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+(* ::Package:: *)
+
+(************************************************************************)
+(* This file was generated automatically by the Mathematica front end. *)
+(* It contains Initialization cells from a Notebook file, which *)
+(* typically will have the same name as this file except ending in *)
+(* ".nb" instead of ".m". *)
+(* *)
+(* This file is intended to be loaded into the Mathematica kernel using *)
+(* the package loading commands Get or Needs. Doing so is equivalent *)
+(* to using the Evaluate Initialization Cells menu command in the front *)
+(* end. *)
+(* *)
+(* DO NOT EDIT THIS FILE. This entire file is regenerated *)
+(* automatically each time the parent Notebook file is saved in the *)
+(* Mathematica front end. Any changes you make to this file will be *)
+(* overwritten. *)
+(************************************************************************)
+
+
+
+BeginPackage["BBHReduce`",{"NRLists`","NRFiles`","NRStrings`","NRWaves`","NinjaBase`","SXSFormat`","NRTimeSeries`"}];
+
+
+ValPrint::usage="ValPrint[x_?StringQ]";
+
+
+RunsFromRunsFile::usage="RunsFromRunsFile[file_?StringQ]";
+ContainsRun::usage="ContainsRun[directory_, runIdentifierStrings_]";
+IsBAMObsoleteDirectory::usage="IsBAMObsoleteDirectory[dirname_?StringQ]";
+IsBAMEvolutionParfile::usage="IsBAMEvolutionParfile[ filecontent_]";
+IsBAMInitialDataParfile::usage="IsBAMInitialDataParfile[ filecontent_]";
+IsBAMEvolutionDirectory::usage="IsBAMEvolutionDirectory[dirname_?StringQ]";
+ParfileInDirectory::usage="ParfileInDirectory[dirname_?StringQ]";
+levelFun::usage="levelFun[str_]";
+HasModesDirectory::usage="HasModesDirectory[dirname_?StringQ]";
+HasModesFiles::usage="HasModesFiles[dirname_?StringQ,pattern_?StringQ], pattern can e.g. be \"hmod*\"";
+ModesDirectory::usage="ModesDirectory[dirname_?StringQ]";
+
+BAMDataDirectories::usage="BAMEvolutionDataDirectories[runName_?StringQ,
+ OptionsPattern[{
+\"RunsRoot\" \[Rule] HomeDirectory,
+\"ReducedRoot\" \[Rule] HomeDirectory ,
+\"TraverseLevels\" \[Rule] 4}]] searches for the evolution and reduced-data directories for a specific run";
+
+
+LocateInitialDataDirectory::usage="LocateInitialDataDirectory[rootDir_, psidfile_]";
+InitialDataParameters::usage="InitialDataParameters[idDir_, psidfile_]";
+
+ParfileToRules::usage="ParfileToRules[filename_String] converts a parameter file to a list of rules.";
+BAMParfileToRules::usage="BAMParfileToRules[filename_String] coverts a initial data parameter file to a list of rules.";
+SXSMetaFilesToRules::usage="SXSMetaFilesToRules[filename_String] converts a SXS metadata.txt file to a list of rules.";
+SXSParClassification::usage="SXSParClassification[sxsdir_,ClassStr_]. Given a list of SXS NR. data folders 'sxsdir', it returns all the cases that match a certain criterion 'ClassStr' (MassRatio range, Precessing or not, Initial Distance, Orbits Number)taking as reference the SXS metadata.txt files. If it is used iteratively, one could do different classifications ";
+BAMMetaFilesToRules::usage="BAMMetaFilesToRules[filename_String] converts a BAM .bbh file to a list of rules."
+RITMetaFilesToRules::usage="RITMetaFilesToRules[filename_String] converts a RIT Metadata file to a list of rules.";
+RITParClassification::usage="RITParClassification[ritdir_,ClassStr_]. Given a list of RIT NR. data folders 'ritdir', it returns all the cases that match a certain criterion 'ClassStr' (MassRatio range, Precessing or not, Initial Distance, Orbits Number)taking as reference the RIT metadata.txt files. If it is used iteratively, one could do different classifications ";
+
+
+BAMStringParameter::usage="BAMStringParameter[directory_, parametername_]";
+BAMNumberParameter::usage="BAMNumberParameter[directory_, parametername_]";
+BAMNumberParameterInFile::usage="BAMNumberParameterInFile[file_, parametername_]";
+BAMNumberParametersInFile::usage="BAMNumberParametersInFile[file_, parametername_]";
+BAMNumberParameters::usage="BAMNumberParameters[directory_, parametername_]";
+PSIDHashedNumberParameter::usage="PSIDHashedNumberParameter[file_, parametername_]";
+PSIDNumberParameter::usage="PSIDNumberParameter[file_, parametername_]";
+PSIDReadHeader::usage="PSIDReadHeader[file_]";
+PSIDReadData::usage="PSIDReadData[file_] reads initial data for function \!\(\*FormBox[\(\(\*SubscriptBox[\(U\), \(ijk\)] = \\\ \(TraditionalForm\`\(\(U\)\((\)\*SubscriptBox[\(A\), \(i\)]\)\), \(TraditionalForm\`\*SubscriptBox[\(B\), \(j\)]\), \(TraditionalForm\`\*SubscriptBox[\(\[CurlyPhi]\), \(k\)]\)\)
+StyleBox[\")\",\nFontSize->10]\),
+TraditionalForm]\). The function which appears in the conformal factor is u = (A-1)U";
+
+PSID2Rules::usage="PSID2Rules[filename_?StringQ] converts a BAM PSID file to a list of rules.";
+
+NMovingLevels::usage="NMovingLevels[parRules_] computes the number of moving levels in a BAM parameter file from a list of rules parRules, which corresponds to the content of the parameter file.";
+
+
+CreateDataReduceDirectory::usage="CreateDataReduceDirectory[dirname_],
+ CreateDataReduceDirectory[reduceroot_, dirname_]";
+LocateMode::usage="LocateMode[modeDir_, lmode_, mmode_]";
+LocateModes::usage="LocateModes[modeDir_, lmode_, mmode_]";
+CopyL2mode::usage="CopyL2mode[configStr_, modesdir_, reducedir_]";
+CopyL2modes::usage="CopyL2modes[configStr_, modesdir_, reducedir_]";
+CopyModes::usage="CopyModes[configStr_, modesdir_, reducedir_, Lmode_, Mmode_] ";
+CopyFiles::usage="CopyFiles[configStr_, modesdir_, reducedir_, patterns_]";
+
+
+FormatPunctureData::usage="FormatPunctureData[mp_,string_,M_].";
+SafeFormatPunctureData2::usage="SafeFormatPunctureData2[mp1_,mp2_,string_,m1_,m2_].";
+SafeFormatPunctureDataCactus::usage="SafeFormatPunctureDataCactus[mp_,string_,m1_,m2_].";
+
+BAMModesFilesTo3Col::usage="BAMModesFilesTo3Col[modesFile_] reads BAM style {r,i}psi4modes_* files and saves the content in 3-colums
+format as {time,Re@values,Im@values};"
+
+BAMHorizonFilesToNRARFiles::usage="BAMHorizonFilesToNRARFiles[File_,OptionsPattern[{\"DeleteSourceFiles\" \[Rule] False}]]
+ converts a BAM-style horizon file to NRAR-style horizon mass, spin, and horizon trajectory files.";
+
+BAMTrajectoryFileTo4Col::usage="BAMTrajectoryFileTo4Col[File_,OptionsPattern[{\"DeleteSourceFiles\" \[Rule] False}]]
+converts a BAM-style puncture trajectory file to NRAR-style trajectory file.";
+
+
+BAMExtractionRadii::usage="BAMExtractionRadii[modesdir_] lists all BAM extraction radii for psi4.";
+
+SymmetriesFromParfile::usage="SymmetriesFromParfile[parfile_].";
+
+WriteModeDecompConfigFile::usage="WriteModeDecompConfigFile[DirectoryRules_?ListQ]";
+
+WaveExtractionRadii::usage="WaveExtractionRadii[rootDir_, modesDir_]";
+ADMReduce::usage="ADMReduce[rootDir_, reduceDir_]";
+BBHDataReduce::usage="BBHDataReduce[modesdir_, IDroot_, ReduceRoot_]";
+
+CurateBBHData::usage="CurateBBHData[modesdir_, IDroot_, ReduceRoot_] is a new development version of BBHDataReduce.";
+
+NRARPsi4ToStrain::usage="NRARPsi4ToStrain[metaFile_,LMAX_,\[Omega]GWStart_] reads a NRAR-style metadata file and converts
+psi4 modes to strain using the FFI algorithm, exporting the results to a directory FFIStrainModes.";
+
+
+CactusThornsAvailable::usage="CactusThornsAvailable[cactusdir_] list available Cactus thorns.";
+NormalizeCactusParfile::usage="NormalizeCactusParfile[parfile_,cactusDir_,OptionsPattern[
+{\"ThornListOutputFile\"\[Rule] \"\",\"ParameterOutputFile\"\[Rule] \"\"}]] normalizes a Cactus parfile for easier comparison or parsing.";
+
+CompleteCactusParfile::usage="CompleteCactusParfile[parfile_,cactusDir_,OptionsPattern[
+{\"ThornListOutputFile\"\[Rule] \"\",\"ParameterOutputFile\"\[Rule] \"\"}]]";
+
+SetParfileEntryValue::usage="SetParfileEntryValue[text_,key_,value_]";
+SetParfileValue::usage="SetParfileValue[text_,key_,value_]";
+SetParfileVectorValue::usage="SetParfileVectorValue[text_,key_,component_,value_]";
+
+
+SXSLuminosityFromMetaFiles::usage="SXSLuminosityFromMetaFiles:[metaFile_,modes_]; Computes Luminosity from the SXS metadata given a list of modes";
+
+
+AHBAMsmall::usage="AHBAMsmall[q,s]. Computes the aparent horizon (horizon radius) for the smallest black hole in the BAM coordinates. See notebook /BBHReduce/AparentHorizonFit.nb"
+AHBAMbig::usage="AHBAMbig[q,s]. Computes the aparent horizon (horizon radius) for the biggest black hole in the BAM coordinates. See notebook /BBHReduce/AparentHorizonFit.nb"
+AHBAMsmall2017::usage="AHBAMsmall2017[q,s]. Computes the aparent horizon (horizon radius) for the smallest black hole in the BAM coordinates. See notebook /BBHReduce/AparentHorizonFit.nb"
+AHBAMbig2017::usage="AHBAMbig2017[q,s]. Computes the aparent horizon (horizon radius) for the biggest black hole in the BAM coordinates. See notebook /BBHReduce/AparentHorizonFit.nb"
+
+
+Begin["`Private`"];
+
+
+ValPrint[x_?StringQ]:=Print[First@StringSplit[x,"$"]<>" = ",ToExpression@x]
+
+
+RunsFromRunsFile[file_?StringQ]:=Module[{content,runs},
+content = StringSplit[Import[file,"String"],EndOfLine];
+
+runs=Flatten@Map[StringCases[#,"*"~~x:Except[WhitespaceCharacter]...~~ WhitespaceCharacter... -> x]&, content];
+StringTrim[#,RegularExpression["/$"]]&/@runs
+];
+
+
+ContainsRun[directory_,runIdentifierStrings_]:=Length@Intersection[{LastInPath@directory},runIdentifierStrings]>0
+
+
+IsBAMObsoleteDirectory[dirname_?StringQ]:=StringMatchQ[dirname, "*_old"]||StringMatchQ[dirname, "*_previous"]
+
+
+IsBAMEvolutionParfile[fileORfilecontent_]:=Module[{joined},
+
+If[ListQ@fileORfilecontent,
+joined=StringJoin@fileORfilecontent;,
+
+If[FileType@fileORfilecontent == File,
+ joined = StringJoin@Import[fileORfilecontent,"String"];
+];
+];
+
+StringMatchQ[joined,"*bampi_*"]&&
+StringMatchQ[joined,"*amr*"]&&StringMatchQ[joined,"*physics*"]
+];
+
+
+IsBAMInitialDataParfile[ fileORfilecontent_]:=Module[{joined},
+
+If[FileType@fileORfilecontent == File,
+joined = StringJoin@Import[fileORfilecontent,"String"];
+];
+
+If[ListQ@fileORfilecontent,
+joined=StringJoin@fileORfilecontent;
+];
+
+ StringMatchQ[joined,"*nx*"]&&
+StringMatchQ[joined,"*iterate*"]&&StringMatchQ[joined,"*physics*"]
+];
+
+
+IsBAMEvolutionDirectory[dirname_?StringQ]:=Module[{parfiles,content,i},
+
+parfiles=Join[
+FileNames["*.par",dirname],
+FileNames["*.par.gz",dirname],
+FileNames["*.par.bz2",dirname]];
+
+content=Table[Import[parfiles[[i]],"String"],{i,1,Length@parfiles}];
+
+IsBAMEvolutionParfile@content
+]
+
+
+ParfileInDirectory[dirname_?StringQ,OptionsPattern[{"Style"-> "BAM"}]]:=Module[{guess,parfiles,sel,style},
+
+style = OptionValue["Style"];
+
+guess=dirname<>"/"<>LastInPath@dirname<>".par";
+If[FileType@guess == File,
+
+ sel = guess,
+
+ parfiles=Join[
+ FileNames["*.par",dirname],
+ FileNames["*.par.gz",dirname],
+ FileNames["*.par.bz2",dirname]
+ ];
+
+Print[parfiles];
+
+sel=Switch[style,
+"BAM",First@Select[parfiles, IsBAMEvolutionParfile@# || IsBAMInitialDataParfile@# &],
+"Cactus",First@parfiles,
+_,First@parfiles
+];
+];
+
+Print["ParfileInDirectory identifies parameter file ", sel];
+
+sel
+];
+
+
+levelFun[str_]:=ToExpression@First@StringCases[str,"hmod.r"~~r:NumberString..~~".l"~~l:NumberString-> {r,l}];
+
+
+HasModesDirectory[dirname_?StringQ]:=
+safeDirectoryQ[StringReplace[dirname<>"/Modes","//"->"/"]]||
+safeDirectoryQ[StringReplace[dirname<>"/Analysis","//"->"/"]]||
+safeDirectoryQ[StringReplace[dirname<>"/analysis","//"->"/"]]||
+safeDirectoryQ[StringReplace[dirname<>"/Psi4ModeDecomp","//"->"/"]]||
+safeDirectoryQ[StringReplace[dirname<>"/NinjaCleanPsi","//"->"/"]]
+
+
+HasModesFiles[dirname_?StringQ,pattern_?StringQ]:=Length@FileNames[pattern,dirname,2]>0
+
+
+ModesDirectory[dirname_?StringQ,pattern_?StringQ]:=Module[{sel},
+
+sel = Select[FileNames["*",dirname],FileType@# == Directory&];
+sel = Select[sel,HasModesFiles[#,pattern]&];
+
+If[Length@sel > 0, First@sel,""]
+];
+
+
+BAMDataDirectories[runName_?StringQ,
+ OptionsPattern[{
+"RunsRoot" -> HomeDirectory,
+"ReducedRoot" -> Global`BBHDataDir,
+"InitialDataRoot" -> HomeDirectory,
+"TraverseLevels" -> 4}]
+]:=Module[{RunsRoot,ReducedRoot,TraverseLevels,runsFound,
+RunsDirectories,obsolete,reducedFound,ReducedDirectories,evolDirHasModes,reducedDirHasModes,
+evolutionModesDir,reducedModesDir,psidfile,InitialDataRoot,IDDir},
+
+RunsRoot = OptionValue["RunsRoot"];
+ReducedRoot = OptionValue["ReducedRoot"];
+InitialDataRoot = OptionValue["InitialDataRoot"];
+TraverseLevels = OptionValue["TraverseLevels"];
+
+(* directory with the original run *)
+runsFound = FileNames[runName,RunsRoot,TraverseLevels];
+Print["Found runs directories: ", RunsDirectories = Select[runsFound,FileType@#==Directory&]];
+Print[" - evolution directories: ", RunsDirectories = Select[RunsDirectories,IsBAMEvolutionDirectory]];
+obsolete = Select[RunsDirectories,IsBAMObsoleteDirectory];
+Print[" - valid evolution directories: ", RunsDirectories = Complement[RunsDirectories,obsolete]];
+
+If[Length@RunsDirectories == 1,
+ RunsDirectories = RunsDirectories[[1]];
+ Print["Evolution directory has psi4 modes: ", evolDirHasModes = HasModesFiles[RunsDirectories,"psi3col*"]];,
+ Print["No unique runs directory found"];
+ RunsDirectories = False;
+ evolDirHasModes = False;
+];
+
+
+(* directory with reduced data *)
+reducedFound = FileNames[RunDir,ReducedRoot,TraverseLevels];
+Print["Found reduced-data directories: ", ReducedDirectories=Select[reducedFound,FileType@#==Directory&]];
+
+If[Length@ReducedDirectories == 1,
+ ReducedDirectories = ReducedDirectories[[1]];
+ Print["Reduced directory has psi4 modes:", reducedDirHasModes = HasModesFiles[ReducedDirectories,"psi3col*"]];,
+ Print["No unique reduced-data directory found"];
+ ReducedDirectories = False;
+ reducedDirHasModes = False;
+];
+
+If[evolDirHasModes, evolutionModesDir = ModesDirectory[ReducedDirectories,"psi3*"], evolutionModesDir = False];
+If[reducedDirHasModes, reducedModesDir = ModesDirectory[RunsDirectories, "psi3*"], reducedModesDir = False];
+
+
+If[StringQ@RunsDirectories,
+ psidfile = BAMStringParameter[RunsDirectories,"punctures_ps_file"];
+ psidfile = Last@StringSplit[psidfile,"/"];
+ psidfile = StringReplace[psidfile," "->""];
+ Print["psid-file determined from evolution parameter file as: ", psidfile];
+ IDDir = LocateInitialDataDirectory[InitialDataRoot,psidfile];,
+ IDDir = False;
+];
+
+{"EvolutionDirectory" -> RunsDirectories, "ReducedDirectory" -> ReducedDirectories,
+"EvolutionDirectoryHasModes" -> evolDirHasModes,"ReducedDirectoryHasModes" -> reducedDirHasModes,
+"EvolutionModesDir"-> evolutionModesDir, "ReducedModesDir"-> reducedModesDir, "InitialDataDir" -> IDDir,
+"PSIDFile"-> IDDir<> "/"<> psidfile}
+]
+
+
+LocateInitialDataDirectory[rootDir_,psidfile_]:=Module[{file,psidFiles,levels=5,guess,result},
+file=StringReplace[psidfile," "->""];
+guess=rootDir<>"/"<>StringSplit[file,"."][[1]]<>"/"<>file;
+Print["Making guess for psid file:", guess];
+If[FileType@guess==File,
+Print["guessed id-file confirmed to be ",guess];
+result=rootDir<>"/"<>StringSplit[file,"."][[1]];
+Print["Taking as psid-result: ", result];
+Return[result]
+];
+
+Print["Looking for psid file: ",file," in directory ",rootDir];
+psidFiles=Union@FileNames[file,rootDir,levels];
+Print["Found matching psid-files:",psidFiles];
+
+If[Length@psidFiles>1,Print["taking first psid-file"];
+];
+
+If[psidFiles!={},
+result=DropLastDirectory[First@psidFiles];,Print["ERROR: LocateInitialDataDirectory could not locate ID-directory"];
+result="";
+];
+
+ToString@result
+];
+
+
+InitialDataParameters[psidfile_]:=Module[{file,m1,m2,madm,sep,abschi1,abschi2,s1x,s1y,s1z,s2x,s2y,s2z,
+x1,y1,z1,x2,y2,z2,px1,py1,pz1,px2,py2,pz2},
+
+file=psidfile;
+Print["InitialDataParameters: Processing psidfile ", file];
+m1=PSIDHashedNumberParameter[file,"M1"];
+m2=PSIDHashedNumberParameter[file,"M2"];
+madm=PSIDHashedNumberParameter[file,"Madm"];
+
+sep=PSIDHashedNumberParameter[file,"d"];
+abschi1=PSIDHashedNumberParameter[file,"S1/M1^2"];
+abschi2=PSIDHashedNumberParameter[file,"S2/M2^2"];
+
+s1x=PSIDNumberParameter[file,"bhsx1"];
+s1y=PSIDNumberParameter[file,"bhsy1"];
+s1z=PSIDNumberParameter[file,"bhsz1"];
+
+s2x=PSIDNumberParameter[file,"bhsx2"];
+s2y=PSIDNumberParameter[file,"bhsy2"];
+s2z=PSIDNumberParameter[file,"bhsz2"];
+
+x1=PSIDNumberParameter[file,"bhx1"];
+y1=PSIDNumberParameter[file,"bhy1"];
+z1=PSIDNumberParameter[file,"bhz1"];
+
+x2=PSIDNumberParameter[file,"bhx2"];
+y2=PSIDNumberParameter[file,"bhy2"];
+z2=PSIDNumberParameter[file,"bhz2"];
+
+px1=PSIDNumberParameter[file,"bhpx1"];
+py1=PSIDNumberParameter[file,"bhpy1"];
+pz1=PSIDNumberParameter[file,"bhpz1"];
+
+px2=PSIDNumberParameter[file,"bhpx2"];
+py2=PSIDNumberParameter[file,"bhpy2"];
+pz2=PSIDNumberParameter[file,"bhpz2"];
+
+{m1,m2,madm,sep,abschi1,abschi2,s1x,s1y,s1z,s2x,s2y,s2z,{x1,y1,z1},{x2,y2,z2},{px1,py1,pz1},{px2,py2,pz2}}
+];
+
+
+InitialDataParameters[idDir_,psidfile_]:=Module[{file},
+
+file=idDir<>"/"<>psidfile;
+
+InitialDataParameters[file]
+];
+
+
+ParfileToRules[filename_String]:=Module[{parlines,rules},
+ parlines=ReadList[filename,String];
+
+ rules=Flatten[DefinitionsFromString/@parlines];
+
+ (*modify selected rules*)
+ rules=ReplaceRuleInRuleList[rules,"amr_nxyz",ToExpression/@StringSplit["amr_nxyz"/.rules]];
+
+ rules
+]
+
+
+BAMParfileToRules[filename_String]:=Module[{parlines,rules,par1,rules2,pos,rulesPn,var,value,list},
+ parlines=ReadList[filename,String];
+
+ rules=Delete[parlines,Position[StringMatchQ[parlines,"*#*"],True]];
+ rulesPn=StringTrim/@StringSplit[Flatten@StringSplit[Flatten[StringSplit[Select[parlines,StringMatchQ[#,"#$$*"]&],"#"]],"$$"],"="];
+ (*pos=Flatten@Position[TakeColumn[rules2,1],StringMatchQ[" ",#]&,True];*)
+
+(*
+ (*modify selected rules*)
+ rules=ReplaceRuleInRuleList[rules,"amr_nxyz",ToExpression/@StringSplit["amr_nxyz"/.rules]];
+*)
+
+ rules=StringTrim/@StringSplit[rules,"="];
+ rulesPn=Flatten[ToExpression@StringReplace[ToString/@Select[StringSplit[ToString/@rulesPn," "],Length@#==2&],",,"->","],1];
+ rules=Join[rules,rulesPn];
+
+ var=ToString/@rules[[All,1]];
+ value=ToExpression/@rules[[All,2]];
+
+
+ list={};
+ Do[
+ If[IsFPNumberQ@value[[i]],
+ value[[i]]=(StringToNumber@#)&/@value[[i]];
+ ];
+ list=AppendTo[list,{var[[i]]->value[[i]]}];
+ ,
+ {i,1,Length@value}];
+
+ Flatten@list
+
+]
+
+
+SXSMetaFilesToRules[filePath_]:=Module[{filepath,fileList,meta1,pos1,meta2,meta3,meta4,value,var,list},
+
+
+If[ListQ@filePath,filepath=filePath[[1]],filepath=filePath];
+If[Not@FileExistsQ@filepath,Print["File not found"];Return[]];
+
+(*Reading the file*)
+fileList=ReadList[filepath,String];
+(*Delete comments*)
+
+meta1=Delete[fileList,Position[StringMatchQ[fileList,"#*"],True]];
+
+(*Fix eccentricity*)
+meta1[[Flatten@Position[StringMatchQ[meta1,"*<*e-*"],True]]]=StringReplace[meta1[[Flatten@Position[StringMatchQ[meta1,"*<*e-*"],True]]],"<"->""];
+
+(*Find = *)
+meta2=meta1[[Flatten@Position[StringMatchQ[meta1,"*=*"],True]]];
+
+meta3=StringSplit[meta2,"="];
+
+(* Select non-empty fields*)
+meta3=Select[meta3,Length@#>1&];
+
+(*Delete spaces*)
+meta4=Transpose[{StringReplace[meta3[[All,1]]," "->""],StringReplace[meta3[[All,2]]," "->""]}];
+
+var=meta4[[All,1]];
+value=meta4[[All,2]];
+
+value=StringSplit[#,","]&/@value;
+(*Delete empty elements*)
+(*value=Select[value, UnsameQ[#, {}] &];*)
+
+list={};
+Do[
+If[Length@value[[i]]==0,
+ {}
+ ,
+ If[IsFPNumberQ@value[[i,1]],
+ value[[i]]=(StringToNumber@#)&/@value[[i]];
+ ];
+ list=AppendTo[list,{var[[i]]->value[[i]]}];
+ ];
+,
+{i,1,Length@value}];
+
+Flatten@list
+
+]
+
+
+RITMetaFilesToRules[filePath_]:=Module[{filepath,fileList,meta1,pos1,meta2,meta3,meta4,value,var,list},
+
+
+If[ListQ@filePath,filepath=filePath[[1]],filepath=filePath];
+If[Not@FileExistsQ@filepath,Print["File not found"];Return[]];
+
+(*Reading the file*)
+fileList=ReadList[filepath,String];
+(*Delete comments*)
+
+meta1=Delete[fileList,Position[StringMatchQ[fileList,"#*"],True]];
+
+(*Fix eccentricity*)
+(*meta1[[Flatten@Position[StringMatchQ[meta1,"*<*e-*"],True]]]=StringReplace[meta1[[Flatten@Position[StringMatchQ[meta1,"*<*e-*"],True]]],"<"\[Rule]""];*)
+(*We do not have < in the MetaFiles of RIT*)
+
+(*Find = *)
+meta2=meta1[[Flatten@Position[StringMatchQ[meta1,"*=*"],True]]];
+
+meta3=StringSplit[meta2,"="];
+
+(* Select non-empty fields*)
+meta3=Select[meta3,Length@#>1&];
+
+(*Delete spaces*)
+meta4=Transpose[{StringReplace[meta3[[All,1]]," "->""],StringReplace[meta3[[All,2]]," "->""]}];
+
+var=meta4[[All,1]];
+value=meta4[[All,2]];
+
+value=StringSplit[#,","]&/@value;
+(*Delete empty elements*)
+(*value=Select[value, UnsameQ[#, {}] &];*)
+
+list={};
+Do[
+If[Length@value[[i]]==0,
+ {}
+ ,
+ If[IsFPNumberQ@value[[i,1]],
+ value[[i]]=(StringToNumber@#)&/@value[[i]];
+ ];
+ list=AppendTo[list,{var[[i]]->value[[i]]}];
+ ];
+,
+{i,1,Length@value}];
+
+Flatten@list
+
+]
+
+
+BAMMetaFilesToRules[filePath_]:=Module[{filepath,fileList,meta1,pos1,meta2,meta3,meta4,value,var,list,pos,rads,posdel},
+
+
+If[ListQ@filePath,filepath=filePath[[1]],filepath=filePath];
+If[Not@FileExistsQ@filepath,Print["File not found"];Return[]];
+
+(*Reading the file*);
+fileList=ToString/@ReadList[filepath,String];
+
+(*Delete comments*)
+meta1=Delete[fileList,Position[StringMatchQ[fileList,"*#*"],True]];
+
+(*Find = *)
+meta2=meta1[[Flatten@Position[StringMatchQ[meta1,"*=*"],True]]];
+meta3=StringSplit[meta2,"="];
+(*Select non-empty arrays*)
+meta4=Select[meta3,Length@#==2&];
+
+(*Delete spaces*)
+meta4=Transpose[{StringTrim/@meta4[[All,1]],StringTrim/@meta4[[All,2]]}];
+(*Delete empty elements*)
+meta4=Select[meta4, UnsameQ[#[[2]], {}] &];
+
+var=meta4[[All,1]];
+value=meta4[[All,2]];
+
+value=StringSplit[#,","]&/@value;
+
+list={};
+Do[
+If[Length@value[[i]]==0,
+ {}
+ ,
+ If[IsFPNumberQ@value[[i,1]],
+ value[[i]]=(StringToNumber@#)&/@value[[i]];
+ ];
+ list=AppendTo[list,{var[[i]]->value[[i]]}];
+ ];
+,
+{i,1,Length@value}];
+
+list=Flatten@list;
+
+(* Fix extraction radius repetition. Assume that the first entry is finite-radii *)
+pos=Position[Flatten@list,"extraction-radius"];
+rads=Select[Flatten@list[[pos[[All,1]],2]],NumberQ@#&];
+list[[pos[[1,1]],2]]=rads;
+posdel=Partition[TakeColumn[pos,1][[2;;-1]],1];
+list=Delete[list,posdel];
+
+(* Gather together the extraction radius per each mode *)
+pos=Select[DuplicatesPosition[list[[All,1]]],Length@#>1&];
+Do[list[[pos[[i,1]],2]]=Flatten@Join[{list[[pos[[i,1]],2]]},list[[pos[[i,2;;-1]],2]]],{i,Length@pos}];
+posdel=Partition[Flatten@Table[pos[[i,2;;-1]],{i,Length@pos}],1];
+
+list=Delete[list,posdel]
+
+]
+
+
+SXSParClassification[sxsdir_?ListQ,ClassStr_?ListQ,OptionsPattern[{"\[Epsilon]"->0.001,"HighSpin"->0.8,"UnRepeated"->False,"Verbose"->False,"Mass1-Str"->"initial-mass1","Mass2-Str"->"initial-mass2"}]]:=Module[{metafiles,metadata,
+orbitStr="number-of-orbits",dStr="initial-separation",mass1Str,mass2Str,spin1Str="initial-dimensionless-spin1",
+spin2Str="initial-dimensionless-spin2",eccStr="relaxed-eccentricity",spin1Dim,spin2Dim,mass1,mass2,massratio,eccentricity,dist,orbit,select,pos,condition,A1,A2,precvalue,precvalueNorm,\[Epsilon],
+spin1Norm,spin2Norm,highspin,spintest,\[Chi]eff,sxsdirout,spinz,spinzDiff,auxDist,posdup,posdupDist,posdistecc,unrepeated,verbose,sxsdiroutaux,precvalue1,precvalue2,precvalueNorm1,precvalueNorm2},
+
+Print["Classification Input Variables. Examples: {{'MassRatio', '0.99<#<1.1'}},{{'Distance', '#>16'}},{{'Orbits', '#>25'}},{{'Precessing'}},
+{{'Non-Precessing'}},{{'High-Spin'}},{{'\[Chi]eff','#>0.6'}},{{'\[Chi]1','#>0.6'}},{{'\[Chi]2','#>0.6'}},{{'Unequal'}}"];
+Print["Take care! Some of the sxs file names are not consistent with the metadata files"];
+Print["The spin definition is consitent with 'initial-spin' values and not relaxed ones"];
+Print["The mass definition is consitent with 'initial-mass' values and not relaxed ones"];
+
+mass1Str=OptionValue["Mass1-Str"];
+mass2Str=OptionValue["Mass2-Str"];
+
+(* Kill the loop if the root directory is wrong *)
+If[And@@(Not/@DirectoryQ/@sxsdir),Print[Style["Directory not found",Red]];Return[{}]];
+
+(* Useful function to detect the duplicates *)
+positionDuplicates[listaux_]:=GatherBy[Range@Length[listaux],listaux[[#]]&];
+
+sxsdirout=sxsdir;
+
+\[Epsilon]=OptionValue["\[Epsilon]"];
+highspin=OptionValue["HighSpin"];
+unrepeated=OptionValue["UnRepeated"];
+verbose=OptionValue["Verbose"];
+
+metafiles=Flatten[FileNames["metadata.txt",#,4]&/@sxsdirout,1];
+metadata=SXSMetaFilesToRules[#]&/@metafiles;
+mass1=Flatten@((mass1Str/.#)&/@metadata);
+mass2=Flatten@((mass2Str/.#)&/@metadata);
+massratio=mass1/mass2;
+dist=Flatten@((dStr/.#)&/@metadata);
+orbit=Flatten@((orbitStr/.#)&/@metadata);
+spin1Dim=((spin1Str/.#)&/@metadata);
+spin2Dim=((spin2Str/.#)&/@metadata);
+A1=(1+3 massratio/(4.));
+A2=(1+3 /(4.*massratio) );
+\[Chi]eff=massratio/(1.+massratio)*spin1Dim +1./(1+massratio)*spin2Dim;
+eccentricity=Flatten[(eccStr/.#)&/@metadata];
+spinz=Chop/@Transpose[{TakeColumn[spin1Dim,3],TakeColumn[spin2Dim,3]}];
+spinzDiff=Abs[(#[[2]]-#[[1]])&/@spinz];
+condition=ClassStr[[All,1]];
+select=Table[If[Length@ClassStr[[i]]==2,ToExpression@(ClassStr[[i,2]]),"Null"],{i,1,Length@ClassStr}];
+pos=Table[i,{i,Length@sxsdirout}];
+
+Do[
+
+Which[condition[[i]]=="MassRatio",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[massratio,_?(Evaluate[select[[i]]]&)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+sxsdirout=sxsdirout[[pos]];,
+
+condition[[i]]== "Distance",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[sxsdirout=sxsdirout[[pos]];,_?(Evaluate[select[[i]]]&)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+
+condition[[i]]== "Orbits",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[orbit,_?(Evaluate[select[[i]]]&)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+
+condition[[i]]== "Non-Precessing",
+
+(*precvalue=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1+(spin2Dim)A2);*)
+precvalue1=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1);
+precvalue2=(#)\[Cross]{0,0,1}&/@((spin2Dim)A2);
+precvalueNorm1=Norm[#]&/@precvalue1;
+precvalueNorm2=Norm[#]&/@precvalue2;
+precvalueNorm=precvalueNorm1^2+precvalueNorm2^2;
+pos=Flatten@Position[precvalueNorm,_?(#<\[Epsilon] &)];
+
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+
+condition[[i]]== "Unequal",
+
+pos=Flatten@Position[spinzDiff,_?(#>\[Epsilon] &)];
+
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+
+condition[[i]]=="Precessing",
+
+precvalue1=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1);
+precvalue2=(#)\[Cross]{0,0,1}&/@((spin2Dim)A2);
+precvalueNorm1=Norm[#]&/@precvalue1;
+precvalueNorm2=Norm[#]&/@precvalue2;
+precvalueNorm=precvalueNorm1^2+precvalueNorm2^2;
+
+(*precvalue=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1+(spin2Dim)A2);*)
+
+pos=Flatten@Position[precvalueNorm,_?(#>\[Epsilon] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+
+condition[[i]]== "High-Spin",
+
+spin1Norm=Norm[#]&/@spin1Dim;
+spin2Norm=Norm[#]&/@spin2Dim;
+
+spintest=Table[If[Abs@spin1Norm[[i]]>=highspin || Abs@spin2Norm[[i]]>=highspin,True,False],{i,1,Length@spin1Norm}];
+pos=Flatten@Position[spintest,True];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+
+condition[[i]]== "\[Chi]eff",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[Norm[#]&/@\[Chi]eff,_?(Evaluate[select[[i]]] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+
+condition[[i]]== "\[Chi]1",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[Norm[#]&/@spin1Dim,_?(Evaluate[select[[i]]] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+
+condition[[i]]== "\[Chi]2",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[Norm[#]&/@spin2Dim,_?(Evaluate[select[[i]]] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+
+
+condition[[i]]== "relaxed-eccentricity",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[eccentricity,_?(Evaluate[select[[i]]] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+sxsdirout=sxsdirout[[pos]];,
+ True,
+Print[Style["Wrong input",Bold,Red,16]];
+Break[];
+];
+,{i,1,Length@ClassStr}];
+
+
+If[unrepeated,
+
+Print["Taking among the repeated cases only those with lower eccentricity and larger D (just in case ei=ej)"];
