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tutorial/tutex/basins.g

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+
+################################################################
+################################################################
+Basins:=function(L)
+local A, M,N, F, i,j,k, min,min2,max,pos,Q,B,P;
+#L is a list of filtered pure cubical complexes
+
+M:=Length(L[1]!.binaryArray);
+N:=Length(L[1]!.binaryArray[1]);
+
+for i in [1..Length(L)] do
+if not (Length(L[i]!.binaryArray)=M
+and Length(L[i]!.binaryArray[1])=N)
+then Print("Filtered complexes are of differing dimensions.\n");
+return fail; fi;
+od;
+A:=0*L[1]!.binaryArray;
+
+for i in [1..M] do
+for j in [1..N] do
+F:=List(L,x->x!.filtration[i][j] * x!.binaryArray[i][j]);
+max:=Maximum(F);
+if max>0 then
+min:=Minimum(Filtered(F,z->z>0));
+pos:=Position(F,min);
+A[i][j]:=pos;
+fi;
+od;od;
+
+P:=PureCubicalComplex(0*L[1]!.binaryArray);
+for k in [1..Length(L)] do
+B:=0*L[1]!.binaryArray;
+for i in [1..M] do
+for j in [1..N] do
+if A[i][j]=k then B[i][j]:=1; fi;
+od;od;
+Q:=PureCubicalComplex(B);
+Q:=PureComplexDifference(Q,BoundaryOfPureCubicalComplex(Q));
+P:=PureComplexUnion(P,Q);
+od;
+
+return P;
+return PureCubicalComplex(A);;
+end;
+################################################################
+################################################################
+
+