# Amira Abdel-Rahman
# (c) Massachusetts Institute of Technology 2020


#############################################multimaterial############################################################

#Based on: https://link.springer.com/article/10.1007/s00158-013-0999-1
function multitop(nx,ny,tol_out,tol_f,iter_max_in,iter_max_out,p,q,e,v,rf)
    anim=Animation()
    alpha = zeros(Float64,nx*ny,p)
    for i = 1:p
        alpha[:,i] .= v[i]
    end
    
    # MAKE FILTER
    H,Hs = make_filter(nx,ny,rf)
    obj=0
    change_out = 2*tol_out; iter_out = 0;
    while (iter_out < iter_max_out) && (change_out > tol_out)
        alpha_old = copy(alpha)
        for a = 1:p
            for b = a+1:p
                obj,alpha = bi_top(a,b,nx,ny,p,v,e,q,alpha,H,Hs,iter_max_in);
            end
        end
        iter_out = iter_out + 1;
        change_out = norm(alpha[:].-alpha_old[:],Inf);
        display("Iter:$iter_out Obj.:$obj change:$change_out");
        #  UPDATE FILTER
        if (change_out < tol_f) && (rf>3)
            tol_f = 0.99*tol_f; rf = 0.99*rf; 
            H,Hs = make_filter(nx,ny,rf);
        end
        #  SCREEN OUT TEMPORAL TOPOLOGY EVERY 5 ITERATIONS
        if mod(iter_out,5)==0
            I = make_bitmap(p,nx,ny,alpha);
            display(RGB.(I[:,:,1],I[:,:,2],I[:,:,3]))
            I = permutedims(I, [3, 1, 2])
            img = colorview(RGB, I)
            heatmap(img,xaxis=nothing,yaxis=nothing,aspect_ratio=:equal)
            frame(anim)
        end
    end
    return anim,alpha
end

function bi_top(a,b,nx,ny,p,v,e,q,alpha_old,H,Hs,maxIter)
    alpha = copy(alpha_old)
    nu = 0.3;
    
    # PREPARE FINITE ELEMENT ANALYSIS
    A11 = [12 3 -6 -3; 3 12 3 0; -6 3 12 -3; -3 0 -3 12];
    A12 = [-6 -3 0 3; -3 -6 -3 -6; 0 -3 -6 3; 3 -6 3 -6];
    B11 = [-4 3 -2 9; 3 -4 -9 4; -2 -9 -4 -3; 9 4 -3 -4];
    B12 = [ 2 -3 4 -9; -3 2 9 -2; 4 9 2 3; -9 -2 3 2];
    KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11]);
    
    nelx=nx
    nely=ny
    
    nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx)
    edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1)
    edofMat = repeat(edofVec,1,8).+repeat([0 1 2*nely.+[2 3 0 1] -2 -1],nelx*nely,1)
    iK = convert(Array{Int},reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1))
    jK = convert(Array{Int},reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1))
    
    # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
    F = sparse([2],[1],[-1.0],2*(nely+1)*(nelx+1),1)
    U = zeros(2*(nely+1)*(nelx+1),1)
    fixeddofs = union(1:2:2*(nely+1),2*(nelx+1)*(nely+1))
    alldofs = 1:(2*(nely+1)*(nelx+1))
    freedofs = setdiff(alldofs,fixeddofs)
    
    o=0;alpha_a=0
    # inner iteration
    for i =0: (maxIter-1)
        # FE-ANALYSIS
        E = e[1]*alpha[:,1].^q
        for phase = 2:p
            E = E + e[phase]*alpha[:,phase].^q;
        end

        sK = reshape(KE[:]*E[:]',64*nelx*nely,1)
        K = sparse(vec(iK),vec(jK),vec(sK)); K = (K+K')/2
        @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
    

        # Objective function and sensitivity analysis
        ce = sum((U[edofMat]*KE).*U[edofMat],dims=2)
        o = sum(sum(E.*ce))
        
        # FILTERING OF SENSITIVITIES 
        dc = 0.0 .-(q .*(e[a].-e[b]).*alpha[:,a].^(q-1)).*ce;
        dc = H*(alpha[:,a].*dc)./Hs./max.(1e-3,alpha[:,a])
        dc = min.(dc,0.0)

        # UPDATE LOWER AND UPPER BOUNDS OF DESIGN VARIABLES
        move = 0.2;
        r = ones(nx*ny,1)
  
        for k = 1:p
            #if (k ~= a) && (k ~= b)
            if (k != a) && (k != b)
                # display("k $k a $a b $b")
                r = r .- alpha[:,k]
            end
        end
        l = max.(0,alpha[:,a] .-move)
        u = min.(r,alpha[:,a] .+move)
        # OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES
        l1 = 0; l2 = 1e9
        while (l2-l1)/(l1+l2) > 1e-3
            lmid = 0.5*(l2+l1)
            alpha_a = max.(l,min.(u,alpha[:,a].*sqrt.(-dc./lmid)));
            if sum(alpha_a) > nx*ny*v[a]
                l1 = lmid
            else
                l2 = lmid 
            end
        end
        alpha[:,a] = alpha_a
        alpha[:,b] = r .-alpha_a

    end
    return o,alpha
end

########

function multitop_compliant(nx,ny,tol_out,tol_f,iter_max_in,iter_max_out,p,q,e,v,rf,Load,Support,Spring,DOut)
    anim=Animation()
    alpha = zeros(Float64,nx*ny,p)
    for i = 1:p
        alpha[:,i] .= v[i]
    end
    