+
+(* Selecting Case with lower e *)
+auxDist=Transpose[{Round[#&/@massratio,0.1],Round[Chop[#,10^(-2)],0.01]&/@spin1Dim,Round[Chop[#,10^(-2)],0.01]&/@spin2Dim,dist,eccentricity}];
+posdup=positionDuplicates@auxDist[[All,1;;3]];
+posdistecc=Flatten[#,1]&/@Table[Position[auxDist[[posdup[[i]],5]],Min@auxDist[[posdup[[i]],5]]],{i,1,Length@posdup}];
+posdistecc=Flatten@Table[posdup[[i,posdistecc[[i]]]],{i,1,Length@posdup}];
+sxsdirout=sxsdirout[[posdistecc]];
+
+(* Selecting Case with larger D *)
+auxDist=auxDist[[posdistecc]];
+posdup=positionDuplicates@auxDist[[All,1;;3]];
+posdistecc=Flatten[#,1]&/@Table[Position[auxDist[[posdup[[i]],4]],Max@auxDist[[posdup[[i]],4]]],{i,1,Length@posdup}];
+posdistecc=Flatten@Table[posdup[[i,posdistecc[[i]]]],{i,1,Length@posdup}];
+
+auxDist=auxDist[[posdistecc]];
+sxsdirout=sxsdirout[[posdistecc]];
+sxsdiroutaux=SortBy[Table[Join[{sxsdirout[[i]]},auxDist[[i]]],{i,1,Length@sxsdirout}],#[[2]]&];
+
+If[verbose,
+Print[Prepend[Table[ToString@#&/@sxsdiroutaux[[i]],{i,1,Length@sxsdiroutaux}],{"Case","q","\[Chi]1","\[Chi]2","D","e"}]//TableForm]];
+
+sxsdiroutaux[[All,1]],
+
+auxDist=Transpose[{Round[#&/@massratio,0.1],Round[Chop[#,10^(-2)],0.01]&/@spin1Dim,Round[Chop[#,10^(-2)],0.01]&/@spin2Dim,dist,eccentricity}];
+(*sxsdiroutaux=Table[Join[{sxsdirout[[i]]},auxDist[[i]]],{i,1,Length@sxsdirout}];*)
+sxsdiroutaux=SortBy[Table[Join[{sxsdirout[[i]]},auxDist[[i]]],{i,1,Length@sxsdirout}],#[[2]]&];
+If[verbose,
+Print[Prepend[Table[ToString@#&/@sxsdiroutaux[[i]],{i,1,Length@sxsdiroutaux}],{"Case","q","\[Chi]1","\[Chi]2","D","e"}]//TableForm]];
+
+sxsdiroutaux[[All,1]]]
+]
+
+
+SXSParClassification2[sxsdir_?ListQ,ClassStr_?ListQ,OptionsPattern[{"\[Epsilon]"->0.001,"HighSpin"->0.8,"UnRepeated"->False,"Verbose"->False}]]:=Module[{metafiles,metadata,
+orbitStr="number-of-orbits",dStr="initial-separation",mass1Str="relaxed-mass1",mass2Str="relaxed-mass2",spin1Str="relaxed-spin1",spin2Str="relaxed-spin1",
+STTOV="relaxed-spin2",eccStr="relaxed-eccentricity",spin1Dim,spin2Dim,mass1,mass2,massratio,eccentricity,dist,orbit,select,pos,condition,A1,A2,precvalue,precvalueNorm,\[Epsilon],
+spin1Norm,spin2Norm,highspin,spintest,\[Chi]eff,sxsdirout,spinz,spinzDiff,auxDist,posdup,posdupDist,posdistecc,unrepeated,verbose,sxsdiroutaux,precvalue1,precvalue2,
+precvalueNorm1,precvalueNorm2,parmatrix,myindex},
+
+Print["Classification Input Variables. Examples: {{'MassRatio', '0.99<#<1.1'}},{{'Distance', '#>16'}},{{'Orbits', '#>25'}},{{'Precessing'}},
+{{'Non-Precessing'}},{{'High-Spin'}},{{'\[Chi]eff','#>0.6'}},{{'\[Chi]1','#>0.6'}},{{'\[Chi]2','#>0.6'}},{{'Unequal'}}"];
+Print["Take care! Some of the sxs file names are not consistent with the metadata files"];
+
+
+
+(* Useful function to detect the duplicates *)
+positionDuplicates[listaux_]:=GatherBy[Range@Length[listaux],listaux[[#]]&];
+
+sxsdirout=sxsdir;
+
+\[Epsilon]=OptionValue["\[Epsilon]"];
+highspin=OptionValue["HighSpin"];
+unrepeated=OptionValue["UnRepeated"];
+verbose=OptionValue["Verbose"];
+
+
+metafiles=Flatten[FileNames["metadata.txt",#,4]&/@sxsdirout,1];
+metadata=SXSMetaFilesToRules[#]&/@metafiles;
+
+
+mass1=Flatten@((mass1Str/.#)&/@metadata);
+mass2=Flatten@((mass2Str/.#)&/@metadata);
+
+massratio=mass1/mass2;
+dist=Flatten@((dStr/.#)&/@metadata);
+orbit=Flatten@((orbitStr/.#)&/@metadata);
+spin1Dim=((spin1Str/.#)&/@metadata)/(mass1*mass1);
+spin2Dim=((spin2Str/.#)&/@metadata)/(mass2*mass2);
+\[Chi]eff=massratio/(1.+massratio)*spin1Dim +1./(1+massratio)*spin2Dim;
+spinzDiff=Abs[(#[[2]]-#[[1]])&/@Transpose[{TakeColumn[spin1Dim,3],TakeColumn[spin2Dim,3]}]];
+A1=(1+3. massratio/(4.));
+A2=(1+3. /(4.*massratio) );
+eccentricity=Flatten[(eccStr/.#)&/@metadata];
+precvalue1=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1);
+precvalue2=(#)\[Cross]{0,0,1}&/@((spin2Dim)A2);
+precvalueNorm1=Norm[#]&/@precvalue1;
+precvalueNorm2=Norm[#]&/@precvalue2;
+precvalueNorm=precvalueNorm1^2+precvalueNorm2^2;
+spin1Norm=Norm[#]&/@spin1Dim;
+spin2Norm=Norm[#]&/@spin2Dim;
+
+parmatrix=Transpose[{massratio,dist,orbit,precvalueNorm,spinzDiff,spin1Norm,spin2Norm,\[Chi]eff,spin1Dim,spin2Dim,eccentricity,sxsdirout}];
+
+condition=ClassStr[[All,1]];
+select=Table[If[Length@ClassStr[[i]]==2,ToExpression@(ClassStr[[i,2]]),"Null"],{i,1,Length@ClassStr}];
+
+Do[
+
+Which[condition[[i]]== "MassRatio",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=1;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+condition[[i]]== "Distance",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=2;
+parmatrix=Select[parmatrix,Evaluate[StringReplace[select[[i]],"#"->ToString@(#[[myindex]])&]]];,
+
+condition[[i]]== "Orbits",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=3;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+condition[[i]]== "Non-Precessing",
+
+myindex=4;
+
+parmatrix=Select[parmatrix,#[[myindex]]<\[Epsilon]&];,
+
+condition[[i]]== "Unequal",
+
+myindex=5;
+parmatrix=Select[parmatrix,#[[myindex]]>\[Epsilon]&];,
+
+condition[[i]]== "Precessing",
+
+myindex=6;
+parmatrix=Select[parmatrix,#[[myindex]]>=\[Epsilon]&];,
+
+condition[[i]]== "High-Spin",
+
+myindex=7;
+parmatrix=Select[parmatrix,#[[myindex]]>=highspin& ||#[[myindex+1]]>=highspin& ];,
+
+condition[[i]]== "\[Chi]eff",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=8;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+condition[[i]]== "\[Chi]1",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=9;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+condition[[i]]== "\[Chi]2",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=10;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+ True,
+Print[Style["Wrong input",Bold,Red,16]];
+Break[];
+];
+,{i,1,Length@ClassStr}];
+
+If[unrepeated,
+
+Print["Taking among the repeated cases only those with lower eccentricity and larger D (just in case ei=ej)"];
+
+(* Selecting Case with lower e *)
+auxDist=Transpose[{Round[#&/@parmatrix[[All,1]],0.1],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,9]],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,10]],parmatrix[[All,2]],parmatrix[[All,11]]}];
+posdup=positionDuplicates@auxDist[[All,1;;3]];
+posdistecc=Flatten[#,1]&/@Table[Position[auxDist[[posdup[[i]],5]],Min@auxDist[[posdup[[i]],5]]],{i,1,Length@posdup}];
+posdistecc=Flatten@Table[posdup[[i,posdistecc[[i]]]],{i,1,Length@posdup}];
+parmatrix=parmatrix[[posdistecc]];
+
+(* Selecting Case with larger D *)
+auxDist=auxDist[[posdistecc]];
+posdup=positionDuplicates@auxDist[[All,1;;3]];
+posdistecc=Flatten[#,1]&/@Table[Position[auxDist[[posdup[[i]],4]],Max@auxDist[[posdup[[i]],4]]],{i,1,Length@posdup}];
+posdistecc=Flatten@Table[posdup[[i,posdistecc[[i]]]],{i,1,Length@posdup}];
+
+auxDist=auxDist[[posdistecc]];
+parmatrix=parmatrix[[posdistecc]];
+
+parmatrix=SortBy[parmatrix,#[[1]]&];
+sxsdiroutaux=Transpose[{#&/@parmatrix[[All,12]],Round[#&/@parmatrix[[All,1]],0.1],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,9]],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,10]],parmatrix[[All,2]],parmatrix[[All,11]]}];
+
+If[verbose,
+Print[Prepend[Table[ToString@#&/@sxsdiroutaux[[i]],{i,1,Length@sxsdiroutaux}],{"Case","q","\[Chi]1","\[Chi]2","D","e"}]//TableForm]];
+
+parmatrix[[All,12]],
+
+sxsdiroutaux=Transpose[{#&/@parmatrix[[All,12]],Round[#&/@parmatrix[[All,1]],0.1],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,9]],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,10]],parmatrix[[All,2]],parmatrix[[All,11]]}];
+
+(*sxsdiroutaux=SortBy[Table[Join[{sxsdirout[[i]]},auxDist[[i]]],{i,1,Length@sxsdirout}],#[[2]]&];*)
+If[verbose,
+Print[Prepend[Table[ToString@#&/@sxsdiroutaux[[i]],{i,1,Length@sxsdiroutaux}],{"Case","q","\[Chi]1","\[Chi]2","D","e"}]//TableForm]];
+
+parmatrix[[All,12]]]
+]
+
+
+RITParClassification[ritdir_?ListQ,ClassStr_?ListQ,OptionsPattern[{"\[Epsilon]"->0.001,"HighSpin"->0.8,"UnRepeated"->False,"Verbose"->False}]]:=Module[{metafiles,metadata,
+orbitStr="number-of-cycles-22",dStr="initial-separation",mass1Str="initial-mass1",mass2Str="initial-mass2",spin1x="initial-bh-chi1x",spin1y="initial-bh-chi1y",spin1z="initial-bh-chi1z",
+spin2x="initial-bh-chi2x",spin2y="initial-bh-chi2y",spin2z="initial-bh-chi2z",eccStr="eccentricity",spin1Dim,spin2Dim,mass1,mass2,massratio,eccentricity,dist,orbit,select,pos,condition,A1,A2,precvalue,precvalueNorm,\[Epsilon],
+spin1Norm,spin2Norm,highspin,spintest,\[Chi]eff,ritdirout,spinz,spinzDiff,auxDist,posdup,posdupDist,posdistecc,unrepeated,verbose,ritdiroutaux,precvalue1,precvalue2,precvalueNorm1,precvalueNorm2},
+
+Print["Classification Input Variables. Examples: {{'MassRatio', '0.99<#<1.1'}},{{'Distance', '#>16'}},{{'Orbits', '#>25'}},{{'Precessing'}},
+{{'Non-Precessing'}},{{'High-Spin'}},{{'\[Chi]eff','#>0.6'}},{{'\[Chi]1','#>0.6'}},{{'\[Chi]2','#>0.6'}},{{'Unequal'}}"];
+Print["Take care! Some of the rit file names are not consistent with the metadata files"];
+Print["The spin definition is consitent with 'initial-spin' values and not relaxed ones"];
+
+(* Useful function to detect the duplicates *)
+positionDuplicates[listaux_]:=GatherBy[Range@Length[listaux],listaux[[#]]&];
+
+ritdirout=ritdir;
+
+\[Epsilon]=OptionValue["\[Epsilon]"];
+highspin=OptionValue["HighSpin"];
+unrepeated=OptionValue["UnRepeated"];
+verbose=OptionValue["Verbose"];
+
+
+metafiles=Flatten[FileNames["Metadata",#,2]&/@ritdirout,1];
+metadata=RITMetaFilesToRules[#]&/@metafiles;
+
+mass1=Flatten@((mass1Str/.#)&/@metadata);
+mass2=Flatten@((mass2Str/.#)&/@metadata);
+
+massratio=mass1/mass2;
+dist=Flatten@((dStr/.#)&/@metadata);
+orbit=Flatten@((orbitStr/.#)&/@metadata);
+spin1Dim=(({spin1x,spin1y,spin1z}/.#)&/@metadata)(*/(mass1*mass1)*); (* In RIT the spin is already adimensional *)
+spin2Dim=(({spin2x,spin2y,spin2z}/.#)&/@metadata)(*/(mass2*mass2)*);
+spin1Dim=Flatten[#,1]&/@spin1Dim;
+spin2Dim=Flatten[#,1]&/@spin2Dim;
+Do[ (* This is to set to 0 ths x and y spin components for aligned cases *)
+ Do[
+ If[Not@NumberQ[spin1Dim[[i,j]]],spin1Dim[[i,j]]=0];
+ If[Not@NumberQ[spin2Dim[[i,j]]],spin2Dim[[i,j]]=0];
+ ,{j,1,2}];
+,{i,Length@metadata}];
+A1=(1+3 massratio/(4.));
+A2=(1+3 /(4.*massratio) );
+\[Chi]eff=massratio/(1.+massratio)*spin1Dim +1./(1+massratio)*spin2Dim;
+eccentricity=Flatten[(eccStr/.#)&/@metadata];
+
+spinz=Transpose[{TakeColumn[spin1Dim,3],TakeColumn[spin2Dim,3]}];
+spinzDiff=Abs[(#[[2]]-#[[1]])&/@spinz];
+
+condition=ClassStr[[All,1]];
+select=Table[If[Length@ClassStr[[i]]==2,ToExpression@(ClassStr[[i,2]]),"Null"],{i,1,Length@ClassStr}];
+
+pos=Table[i,{i,1,Length@ritdirout}];
+
+Do[
+
+Which[condition[[i]]== "MassRatio",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[massratio,_?(Evaluate[select[[i]]]&)];
+
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+condition[[i]]== "Distance",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[ritdirout=ritdirout[[pos]];,_?(Evaluate[select[[i]]]&)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+condition[[i]]== "Orbits",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[orbit,_?(Evaluate[select[[i]]]&)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+condition[[i]]== "Non-Precessing",
+
+(*precvalue=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1+(spin2Dim)A2);*)
+precvalue1=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1);
+precvalue2=(#)\[Cross]{0,0,1}&/@((spin2Dim)A2);
+precvalueNorm1=Norm[#]&/@precvalue1;
+precvalueNorm2=Norm[#]&/@precvalue2;
+precvalueNorm=precvalueNorm1^2+precvalueNorm2^2;
+
+pos=Flatten@Position[precvalueNorm,_?(#<\[Epsilon] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+condition[[i]]== "Unequal",
+
+pos=Flatten@Position[spinzDiff,_?(#>\[Epsilon] &)];
+
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+condition[[i]]== "Precessing",
+
+precvalue1=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1);
+precvalue2=(#)\[Cross]{0,0,1}&/@((spin2Dim)A2);
+precvalueNorm1=Norm[#]&/@precvalue1;
+precvalueNorm2=Norm[#]&/@precvalue2;
+precvalueNorm=precvalueNorm1^2+precvalueNorm2^2;
+
+(*precvalue=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1+(spin2Dim)A2);*)
+
+pos=Flatten@Position[precvalueNorm,_?(#>\[Epsilon] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+condition[[i]]== "High-Spin",
+
+spin1Norm=Norm[#]&/@spin1Dim;
+spin2Norm=Norm[#]&/@spin2Dim;
+
+spintest=Table[If[Abs@spin1Norm[[i]]>=highspin || Abs@spin2Norm[[i]]>=highspin,True,False],{i,1,Length@spin1Norm}];
+pos=Flatten@Position[spintest,True];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+condition[[i]]== "\[Chi]eff",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[Norm[#]&/@\[Chi]eff,_?(Evaluate[select[[i]]] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+condition[[i]]== "\[Chi]1",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[Norm[#]&/@spin1Dim,_?(Evaluate[select[[i]]] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+condition[[i]]== "\[Chi]2",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[Norm[#]&/@spin2Dim,_?(Evaluate[select[[i]]] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+
+
+condition[[i]]== "relaxed-eccentricity",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+
+pos=Flatten@Position[eccentricity,_?(Evaluate[select[[i]]] &)];
+massratio=massratio[[pos]];
+dist=dist[[pos]];
+orbit=orbit[[pos]];
+spin1Dim=spin1Dim[[pos]];
+spin2Dim=spin2Dim[[pos]];
+A1=A1[[pos]];
+A2=A2[[pos]];
+spinzDiff=spinzDiff[[pos]];
+eccentricity=eccentricity[[pos]];
+\[Chi]eff=\[Chi]eff[[pos]];
+
+ritdirout=ritdirout[[pos]];,
+ True,
+Print[Style["Wrong input",Bold,Red,16]];
+Break[];
+];
+,{i,1,Length@ClassStr}];
+
+
+If[unrepeated,
+
+Print["Taking among the repeated cases only those with lower eccentricity and larger D (just in case ei=ej)"];
+
+(* Selecting Case with lower e *)
+auxDist=Transpose[{Round[#&/@massratio,0.1],Round[Chop[#,10^(-2)],0.01]&/@spin1Dim,Round[Chop[#,10^(-2)],0.01]&/@spin2Dim,dist,eccentricity}];
+posdup=positionDuplicates@auxDist[[All,1;;3]];
+posdistecc=Flatten[#,1]&/@Table[Position[auxDist[[posdup[[i]],5]],Min@auxDist[[posdup[[i]],5]]],{i,1,Length@posdup}];
+posdistecc=Flatten@Table[posdup[[i,posdistecc[[i]]]],{i,1,Length@posdup}];
+ritdirout=ritdirout[[posdistecc]];
+
+(* Selecting Case with larger D *)
+auxDist=auxDist[[posdistecc]];
+posdup=positionDuplicates@auxDist[[All,1;;3]];
+posdistecc=Flatten[#,1]&/@Table[Position[auxDist[[posdup[[i]],4]],Max@auxDist[[posdup[[i]],4]]],{i,1,Length@posdup}];
+posdistecc=Flatten@Table[posdup[[i,posdistecc[[i]]]],{i,1,Length@posdup}];
+
+auxDist=auxDist[[posdistecc]];
+ritdirout=ritdirout[[posdistecc]];
+ritdiroutaux=SortBy[Table[Join[{ritdirout[[i]]},auxDist[[i]]],{i,1,Length@ritdirout}],#[[2]]&];
+
+If[verbose,
+Print[Prepend[Table[ToString@#&/@ritdiroutaux[[i]],{i,1,Length@ritdiroutaux}],{"Case","q","\[Chi]1","\[Chi]2","D","e"}]//TableForm]];
+
+ritdiroutaux[[All,1]],
+
+auxDist=Transpose[{Round[#&/@massratio,0.1],Round[Chop[#,10^(-2)],0.01]&/@spin1Dim,Round[Chop[#,10^(-2)],0.01]&/@spin2Dim,dist,eccentricity}];
+(*ritdiroutaux=Table[Join[{ritdirout[[i]]},auxDist[[i]]],{i,1,Length@ritdirout}];*)
+ritdiroutaux=SortBy[Table[Join[{ritdirout[[i]]},auxDist[[i]]],{i,1,Length@ritdirout}],#[[2]]&];
+If[verbose,
+Print[Prepend[Table[ToString@#&/@ritdiroutaux[[i]],{i,1,Length@ritdiroutaux}],{"Case","q","\[Chi]1","\[Chi]2","D","e"}]//TableForm]];
+
+ritdiroutaux[[All,1]]]
+]
+
+
+ritParClassification2[ritdir_?ListQ,ClassStr_?ListQ,OptionsPattern[{"\[Epsilon]"->0.001,"HighSpin"->0.8,"UnRepeated"->False,"Verbose"->False}]]:=Module[{metafiles,metadata,
+orbitStr="number-of-orbits",dStr="initial-separation",mass1Str="relaxed-mass1",mass2Str="relaxed-mass2",spin1Str="relaxed-spin1",
+spin2Str="relaxed-spin2",eccStr="relaxed-eccentricity",spin1Dim,spin2Dim,mass1,mass2,massratio,eccentricity,dist,orbit,select,pos,condition,A1,A2,precvalue,precvalueNorm,\[Epsilon],
+spin1Norm,spin2Norm,highspin,spintest,\[Chi]eff,ritdirout,spinz,spinzDiff,auxDist,posdup,posdupDist,posdistecc,unrepeated,verbose,ritdiroutaux,precvalue1,precvalue2,
+precvalueNorm1,precvalueNorm2,parmatrix,myindex},
+
+Print["Classification Input Variables. Examples: {{'MassRatio', '0.99<#<1.1'}},{{'Distance', '#>16'}},{{'Orbits', '#>25'}},{{'Precessing'}},
+{{'Non-Precessing'}},{{'High-Spin'}},{{'\[Chi]eff','#>0.6'}},{{'\[Chi]1','#>0.6'}},{{'\[Chi]2','#>0.6'}},{{'Unequal'}}"];
+Print["Take care! Some of the rit file names are not consistent with the metadata files"];
+
+(* Useful function to detect the duplicates *)
+positionDuplicates[listaux_]:=GatherBy[Range@Length[listaux],listaux[[#]]&];
+
+ritdirout=ritdir;
+
+\[Epsilon]=OptionValue["\[Epsilon]"];
+highspin=OptionValue["HighSpin"];
+unrepeated=OptionValue["UnRepeated"];
+verbose=OptionValue["Verbose"];
+
+
+metafiles=Flatten[FileNames["metadata.txt",#,4]&/@ritdirout,1];
+metadata=ritMetaFilesToRules[#]&/@metafiles;
+
+
+mass1=Flatten@((mass1Str/.#)&/@metadata);
+mass2=Flatten@((mass2Str/.#)&/@metadata);
+
+massratio=mass1/mass2;
+dist=Flatten@((dStr/.#)&/@metadata);
+orbit=Flatten@((orbitStr/.#)&/@metadata);
+spin1Dim=((spin1Str/.#)&/@metadata)/(mass1*mass1);
+spin2Dim=((spin2Str/.#)&/@metadata)/(mass2*mass2);
+\[Chi]eff=massratio/(1.+massratio)*spin1Dim +1./(1+massratio)*spin2Dim;
+spinzDiff=Abs[(#[[2]]-#[[1]])&/@Transpose[{TakeColumn[spin1Dim,3],TakeColumn[spin2Dim,3]}]];
+A1=(1+3. massratio/(4.));
+A2=(1+3. /(4.*massratio) );
+eccentricity=Flatten[(eccStr/.#)&/@metadata];
+precvalue1=(#)\[Cross]{0,0,1}&/@((spin1Dim)A1);
+precvalue2=(#)\[Cross]{0,0,1}&/@((spin2Dim)A2);
+precvalueNorm1=Norm[#]&/@precvalue1;
+precvalueNorm2=Norm[#]&/@precvalue2;
+precvalueNorm=precvalueNorm1^2+precvalueNorm2^2;
+spin1Norm=Norm[#]&/@spin1Dim;
+spin2Norm=Norm[#]&/@spin2Dim;
+
+parmatrix=Transpose[{massratio,dist,orbit,precvalueNorm,spinzDiff,spin1Norm,spin2Norm,\[Chi]eff,spin1Dim,spin2Dim,eccentricity,ritdirout}];
+
+condition=ClassStr[[All,1]];
+select=Table[If[Length@ClassStr[[i]]==2,ToExpression@(ClassStr[[i,2]]),"Null"],{i,1,Length@ClassStr}];
+
+Do[
+
+Which[condition[[i]]== "MassRatio",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=1;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+condition[[i]]== "Distance",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=2;
+parmatrix=Select[parmatrix,Evaluate[StringReplace[select[[i]],"#"->ToString@(#[[myindex]])&]]];,
+
+condition[[i]]== "Orbits",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=3;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+condition[[i]]== "Non-Precessing",
+
+myindex=4;
+
+parmatrix=Select[parmatrix,#[[myindex]]<\[Epsilon]&];,
+
+condition[[i]]== "Unequal",
+
+myindex=5;
+parmatrix=Select[parmatrix,#[[myindex]]>\[Epsilon]&];,
+
+condition[[i]]== "Precessing",
+
+myindex=6;
+parmatrix=Select[parmatrix,#[[myindex]]>=\[Epsilon]&];,
+
+condition[[i]]== "High-Spin",
+
+myindex=7;
+parmatrix=Select[parmatrix,#[[myindex]]>=highspin& ||#[[myindex+1]]>=highspin& ];,
+
+condition[[i]]== "\[Chi]eff",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=8;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+condition[[i]]== "\[Chi]1",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=9;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+condition[[i]]== "\[Chi]2",
+
+If[Length@ClassStr[[i]]!= 2,Print["Wrong input"];Break[]];
+myindex=10;
+pos=Flatten@Position[parmatrix[[All,myindex]],_?(Evaluate[select[[i]]]&)];
+parmatrix=parmatrix[[pos]];,
+
+ True,
+Print[Style["Wrong input",Bold,Red,16]];
+Break[];
+];
+,{i,1,Length@ClassStr}];
+
+
+If[unrepeated,
+
+Print["Taking among the repeated cases only those with lower eccentricity and larger D (just in case ei=ej)"];
+
+(* Selecting Case with lower e *)
+auxDist=Transpose[{Round[#&/@parmatrix[[All,1]],0.1],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,9]],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,10]],parmatrix[[All,2]],parmatrix[[All,11]]}];
+posdup=positionDuplicates@auxDist[[All,1;;3]];
+posdistecc=Flatten[#,1]&/@Table[Position[auxDist[[posdup[[i]],5]],Min@auxDist[[posdup[[i]],5]]],{i,1,Length@posdup}];
+posdistecc=Flatten@Table[posdup[[i,posdistecc[[i]]]],{i,1,Length@posdup}];
+parmatrix=parmatrix[[posdistecc]];
+
+(* Selecting Case with larger D *)
+auxDist=auxDist[[posdistecc]];
+posdup=positionDuplicates@auxDist[[All,1;;3]];
+posdistecc=Flatten[#,1]&/@Table[Position[auxDist[[posdup[[i]],4]],Max@auxDist[[posdup[[i]],4]]],{i,1,Length@posdup}];
+posdistecc=Flatten@Table[posdup[[i,posdistecc[[i]]]],{i,1,Length@posdup}];
+
+auxDist=auxDist[[posdistecc]];
+parmatrix=parmatrix[[posdistecc]];
+
+parmatrix=SortBy[parmatrix,#[[1]]&];
+ritdiroutaux=Transpose[{#&/@parmatrix[[All,12]],Round[#&/@parmatrix[[All,1]],0.1],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,9]],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,10]],parmatrix[[All,2]],parmatrix[[All,11]]}];
+
+If[verbose,
+Print[Prepend[Table[ToString@#&/@ritdiroutaux[[i]],{i,1,Length@ritdiroutaux}],{"Case","q","\[Chi]1","\[Chi]2","D","e"}]//TableForm]];
+
+parmatrix[[All,12]],
+
+ritdiroutaux=Transpose[{#&/@parmatrix[[All,12]],Round[#&/@parmatrix[[All,1]],0.1],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,9]],Round[Chop[#,10^(-2)],0.01]&/@parmatrix[[All,10]],parmatrix[[All,2]],parmatrix[[All,11]]}];
+
+(*ritdiroutaux=SortBy[Table[Join[{ritdirout[[i]]},auxDist[[i]]],{i,1,Length@ritdirout}],#[[2]]&];*)
+If[verbose,
+Print[Prepend[Table[ToString@#&/@ritdiroutaux[[i]],{i,1,Length@ritdiroutaux}],{"Case","q","\[Chi]1","\[Chi]2","D","e"}]//TableForm]];
+
+parmatrix[[All,12]]]
+]
+
+
+BAMStringParameter[directory_,parametername_]:=Module[{file,dirname,content},
+
+file = directory;
+
+ If[TrueQ[FileType@directory == Directory],
+ file=ZippedOrUnzipped@ParfileInDirectory[directory];
+];
+
+Print["BAMStringParameter identified parameter file ",file];
+
+If[FileType@file==File,content=StringSplit[Import[file,"String"],EndOfLine],content={}];
+If[content=={},Print["parameter file does not exist"],content=Map[StringCases[#,StartOfLine~~parametername~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x__~~WhitespaceCharacter...~~EndOfLine->x]&,content];
+content=First@Flatten@content;
+content=First@StringSplit[content,EndOfLine];];
+content
+];
+
+
+BAMNumberParameter[directory_,parametername_]:=Module[{file,dirname,content},
+
+file = directory;
+
+If[TrueQ[FileType@directory == Directory],
+ file=ZippedOrUnzipped@ParfileInDirectory[directory];
+];
+
+Print["BAMStringParameter identified parameter file ",file];
+
+If[FileType@file==File,content=StringSplit[Import[file,"String"],EndOfLine],content={}];
+
+Print["Read ",Length@content, " parameter file entries"];
+
+If[content== {},
+Print["parameter file does not exist"],
+content=Flatten@Map[StringCases[#,parametername~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x:NumberString-> x]&, content];
+content=Map[ToExpression,content];
+
+content=First@Select[content,NumberQ]
+];
+content
+];
+
+
+BAMNumberParameterInFile[file_,parametername_,default_]:=Module[{dirname,content},
+
+If[FileType@file==File,content=StringSplit[Import[file,"String"],EndOfLine],content={}];
+
+If[content== {},
+Print["parameter file does not exist"],
+content=Flatten@Map[StringCases[#,parametername~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x:NumberString-> x]&, content];
+content=Map[ToExpression,content];
+
+If[content == {},
+ content = default,
+ content=First@Select[content,NumberQ]
+]
+];
+content
+];
+
+
+BAMNumberParameterInFile[file_,parametername_]:=BAMNumberParameterInFile[file,parametername,Indeterminate]
+
+
+BAMNumberParametersInFile[file_,parametername_]:=Module[{dirname,content,x},
+
+If[FileType@file==File,content=StringSplit[Import[file,"String"],EndOfLine],content={}];
+
+If[content== {},
+Print["parameter file does not exist"],
+content=Flatten@Map[StringCases[#,parametername~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x__..-> x]&, content];
+
+content=Map[StringSplit[#,"#"]&,content];
+content=Map[First,content];
+content=StringReplace[content,Whitespace-> ","];
+content=Map[StringReplace[#, ","~~EndOfString->""]&,content];
+content=Map["{"<>#<>"}"&,content];
+content=Map[ToExpression,content][[1]]
+];
+content
+];
+
+
+BAMNumberParameters[directory_,parametername_]:=Module[{file,dirname,content,x},
+
+file=ParfileInDirectory[directory];
+file=ZippedOrUnzipped@file;
+Print["Identified parameter file ",file];
+If[FileType@file==File,content=StringSplit[Import[file,"String"],EndOfLine],content={}];
+
+Print["Read ",Length@content, " parameter file entries"];
+
+If[content== {},
+Print["parameter file does not exist"],
+content=Flatten@Map[StringCases[#,parametername~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x__..-> x]&, content];
+
+content=Map[StringSplit[#,"#"]&,content];
+content=Map[First,content];
+content=StringReplace[content,Whitespace-> ","];
+content=Map[StringReplace[#, ","~~EndOfString->""]&,content];
+content=Map["{"<>#<>"}"&,content];
+content=Map[ToExpression,content][[1]]
+];
+content
+];
+
+
+PSIDHashedNumberParameter[file_,parametername_]:=Module[{content,x},
+
+ content = PSIDReadHeader[file];
+
+ If[content == {},
+ Print["psid file does not exist"],
+ content = Flatten@Map[StringCases[#,"# "~~parametername~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x:NumberString-> x]&, content];
+ content = Map[ToExpression,content];
+
+ content = First@Select[content,NumberQ]
+ ];
+ content
+];
+
+
+PSIDNumberParameter[file_,parametername_]:=Module[{content,x},
+
+ content = PSIDReadHeader[file];
+
+ If[content == {},
+ Print["psid file does not exist"],
+ content = Flatten@Map[StringCases[#,StartOfLine~~parametername~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x___-> x]&, content];
+ content = Map[StringToNumber,content];
+
+ content = First@Select[content,NumberQ]
+ ];
+ content
+];
+
+
+PSIDReadHeader[file_]:=Module[{content,psidStream,str},
+ (* only read the header of the psid file until the ID section starting with "data xx xx xx" *)
+
+ If[FileType@file == File,
+ psidStream = OpenRead[file];
+ content = {}; str = {};
+ While[True,
+ str = Read[psidStream, String];
+ If[StringMatchQ[str, RegularExpression["data[\\s\\d+]+"]],
+ Break[]
+ ];
+ AppendTo[content, str];
+ ];
+ Close[psidStream];
+ ,
+ content = {};
+ ];
+ content
+];
+
+
+PSIDReadData[file_]:=Module[{header,data,str,dims},
+ (* helper function to partition flat data *)
+ unflatten[e_,{d__?((IntegerQ[#]&&Positive[#])&)}]:= Fold[Partition,e,Take[{d},{-1,2,-1}]] /;(Length[e]===Times[d]);
+
+ data = {};
+ If[FileType@file == File,
+ psidStream = OpenRead[file];
+ header = {}; data={}; str = {};
+
+ (* read header *)
+ While[True,
+ str = Read[psidStream, String];
+ If[StringMatchQ[str, RegularExpression["data[\\s\\d+]+"]], Break[]];
+ AppendTo[header, str];
+ ];
+
+ (* get dimensions (nz,ny,nx) *)
+ dims = Reverse@ToExpression@StringCases[str, RegularExpression["\\d+"]];
+
+ (* read data *)
+ data = ReadList[psidStream,Real];
+
+ (* partition into array according to dimensions *)
+ data = unflatten[data, dims];
+ Close[psidStream];
+ ];
+
+ data
+];
+
+
+PSID2Rules[filename_?StringQ]:=Module[{M1,M2,x1,y1,z1,x2,y2,z2,px1,py1,pz1
+,px2,py2,pz2,s1x,s1y,s1z,s2x,s2y,s2z,mtot,sep,sepInM,prel,xrel,Madm,m1,m2},
+
+M1=PSIDHashedNumberParameter[filename,"M1"];
+M2=PSIDHashedNumberParameter[filename,"M2"];
+
+Madm=PSIDHashedNumberParameter[filename,"Madm"];
+
+m1=PSIDNumberParameter[filename,"bhmass1"];
+m2=PSIDNumberParameter[filename,"bhmass2"];
+
+x1=PSIDNumberParameter[filename,"bhx1"];
+y1=PSIDNumberParameter[filename,"bhy1"];
+z1=PSIDNumberParameter[filename,"bhz1"];
+
+x2=PSIDNumberParameter[filename,"bhx2"];
+y2=PSIDNumberParameter[filename,"bhy2"];
+z2=PSIDNumberParameter[filename,"bhz2"];
+
+px1=PSIDNumberParameter[filename,"bhpx1"];
+py1=PSIDNumberParameter[filename,"bhpy1"];
+pz1=PSIDNumberParameter[filename,"bhpz1"];
+
+px2=PSIDNumberParameter[filename,"bhpx2"];
+py2=PSIDNumberParameter[filename,"bhpy2"];
+pz2=PSIDNumberParameter[filename,"bhpz2"];
+
+s1x=PSIDNumberParameter[filename,"bhsx1"];
+s1y=PSIDNumberParameter[filename,"bhsy1"];
+s1z=PSIDNumberParameter[filename,"bhsz1"];
+
