persistent betti numbers

lib/Homology/new_persistent.gi

@@ -1,10 +1,13 @@
+#RT:=0;
 
 ###################################################
 ###################################################
 InstallGlobalFunction(PersistentBettiNumbersViaContractions,
-function(FF,n,p)
-local F, W, L, E, chnmap, cwmap, map, ln, k, f, homs;
+function(FF,N,p)
+local n,F, W, L, E, chnmap, cwmap, map, ln, k, f, homs;
 
+if not (IsInt(N) or IsList(N)) then return fail; fi;
+if IsInt(N) then n:=N; fi;
 #F:=ContractedFilteredRegularCWComplex(FF);
 F:=FF;
 ln:=EvaluateProperty(F,"filtration_length");
@@ -24,19 +27,38 @@ cwmap:=Objectify( HapRegularCWMap,
 Add(L,ChainMapOfRegularCWMap(cwmap));
 od;
 
-
 E:=[];
 for k in [1..ln] do
 Add(E,ChainComplexEquivalenceOfRegularCWComplex(W[k]));
 od;
 
-
+if IsInt(N) then
 homs:=[];
 for k in [1..ln-1] do
 f:=Compose( E[k+1][1], Compose(L[k],E[k][2]) );
 Add(homs,HomologyVectorSpace(TensorWithIntegersModP(f,p),n));
 od;
 return LinearHomomorphismsPersistenceMat(homs);
+fi;
+
+homs:=[];
+for n in N do
+homs[n+1]:=[];
+od;
+
+N:=SortedList(N); 
+
+for k in [1..ln-1] do
+f:=Compose( E[k+1][1], Compose(L[k],E[k][2]) );
+for n in N do
+#RT:=0-Runtime();
+Add(homs[n+1],HomologyVectorSpace(TensorWithIntegersModP(f,p),n));
+#RT:=RT+Runtime(); Print([k,n,RT],"\n");
+od;
+od;
+
+homs:=List(N,n-> LinearHomomorphismsPersistenceMat(homs[n+1]) );
+return homs;
 end);
 ###################################################
 ###################################################

lib/Homology/persistent.gi

@@ -409,7 +409,7 @@ local
 	LM,deg,prime,
         M,triv,ChnCmps,vsmaps,A,S,TS,TM,L,
         bool,x,y,i,F,PC;
-
+Print("This function is unreliable, slow and should not be used.\n");
 ##Input###################
 LM:=arg[1];
 deg:=arg[2];
@@ -488,7 +488,7 @@ function(arg)
 local
         M,Bettis,triv,Persist,deg,prime,TM,L,SL,bool,CollapseMat,
         Collapses_dim2,Fun,x,y;
-
+Print("This function is unreliable, slow and should not be used.\n");
 ##Input###################
 deg:=arg[2];
 prime:=arg[3];
@@ -746,6 +746,10 @@ Disp:=DISPLAY_PATH;
 fi;
 ###############
 
+if IsMatrix(P[1]) then
+HAP_BarCodeCompactDisplayList(P);
+else
+
 B:=BarCode(P);
 B:=Collected(B);
 
@@ -791,6 +795,95 @@ od;
 
 AppendTo(barcodedot,"}");
 