    # MAKE FILTER
    H,Hs = make_filter(nx,ny,rf)
    obj=0
    change_out = 2*tol_out; iter_out = 0;
    while (iter_out < iter_max_out) && (change_out > tol_out)
        alpha_old = copy(alpha)
        for a = 1:p
            for b = a+1:p
                obj,alpha = bi_top_compliant(a,b,nx,ny,p,v,e,q,alpha,H,Hs,iter_max_in);
            end
        end
        iter_out = iter_out + 1;
        change_out = norm(alpha[:].-alpha_old[:],Inf);
        display("Iter:$iter_out Obj.:$obj change:$change_out");
        #  UPDATE FILTER
        if (change_out < tol_f) && (rf>3)
            tol_f = 0.99*tol_f; rf = 0.99*rf; 
            H,Hs = make_filter(nx,ny,rf);
        end
        #  SCREEN OUT TEMPORAL TOPOLOGY EVERY 5 ITERATIONS
        if mod(iter_out,5)==0
            I = make_bitmap_compliant(p,nx,ny,alpha);
            display(RGB.(I[:,:,1],I[:,:,2],I[:,:,3]))
            I = permutedims(I, [3, 1, 2])
            img = colorview(RGB, I)
            heatmap(img,xaxis=nothing,yaxis=nothing,aspect_ratio=:equal)
            frame(anim)
        end
    end
    return anim,alpha
end

function bi_top_compliant(a,b,nx,ny,p,v,e,q,alpha_old,H,Hs,maxIter,Load,Support,Spring,DOut)
    alpha = copy(alpha_old)
    nu = 0.3;
    
    # PREPARE FINITE ELEMENT ANALYSIS
    A11 = [12 3 -6 -3; 3 12 3 0; -6 3 12 -3; -3 0 -3 12];
    A12 = [-6 -3 0 3; -3 -6 -3 -6; 0 -3 -6 3; 3 -6 3 -6];
    B11 = [-4 3 -2 9; 3 -4 -9 4; -2 -9 -4 -3; 9 4 -3 -4];
    B12 = [ 2 -3 4 -9; -3 2 9 -2; 4 9 2 3; -9 -2 3 2];
    KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11]);
    
    nelx=nx
    nely=ny
    
    nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx)
    edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1)
    edofMat = repeat(edofVec,1,8).+repeat([0 1 2*nely.+[2 3 0 1] -2 -1],nelx*nely,1)
    iK = convert(Array{Int},reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1))
    jK = convert(Array{Int},reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1))

    

    # # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
    # F = sparse([2],[1],[-1.0],2*(nely+1)*(nelx+1),1)
    # U = zeros(2*(nely+1)*(nelx+1),1)
    # fixeddofs = union(1:2:2*(nely+1),2*(nelx+1)*(nely+1))
    # alldofs = 1:(2*(nely+1)*(nelx+1))
    # freedofs = setdiff(alldofs,fixeddofs)

    # DEFINE LOADS AND SUPPORTS 
    F = sparse(2 .*Load[:,1] .-2 .+ Load[:,2],ones(size(Load,1)),Load[:,3],2*(nely+1)*(nelx+1),2)
    DofDOut = 2 * DOut[1] - 2 +DOut[2]; #only one
    F=Array(F)
    F[DofDOut,2]=-1
    fixeddofs = 2 .*Support[:,1] .-2 .+ Support[:,2]
    NSpring = size(Spring,1);
    s = sparse(2 .*Spring[:,1] .-2 .+ Spring[:,2],ones(size(Spring,1)),Spring[:,3],2*(nely+1)*(nelx+1),2)
    m=Array(s)[:,1]
    S= sparse(diagm(m))
    
    U = zeros(2*(nely+1)*(nelx+1),2)

    alldofs = 1:(2*(nely+1)*(nelx+1))
    freedofs = setdiff(alldofs,fixeddofs)
    
    o=0;alpha_a=0
    # inner iteration
    for i =0: (maxIter-1)
        # FE-ANALYSIS
        E = e[1]*alpha[:,1].^q
        for phase = 2:p
            E = E + e[phase]*alpha[:,phase].^q;
        end

        sK = reshape(KE[:]*E[:]',64*nelx*nely,1)


        K = sparse(vec(iK),vec(jK),vec(sK));
        K[din,din] = K[din,din] + 0.1;
        K[dout,dout] = K[dout,dout] + 0.1;
        K = (K+K')/2
        # @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
        @timed U[freedofs,:] = K[freedofs,freedofs] \ Array(F[freedofs,:])
        U1=U[:,1]
        U2=U[:,2]


        # Objective function and sensitivity analysis
        # ce = sum((U[edofMat]*KE).*U[edofMat],dims=2)
        ce =-sum((U1[edofMat]*KE).*U2[edofMat],dims=2)
        # o = sum(sum(E.*ce))

        o=U[DofDOut,1]
        
        # FILTERING OF SENSITIVITIES 
        dc = 0.0 .-(q .*(e[a].-e[b]).*alpha[:,a].^(q-1)).*ce;
        dc = H*(alpha[:,a].*dc)./Hs./max.(1e-3,alpha[:,a])
        dc = min.(dc,0.0)

        # UPDATE LOWER AND UPPER BOUNDS OF DESIGN VARIABLES
        move=0.1;
        r = ones(nx*ny,1)
  
        for k = 1:p
            #if (k ~= a) && (k ~= b)
            if (k != a) && (k != b)
                # display("k $k a $a b $b")
                r = r .- alpha[:,k]
            end
        end
        l = max.(0,alpha[:,a] .-move)
        u = min.(r,alpha[:,a] .+move)
        # OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES
        l1 = 0; l2 = 1e9
        while (l2-l1)/(l2+l1) > 1e-4 && l2>1e-40
        # while (l2-l1)/(l1+l2) > 1e-3
            lmid = 0.5*(l2+l1)
            alpha_a = max.(l,min.(u,alpha[:,a].*((max.(1e-10,-dc./lmid)).^0.3 )));

            if sum(alpha_a) > nx*ny*v[a]
                l1 = lmid
            else
                l2 = lmid 
            end
        end
        alpha[:,a] = alpha_a
        alpha[:,b] = r .-alpha_a

    end
    return o,alpha
end

########

function multitop3D(nx,ny,nz,tol_out,tol_f,iter_max_in,iter_max_out,p,q,e,v,rf)
    anim=Animation()
    alpha = zeros(Float64,nx*ny*nz,p)
    for i = 1:p
        alpha[:,i] .= v[i]
    end
    