+s2x=PSIDNumberParameter[filename,"bhsx2"];
+s2y=PSIDNumberParameter[filename,"bhsy2"];
+s2z=PSIDNumberParameter[filename,"bhsz2"];
+
+mtot=M1+M2;
+
+sep={x1,y1,z1}-{x2,y2,z2};
+sep=Sqrt[sep.sep];
+sepInM = sep/mtot;
+
+prel={px1,py1,pz1}-{px2,py2,pz2};
+xrel={x1,y1,z1}-{x2,y2,z2};
+
+
+{"M1"->M1,"M2"->M2,"M"->mtot,
+"x1"->x1,"y1"->y1,"z1"->z1,"px1"->px1,"py1"->py1,"pz1"->pz1,"s1x"->s1x,"s1y"->s1y,"s1z"->s1z,
+"x2"->x2,"y2"->y2,"z2"->z2,"px2"->px2,"py2"->py2,"pz2"->pz2,"s2x"->s2x,"s2y"->s2y,"s2z"->s2z,
+"D[M]"->sepInM, "Madm"-> Madm, "BHMassParam1" -> m1, "BHMassParam2" -> m2
+}
+]
+
+
+NMovingLevels[parRules_]:="amr_lmax"-"amr_move_lcube"/.parRules
+
+
+CactusThornsAvailable[cactusdir_]:=Module[{arrDir,arrangements,thorns,allThorns},
+
+arrDir=FileNameJoin[{cactusdir,"arrangements"}];
+arrangements=FileNames["*",arrDir];
+arrangements=FileNameTake[#,-2]& /@Select[arrangements,FileType@#==Directory&];
+
+
+thorns=FileNames["*",arrDir,2];
+thorns=FileNameTake[#,-2]& /@ Select[thorns,FileType@#==Directory&];
+allThorns=Select[Complement[thorns,arrangements],Not@StringMatchQ[#,".*"]&];
+
+
+{"Arrangements"-> arrangements, "Thorns"-> allThorns}
+];
+
+
+NormalizeCactusParfile[parfile_,cactusDir_,OptionsPattern[
+{"ThornListOutputFile"-> "","ParameterOutputFile"-> ""}]]:=Module[{temp,arrangements,allThorns,
+import,activeThorns,flatThornList,fullNameThorns,
+outThornList,outcontent,content,i,thorn,outparfile},
+
+outThornList = OptionValue["ThornListOutputFile"];
+outparfile = OptionValue["ParameterOutputFile"];
+
+temp=CactusThornsAvailable@cactusDir;
+arrangements = "Arrangements"/.temp;
+allThorns="Thorns"/.temp;
+
+import = Import[parfile,"String"];
+import=StringReplace[import,{
+"\n "-> " ",
+"\n"~~Whitespace...~~"\""->"\"",
+ "\n"~~Whitespace...~~"="->"\""," "...~~"="->" ="
+}];
+
+
+import=Flatten@StringSplit[StringSplit[import,EndOfLine],"\n"];
+import=Map[StringReplace[#,WhitespaceCharacter...~~x__~~WhitespaceCharacter...~~"#"~~y___->x]&,import];
+import=Map[StringReplace[#,WhitespaceCharacter...~~x__->x]&,import];
+import=Map[StringReplace[#,WhitespaceCharacter...~~"#"~~x___->""]&,import];
+import=Map[StringReplace[#,"\t"->" "]&,import];
+import=Select[import,StringLength@#>1&];
+
+activeThorns=Select[import,StringMatchQ[#,"*ActiveThorns*"]&];
+activeThorns=Map[StringReplace[#,
+ "ActiveThorns"~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x__->x]&,
+ activeThorns];
+activeThorns=Map[StringSplit[#," "]&,activeThorns];
+
+
+flatThornList=Sort@Union@(StringReplace[#,"\""-> ""]&/@Flatten@activeThorns);
+flatThornList=Select[flatThornList,# != ""& ];
+
+fullNameThorns=Flatten@Table[
+Select[allThorns,StringMatchQ[#,"*/"<>flatThornList[[i]]]&],{i,1,Length@flatThornList}];
+
+outcontent=StringJoin[#<>"\n"&/@fullNameThorns];
+
+If[outThornList!= "",
+ Print["Exporting thornlist to file ", outThornList];
+ Export[outThornList,outcontent,"Text"];
+];
+
+temp=Table[thorn=flatThornList[[i]]; {"\nActiveThorns = \""<>thorn<>"\"",
+ Sort@Union@Select[import,StringMatchQ[#,thorn<>"::*"]&]} ,{i,1,Length@flatThornList}];
+temp = Flatten@{"# thornlist created by NormalizeCactusParfile from file "<>parfile, temp};
+
+If[outThornList!= "",
+ Print["Exporting normalized parameters to file ", outparfile];
+ Export[outparfile,Flatten@temp,"Text"];
+];
+
+
+{"AvailableArrangements"-> arrangements,"AvailableThorns"-> allThorns,
+"ActiveThorns"-> activeThorns,"FullNameThorns"-> fullNameThorns,"Parameters"-> import,
+"NormalizedParfile"-> temp}
+];
+
+
+CompleteCactusParfile[parfile_,cactusDir_,OptionsPattern[
+{"ThornListOutputFile"-> "","ParameterOutputFile"-> ""}]]:=Module[{temp,arrangements,allThorns,
+import,activeThorns,flatThornList,fullNameThorns,
+outThornList,outcontent,content,i,thorn,outparfile},
+
+outThornList = OptionValue["ThornListOutputFile"];
+outparfile = OptionValue["ParameterOutputFile"];
+
+temp=CactusThornsAvailable@cactusDir;
+arrangements = "Arrangements"/.temp;
+allThorns="Thorns"/.temp;
+
+import = Import[parfile,"String"];
+import=StringReplace[import,{
+"\n "-> " ",
+"\n"~~Whitespace...~~"\""->"\"",
+ "\n"~~Whitespace...~~"="->"\""," "...~~"="->" ="
+}];
+
+
+import=Flatten@StringSplit[StringSplit[import,EndOfLine],"\n"];
+import=Map[StringReplace[#,WhitespaceCharacter...~~x__~~WhitespaceCharacter...~~"#"~~y___->x]&,import];
+import=Map[StringReplace[#,WhitespaceCharacter...~~x__->x]&,import];
+import=Map[StringReplace[#,WhitespaceCharacter...~~"#"~~x___->""]&,import];
+import=Map[StringReplace[#,"\t"->" "]&,import];
+import=Select[import,StringLength@#>1&];
+
+(* *)
+activeThorns=Select[import,StringMatchQ[#,"*ActiveThorns*"]&];
+activeThorns=Map[StringReplace[#,
+ "ActiveThorns"~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x__->x]&,
+ activeThorns];
+activeThorns=Map[StringSplit[#," "]&,activeThorns];
+
+
+flatThornList=Sort@Union@(StringReplace[#,"\""-> ""]&/@Flatten@activeThorns);
+flatThornList=Select[flatThornList,# != ""& ];
+
+fullNameThorns=Flatten@Table[
+Select[allThorns,StringMatchQ[#,"*/"<>flatThornList[[i]]]&],{i,1,Length@flatThornList}];
+
+outcontent=StringJoin[#<>"\n"&/@fullNameThorns];
+
+If[outThornList!= "",
+ Print["Exporting thornlist to file ", outThornList];
+ Export[outThornList,outcontent,"Text"];
+];
+
+
+temp=Table[thorn=flatThornList[[i]]; {"\nActiveThorns = \""<>thorn<>"\"",
+ Sort@Union@Select[import,StringMatchQ[#,thorn<>"::*"]&]} ,{i,1,Length@flatThornList}];
+temp = Flatten@{"# thornlist created by NormalizeCactusParfile from file "<>parfile, temp};
+
+If[outThornList!= "",
+ Print["Exporting normalized parameters to file ", outparfile];
+ Export[outparfile,Flatten@temp,"Text"];
+];
+
+
+{"AvailableArrangements"-> arrangements,"AvailableThorns"-> allThorns,
+"ActiveThorns"-> activeThorns,"FullNameThorns"-> fullNameThorns,"Parameters"-> import,
+"NormalizedParfile"-> temp}
+];
+
+
+SetParfileEntryValue[text_,key_,value_]:=
+StringReplace[text,key~~ws1:WhitespaceCharacter... ~~\!\(\*
+TagBox[
+StyleBox["\"\<=\>\"",
+ShowSpecialCharacters->False,
+ShowStringCharacters->True,
+NumberMarks->True],
+FullForm]\)~~ws2:WhitespaceCharacter...~~x__~~EndOfLine:> key<>ws1<>"="<>ws2<>ToString@value]
+
+
+SetParfileValue[text_,key_,value_]:=Module[{entry,temp,len,new,x,out},
+
+entry=StringCases[text,Shortest[key~~WhitespaceCharacter...~~"="~~WhitespaceCharacter...~~x___~~EndOfLine]];
+(* Print@entry; *)
+
+out = text;
+
+If[Length@entry > 0,
+ entry=Last@entry;
+
+ new = SetParfileEntryValue[entry,key,value];
+
+ If[StringQ@entry,
+ out = StringReplace[text,entry :> new];
+ ];
+];
+
+out
+];
+
+
+SetParfileVectorValue[text_,key_,component_,value_]:=Module[{entry,temp,len,new,s,x,out},
+s = "["~~WhitespaceCharacter...~~ ToString@component ~~WhitespaceCharacter...~~ "]";
+
+entry = StringCases[text,Shortest[key~~WhitespaceCharacter...~~ s ~~WhitespaceCharacter...~~"= "~~x__~~EndOfLine]];
+(* Print[entry]; *)
+
+out = text;
+
+If[Length@entry > 0,
+entry=Last@entry;
+
+s = "[" <> ToString@component <> "]";
+new = key <> s <> " = " <> ToString@value;
+
+If[StringQ@entry,
+ out = StringReplace[text,entry -> new];
+];
+];
+
+out
+];
+
+
+CreateDataReduceDirectory[dirname_]:=CreateDirectory[dirname<>"/DataReduce"]
+
+
+CreateDataReduceDirectory[reduceroot_,dirname_]:=CreateDirectory[reduceroot<>"/"<>LastInPath@dirname<>"/DataReduce"]
+
+
+LocateMode[modeDir_,lmode_,mmode_]:=Module[{searchString,modeFiles,file,radii,outerradius,level},
+
+searchString="hmod.r*.l*.l"<>ToString@lmode<>".m"<>ToString@mmode<>"*";
+Print["Searching for files matching ", searchString];
+modeFiles=FileNames[searchString,modeDir];
+
+Print["Found mode files: ", modeFiles];
+
+level=Union@Map[IntegerPart,Map[levelFun,modeFiles]];
+Print["Available refinement levels: ", level];
+
+radii=Sort@TakeColumn[level,1];
+level=Sort@TakeColumn[level,2];
+
+outerradius={ToString@Last@radii,ToString@First@level};
+
+file="hmod.r"<>outerradius[[1]]<>".l"<>outerradius[[2]]<>".l"<>ToString@lmode<>".m"<>ToString@mmode;
+file=ZippedOrUnzipped[file];
+If[FileType@file!= File,Print["cannot find hmod file"];file="";];
+
+file
+];
+
+
+LocateModes[modeDir_,lmode_,mmode_]:=Module[{searchString,modeFiles,file,radii,outerradius,level,levelFun},
+
+searchString="hmod.r*.l*.l"<>ToString@lmode<>".m"<>ToString@mmode<>"*";
+Print["Searching for files matching ", searchString];
+FileNames[searchString,modeDir]
+];
+
+
+CopyL2mode[configStr_,modesdir_,reducedir_]:=Module[{command,modeFile,source,fname},
+modeFile=LocateMode[modesdir,2,2];
+Print["Called CopyL2mode with mode file ", modeFile];
+
+source=modesdir<>"/"<>modeFile;
+source=ZippedOrUnzipped@source;
+If[FileType@source==File,
+fname=Last@StringSplit[source,"/"];
+command="cp "<>source<>" "<>reducedir<>"/"<>configStr<>"_"<>fname;
+Print["Running command ",command];
+Run[Evaluate@command];,
+Print["ERROR: Could not find hmod modes file"];
+];
+
+source=ZippedOrUnzipped@StringReplace[source,"hmod"-> "psi3col"];
+If[FileType@source==File,
+fname=Last@StringSplit[source,"/"];
+command="cp "<>source<>" "<>reducedir<>"/"<>configStr<>"_"<>fname;
+Print["Running command ",command];
+Run[Evaluate@command];,
+Print["ERROR: Could not find psi4 modes file"];
+];
+];
+
+
+CopyL2modes[configStr_,modesdir_,reducedir_]:=Module[{command,modeFiles,modeFile,source,fname,i},
+modeFiles=LocateModes[modesdir,2,2];
+Print["Called CopyL2modes with mode files ", modeFiles];
+
+Do[
+source=modeFiles[[i]];
+
+If[FileType@source==File,
+fname=Last@StringSplit[source,"/"];
+command="cp "<>source<>" "<>reducedir<>"/"<>configStr<>"_"<>fname;
+Print["CopyL2modes running command ",command];
+Run[Evaluate@command];,
+Print["ERROR: Could not find hmod modes file"];
+];
+source=ZippedOrUnzipped@StringReplace[source,"hmod"-> "psi3col"];
+If[FileType@source==File,
+fname=Last@StringSplit[source,"/"];
+command="cp "<>source<>" "<>reducedir<>"/"<>configStr<>"_"<>fname;
+Print["CopyL2modes running command ",command];
+Run[Evaluate@command];,
+Print["ERROR: Could not find psi4 modes file"];
+];,{i,1,Length@modeFiles}];
+];
+
+
+CopyModes[configStr_,modesdir_,reducedir_,Lmode_,Mmode_]:=Module[{command,modeFiles,modeFile,source,fname,i},
+modeFiles=LocateModes[modesdir,Lmode,Mmode];
+Print["Called CopyModes with mode files ", modeFiles];
+
+Do[
+source=modeFiles[[i]];
+
+If[FileType@source==File,
+fname=Last@StringSplit[source,"/"];
+command="cp "<>source<>" "<>reducedir<>"/"<>configStr<>"_"<>fname;
+Print["CopyModes running command ",command];
+Run[Evaluate@command];,
+Print["ERROR: Could not find hmod modes file"];
+];
+source=ZippedOrUnzipped@StringReplace[source,"hmod"-> "psi3col"];
+If[FileType@source==File,
+fname=Last@StringSplit[source,"/"];
+command="cp "<>source<>" "<>reducedir<>"/"<>configStr<>"_"<>fname;
+Print["CopyModes running command ",command];
+Run[Evaluate@command];,
+Print["ERROR: Could not find psi4 modes file"];
+];,{i,1,Length@modeFiles}];
+];
+
+
+CopyFiles[configStr_,modesdir_,reducedir_,patterns_]:=Module[{command,files,modeFile,source,fname,i,prefix},
+
+files=Map[FileNames[#,modesdir]&,patterns];
+
+(* Print["CopyFiles found files ", files]; *)
+
+files=Flatten@files;
+
+If[configStr == "",
+prefix = "",
+prefix = configStr<>"_";
+];
+
+Do[
+source=files[[i]];
+
+If[FileType@source==File || FileType@source==Directory,
+fname=Last@StringSplit[source,"/"];
+command="cp -r "<>source<>" "<>reducedir<>"/"<>prefix<>fname;
+(* Print["CopyFiles running command ",command];*)
+Run[Evaluate@command];,
+Print["ERROR: CopyFiles could not find file"];
+];,{i,1,Length@files}];
+
+
+];
+
+
+FormatPunctureData[mp_,string_,M_]:=Module[{xl,yl,zl,vxl,vyl,vzl,rl,wl,\[Omega]l,times},xl=TakeColumn[Position/.mp,1];
+yl=TakeColumn[Position/.mp,2];
+zl=TakeColumn[Position/.mp,3];
+vxl=TakeColumn[Speed/.mp,1];
+vyl=TakeColumn[Speed/.mp,2];
+vzl=TakeColumn[Speed/.mp,3];
+times=Times/.mp;
+times=times/M;
+xl=xl/M;
+yl=yl/M;
+zl=zl/M;
+Clear[Evaluate["times"<>string],Evaluate["xlist"<>string],Evaluate["ylist"<>string],Evaluate["zlist"<>string],Evaluate["vxlist"<>string],Evaluate["vylist"<>string],Evaluate["vzlist"<>string],Evaluate["xf"<>string],Evaluate["yf"<>string],Evaluate["zf"<>string],Evaluate["vxf"<>string],Evaluate["vyf"<>string],Evaluate["vzf"<>string],Evaluate["rlist"<>string],Evaluate["rf"<>string],Evaluate["wlist"<>string],Evaluate["wf"<>string],Evaluate["\[Omega]list"<>string],Evaluate["\[Omega]f"<>string]];
+Print["Defining the quantities: \n",Evaluate["times"<>string]," , ",Evaluate["[xyz]list"<>string]," , ",Evaluate["v[xyz]list"<>string]," , ",Evaluate["v[xyz]f"<>string]," , ",Evaluate["rlist"<>string]," , ",Evaluate["rf"<>string]," , ",Evaluate["wlist"<>string]," , ",Evaluate["wf"<>string]];
+Evaluate@ToExpression["times"<>string]=times;
+Evaluate@ToExpression["xf"<>string]=Interpolation[Union@CombineColumns[times,xl]];
+Evaluate@ToExpression["yf"<>string]=Interpolation[Union@CombineColumns[times,yl]];
+Evaluate@ToExpression["zf"<>string]=Interpolation[Union@CombineColumns[times,zl]];
+Evaluate@ToExpression["vxf"<>string]=Interpolation[Union@CombineColumns[times,vxl]];
+Evaluate@ToExpression["vyf"<>string]=Interpolation[Union@CombineColumns[times,vyl]];
+Evaluate@ToExpression["vzf"<>string]=Interpolation[Union@CombineColumns[times,vzl]];
+Evaluate@ToExpression["xlist"<>string]=xl;
+Evaluate@ToExpression["ylist"<>string]=yl;
+Evaluate@ToExpression["zlist"<>string]=zl;
+Evaluate@ToExpression["vxlist"<>string]=vxl;
+Evaluate@ToExpression["vylist"<>string]=vyl;
+Evaluate@ToExpression["vzlist"<>string]=vzl;
+rl=Sqrt[xl^2+yl^2+zl^2];
+Evaluate@ToExpression["rf"<>string]=Interpolation[Union@CombineColumns[times,rl]];
+wl=Sqrt[vxl^2+vyl^2+vzl^2]/Sqrt[xl^2+yl^2+zl^2];
+Evaluate@ToExpression["wf"<>string]=Interpolation[Union@CombineColumns[times,wl]];
+\[Omega]l=(vyl xl-vxl yl)/(xl^2+yl^2+zl^2);
+Evaluate@ToExpression["\[Omega]f"<>string]=Interpolation[Union@CombineColumns[times,\[Omega]l]];
+Evaluate@ToExpression["rlist"<>string]=rl;
+Evaluate@ToExpression["wlist"<>string]=wl;
+Evaluate@ToExpression["\[Omega]list"<>string]=\[Omega]l;];
+
+
+
+SafeFormatPunctureData2[mp1_,mp2_,string_,m1_,m2_]:=Module[{M,xl1,yl1,zl1,xl2,yl2,zl2,xlc,ylc,zlc,dxl,dyl,dzl,
+vxl1,vyl1,vzl1,vxl2,vyl2,vzl2,vxlc,vylc,vzlc,rl,wl,\[Omega]l,vrxl,vryl,vrzl,wxl,wyl,wzl,vrl,vtl,times,timesSorted,timesSorted1,timesSorted2,pos},M=m1+m2;
+xl1=TakeColumn[Position/.mp1,1];
+yl1=TakeColumn[Position/.mp1,2];
+zl1=TakeColumn[Position/.mp1,3];
+vxl1=TakeColumn[Speed/.mp1,1];
+vyl1=TakeColumn[Speed/.mp1,2];
+vzl1=TakeColumn[Speed/.mp1,3];
+xl2=TakeColumn[Position/.mp2,1];
+yl2=TakeColumn[Position/.mp2,2];
+zl2=TakeColumn[Position/.mp2,3];
+vxl2=TakeColumn[Speed/.mp2,1];
+vyl2=TakeColumn[Speed/.mp2,2];
+vzl2=TakeColumn[Speed/.mp2,3];
+times=Times/.mp1;
+timesSorted1=Union@times;
+
+times=Times/.mp2;
+timesSorted2=Union@times;
+
+If[Length@timesSorted2 >= Length@timesSorted1, timesSorted = timesSorted1,timesSorted = timesSorted2]
+
+Clear[timesSorted1,timesSorted2];
+
+pos=Table[Position[times,timesSorted[[i]]],{i,1,Length@timesSorted}];
+pos=Flatten@Map[First,pos];
+times=Table[times[[pos[[i]]]],{i,1,Length@pos}];
+xl1=Table[xl1[[pos[[i]]]],{i,1,Length@pos}];
+yl1=Table[yl1[[pos[[i]]]],{i,1,Length@pos}];
+zl1=Table[zl1[[pos[[i]]]],{i,1,Length@pos}];
+xl2=Table[xl2[[pos[[i]]]],{i,1,Length@pos}];
+yl2=Table[yl2[[pos[[i]]]],{i,1,Length@pos}];
+zl2=Table[zl2[[pos[[i]]]],{i,1,Length@pos}];
+vxl1=Table[vxl1[[pos[[i]]]],{i,1,Length@pos}];
+vyl1=Table[vyl1[[pos[[i]]]],{i,1,Length@pos}];
+vzl1=Table[vzl1[[pos[[i]]]],{i,1,Length@pos}];
+vxl2=Table[vxl2[[pos[[i]]]],{i,1,Length@pos}];
+vyl2=Table[vyl2[[pos[[i]]]],{i,1,Length@pos}];
+vzl2=Table[vzl2[[pos[[i]]]],{i,1,Length@pos}];
+(*scale to units of M*)times=times/M;
+xl1=xl1/M;
+yl1=yl1/M;
+zl1=zl1/M;
+xl2=xl2/M;
+yl2=yl2/M;
+zl2=zl2/M;
+(*center-of-mass vector*)xlc=(m1 xl1+m2 xl2)/M;
+ylc=(m1 yl1+m2 yl2)/M;
+zlc=(m1 zl1+m2 zl2)/M;
+(*relative coordinates*)xl1=xl1-xlc;
+yl1=yl1-ylc;
+zl1=zl1-zlc;
+xl2=xl2-xlc;
+yl2=yl2-ylc;
+zl2=zl2-zlc;
+Clear[Evaluate["times"<>string],Evaluate["xlista"<>string],Evaluate["ylista"<>string],Evaluate["zlista"<>string],Evaluate["vxlista"<>string],Evaluate["vylista"<>string],Evaluate["vzlista"<>string],Evaluate["xfa"<>string],Evaluate["yfa"<>string],Evaluate["zfa"<>string],Evaluate["vxfa"<>string],Evaluate["vyfa"<>string],Evaluate["vzfa"<>string],Evaluate["rlist"<>string],Evaluate["rf"<>string],Evaluate["wlist"<>string],Evaluate["wf"<>string],Evaluate["\[Omega]list"<>string],Evaluate["\[Omega]f"<>string],Evaluate["xlistb"<>string],Evaluate["ylistb"<>string],Evaluate["zlistb"<>string],Evaluate["vxlistb"<>string],Evaluate["vylistb"<>string],Evaluate["vzlistb"<>string],Evaluate["xfb"<>string],Evaluate["yfb"<>string],Evaluate["zfb"<>string],Evaluate["vxfb"<>string],Evaluate["vyfb"<>string],Evaluate["vzfb"<>string]];
+Print["Defining the quantities: \n",Evaluate["times"<>string]," , ",Evaluate["[xyz]list"<>string]," , ",Evaluate["v[xyz]list"<>string]," , ",Evaluate["v[xyz]f"<>string]," , ",Evaluate["rlist"<>string]," , ",Evaluate["rf"<>string]," , ",Evaluate["wlist"<>string]," , ",Evaluate["wf"<>string]];
+Evaluate@ToExpression["times"<>string]=times;
+Evaluate@ToExpression["xfa"<>string]=Interpolation[CombineColumns[times,xl1]];
+Evaluate@ToExpression["yfa"<>string]=Interpolation[CombineColumns[times,yl1]];
+Evaluate@ToExpression["zfa"<>string]=Interpolation[CombineColumns[times,zl1]];
+Evaluate@ToExpression["vxfa"<>string]=Interpolation[CombineColumns[times,vxl1]];
+Evaluate@ToExpression["vyfa"<>string]=Interpolation[CombineColumns[times,vyl1]];
+Evaluate@ToExpression["vzfa"<>string]=Interpolation[CombineColumns[times,vzl1]];
+Evaluate@ToExpression["xlista"<>string]=xl1;
+Evaluate@ToExpression["ylista"<>string]=yl1;
+Evaluate@ToExpression["zlista"<>string]=zl1;
+Evaluate@ToExpression["vxlista"<>string]=vxl1;
+Evaluate@ToExpression["vylista"<>string]=vyl1;
+Evaluate@ToExpression["vzlista"<>string]=vzl1;
+Evaluate@ToExpression["xfb"<>string]=Interpolation[CombineColumns[times,xl2]];
+Evaluate@ToExpression["yfb"<>string]=Interpolation[CombineColumns[times,yl2]];
+Evaluate@ToExpression["zfb"<>string]=Interpolation[CombineColumns[times,zl2]];
+Evaluate@ToExpression["vxfb"<>string]=Interpolation[CombineColumns[times,vxl2]];
+Evaluate@ToExpression["vyfb"<>string]=Interpolation[CombineColumns[times,vyl2]];
+Evaluate@ToExpression["vzfb"<>string]=Interpolation[CombineColumns[times,vzl2]];
+Evaluate@ToExpression["xlistb"<>string]=xl2;
+Evaluate@ToExpression["ylistb"<>string]=yl2;
+Evaluate@ToExpression["zlistb"<>string]=zl2;
+Evaluate@ToExpression["vxlistb"<>string]=vxl2;
+Evaluate@ToExpression["vylistb"<>string]=vyl2;
+Evaluate@ToExpression["vzlistb"<>string]=vzl2;
+rl=Sqrt[(xl1-xl2)^2+(yl1-yl2)^2+(zl1-zl2)^2];
+rl=Table[Max[rl[[i]],$MachineEpsilon],{i,1,Length@rl}];
+Evaluate@ToExpression["rf"<>string]=Interpolation[CombineColumns[times,rl]];
+wl=Sqrt[(vxl1-vxl2)^2+(vyl1-vyl2)^2+(vzl1-vzl2)^2]/rl;
+Evaluate@ToExpression["wf"<>string]=Interpolation[CombineColumns[times,wl]];
+dxl=(xl2-xl1)/rl;
+dyl=(yl2-yl1)/rl;
+dzl=(zl2-zl1)/rl;
+(*w=drl\[Cross]\[CapitalDelta]yl*)wxl=dyl (vzl2-vzl1)-dzl (vyl2-vyl1);
+wyl=dzl (vxl2-vxl1)-dxl (vzl2-vzl1);
+wzl=dxl (vyl2-vyl1)-dyl (vxl2-vxl1);
+(*\[Omega]=(|drl\[Cross]\[CapitalDelta]yl|)/rl*)\[Omega]l=Sqrt[wxl^2+wyl^2+wzl^2]/rl;
+Evaluate@ToExpression["\[Omega]f"<>string]=Interpolation[CombineColumns[times,\[Omega]l]];
+Evaluate@ToExpression["rlist"<>string]=rl;
+Evaluate@ToExpression["wlist"<>string]=wl;
+Evaluate@ToExpression["\[Omega]list"<>string]=\[Omega]l;];
+
+
+SafeFormatPunctureDataCactus[mp_,string_,m1_,m2_]:=Module[{M,xl1,yl1,zl1,xl2,yl2,zl2,xlc,ylc,zlc,dxl,dyl,dzl,vxl1,vyl1,vzl1,vxl2,vyl2,vzl2,vxlc,vylc,vzlc,rl,wl,\[Omega]l,vrxl,vryl,vrzl,wxl,wyl,wzl,vrl,vtl,times,timesSorted,pos},M=m1+m2;
+xl1=TakeColumn[mp,23];
+yl1=TakeColumn[mp,33];
+zl1=TakeColumn[mp,43];
+xl2=TakeColumn[mp,24];
+yl2=TakeColumn[mp,34];
+zl2=TakeColumn[mp,44];
+times=TakeColumn[mp,9];
+timesSorted=Union@times;
+pos=Table[Position[times,timesSorted[[i]]],{i,1,Length@timesSorted}];
+pos=Flatten@Map[First,pos];
+times=Table[times[[pos[[i]]]],{i,1,Length@pos}];
+xl1=Table[xl1[[pos[[i]]]],{i,1,Length@pos}];
+yl1=Table[yl1[[pos[[i]]]],{i,1,Length@pos}];
+zl1=Table[zl1[[pos[[i]]]],{i,1,Length@pos}];
+xl2=Table[xl2[[pos[[i]]]],{i,1,Length@pos}];
+yl2=Table[yl2[[pos[[i]]]],{i,1,Length@pos}];
+zl2=Table[zl2[[pos[[i]]]],{i,1,Length@pos}];
+times=times/M;
+vx1=D[Interpolation[CombineColumns[times,xl1]][t],t]/.ff1_[tt_]->ff1;
+vy1=D[Interpolation[CombineColumns[times,yl1]][t],t]/.ff2_[tt_]->ff2;
+vz1=D[Interpolation[CombineColumns[times,zl1]][t],t]/.ff3_[tt_]->ff3;
+vx2=D[Interpolation[CombineColumns[times,xl2]][t],t]/.ff4_[tt_]->ff4;
+vy2=D[Interpolation[CombineColumns[times,yl2]][t],t]/.ff5_[tt_]->ff5;
+vz2=D[Interpolation[CombineColumns[times,zl2]][t],t]/.ff6_[tt_]->ff6;
+vxl1=Map[vx1,times];
+vyl1=Map[vy1,times];
+vzl1=Map[vz1,times];
+vxl2=Map[vx2,times];
+vyl2=Map[vy2,times];
+vzl2=Map[vz2,times];
+xl1=xl1/M;
+yl1=yl1/M;
+zl1=zl1/M;
+xl2=xl2/M;
+yl2=yl2/M;
+zl2=zl2/M;
+xlc=m1 xl1+m2 xl2;
+ylc=m1 yl1+m2 yl2;
+zlc=m1 zl1+m2 zl2;
+xl1=xl1-xlc;
+yl1=yl1-ylc;
+zl1=zl1-zlc;
+xl2=xl2-xlc;
+yl2=yl2-ylc;
+zl2=zl2-zlc;
+Clear[Evaluate["times"<>string],Evaluate["xlista"<>string],Evaluate["ylista"<>string],Evaluate["zlista"<>string],Evaluate["vxlista"<>string],Evaluate["vylista"<>string],Evaluate["vzlista"<>string],Evaluate["xfa"<>string],Evaluate["yfa"<>string],Evaluate["zfa"<>string],Evaluate["vxfa"<>string],Evaluate["vyfa"<>string],Evaluate["vzfa"<>string],Evaluate["rlist"<>string],Evaluate["rf"<>string],Evaluate["wlist"<>string],Evaluate["wf"<>string],Evaluate["\[Omega]list"<>string],Evaluate["\[Omega]f"<>string],Evaluate["xlistb"<>string],Evaluate["ylistb"<>string],Evaluate["zlistb"<>string],Evaluate["vxlistb"<>string],Evaluate["vylistb"<>string],Evaluate["vzlistb"<>string],Evaluate["xfb"<>string],Evaluate["yfb"<>string],Evaluate["zfb"<>string],Evaluate["vxfb"<>string],Evaluate["vyfb"<>string],Evaluate["vzfb"<>string]];
+Print["Defining the quantities: \n",Evaluate["times"<>string]," , ",Evaluate["[xyz]list"<>string]," , ",Evaluate["rlist"<>string]," , ",Evaluate["rf"<>string]," , ",Evaluate["wlist"<>string]," , ",Evaluate["wf"<>string]];
+Evaluate@ToExpression["times"<>string]=times;
+Evaluate@ToExpression["xfa"<>string]=Interpolation[CombineColumns[times,xl1]];
+Evaluate@ToExpression["yfa"<>string]=Interpolation[CombineColumns[times,yl1]];
+Evaluate@ToExpression["zfa"<>string]=Interpolation[CombineColumns[times,zl1]];
+Evaluate@ToExpression["xfb"<>string]=Interpolation[CombineColumns[times,xl2]];
+Evaluate@ToExpression["yfb"<>string]=Interpolation[CombineColumns[times,yl2]];
+Evaluate@ToExpression["zfb"<>string]=Interpolation[CombineColumns[times,zl2]];
+Evaluate@ToExpression["xlista"<>string]=xl1;
+Evaluate@ToExpression["ylista"<>string]=yl1;
+Evaluate@ToExpression["zlista"<>string]=zl1;
+Evaluate@ToExpression["xlistb"<>string]=xl2;
+Evaluate@ToExpression["ylistb"<>string]=yl2;
+Evaluate@ToExpression["zlistb"<>string]=zl2;
+rl=Sqrt[(xl1-xl2)^2+(yl1-yl2)^2+(zl1-zl2)^2];
+rl=Table[Max[rl[[i]],$MachineEpsilon],{i,1,Length@rl}];
+Evaluate@ToExpression["rf"<>string]=Interpolation[CombineColumns[times,rl]];
+wl=Sqrt[(vxl1-vxl2)^2+(vyl1-vyl2)^2+(vzl1-vzl2)^2]/rl;
+Evaluate@ToExpression["wf"<>string]=Interpolation[CombineColumns[times,wl]];
+dxl=(xl2-xl1)/rl;
+dyl=(yl2-yl1)/rl;
+dzl=(zl2-zl1)/rl;
+wxl=dyl (vzl2-vzl1)-dzl(vyl2-vyl1);
+wyl=dzl (vxl2-vxl1)-dxl(vzl2-vzl1);
+wzl=dxl (vyl2-vyl1)-dyl(vxl2-vxl1);
+\[Omega]l=Sqrt[wxl^2+wyl^2+wzl^2]/rl;
+Evaluate@ToExpression["\[Omega]f"<>string]=Interpolation[CombineColumns[times,\[Omega]l]];
+Evaluate@ToExpression["rlist"<>string]=rl;
+Evaluate@ToExpression["wlist"<>string]=wl;
+Evaluate@ToExpression["\[Omega]list"<>string]=\[Omega]l;];
+
+
+BAMModesFilesTo3Col[modesFile_,OptionsPattern[{"DeleteSourceFiles" -> False}]]:=Module[{rootString,path,noPath,reData,imData,rad,lev,modeString,timesRe,timesIm,
+col3Data,file,col3data,deleteSourceFiles,lm,commonTimes},
+deleteSourceFiles = OptionValue["DeleteSourceFiles"];
+
+path = FileNameTake[modesFile,FileNameDepth[modesFile]-1];
+noPath=FileNameTake[modesFile,-1];
+rootString = StringCases[modesFile,{"r","i"}~~"psi4mode"~~postfix__:> {"rpsi4mode"<>postfix,"ipsi4mode"<>postfix}];
+
+If[rootString != {},
+
+ {rad,lev}=First@StringCases[modesFile,"r"~~rad:NumberString~~".t"~~lev:NumberString~~___ :> {rad,lev}];
+
+ modeString = First@StringCases[modesFile,{"r","i"}~~"psi4mode"~~mode__~~"_r"~~postfix__:> mode];
+ lm = Switch[modeString,
+ "20", {2, 0},
+ "2m1", {2,-1},
+ "21", {2, 1},
+ "2m2", {2,-2},
+ "22", {2, 2}
+ ];
+
+ file = FileNameJoin[{path,rootString[[1,1]]}];
+ If[FileType@file != File,
+ Print["BAMModesFilesTo3Col:: File not found: ", file]; Return[];,
+
+ reData = TimeUnion@NRFiles`ReadColData[file,2,1];
+ If[deleteSourceFiles,DeleteFile[file];];
+ timesRe = NRLists`TakeColumn[reData,1];
+
+ If[lm[[2]]!=0,
+ file = FileNameJoin[{path,rootString[[1,2]]}];
+
+ If[FileType@file != File,
+ Print["BAMModesFilesTo3Col:: File not found: ", file];
+ imData = {};,
+ timesIm = {};
+ imData = TimeUnion@NRFiles`ReadColData[file,2,1];
+ If[deleteSourceFiles,DeleteFile[file];];
+ timesIm = NRLists`TakeColumn[imData,1];
+ ];,
+ timesIm = timesRe;
+ imData = Transpose@{timesIm,0*timesIm};
+ ];
+
+ If[timesIm==timesRe,
+ col3data = Transpose@{timesRe, NRLists`TakeColumn[reData,2], NRLists`TakeColumn[imData,2]};
+ file = path<>"/psi3col_bam_r"<>ToString@rad<>".l"<>ToString@lev<>".l"<>ToString@lm[[1]]<>".m"<>ToString@lm[[2]]<>".gz";
+ Print["Exporting file ", file];
+ Export[file,col3data,{"GZIP","Table"}],
+ Print["BAMModesFilesTo3Col:: fixing inconsistent lengths of real and imaginary part"];
+ Print["Length@Re@wave = ", Length@timesRe, ", ", "Length@Im@wave = ", Length@timesIm];
+ commonTimes = Intersection[timesIm,timesRe];
+ reData = Select[reData,MemberQ[commonTimes,#[[1]]]&];
+ imData = Select[imData,MemberQ[commonTimes,#[[1]]]&];
+
+ col3data = Transpose@{commonTimes, NRLists`TakeColumn[reData,2], NRLists`TakeColumn[imData,2]};
+ file = path<>"/psi3col_bam_r"<>ToString@rad<>".l"<>ToString@lev<>".l"<>ToString@lm[[1]]<>".m"<>ToString@lm[[2]]<>".gz";
+ Print["Exporting file ", file];
+ Export[file,col3data,{"GZIP","Table"}]
+ ];
+ ];
+];
+];
+
+
+BAMTrajectoryFileTo4Col[inFile_,OptionsPattern[{"DeleteSourceFiles" -> False}]]:=Module[{path,noPath,data,
+lev,bh,modeString,timesRe,times,
+file,col4data,deleteSourceFiles},
+
+deleteSourceFiles = OptionValue["DeleteSourceFiles"];
+
+If[FileType@inFile == File,
+
+path = path = FileNameTake[inFile,FileNameDepth[inFile]-1];
+noPath = FileNameTake[inFile,-1];
+
+{bh,lev} = First@StringCases[noPath,
+ "moving_puncture_integrate"~~bh:NumberString~~".txyz"~~lev:NumberString~~X___ :> {bh,lev}];
+
+lev = StringReplace[lev, "."->""];
+
+data = Import@inFile;
+If[deleteSourceFiles,DeleteFile[inFile];];
+col4data = TimeUnion@NRLists`TakeColumn[data,{7,1,2,3}];
+
+file = path<>"/traj_"<>ToString@bh<>".l"<> ToString@lev<>".gz";
+Print["Exporting file ", file];
+Export[file,col4data,{"GZIP","Table"}];
+];
+];
+
+
+BAMHorizonFilesToNRARFiles[inFile_,OptionsPattern[{"DeleteSourceFiles" -> False}]]:=Module[{path,noPath,data,lev,bh,modeString,timesRe,times,
+file,col4data,deleteSourceFiles,
+hmass,hspin,totalSpin,htraj,
+t,m},
+
+deleteSourceFiles = OptionValue["DeleteSourceFiles"];
+
+If[FileType@inFile == File,
+
+path = path = FileNameTake[inFile,FileNameDepth[inFile]-1];
+noPath = FileNameTake[inFile,-1];
+Print["BAMHorizonFilesToNRARFiles: filename: ", noPath];
+
+bh = First@StringCases[noPath,"horizon_"~~bh:NumberString :> bh];
+Print["BAMHorizonFilesToNRARFiles: bh: ", bh];
+bh = ToExpression@bh + 1;
+
+data = TimeUnion@ReadColData[inFile,9,1];
+If[deleteSourceFiles, DeleteFile[inFile];];
+
+times = TakeColumn[data,1];
+hmass = TakeColumn[data,5];
+hspin = TakeColumn[data,{1,6,7,8}];
+
+
+totalSpin = TakeColumn[data,9];
+
+hmass = Sqrt[hmass^2+1/4 totalSpin^2/hmass^2];
+hmass = CombineColumns[times,hmass];
+
+
+htraj = TakeColumn[data,{1,2,3,4}];
+
+
+file = path<>"/hmass_"<>ToString@bh<>".gz";
