###### The following code works when projecting from Shannon outer bound.

Permute_marginalAndJoin:=function(ncinstance)

local A,numofVar,i;

numofVar:=ncinstance[3];

A:=[set2int([numofVar])+2^numofVar..set2int([numofVar])+2^(numofVar+1)-2];

for i in [1..numofVar] do

A[set2int([i])]:=set2int([i]);

od;

for i in [1..Size(ncinstance[1])] do

A[set2int(ncinstance[1][i])]:=set2int([numofVar])+set2int(ncinstance[1][i]);

od;

return A;

end;

AddconstraintsTopAndBottom:=function(ncinstancetop)

local linrows,i,ShOB1,con,j,conlin;

ShOB1 := GenShannonUnBounded( ncinstancetop[3] );

i := Size( ShOB1[1] ) + 1;

linrows := [ ];

for con in ncinstancetop[1] do #### H(Out(t),In(t))=H(In(t))

conlin := ZeroMutable( [ 1 .. 2 ^ ncinstancetop[3] - 1 ] );

conlin[set2int( con[1] )] := 1;

conlin[set2int( con[2] )] := -1;

Append( ShOB1[1], [ conlin ] );

Append( ShOB1[2], [ 0 ] );

Append( linrows, [ i ] );

i := i + 1;

od;

conlin := ZeroMutable( [ 1 .. 2 ^ ncinstancetop[3] - 1 ] );

if ncinstancetop[2]>1 then

for j in [ 1 .. ncinstancetop[2] ] do #### H(s1,s2,..,sj)=H(s1)+H(s2)+,...,+H(sj)

conlin[set2int( [ j ] )] := 1;

od;

conlin[set2int( [ 1 .. ncinstancetop[2] ] )] := -1;

Append( ShOB1[1], [ conlin ] );

Append( ShOB1[2], [ 0 ] );

Append( linrows, [ i ] );

i := i + 1;

fi;

return [ShOB1[1],ShOB1[2],linrows];

end;

##Project onto useful variables SH_P*X<=Sb1 denotes the permuted shannon outer bound

ProjectOntoUseful_Var:=function(SH_P,Sb1,numofVar,linrows)

local proj_SH,proj_Sb,conlin,j,G,rlist;

proj_SH:=ShallowCopy(SH_P);

proj_Sb:=ShallowCopy(Sb1);

for j in [1..numofVar] do

conlin := ZeroMutable( [ 1 .. Size(SH_P[1]) ] );

conlin[j] := -1;

Append( proj_SH, [ conlin ] );

Append( proj_Sb, [ 0 ] );

od;

conlin := ZeroMutable( [ 1 .. Size(SH_P[1]) ] );

for j in [ 1 .. numofVar ] do #### sum<=1

conlin[j] :=1;

od;

Append( proj_SH, [ conlin ] );

Append( proj_Sb, [ 1 ] );

G := Group( [ () ] );

rlist := symCHM( proj_SH, proj_Sb, linrows, numofVar, G, OnProjPts, OnProjIneq, false );

return rlist;

end;

Permute_matrix_parallel:=function(B,A)

local Bt,Bf,A1;

Bt:=TransposedMat(B);

Bt:=ShallowCopy(Bt);

A1:=ShallowCopy(A);

SortParallel(A1,Bt);

Bf:=TransposedMat(Bt);

return [Bf,A1];

end;

MatrixRemoveColumn:=function(A,index) ##subfunction

local AT,Af;

AT:=TransposedMat(A);

AT:=ShallowCopy(AT);

Remove(AT,index);

Af:=TransposedMat(AT);

return Af;

end;

MatrixGetColumn:=function(A,index) ##subfunction

local AT,b;

AT:=TransposedMat(A);

AT:=ShallowCopy(AT);

b:=AT[index];

return b;

end;

AddzeroColumn:=function(A,index) ##subfunction

local AT, v, w, i,Zvector,A1;

AT:=TransposedMat(A);

AT:=ShallowCopy(AT);

Zvector:=ZeroMutable([1..Size(AT[1])]);

for i in index do

Add(AT,Zvector,i);

od;

A1:=TransposedMat(AT);

return A1;

end;

AddcutProject:=function(rlisttop,rlistbottom,ncinstancecut,A1,addzerocolumn_index) #addzerocolumn_index:=[3,4]

local Rlist,bottom,Addbottom,top,b,A,i,linrows,numofMarginal,numofSour,con,conlin,G,rlist1;

if Size(rlisttop[2][1])>Size(rlistbottom[2][1]) then

Rlist:=ShallowCopy(rlisttop[2]);

bottom:=ShallowCopy(rlistbottom[2]);