    # MAKE FILTER
    H,Hs = make_filter3D(nx,ny,nz,rf)
    obj=0
    change_out = 2*tol_out; iter_out = 0;
    while (iter_out < iter_max_out) && (change_out > tol_out)
        alpha_old = copy(alpha)
        for a = 1:p
            for b = a+1:p
                obj,alpha = bi_top3D(a,b,nx,ny,nz,p,v,e,q,alpha,H,Hs,iter_max_in);
            end
        end
        iter_out = iter_out + 1;
        change_out = norm(alpha[:].-alpha_old[:],Inf);
        display("Iter:$iter_out Obj.:$obj change:$change_out");
        #  UPDATE FILTER
        if (change_out < tol_f) && (rf>3)
            tol_f = 0.99*tol_f; rf = 0.99*rf; 
            H,Hs = make_filter3D(nx,ny,nz,rf)
        end
        #  SCREEN OUT TEMPORAL TOPOLOGY EVERY 5 ITERATIONS
        if mod(iter_out,5)==0
            I = make_bitmap_3d(p,nx,ny,nz,alpha)
            threshold=0.05
            display(topplotmulti3d(nx,ny,nz,I,threshold))
            frame(anim)
        end
    end
    return anim,alpha
end

function bi_top3D(a,b,nx,ny,nz,p,v,e,q,alpha_old,H,Hs,maxIter)
    alpha = copy(alpha_old)
    nu = 0.3;

    
    
    # PREPARE FINITE ELEMENT ANALYSIS
    KE=lk_H8(nu)
    
    nelx=nx
    nely=ny
    nelz=nz
    nele = nelx*nely*nelz
    ndof = 3*(nelx+1)*(nely+1)*(nelz+1)

    nodenrs = reshape(1:(1+nelx)*(1+nely)*(1+nelz),1+nely,1+nelx,1+nelz)
    edofVec = reshape(3*nodenrs[1:end-1,1:end-1,1:end-1].+1,nelx*nely*nelz,1)
    edofMat = repeat(edofVec,1,24).+repeat([0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1 3*(nely+1)*(nelx+1).+[0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1]],nelx*nely*nelz,1)
        
    iK = convert(Array{Int},reshape(kron(edofMat,ones(24,1))',24*24*nele,1))
    jK = convert(Array{Int},reshape(kron(edofMat,ones(1,24))',24*24*nele,1))
    

    # USER-DEFINED LOAD DOFs
    m= Matlab.meshgrid(nelx:nelx, 0:0, 0:nelz)
    il=m[1]
    jl=m[2]
    kl=m[3]
    loadnid = kl.*(nelx+1).*(nely+1).+il.*(nely+1).+(nely+1 .-jl)
    loaddof = 3 .*loadnid[:] .- 1; 
    # USER-DEFINED SUPPORT FIXED DOFs
    m= Matlab.meshgrid(0:0,0:nely,0:nelz)# Coordinates
    iif=m[1]
    jf=m[2]
    kf=m[3]
    fixednid = kf.*(nelx+1).*(nely+1) .+iif .*(nely .+1) .+(nely .+1 .-jf) # Node IDs
    fixeddof = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs
    
    
    # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
    F= sparse(loaddof,fill(1,length(loaddof)),fill(-1,length(loaddof)),ndof,1);
    U = zeros(ndof,1)
    alldofs = 1:ndof
    freedofs = setdiff(1:ndof,fixeddof)
    
    o=0;alpha_a=0
    # inner iteration
    for i =0: (maxIter-1)
        # FE-ANALYSIS
        E = e[1]*alpha[:,1].^q
        for phase = 2:p
            E = E + e[phase]*alpha[:,phase].^q;
        end

        sK = reshape(KE[:]*E[:]',24*24*nelx*nely*nelz,1)
        K = sparse(vec(iK),vec(jK),vec(sK)); K = (K+K')/2
        @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
    

        # Objective function and sensitivity analysis
        ce = sum((U[edofMat]*KE).*U[edofMat],dims=2)
        o = sum(sum(E.*ce))
        
        # FILTERING OF SENSITIVITIES 
        dc = 0.0 .-(q .*(e[a].-e[b]).*alpha[:,a].^(q-1)).*ce;
        dc = H*(alpha[:,a].*dc)./Hs./max.(1e-3,alpha[:,a])
        dc = min.(dc,0.0)

        # UPDATE LOWER AND UPPER BOUNDS OF DESIGN VARIABLES
        move = 0.2;
        r = ones(nx*ny*nz,1)
  
        for k = 1:p
            #if (k ~= a) && (k ~= b)
            if (k != a) && (k != b)
                # display("k $k a $a b $b")
                r = r .- alpha[:,k]
            end
        end
        l = max.(0,alpha[:,a] .-move)
        u = min.(r,alpha[:,a] .+move)
        # OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES
        l1 = 0; l2 = 1e9
        while (l2-l1)/(l1+l2) > 1e-3
            lmid = 0.5*(l2+l1)
            alpha_a = max.(l,min.(u,alpha[:,a].*sqrt.(-dc./lmid)));
            if sum(alpha_a) > nx*ny*v[a]
                l1 = lmid
            else
                l2 = lmid 
            end
        end
        alpha[:,a] = alpha_a
        alpha[:,b] = r .-alpha_a

    end
    return o,alpha
end

########

function multitop3D_compliant(nx,ny,nz,tol_out,tol_f,iter_max_in,iter_max_out,p,q,e,v,rf,getProblem=inverter)
    anim=Animation()
    alpha = zeros(Float64,nx*ny*nz,p)
    for i = 1:p
        alpha[:,i] .= v[i]
    end
    