+Print["Exporting file ", file];
+Export[file,hmass,{"GZIP","Table"}];
+
+file = path<>"/htraj_"<>ToString@bh<>".gz";
+Print["Exporting file ", file];
+Export[file,htraj,{"GZIP","Table"}];
+
+file = path<>"/hspin_"<>ToString@bh<>".gz";
+Print["Exporting file ", file];
+Export[file,hspin,{"GZIP","Table"}];
+];
+];
+
+
+WaveExtractionRadii[rootDir_,modesDir_]:=Module[{admFiles,adm,i,admradii,outerradius,level,massScale=1,len},
+
+admFiles=FileNames["hmod.r*.l*.l*.m*",modesDir];
+
+If[admFiles == {},
+Print["ERROR: could not find any hmod data in directory ", LastInPath@modesDir];
+Return[];
+];
+
+level=Union@Map[IntegerPart,Map[levelFun,admFiles]];
+Print["WaveExtractionRadii: Available refinement levels: ", level];
+
+outerradius=TakeColumn[level,1];
+Print["Wave extraction indices: ", outerradius];
+outerradius=Max@Map[ToExpression,outerradius];
+Print["Maximal wave extraction radius: ", outerradius];
+
+admradii=BAMNumberParameters[rootDir,"invariants_modes_r"];
+Print["Wave extraction radii: ", admradii];
+
+admradii
+];
+
+
+ADMReduce[rootDir_,reduceDir_]:=Module[{admFiles,adm,i,admradii,outerradius,level,levelFun,massScale=1,len},
+
+admFiles=FileNames["*ADM_mass_r*",rootDir];
+
+Print["ADM data files: ", admFiles];
+
+If[admFiles == {},
+Print["ERROR: ADMReduce could not find any ADM data in directory ", LastInPath@rootDir];Return[];,
+Print["Starting ADM analysis"];
+];
+
+levelFun[str_]:=ToExpression@First@StringCases[str,"ADM_mass_r"~~NumberString..~~".t"~~x:NumberString-> x];
+
+level=Map[IntegerPart,Map[levelFun,admFiles]];
+Print["Available refinement levels: ", level];
+
+outerradius=Map[Last@StringSplit[#,"/"]&,admFiles];
+outerradius=Union@Map[StringSplit[#,"_"][[3]]&,outerradius];
+outerradius=Union@Map[StringSplit[#,"."][[1]]&,outerradius];
+outerradius=Union@StringReplace[outerradius,"r"-> ""];
+
+Print["ADM-style integrals extraction indices: ", outerradius];
+outerradius=Max@Map[ToExpression,outerradius];
+Print["Maximal ADM-stlye integral extraction radius: ", outerradius];
+
+admradii=BAMNumberParameters[rootDir,"ADM_mass_r"];
+Print["ADM-style integrals extraction radii: ", admradii];
+
+len=Length@admradii;
+level=First@Union@Flatten@Select[myGather[level],Length@#==len&];
+Print["All extraction radii seem present at level ", level];
+
+
+admFiles=FileNames["*ADM_mass_r*.t"<>ToString@level<>"*",rootDir];
+Print["Reading data from files ", admFiles, " at level ", level];
+adm=Table[{admFiles[[i]],admradii[[i]]} , {i,1,Length@admFiles}];
+
+ADMFit1Res[adm,massScale];
+];
+
+
+BBHDataReduce[modesdir_,IDroot_,ReduceRoot_]:=Module[{modesroot,reducedir,outerradius,psidfile,configStr,
+idDir,m1,m2,madm,sep,abschi1,abschi2,s1x,s1y,s1z,s2x,s2y,s2z,a1x,a1y,a1z,a2x,a2y,a2z,q,eta,mtot,qString,
+dString,chiString,myround,tmpString,modeDecompConfig,bitant,lmax=6,cleanModeConfig,extractionRadii,
+extractionRadiiString,modesDecompDir,levels,radii,stdout},
+
+tmpString = Map[ToString,{m1,m2,madm,sep,abschi1,abschi2,q}];
+
+modesroot = ParentDirectory@modesdir;
+Print["========================================================"];
+Print["Start case modesroot = ", modesroot];
+
+
+If[ReduceRoot==".",
+ reducedir=modesroot<>"/DataReduce",
+ reducedir=ReduceRoot<>"/"<>Last@StringSplit[modesroot,"/"]<>"/DataReduce"
+];
+
+Print["Data reduction directory is ", reducedir];
+CreateDirectory[reducedir];
+
+modesDecompDir = reducedir<>"/ModeDecomp";
+Print["Mode decomposition directory is ", modesDecompDir];
+CreateDirectory[modesDecompDir];
+
+outerradius = FileNames["*hmod.r*.l*",modesdir];
+
+outerradius = Map[Last@StringSplit[#,"/"]&,outerradius];
+levels = Map[IntegerPart,Union@Map[levelFun,outerradius]];
+Print["Levels ", levels];
+radii = TakeColumn[levels,1];
+levels = TakeColumn[levels,2];
+outerradius = Union@Map[StringSplit[#,"."][[2]]&,outerradius];
+outerradius = Union@StringReplace[outerradius,"r"-> ""];
+
+extractionRadii = outerradius;
+Print["Radiation extraction radii: ", extractionRadii];
+outerradius = Max@Map[ToExpression,outerradius];
+Print["Maximal radiation extraction radius: ", outerradius];
+
+psidfile = BAMStringParameter[modesroot,"punctures_ps_file"];
+psidfile = Last@StringSplit[psidfile,"/"];
+psidfile = StringReplace[psidfile," "->""];
+Print["psid-file determined from evolution parameter file as: ", psidfile];
+idDir = LocateInitialDataDirectory[IDroot,psidfile];
+{m1,m2,madm,sep,abschi1,abschi2,s1x,s1y,s1z,s2x,s2y,s2z} = InitialDataParameters[idDir,psidfile];
+mtot = m1+m2;
+q = Max[m1,m2]/Min[m1,m2];
+{a1x,a1y,a1z}={s1x,s1y,s1z}/m1^2;
+{a2x,a2y,a2z}={s2x,s2y,s2z}/m2^2;
+
+Map[ValPrint,tmpString];
+Print["a1 =", {a1x,a1y,a1z}];
+Print["a2 =", {a2x,a2y,a2z}];
+
+myround[x_]:=N[Round[10000x]/10000];
+
+qString = ToString@myround[q];
+dString = ToString@myround[sep/mtot];
+
+bitant = False;
+If[s1x==s1y==s2x==s2y==0,
+Print["Aligned spins!"];
+bitant = True;
+chiString = ToString@myround@a1z<>"_"<>ToString@myround@a2z;,
+Print["Precessing spins!"];
+chiString = "Precess"<>ToString@myround@a1x<>"_"<>ToString@myround@a1y<>ToString@myround@a1z<>"_"<>ToString@myround@a2x<>ToString@myround@a1y<>"_"<>ToString@myround@a2z;
+];
+
+configStr = "D"<>dString<>"_q"<> qString<>"_"<>chiString;
+Print["Generated configuration string ", configStr];
+Print["Finished Initialization, starting analysis"];
+
+modeDecompConfig="dirnames = {\""<>modesroot<>"\"};\n\n"<>
+"mass1 = {"<>ToString@m1<>"};\n"<>
+"mass2 = {"<>ToString@m2<>"};\n\n"<>
+"minradius = "<>ToString@Min@radii<>";\n"<>
+"maxradius = "<>ToString@Max@radii<>";\n"<>
+"level = "<>ToString@Max@levels<>";\n\n"<> (* This is not really correct, want a list here. *)
+"lmin = 2;\n"<>
+"lmax = "<>ToString@lmax<>";\n\n"<>
+"BITANT = "<>ToString@bitant<>";";
+
+Export[modesDecompDir<>"/allmodesH.in.m",modeDecompConfig,"Text"];
+
+extractionRadii=WaveExtractionRadii[modesroot,modesdir];
+extractionRadiiString=ToString@extractionRadii;
+
+cleanModeConfig="dirnames = {\""<>modesDecompDir<>"\"};\n\n"<>
+"RadiusValue = "<>ToString@extractionRadiiString<>";\n"<>
+"winoffset = -1;\n\n"<>
+"minradius = "<>ToString@Min@radii<>";\n"<>
+"maxradius = "<>ToString@Max@radii<>";\n"<>
+"level = "<>ToString@Max@levels<>";\n\n"<> (* This is not really correct, want a list here. *)
+"lmin = 2;\n"<>
+"lmax = "<>ToString@lmax<>";\n\n"<>
+"dtResample = -1;\n"<>
+"mintime = 150\n"<>
+"maxtime = 5000";
+
+Export[modesDecompDir<>"/cleanPsi.in.m",cleanModeConfig,"Text"];
+
+ADMReduce[modesroot,reducedir];
+
+(* CopyL2mode[configStr,modesdir,reducedir];
+CopyL2modes[configStr,modesdir,reducedir];
+CopyModes[configStr,modesdir,reducedir,2,1];
+CopyModes[configStr,modesdir,reducedir,3,2];
+CopyModes[configStr,modesdir,reducedir,3,3];
+CopyModes[configStr,modesdir,reducedir,4,4];*)
+
+CopyFiles[configStr,modesdir,reducedir,
+{
+"hmod.r*",
+"psi3col.r*"
+}];
+
+stdout = Last@FileNameSplit@First@FileNames["stdout.*",modesroot];
+Print["Found example stdout file: ", stdout];
+
+(* overwrite modes files if we find some in the main directory *)
+CopyFiles[configStr,modesroot,reducedir,
+{
+"d*dt_r*.t*","ADM_mass_r*.t*",
+"moving_puncture_integrate1.txyz*",
+"moving_puncture_integrate2.txyz*",
+"hmod.r*",
+"psi3col.r*",
+"system.log*",
+stdout
+}];
+
+Print["========================================================\n\n"];
+];
+
+
+SymmetriesFromParfile[parfile_]:=Module[{grid,bitant, quadrant},
+
+grid = BAMStringParameter[FileNameDrop[parfile,-1], "grid"];
+
+If[StringMatchQ[grid, "*quadrant*"], quadrant = True, quadrant = False];
+If[StringMatchQ[grid, "*bitant*"], bitant = True, bitant = False];
+
+{bitant, quadrant}
+];
+
+
+WriteModeDecompConfigFile[DirectoryRules_?ListQ,
+ OptionsPattern[{"LMin" -> 2,"LMax" -> 6, "RunDecomp"-> False, "ModesTargetDirectory" -> "","JustPretendCalculation"-> False}]]:=Module[{modeDecompConfig,
+evDir,targetDir,evDirHasModes,redDirHasModes,modesroot,parfile,
+evModesDir,idDir,exportFile,
+psidFile,psidRules,
+M1,M2,radii,bitant,quadrant,
+modesDecompDir,levels,lmin,lmax,runDecomp,command,justPretendCalculation},
+
+Print["======= entering WriteModeDecompConfigFile ======="];
+
+lmin = OptionValue["LMin"];
+lmax = OptionValue["LMax"];
+runDecomp = OptionValue["RunDecomp"];
+targetDir = OptionValue["ModesTargetDirectory"];
+justPretendCalculation = OptionValue["JustPretendCalculation"];
+
+evDir = "EvolutionDirectory" /. DirectoryRules;
+If[TrueQ[targetDir == ""], targetDir = evDir];
+
+evDirHasModes = "EvolutionDirectoryHasModes"/. DirectoryRules;
+(* targetDirHasModes = "ModesTargetDirectoryHasModes" /. DirectoryRules;*)
+
+evModesDir = "EvolutionModesDir" /. DirectoryRules;
+
+idDir = "InitialDataDir" /. DirectoryRules;
+psidFile = "PSIDFile" /. DirectoryRules;
+
+psidRules = PSID2Rules[psidFile];
+
+modesDecompDir = FileNameJoin[{targetDir,"Psi4ModeDecomp"}];
+
+If[FileType@modesDecompDir != None, modesDecompDir == modesDecompDir <> "_new"];
+If[FileType@modesDecompDir != None, Print["modes directory already exists!"]; Return[]];
+
+CreateDirectory[modesDecompDir];
+
+M1 = "M1" /. psidRules;
+M2 = "M2" /. psidRules;
+
+radii = Range@Length@BAMExtractionRadii[evDir];
+
+levels = Union@Flatten@TakeColumn[BAMExtractionRadii[evDir],2];
+
+parfile = ParfileInDirectory[evDir];
+{bitant, quadrant} = SymmetriesFromParfile[parfile];
+
+modesroot = evDir;
+modeDecompConfig =
+"(* run as cd " <> modesDecompDir <> "; math < " <> Global`BAMToolsDir <> "/ModeDecomp/allmodes.m > out.m 2> err.m & *)\n\n" <>
+"dirnames = {\""<>modesroot<>"\"};\n\n"<>
+"mass1 = {"<> ToString@M1 <>"};\n"<>
+"mass2 = {"<> ToString@M2 <>"};\n\n"<>
+"minradius = "<>ToString@Min@radii<>";\n"<>
+"maxradius = "<> ToString@Max@radii<>";\n"<>
+"level = " <> ToString@Max@levels<>";\n\n"<> (* This is not really correct, want a list here. *)
+"lmin = " <> ToString@lmin <>";\n"<>
+"lmax = " <> ToString@lmax<>";\n\n"<>
+"PISYM = " <> ToString@quadrant<>";\n" <>
+"BITANT = " <> ToString@bitant<>";\n\n" <>
+"ExportRPsi4IPsi4 = False;";
+
+If[justPretendCalculation,
+ modeDecompConfig = modeDecompConfig <> "\n\nJustPretendCalculation = True;";
+];
+
+(* export mode decomp config file *)
+exportFile = modesDecompDir<>"/allmodes.in.m";
+Print["Exporting file: ", exportFile];
+Export[exportFile,modeDecompConfig,"Text"];
+
+
+CopyFile[Global`BAMToolsDir <> "/ModeDecomp/allmodes.m", modesDecompDir <>"/allmodes.m"]; (* copy the mode decomp file *)
+
+(* now write a shell script *)
+modeDecompConfig =
+"#!/bin/bash\n" <>
+"rm -f ModeDecomp_Done\n\n" <>
+"cd " <> modesDecompDir <> "; math < allmodes.m > out.m 2> err.m\n\n" <>
+"rm -f *psi*m-0.gz";
+
+If[Not@justPretendCalculation,
+ modeDecompConfig = modeDecompConfig <> "\ntouch ModeDecomp_Done";
+];
+
+
+exportFile = modesDecompDir<>"/runModeDecomp.sh";
+Print["Exporting file: ", exportFile];
+Export[exportFile,modeDecompConfig,"Text"];
+
+(* change file permissions to execute *)
+command = "cd " <> modesDecompDir <> "; chmod u+x runModeDecomp.sh";
+Print["Running command ", command];
+Run[command];
+
+If[runDecomp,
+Print["Running mode decomposition in batch mode"];
+If[justPretendCalculation,
+ command = "cd " <> modesDecompDir <> "; ./runModeDecomp.sh > out 2> err";, (* wait for result *)
+ command = "cd " <> modesDecompDir <> "; ./runModeDecomp.sh > out 2> err &"; (* do not wait for result *)
+];
+
+Print["Running command ", command];
+Run[command];
+];
+
+Print["======= exiting WriteModeDecompConfigFile ======="];
+];
+
+
+BAMExtractionRadii[evolutiondir_]:=Module[{outerradius,levels,radii,extractionRadii,levelfun,
+evolutionParfile,collectLevels,r,l,i},
+
+levelfun[str_]:=ToExpression@First@StringCases[str,"rpsi4.r"~~r:NumberString..~~".l"~~l:NumberString-> {r,l}];
+
+collectLevels[level_,levels_] := Map[Last,Select[levels,#[[1]]==level&]];
+
+outerradius = FileNames["rpsi4.r*.l*",evolutiondir];
+
+outerradius = Map[Last@StringSplit[#,"/"]&,outerradius];
+
+levels = Map[IntegerPart,Union@Map[levelfun,outerradius]];
+
+outerradius = Union@Map[StringSplit[#,"."][[2]]&,outerradius];
+outerradius = Union@StringReplace[outerradius,"r"-> ""];
+
+extractionRadii = outerradius;
+Print["Radiation extraction radii from psi4 file names: ", extractionRadii];
+
+evolutionParfile = ParfileInDirectory[evolutiondir];
+
+radii = BAMNumberParametersInFile[evolutionParfile, "invariants_modes_r"];
+
+If[Length@radii > Length@extractionRadii,
+ Print["Found inconsistent extraction radii, assume outermost radius did not fit on extraction levels"];
+ Print["BAMExtractionRadii: radii = ", radii];
+ Print["BAMExtractionRadii: radii = ", extractionRadii];
+];
+
+If[Length@radii < Length@extractionRadii,
+ Print["Found inconsistent extraction radii!"];
+ Print["radii : extractionRadii ", Length@radii, " : ", Length@extractionRadii];
+ Print["BAMExtractionRadii: radii = ", radii];
+ Print["BAMExtractionRadii: radii = ", extractionRadii];
+Return[{False,False}];
+];
+
+Table[{radii[[i]],collectLevels[i,levels]},{i,1,Length@radii}]
+];
+
+
+CurateBBHData[DirectoryRules_?ListQ,
+ OptionsPattern[{"DestinationDirectory" -> ".", "SubmitterEmail" -> "Sascha Husa <sascha.husa@gmail.zebra.elephant.com>",
+ "ModeDecomp"-> False,"VivekModesSource"-> {} }]]:=Module[{reducedir,outerradius,psidfile,configString,filePrefix,
+idDir,m1,m2,madm,sep,abschi1,abschi2,s1x,s1y,s1z,s2x,s2y,s2z,a1x,a1y,a1z,a2x,a2y,a2z,q,eta,mtot,qString,
+dString,chiString,myround,tmpString,modeDecompConfig,bitant,lmax,extractionRadii,
+extractionRadiiString,modesDecompDir,levels,radii,stdout,evDir,redDir,evDirHasModes,redDirHasModes,modesroot,parfile,
+evModesDir,redModesDir,exportFile,
+psidFile,psidRules,modesdir,modesString,timer,destinationDir,myDestinationDir,X1,X2,P1,P2,
+modesFiles,selectFiles,str,
+rad,lev,l,m,tmp,rules,
+modesFilesAndRadii,trajectoriesSection,metadataFile,baseSection,psi4BAMModesSections,psi4ModesSections,metadataContent,physicsSection,
+evParfileRules,resolution,L,eccentricityData,metaFile,metaFile2,
+radius,startTime,nCycles,startFreq,cycleInfo,
+afterJunkTime=140,
+tt,sx,sy,sz,
+pickHighestLevel,
+BAMLogDir,EnergyMomentumDir,Psi4ModesDir,Psi4BAMModesDir,
+submitterEmail,modeDecomp,canCreateModeFiles,VivekModesSource},
+
+Print["Entering Function CurateBBHData"];
+
+(* determine where we can find data, and where we will put data *)
+destinationDir = OptionValue["DestinationDirectory"];
+submitterEmail = OptionValue["SubmitterEmail"];
+modeDecomp = OptionValue["ModeDecomp"];
+
+Print["DirectoryRules: ", DirectoryRules];
+
+evDir = "EvolutionDirectory"/. DirectoryRules;
+redDir = "ReducedDirectory" /. DirectoryRules;
+
+VivekModesSource = OptionValue["VivekModesSource"];
+Print["Value of VivekModesSource: ", VivekModesSource];
+
+configString = FileNameTake[evDir,-1];
+Print["Configuration Name = ", configString];
+
+evDirHasModes = "EvolutionDirectoryHasModes"/. DirectoryRules;
+redDirHasModes = "ReducedDirectoryHasModes" /. DirectoryRules;
+
+evModesDir = "EvolutionModesDir" /. DirectoryRules;
+redModesDir = "ReducedModesDir" /. DirectoryRules;
+
+idDir = "InitialDataDir" /. DirectoryRules;
+psidFile = "PSIDFile" /. DirectoryRules;
+
+parfile = ParfileInDirectory[evDir];
+
+(* create uuid and basic.bbh files in evolution directory, if they do not alrady exist *)
+tmp = FileNames["uuid",evDir];
+If[Length@tmp == 0,
+ Run["cd "<> evDir <> "; uuidgen > uuid"];
+];
+
+tmp = FileNames["basic.bbh",evDir];
+If[Length@tmp == 0,
+ Run["cd "<> evDir <> "; cp " <> FileNameJoin[{Global`BBHReduceDir, "bam_metadata_template.bbh"}] <> " basic.bbh"];
+];
+
+
+(* determine from where we will take the psi4-modes*)
+modesString = "psi3col*";
+If[StringQ@redModesDir,
+ Print["Using modes from reduced-data directory: ", redModesDir];
+ modesdir = redModesDir,
+ If[StringQ@evModesDir,
+ Print["Using modes from reduced-data directory: ", evModesDir];
+ modesdir = evModesDir,
+ Print["Using l=2 modes from BAM on-the-fly integration in directory: ", evDir];
+ modesString = "*psi4*mode*";
+];
+];
+
+
+myDestinationDir = FileNameJoin[{destinationDir,configString}];
+Print["file destination directory: ", myDestinationDir];
+
+If[FileType@destinationDir == Directory,
+ Print["Destination directory already exists!"];,
+ CreateDirectory[destinationDir];
+];
+
+If[FileType@myDestinationDir == Directory,
+ Print["Configuration-specific destination directory already exists"];,
+ CreateDirectory[myDestinationDir];
+ Print[myDestinationDir]
+];
+
+CreateDirectory[myDestinationDir];
+
+
+(* determine simulation parameters *)
+psidRules = PSID2Rules[psidFile];
+evParfileRules = ParfileToRules[parfile];
+
+tmpString = Map[ToString,{m1,m2,madm,sep,abschi1,abschi2,q}];
+{m1,m2,madm,sep,abschi1,abschi2,s1x,s1y,s1z,s2x,s2y,s2z,X1,X2,P1,P2} = InitialDataParameters[psidFile];
+
+mtot = m1 + m2;
+
+q = Max[m1,m2]/Min[m1,m2];
+
+{a1x,a1y,a1z}={s1x,s1y,s1z}/m1^2;
+{a2x,a2y,a2z}={s2x,s2y,s2z}/m2^2;
+Print["a1 =", {a1x,a1y,a1z}];
+Print["a2 =", {a2x,a2y,a2z}];
+
+resolution = "UNDEFINED";
+
+If[IsFPNumberQ@ToString["nxyz" /. evParfileRules],
+ resolution = "nxyz" /. evParfileRules;
+];
+
+If[IsFPNumberQ@ToString["amr_move_nxyz" /. evParfileRules],
+ resolution = "amr_move_nxyz" /. evParfileRules;
+];
+
+tmp = "amr_nxyz" /. evParfileRules;
+If[ListQ@tmp,
+ If[IsFPNumberQ@ToString@Last@tmp,
+ resolution = Last["amr_nxyz" /. evParfileRules];
+ ];
+];
+
+L = (X1-X2)\[Cross]P1;
+
+physicsSection = {
+"submitter-email" -> submitterEmail,
+"simulation-name" -> configString,
+"resolution" -> resolution,
+"initial-ADM-energy" -> "Madm" /. psidRules,
+"initial-angular-momentumx" -> L[[1]],
+"initial-angular-momentumy" -> L[[2]],
+"initial-angular-momentumz" -> L[[3]],
+"initial-separation" -> sep,
+(* *)
+"eccentricity" -> "",
+(* *)
+"freq-start-22" -> "",
+"number-of-cycles-22" -> "",
+(* *)
+"phase-error" -> "",
+"amplitude-error-relative" -> "",
+(* *)
+"after-junkradiation-time" -> afterJunkTime,
+(* *)
+"mass1" -> m1,
+"mass2" -> m2,
+(* *)
+"initial-bh-position1x" -> X1[[1]],
+"initial-bh-position1y" -> X1[[2]],
+"initial-bh-position1z" -> X1[[3]],
+(* *)
+"initial-bh-position2x" -> X2[[1]],
+"initial-bh-position2y" -> X2[[2]],
+"initial-bh-position2z" -> X2[[3]],
+(* *)
+"initial-bh-momentum1x" -> P1[[1]],
+"initial-bh-momentum1y" -> P1[[2]],
+"initial-bh-momentum1z" -> P1[[3]],
+(* *)
+"initial-bh-momentum2x" -> P2[[1]],
+"initial-bh-momentum2y" -> P2[[2]],
+"initial-bh-momentum2z" -> P2[[3]],
+(* *)
+"initial-bh-spin1x" -> s1x,
+"initial-bh-spin1y" -> s1y,
+"initial-bh-spin1z" -> s1z,
+(* *)
+"initial-bh-spin2x" -> s2x,
+"initial-bh-spin2y" -> s2y,
+"initial-bh-spin2z" -> s2z,
+(* *)
+"after-junkradiation-spin1x" -> "",
+"after-junkradiation-spin1y" -> "",
+"after-junkradiation-spin1z" -> "",
+(* *)
+"after-junkradiation-spin2x" -> "",
+"after-junkradiation-spin2y" -> "",
+"after-junkradiation-spin2z" -> ""
+};
+physicsSection = Drop[ComposeConfigSection["dummy",physicsSection],1];
+
+Map[ValPrint,tmpString];
+
+myround[x_]:=N[Round[10000x]/10000];
+
+qString = ToString@myround[q];
+dString = ToString@myround[sep/mtot];
+
+bitant = False;
+If[s1x==s1y==s2x==s2y==0,
+Print["Aligned spins!"];, (* TODO: check consistency with settings in evolution-parfile *)
+Print["Precessing spins!"];
+];
+
+(* copy and create files *)
+filePrefix = ""; (* do not prefix files *)
+
+(* stdout and timer files: only copy 2 files each *)
+stdout = FileNames["stdout.*",evDir];
+If[Length@stdout >= 1,
+ stdout = {Last@FileNameSplit@First@stdout, Last@FileNameSplit@Last@stdout}
+];
+Print["Found example stdout file: ", stdout];
+
+timer = FileNames["timer.*",evDir];
+If[Length@timer >= 1,
+ timer = {Last@FileNameSplit@First@FileNames["timer.*",evDir], Last@FileNameSplit@Last@FileNames["timer.*",evDir]};
+];
+Print["Found example timer file: ", timer];
+
+BAMLogDir = FileNameJoin[{myDestinationDir,"BAMLogs"}];
+CreateDirectory[BAMLogDir];
+
+If[Length@stdout > 0, CopyFiles[filePrefix, evDir, BAMLogDir, stdout]];
+If[Length@timer > 0, CopyFiles[filePrefix, evDir, BAMLogDir, timer]];
+
+(* GW modes *)
+Psi4BAMModesDir = FileNameJoin[{myDestinationDir,"Psi4BAMModes"}];
+CreateDirectory[Psi4BAMModesDir];
+
+(* Psi4ModesDir = FileNameJoin[{myDestinationDir,"Psi4Modes"}];*)
+Psi4ModesDir = myDestinationDir;
+(*CreateDirectory[Psi4ModesDir];*)
+
+
+
+Print["Copying GW modes of the form ", modesString];
+CopyFiles[filePrefix,evDir,Psi4BAMModesDir, {modesString}];
+
+modesFiles = FileNames[modesString,myDestinationDir,2];
+
+selectFiles= Select[modesFiles,StringMatchQ[#,"*/rpsi4mode*"]&];
+
+Map[BAMModesFilesTo3Col[#,"DeleteSourceFiles"-> True]&,selectFiles];
+modesString = "psi3col*";
+
+(* now that we have a unified naming convention for psi4-files, compose modes metadata sections *)
+modesFiles = FileNames[modesString,myDestinationDir,2];
+
+Print["Calling BAMExtractionRadii"];
+radii = TakeColumn[BAMExtractionRadii[evDir],1];
+Print["BAMExtractionRadii found radii = ", radii];
+
+modesFilesAndRadii = Table[
+str = modesFiles[[i]];
+{StringCases[str,"r"~~rad:NumberString~~".l"~~lev:NumberString~~".l"~~l:NumberString~~".m"~~m:NumberString~~___ :>
+ {rad,lev}],str},{i,1,Length@modesFiles}];
+
+pickHighestLevel[xxx_?ListQ]:=\[NonBreakingSpace]Last@Gather[xxx, First@#1 ==First@#2 &];
+
+tmp = Gather[modesFilesAndRadii, First@First@First@#1 == First@First@First@#2 &];
+modesFilesAndRadii = Map[pickHighestLevel,tmp];
+
+
+psi4BAMModesSections = Table[
+ modesFiles = TakeColumn[modesFilesAndRadii[[i]],2];
+ {rad,lev} = TakeColumn[modesFilesAndRadii[[i]], 1][[1, 1]];
+
+ str = radii[[ToExpression@rad]];
+
+ tmp=ComposeStrainModesSection[First@modesFiles,
+ "Verbose"-> False,"SectionHeader"-> "psi4t-data",
+ "Modes"-> "All","Path" -> "Psi4BAMModes/"];
+ tmp[[2]] = {tmp[[2]], "extraction-radius = "<> ToString@str <>"\n"};
+ AppendTo[tmp, "\n\n"];
+ Flatten@tmp,
+{i,1,Length@modesFilesAndRadii}];
+ExportText[FileNameJoin[{myDestinationDir,"psi4BAMmodes.bbh"}], Flatten@psi4BAMModesSections,"Overwrite"->True];
+
+(* NOW THE WHOLE THING AGAIN FOR THE FULL MODES *)
+
+(* First, check if Vivek-style modes are available *)
+VivekModesFiles = FileNames[modesString,VivekModesSource,2];
+Print["Found Vivek-style modes files: ", VivekModesFiles];
+
+If[Length@VivekModesFiles > 0,
+modesFiles=VivekModesFiles;
+modesDecompDir = FileNameJoin[{Psi4ModesDir,"Psi4ModeDecomp"}];
+(*CreateDirectory[modesDecompDir];*)
+
+CopyDirectory[VivekModesSource<>"/data",modesDecompDir];
+
+canCreateModeFiles = False;,
+
+(* check for psi4 source files and whether mode decomp can be run *)
+WriteModeDecompConfigFile[DirectoryRules,"RunDecomp"-> True,
+ "ModesTargetDirectory"-> Psi4ModesDir,"JustPretendCalculation"-> True];
+
+modesFiles = FileNames[modesString,Psi4ModesDir<>"/Psi4ModeDecomp",2];
+If[Length@modesFiles == 0,
+ Print["Mode decomposition yields no results - no mode files can be created."];
+ canCreateModeFiles = False;,
+ canCreateModeFiles = True;
+];
+];
+
+modesFilesAndRadii = Table[
+str = modesFiles[[i]];
+{StringCases[str,"r"~~rad:NumberString~~".l"~~lev:NumberString~~".l"~~l:NumberString~~".m"~~m:NumberString~~___ :>
+ {rad,lev}],str},{i,1,Length@modesFiles}];
+
+pickHighestLevel[xxx_?ListQ]:=\[NonBreakingSpace]Last@Gather[xxx, First@#1 ==First@#2 &];
+
+tmp = Gather[modesFilesAndRadii, First@First@First@#1 == First@First@First@#2 &];
+modesFilesAndRadii = Map[pickHighestLevel,tmp];
+
+psi4ModesSections = Table[
+ modesFiles = TakeColumn[modesFilesAndRadii[[i]],2];
+ {rad,lev} = TakeColumn[modesFilesAndRadii[[i]], 1][[1, 1]];
+
+ str = radii[[ToExpression@rad]];
+
+ tmp=ComposeStrainModesSection[First@modesFiles,
+ "Verbose"-> False,"SectionHeader"-> "psi4t-data",
+ "Modes"-> "All","Path" -> "Psi4ModeDecomp/"];
+ tmp[[2]] = {tmp[[2]], "extraction-radius = "<> ToString@str <>"\n"};
+ AppendTo[tmp, "\n\n"];
+ Flatten@tmp,
+{i,1,Length@modesFilesAndRadii}];
+
+Export[FileNameJoin[{myDestinationDir,"psi4modes.bbh"}], Flatten@psi4ModesSections,"Text"];
+
+
+(* overwrite modes files if we find some in the main directory *)
+CopyFiles[filePrefix,evDir,myDestinationDir,
+{
+"moving_puncture_integrate1.txyz*",
+"moving_puncture_integrate2.txyz*",
+"psi3col.r*",
+"*.par*",
+"horizon_*",
+"ah.xy*",
+"basic.bbh",
+"uuid"
+}];
+
+
+CopyFiles[filePrefix,evDir,BAMLogDir,
+{"system.log*"}];
+
+EnergyMomentumDir = FileNameJoin[{myDestinationDir,"EnergyMomentum"}];
+CreateDirectory[EnergyMomentumDir];
+
+CopyFiles[filePrefix,evDir,EnergyMomentumDir,
+{"d*dt_r*.t*","ADM_mass_r*.t*"}];
+
+(* compress some files *)
+Run["cd "<> myDestinationDir <> "; " <>
+ "gzip moving_puncture_integrate* system.log* ah.xy*/*"];
+
+Run["cd "<> EnergyMomentumDir <> "; " <>
+ "gzip d*dt_r*.t* ADM_mass_r*.t*"];
+
+Run["cd "<> BAMLogDir <> "; " <>
+ "gzip *"];
+
+(* convert horizon and puncture track files to NRAR format and add entries to metadata file *)
+rules={};
+
+tmp = FileNames["horizon_*",myDestinationDir,2];
+If[Length@tmp == 0,
+Print["Could not find horizon files!"];,
+
+Map[BAMHorizonFilesToNRARFiles[#,"DeleteSourceFiles"-> False]&,tmp];
+
+tmp = LastInPath@First@FileNames["hmass_1.*",myDestinationDir,2];
+AppendTo[rules, "horizon-mass1" -> tmp];
+
+tmp = LastInPath@First@FileNames["hmass_2.*",myDestinationDir,2];
+AppendTo[rules, "horizon-mass2" -> tmp];
+
+tmp = LastInPath@First@FileNames["hspin_1.*",myDestinationDir,2];
+AppendTo[rules, "spin1" -> tmp];
+
+tmp = LastInPath@First@FileNames["hspin_2.*",myDestinationDir,2];
+AppendTo[rules, "spin2" -> tmp];
+
+tmp = LastInPath@First@FileNames["htraj_1.*",myDestinationDir,2];
+AppendTo[rules, "horizon-center1" -> tmp];
+
+tmp = LastInPath@First@FileNames["htraj_2.*",myDestinationDir,2];
+AppendTo[rules, "horizon-center2" -> tmp];
+];
+
+tmp = Join[FileNames["moving_puncture_integrate1.txyz*",myDestinationDir,2],
+ FileNames["moving_puncture_integrate2.txyz*",myDestinationDir,2]];
+
+If[Length@tmp == 0,
+Print["Could not find puncture track files!"];,
+Print["Found puncture track files: ", tmp];
+Map[BAMTrajectoryFileTo4Col[#,"DeleteSourceFiles"-> False]&,tmp];
+
+(* below, Last is used to get data at the finest available level *)
+tmp = Last@FileNames["traj_1.l*",myDestinationDir,2];
+AppendTo[rules,"trajectory1" -> FileNameTake[tmp,-1]];
+
+tmp = Last@FileNames["traj_2.l*",myDestinationDir,2];
+AppendTo[rules, "trajectory2" -> FileNameTake[tmp,-1]];
+];
+
+
+trajectoriesSection = ComposeConfigSection["body-data", Flatten@rules, "Verbose" -> True];
+
+tmp=FileNames["basic.bbh",myDestinationDir,2];
+If[Length@tmp == 0,
+ Print["Missing metadata file basic.bbh!"];
+ baseSection = {"[metadata]","# empty"};,
+ metadataFile = First@tmp;
+ If[FileType@metadataFile == File,
+ tmp = ConfigFileToRules@metadataFile;
+ baseSection = Flatten@StringSplit[StringSplit[Import[metadataFile,"String"],EndOfLine],"\n"];
+ DeleteFile@metadataFile;
+];
+];
+
+
+metadataContent = Flatten@Join[baseSection,physicsSection,trajectoriesSection,psi4BAMModesSections];
+metaFile = FileNameJoin[{myDestinationDir, configString<>".raw.bbh"}];
+ExportText[metaFile,metadataContent,"Overwrite"-> True];
+
+metadataContent = Flatten@Join[baseSection,physicsSection,trajectoriesSection,psi4ModesSections];
+metaFile2 = FileNameJoin[{myDestinationDir, configString<>".bbh"}];
+ExportText[metaFile2,metadataContent,"Overwrite"-> True];
+
+
+(* compute eccentricity and modify metadata *)
+
+(* use the maximal finite extraction radius *)
+eccentricityData = NinjaBase`NinjaEccentricity[metaFile,"SectionInstance" -> "MaxRad","Verbose"-> True];
+ChangeConfigEntry[metaFile,metaFile, "eccentricity", ToString@eccentricityData[[1]]];
+ChangeConfigEntry[metaFile2,metaFile2, "eccentricity", ToString@eccentricityData[[1]]];
+
+Print["select max from metaFile ", metaFile];
+radius=ReadNinjaModes[FileNameTake[metaFile,FileNameDepth@metaFile-1],FileNameTake[metaFile,-1],
+ "MModes"-> {2,2}, "DataSection" -> "psi4t-data","SectionInstance" -> "MaxRad", "Tag" -> "mode22","Verbose" -> True,
+ "OnlyComputeExtractionInfo" -> True];
+
+Print[];
+Print["Found extraction radii = ", FullForm@radius];
+Print["Found max radius = ", radius=Max[StringToNumber /@ radius]];
+
+
+(* compute start frequency and number of cycles, and modify metadata *)
