1)./6,EYES.*(-1)./6,EYES.*( 1)./6;
%              EYES.*(-1)./6,EYES.*( 1)./6,EYES.*( 1)./6;
%              dv(:)' / (volfrac*nele)]; % m X n
% dfdx  = dv(:)' / (volfrac*nele);
[xmma, ~, ~, ~, ~, ~, ~, ~, ~, low,upp] = ...
    mmasub(m, n, loop, xval, xmin, xmax, xold1, xold2, ...
    f0val,df0dx,fval,dfdx,low,upp,a0,a1,c_MMA,d);
    a = reshape(xmma(1:nele),nz,ny,nx);
    b = reshape(xmma((nele+1):2*nele),nz,ny,nx);
    c = reshape(xmma((2*nele+1):n),nz,ny,nx);
    aPhys(:) = (double(H)*double(a(:)))./double(Hs);
    bPhys(:) = (double(H)*double(b(:)))./double(Hs);
    cPhys(:) = (double(H)*double(c(:)))./double(Hs);
%     aPhys=a;bPhys=b;cPhys=c;
    
    xold2    = xold1(:);
    xold1    = xval(:);
    change = max(max(abs([a(:);b(:);c(:)]-xval)));
%     [a,b,c,aPhys,bPhys,cPhys,xold1,xold2,change,compliance,vol,low,upp,comp]=...
%         optimizeABC(a,b,c,aPhys,bPhys,cPhys,xold1,xold2,Hs,H,volfrac,low,upp,nx,ny,nz,loop,a0,a1,x_MMA,d,...
%         n,m,xmin,xmax);
    sumCompliance(loop,1)=compliance;
    volfraction(loop,1) = mean(vol);
    disp([' It.: ' sprintf('%4i',loop)...
      ' compliance.: ' sprintf('%10.10f',compliance)...
      ' volfrac:' sprintf('%10.10f',mean(vol))...
      '  change.: ' sprintf('%6.3f',change )]);
  a_log{loop,1}=a;a_log{loop,2}=aPhys;  
  b_log{loop,1}=b;b_log{loop,2}=bPhys;
  c_log{loop,1}=c;c_log{loop,2}=cPhys;   
%     num_unconnect=connect_check(a,b,c).'
%     [num_unconnect,cnstrt1,cnstrt2,cnstrt3,cnstrt4]=connect_check(a,b,c);
%     disp(num_unconnect.')
%     disp([sum(cnstrt1),sum(cnstrt2),sum(cnstrt3),sum(cnstrt4)])
%     plot_comp(comp);

%     plot_distributions(aPhys,bPhys,cPhys);
    plot_convergence_all(loop,maxloop,sumCompliance,volfraction);
    
    tim(loop)=toc;
%     save('ani_fittingALL_pnorm5.mat','aPhys','bPhys','cPhys',...
%     'sumCompliance','volfraction','a_log','b_log','c_log','tim');
%     save ani_DATA_cab.mat
end
disp(['Time = ',num2str(sum(tim))])
% ch=interp_ch(aPhys,bPhys,cPhys);
% [ch_dc]=interp_ch_dc(aPhys,bPhys,cPhys);
% ke_all=lk_all(ch);ke_dc=lk_all(ch_dc);
% U=FEM_Beam(nx,ny,nz,ke_all);
% [comp,compliance,dcdc] = COMP(U,ke_all,ke_dc,nx,ny,nz);

disp(['C = ',num2str(compliance)])
figure()
set(gcf,'position',[100 650 300 300])
cc = squeeze(comp(:,1,:));
colormap(1-gray); imagesc(cc);
axis equal; axis tight; axis off;
% title('Compliance Distribution')
set(gca,'YDir','normal')
end

function plot_convergence_all(loop,maxloop,sumCompliance,volfraction)
figure(3)
% figure()
% loop=75;maxloop=loop;
set(gcf,'position',[100 100 1200 400])
subplot(2,1,1)
plotC=sumCompliance.';
plot([1:loop].',plotC(1:loop))
xlim([0 maxloop])
subplot(2,1,2)
plotV=volfraction.';
plot([1:loop].',plotV(1:loop))
xlim([0 maxloop])
pause(1e-6);
end

function [a,b,c,aPhys,bPhys,cPhys,xold1,xold2,change,compliance,vol,low,upp,comp]=...
        optimizeABC(a,b,c,aPhys,bPhys,cPhys,xold1,xold2,Hs,H,volfrac,low,upp,nx,ny,nz,loop,a0,a1,x_MMA,d,...
        n,m,xmin,xmax)
nele  = nx * ny * nz;
ch=interp_ch(aPhys,bPhys,cPhys);
ke_all=lk_all(ch);
U=FEM_Beam(nx,ny,nz,ke_all);
    
[ch_da]=interp_ch_da(aPhys,bPhys,cPhys);
[ch_db]=interp_ch_db(aPhys,bPhys,cPhys);
[ch_dc]=interp_ch_dc(aPhys,bPhys,cPhys);
ke_da=lk_all(ch_da);
ke_db=lk_all(ch_db);
ke_dc=lk_all(ch_dc);
[~,~,dcdb] = COMP(U,ke_all,ke_db,nx,ny,nz);
[~,~,dcda] = COMP(U,ke_all,ke_da,nx,ny,nz);
[comp,compliance,dcdc] = COMP(U,ke_all,ke_dc,nx,ny,nz);

[dvda]=interp_dvda(aPhys(:),bPhys(:),cPhys(:));
[dvdb]=interp_dvdb(aPhys(:),bPhys(:),cPhys(:));
[dvdc]=interp_dvdc(aPhys(:),bPhys(:),cPhys(:));

dv=[dvda;dvdb;dvdc];
xval=[aPhys(:);bPhys(:);cPhys(:)];
f0val = compliance;
df0dx = [dcda(:);dcdb(:);dcdc(:)];
vol=interp_v(aPhys(:),bPhys(:),cPhys(:));
fval = sum(vol)/(volfrac*nele)-1;
dfdx  = dv(:)' / (volfrac*nele);
    
    
[xmma, ~, ~, ~, ~, ~, ~, ~, ~, low,upp] = ...
    mmasub(m, n, loop, xval, xmin, xmax, xold1, xold2, ...
    f0val,df0dx,fval,dfdx,low,upp,a0,a1,x_MMA,d);
    
a = reshape(xmma(1:nele),nz,ny,nx);
b = reshape(xmma((nele+1):2*nele),nz,ny,nx);
c = reshape(xmma((2*nele+1):n),nz,ny,nx);
aPhys(:) = (double(H)*double(a(:)))./double(Hs);
bPhys(:) = (double(H)*double(b(:)))./double(Hs);
cPhys(:) = (double(H)*double(c(:)))./double(Hs);
xold2    = xold1(:);
xold1    = xval(:);

change = max(max(abs([a(:);b(:);c(:)]-xval)));     

end

function [num_unconnect,cnstrt1,cnstrt2,cnstrt3,cnstrt4]=connect_check(a,b,c)
num_unconnect=zeros(4,1);
cnstrt1 = -1-a(:)-b(:)-c(:);
cnstrt2 = -(-1+a(:)+b(:)-c(:));
cnstrt3 = -(1-a(:)+b(:)-c(:));
cnstrt4 = -(1+a(:)-b(:)-c(:));
num_unconnect(1)=sum(cnstrt1>0);
num_unconnect(2)=sum(cnstrt2>0);
num_unconnect(3)=sum(cnstrt3>0);
num_unconnect(4)=sum(cnstrt4>0);
end