    # MAKE FILTER
    H,Hs = make_filter3D(nx,ny,nz,rf)
    obj=0
    change_out = 2*tol_out; iter_out = 0;
    while (iter_out < iter_max_out) && (change_out > tol_out)
        alpha_old = copy(alpha)
        for a = 1:p
            for b = a+1:p
                obj,alpha = bi_top3D_compliant(a,b,nx,ny,nz,p,v,e,q,alpha,H,Hs,iter_max_in,getProblem);
            end
        end
        iter_out = iter_out + 1;
        change_out = norm(alpha[:].-alpha_old[:],Inf);
        display("Iter:$iter_out Obj.:$obj change:$change_out");
        #  UPDATE FILTER
        if (change_out < tol_f) && (rf>3)
            tol_f = 0.99*tol_f; rf = 0.99*rf; 
            H,Hs = make_filter3D(nx,ny,nz,rf)
        end
        #  SCREEN OUT TEMPORAL TOPOLOGY EVERY 5 ITERATIONS
        if mod(iter_out,5)==0
            I = make_bitmap_3d(p,nx,ny,nz,alpha)
            threshold=0.05
            display(topplotmulti3d(nx,ny,nz,I,threshold))
            frame(anim)
        end
    end
    return anim,alpha
end

function bi_top3D_compliant(a,b,nx,ny,nz,p,v,e,q,alpha_old,H,Hs,maxIter,getProblem=inverter)
    alpha = copy(alpha_old)
    nu = 0.3;

    
    
    # PREPARE FINITE ELEMENT ANALYSIS
    KE=lk_H8(nu)
    
    nelx=nx
    nely=ny
    nelz=nz
    nele = nelx*nely*nelz
    ndof = 3*(nelx+1)*(nely+1)*(nelz+1)

    nodenrs = reshape(1:(1+nelx)*(1+nely)*(1+nelz),1+nely,1+nelx,1+nelz)
    edofVec = reshape(3*nodenrs[1:end-1,1:end-1,1:end-1].+1,nelx*nely*nelz,1)
    edofMat = repeat(edofVec,1,24).+repeat([0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1 3*(nely+1)*(nelx+1).+[0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1]],nelx*nely*nelz,1)
        
    iK = convert(Array{Int},reshape(kron(edofMat,ones(24,1))',24*24*nele,1))
    jK = convert(Array{Int},reshape(kron(edofMat,ones(1,24))',24*24*nele,1))
    
    # # USER-DEFINED LOAD DOFs
    # il = [0 nelx]; jl = [nely nely]; kl = [0 0];
    # loadnid = kl .*(nelx+1) .*(nely+1) .+il .*(nely .+1) .+(nely+1 .-jl);
    # loaddof = 3 .*loadnid[:] .- 2;
    # din = loaddof[1]; dout = loaddof[2];
    # F = sparse(loaddof,[1;2],[1;-1],ndof,2);
    
    # # USER-DEFINED SUPPORT FIXED DOFs
    # # Top face
    # m = Matlab.meshgrid(0:nelx,0:nelz)
    # iif=m[1]
    # kf=m[2]
    # fixednid = kf .*(nelx+1) .*(nely+1) .+iif .*(nely+1) .+1;
    # fixeddof_t = 3 .*fixednid[:] .-1;
    # # Side face
    # m = Matlab.meshgrid(0:nelx,0:nely)
    # iif=m[1]
    # jf=m[2]
    # fixednid = iif .*(nely+1) .+(nely+1 .-jf);
    # fixeddof_s = 3*fixednid[:];
    # # Two pins
    # iif = [0;0]; jf = [0;1]; kf = [nelz;nelz];
    # fixednid = kf .*(nelx+1) .*(nely .+1) .+iif .*(nely .+1) .+(nely+1 .-jf)
    # fixeddof_p = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs
    # # Fixed DOFs
    # fixeddof = union(fixeddof_t,fixeddof_s);
    # fixeddof = union(fixeddof, fixeddof_p);
    # fixeddof = sort(fixeddof);
    
    # # Displacement vector
    # U = zeros(ndof,2);
    # freedofs = setdiff(1:ndof,fixeddof)

    U,F,freedofs,din,dout=getProblem(nelx,nely,nelz)
    
    
    o=0;alpha_a=0
    # inner iteration
    for i =0: (maxIter-1)
        # FE-ANALYSIS
        E = e[1]*alpha[:,1].^q
        for phase = 2:p
            E = E + e[phase]*alpha[:,phase].^q;
        end

        sK = reshape(KE[:]*E[:]',24*24*nelx*nely*nelz,1)
        K = sparse(vec(iK),vec(jK),vec(sK));
        K[din,din] = K[din,din] + 0.1;
        K[dout,dout] = K[dout,dout] + 0.1;
        K = (K+K')/2;

        # @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
        @timed U[freedofs,:] = K[freedofs,freedofs] \ Array(F[freedofs,:])
        U1 = U[:,1]
        U2 = U[:,2]
    

        # Objective function and sensitivity analysis
        ce = -sum((U1[edofMat]*KE).*U2[edofMat],dims=2)

        # o = sum(sum(E.*ce))
        o  = U[dout,1]
        
        # FILTERING OF SENSITIVITIES 
        dc = 0.0 .-(q .*(e[a].-e[b]).*alpha[:,a].^(q-1)).*ce;
        dc = H*(alpha[:,a].*dc)./Hs./max.(1e-3,alpha[:,a])
        dc = min.(dc,0.0)

        # UPDATE LOWER AND UPPER BOUNDS OF DESIGN VARIABLES
        move = 0.1;
        r = ones(nx*ny*nz,1)
  
        for k = 1:p
            #if (k ~= a) && (k ~= b)
            if (k != a) && (k != b)
                # display("k $k a $a b $b")
                r = r .- alpha[:,k]
            end
        end
        l = max.(0,alpha[:,a] .-move)
        u = min.(r,alpha[:,a] .+move)
        # OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES
        l1 = 0; l2 = 1e9
        # while (l2-l1)/(l1+l2) > 1e-3
        while (l2-l1)/(l1+l2) > 1e-4 && l2 > 1e-40
            lmid = 0.5*(l2+l1)
            # alpha_a = max.(l,min.(u,alpha[:,a].*sqrt.(-dc./lmid)));
            alpha_a = max.(l,min.(u,alpha[:,a].*((max.(1e-10,-dc./lmid)).^0.3 )));
            if sum(alpha_a) > nx*ny*v[a]
                l1 = lmid
            else
                l2 = lmid 
            end
        end
        alpha[:,a] = alpha_a
        alpha[:,b] = r .-alpha_a

    end
    return o,alpha
end

########
function multitop3DKE(nx,ny,nz,tol_out,tol_f,iter_max_in,iter_max_out,p,q,KEs,Es,v,rf)
    anim=Animation()
    alpha = zeros(Float64,nx*ny*nz,p)
    for i = 1:p
        alpha[:,i] .= v[i]
    end
    