+startTime = afterJunkTime + radius;
+Print["Calling NinjaCyclesStartFreq with startTime = ", startTime];
+cycleInfo = NinjaCyclesStartFreq[metaFile,startTime];
+
+startFreq = "freq-start-22" /.cycleInfo;
+nCycles = "number-of-cycles-22" /. cycleInfo;
+
+Print["found start freq = ", startFreq, ", ", "#\[NonBreakingSpace]of cycles = ", nCycles ];
+
+(* tmp = ListPlot[{Abs@ninjlm["mode22",2,2],Re@ninjlm["mode22",2,2],
+ {{afterJunkTime + radius,0},{afterJunkTime + radius,Max[TakeColumn[Abs@ninjlm["mode22",2,2],2]]}}},
+PlotRange\[Rule] All,Joined\[Rule] True];
+Export[FileNameJoin[{myDestinationDir,"timedomain_psi4_22.pdf"}],tmp]; *)
+
+ChangeConfigEntry[metaFile,metaFile, "freq-start-22", ToString@startFreq];
+ChangeConfigEntry[metaFile,metaFile, "number-of-cycles-22", ToString@nCycles];
+
+ChangeConfigEntry[metaFile2,metaFile2, "freq-start-22", ToString@startFreq];
+ChangeConfigEntry[metaFile2,metaFile2, "number-of-cycles-22", ToString@nCycles];
+
+
+Print["changed metadata entries for freq-start-22 and number-of-cycles-22"];
+
+(* compute spins after junk-radiation, and modify metadata *)
+Clear[tt,sx,sy,sz];
+tmp = ReadNinjaData[metaFile,"body-data", "spin1"];
+If[ListQ@tmp,
+ tmp = tmp /. {tt_?NumberQ,sx_?NumberQ,sy_?NumberQ,sz_?NumberQ} -> {tt,{sx,sy,sz}};
+ tmp = Interpolation@tmp;
+ tmp = Chop/@ tmp@afterJunkTime;
+ Print["spin1 after junk = ", tmp];
+ ChangeConfigEntry[metaFile,metaFile, "after-junkradiation-spin1x", ToString@tmp[[1]]];
+ ChangeConfigEntry[metaFile,metaFile, "after-junkradiation-spin1y", ToString@tmp[[2]]];
+ ChangeConfigEntry[metaFile,metaFile, "after-junkradiation-spin1z", ToString@tmp[[3]]];
+
+ ChangeConfigEntry[metaFile2,metaFile2, "after-junkradiation-spin1x", ToString@tmp[[1]]];
+ ChangeConfigEntry[metaFile2,metaFile2, "after-junkradiation-spin1y", ToString@tmp[[2]]];
+ ChangeConfigEntry[metaFile2,metaFile2, "after-junkradiation-spin1z", ToString@tmp[[3]]];
+];
+
+
+tmp = ReadNinjaData[metaFile,"body-data", "spin2"] /. {tt_,sx_,sy_,sz_} -> {tt,{sx,sy,sz}};
+If[ListQ@tmp,
+ tmp = Interpolation@tmp;
+ tmp = Chop /@ tmp@afterJunkTime;
+ Print["spin2 after junk = ", tmp];
+ ChangeConfigEntry[metaFile,metaFile, "after-junkradiation-spin2x", ToString@tmp[[1]]];
+ ChangeConfigEntry[metaFile,metaFile, "after-junkradiation-spin2y", ToString@tmp[[2]]];
+ ChangeConfigEntry[metaFile,metaFile, "after-junkradiation-spin2z", ToString@tmp[[3]]];
+
+ ChangeConfigEntry[metaFile2,metaFile2, "after-junkradiation-spin2x", ToString@tmp[[1]]];
+ ChangeConfigEntry[metaFile2,metaFile2, "after-junkradiation-spin2y", ToString@tmp[[2]]];
+ ChangeConfigEntry[metaFile2,metaFile2, "after-junkradiation-spin2z", ToString@tmp[[3]]];
+];
+
+Print["Deleting file ", FileNameJoin[{myDestinationDir,"psi4BAMmodes.bbh"}]];
+DeleteFile[FileNameJoin[{myDestinationDir,"psi4BAMmodes.bbh"}]];
+
+If[canCreateModeFiles,
+ WriteModeDecompConfigFile[DirectoryRules,"RunDecomp"-> modeDecomp,"ModesTargetDirectory"-> Psi4ModesDir];,
+ CopyFile[metaFile, metaFile2];
+];
+
+Print["========================================================\n\n"];
+];
+
+
+NRARPsi4ToStrain[metaFile_,LMAX_,\[Omega]GWStart_]:=Module[{newMetaFile,dir,newMeta,tmp,psi4tInstances,readOut,filesRead,originalFile,newFile,times,data,col3data,file},
+
+newMetaFile=StringReplace[metaFile,".bbh"->".hFFI.bbh"];
+dir=FileNameTake[metaFile,FileNameDepth[metaFile]-1];
+
+myDestinationDir=FileNameJoin[{FileNameDrop[metaFile,-1],"FFIStrainModes"}];
+
+If[FileType@myDestinationDir==None,
+ CreateDirectory[myDestinationDir],
+ RenameDirectory[myDestinationDir,myDestinationDir<>"_bak"];
+];
+
+Run["cp "<>metaFile<>" "<>newMetaFile];
+
+newMeta=Import[newMetaFile,"Text"];
+tmp=StringReplace[newMeta,"[psi4t-data]"->"[ht-data]"];
+tmp=StringReplace[tmp,"Psi4ModeDecomp/psi"->"FFIStrainModes/h"];
+Export[newMetaFile,tmp,"Text"];
+
+psi4tInstances=Length@Cases[ConfigSectionHeaders[metaFile,"Union"-> False],"psi4t-data"];
+
+Do[
+readOut=ReadNinjaModes[dir,FileNameTake[metaFile,-1],"DataSection"->"psi4t-data","LMax"->LMAX,"SectionInstance"->i,"Tag"->"dummy"];
+filesRead=readOut[[2]];
+
+Print@readOut;
+
+Do[
+
+If[m!=0,strain=hFromPsi4FFI[ninjlm["dummy",l,m],(Abs@m/2)\[Omega]GWStart/(2 \[Pi])];,strain=hFromPsi4FFI[ninjlm["dummy",l,m],(1/2)\[Omega]GWStart/(2 \[Pi])];];
+
+originalFile=Last@First@Select[filesRead,#[[1]]=={l,m}&];
+newFile=StringReplace[originalFile,"Psi4ModeDecomp/psi"->"FFIStrainModes/h"];
+
+times=TakeColumn[strain,1];
+data=TakeColumn[strain,2];
+
+col3data=Transpose@{times,Re@data,Im@data};
+file=FileNameJoin[{FileNameDrop[myDestinationDir,-1],newFile}];
+Print["Exporting file ",file];
+Export[file,col3data,{"GZIP","Table"}],{l,2,LMAX},{m,-l,l}]
+,{i,psi4tInstances}]
+]
+
+
+Options[SXSLuminosityFromMetaFiles]={"PrecessingTolerance"->0.001`,"OutputTag"->"SXSLuminosities_","OutputDir"->".","ExtrapOrder"->{2},"Verbose"->"False"}
+
+
+SXSLuminosityFromMetaFiles[metadata_?ListQ,modes_?ListQ,OptionsPattern[]]:=Module[{tags,metarules,\[CapitalOmega]startMetadata,M1,M2,\[Chi]1vect,\[Chi]2vect,\[Chi]1,\[Chi]2,M,\[Eta],q,A1,A2,Lx,Ly,Lz,Lvect,
+LvectNorm,precvalue1,precvalue2,precvalueNorm1,precvalueNorm2,precvalueNorm,precessing,\[Chi]1p,\[Chi]2p,Initial\[Chi]Plane,\[Chi]1vect\[Chi]2vect,fnameBase,myFile,mymodes,h5file,dir,
+ta,test\[Psi],pos,test\[Psi]22,domain,times,f0,mm,lum,sumModes,sumModesDominant,sumModesLum,sumModesLumDom,tmaxSum,tmaxSumDom,modesMaxima,data,int,verbose,lmax,ls,lsms,
+lsmsm1,dommodes,testdommodes,posdom,domsneg,precessingtolerance,outputtag,outputdir,xx,yy,extraporder},
+
+mymodes=modes;
+
+verbose=OptionValue["Verbose"];
+precessingtolerance=OptionValue["PrecessingTolerance"];
+outputtag=OptionValue["OutputTag"];
+outputdir=OptionValue["OutputDir"];
+extraporder=OptionValue["ExtrapOrder"];
+
+(* read metadata and convert to physical quantities *)
+tags=(FileNameTake[#1,{-3}]&)/@metadata;
+metarules=SXSMetaFilesToRules/@metadata;
+\[CapitalOmega]startMetadata[tags]="initial-orbital-frequency"/. metarules;
+M1=Flatten["initial-mass1"/. metarules,1];
+M2=Flatten["initial-mass2"/. metarules,1];
+M=M1+M2;\[Eta]=(M1 M2)^2/M^2;
+q=(Max[#1,1]&)/@(M1/M2);
+
+\[Chi]1vect=("initial-spin1"/. metarules)/M1^2;
+\[Chi]2vect=("initial-spin2"/. metarules)/M2^2;
+\[Chi]1vect\[Chi]2vect=Transpose[{\[Chi]1vect,\[Chi]2vect}];
+\[Chi]1=Norm/@\[Chi]1vect;
+\[Chi]2=Norm/@\[Chi]2vect;
+
+Lvect="initial-ADM-angular-momentum"/. metarules;
+LvectNorm=Lvect/(Norm/@Lvect);
+Initial\[Chi]Plane=Table[{\[Chi]1vect\[Chi]2vect[[i,1]]-Lvect[[i]] Lvect[[i]].\[Chi]1vect\[Chi]2vect[[i,2]],\[Chi]1vect\[Chi]2vect[[i,2]]-Lvect[[i]] Lvect[[i]].\[Chi]1vect\[Chi]2vect[[i,2]]},{i,Length[Lvect]}];
+\[Chi]1p=Norm/@Initial\[Chi]Plane[[All,1]];
+\[Chi]2p=Norm/@Initial\[Chi]Plane[[All,2]];
+
+
+(* Is it precessing? *)
+A1=1+3/4. q;
+A2=1+3/(4. q);
+precvalue1=Table[(\[Chi]1vect[[i]] A1[[i]])\[Cross]LvectNorm[[i]],{i,Length[tags]}];
+precvalue2=Table[(\[Chi]2vect[[i]] A2[[i]])\[Cross]LvectNorm[[i]],{i,Length[tags]}];
+precvalueNorm1=Norm/@precvalue1;
+precvalueNorm2=Norm/@precvalue2;
+precvalueNorm=precvalueNorm1^2+precvalueNorm2^2;
+Do[If[precvalueNorm[[i]]<0.001,precessing[tags[[i]]]=False,precessing[tags[[i]]]=True],{i,Length[tags]}];
+
+(* Compute Luminosity *)
+Table[
+ (* Find rpsi4 files *)
+ fnameBase=ToString[outputtag];
+ Print["Computing Luminosity from: ",tags[[i]]];
+ myFile=ToString[outputdir]<>"/"<>fnameBase<>ToString[tags[[i]]]<>".dat";
+
+ dir=FileNameDrop[metadata[[i]],-2];
+ h5file=First[FileNames["rMPsi4_Asymptotic_GeometricUnits.h5",dir,2]];
+
+ If[FileExistsQ[h5file],Print["Found ",h5file," . Continue"];,Print["Not found ",h5file," . Bye"];Return[]];
+ If[precessing[tags[[i]]],Print["Precessing run. Non simetry. Taking all modes"];,Print["Non-Precessing run. Assuming simetry. Taking only m>0 modes"];mymodes=Select[mymodes,#1[[2]]>=0&];];
+ Print["Modes selection : ",mymodes];
+
+ (* How many dominant modes are present? eg. {{2,2},{2,1},{2,-2}}? *)
+ lmax=Max[mymodes[[All,1]]];
+ ls=DeleteDuplicates[mymodes[[All,1]]];
+ lsms=CombineColumns[ls,ls];
+ lsmsm1=CombineColumns[ls,ls-1];
+ dommodes=Sort[Join[lsms,lsmsm1]];
+ domsneg=dommodes/. {xx_,yy_}->{xx,-yy};
+ dommodes=Sort[Join[dommodes,domsneg]];
+ testdommodes=(MemberQ[mymodes,#1]&)/@dommodes;
+ posdom=Flatten[Position[testdommodes,True]];
+ dommodes=dommodes[[posdom]];Print["Dominant modes : ",dommodes];
+
+ ta=Table[
+ (* Load and process data *)
+ Print["Extrapolation order : ",j];
+ test\[Psi]=GetAsymptoticMultiMode[h5file,j,mymodes];
+ Print["Modes Loaded"];
+
+ pos=First[First[Position[mymodes,{2,2}]]];
+ test\[Psi]22=test\[Psi][[pos]];
+ domain={First[First[test\[Psi]22]],First[Last[test\[Psi]22]]};
+ times=Range[First[domain],Last[domain],0.5];
+ test\[Psi]=Interpolation/@test\[Psi];
+ test\[Psi]=Table[CombineColumns[times,test\[Psi][[i]][times]],{i,Length[test\[Psi]]}];
+
+ (* 22 mode guess frequency *)
+ f0=Abs[First[GuessFFIf0[test\[Psi][[pos]],"MinTime"->First[First[test\[Psi][[pos]]]]+250]]];
+
+ (* compute Luminosoties *)
+
+ Do[If[mymodes[[l,2]]!=0,mm=mymodes[[l,2]]/2,mm=(mymodes[[l,2]]+1)/2];
+ lum[mymodes[[l,1]],mymodes[[l,2]]]=Abs[TakeColumn[NewsFromPsi4FFI[test\[Psi][[l]],0.75f0 Abs[mm]],2]]^2;Print[mymodes[[l]]];,{l,Length[mymodes]}];
+
+ If[precessing[tags[[i]]],
+ sumModes=1/(16 \[Pi])Sum[lum[mymodes[[l,1]],mymodes[[l,2]]],{l,Length@mymodes}];
+ sumModesDominant=1/(16 \[Pi])Sum[lum[dommodes[[l,1]],dommodes[[l,2]]],{l,Length@dommodes}];
+ ,
+ sumModes=1/(8 \[Pi])Sum[lum[mymodes[[l,1]],mymodes[[l,2]]],{l,Length@mymodes}];
+ sumModesDominant=1/(8 \[Pi])Sum[lum[dommodes[[l,1]],dommodes[[l,2]]],{l,Length@dommodes}];];
+
+
+ sumModesLum=CombineColumns[times,sumModes];
+ sumModesLumDom=CombineColumns[times,sumModesDominant];
+ tmaxSum=TimeOfMaximum[sumModesLum];
+ tmaxSumDom=TimeOfMaximum[sumModesLumDom];
+ modesMaxima=Table[data=CombineColumns[times,lum[mymodes[[l,1]],mymodes[[l,2]]]];
+ int=Interpolation[data];
+ {ValueOfMaximum[data],int[tmaxSum],int[tmaxSumDom]},{l,Length[mymodes]}];
+
+If[verbose,Print[ListPlot[{sumModesLum,sumModesLumDom},Joined->True,PlotRange->All]];];
+Flatten[{tags[[i]],\[Eta][[i]],\[Chi]1[[i]],\[Chi]2[[i]],\[Chi]1p[[i]],\[Chi]2p[[i]],Initial\[Chi]Plane[[i]],j,ValueOfMaximum[sumModesLum],tmaxSum,ValueOfMaximum[sumModesLumDom],tmaxSumDom,Flatten[modesMaxima]}],{j,extraporder}];
+
+Print["Exporting results to : ",myFile];Export[myFile,ta];
+,{i,Length[tags]}];
+
+ta]
+
+
+Options[BAMLuminosityFromMetaFiles]={"PrecessingTolerance"->0.001,"OutputTag"->"BAMLuminosities_","OutputDir"->".","ExtractionRadius"->{},"Verbose"->"False"};
+
+
+BAMLuminosityFromMetaFiles[metadata_?ListQ,modes_?ListQ,OptionsPattern[]]:=Module[{tags,metarules,\[CapitalOmega]startMetadata,M1,M2,\[Chi]1vect,\[Chi]2vect,\[Chi]1,\[Chi]2,M,\[Eta],q,A1,A2,Lx,Ly,Lz,Lvect,
+LvectNorm,precvalue1,precvalue2,precvalueNorm1,precvalueNorm2,precvalueNorm,precessing,\[Chi]1p,\[Chi]2p,Initial\[Chi]Plane,\[Chi]1vect\[Chi]2vect,fnameBase,myFile,mymodes,h5file,dir,
+ta,test\[Psi],pos,test\[Psi]22,domain,times,f0,mm,lum,sumModes,sumModesDominant,sumModesLum,sumModesLumDom,tmaxSum,tmaxSumDom,modesMaxima,data,int,verbose,lmax,ls,lsms,
+lsmsm1,dommodes,testdommodes,posdom,domsneg,precessingtolerance,outputtag,outputdir,xx,yy,extractionradius,p1,p2,r1,r2,InitialOrbitalAngularMomentum,InitialAngularMomentum,
+extraddef,myRad,myrads},
+
+mymodes=modes;
+
+verbose=OptionValue["Verbose"];
+precessingtolerance=OptionValue["PrecessingTolerance"];
+outputtag=OptionValue["OutputTag"];
+outputdir=OptionValue["OutputDir"];
+extractionradius=OptionValue["ExtractionRadius"];
+
+(* read metadata and convert to physical quantities *)
+tags=FileNameTake[#,{-3}]&/@metadata;
+metarules=BAMMetaFilesToRules/@metadata;
+
+M1=Flatten["mass1"/. metarules,1];
+M2=Flatten["mass2"/. metarules,1];
+M=M1+M2;
+\[Eta]=(M1 M2)^2/M^2;
+q=(Max[#1,1]&)/@(M2/M1);
+
+\[Chi]1vect=Transpose@{(("initial-bh-spin1x"/. metarules)/M1^2)[[All,1]],(("initial-bh-spin1y"/. metarules)/M1^2)[[All,1]],(("initial-bh-spin1z"/. metarules)/M1^2)[[All,1]]};
+
+\[Chi]2vect=Transpose@{(("initial-bh-spin2x"/. metarules)/M2^2)[[All,1]],(("initial-bh-spin2y"/. metarules)/M2^2)[[All,1]],(("initial-bh-spin2z"/. metarules)/M2^2)[[All,1]]};
+\[Chi]1vect\[Chi]2vect=Transpose[{\[Chi]1vect,\[Chi]2vect}];
+\[Chi]1=Norm/@\[Chi]1vect;
+\[Chi]2=Norm/@\[Chi]2vect;
+
+
+r1=Transpose[{("initial-bh-position1x"/.metarules)[[All,1]],("initial-bh-position1y"/.metarules)[[All,1]],("initial-bh-position1z"/.metarules)[[All,1]]}];
+r2=Transpose[{("initial-bh-position2x"/.metarules)[[All,1]],("initial-bh-position2y"/.metarules)[[All,1]],("initial-bh-position2z"/.metarules)[[All,1]]}];
+p1=Transpose[{("initial-bh-momentum1x"/.metarules)[[All,1]],("initial-bh-momentum1y"/.metarules)[[All,1]],("initial-bh-momentum1z"/.metarules)[[All,1]]}];
+p2=Transpose[{("initial-bh-momentum2x"/.metarules)[[All,1]],("initial-bh-momentum2y"/.metarules)[[All,1]],("initial-bh-momentum2z"/.metarules)[[All,1]]}];
+
+Lvect= Table[p1[[i]]\[Cross]r1[[i]] + p2[[i]]\[Cross]r2[[i]],{i,Length@metadata}];
+LvectNorm=Lvect/(Norm/@Lvect);
+Initial\[Chi]Plane=Table[{\[Chi]1vect\[Chi]2vect[[i,1]]-Lvect[[i]] Lvect[[i]].\[Chi]1vect\[Chi]2vect[[i,2]],\[Chi]1vect\[Chi]2vect[[i,2]]-Lvect[[i]] Lvect[[i]].\[Chi]1vect\[Chi]2vect[[i,2]]},{i,Length[Lvect]}];
+
+\[Chi]1p=Norm/@Initial\[Chi]Plane[[All,1]];
+\[Chi]2p=Norm/@Initial\[Chi]Plane[[All,2]];
+
+
+(* Is it precessing? *)
+A1=1+3/4. q;
+A2=1+3/(4. q);
+precvalue1=Table[(\[Chi]1vect[[i]] A1[[i]])\[Cross]LvectNorm[[i]],{i,Length[tags]}];
+precvalue2=Table[(\[Chi]2vect[[i]] A2[[i]])\[Cross]LvectNorm[[i]],{i,Length[tags]}];
+precvalueNorm1=Norm/@precvalue1;
+precvalueNorm2=Norm/@precvalue2;
+precvalueNorm=precvalueNorm1^2+precvalueNorm2^2;
+Do[If[precvalueNorm[[i]]<0.001,precessing[tags[[i]]]=False,precessing[tags[[i]]]=True],{i,Length[tags]}];
+
+extraddef=Table["extraction-radius"/.metarules[[i]],{i,Length@metarules}];
+
+If[Length@extractionradius!=0,extraddef==TakeColumn[extraddef,extractionradius]];
+
+(* Compute Luminosity *)
+Table[
+ (* Find rpsi4 files *)
+ fnameBase=ToString[outputtag];
+ Print["Computing Luminosity from: ",tags[[i]]];
+ myFile=ToString[outputdir]<>"/"<>fnameBase<>ToString[tags[[i]]]<>".dat";
+
+ dir=FileNameTake[metadata[[i]],FileNameDepth[metadata[[i]]]-1];
+ myrads=extraddef[[i]];
+
+ If[FileExistsQ[dir],Print["Found ",dir," . Continue"];,Print["Not found ",dir," . Bye"];Return[]];
+ If[precessing[tags[[i]]],Print["Precessing run. Non simetry. Taking all modes"];,Print["Non-Precessing run. Assuming simetry. Taking only m>0 modes"];mymodes=Select[mymodes,#1[[2]]>=0&];];
+ Print["Modes selection : ",mymodes];
+
+ (* How many dominant modes are present? eg. {{2,2},{2,1},{2,-2}}? *)
+ lmax=Max[mymodes[[All,1]]];
+ ls=DeleteDuplicates[mymodes[[All,1]]];
+ lsms=CombineColumns[ls,ls];
+ lsmsm1=CombineColumns[ls,ls-1];
+ dommodes=Sort[Join[lsms,lsmsm1]];
+ domsneg=dommodes/. {xx_,yy_}->{xx,-yy};
+ dommodes=Sort[Join[dommodes,domsneg]];
+ testdommodes=(MemberQ[mymodes,#1]&)/@dommodes;
+ posdom=Flatten[Position[testdommodes,True]];
+ dommodes=dommodes[[posdom]];Print["Dominant modes : ",dommodes];
+
+ ta=Table[
+ (* Load and process data *)
+ Clear[ninjlm];
+ Print["Extraction radius : ",myrads[[j]]];
+
+ Do[myReadNinjaModes[dir,FileNameTake[metadata[[i]],-1],"DataSection"-> "psi4t-data","LMax" -> 2,"MModes" -> {mymodes[[l,1]],mymodes[[l,2]]}, "SectionInstance" -> j,
+ "Tag"-> "dummy"];,{l,Length@mymodes}];
+ Print["Modes Loaded"];
+
+ (* 22 mode guess frequency *)
+ test\[Psi]=TimeUnion@ninjlm["dummy",2,2];
+ f0=Abs@First@GuessFFIf0[test\[Psi], "MinTime"-> First@First@test\[Psi]+250];
+ times=TakeColumn[test\[Psi],1];
+
+ (* compute Luminosoties *)
+ Do[If[mymodes[[l,2]]!=0,mm=mymodes[[l,2]]/2,mm=(mymodes[[l,2]]+1)/2];
+ test\[Psi]=TimeUnion@ninjlm["dummy",mymodes[[l,1]],mymodes[[l,2]]];
+ lum[mymodes[[l,1]],mymodes[[l,2]]]=Abs[TakeColumn[NewsFromPsi4FFI[test\[Psi],0.75f0 Abs[mm]],2]]^2;Print[mymodes[[l]]];,{l,Length[mymodes]}];
+
+ If[precessing[tags[[i]]],
+ sumModes=1/(16 \[Pi])Sum[lum[mymodes[[l,1]],mymodes[[l,2]]],{l,Length@mymodes}];
+ sumModesDominant=1/(16 \[Pi])Sum[lum[dommodes[[l,1]],dommodes[[l,2]]],{l,Length@dommodes}];
+ ,
+ sumModes=1/(8 \[Pi])Sum[lum[mymodes[[l,1]],mymodes[[l,2]]],{l,Length@mymodes}];
+ sumModesDominant=1/(8 \[Pi])Sum[lum[dommodes[[l,1]],dommodes[[l,2]]],{l,Length@dommodes}];];
+
+
+ sumModesLum=CombineColumns[times,sumModes];
+ sumModesLumDom=CombineColumns[times,sumModesDominant];
+ tmaxSum=TimeOfMaximum[sumModesLum];
+ tmaxSumDom=TimeOfMaximum[sumModesLumDom];
+ modesMaxima=Table[data=CombineColumns[times,lum[mymodes[[l,1]],mymodes[[l,2]]]];
+ int=Interpolation[data];
+ {ValueOfMaximum[data],int[tmaxSum],int[tmaxSumDom]},{l,Length[mymodes]}];
+
+If[verbose,Print[ListPlot[{sumModesLum,sumModesLumDom},Joined->True,PlotRange->All]];];
+Flatten[{tags[[i]],\[Eta][[i]],\[Chi]1[[i]],\[Chi]2[[i]],\[Chi]1p[[i]],\[Chi]2p[[i]],Initial\[Chi]Plane[[i]],myrads[[j]],ValueOfMaximum[sumModesLum],tmaxSum,ValueOfMaximum[sumModesLumDom],tmaxSumDom,Flatten[modesMaxima]}],{j,Length@myrads}];
+
+Print["Exporting results to : ",myFile];
+Export[myFile,ta];
+
+,{i,Length[tags]}];
+
+ta
+]
+
+
+AHBAMsmall[q_,s_]:=Sqrt[0.7599216762029171` -0.6443660299643744` s^2]/(1+q)
+AHBAMbig[q_,s_]:=(q Sqrt[0.9466225527668473` -0.8578738205662785` s^2])/(1+q)
+
+
+AHBAMsmall2017[q_,s_]:=(0.9097788740970632` Sqrt[1-0.8630715321085808` s^2]-0.013097939946145838` q Sqrt[1-0.8630715321085808` s^2])1/(1+q)
+AHBAMbig2017[q_,s_]:=(0.9092695479821113` Sqrt[1-0.9004695426988402` s^2]+0.025102624533684333` q Sqrt[1-0.9004695426988402` s^2])q/(1+q)
+
+
+End[];
+EndPackage[];
+
+
+
diff --git a/code/DataFits.m b/code/DataFits.m
new file mode 100644
index 0000000000000000000000000000000000000000..315fbe96baddee87d94337a0464bbcd50858085d
--- /dev/null
+++ b/code/DataFits.m
@@ -0,0 +1,2224 @@
+(* ::Package:: *)
+
+(************************************************************************)
+(* This file was generated automatically by the Mathematica front end. *)
+(* It contains Initialization cells from a Notebook file, which *)
+(* typically will have the same name as this file except ending in *)
+(* ".nb" instead of ".m". *)
+(* *)
+(* This file is intended to be loaded into the Mathematica kernel using *)
+(* the package loading commands Get or Needs. Doing so is equivalent *)
+(* to using the Evaluate Initialization Cells menu command in the front *)
+(* end. *)
+(* *)
+(* DO NOT EDIT THIS FILE. This entire file is regenerated *)
+(* automatically each time the parent Notebook file is saved in the *)
+(* Mathematica front end. Any changes you make to this file will be *)
+(* overwritten. *)
+(************************************************************************)
+
+
+
+(* ::Code::Initialization:: *)
+BeginPackage["DataFits`",{"NRLists`","ErrorBarPlots`"}];
+
+
+(* ::Code::Initialization:: *)
+\[Eta]::usage="\[Eta] for local usage";
+S::usage="S for local usage";
+\[Chi]1::usage="\[Chi]1 for local usage";
+\[Chi]2::usage="\[Chi]2 for local usage";
+\[Delta]\[Chi]::usage="\[Delta]\[Chi] for local usage";
+
+a0::usage="a0 for local usage";
+a1::usage="a1 for local usage";
+a2::usage="a2 for local usage";
+
+sTot::usage="";
+sTot3::usage="";
+\[Chi]Tot::usage="";
+
+\[Chi]diffplus::usage="";
+\[Chi]diffstan::usage="";
+
+DataFitFunction::usage="DataFitFunction[data_?ListQ,ansatzList_?ListQ,OptionsPattern[]]";
+
+DataFitFunctionAll::usage="DataFitFunctionAll[dataraw_?ListQ,OptionsPattern[]]";
+DataFitFunctionAllNoWeights::usage="DataFitFunctionAllWeights[dataraw_?ListQ,OptionsPattern[]]";
+
+AnsatzRestrictions::usage="AnsatzRestrictions[nsfit_, q1fit_, ansatzGen_]";
+
+Plot2DFits::usage="Plot2DFits[data_?ListQ,fitlist_?ListQ,fitvars_?ListQ, OptionsPattern[]]";
+myListPlot3D::usage="myListPlot3D[data_?ListQ,options]: Plot 3d data + interpolated function";
+ColorGradient::usage="ColorGradient[data,colors,options]. Create a linear gradient of colors for the data";
+CreateColors::usage="CreateColors[codes,colors]. Set different colors for each NR code";
+
+CleanAnsatzParams::usage="cleanAnsatzParams[paramsGuess_, vars_]";
+
+Generate1DPolynomialAnsatz::usage="Generate1DPolynomialAnsatz[CoefficientPrefixString_?StringQ,variable_,MinOrder_?IntegerQ,MaxOrder_?IntegerQ] creates a polynomial function ansatz.";
+
+Residuals::usage="Residuals[data_,fit_,vars_] computes fit residuals.";
+AtomsList::usage="Take the coefficients out";
+
+GeneralizeFunction::usage="GeneralizeFunction[expr_,x_] insert free coefficient at all (non-exact) real numbers in a function";
+GeneralizeFunction::usage="GeneralizeFunction[expr_,x_,coord_,orderNum,orderDenom_] insert polynomial with free coefficients at all (non-exact) real numbers in a function";
+
+ExactPade::usage="ExactPade[ansatz_,coeffRules_,padeOptions_] get Pade approximant while keeping exact coefficients fixed.";
+Generate1DPadeAnsatzList::usage="Generate1DPadeAnsatzList[ansatz_,\!\(\*
+StyleBox[\"coeffRules_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)\!\(\*
+StyleBox[\"variable_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)\!\(\*
+StyleBox[\"paramName_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)\!\(\*
+StyleBox[\"minPadeTypeSum_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)\!\(\*
+StyleBox[\"maxPadeTypeSum_\", \"Code\"]\)] make a list of all Pade ansaetze with type (num+denom) summing up between [min,max].";
+
+InvertRules::usage="InvertRules[rules_] invert a list of rules";
+Get1dInverseRules::usage="Get1dInverseRules[ansatz_,coeffRules_] invert a set of 1d rules in eta or S, taking care of the Pade form";
+Get1dInverseRulesS::usage="Get1dInverseRulesS[ansatz_,coeffRules_,productAnsatz_] invert the 1d rules in S, taking care of normalization and Pade form";
+
+FitPredictionIntervalFunctionFinalOnly::usage="FitPredictionIntervalFunctionFinalOnly[fit_,ansatzRules_] return function for the fit uncertainty (prediction interval), final fit statistics only";
+FitPredictionIntervalFunctionFinalOnlyq1::usage="FitPredictionIntervalFunctionFinalOnlyq1[fit_,ansatzRules_] return function for the fit uncertainty (prediction interval), in the limit of q=1, final fit statistics only";
+FitPredictionIntervalFinalOnly::usage="FitPredictionIntervalFinalOnly[fit_,ansatzRules_,etain_,chi1in_,chi2in_] estimate the fit uncertainty (prediction interval) at a given point, final fit statistics only";
+FitPredictionIntervalStderrSq::usage="FitPredictionIntervalStderrSq[\!\(\*
+StyleBox[\"finalFit_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)\!\(\*
+StyleBox[\"finalAnsatzRules_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)\!\(\*
+StyleBox[\"fit2dParts_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)\[Eta]0stuff_,extraCoeffRules_,productAnsatz_,q1_] evaluate the various stderrsq contributions for fit uncertainty intervals";
+FitPredictionIntervalFunction::usage="FitPredictionIntervalFunction[finalFit_,finalAnsatzRules_,fit2dParts_,\[Eta]0stuff_,extraCoeffRules_,productAnsatz_] return function for the fit uncertainty (prediction interval)";
+FitPredictionIntervalFunctionq1::usage="FitPredictionIntervalFunctionq1[finalFit_,finalAnsatzRules_,fit2dParts_,\[Eta]0stuff_,extraCoeffRules_,productAnsatz_] return function for the fit uncertainty (prediction interval), in the limit of q=1";
+FitPredictionInterval::usage="FitPredictionInterval[finalFit_,finalAnsatzRules_,fit2dParts_,\[Eta]0fit_,extraCoeffRules_,productAnsatz_,etain_,chi1in_,chi2in_] estimate the fit uncertainty (prediction interval) at a given point";
+
+TeXExportCoeffTable::usage="TeXExportCoeffTable[fit_,filename_] export a fit coefficient table into a nice TeX file.";
+TeXExportCovarMatrixTable::usage="TeXExportCovarMatrixTable[fitCovar_,fitCoeffRules_,filename_] export fit covariance matrix into a nice TeX file.";
+SubscriptRules::usage="SubscriptRules[rules_] make a subscript rule from a numeric coefficient rule.";
+GetRawTwoDAnsatz::usage="GetRawTwoDAnsatz[finalfit_,fit2dParts_,productAnsatz_,constrained_] put together raw 2d ansatz equation.";
+GetAllRules::usage="GetAllRules[finalfit_,fit2dParts_,twodrules_] collect all 1d, 2d and 3d coefficient rules";
+TeXFormatAnsatz::usage="TeXFormatAnsatz[ansatz_,formattingRules_,coeffRules_] format an ansatz nicer in TeX";
+TeXExportAnsatz::usage="TeXExportAnsatz[ansatz_,formattingRules_,coeffRules_,filename_] export a nicely formatted ansatz to TeX.";
+TeXExportTwoDAnsatz::usage="TeXExportTwoDAnsatz[finalfit_,fit2dParts_,twodrules_,formattingRules_,productAnsatz_,constrained_,filename_] format the 2d part of the final ansatz.";
+TeXExportChiDiffTerms::usage="TeXExportChiDiffTerms[chidiffAnsaetze_,formattingRules_,coeffRules_,filename_] concatenate and export to TeX the various chidiff ansatz terms.";
+TeXExportFinalAnsatz::usage="TeXExportFinalAnsatz[finalfit_,fit2dParts_,twodrules_,chidiffAnsaetze_,formattingRules_,productAnsatz_,twodConstrained_,filename_] format the final ansatz nicely.";
+TexExportCoeffTable::usage="TeXExportCoeffTable[coeffRules_,covar_,filename_] format a fit coefficient table without t-stat nor p-value.";
+TeXExportTabularTable::usage="TeXExportTabularTable[datatable_,filename_,rowHeadings_,colHeadings_,padZeroes_] export a table with array->tabular and formatting fixes.";
+
+PyExportFinalFit::usage="PyExportFinalFit[fit_,extraFormattingRules_,filename_] export the final fit (with numerical coefficients) for python LAL uise.";
+PyExportFinalAnsatz::usage="PyExportFinalAnsatz[finalfit_,fit2dParts_,chidiffAnsaetze_,productAnsatz_,extraFormattingRules_,filename_] export the final ansatz (with symbolic coefficients) for python LAL uise.";
+PyExportFinalFitCoeffs::usage="PyExportFinalFitCoeffs[finalfit_,fit2dParts_,\!\(\*
+StyleBox[\"all2dconstraints_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)filename_] export the numerical coefficients to be used together with the ansatz.";
+
+SupplExportAllFitCoeffs::usage="SupplExportAllFitCoeffs[finalfit_,fit2dParts_,\!\(\*
+StyleBox[\"all2dconstraints_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)\!\(\*
+StyleBox[\"eta0covar_\", \"Code\"]\)\!\(\*
+StyleBox[\",\", \"Code\"]\)filename_] export the numerical coefficients to a plain ASCII table file.";
+SupplExportCovarMatrix::usage="SupplExportCovarMatrix[covar_,coeffRules_,fileName_] export covariance matrices as simple ASCII table files.";
+
+AIC::usage="AIC[data,fitname,variables,number of parameters]: Explicit computation of the AIC value given by NonlinearModelFit. In data [[#,-2]]: values, [[#,-1]]: weights. Fit is the fit name e.g FinalSpin0815. Does not work for RITFinalSpinNonPrec2014";
+AICc::usage="AIC[data,fitname,variables,number of parameters]: Explicit computation of the AICc value given by NonlinearModelFit. In data [[#,-2]]: values, [[#,-1]]: weights. Fit is the fit name e.g FinalSpin0815. Does not work for RITFinalSpinNonPrec2014";
+BIC::usage="AIC[data,fitname,variables,number of parameters]: Explicit computation of the BIC value given by NonlinearModelFit. In data [[#,-2]]: values, [[#,-1]]: weights. Fit is the fit name e.g FinalSpin0815. Does not work for RITFinalSpinNonPrec2014";
+KullbagLeiblerDiv::usage="KullbagLeiblerDiv[p1_?ListQ,p2_?ListQ]: Computation of the KL criterion";
+JensenShanonDiv::usage="JensenShanonDiv[p1_?ListQ,p2_?ListQ]: Computation of the JS criterion";
+KL::usage="KL[p1_?ListQ,p2_?ListQ],lim: Computation of the KL criterion";
+JS::usage="JS[p1_?ListQ,p2_?ListQ,lim]: Computation of the JS criterion";
+
+
+CredibleRegion::usage="CredibleRegion[data_,level_]: Computation of the credible region";
+ComputeEdges::usage="ComputeEdges[pts]";
+CredibleInterval::usage="CredibleInterval[data_,level_]: Computation of the credible intervals";
+
+
+(* ::Code::Initialization:: *)
+Begin["`Private`"];
+
+
+(* ::Code::Initialization:: *)
+AtomsList[expr_]:=Union@Select[Level[expr,{0,Infinity}],AtomQ];
+
+
+InterpolationDomain[fun_]:=Module[{min,max},{min,max}={fun[[1,1,1]],fun[[1,1,2]]}];
+
+
+q\[Eta][\[Eta]_]:=-(1.-1/(2\[Eta]))+Sqrt[(1-1/(2\[Eta]))^2 -1]
+
+
+\[Eta]q[q_]:=q/(1.+q)^2.