Addbottom:=AddzeroColumn(bottom,addzerocolumn_index);

Append(Rlist,Addbottom);

elif Size(rlisttop[2][1])<Size(rlistbottom[2][1]) then

top:=ShallowCopy(rlisttop[2]);

Rlist:=AddzeroColumn(top,addzerocolumn_index);

Rlist:=ShallowCopy(Rlist);

Append(Rlist, rlistbottom[2]);

else

Rlist:=ShallowCopy(rlisttop[2]);

Append(Rlist,rlistbottom[2]);

fi;

b:=MatrixGetColumn(Rlist,Size(Rlist[1]));

b:=ShallowCopy(b);

A:=MatrixRemoveColumn(Rlist,Size(Rlist[1]));

A:=ShallowCopy(A);

i:=Size(b)+1;

linrows:=[];

numofMarginal:=ncinstancecut[3];

numofSour:=ncinstancecut[2];

for con in ncinstancecut[1] do #### H(Out(t),In(t))=H(In(t))

conlin:=ZeroMutable([1..Size(A[1])]);

if Size(con[1])>1 then

conlin[Position(A1,set2int(con[1])+set2int([numofMarginal]))]:=1;

else

conlin[Position(A1,set2int(con[1]))]:=1;

fi;

if Size(con[2])>1 then

conlin[Position(A1,set2int(con[2])+set2int([numofMarginal]))]:=-1;

else

conlin[Position(A1,set2int(con[2]))]:=-1;

fi;

Append(A,[conlin]);

Append(b,[0]);

Append(linrows,[i]);

i:=i+1;

od;

G:=Group( [ () ] );

rlist1 := symCHM( A, b, linrows, numofMarginal, G, OnProjPts, OnProjIneq, false );

return rlist1;

end;

######## An example for main function

#### ncinstancetop:=[[[[1,2],[1,2,3]],[[2,3],[2,3,4]],[[3],[3,5]],[[3,4],[3,4,6]]],2,8];

#### ncinstancebottom:=[[[[5],[1,5]],[[5,6],[2,5,6]]],2,6];

#### ncinstancecut:=[[[[5,6],[5,6,7]],[[6,7],[6,7,8]]],2,8];

#### cutVar_top:=[[[5,6],[5,6,7],[6,7],[6,7,8]],2,8];

#### cutVar_bottom:=[[[3,4],[3,4,5],[4,5],[4,5,6]],2,6];

#### ncinstance:=[[[[1,2],[1,2,3]],[[2,3],[2,3,4]],[[3],[3,5]],[[3,4],[3,4,6]],[[5,6],[5,6,7]],[[6,7],[6,7,8]],[[7],[1,7]],[[7,8],[2,7,8]]],2,8];

TopBottomPastingMain:=function(ncinstancetop,cutVar_top,cutVar_bottom,ncinstancecut,ncinstancebottom,numofCutandSingle_top,numofCutandSingle_bottom,addzerocolumn_index)

local SHLT,AAT,AAB,A1,B1,AB,SHTA,SHT_P,SbT,linrowsT,rlistTop,SHLB,SHBA,SHB_P,SbB,linrowsB,rlistBottom,rlist1;

SHLT:=AddconstraintsTopAndBottom(ncinstancetop);

AAT:=Permute_marginalAndJoin(cutVar_top);

SHTA:=Permute_matrix_parallel(SHLT[1],AAT);

SHT_P:=SHTA[1];

SbT:=SHLT[2];

A1:=SHTA[2];

linrowsT:=SHLT[3];

rlistTop:=ProjectOntoUseful_Var(SHT_P,SbT,numofCutandSingle_top,linrowsT);

SHLB:=AddconstraintsTopAndBottom(ncinstancebottom);

AAB:=Permute_marginalAndJoin(cutVar_bottom);

SHBA:=Permute_matrix_parallel(SHLB[1],AAB);

B1:=SHBA[2];

if Size(A1)>Size(B1) then

AB:=A1;

else

AB:=B1;

fi;

SHB_P:=SHBA[1];

SbB:=SHLB[2];

linrowsB:=SHLB[3];

rlistBottom:=ProjectOntoUseful_Var(SHB_P,SbB,numofCutandSingle_bottom,linrowsB);

rlist1:=AddcutProject(rlistTop,rlistBottom,ncinstancecut,AB,addzerocolumn_index);

return rlist1;

end;