    # MAKE FILTER
    H,Hs = make_filter3D(nx,ny,nz,rf)
    obj=0
    change_out = 2*tol_out; iter_out = 0;
    while (iter_out < iter_max_out) && (change_out > tol_out)
        alpha_old = copy(alpha)
        for a = 1:p
            for b = a+1:p
                obj,alpha = bi_top3DKE(a,b,nx,ny,nz,p,v,KEs,Es,q,alpha,H,Hs,iter_max_in);
            end
        end
        iter_out = iter_out + 1;
        change_out = norm(alpha[:].-alpha_old[:],Inf);
        display("Iter:$iter_out Obj.:$obj change:$change_out");
        #  UPDATE FILTER
        if (change_out < tol_f) && (rf>3)
            tol_f = 0.99*tol_f; rf = 0.99*rf; 
            H,Hs = make_filter3D(nx,ny,nz,rf)
        end
        #  SCREEN OUT TEMPORAL TOPOLOGY EVERY 5 ITERATIONS
        if mod(iter_out,5)==0
            I = make_bitmap_3d(p,nx,ny,nz,alpha)
            threshold=0.05*2.0
            display(topplotmulti3d(nx,ny,nz,I,threshold))
            frame(anim)
        end
    end
    return anim,alpha
end

function bi_top3DKE(a,b,nx,ny,nz,p,v,KEs,Es,q,alpha_old,H,Hs,maxIter)
    alpha = copy(alpha_old)
    nu = 0.3;

    # PREPARE FINITE ELEMENT ANALYSIS
    # KE=lk_H8(nu)
    
    nelx=nx
    nely=ny
    nelz=nz
    nele = nelx*nely*nelz
    ndof = 3*(nelx+1)*(nely+1)*(nelz+1)
    nnx = nelx+1; nny = nely+1; nnz = nelz+1;

    nodenrs = reshape(1:(1+nelx)*(1+nely)*(1+nelz),1+nely,1+nelx,1+nelz)
    edofVec = reshape(3*nodenrs[1:end-1,1:end-1,1:end-1].+1,nelx*nely*nelz,1)
    edofMat = repeat(edofVec,1,24).+repeat([0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1 3*(nely+1)*(nelx+1).+[0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1]],nelx*nely*nelz,1)
        
    iK = convert(Array{Int},reshape(kron(edofMat,ones(24,1))',24*24*nele,1))
    jK = convert(Array{Int},reshape(kron(edofMat,ones(1,24))',24*24*nele,1))
    

    # USER-DEFINED LOAD DOFs
    m= Matlab.meshgrid(nelx:nelx, 0:0, 0:nelz)
    il=m[1]
    jl=m[2]
    kl=m[3]
    loadnid = kl.*(nelx+1).*(nely+1).+il.*(nely+1).+(nely+1 .-jl)
    loaddof = 3 .*loadnid[:] .- 1; 
    # USER-DEFINED SUPPORT FIXED DOFs
    m= Matlab.meshgrid(0:0,0:nely,0:nelz)# Coordinates
    iif=m[1]
    jf=m[2]
    kf=m[3]
    fixednid = kf.*(nelx+1).*(nely+1) .+iif .*(nely .+1) .+(nely .+1 .-jf) # Node IDs
    fixeddof = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs
    
    
    # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
    F= sparse(loaddof,fill(1,length(loaddof)),fill(-1,length(loaddof)),ndof,1);
    U = zeros(ndof,1)
    alldofs = 1:ndof
    freedofs = setdiff(1:ndof,fixeddof)
    
    o=0;alpha_a=0
    # inner iteration
    for i =0: (maxIter-1)
        # FE-ANALYSIS
        # KE[:]*E[:]'
        KEE = KEs[1][:]*alpha[:,1][:]'.^q
        for phase = 2:p
            KEE = KEE + KEs[phase][:]*alpha[:,phase][:]'.^q;
        end

        EE = mean(Es[1])*alpha[:,1].^q
        for phase = 2:p
            EE = EE + mean(Es[phase])*alpha[:,phase].^q;
        end

        

        sK = reshape(KEE[:],24*24*nelx*nely*nelz,1)
        K = sparse(vec(iK),vec(jK),vec(sK)); K = (K+K')/2
        @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])


        

        KE=reshape(sum(KEE,dims=2),24,24)
        # dc=zeros(nelx* nely* nelz)
        # for i=1:Int(nelx* nely* nelz)
        #     KE=(q .*(KEs[a].-KEs[b]).*alpha[i,a].^(q-1))
        #     # ce[i]=sum((U[edofMat][i,:]'*KE).*U[edofMat][i,:]')
        #     dc[i]=-sum((U[edofMat][i,:]'*KE).*U[edofMat][i,:]')
        # end

        ce=zeros(nelx* nely* nelz)
        for i=1:Int(nelx* nely* nelz)
            KE = KEs[1].*alpha[i,1]
            for phase = 2:p
                KE = KE + KEs[phase].*alpha[i,phase]
            end
            ce[i]=sum((U[edofMat][i,:]'*KE).*U[edofMat][i,:]')
        end

        # display(size(KEE))
        # OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
        # cc = 0.0; 
        # dc = zeros(nelx, nely, nelz);
        # for elz = 1:nelz
        #     for ely = 1:nely 
        #         for elx = 1:nelx
        #             # KE   = get_KE(truss, x, Es, vs, Gs, elx, ely, elz, false);
        #             # DKE  = get_KE(truss, x, Es, vs, Gs, elx, ely, elz, true);
        #             # KE=reshape(KEEE[:,get_num(nelx, nely, nelz, elx, ely, elz)] ,24,24)
        #             # display(get_num1(nelx, nely, nelz, elx, ely, elz))
        #             # display(get_num(nnx, nny, nnz, elx, ely, elz))