+
+
+\[Chi]diffplus[\[Eta]_,xx_,yy_]:=Module[{s},s=(1/2(1+Sqrt[1-4 \[Eta]])xx - 1/2(1-Sqrt[1-4 \[Eta]])yy)]
+
+
+\[Chi]diffstan[\[Eta]_,xx_,yy_]:=Module[{s},s=xx-yy]
+
+
+myListPlot3D[list_,opt___]:=Module[{p1,p2},
+ p1=ListPlot3D[If[(Length@Dimensions@list)>1,list[[1]],list],InterpolationOrder-> 3];
+ p2=ListPointPlot3D[list,PlotStyle-> PointSize-> Large,opt];
+ Show[p1,p2]
+];
+
+
+myListPlot3D[list_,opt___]:=Module[{p1,p2},
+ p1=ListPlot3D[list,InterpolationOrder-> 3,opt];
+ p2=ListPointPlot3D[list,PlotStyle-> PointSize-> Large,opt];
+ Show[p1,p2]
+];
+
+
+\[Chi]Tot[\[Eta]_,\[Chi]1_,\[Chi]2_]:=Module[{m1,m2,s},
+
+m1=1/2 (1+Sqrt[1-4 \[Eta]]);
+m2=1/2 (1-Sqrt[1-4 \[Eta]]);
+
+s=(m1 \[Chi]1 + m2 \[Chi]2)/(m1+ m2)
+]
+
+
+sTot[\[Eta]_,\[Chi]1_,\[Chi]2_]:=Module[{m1,m2},
+
+m1=1/2 (1+Sqrt[1-4 \[Eta]]);
+m2=1/2 (1-Sqrt[1-4 \[Eta]]);
+
+(m1^2 \[Chi]1 + m2^2 \[Chi]2)
+]
+
+
+sTotR[\[Eta]_,\[Chi]1_,\[Chi]2_]:=Module[{m1,m2},
+m1=1/2 (1+Sqrt[1-4 \[Eta]]);
+m2=1/2 (1-Sqrt[1-4 \[Eta]]);
+
+(m1^2 \[Chi]1 + m2^2 \[Chi]2)/(m1^2 + m2^2)
+]
+
+
+sTot3[\[Eta]_,\[Chi]1_,\[Chi]2_]:=Module[{m1,m2},
+m1=1/2 (1+Sqrt[1-4 \[Eta]]);
+m2=1/2 (1-Sqrt[1-4 \[Eta]]);
+
+(m1^2 \[Chi]1 + m2^2 \[Chi]2)/(m1^2 + m2^2)
+]
+
+
+countSummands[expr_]:=If[Head[expr]===Plus,Length[expr],If[expr===0,0,1]]
+
+
+GeneralizeFunction[expr_,x_]:=Module[{num,numTermsNum,numSymbolsFirstTerm,i,termsNum,termsDenom,iStart,rule0,rulesNum,rulesDenom,reals},
+
+num=Numerator[expr];
+numTermsNum = countSummands[num];
+If[numTermsNum==1,
+termsNum = {num};
+numSymbolsFirstTerm=1;
+,
+termsNum = Level[num,{1,1}];
+numSymbolsFirstTerm=Length[Cases[Level[termsNum[[1]],{1,Infinity}],y_Symbol]];
+];
+
+If[numSymbolsFirstTerm==0,
+ iStart=2;
+ reals=Cases[Tally[Select[Level[termsNum[[1]],{0,Infinity}],AtomQ]][[All,1]],y_Real];
+ If[Length[reals]>0,
+ rule0={termsNum[[1]]->termsNum[[1]] ToExpression[ToString@x<>"0"]};
+ ,
+ rule0={};
+ ];
+ ,
+ iStart=1;
+ rule0={};
+];
+rulesNum=rule0;
+
+For[i=iStart,i<=Length[termsNum],i++,
+ reals=Cases[Tally[Select[Level[termsNum[[i]],{0,Infinity}],AtomQ]][[All,1]],y_Real];
+ If[Length[reals]>0,
+ rulesNum=Join[rulesNum,{termsNum[[i]] -> termsNum[[i]] ToExpression[ToString@x<>ToString[i-iStart+1]]}];
+ ];
+];
+
+(* currently assumes that denominator always has a -1 in front, can be easily generalized with countSummands as for numerator *)
+termsDenom = Level[Denominator[expr],{1,1}];
+rulesDenom = {};
+For[i=1,i<=Length[termsDenom],i++,
+ reals=Cases[Tally[Select[Level[termsDenom[[i]],{0,Infinity}],AtomQ]][[All,1]],y_Real];
+ If[Length[reals]>0,
+ rulesDenom=Join[rulesDenom,{termsDenom[[i]] -> termsDenom[[i]] ToExpression[ToString@x<>ToString[Length[termsNum]-iStart+1+i]]}];
+ ];
+];
+
+Return[(Numerator[expr]/.rulesNum)/(Denominator[expr]/.rulesDenom)]
+]
+
+
+GeneralizeFunction[expr_,x_,coord_,orderNum_,orderDenom_]:=Module[{num,numTermsNum,numSymbolsFirstTerm,i,termsNum,termsDenom,iStart,rule0,rulesNum,rulesDenom,reals},
+
+num=Numerator[expr];
+numTermsNum = countSummands[num];
+If[numTermsNum==1,
+termsNum = {num};
+numSymbolsFirstTerm=1;
+,
+termsNum = Level[num,{1,1}];
+numSymbolsFirstTerm=Length[Cases[Level[termsNum[[1]],{1,Infinity}],y_Symbol]];
+];
+
+If[numSymbolsFirstTerm==0,
+ iStart=2;
+ reals=Cases[Tally[Select[Level[termsNum[[1]],{0,Infinity}],AtomQ]][[All,1]],y_Real];
+ If[Length[reals]>0,
+ rule0={termsNum[[1]]->termsNum[[1]](Sum[coord^j ToExpression/@ToExpression@(ToString@x<>"0"<>ToString@j),{j,0,orderNum}])};
+ ,
+ rule0={};
+ ];
+ ,
+ iStart=1;
+ rule0={};
+];
+rulesNum=rule0;
+
+For[i=iStart,i<=Length[termsNum],i++,
+ reals=Cases[Tally[Select[Level[termsNum[[i]],{0,Infinity}],AtomQ]][[All,1]],y_Real];
+ If[Length[reals]>0,
+ rulesNum=Join[rulesNum,{termsNum[[i]] -> termsNum[[i]](Sum[coord^j ToExpression@(ToString@x<>ToString[i-iStart+1]<>ToString@j),{j,0,orderNum}])}];
+ ];
+];
+
+(* currently assumes that denominator always has a -1 in front, can be easily generalized with countSummands as for numerator *)
+termsDenom = Level[Denominator[expr],{1,1}];
+rulesDenom = {};
+For[i=1,i<=Length[termsDenom],i++,
+ reals=Cases[Tally[Select[Level[termsDenom[[i]],{0,Infinity}],AtomQ]][[All,1]],y_Real];
+ If[Length[reals]>0,
+ rulesDenom=Join[rulesDenom,{termsDenom[[i]] -> termsDenom[[i]](Sum[coord^j ToExpression/@ToExpression@(ToString@x<>ToString[Length[termsNum]-iStart+1+i]<>ToString@j),{j,0,orderDenom}])}];
+ ];
+];
+
+(Numerator[expr]/.rulesNum)/(Denominator[expr]/.rulesDenom)
+]
+
+
+(*wrapper to Pade approximant that keeps exact coefficients like Sqrt[2] exact, so that GeneralizeFunction won't assign extra coefficients to them.*)
+ExactPade[ansatz_,coeffRules_,padeOptions_]:=PadeApproximant[ansatz,padeOptions]/.coeffRules;
+
+
+myRound[x_,d_] := Module[{mantExp,mant,exp},
+mantExp = MantissaExponent[x];
+mant = mantExp[[1]];
+exp = mantExp[[2]];
+If[mant<1.0,
+ mant = 10*mant;
+ exp = exp-1;
+];
+mant = Round[mant,0.1^d];
+(*
+If[exp<0,
+ mant = Round[mant,0.1^(d-1)];
+ ,
+ mant = Round[mant,0.1^d];
+];
+*)
+Return[mant*10^exp]
+]
+
+
+Generate1DPadeAnsatzList[ansatz_,coeffRules_,variable_,paramName_,minPadeTypeSum_,maxPadeTypeSum_]:=Module[{i,j,ansatzDegree,padeAnsatzList,padeType,exactPade,genPade,genPadeList,exactPadeReals,exactPadeRounding},
+For[i=1,i<maxPadeTypeSum,i++,
+ j=Max[1,minPadeTypeSum-i];
+ While[(j<=i)&&(i+j<=maxPadeTypeSum),
+ ansatzDegree = Exponent[ansatz,variable];
+ If[(j==1)&&(i==ansatzDegree),
+ Print["Not generating Pade approximant for type ("<>ToString[i]<>","<>ToString[j]<>") with polynomial ansatz of order "<>ToString[ansatzDegree]<>", as it would just duplicate the polynomial."];
+ ,
+ padeType = {i,j};
+ exactPade = ExactPade[ansatz,coeffRules,{variable,0,padeType}];
+ exactPadeReals=Cases[AtomsList[exactPade],y_Real];
+ exactPadeRounding=Table[exactPadeReals[[i]]->myRound[exactPadeReals[[i]],2],{i,1,Length@exactPadeReals}];
+ exactPade = exactPade /. exactPadeRounding;
+ genPade = GeneralizeFunction[exactPade,paramName];
+ If[!ValueQ[genPadeList],
+ genPadeList={{genPade,{variable}}};
+ ,
+ AppendTo[genPadeList,{genPade,{variable}}];
+ ]
+ ];
+ j++;
+ ];
+ ];
+Print["Generated these Pade approximants:"];
+Print[genPadeList];
+Return[genPadeList];
+]
+
+
+InvertRules[rules_]:=Module[{},
+Table[rules[[i,2]]->rules[[i,1]],{i,Length@rules}]
+]
+
+
+Get1dInverseRules[ansatz_,coeffRules_]:=Module[{origCoeffs,inverseRules},
+
+(* in case this is a Pade rational ansatz, disentangle it *)
+origCoeffs = Cases[Select[Join[Level[Numerator[ansatz],{1,Infinity}],Level[Denominator[ansatz],{1,Infinity}]],AtomQ],y_Real];
+
+If[Length[origCoeffs]>0,
+ inverseRules = Table[origCoeffs[[i]]*coeffRules[[i,2]] -> origCoeffs[[i]]*coeffRules[[i,1]], {i,Length@coeffRules}];
+ ,
+ inverseRules = InvertRules[coeffRules];
+];
+
+Return[inverseRules];
+
+]
+
+
+Get1dInverseRulesS[ansatz_,coeffRules_,productAnsatz_]:=Module[{ansatzWithoutS0,inverseRules},
+
+If[productAnsatz,
+ansatzWithoutS0 = ansatz/(ansatz/.S->0)/.{1.->1};
+,
+ansatzWithoutS0 = ansatz-(ansatz/.S->0)/.{0.->0};
+];
+
+inverseRules = Get1dInverseRules[ansatzWithoutS0,coeffRules];
+Return[inverseRules];
+
+]
+
+
+ColorGradient[data_,ColorList_,OptionsPattern[{"Weights"->"","Verbose"->False}]]:=Module[{min,max,weights,wc,blendtab,\[Delta]n,verbose},
+
+weights=OptionValue["Weights"];
+verbose=OptionValue["Verbose"];
+
+min=Min[data];
+max=Max[data];
+\[Delta]n=(max-min)1./(Length@ColorList-1);
+
+If[Not@ListQ@weights,weights=Table[min + \[Delta]n(i-1),{i,Length@ColorList}];,weights=weights Table[min + \[Delta]n(i-1),{i,Length@ColorList}];];
+blendtab=Table[{weights[[i]],ColorList[[i]]},{i,Length@ColorList}];
+
+If[verbose,Print["Weights: ",weights]];
+
+Table[Blend[blendtab,data[[i]]],{i,Length@data}]
+]
+
+
+CreateColors[code_,colors_]:=Module[{},
+Which[code=="BAM",colors[[1]],code=="SXS",colors[[2]],code=="GaTech",colors[[3]],code=="RIT",colors[[4]],True,colors[[5]]]]
+
+
+FitPredictionIntervalFunctionFinalOnly[fit_,ansatzRules_]:=Module[{ansatz,coeffNames,coeffRules,Ncoeff,Ndata,EstVar,quant95,covarMatrix,coeffGrad,stderrsq},
+
+ansatz = fit[[15]];
+coeffRules = fit[[2]];
+coeffNames = coeffRules[[All,1]];
+Ncoeff = Length@coeffNames;
+Ndata = Length@Last@fit; (* length of residuals vector *)
+EstVar = fit[[16]]; (* would be = Total[resid^2]/(Ndata-Ncoeff) without weights *)
+
+(* take gradient vector in the coefficients *)
+coeffGrad = Table[D[ansatz/.ansatzRules,coeffNames[[i]]],{i,Ncoeff}] /. coeffRules;
+
+(* estimate of fit error: multiply coefficient gradient with covariance matrix *)
+covarMatrix = fit[[14]];
+stderrsq = (coeffGrad.covarMatrix.coeffGrad);
+
+(* report back the 95% student-t quantile (applied on both sides, this gives a 90% interval) *)
+quant95 = Quantile[StudentTDistribution[Ndata-Ncoeff],0.95];
+Return[quant95 * Sqrt[ EstVar + stderrsq ]];
+]
+
+
+FitPredictionIntervalFunctionFinalOnlyq1[fit_,ansatzRules_]:=Module[{ansatz,coeffNames,coeffRules,Ncoeff,Ndata,EstVar,quant95,covarMatrix,coeffGrad,stderrsq,chidiffcoeff,chidiff2coeff},
+
+ansatz = fit[[15]];
+coeffRules = fit[[2]];
+coeffNames = coeffRules[[All,1]];
+Ncoeff = Length@coeffNames;
+Ndata = Length@Last@fit; (* length of residuals vector *)
+EstVar = fit[[16]]; (* would be = Total[resid^2]/(Ndata-Ncoeff) without weights *)
+
+(* take gradient vector in the coefficients *)
+coeffGrad = Table[D[ansatz/.ansatzRules,coeffNames[[i]]],{i,Ncoeff}] /. coeffRules;
+
+(* take care of issues in the q=1, eta=0.25 limit of the spin-diff terms *)
+chidiffcoeff = Coefficient[coeffGrad,(\[Chi]1-\[Chi]2)];
+chidiff2coeff = Coefficient[coeffGrad,(\[Chi]1-\[Chi]2)^2];
+coeffGrad = coeffGrad - chidiffcoeff(\[Chi]1-\[Chi]2) + Limit[chidiffcoeff,\[Eta]->0.25](\[Chi]1-\[Chi]2) - chidiff2coeff (\[Chi]1-\[Chi]2)^2 + Limit[chidiff2coeff,\[Eta]->0.25](\[Chi]1-\[Chi]2)^2;
+
+(* estimate of fit error: multiply coefficient gradient with covariance matrix *)
+covarMatrix = fit[[14]];
+stderrsq = (coeffGrad.covarMatrix.coeffGrad);
+
+(* report back the 95% student-t quantile (applied on both sides, this gives a 90% interval) *)
+quant95 = Quantile[StudentTDistribution[Ndata-Ncoeff],0.95];
+Return[quant95 * Sqrt[ EstVar + stderrsq ]];
+]
+
+
+FitPredictionIntervalFinalOnly[fit_,ansatzRules_,etain_,chi1in_,chi2in_]:=Module[{fiterrFunc,fiterrFuncq1,fiterrs,i,eta,chi1,chi2},
+
+(* so we can deal with both scalars and lists *)
+If[Length[etain]==0,
+ eta = {etain};
+ chi1 = {chi1in};
+ chi2 = {chi2in};
+ ,
+ eta = etain;
+ chi1 = chi1in;
+ chi2 = chi2in;
+];
+
+(* evaluate the general error estimate *)
+fiterrFunc = FitPredictionIntervalFunctionFinalOnly[fit,ansatzRules];
+
+(* avoid indeterminates at q=1, eta=0.25 *)
+If[MemberQ[eta,0.25],
+ fiterrFuncq1 = FitPredictionIntervalFunctionFinalOnlyq1[fit,ansatzRules];
+];
+fiterrs = Table[fiterrFunc,{i,1,Length@eta}];
+For[i=1,i<=Length@eta,i++,
+ If[eta[[i]]==0.25,
+ fiterrs[[i]]=fiterrFuncq1;
+ ];
+];
+
+(* switch spin parametrization and insert user values *)
+fiterrs = fiterrs/.{S->sTot3[\[Eta],\[Chi]1,\[Chi]2]};
+Return[Table[fiterrs[[i]]/.{\[Eta]->eta[[i]],\[Chi]1->chi1[[i]],\[Chi]2->chi2[[i]]},{i,1,Length@eta}]];
+
+]
+
+
+FitPredictionIntervalStderrSq[finalFit_,finalAnsatzRules_,fit2dParts_,\[Eta]0stuff_,extraCoeffRules_,productAnsatz_,q1_]:=Module[{finalAnsatz,finalCoeffNames,finalCoeffRules,NfinalCoeffs,finalCovarMatrix,finalCoeffGrad,chidiffcoeff,chidiff2coeff,
+etaCoeffRules,etaCoeffNames,NetaCoeffs,etaAnsatz,etaInverseRules,etaCoeffGrad,etaCovarMatrix,
+SCoeffRules,SCoeffNames,NSCoeffs,SAnsatz,SInverseRules,SCoeffGrad,SCovarMatrix,
+twodCoeffRules,ansatz2dRaw,zeroRules,
+\[Eta]0fit,\[Eta]0Constraints,\[Eta]0CoeffRules,\[Eta]0CoeffNames,N\[Eta]0Coeffs,\[Eta]0CovarMatrix,\[Eta]0Coeffgrad,
+finalStderrSq,etaStderrSq,SStderrSq,twodStderrSq,\[Eta]0StderrSq,
+allStderrSq},
+
+finalAnsatz = finalFit[[15]];
+finalCoeffRules = finalFit[[2]];
+finalCoeffNames = finalCoeffRules[[All,1]];
+NfinalCoeffs = Length@finalCoeffNames;
+
+(* take gradient vector in the coefficients *)
+finalCoeffGrad = Table[D[finalAnsatz/.finalAnsatzRules,finalCoeffNames[[i]]],{i,NfinalCoeffs}] /. finalCoeffRules;
+
+(* take care of issues in the q=1, eta=0.25 limit of the spin-diff terms *)
+If[q1,
+ chidiffcoeff = Coefficient[finalCoeffGrad,(\[Chi]1-\[Chi]2)];
+ chidiff2coeff = Coefficient[finalCoeffGrad,(\[Chi]1-\[Chi]2)^2];
+ finalCoeffGrad = finalCoeffGrad - chidiffcoeff(\[Chi]1-\[Chi]2) + Limit[chidiffcoeff,\[Eta]->0.25](\[Chi]1-\[Chi]2) - chidiff2coeff (\[Chi]1-\[Chi]2)^2 + Limit[chidiff2coeff,\[Eta]->0.25](\[Chi]1-\[Chi]2)^2;
+ finalCoeffGrad = Limit[finalCoeffGrad,\[Eta]->0.25];
+];
+
+(* estimate of fit error: multiply coefficient gradient with covariance matrix *)
+finalCovarMatrix = finalFit[[14]];
+finalStderrSq = (finalCoeffGrad.finalCovarMatrix.finalCoeffGrad);
+
+(* also get contributions from 1D eta and S fits *)
+etaAnsatz = fit2dParts[[2]];
+etaCoeffRules = fit2dParts[[3]];
+etaCoeffNames = etaCoeffRules[[All,1]];
+NetaCoeffs = Length@etaCoeffNames;
+etaCovarMatrix = fit2dParts[[4]];
+
+SAnsatz = fit2dParts[[5]];
+SCoeffRules = fit2dParts[[6]];
+SCoeffNames = SCoeffRules[[All,1]];
+NSCoeffs = Length@SCoeffNames;
+SCovarMatrix = fit2dParts[[7]];
+
+(* construct raw 2D ansatz *)
+etaInverseRules = Get1dInverseRules[etaAnsatz,etaCoeffRules];
+SInverseRules = Get1dInverseRulesS[SAnsatz,SCoeffRules,productAnsatz];
+twodCoeffRules = Join[fit2dParts[[8]],fit2dParts[[9]]];
+If[Not@productAnsatz,
+ zeroRules = Table[ToExpression["f"<>ToString@i<>"0"]->0,{i,0,Exponent[Numerator[fit2dParts[[1]]],S]}];
+ twodCoeffRules = Join[twodCoeffRules/.zeroRules,zeroRules];
+];
+ansatz2dRaw = fit2dParts[[1]]/.etaInverseRules/.SInverseRules;
+
+(* take gradient vectors of the final ansatz (only 2D part needed) in the previously-determined coefficients *)
+etaCoeffGrad = Table[D[ansatz2dRaw, etaCoeffNames[[i]]], {i,NetaCoeffs}] /. Join[etaCoeffRules,SCoeffRules,twodCoeffRules];
+SCoeffGrad = Table[D[ansatz2dRaw, SCoeffNames[[i]]], {i,NSCoeffs}] /. Join[etaCoeffRules,SCoeffRules,twodCoeffRules];
+
+(* also get contribution from extreme-mass ratio limit fit *)
+If[ListQ[\[Eta]0stuff]&&(Length[\[Eta]0stuff]==0),
+ \[Eta]0StderrSq=0;
+ etaCoeffGrad = etaCoeffGrad /. Join[finalCoeffRules,extraCoeffRules];
+ SCoeffGrad = SCoeffGrad /. Join[finalCoeffRules,extraCoeffRules];
+ ,
+ If[ListQ[\[Eta]0stuff],
+ \[Eta]0fit = \[Eta]0stuff[[1]];
+ \[Eta]0Constraints = \[Eta]0stuff[[2]];
+ ,
+ \[Eta]0fit = \[Eta]0stuff;
+ \[Eta]0Constraints = {};
+ ];
+ \[Eta]0CoeffRules = \[Eta]0fit["BestFitParameters"];
+ \[Eta]0CoeffNames = \[Eta]0CoeffRules[[All,1]];
+ N\[Eta]0Coeffs = Length@\[Eta]0CoeffNames;
+ \[Eta]0CovarMatrix = \[Eta]0fit["CovarianceMatrix"];
+ \[Eta]0Coeffgrad = Table[D[ansatz2dRaw/.twodCoeffRules/.\[Eta]0Constraints, \[Eta]0CoeffNames[[i]]], {i,N\[Eta]0Coeffs}] /. Join[etaCoeffRules,SCoeffRules] /. Join[\[Eta]0CoeffRules,finalCoeffRules,extraCoeffRules];
+ If[q1,
+ \[Eta]0Coeffgrad = Limit[\[Eta]0Coeffgrad, \[Eta]->0.25];
+ ];
+ \[Eta]0StderrSq = (\[Eta]0Coeffgrad.\[Eta]0CovarMatrix.\[Eta]0Coeffgrad);
+ etaCoeffGrad = etaCoeffGrad /. \[Eta]0Constraints /. Join[\[Eta]0CoeffRules,finalCoeffRules,extraCoeffRules];
+ SCoeffGrad = SCoeffGrad /. \[Eta]0Constraints /. Join[\[Eta]0CoeffRules,finalCoeffRules,extraCoeffRules];
+];
+
+(* dot gradient vectors together with the corresponding covar matrices *)
+etaStderrSq = (etaCoeffGrad.etaCovarMatrix.etaCoeffGrad);
+SStderrSq = (SCoeffGrad.SCovarMatrix.SCoeffGrad);
+
+If[q1,
+ etaCoeffGrad = Limit[etaCoeffGrad, \[Eta]->0.25];
+ SCoeffGrad = Limit[SCoeffGrad, \[Eta]->0.25];
+];
+
+allStderrSq = {finalStderrSq,etaStderrSq,SStderrSq,\[Eta]0StderrSq};
+Return[allStderrSq];
+]
+
+
+FitPredictionIntervalFunction[finalFit_,finalAnsatzRules_,fit2dParts_,\[Eta]0fit_,extraCoeffRules_,productAnsatz_]:=Module[{finalCoeffRules,finalCoeffNames,NfinalCoeffs,Ndata,EstVar,quant95,stderrsq,stderrSqContribs,q1},
+
+finalCoeffRules = finalFit[[2]];
+finalCoeffNames = finalCoeffRules[[All,1]];
+NfinalCoeffs = Length@finalCoeffNames;
+Ndata = Length@Last@finalFit; (* length of residuals vector *)
+EstVar = finalFit[[16]]; (* would be = Total[resid^2]/(Ndata-Ncoeff) without weights *)
+
+q1=False;
+stderrSqContribs = FitPredictionIntervalStderrSq[finalFit,finalAnsatzRules,fit2dParts,\[Eta]0fit,extraCoeffRules,productAnsatz,q1];
+
+(* add up all error contributions in quadrature *)
+stderrsq = Total[stderrSqContribs];
+
+(* report back the 95% student-t quantile (applied on both sides, this gives a 90% interval), adding up also the variance contribution for PREDICTION interval (not mean confidence) *)
+quant95 = Quantile[StudentTDistribution[Ndata-NfinalCoeffs],0.95];
+Return[quant95 * Sqrt[ EstVar + stderrsq ]];
+]
+
+
+FitPredictionIntervalFunctionq1[finalFit_,finalAnsatzRules_,fit2dParts_,\[Eta]0stuff_,extraCoeffRules_,productAnsatz_]:=Module[{finalCoeffRules,finalCoeffNames,NfinalCoeffs,Ndata,EstVar,quant95,stderrsq,stderrSqContribs,q1},
+
+finalCoeffRules = finalFit[[2]];
+finalCoeffNames = finalCoeffRules[[All,1]];
+NfinalCoeffs = Length@finalCoeffNames;
+Ndata = Length@Last@finalFit; (* length of residuals vector *)
+EstVar = finalFit[[16]]; (* would be = Total[resid^2]/(Ndata-Ncoeff) without weights *)
+
+q1=True;
+stderrSqContribs = FitPredictionIntervalStderrSq[finalFit,finalAnsatzRules,fit2dParts,\[Eta]0stuff,extraCoeffRules,productAnsatz,q1];
+
+(* add up all error contributions in quadrature *)
+stderrsq = Total[stderrSqContribs];
+
+(* report back the 95% student-t quantile (applied on both sides, this gives a 90% interval), adding up also the variance contribution for PREDICTION interval (not mean confidence) *)
+quant95 = Quantile[StudentTDistribution[Ndata-NfinalCoeffs],0.95];
+Return[quant95 * Sqrt[ EstVar + stderrsq ]];
+]
+
+
+FitPredictionInterval[finalFit_,finalAnsatzRules_,fit2dParts_,\[Eta]0stuff_,extraCoeffRules_,productAnsatz_,etain_,chi1in_,chi2in_]:=Module[{fiterrFunc,fiterrFuncq1,fiterrs,i,eta,chi1,chi2},
+
+(* so we can deal with both scalars and lists *)
+If[Length[etain]==0,
+ eta = {etain};
+ chi1 = {chi1in};
+ chi2 = {chi2in};
+ ,
+ eta = etain;
+ chi1 = chi1in;
+ chi2 = chi2in;
+];
+
+(* evaluate the general error estimate *)
+fiterrFunc = FitPredictionIntervalFunction[finalFit,finalAnsatzRules,fit2dParts,\[Eta]0stuff,extraCoeffRules,productAnsatz];
+
+(* avoid indeterminates at q=1, eta=0.25 *)
+If[MemberQ[eta,0.25],
+ fiterrFuncq1 = FitPredictionIntervalFunctionq1[finalFit,finalAnsatzRules,fit2dParts,\[Eta]0stuff,extraCoeffRules,productAnsatz];
+];
+fiterrs = Table[fiterrFunc,{i,1,Length@eta}];
+For[i=1,i<=Length@eta,i++,
+ If[eta[[i]]==0.25,
+ fiterrs[[i]]=fiterrFuncq1;
+ ];
+];
+
+(* switch spin parametrization and insert user values *)
+fiterrs = fiterrs/.{S->sTot3[\[Eta],\[Chi]1,\[Chi]2]};
+Return[Table[fiterrs[[i]]/.{\[Eta]->eta[[i]],\[Chi]1->chi1[[i]],\[Chi]2->chi2[[i]]},{i,1,Length@eta}]];
+
+]
+
+
+TeXExportCoeffTable[coeffTable_,filename_]:=Module[{texTable},
+texTable = StringReplace[ToString[TeXForm[NumberForm[coeffTable,3]]],{"$\\grave{ }$*${}^{\\wedge}$"->"}\\cdot10^{"}];
+Export[filename, texTable, "Text"];
+]
+
+
+TeXExportCovarMatrixTable[fitCovar_,fitCoeffRules_,filename_]:=Module[{covarMatrix,paramNames,fullMatrix,texTable},
+covarMatrix = fitCovar;
+paramNames = fitCoeffRules[[All,1]];
+fullMatrix = Join[List/@Join[{""},paramNames],Join[{paramNames},covarMatrix,1],2];
+texTable = StringReplace[ToString[TeXForm[NumberForm[fullMatrix,3]]],{"$\\grave{ }$*${}^{\\wedge}$"->"}\\cdot10^{"}];
+Export[filename,texTable,"Text"];
+(* then run on the resulting file: sed -i 's/{/[/g;s/}/],/g;s/*^/e/g' PeakLuminosityUIBCovMatrix_S5.txt *)
+]
+
+
+SubscriptRules[rules_]:=Module[{},
+Return[Table[rules[[i,1]]->Subscript[ToExpression[StringTake[ToString@rules[[i,1]],1]],ToExpression[StringTake[ToString@rules[[i,1]],2;;]]],{i,1,Length@rules}]];
+]
+
+
+TeXFormatAnsatz[ansatz_,formattingRules_,coeffRules_]:=Module[{subscripts,formattedAnsatz,TeXansatz},
+
+subscripts = SubscriptRules[coeffRules];
+
+formattedAnsatz = ansatz/.formattingRules/.subscripts;
+
+(*
+ansatzReals=Cases[AtomsList[ansatzRaw],y_Real];
+ansatzRounding=Table[ansatzReals[[i]]\[Rule]NumberForm[ansatzReals[[i]],{2,2}],{i,1,Length@ansatzReals}];
+formattedAnsatz = formattedAnsatz ./ .ansatzRounding;
+*)
+
+TeXansatz = TeXForm[formattedAnsatz];
+TeXansatz = StringReplace[ToString@TeXansatz," _"->"_"];
+TeXansatz = StringReplace[TeXansatz,"{}"->""];
+TeXansatz = StringReplace[TeXansatz,"\\overset{\\land }"->"\\widehat"];
+TeXansatz = StringReplace[TeXansatz,"\\hat"->"\\widehat"];
+Return[TeXansatz];
+]
+
+
+TeXExportAnsatz[ansatz_,formattingRules_,coeffRules_,filename_]:=Module[{TeXansatz},
+TeXansatz = TeXFormatAnsatz[ansatz,formattingRules,coeffRules];
+Export[filename, TeXansatz, "Text"];
+]
+
+
+GetRawTwoDAnsatz[finalfit_,fit2dParts_,productAnsatz_,constrained_]:=Module[{etaAnsatz,etaCoeffRules,etaInverseRules,SAnsatz,SCoeffRules,SInverseRules,ansatzRaw},
+
+etaAnsatz = fit2dParts[[2]];
+etaCoeffRules = fit2dParts[[3]];
+etaInverseRules = Get1dInverseRules[etaAnsatz,etaCoeffRules];
+
+SAnsatz = fit2dParts[[5]];
+SCoeffRules = fit2dParts[[6]];
+SInverseRules = Get1dInverseRulesS[SAnsatz,SCoeffRules,productAnsatz];
+
+ansatzRaw = (fit2dParts[[1]]/.etaInverseRules/.SInverseRules);
+
+If[constrained,
+ ansatzRaw = ansatzRaw /. fit2dParts[[8]] /. fit2dParts[[9]] /. {4.->4, 16.->16, 64.->64, 256.->256} /. {-4.->-4, -16.->-16, -64.->-64, -256.->-256};
+];
+
+Return[ansatzRaw];
+
+]
+
+
+GetAllRules[finalfit_,fit2dParts_,twodrules_]:=Module[{allRules},
+allRules=Join[fit2dParts[[3]],fit2dParts[[6]],fit2dParts[[8]],fit2dParts[[9]],finalfit[[2]]]; (* etaCoeffRules, SCoeffRules, 2dconstraintsNumerator, 2dconstraintsDenominator, finalfitCoeffRules *)