+Exec(Concatenation("dot -Tgif ",barcodedot ,">", barcodegif));
+Exec(Concatenation(Disp," ",barcodegif));
+Sleep(2);
+Exec(Concatenation("rm -r ",barcodegif{[1..Length(barcodegif)-9]}));
+fi;
+end);
+#################################################################
+#################################################################
+
+###########################################################
+###########################################################
+InstallGlobalFunction(HAP_BarCodeCompactDisplayList,
+function(arg)
+local cnt,Q,BB,P,B,i,j,Disp,tmpDir,barcodedot,barcodegif, lb, AppendTo, PrintTo;
+#SHOULD MERGE THIS INTO PRECEDING FUNCTION
+AppendTo:=HAP_AppendTo;
+PrintTo:=HAP_PrintTo;
+
+###############
+P:=arg[1];
+if Length(arg)=2 then
+Disp:=arg[2];
+else
+Disp:=DISPLAY_PATH;
+fi;
+###############
+
+B:=[];
+
+cnt:=-1;;
+for Q in P do
+cnt:=cnt+1;
+BB:=BarCode(Q);
+BB:=Collected(BB);
+Append(B,BB);
+i:=[1..Length(B[1][1])]*0;;
+j:=[1..Length(B[1][1])]*0;;
+Add(B,[i,Concatenation("Betti  ", String(cnt))]);
+Add(B,[j,0]);
+od;
+
+tmpDir:=DirectoryTemporary();
+barcodedot:=Filename(tmpDir,"tmpIn.log");
+barcodegif:=Filename(tmpDir,"basic.gif");
+
+
+PrintTo(barcodedot,"digraph finite_state_machine {\n\n");
+AppendTo(barcodedot, "rankdir=LR;\n\n");
+AppendTo(barcodedot,
+"node [style=filled,shape=point]\n\n");
+
+lb:=Length(B[1][1]);
+for i in [1..Length(B)] do
+for j in [1..Length(B[1][1])] do
+if B[i][1][j]>0 then
+AppendTo(barcodedot,"node [color=black,fontcolor=black];\n",i,".",j,"\n");
+else
+AppendTo(barcodedot,"node [color=white,fontcolor=white];\n",i,".",j,"\n");
+fi;
+od;
+od;
+
+
+for i in [1..Length(B)] do
+
+if IsString(B[i][2]) then
+AppendTo(barcodedot,i,".",1,"->",i,".",1+1," [label =\"",B[i][2]," \",color=white,arrowhead=none];\n");
+fi;
+
+for j in [1..Length(B[1][1])-1] do
+
+if B[i][1][j]>0 and B[i][1][j+1]>0 then
+  if j=Position(B[i][1],1) or (Position(B[i][1],1)=lb and j=lb-1) then
+  AppendTo(barcodedot,i,".",j,"->",i,".",j+1," [label =\"",B[i][2]," \",color=black,arrowhead=none];\n");
+  else
+  AppendTo(barcodedot,i,".",j,"->",i,".",j+1," [color=black,arrowhead=none];\n");
+  fi;
+else
+  if j=Position(B[i][1],1) or (Position(B[i][1],1)=lb and j=lb-1) then
+  AppendTo(barcodedot,i,".",j,"->",i,".",j+1," [label =\"",B[i][2]," \",color=white,arrowhead=none];\n");
+  else
+  AppendTo(barcodedot,i,".",j,"->",i,".",j+1," [color=white,arrowhead=none];\n");
+  fi;
+fi;
+od;
+od;
+
+AppendTo(barcodedot,"}");
+
 Exec(Concatenation("dot -Tgif ",barcodedot ,">", barcodegif));
 Exec(Concatenation(Disp," ",barcodegif));
 Sleep(2);
@@ -1008,6 +1101,7 @@ local
         ChnCmps,vsmaps,L,
         U,CU,V,CV,W,CW,
         x,y,i,F,PC,correction;
+Print("This function is unreliable, slow and should not be used.\n");
 
 ##Input###################
 LM:=arg[1];
@@ -1096,6 +1190,7 @@ end);
 InstallGlobalFunction(PersistentHomologyOfFilteredPureCubicalComplex,
 function(F,n)
 local FF, C, D;
+Print("This function is unreliable, slow and should not be used.\n"); 
 
 ############################
 if n=0 and IsHapFilteredPureCubicalComplex(F) then
@@ -1131,6 +1226,7 @@ InstallGlobalFunction(PersistentHomologyOfFilteredPureCubicalComplex_alt,
 function(FF,deg)
 local flen, HEMin, HEMax, FT, PH, D, PHfirst, Pmat, PB, F, r, s,n;
 
+Print("This function is unreliable, slow and should not be used.\n");
 #############################
 if IsBound(FF!.persistentHomology) then
 if IsBound(FF!.persistentHomology[deg+1]) then

lib/Manifolds/manifolds.gi

@@ -85,6 +85,29 @@ end);
 #####################################################
 #####################################################
 
+#####################################################
+#####################################################
+InstallOtherMethod(ClosedSurface,
+"simplicial surface or genus +/- g (where - means nonorientable)",
+[IsInt,IsString],
+function(n,str)
+local Y;
+if str="CW" then
+Y:=ClosedSurface(n);
+Y:=RegularCWComplex(Y);;
+Y:=BarycentricallySimplifiedComplex(Y);
+return Y;
+fi;
+if str="Simplicial" then
+Y:=ClosedSurface(n);
+return Y;
+fi;
+Print("The second argument should be \"CW\" or \"Simplicial\".\n");
+return fail;
+end);
+#####################################################
+#####################################################
+
 