        #             # KE = (KEs[a].*reshape(alpha[:,a][:],nelx, nely, nelz)[elx, ely, elz])-(KEs[b].*reshape(alpha[:,b][:],nelx, nely, nelz)[elx, ely, elz])


        #             # KE = KEs[1].*reshape(alpha[:,1][:],nelx, nely, nelz)[elx, ely, elz]
        #             # for phase = 2:p
        #             #     KE = KE + KEs[phase].*reshape(alpha[:,phase][:],nelx, nely, nelz)[elx, ely, elz];
        #             # end
        #             DKE=KE
        #             dofs1 = get_elem_dofs(nnx, nny, nnz, elx, ely, elz);
        #             dofs1 = get_elem_dofs(nelx, nely, nelz, elx, ely, elz);
        #             # display(dofs1)
        #             Ue = U[dofs1];
        #             cc = cc + Ue'*KE*Ue;
        #             dc[elx,ely,elz] = Ue'*DKE*Ue;
        #         end
        #     end
        # end

        # display(size(dc))
        # display(c)

        # ce=dc[:]
        # o=cc


        # display(ce)
        # display(sum(o))
        # dc=dc[:]

        

        
        # Objective function and sensitivity analysis
        # ce= sum((U[edofMat]*KE).*U[edofMat],dims=2)
        o = sum(sum(EE.*ce))

        # o = sum(sum(-dc))

        # display(ce)
        # display(sum(o1))

        # display(size(ce))
        # display(size(EE))
        
        # FILTERING OF SENSITIVITIES 
        dc = 0.0 .-(q .*mean(Es[a].-Es[b]).*alpha[:,a].^(q-1)).*ce;
        dc = H*(alpha[:,a].*dc)./Hs./max.(1e-3,alpha[:,a])
        dc = min.(dc,0.0)

        # UPDATE LOWER AND UPPER BOUNDS OF DESIGN VARIABLES
        move = 0.2;
        r = ones(nx*ny*nz,1)
  
        for k = 1:p
            #if (k ~= a) && (k ~= b)
            if (k != a) && (k != b)
                # display("k $k a $a b $b")
                r = r .- alpha[:,k]
            end
        end
        l = max.(0,alpha[:,a] .-move)
        u = min.(r,alpha[:,a] .+move)
        # OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES
        l1 = 0; l2 = 1e9
        while (l2-l1)/(l1+l2) > 1e-3
            lmid = 0.5*(l2+l1)
            alpha_a = max.(l,min.(u,alpha[:,a].*sqrt.(-dc./lmid)));
            if sum(alpha_a) > nx*ny*v[a]
                l1 = lmid
            else
                l2 = lmid 
            end
        end
        alpha[:,a] = alpha_a
        alpha[:,b] = r .-alpha_a

    end
    return o,alpha
end

function bi_top3DKEOldKindofWorking(a,b,nx,ny,nz,p,v,KEs,Es,q,alpha_old,H,Hs,maxIter)
    alpha = copy(alpha_old)
    nu = 0.3;

    # PREPARE FINITE ELEMENT ANALYSIS
    # KE=lk_H8(nu)
    
    nelx=nx
    nely=ny
    nelz=nz
    nele = nelx*nely*nelz
    ndof = 3*(nelx+1)*(nely+1)*(nelz+1)
    nnx = nelx+1; nny = nely+1; nnz = nelz+1;

    nodenrs = reshape(1:(1+nelx)*(1+nely)*(1+nelz),1+nely,1+nelx,1+nelz)
    edofVec = reshape(3*nodenrs[1:end-1,1:end-1,1:end-1].+1,nelx*nely*nelz,1)
    edofMat = repeat(edofVec,1,24).+repeat([0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1 3*(nely+1)*(nelx+1).+[0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1]],nelx*nely*nelz,1)
        
    iK = convert(Array{Int},reshape(kron(edofMat,ones(24,1))',24*24*nele,1))
    jK = convert(Array{Int},reshape(kron(edofMat,ones(1,24))',24*24*nele,1))
    

    # USER-DEFINED LOAD DOFs
    m= Matlab.meshgrid(nelx:nelx, 0:0, 0:nelz)
    il=m[1]
    jl=m[2]
    kl=m[3]
    loadnid = kl.*(nelx+1).*(nely+1).+il.*(nely+1).+(nely+1 .-jl)
    loaddof = 3 .*loadnid[:] .- 1; 
    # USER-DEFINED SUPPORT FIXED DOFs
    m= Matlab.meshgrid(0:0,0:nely,0:nelz)# Coordinates
    iif=m[1]
    jf=m[2]
    kf=m[3]
    fixednid = kf.*(nelx+1).*(nely+1) .+iif .*(nely .+1) .+(nely .+1 .-jf) # Node IDs
    fixeddof = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs
    
    
    # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
    F= sparse(loaddof,fill(1,length(loaddof)),fill(-1,length(loaddof)),ndof,1);
    U = zeros(ndof,1)
    alldofs = 1:ndof
    freedofs = setdiff(1:ndof,fixeddof)
    
    o=0;alpha_a=0
    # inner iteration
    for i =0: (maxIter-1)
        # FE-ANALYSIS
        # KE[:]*E[:]'
        KEE = KEs[1][:]*alpha[:,1][:]'.^q
        for phase = 2:p
            KEE = KEE + KEs[phase][:]*alpha[:,phase][:]'.^q;
        end

        EE = mean(Es[1])*alpha[:,1].^q
        for phase = 2:p
            EE = EE + mean(Es[phase])*alpha[:,phase].^q;
        end

        

        sK = reshape(KEE[:],24*24*nelx*nely*nelz,1)
        K = sparse(vec(iK),vec(jK),vec(sK)); K = (K+K')/2
        @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])


        

        KE=reshape(sum(KEE,dims=2),24,24)
        ce=zeros(nelx* nely* nelz)