+If[ListQ@twodrules&&(Length@twodrules>0),
+ allRules=Join[allRules,twodrules];
+];
+Return[allRules];
+]
+
+
+TeXExportTwoDAnsatz[finalfit_,fit2dParts_,twodrules_,formattingRules_,productAnsatz_,constrained_,filename_]:=Module[{ansatzRaw,allRules,zeroRules},
+ansatzRaw = GetRawTwoDAnsatz[finalfit,fit2dParts,productAnsatz,constrained];
+allRules = GetAllRules[finalfit,fit2dParts,twodrules];
+If[Not@productAnsatz,
+ zeroRules=Table[ToExpression["f"<>ToString@i<>"0"]->0,{i,0,Exponent[Numerator[fit2dParts[[1]]],S]}];
+ allRules=Join[allRules,zeroRules];
+];
+TeXExportAnsatz[ansatzRaw,formattingRules,allRules,filename];
+]
+
+
+TeXExportChiDiffTerms[chidiffAnsaetze_,formattingRules_,coeffRules_,filename_]:=Module[{fullTeX,numChiDiffTerms,thisTerm},
+
+fullTeX = "";
+
+numChiDiffTerms = Length@chidiffAnsaetze;
+If[numChiDiffTerms>=1,
+ thisTerm = TeXFormatAnsatz[chidiffAnsaetze[[1]],formattingRules,coeffRules];
+ fullTeX = "A_1(\\eta)&="<>thisTerm;
+];
+If[numChiDiffTerms>=2,
+ thisTerm = TeXFormatAnsatz[chidiffAnsaetze[[2]],formattingRules,coeffRules];
+ fullTeX = fullTeX<>" \\\\\nA_2(\\eta)&="<>thisTerm;
+];
+If[numChiDiffTerms>=3,
+ thisTerm = TeXFormatAnsatz[chidiffAnsaetze[[3]],formattingRules,coeffRules];
+ fullTeX = fullTeX<>" \\\\\nA_3(\\eta)&="<>thisTerm;
+];
+
+Export[filename, fullTeX, "Text"];
+
+]
+
+
+TeXExportFinalAnsatz[finalfit_,fit2dParts_,twodrules_,chidiffAnsaetze_,formattingRules_,productAnsatz_,twodConstrained_,filename_]:=Module[{ansatzRaw,numChiDiffTerms,allRules},
+
+ansatzRaw = GetRawTwoDAnsatz[finalfit,fit2dParts,productAnsatz,twodConstrained];
+
+numChiDiffTerms = Length@chidiffAnsaetze;
+If[numChiDiffTerms>=1,
+ ansatzRaw = ansatzRaw + chidiffAnsaetze[[1]] (\[Chi]1-\[Chi]2);
+];
+If[numChiDiffTerms>=2,
+ ansatzRaw = ansatzRaw + chidiffAnsaetze[[2]] (\[Chi]1-\[Chi]2)^2;
+];
+If[numChiDiffTerms>=3,
+ ansatzRaw = ansatzRaw + chidiffAnsaetze[[3]] S (\[Chi]1-\[Chi]2);
+];
+
+allRules = GetAllRules[finalfit,fit2dParts,twodrules];
+
+TeXExportAnsatz[ansatzRaw,formattingRules,allRules,filename];
+
+]
+
+
+TeXExportCoeffTable[coeffRules_,covar_,filename_]:=Module[{coeffNames,coeffErrs,headerLine,coeffTable,texTable},
+coeffNames = coeffRules[[All,1]]/.SubscriptRules[coeffRules];
+coeffErrs = Sqrt[Diagonal[covar]];
+headerLine = {"estimate","std.err.","rel.err.[%]"};
+(*
+coeffTable = TableForm[Table[{coeffRules[[i,2]],coeffErrs[[i]],Abs[100*coeffErrs[[i]]/coeffRules[[i,2]]]},{i,Length@coeffRules}],TableHeadings\[Rule]{coeffNames,headerLine}];
+texTable = StringReplace[ToString[TeXForm[NumberForm[coeffTable,3]]],{"$\\grave{ }$*${}^{\\wedge}$"\[Rule]"}\\cdot10^{"}];
+Export[filename,texTable, "Text"];
+*)
+(*
+TeXExportTabularTable[Map[NumberForm[#,3]&,Table[{coeffRules[[i,2]],coeffErrs[[i]],Abs[100*coeffErrs[[i]]/coeffRules[[i,2]]]},{i,Length@coeffRules}],{2}], filename, coeffNames, headerLine]
+*)
+TeXExportTabularTable[Table[{NumberForm[coeffRules[[i,2]],3],NumberForm[coeffErrs[[i]],3],NumberForm[Abs[100*coeffErrs[[i]]/coeffRules[[i,2]]],{3,1}]},{i,Length@coeffRules}],
+ filename, coeffNames, headerLine, 0]
+]
+
+
+TeXExportTabularTable[datatable_,filename_,rowLabels_,colHeadings_,padZeroes_]:=Module[{nRows,tableFormatted,texTable,tableAtoms,maxDecDigits},
+nRows = Length@datatable;
+
+tableFormatted = TableForm[datatable, TableHeadings->{rowLabels,colHeadings}];
+texTable = ToString[TeXForm[tableFormatted]];
+texTable = StringReplace[texTable,{"array"->"tabular"}];
+texTable = StringReplace[texTable,{"&"->"$&$"}]; (* close and open math mode at each field separator *)
+texTable = StringReplace[texTable,{"$&$"->"&$"},1]; (* remove the extra open$ at first separator *)
+texTable = StringReplace[texTable,{"$\$&$$"->"\&"},1];(* remove the extra elements when exporting & *)
+texTable = StringReplace[texTable,{"\\\\"->"$\\\\"}]; (* close math mode at each line break *)
+texTable = StringReplace[texTable,{"\\\\"->"\\\\$"},nRows]; (* reopen math mode after each line break, but only for numrows (not at last one) *)
+texTable = StringReplace[texTable,{"\\\\"->"\\\\\\hline"},1]; (* add a horizontal line after the first (headers) line *)
+texTable = StringReplace[texTable,{"{tabular}{c"->"{tabular}{l"}]; (* make row-headers column left-centered *)
+texTable = StringReplace[texTable,{"cc}"->"cc}\\hline\\hline"}]; (* add initial double line *)
+texTable = StringReplace[texTable,{"\\end{tabular}"->"\\hline\\hline\\end{tabular}"}]; (* final double lines at end of table *)
+
+If[padZeroes==1, (* pad trailing zeroes *)
+texTable = StringReplace[texTable,{".\\times"->".0\\times"}];
+,
+If[padZeroes==2,
+texTable = StringReplace[texTable,{".\\times"->".00\\times"}];
+texTable = StringReplace[texTable,Table["."<>ToString@i<>"\\times"->"."<>ToString@i<>"0\\times",{i,0,9}]];
+,
+If[padZeroes==3,
+texTable = StringReplace[texTable,{".\\times"->".000\\times"}];
+texTable = StringReplace[texTable,Table["."<>ToString@i<>"\\times"->"."<>ToString@i<>"00\\times",{i,0,9}]];
+texTable = StringReplace[texTable,Flatten[Table[Table["."<>ToString@i<>ToString@j<>"\\times"->"."<>ToString@i<>ToString@j<>"0\\times",{i,0,9}],{j,0,9}]]];
+];
+];
+];
+
+Export[filename, texTable, "Text"];
+]
+
+
+PyExportFinalFit[fit_,extraFormattingRules_,filename_]:=Module[{fitCform,pyRules1,pyRules2,pyRules3,fitPyform},
+
+fitCform = ToString@CForm[fit];
+
+(* formatting hacks: greek letters, powers, Shat (FIXME: not yet variable wrt to effective-spin parameter choice!) *)
+pyRules1 = {"\[Eta]"->"eta","\[Chi]"->"chi","Sqrt(2)"->"sqrt2","Sqrt(3)"->"sqrt3"};
+pyRules2 = Join[{"(chi1 - chi2)"->"chidiff","Power(chi1 - chi2,2)"->"chidiff2"},
+ Table["Power(eta,"<>ToString@i<>")"->"eta"<>ToString@i,{i,2,9}],
+ Table["Power(S,"<>ToString@i<>")"->"S"<>ToString@i,{i,2,9}],
+ {"Power(1 - 4*eta,0.5)"->"sqrt1m4eta"}];
+pyRules3 = {"S"->"Shat","1 "->"1. ","0 "->"0. "};
+fitPyform = StringReplace[StringReplace[StringReplace[StringReplace[fitCform,pyRules1],pyRules2],pyRules3],extraFormattingRules];
+
+fitPyform = fitPyform<>"\n";
+Export[filename, fitPyform, "Text"];
+
+]
+
+
+PyExportFinalAnsatz[finalfit_,fit2dParts_,chidiffAnsaetze_,keepfi0_,extraFormattingRules_,filename_]:=Module[{ansatzRaw,numChiDiffTerms,zeroRules,ansatzCform,
+pyRules1,pyRules2,pyRules3,ansatzPyform,sqrti,sqrtRules,fracs,fracStrings,fracReals,fracRules,twodConstrained},
+
+twodConstrained = True;
+ansatzRaw = GetRawTwoDAnsatz[finalfit,fit2dParts,productAnsatz,twodConstrained];
+
+numChiDiffTerms = Length@chidiffAnsaetze;
+If[numChiDiffTerms>=1,
+ ansatzRaw = ansatzRaw + chidiffAnsaetze[[1]] (\[Chi]1-\[Chi]2);
+];
+If[numChiDiffTerms>=2,
+ ansatzRaw = ansatzRaw + chidiffAnsaetze[[2]] (\[Chi]1-\[Chi]2)^2;
+];
+If[numChiDiffTerms>=3,
+ ansatzRaw = ansatzRaw + chidiffAnsaetze[[3]] S (\[Chi]1-\[Chi]2);
+];
+
+If[Not@keepfi0,
+ zeroRules = Table[ToExpression["f"<>ToString@i<>"0"]->0,{i,0,Exponent[Numerator[fit2dParts[[1]]],S]}];
+ ansatzRaw = ansatzRaw/.zeroRules;
+];
+
+(* hack to avoid rounding of square-roots *)
+sqrti = {2,3,5,6,7};
+sqrtRules = Table[Sqrt[sqrti[[i]]]->ToExpression["sqrt"<>ToString@sqrti[[i]]<>""],{i,Length@sqrti}];
+(* hack to avoid rounding of fractions, first part: replace by named string before ToString@CForm[SetPrecision[...]] *)
+fracs = {1/3,2/3,4/3,5/3};
+fracs = Join[fracs,-fracs];
+fracStrings = Table[ToExpression["frac"<>StringReplace[ToString@Numerator@fracs[[i]],{"-"->"m"}]<>ToString@Denominator@fracs[[i]]],{i,Length@fracs}];
+fracRules = Table[fracs[[i]]->fracStrings[[i]],{i,Length@fracs}];
+
+ansatzCform = ToString@CForm[SetPrecision[ansatzRaw/.sqrtRules/.fracRules,3]];
+
+(* hack to avoid rounding of fractions, second part: replace named string back to real number fractions *)
+fracReals = Table[ToString@SetPrecision[Numerator@fracs[[i]],2]<>"/"<>ToString@SetPrecision[Denominator@fracs[[i]],2],{i,Length@fracs}];
+fracRules = Table[ToString@fracStrings[[i]]->fracReals[[i]],{i,Length@fracs}];
+ansatzCform = StringReplace[ansatzCform,fracRules];
+
+(* more formatting hacks: greek letters, powers, Shat (FIXME: not yet variable wrt to effective-spin parameter choice!) *)
+pyRules1 = {"\[Eta]"->"eta","\[Chi]"->"chi"};
+pyRules2 = Join[{"(chi1 - 1.*chi2)"->"chidiff","Power(chi1 - 1.*chi2,2)"->"chidiff2"},
+ Table["Power(eta,"<>ToString@i<>")"->"eta"<>ToString@i,{i,2,9}],
+ Table["Power(S,"<>ToString@i<>")"->"S"<>ToString@i,{i,2,9}],
+ {"Power(1. - 4.*eta,0.5)"->"sqrt1m4eta"},{"Sqrt(1. - 4.*eta)"->"sqrt1m4eta"}];
+pyRules3 = {"S"->"Shat"};
+ansatzPyform = StringReplace[StringReplace[StringReplace[StringReplace[ansatzCform,pyRules1],pyRules2],pyRules3],extraFormattingRules];
+
+ansatzPyform = ansatzPyform<>"\n";
+Export[filename, ansatzPyform, "Text"];
+
+]
+
+
+PyExportFinalFitCoeffs[finalfit_,fit2dParts_,all2dconstraints_,filename_]:=Module[{pyCoeffsList,pyCoeffsString},
+
+pyCoeffsList = Join[Table[ToString@fit2dParts[[3,i,1]]<>" = "<>ToString@CForm@fit2dParts[[3,i,2]],{i,Length@fit2dParts[[3]]}],
+ Table[ToString@fit2dParts[[6,i,1]]<>" = "<>ToString@CForm@fit2dParts[[6,i,2]],{i,Length@fit2dParts[[6]]}],
+ Table[ToString@all2dconstraints[[i,1]]<>" = "<>ToString@CForm[all2dconstraints[[i,2]]/.{1->1.,0->0.}],{i,Length@all2dconstraints}],
+ (*{ToString@\[Eta]0derconstv3[[1,1]]<>" = "<>ToString@CForm[\[Eta]0derconstv3[[1,2]]]}, *)
+ Table[ToString@finalfit[[2,i,1]]<>" = "<>ToString@CForm@finalfit[[2,i,2]],{i,Length@finalfit[[2]]}]
+];
+
+pyCoeffsString = "";
+For[i=1, i <= Length@pyCoeffsList, i++,
+ pyCoeffsString = pyCoeffsString<>" "<>pyCoeffsList[[i]]<>"\n"];
+
+Export[filename, pyCoeffsString, "Text"];
+
+]
+
+
+SupplExportAllFitCoeffs[finalfit_,fit2dParts_,all2dconstraints_,eta0covar_,filename_]:=Module[{coeffsList,coeffsString,stdErrsEta,stdErrsS,stdErrs2D,stdErrsFinal},
+
+stdErrsEta = Sqrt[Diagonal[fit2dParts[[4]]]];
+stdErrsS = Sqrt[Diagonal[fit2dParts[[7]]]];
+stdErrs2D = Join[Sqrt[Diagonal[eta0covar]],ConstantArray[0.0,Length[all2dconstraints]-Length[eta0covar]]];
+stdErrsFinal = Sqrt[Diagonal[finalfit[[14]]]];
+
+coeffsList = Join[Table[ToString@fit2dParts[[3,i,1]]<>" "<>ToString@CForm@fit2dParts[[3,i,2]]<>" "<>ToString@CForm@stdErrsEta[[i]],{i,Length@fit2dParts[[3]]}],
+ Table[ToString@fit2dParts[[6,i,1]]<>" "<>ToString@CForm@fit2dParts[[6,i,2]]<>" "<>ToString@CForm@stdErrsS[[i]],{i,Length@fit2dParts[[6]]}],
+ Table[ToString@all2dconstraints[[i,1]]<>" "<>ToString@CForm[all2dconstraints[[i,2]]/.{1->1.,0->0.}]<>" "<>ToString@CForm@stdErrs2D[[i]],{i,Length@all2dconstraints}],
+ (*{ToString@\[Eta]0derconstv3[[1,1]]<>" "<>ToString@CForm[\[Eta]0derconstv3[[1,2]]]}, *)
+ Table[ToString@finalfit[[2,i,1]]<>" "<>ToString@CForm@finalfit[[2,i,2]]<>" "<>ToString@CForm@stdErrsFinal[[i]],{i,Length@finalfit[[2]]}]
+];
+
+coeffsString = "# coeff estimate stderr\n";
+For[i=1, i <= Length@coeffsList, i++,
+ coeffsString = coeffsString<>coeffsList[[i]]<>"\n"];
+
+coeffsString = StringReplace[coeffsString,{". "->".0 ",".\n"->".0\n"}];
+
+Export[filename, coeffsString, "Text"];
+
+]
+
+
+SupplExportCovarMatrix[covar_,coeffRules_,fileName_]:=Module[{coeffNames,fullMatrix,covarString},
+
+coeffNames = coeffRules[[All,1]];
+
+covarString = "# coeffs:";
+For[i=1, i <= Length@coeffRules, i++,
+ covarString = covarString<>" "<>ToString@coeffRules[[i,1]];
+ ];
+covarString = covarString<>"\n";
+For[i=1, i <= Length@covar, i++,
+ For[j=1, j <= Length@covar, j++,
+ covarString = covarString<>" "<>ToString@NumberForm[covar[[i,j]], {16, 16}, ExponentFunction -> (If[-10 < # < 10, Null, #] &)];
+ ];
+ covarString = covarString<>"\n";
+ ];
+
+Export[fileName, covarString, "Text"];
+
+]
+
+
+Options[AIC]={"Weights"->False};
+AIC[data_,fit_,fitvars_,OptionsPattern[]]:=Module[{bracketedvars,coeff,datapnts,err,n,res,ress,weigths},
+
+n=Length@data;
+coeff=Length@fitvars;
+weigths=OptionValue["Weights"];
+If[weigths,err=data[[All,-1]];datapnts=data[[All,-2]];,err=1;datapnts=data[[All,-1]];];
+
+res=Table[data[[i,-2]]-(fit/.Table[fitvars[[j]]->data[[i,j]],{j,Length@fitvars}]),{i,Length@data}];
+ress=Total[err (res)^2];
+n + n Log[2\[Pi]]+n Log[ress/n]+2(coeff+1)
+
+]
+
+
+Options[AICc]=Options[AIC];
+AICc[data_,fit_,fitvars_,OptionsPattern[]]:=Module[{coeff,n,res,newfit,bracketedvars,ress,weigths},
+weigths=OptionValue["Weights"];
+n=Length@data;
+coeff=Length@fitvars;
+
+AIC[data,fit,fitvars,"Weights"->weigths]+(2*coeff(coeff+1) )/(n - coeff -1)
+
+]
+
+
+BIC[data_,fit_,fitvars_,coeff_]:=Module[{n,res,newfit,bracketedvars,ress},
+
+n=Length@data;
+bracketedvars=StringReplace[StringReplace[ToString@fitvars,"{"->"["],"}"->"]"];
+newfit=ToExpression[ToString@fit<>bracketedvars];
+
+res=Table[data[[i,-2]]-(newfit/.Table[fitvars[[j]]->data[[i,j]],{j,Length@fitvars}]),{i,Length@data}];
+ress=Total[data[[All,-1]](res)^2];
+n + n Log[2\[Pi]]+n Log[ress/n]+Log[n](coeff+1)
+
+]
+
+
+Residuals[data_,fit_,vars_,OptionsPattern[{"Verbose"->False,"Relative"->False}]]:=Module[{datvals,relative,fitvals,res,verbose},
+
+verbose=OptionValue["Verbose"];
+relative=OptionValue["Relative"];
+
+
+If[verbose,Print["variables -> ",vars]];
+
+datvals=TakeColumn[data,-1];
+fitvals=fit/.Table[(vars[[j]]->data[[All,j]]),{j,Length@vars}];
+If[relative,res=1-fitvals/datvals,res=datvals-fitvals]
+]
+
+
+KullbagLeiblerDiv[p1_?ListQ,p2_?ListQ]:=Module[{fun},
+fun=1.Function[{p,q},Limit[p*Log[(p+\[Epsilon])/(q+\[Epsilon])],\[Epsilon]->0]][p2,p1];
+Total[fun]
+]
+
+
+KL[data1_,data2_,lim_]:=Module[{n,res},
+
+n=Length@data1;
+
+NIntegrate[PDF[data1,x] Log[PDF[data1,x]/PDF[data2,x]], {x,-lim,lim}]
+
+]
+
+
+JensenShanonDiv[p1_?ListQ,p2_?ListQ]:=Module[{m,fun},
+m=0.5 (p1+p2);
+fun=Function[{p,q,m},Limit[p*Log[(p+\[Epsilon])/(m+\[Epsilon])]+ q*Log[(q+ \[Epsilon])/(m+\[Epsilon])],\[Epsilon]->0]][p1,p2,m];
+Total[fun]
+]
+
+
+JS[data1_,data2_,lim_]:=Module[{n,res},
+
+n=Length@data1;
+
+1/2 NIntegrate[PDF[data1,x] Log[PDF[data1,x]/(PDF[data2,x]+ PDF[data1,x])], {x,-lim,lim}] + 1/2 NIntegrate[PDF[data2,x] Log[PDF[data2,x]/(PDF[data2,x]+PDF[data1,x])] , {x,-lim,lim}]
+]
+
+
+ComputeEdges[pts_]:=Module[{ptsx,auxvar,auxvar2,nears,i},
+ptsx=SortBy[pts,First];
+auxvar={};
+i=1;
+AppendTo[auxvar,{ptsx[[i]]}];
+While[i<= Length@ptsx-1,
+If[ptsx[[i+1,1]]==ptsx[[i,1]],i=i+1,AppendTo[auxvar,{ptsx[[i]]}];i=i+1]
+];
+AppendTo[auxvar,{ptsx[[i]]}];
+auxvar=Flatten[auxvar,1];
+
+i=Length@ptsx-1;
+While[i> 1,
+If[ptsx[[i+1,1]]==ptsx[[i,1]],i=i-1,AppendTo[auxvar,ptsx[[i+1]]];i=i-1]
+];
+AppendTo[auxvar,ptsx[[i]]];
+Do[auxvar=AppendTo[auxvar,0.5auxvar[[1]]+0.5auxvar[[-1]]],{i,3}];
+auxvar
+]
+
+
+CredibleRegion[data_,level_]:=Module[{datasrt,prob,cumprob,pbound},
+(* Last column must be the PDF *)
+datasrt=SortBy[data,Last];
+prob=TakeColumn[datasrt,-1];
+cumprob=Accumulate[prob]/Total[prob];
+
+pbound=Quiet@Position[cumprob,_?(#>= (1-level) cumprob[[-1]]& ),1][[1,1]];
+
+ComputeEdges[datasrt[[pbound-1;;-1]]][[All,1;;-2]]
+]
+
+
+CredibleInterval[data_,level_]:=Module[{datasrt,prob,cumprob,pbound},
+(* Last column must be the PDF *)
+datasrt=SortBy[data,Last];
+prob=TakeColumn[datasrt,-1];
+cumprob=Accumulate[prob]/Total[prob];
+
+pbound=Quiet@Position[cumprob,_?(#>= (1-level) cumprob[[-1]]& ),1][[1,1]];
+datasrt[[pbound;;-1]]
+]
+
+
+Generate1DPolynomialAnsatz[CoefficientPrefixString_?StringQ,variable_,MinOrder_?IntegerQ,MaxOrder_?IntegerQ]:=Module[{ansatz,i,j},
+ansatz = Total/@Table[ToExpression[CoefficientPrefixString<>ToString@i] * variable^i,{j,MinOrder,MaxOrder},{i,0,j}];
+
+Transpose[{ansatz,Table[{variable},{i,Length@ansatz}]}]
+]
+
+
+CleanAnsatzParams[paramsGuess_, vars_]:=Module[{pos,params,varsStr,paramsStr,tmp},
+
+params = DeleteDuplicates@Flatten@paramsGuess;
+
+tmp=Select[params, Not@NumberQ@#& ];
+
+varsStr = ToString/@vars;
+paramsStr= ToString/@tmp;
+
+(* Clean the variables from the parameters and identify variables *)
+pos = Flatten[Position[paramsStr,#]&/@varsStr,1];
+params=Delete[tmp,pos];
+
+params
+];
+
+
+(* ::Code::Initialization:: *)
+Options[DataFitFunction]={
+"FitAll" -> True,
+"AxesTag" -> "Amplitude",
+"Verbose" -> 1,
+"StatisticalTest" -> "AIC",
+"Sorted" -> True,
+"Weights" -> {},
+"PlotRange" -> All,
+"ToolTipTags" -> "",
+"Domain" -> {0,1},
+"GetIntervals" -> False
+};
+
+
+DataFitFunction[dataRAW_?ListQ,ansatzList_?ListQ,OptionsPattern[]]:=Module[{ansatz,ansatzaparams,ansatzvars,cleartrue,fit,stats,verbose,
+ansatzparamsStr,ansatzvarsStr,outparams,fittab,plot1,plot2,datasorted,plotdomain,myvar,plotdomain1,axestag,aic,aicc,bic,rsquared,rmse,
+statisticaltest,stattoplot,sortfield,residuals,minexp,maxexp,minexp2,maxexp2,sorted,paramerrors,residualsplot,weights,plotrange,print,
+ansatzaparamsGuess,paramTStat,overview,data,dimWeights,tooltiptags,inner,confidenceinttable,userPlotDomain,vcov,
+estvar,confbands,predbands,getintervals,loglikelihood},
+
+verbose = OptionValue["Verbose"];
+axestag = OptionValue["AxesTag"];
+statisticaltest = OptionValue["StatisticalTest"];
+sorted = OptionValue["Sorted"];
+weights = OptionValue["Weights"];
+plotrange = OptionValue["PlotRange"];
+tooltiptags = OptionValue["ToolTipTags"];
+userPlotDomain = OptionValue["Domain"];
+getintervals = OptionValue["GetIntervals"];
+
+If[TrueQ@weights,
+ dimWeights = Last@Dimensions@dataRAW;
+ weights = TakeColumn[dataRAW,dimWeights];
+ data = TakeColumn[dataRAW, Range[dimWeights-1]],
+ data = dataRAW[[All,1;;Length@dataRAW[[1]]]];
+ If[verbose,Print["Raw data with no weights on the lists!"]];
+];
+
+If[verbose>=2,
+ print[x___]:=Print[x],
+ print[x___]:={}
+];
+
+ansatz = Chop/@ (ansatzList[[All,1]]);
+ansatzvars = ansatzList[[All,2]];
+
+ansatzaparamsGuess = N/@AtomsList/@ansatz;
+
+ansatzaparams = Table[CleanAnsatzParams[ansatzaparamsGuess[[i]], ansatzvars[[i]]],{i,Length@ansatzvars}];
+
+(*
+print["Ans\[ADoubleDot]tze -> ", ansatz//TableForm];
+print["#\[NonBreakingSpace]data points -> ", Length@data];
+print["#\[NonBreakingSpace]data points -> ", Length@Union[data, SameTest->(Abs[#1[[1]]-#2[[1]]] < 0.01 &)], " identifying x-values deviating < 0.01"];
+*)
+
+(*Print["Weights: ", If[Length@weights>0,weights,Automatic]];*)
+
+fittab=Table[
+If[Length@ansatzaparams[[i]]>=1,
+ fit = NonlinearModelFit[data,ansatz[[i]],ansatzaparams[[i]],ansatzvars[[i]],MaxIterations->1000,Weights->If[Length@weights>0,weights,Automatic]];
+ outparams = fit["BestFitParameters"];
+ stats = fit["ParameterTable"];
+ paramerrors = fit["ParameterErrors"];
+ paramTStat = fit["ParameterTStatistics"];
+ residuals = fit["FitResiduals"];
+
+ aic = fit["AIC"];
+ aicc = aic + (2*Length@outparams(Length@outparams+1) )/(Length@data - Length@outparams -1);
+ bic = fit["BIC"];
+ rsquared = fit["RSquared"];
+ rmse = Sqrt@Mean[residuals^2];
+ confidenceinttable = fit["ParameterConfidenceIntervalTable"];
+ vcov = fit["CovarianceMatrix"];
+ estvar = fit["EstimatedVariance"];
+
+If[getintervals,
+ confbands = fit["MeanPredictionBands",ConfidenceLevel->0.9];
+ predbands = fit["SinglePredictionBands",ConfidenceLevel->0.9];
+ ,
+ confbands = {};
+ predbands = {};
+];
+ (* 1 2 3 4 5 6 7 8 9 *)
+ {Normal@fit, outparams, stats, aic, aicc, bic, rsquared, ScientificForm@rmse, paramerrors,
+ (* 10 11 12 13 14 15 *)
+ Sort[CombineColumns[ansatzaparams[[i]],paramTStat],Abs@#1[[2]]<Abs@#2[[2]]&], Length@ansatzaparams[[i]], rmse, confidenceinttable, vcov, ansatz[[i]],
+ (* 16 17 18 19 *)
+ estvar, confbands, predbands, residuals },
+ {ansatz[[i]],"dummy","dummy","dummy","dummy","dummy","dummy","dummy","dummy","dummy"}]
+,{i,Length@ansatzList}];
+
+Which[statisticaltest=="AIC",
+ stattoplot=aic;
+ sortfield=4;
+ ,
+ statisticaltest=="AICc",
+ stattoplot=aicc;
+ sortfield=5;
+ ,
+ statisticaltest=="BIC",
+ stattoplot=bic;
+ sortfield=6;
+ ,
+ statisticaltest=="RSquared",
+ stattoplot=rsquared;
+ sortfield=7;
+ ,
+ statisticaltest=="RMSE",
+ stattoplot=rmse;
+ sortfield=12;
+ ];
+
+If[sorted, fittab = SortBy[fittab,#[[sortfield]]& ]];
+overview = TakeColumn[fittab,{1,11,7,8,5,6,3}]; (* fit eqn, numParams, Rsquared, RSME, AICc, BIC, coefficient table *)
+residuals = fittab[[All,19]];
+
+(*
+resVSaic = TakeColumn[fittab, {4,7}];
+resVSaicc = TakeColumn[fittab, {5,7}];
+resVSbic = TakeColumn[fittab, {6,7}];
+Print[ListLogPlot[{resVSaic,resVSaicc,resVSbic},PlotRange\[Rule]All,PlotStyle\[Rule]{Red,Blue,Green},PlotLegends\[Rule] {"AIC","AICc","BIC"},
+Frame\[Rule] True,FrameLabel\[Rule] {"*IC*","RMSE"}]];
+*)
+
+If[verbose>=1,
+ Print[overview//TableForm];
+];
+
+If[verbose>=2,
+
+ Which[Length@ansatzvars[[1]]==1,
+ (* {minexp,maxexp}={Min[Exponent[#,ansatzvars]&/@ansatz],Max[Exponent[#,ansatzvars]&/@ansatz]}; *)
+ {minexp,maxexp}={Min[Table[Length[fittab[[i,2]]],{i,Length@ansatzList}]],Max[Table[Length[fittab[[i,2]]],{i,Length@ansatzList}]]};
+ datasorted=SortBy[data,First];
+
+ plotdomain={Min[First@First@datasorted,First@userPlotDomain],Max[First@Last@datasorted,Last@userPlotDomain]};
+
+ (*plot1=Plot[Evaluate[Table[fittab[[i,1]]/.ansatzvars[[i,1]]\[Rule]x,{i,Length@ansatzList}]],{x,First@plotdomain,Last@plotdomain},
+ Epilog\[Rule]{Point[Table[Tooltip[#,If[ListQ@tooltiptags,tooltiptags[[i]],ToString[data[[i]]]]],{i,Length@data}]&/@data]},
+ PlotRange\[Rule]plotrange,Frame\[Rule]True,PlotStyle\[Rule]Red,FrameLabel\[Rule]{Style[ToString@ansatzvars[[1,1]],14],Style["f("<>ToString@ansatzvars[[1,1]]<>")",14]}];*)
+ plot1=Plot[Evaluate[Table[fittab[[i,1]]/.ansatzvars[[i,1]]->x,{i,Length@ansatzList}]],{x,First@plotdomain,Last@plotdomain},PlotLegends->Evaluate[Table[fittab[[i,1]],{i,Length@ansatzList}]]];
+ plot2=ListPlot[Table[Tooltip[data[[i]],If[ListQ@tooltiptags,tooltiptags[[i]],ToString[data[[i]]]]],{i,Length@data}], PlotStyle->Red];
+
+ stattoplot=Transpose[{Table[Length[fittab[[i,2]]],{i,Length@ansatzList}],TakeColumn[fittab,sortfield]}];
+
+ inner=(Inner[List,data[[All,1]],#,List]&/@residuals);
+