 #####################################################
 #####################################################
@@ -194,7 +217,7 @@ Print("The simplicial manifolds must have the same dimension.\n");
 return fail;
 fi;
 
-e:=arg[3]; 
+e:=-arg[3]; 
 maxK:=1*K!.simplicesLst[Dimension(K)+1];
 maxL:=1*L!.simplicesLst[Dimension(L)+1];
 

lib/Operations/hapOps.gi

@@ -1011,6 +1011,10 @@ InstallOtherMethod(PersistentBettiNumbers,
 function(Y,n)
 local W;
 
+if n=0 and EvaluateProperty(Y,"monotonic")=true then
+return HAP_BettiZeroMonotonic(Y);
+fi;
+
 W:=ContractedFilteredPureCubicalComplex(Y);
 W:= FilteredPureCubicalComplexToCubicalComplex(W);
 W:=FilteredCubicalComplexToFilteredRegularCWComplex(W);
@@ -1030,6 +1034,10 @@ InstallOtherMethod(PersistentBettiNumbers,
 [IsHapFilteredPureCubicalComplex,IsInt,IsInt],
 function(Y,n,prime)
 local W;
+if n=0 and EvaluateProperty(Y,"monotonic")=true then
+return HAP_BettiZeroMonotonic(Y);
+fi;
+
 W:=ContractedFilteredPureCubicalComplex(Y);
 W:= FilteredPureCubicalComplexToCubicalComplex(W);
 W:=FilteredCubicalComplexToFilteredRegularCWComplex(W);
@@ -1045,6 +1053,10 @@ InstallOtherMethod(PersistentBettiNumbersAlt,
 [IsHapFilteredPureCubicalComplex,IsInt,IsInt],
 function(Y,n,prime)
 local W;
+if n=0 and EvaluateProperty(Y,"monotonic")=true then
+return HAP_BettiZeroMonotonic(Y);
+fi;
+
 W:=ContractedFilteredPureCubicalComplex(Y);
 W:= FilteredPureCubicalComplexToCubicalComplex(W);
 W:=FilteredCubicalComplexToFilteredRegularCWComplex(W);
@@ -1053,6 +1065,8 @@ end);
 ##########################################################
 ##########################################################
 
+
+
 ##########################################################
 ##########################################################
 InstallOtherMethod(PersistentBettiNumbersAlt,
@@ -1061,6 +1075,10 @@ InstallOtherMethod(PersistentBettiNumbersAlt,
 function(Y,n)
 local W;
 
+if n=0 and EvaluateProperty(Y,"monotonic")=true then
+return HAP_BettiZeroMonotonic(Y);
+fi;
+
 W:=ContractedFilteredPureCubicalComplex(Y);
 W:= FilteredPureCubicalComplexToCubicalComplex(W);
 W:=FilteredCubicalComplexToFilteredRegularCWComplex(W);
@@ -1069,6 +1087,31 @@ end);
 ##########################################################
 ##########################################################
 
+##########################################################
+##########################################################
+InstallOtherMethod(PersistentBettiNumbersAlt,
+"Betti number of a filtered pure cubical complex",
+[IsHapFilteredPureCubicalComplex,IsList],
+function(Y,N)
+local W,P, NN;
+
+W:=ContractedFilteredPureCubicalComplex(Y);
+
+if 0 in N and EvaluateProperty(Y,"monotonic")=true then
+P:=[ HAP_BettiZeroMonotonic(Y) ];
+NN:=Filtered(N,i->not i=0);
+Append(P,PersistentBettiNumbersAlt(W,NN));
+return P;
+fi;
+
+W:= FilteredPureCubicalComplexToCubicalComplex(W);
+W:=FilteredCubicalComplexToFilteredRegularCWComplex(W);
+return PersistentBettiNumbersAlt(W,N);
+end);
+##########################################################
+##########################################################
+
+
 
 
 
@@ -1182,6 +1225,19 @@ end);
 ##########################################################
 ##########################################################
 
+##########################################################
+##########################################################
+InstallOtherMethod(PersistentBettiNumbersAlt,
+"Betti number of a filtered regular CW-complex",
+[IsHapFilteredRegularCWComplex,IsList],
+function(Y,N);
+Print("Using homology over GF(2).\n");
+return PersistentBettiNumbersViaContractions(Y,N,2);
+end);
+##########################################################
+##########################################################
+
+