        # display(size(U[edofMat]))

        for i=1:Int(nelx* nely* nelz)
            KE = KEs[1].*alpha[i,1]
            for phase = 2:p
                KE = KE + KEs[phase].*alpha[i,phase]
            end
            # ce[i]=sum((U[edofMat][i,:]'*reshape(KE[:,i],24,24)).*U[edofMat][i,:]')
            ce[i]=sum((U[edofMat][i,:]'*KE).*U[edofMat][i,:]')
        end

        # display(size(KEE))
        # OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
        # cc = 0.0; 
        # dc = zeros(nelx, nely, nelz);
        # for elz = 1:nelz
        #     for ely = 1:nely 
        #         for elx = 1:nelx
        #             # KE   = get_KE(truss, x, Es, vs, Gs, elx, ely, elz, false);
        #             # DKE  = get_KE(truss, x, Es, vs, Gs, elx, ely, elz, true);
        #             # KE=reshape(KEEE[:,get_num(nelx, nely, nelz, elx, ely, elz)] ,24,24)
        #             # display(get_num1(nelx, nely, nelz, elx, ely, elz))
        #             # display(get_num(nnx, nny, nnz, elx, ely, elz))

        #             # KE = (KEs[a].*reshape(alpha[:,a][:],nelx, nely, nelz)[elx, ely, elz])-(KEs[b].*reshape(alpha[:,b][:],nelx, nely, nelz)[elx, ely, elz])


        #             # KE = KEs[1].*reshape(alpha[:,1][:],nelx, nely, nelz)[elx, ely, elz]
        #             # for phase = 2:p
        #             #     KE = KE + KEs[phase].*reshape(alpha[:,phase][:],nelx, nely, nelz)[elx, ely, elz];
        #             # end
        #             DKE=KE
        #             dofs1 = get_elem_dofs(nnx, nny, nnz, elx, ely, elz);
        #             dofs1 = get_elem_dofs(nelx, nely, nelz, elx, ely, elz);
        #             # display(dofs1)
        #             Ue = U[dofs1];
        #             cc = cc + Ue'*KE*Ue;
        #             dc[elx,ely,elz] = Ue'*DKE*Ue;
        #         end
        #     end
        # end

        # display(size(dc))
        # display(c)

        # ce=dc[:]
        # o=cc


        # display(ce)
        # display(sum(o))
        # dc=dc[:]

        

        
        # Objective function and sensitivity analysis
        # ce= sum((U[edofMat]*KE).*U[edofMat],dims=2)
        o = sum(sum(EE.*ce))

        # display(ce)
        # display(sum(o1))

        # display(size(ce))
        # display(size(EE))
        
        # FILTERING OF SENSITIVITIES 
        dc = 0.0 .-(q .*mean(Es[a].-Es[b]).*alpha[:,a].^(q-1)).*ce;
        dc = H*(alpha[:,a].*dc)./Hs./max.(1e-3,alpha[:,a])
        dc = min.(dc,0.0)

        # UPDATE LOWER AND UPPER BOUNDS OF DESIGN VARIABLES
        move = 0.2;
        r = ones(nx*ny*nz,1)
  
        for k = 1:p
            #if (k ~= a) && (k ~= b)
            if (k != a) && (k != b)
                # display("k $k a $a b $b")
                r = r .- alpha[:,k]
            end
        end
        l = max.(0,alpha[:,a] .-move)
        u = min.(r,alpha[:,a] .+move)
        # OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES
        l1 = 0; l2 = 1e9
        while (l2-l1)/(l1+l2) > 1e-3
            lmid = 0.5*(l2+l1)
            alpha_a = max.(l,min.(u,alpha[:,a].*sqrt.(-dc./lmid)));
            if sum(alpha_a) > nx*ny*v[a]
                l1 = lmid
            else
                l2 = lmid 
            end
        end
        alpha[:,a] = alpha_a
        alpha[:,b] = r .-alpha_a

    end
    return o,alpha
end

####
########

function multitop3D_compliantKE(nx,ny,nz,tol_out,tol_f,iter_max_in,iter_max_out,p,q,KEs,Es,v,rf,getProblem=inverter)
    anim=Animation()
    alpha = zeros(Float64,nx*ny*nz,p)
    for i = 1:p
        alpha[:,i] .= v[i]
    end
    
    # MAKE FILTER
    H,Hs = make_filter3D(nx,ny,nz,rf)
    obj=0
    change_out = 2*tol_out; iter_out = 0;
    while (iter_out < iter_max_out) && (change_out > tol_out)
        alpha_old = copy(alpha)
        for a = 1:p
            for b = a+1:p
                obj,alpha = bi_top3D_compliantKE(a,b,nx,ny,nz,p,v,KEs,Es,q,alpha,H,Hs,iter_max_in,getProblem);
            end
        end
        iter_out = iter_out + 1;
        change_out = norm(alpha[:].-alpha_old[:],Inf);
        display("Iter:$iter_out Obj.:$obj change:$change_out");
        #  UPDATE FILTER
        if (change_out < tol_f) && (rf>3)
            tol_f = 0.99*tol_f; rf = 0.99*rf; 
            H,Hs = make_filter3D(nx,ny,nz,rf)
        end
        #  SCREEN OUT TEMPORAL TOPOLOGY EVERY 5 ITERATIONS
        if mod(iter_out,5)==0
            I = make_bitmap_3d(p,nx,ny,nz,alpha)
            threshold=0.05
            display(topplotmulti3d(nx,ny,nz,I,threshold))
            frame(anim)
        end
    end
    return anim,alpha
end

function bi_top3D_compliantKE(a,b,nx,ny,nz,p,v,KEs,Es,q,alpha_old,H,Hs,maxIter,getProblem=inverter)
    alpha = copy(alpha_old)
    nu = 0.3;

    
    
    # PREPARE FINITE ELEMENT ANALYSIS
    # KE=lk_H8(nu)
    
    nelx=nx
    nely=ny
    nelz=nz
    nele = nelx*nely*nelz
    ndof = 3*(nelx+1)*(nely+1)*(nelz+1)

    nodenrs = reshape(1:(1+nelx)*(1+nely)*(1+nelz),1+nely,1+nelx,1+nelz)
    edofVec = reshape(3*nodenrs[1:end-1,1:end-1,1:end-1].+1,nelx*nely*nelz,1)
    edofMat = repeat(edofVec,1,24).+repeat([0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1 3*(nely+1)*(nelx+1).+[0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1]],nelx*nely*nelz,1)
        
    iK = convert(Array{Int},reshape(kron(edofMat,ones(24,1))',24*24*nele,1))
    jK = convert(Array{Int},reshape(kron(edofMat,ones(1,24))',24*24*nele,1))
    
    # # USER-DEFINED LOAD DOFs
    # il = [0 nelx]; jl = [nely nely]; kl = [0 0];
    # loadnid = kl .*(nelx+1) .*(nely+1) .+il .*(nely .+1) .+(nely+1 .-jl);
    # loaddof = 3 .*loadnid[:] .- 2;
    # din = loaddof[1]; dout = loaddof[2];
    # F = sparse(loaddof,[1;2],[1;-1],ndof,2);
    
    # # USER-DEFINED SUPPORT FIXED DOFs
    # # Top face
    # m = Matlab.meshgrid(0:nelx,0:nelz)
    # iif=m[1]
    # kf=m[2]
    # fixednid = kf .*(nelx+1) .*(nely+1) .+iif .*(nely+1) .+1;
    # fixeddof_t = 3 .*fixednid[:] .-1;
    # # Side face
    # m = Matlab.meshgrid(0:nelx,0:nely)
    # iif=m[1]
    # jf=m[2]
    # fixednid = iif .*(nely+1) .+(nely+1 .-jf);
    # fixeddof_s = 3*fixednid[:];
    # # Two pins
    # iif = [0;0]; jf = [0;1]; kf = [nelz;nelz];
    # fixednid = kf .*(nelx+1) .*(nely .+1) .+iif .*(nely .+1) .+(nely+1 .-jf)
    # fixeddof_p = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs
    # # Fixed DOFs
    # fixeddof = union(fixeddof_t,fixeddof_s);
    # fixeddof = union(fixeddof, fixeddof_p);
    # fixeddof = sort(fixeddof);
    
    # # Displacement vector
    # U = zeros(ndof,2);
    # freedofs = setdiff(1:ndof,fixeddof)

    U,F,freedofs,din,dout=getProblem(nelx,nely,nelz)

    
    
    o=0;alpha_a=0
    # inner iteration
    for i =0: (maxIter-1)
        # FE-ANALYSIS
        # E = e[1]*alpha[:,1].^q
        # for phase = 2:p
        #     E = E + e[phase]*alpha[:,phase].^q;
        # end

        KEE = KEs[1][:]*alpha[:,1][:]'.^q
        for phase = 2:p
            KEE = KEE + KEs[phase][:]*alpha[:,phase][:]'.^q
        end

        # EE = mean(Es[1])*alpha[:,1].^q
        # for phase = 2:p
        #     EE = EE + mean(Es[phase])*alpha[:,phase].^q;
        # end

        

        sK = reshape(KEE[:],24*24*nelx*nely*nelz,1)
        

        # sK = reshape(KE[:]*E[:]',24*24*nelx*nely*nelz,1)
        K = sparse(vec(iK),vec(jK),vec(sK));
        K[din,din] = K[din,din] + 0.1;
        K[dout,dout] = K[dout,dout] + 0.1;
        K = (K+K')/2;

        # @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
        @timed U[freedofs,:] = K[freedofs,freedofs] \ Array(F[freedofs,:])
        U1 = U[:,1]
        U2 = U[:,2]

        KE=reshape(sum(KEE,dims=2),24,24)
        # ce=zeros(nelx* nely* nelz)
        # for i=1:Int(nelx* nely* nelz)
        #     KE = KEs[1].*alpha[i,1]
        #     for phase = 2:p
        #         KE = KE + KEs[phase].*alpha[i,phase]
        #     end
        #     ce[i]=-sum((U1[edofMat][i,:]'*KE).*U2[edofMat][i,:]')
        # end

        ce=zeros(nelx* nely* nelz)
        for i=1:Int(nelx* nely* nelz)
            KE = KEs[1].*alpha[i,1]
            for phase = 2:p
                KE = KE + KEs[phase].*alpha[i,phase]
            end
            ce[i]=-sum((U1[edofMat][i,:]'*KE).*U2[edofMat][i,:]')
        end
    

        # Objective function and sensitivity analysis
        # ce = -sum((U1[edofMat]*KE).*U2[edofMat],dims=2)

        # o = sum(sum(E.*ce))
        o  = U[dout,1]
        
        # FILTERING OF SENSITIVITIES 
        # dc = 0.0 .-(q .*(e[a].-e[b]).*alpha[:,a].^(q-1)).*ce;
        dc = 0.0 .-(q .*mean(Es[a].-Es[b]).*alpha[:,a].^(q-1)).*ce;
        dc = H*(alpha[:,a].*dc)./Hs./max.(1e-3,alpha[:,a])
        dc = min.(dc,0.0)

        # UPDATE LOWER AND UPPER BOUNDS OF DESIGN VARIABLES
        move = 0.1;
        r = ones(nx*ny*nz,1)
  
        for k = 1:p
            #if (k ~= a) && (k ~= b)
            if (k != a) && (k != b)
                # display("k $k a $a b $b")
                r = r .- alpha[:,k]
            end
        end
        l = max.(0,alpha[:,a] .-move)
        u = min.(r,alpha[:,a] .+move)
        # OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES
        l1 = 0; l2 = 1e9
        # while (l2-l1)/(l1+l2) > 1e-3
        while (l2-l1)/(l1+l2) > 1e-4 && l2 > 1e-40
            lmid = 0.5*(l2+l1)
            # alpha_a = max.(l,min.(u,alpha[:,a].*sqrt.(-dc./lmid)));
            alpha_a = max.(l,min.(u,alpha[:,a].*((max.(1e-10,-dc./lmid)).^0.3 )));
            if sum(alpha_a) > nx*ny*v[a]
                l1 = lmid
            else
                l2 = lmid 
            end
        end
        alpha[:,a] = alpha_a
        alpha[:,b] = r .-alpha_a

    end
    return o,alpha
end