+ Print@{Show[plot1, plot2, ImageSize->450, Frame->True, FrameLabel->{Style[ToString@ansatzvars[[1,1]],14],Style["f("<>ToString@ansatzvars[[1,1]]<>")",14]}],
+ ListPlot[Partition[stattoplot,1],Frame->True,FrameLabel->{Style["\!\(\*SubscriptBox[\(N\), \(coeff\)]\)",14],Style[statisticaltest,14]},ImageSize->450,PlotRange->{{minexp-1,maxexp+1},All},
+ PlotLegends->Table[fittab[[i,1]],{i,Length@ansatzList}]],
+ ListPlot[Table[Tooltip[#[[i]],If[ListQ@tooltiptags,tooltiptags[[i]],ToString[data[[i]]]]],{i,Length@data}]&/@inner,PlotRange->{plotdomain,All},
+ ImageSize->450,Frame->True,FrameLabel->{Style[ToString@ansatzvars[[1,1]],14],Style["data-fit",14]}]
+ };
+ ,
+ Length@ansatzvars[[1]]==2,
+
+ (*
+ {minexp,maxexp} ={Min[Exponent[#,ansatzvars[[1,1]]]&/@ansatz],Max[Exponent[#,ansatzvars[[1,1]]]&/@ansatz]};
+ {minexp2,maxexp2}={Min[Exponent[#,ansatzvars[[1,2]]]&/@ansatz],Max[Exponent[#,ansatzvars[[1,2]]]&/@ansatz]};
+ *)
+
+ plot2=ListPointPlot3D[data,PlotRange->plotrange,PlotStyle->PointSize[0.02],PlotLegends->{"data"}];
+ plot1=Plot3D[Evaluate[Table[fittab[[i,1]]/.ansatzvars[[i,1]]->x/.ansatzvars[[1,2]]->y,{i,Length@ansatzList}]],
+ {x,First@First@userPlotDomain,Last@First@userPlotDomain}, {y,First@Last@userPlotDomain,Last@Last@userPlotDomain}, PlotRange->plotrange,
+ AxesLabel->{Style[ToString@ansatzvars[[1,1]],14],Style[ToString@ansatzvars[[1,2]],14],Style["f("<>ToString@ansatzvars[[1,1]]<>","<>ToString@ansatzvars[[1,2]]<>")",14]},
+ PlotLegends->(*Evaluate[Table[fittab[[i,1]],{i,Length@ansatzList}]]*)Table["Ansatz "<>ToString[i],{i,Length@ansatzList}]];
+
+ stattoplot=Table[{Exponent[fittab[[i,1]], ansatzvars[[i,1]]],Exponent[fittab[[i,1]], ansatzvars[[i,2]]],fittab[[i,4]]},{i,Length@ansatzList}];
+ residualsplot=Table[Transpose[{data[[All,1]],data[[All,2]],residuals[[i]]}],{i,Length@ansatzList}];
+
+ Print@{Show[plot1,plot2,ImageSize->450],
+ (* ListPointPlot3D[stattoplot,PlotStyle\[Rule]Red,AxesLabel\[Rule]{"order "<>ToString@ansatzvars[[1,1]],"order "<>ToString@ansatzvars[[1,2]],statisticaltest},ImageSize\[Rule]450,PlotRange\[Rule]{{minexp-0.2,maxexp+0.2},{minexp2-0.2,maxexp2+0.2},Automatic}],*)
+ (*myListPlot3D[residualsplot,AxesLabel\[Rule]{Style[ToString@ansatzvars[[1,1]],14],Style[ToString@ansatzvars[[1,2]],14],""},PlotLabel->Style["Residuals",14],ImageSize\[Rule]450],*)
+ myListPlot3D[residualsplot,AxesLabel->{Style[ToString@ansatzvars[[1,1]],14],Style[ToString@ansatzvars[[1,2]],14],Style["data-fit",14]},ImageSize->450,PlotRange->plotrange]};
+ Print[];
+ ,True,
+ Print["More than 2 variables can not be plotted :) "];
+ ];
+];
+
+Return[fittab];
+]
+
+
+Options[DataFitFunctionAll]={
+"NSFitindex" -> 1, (* which fit to pick *)
+"q1Fitindex" -> 1,
+"FitCase" -> 1, (* 1: 1D fits, 2: 1D+2D fits, return 2D only: 3: 1D+2D fits, return both; 4: 1D+2D+3D fits, return only 2D+3D; 5: 1D+2D+3D fits, return all, but with reduced verbosity *)
+"MassRatioUnequalFits" -> {1,1.5,2.,3.,4.,8.,18.},
+"NonSpinningAnsatzList" -> {{a1 \[Eta]+a2 \[Eta]^2+a3 \[Eta]^3,{\[Eta]}},{a1 \[Eta]+a2 \[Eta]^2+a3 \[Eta]^3+a4 \[Eta]^4,{\[Eta]}},{a1 \[Eta]+a2 \[Eta]^2+a3 \[Eta]^3+a4 \[Eta]^4+a5 \[Eta]^5,{\[Eta]}}},
+"EqualBHAnsatzList" -> {{b1 S+b2 S^2+b3 S^3,{S}},{b1 S+b2 S^2+b3 S^3+b4 S^4,{S}},{b1 S+b2 S^2+b3 S^3+b4 S^4+b5 S^5,{S}},{b1 S+b2 S^2+b3 S^3+b4 S^4+b5 S^5+b6 S^6,{S}},{b1 S+b2 S^2+b3 S^3+b4 S^4+b5 S^5+b6 S^6+b7 S^7,{S}},
+ {b1 S+b2 S^2+b3 S^3+b4 S^4+b5 S^5+b6 S^6+b7 S^7+b8 S^8,{S}}},
+"Addq1Ansatz" -> {},
+"AddNSAnsatz" -> {},
+"AddGenAnsatz" -> {},
+"StatisticalTest" -> "BIC",
+"AnsatzTestCombinations" -> {{1},{1}},
+"PlotRange" -> All,
+"RationalFunctions" -> True,
+"ProductAnsatz" -> False,
+"GeneralAnsatzRules" -> {},
+"ToolTipTags" -> "",
+"ProductGeneralizeOrder" -> 2,
+"ProductGeneralizeOrderDenom" -> -1,
+"ProductGeneralizeMinPowerNum" -> -1,
+"TwoDSpinAnsatzOrderNum" -> -1,
+"TwoDSpinAnsatzOrderDenom" -> -1,
+"SpinDiffWeights" -> True,
+"Weights" -> True,
+"AddSpinDiffLinAnsatz" -> {},
+"AddSpinDiffQuadAnsatz" -> {},
+"AddSpinDiffMixAnsatz" -> {},
+"SpinDifferenceRules" -> {},
+"\[Eta]LimitEqualSpin" -> 0,
+"GetIntervals" -> False,
+"SpinParameter" -> sTot3,
+"SpinDiffParameter" -> \[Chi]diffstan(*(\[Chi]1-\[Chi]2)*),
+"FastAnalysis" -> False,
+"Addf00ToAnsatz" -> False
+};
+
+
+DataFitFunctionAll[data_?ListQ,OptionsPattern[]]:=Module[{datans,nsfits,nsansatz,ansatzvars,dataq1,dataq1sorted,ansatzq1,nsfitindex,q1fit,ansatz,nsfit,sys,solNS,coeffs,ansatzS,solq1,ansatzFinal,
+ansatzFinal\[Delta]\[Chi],allData,fitEq,allDataEqS,dataeqs,my\[Eta],myd\[Eta],dataq1Sym,pos,massratioplots,myfit,tabfits,uneqfits,massratiounequalfits,
+uneqfit2,uneqfit,uneqfit3,q1fitopt,q1fitindex,expans,expns,mydq,thisq,oneDverbosity,perqVerbosity,
+ansatzFinal\[Delta]\[Chi]1,ansatzFinal\[Delta]\[Chi]2,lplot,lqplotl,lqplotq,lmplotl,lmplotm,lmqplotl,lmqplotm,lmqplotq,
+addnsansatz,addq1ansatz,\[Eta]sfit,statisticaltest,nsdegree,q1degree,addgenansatz,genansatzindex,ansatzchidifflinear,ansatzchidiffquadratic,plot1,plot2,plot3,plot4,plot4a,plot4b,plot4mirror,
+testansatzcomb,myfit2,q1fits,ansatzAll,fitcase,alldataeqfit,alldataeqfitv2,eqdatafit,linearpar,linearparerr,linearpar2,linearpar2err,quadpar,quadparerr,
+linearfit1,quadfit,ansatz\[Eta]1,ansatz\[Eta]2,linearfit2,plotrange,uneqredunfit,uneqredunfit2,ansatzFinalS\[Delta]\[Chi],spindiffterm,
+spindiffterm2,ansatz\[Eta]3,ansatz\[Eta]4,spindiffterm21,spindiffterm22,generalAnsatzRules,weights,num,denom,zeroRules,spinAnsatz,q1fitS0,fitabc,tooltiptags,dataq1tag,mysel,dataq1pos,tooltiptagsaux,
+\[Eta]0Ansatz,spinpart,spindifferencerules,spindiffweights,datauneqs,dataeqs2,addspindifflinansatz,addspindiffquadansatz,addspindiffmixansatz,ansatzchidiffmix,
+tooltiptagsns,tooltiptagseq,dataq1mixterm,myfitmixterm,linearpar3,linearpar3err,mixpar,mixparerr,linearfit3,mixfit,spindiffterm31,spindiffterm32,ansatzS\[Delta]\[Chi]raw,ansatzFinalS\[Delta]\[Chi]\[Chi]2,
+ansatzS\[Delta]\[Chi]\[Chi]2raw,myfitmixquadterm,dataq1mixquadterm,linearpar4err,linearpar4,linearfit4,mixparerr2,mixpar2,quadparerr2,quadpar2,mixfit2,quadfit2,spindiffterm41,spindiffterm42,
+spindiffterm43,unphysical,numRestrictions,denomRestrictions,extraStuff,ansatzRaw,spinAnsatzRaw,etaAnsatz,etaCoeffRules,etaCovar,SAnsatz,SCoeffRules,SCovar,getintervals,data\[Eta]S\[Chi]diff,
+spinparameter,avgerrperq,avgwgthperq,extrawght,dataeqsunmass,allDataEqSv2,eqdatafitv2,dataunconstr,allDataUnconstr,spindiffparameter,
+productAnsatz,productGeneralizeOrderNum,productGeneralizeOrderDenom,productGeneralizeMinPowerNum,twoDSpinAnsatzOrderNum,twoDSpinAnsatzOrderDenom,
+q1fitS0orderNum,q1fitS0orderDenom,spinAnsatzToGeneralize,spinAnsatzNum,spinAnsatzDenom,q1AnsatzRaw,q1AnsatzRawS0,spinAnsatzRawNum,spinAnsatzRawDenom,spinAnsatzRawToGeneralize,
+dfitspindiffterm,dfitspindiffterm21,dfitspindiffterm22,dfitspindiffterm31,dfitspindiffterm32,dfitspindiffterm41,dfitspindiffterm42,dfitspindiffterm43,fastanalysis,plot3a,dataq1a},
+
+(* Input field "data" is expected in the form {\[Eta], \[Chi]1, \[Chi]2, value}, convention: m1 \[GreaterEqual] m2 !!!!CHECK!!!! *)
+
+nsfitindex = OptionValue["NSFitindex"];
+q1fitindex = OptionValue["q1Fitindex"];
+addnsansatz = OptionValue["AddNSAnsatz"];
+addq1ansatz = OptionValue["Addq1Ansatz"];
+fitcase = OptionValue["FitCase"];
+statisticaltest= OptionValue["StatisticalTest"];
+addgenansatz = OptionValue["AddGenAnsatz"];
+testansatzcomb = OptionValue["AnsatzTestCombinations"];
+plotrange = OptionValue["PlotRange"];
+generalAnsatzRules = OptionValue["GeneralAnsatzRules"];
+tooltiptags=OptionValue["ToolTipTags"];
+spindifferencerules=OptionValue["SpinDifferenceRules"];
+spindiffweights=OptionValue["SpinDiffWeights"];
+weights=OptionValue["Weights"];
+massratiounequalfits=\[Eta]q[OptionValue["MassRatioUnequalFits"]];
+addf00toansatz=OptionValue["Addf00ToAnsatz"];
+addspindifflinansatz=OptionValue["AddSpinDiffLinAnsatz"];
+addspindiffquadansatz=OptionValue["AddSpinDiffQuadAnsatz"];
+addspindiffmixansatz=OptionValue["AddSpinDiffMixAnsatz"];
+getintervals=OptionValue["GetIntervals"];
+spinparameter=OptionValue["SpinParameter"];
+spindiffparameter=OptionValue["SpinDiffParameter"];
+productAnsatz = OptionValue["ProductAnsatz"];
+productGeneralizeOrderNum = OptionValue["ProductGeneralizeOrder"];
+productGeneralizeOrderDenom = OptionValue["ProductGeneralizeOrderDenom"];
+productGeneralizeMinPowerNum = OptionValue["ProductGeneralizeMinPowerNum"];
+If[productGeneralizeOrderDenom<0, productGeneralizeOrderDenom = productGeneralizeOrderNum;];
+If[productGeneralizeMinPowerNum<0, productGeneralizeMinPowerNum = If[productAnsatz,0,1];]; (* by default, set the fi0 terms to zero in a sum ansatz, but keep them in a product ansatz; can be user-overriden *)
+twoDSpinAnsatzOrderNum = OptionValue["TwoDSpinAnsatzOrderNum"];
+twoDSpinAnsatzOrderDenom = OptionValue["TwoDSpinAnsatzOrderDenom"];
+fastanalysis = OptionValue["FastAnalysis"];
+
+nsansatz = OptionValue["NonSpinningAnsatzList"];
+
+If[Length@addnsansatz>0,Do[nsansatz=Append[nsansatz,addnsansatz[[i]]];,{i,Length@addnsansatz}]];
+
+unphysical = Select[data,#1[[1]] > 0.25 &];
+Print["data points with \[Eta] > 0.25: ", unphysical];
+
+datans = Select[data, #1[[2]]^2+#1[[3]]^2 < 0.01 &]; (* zero spin, for 1d fit *)
+dataeqs = Select[data, (Abs[#1[[2]]-#1[[3]]] < 0.01)||(#1[[1]]< OptionValue["\[Eta]LimitEqualSpin"]) &]; (* all equal spins, including zero *)
+datauneqs = Complement[data,dataeqs]; (* all unequal spins *)
+dataq1 = Select[dataeqs, (Abs[#1[[1]]-0.25] < 0.0001) && (#1[[2]]^2+#1[[3]]^2 >= 0.01) &]; (* equal nonzero spins, equal mass, for 1d fit *)
+dataeqsunmass = Select[dataeqs, (Abs[#1[[1]]-0.25] > 0.0001) && (#1[[2]]^2+#1[[3]]^2 >= 0.01) &]; (* equal nonzero spins, unequal mass, for 2d fit *)
+dataunconstr = Complement[data,Join[datans,dataq1]]; (* not 1D constrained: unequal-spin equal-mass or nonzero-spin unequal-mass, for 3d fit *)
+
+If[ListQ@tooltiptags,
+pos = Flatten[Position[data,#]&/@datans];
+tooltiptagsns = tooltiptags[[pos]];
+];
+
+Print["#\[NonBreakingSpace]of data points: ", Length@data];
+Print["#\[NonBreakingSpace]of non-spinning data points: ", Length@datans];
+Print["#\[NonBreakingSpace]of equal-spin equal-mass data points: ", Length@dataq1];
+Print["#\[NonBreakingSpace]of equal-spin unequal-mass data points: ", Length@dataeqsunmass];
+Print["#\[NonBreakingSpace]of unequal-spin data points: ", Length@datauneqs];
+Print["# of non-zero-spin unequal-mass data points: ", Length@dataunconstr];
+Print["Sums of subspaces: S=0 + q=1 + equal-spin + unequal-spin cases: ", Length@datans + Length@dataq1 + Length@dataeqsunmass + Length@datauneqs];
+Print[" S=0 + q=1 + others: ", Length@datans + Length@dataq1 + Length@dataunconstr];
+
+Print["Eff. spin parameter: ",spinparameter];
+Print["Spin-diff parameter: ",spindiffparameter];
+(*
+Print["Rules for General Anzatze : ", generalAnsatzRules];
+Print["Rules for Spin Difference Anzatze : ", spindifferencerules];
+*)
+
+allData = TakeColumn[data, {1,2,3,4,5}]/. {\[Eta]\[Eta]_,c1_,c2_,res_,ww_}->{\[Eta]\[Eta],spinparameter[\[Eta]\[Eta],c1,c2],res,ww};
+allDataEqS = TakeColumn[dataeqs, {1,2,3,4,5}]/. {\[Eta]\[Eta]_,c1_,c2_,res_,ww_}->{\[Eta]\[Eta],spinparameter[\[Eta]\[Eta],c1,c2],res,ww};
+allDataEqSv2 = TakeColumn[dataeqsunmass, {1,2,3,4,5}]/. {\[Eta]\[Eta]_,c1_,c2_,res_,ww_}->{\[Eta]\[Eta],spinparameter[\[Eta]\[Eta],c1,c2],res,ww};
+allDataUnconstr = TakeColumn[dataunconstr, {1,2,3,4,5}]/. {\[Eta]\[Eta]_,c1_,c2_,res_,ww_}->{\[Eta]\[Eta],spinparameter[\[Eta]\[Eta],c1,c2],res,ww};
+
+If[(fitcase==3)||(fitcase>=5),
+ oneDverbosity = 0;
+ ,
+ oneDverbosity = 2;
+];
+
+(* non-spinning fit *)
+Print[Style["Non-Spinning Fit",Blue]];
+nsfits = DataFitFunction[TakeColumn[datans,{1,4,5}], nsansatz, "Domain"->{0,0.25}, "PlotRange"->plotrange, "StatisticalTest"->statisticaltest, "Verbose"->oneDverbosity, "Weights"->weights,
+ "ToolTipTags"->tooltiptagsns, "GetIntervals"->getintervals&&(fitcase==1)];
+
+Print["---------------------"];
+Print["Select \[Chi]1=\[Chi]2=0 Fit with nsfitindex = ", nsfitindex, " -> ", nsfit = nsfits[[nsfitindex,1]] ];
+Print["---------------------"];
+
+(* equal mass/equal spin fit *)
+Print[Style["q=1, \[Chi]1=\[Chi]2 Fit",Blue]];
+
+dataq1sorted = Sort[TakeColumn[dataq1,{2,3,4,5}]]/. {xx_?NumberQ,yy_,zz_,ww_}->{spinparameter[0.25,xx,yy],zz,ww};
+
+If[ListQ@tooltiptags,
+ pos = Flatten[Position[data,#]&/@dataq1sorted];
+ tooltiptagseq = tooltiptags[[pos]];
+];
+
+Clear[b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,S];
+(* ansatzq1 = Total/@Table[ToExpression["b"<>ToString@i] * S^i,{j,3,8},{i,1,j}];
+ansatzq1 = Transpose[{ansatzq1,Table[{S},{i,Length@ansatzq1}]}]; *)
+
+ansatzq1 = OptionValue["EqualBHAnsatzList"];
+
+If[Length@addq1ansatz>0,Do[ansatzq1=Append[ansatzq1,addq1ansatz[[i]]];,{i,Length@addq1ansatz}]];
+
+
+If[productAnsatz,
+ ansatzq1[[All,1]]=(nsfit/. \[Eta]->0.25) * ansatzq1[[All,1]];
+ ,
+ ansatzq1[[All,1]]=(nsfit/. \[Eta]->0.25) + ansatzq1[[All,1]];
+];
+
+If[ListQ@tooltiptags,
+ pos = Flatten[Position[TakeColumn[data,{2,3,4,5}]/. {xx_?NumberQ,yy_,zz_,ww_}->{spinparameter[0.25,xx,yy],zz,ww},#]&/@dataq1sorted];
+ tooltiptagseq = tooltiptags[[pos]];
+];
+q1fits = DataFitFunction[dataq1sorted, ansatzq1, "Domain"-> {-1,1}, "PlotRange"->plotrange, "StatisticalTest"->statisticaltest, "Verbose"->oneDverbosity, "Weights"->weights,
+ "ToolTipTags"->tooltiptagseq, "GetIntervals"->getintervals&&(fitcase==1)];
+
+If[fitcase==1, Return[{nsfits,q1fits}]];
+
+etaAnsatz = nsfits[[nsfitindex,15]];
+etaCoeffRules = nsfits[[nsfitindex,2]];
+etaCovar = nsfits[[nsfitindex,14]];
+SAnsatz = q1fits[[q1fitindex,15]];
+SCoeffRules = q1fits[[q1fitindex,2]];
+SCovar = q1fits[[q1fitindex,14]];
+
+q1fit = q1fits[[q1fitindex,1]];
+
+Print["---------------------"];
+Print["Select q=1 Fit with q1fitindex = ", q1fitindex, " -> ", q1fit];
+Print["---------------------"];
+
+
+Print[Style["{\[Eta],S} Fit",Blue]];
+
+nsdegree = Exponent[nsfit,\[Eta],List];
+q1degree = Exponent[q1fit,S,List];
+
+ansatz={Flatten[Total@Table[Total@Table[ToExpression["f"<>ToString@i<>ToString@j] *S^j,{j,q1degree}]*\[Eta]^i,{i,nsdegree}]],{\[Eta],S}};
+If[productAnsatz,
+ ansatz=Collect[nsfit * Flatten[Total@Table[Total@Table[ToExpression["f"<>ToString@i<>ToString@j] * S^j, {j,4}]*\[Eta]^i, {i,4}]], S];
+ ,
+ ansatz=Collect[nsfit + Flatten[Total@Table[Total@Table[ToExpression["f"<>ToString@i<>ToString@j] * S^j, {j,4}]*\[Eta]^i, {i,4}]], S];
+];
+
+(*If[Length@addgenansatz>0,ansatz=addgenansatz[[1]];];*)
+(*ansatzFinal=Table[AnsatzRestrictions[ansatzAll[[i,1]],ansatzAll[[i,2]],ansatzAll[[i,3]]],{i,Length@ansatzAll}];*)
+
+If[fitcase<=4,
+ Print["\[InvisibleSpace]using nsfit: ", nsfit];
+ Print["\[InvisibleSpace]using q1fit: ", q1fit];
+];
+
+If[Length@addgenansatz>0
+ ,
+ ansatzFinal=addgenansatz[[1]];
+ Print[Style["Selecting ansatz from AddGenAnsatz",Blue]];
+ ,
+If[OptionValue["RationalFunctions"],
+
+Print[];
+
+If[productAnsatz,
+ q1fitS0 = q1fit/(q1fit/. S-> 0);
+ ,
+ q1fitS0 = q1fit-(q1fit/. S-> 0);
+];
+q1fitS0 = Chop[q1fitS0]/.{1.->1};
+
+q1fitS0orderNum = Exponent[Numerator[q1fitS0],S];
+q1fitS0orderDenom = Exponent[Denominator[q1fitS0],S];
+If[twoDSpinAnsatzOrderNum<0, twoDSpinAnsatzOrderNum = q1fitS0orderNum];
+If[twoDSpinAnsatzOrderDenom<0, twoDSpinAnsatzOrderDenom = q1fitS0orderDenom];
+If[(twoDSpinAnsatzOrderNum>q1fitS0orderNum)||(twoDSpinAnsatzOrderDenom>q1fitS0orderDenom),
+ spinAnsatzNum = Numerator[q1fitS0] + Sum[1.0*S^i,{i,q1fitS0orderNum+1,twoDSpinAnsatzOrderNum}];
+ spinAnsatzDenom = Denominator[q1fitS0] + Sum[1.0*S^i,{i,q1fitS0orderDenom+1,twoDSpinAnsatzOrderDenom}];
+ spinAnsatzToGeneralize = spinAnsatzNum/spinAnsatzDenom;
+ ,
+ spinAnsatzToGeneralize = q1fitS0;
+];
+
+spinAnsatz = GeneralizeFunction[spinAnsatzToGeneralize, "f", \[Eta], productGeneralizeOrderNum, productGeneralizeOrderDenom];
+Print["spinAnsatz before boundary conditions = ", spinAnsatz];
+
+(* spinAnsatzRaw = spinAnsatz /. InvertRules[SCoeffRules]; *)
+q1AnsatzRaw = q1fits[[q1fitindex,15]];
+If[productAnsatz,
+ q1AnsatzRawS0 = q1AnsatzRaw/(q1AnsatzRaw/.S->0);
+ ,
+ q1AnsatzRawS0 = q1AnsatzRaw-(q1AnsatzRaw/.S->0);
+];
+q1AnsatzRawS0 = Chop[q1AnsatzRawS0]/.{1.->1};
+If[(twoDSpinAnsatzOrderNum>q1fitS0orderNum)||(twoDSpinAnsatzOrderDenom>q1fitS0orderDenom),
+ spinAnsatzRawNum = Numerator[q1AnsatzRawS0] + Sum[1.0*S^i,{i,q1fitS0orderNum+1,twoDSpinAnsatzOrderNum}];
+ spinAnsatzRawDenom = Denominator[q1AnsatzRawS0] + Sum[1.0*S^i,{i,q1fitS0orderDenom+1,twoDSpinAnsatzOrderDenom}];
+ spinAnsatzRawToGeneralize = spinAnsatzRawNum/spinAnsatzRawDenom;
+ ,
+ spinAnsatzRawToGeneralize = q1AnsatzRawS0;
+];
+spinAnsatzRaw = GeneralizeFunction[spinAnsatzRawToGeneralize, "f", \[Eta], productGeneralizeOrderNum, productGeneralizeOrderDenom];
+
+numRestrictions = AnsatzRestrictions[Numerator[q1fitS0],Numerator[spinAnsatz],"Parameters"->True];
+denomRestrictions = AnsatzRestrictions[Denominator[q1fitS0],Denominator[spinAnsatz],"Parameters"->True];
+
+num = Collect[Numerator[spinAnsatz]/.numRestrictions,{S,\[Eta]}];
+If[productGeneralizeMinPowerNum>0,
+ zeroRules = Flatten@Table[ToExpression["f"<>ToString@i<>ToString@j]->0,{i,0,Exponent[num,S]},{j,0,productGeneralizeMinPowerNum-1}];
+ Print["setting the following coefficients to zero:"];
+ Print[zeroRules];
+ num = num/.zeroRules;
+];
+
+denom = Collect[Denominator[spinAnsatz]/.denomRestrictions,{S,\[Eta]}];
+spinpart = num/denom;
+Print["spinAnsatz after equal mass boundary conditions = ",spinpart];
+
+Print["applying user-set generalAnsatzRules:"];
+Print[generalAnsatzRules];
+
+If[productAnsatz,
+ ansatzFinal = (nsfit * spinpart) /. generalAnsatzRules;
+ (* \[Eta]0Ansatz =Limit[(spinAnsatz/\[Eta]), \[Eta]\[Rule] 0]//Chop//Simplify; *)
+ ansatzRaw = nsfit * spinAnsatzRaw;
+ ,
+ ansatzFinal = (nsfit + spinpart) /. generalAnsatzRules;
+ (* \[Eta]0Ansatz =Limit[(spinpart/\[Eta]), \[Eta]\[Rule] 0]//Chop//Simplify; *)
+ ansatzRaw = nsfit + spinAnsatzRaw;
+];
+
+Print[];
+(* 1 2 3 4 5 6 7 8 9 *)
+extraStuff = {ansatzRaw, etaAnsatz, etaCoeffRules, etaCovar, SAnsatz, SCoeffRules, SCovar, numRestrictions, denomRestrictions};
+
+,
+(* Constrain the ansatz to non spinning and q=1 cases *)
+(*ansatzFinal=AnsatzRestrictions[nsfit,q1fit,ansatz] /. generalAnsatzRules;*)
+ansatzFinal=AnsatzRestrictions[ nsfit,q1fit,ansatz];
+];
+];
+
+Print["\[InvisibleSpace]ansatzFinal: ", ansatzFinal];
+Print[];
+
+(*
+(* this is redundant and should only differ from 'v2' in uncertainty interval widths *)
+If[fitcase\[LessEqual]4,
+ Print[Style["eqS fit to all "<>ToString@Length@allData<>" data points:",Blue]];
+ alldataeqfit = DataFitFunction[allData, {{ansatzFinal,{\[Eta],S}}}, "PlotRange"\[Rule]{{0,0.25},{-1,1},All}, "Domain"\[Rule]{{0,0.25},{-1,1}},
+ "Verbose"\[Rule]2, "Weights"\[Rule]weights,"StatisticalTest"\[Rule]statisticaltest, "GetIntervals"\[Rule]getintervals];
+];
+*)
+Print[Style["eqS fit to all "<>ToString@Length@allDataUnconstr<>" data points without 1D regions:",Blue]];
+alldataeqfitv2 = DataFitFunction[allDataUnconstr, {{ansatzFinal,{\[Eta],S}}}, "PlotRange"->{{0,0.25},{-1,1},All}, "Domain"->{{0,0.25},{-1,1}},
+ "Verbose"->2, "Weights"->weights,"StatisticalTest"->statisticaltest, "GetIntervals"->getintervals];
+(*
+(* this is redundant and should only differ from 'v2' in uncertainty interval widths *)
+If[fitcase\[LessEqual]4,
+ Print[Style["eqS fit to "<>ToString@Length@allDataEqS<>" equal-spin data points:",Blue]];
+ eqdatafit = DataFitFunction[allDataEqS, {{ansatzFinal,{\[Eta],S}}}, "PlotRange"\[Rule]{{0,0.25},{-1,1},All}, "Domain"\[Rule]{{0,0.25},{-1,1}},
+ "Verbose"\[Rule]2, "Weights"\[Rule]weights,"StatisticalTest"\[Rule]statisticaltest, "GetIntervals"\[Rule]getintervals];
+];
+*)
+Print[Style["eqS fit to "<>ToString@Length@allDataEqSv2<>" equal-spin data points without 1D regions:",Blue]];
+eqdatafitv2 = DataFitFunction[allDataEqSv2, {{ansatzFinal,{\[Eta],S}}}, "PlotRange"->{{0,0.25},{-1,1},All}, "Domain"->{{0,0.25},{-1,1}},
+ "Verbose"->2, "Weights"->weights,"StatisticalTest"->statisticaltest, "GetIntervals"->getintervals];
+
+(* 2DeqS 2Dall 3D placeholders 1D2Dparts 1Deta 1DS 2DSansatz *)
+If[fitcase<=3, Return[{eqdatafitv2, alldataeqfitv2, {}, {}, {}, {}, extraStuff, nsfits, q1fits, spinpart}];];
+
+Print[Style["(fit to allData) - (fit to allDataEqS):",Blue]];
+Print[Plot3D[alldataeqfitv2[[1,1]]-eqdatafitv2[[1,1]],{\[Eta],0,0.25`},{S,-1,1},AxesLabel->{Style["\[Eta]",Black,14],Style["S",Black,14],Style["diff",14]}]];
+
+Clear[a0,a1,a2,a3,\[Chi]diff,q];
+(* Fit the spin difference terms *)
+Print["----------------"];
+Print[Style["{\[Eta],S,\[Chi]diff}",Blue]];
+
+mydq=0.005;
+tabfits=Table[
+ Print[Style["MassRatio -> ",Blue],q\[Eta][i]];
+ my\[Eta]=i;
+ thisq=q\[Eta][i];
+ If[ thisq < 2,
+ myd\[Eta] = Abs[0.0001+mydq (-2 thisq/(1+thisq)^3 + 1./(1+thisq)^2) ];,
+ myd\[Eta] = 0.001;
+ ];
+ Print["myd\[Eta] = ", myd\[Eta] ];
+
+ mysel = Select[data,my\[Eta]-myd\[Eta]<#1[[1]]<my\[Eta]+myd\[Eta]&];
+ dataq1 = TakeColumn[mysel,{2,3,4,5}]/. {xx_?NumberQ,yy_,zz_,ww_}->{xx,yy,eqdatafitv2[[1,1]]/. \[Eta]->my\[Eta]/. S->spinparameter[my\[Eta],xx,yy],ww};
+ avgwgthperq = Mean[dataq1[[All,-1]]];
+
+ If[fitcase>=5,
+ perqVerbosity = 0; (* for higher fit cases, still do the per-q analysis, but suppress the plots *)
+ ,
+ perqVerbosity = 1;
+ If[ListQ@tooltiptags,
+ dataq1pos = Flatten[Position[data,#]&/@mysel];
+ tooltiptagsaux = tooltiptags[[dataq1pos]];
+ ];
+
+ If[0.25 -myd\[Eta]<my\[Eta]<0.25 +myd\[Eta],
+ dataq1Sym = dataq1/. {xx_?NumberQ,yy_,zz_,ww_}->{yy,xx,zz,ww};
+ dataq1 = Join[dataq1,dataq1Sym];
+ ];
+ plot1 = myListPlot3D[dataq1[[All,1;;3]], AxesLabel->{Style["\[Chi]1",14],Style["\[Chi]2",14],""}, PlotRange->{{-1,1},{-1,1},All}, PlotLabel->Style["data(\[Chi]1,\[Chi]2)",14], ImageSize->250];
+
+ dataq1 = TakeColumn[mysel,{2,3,4,5}]/. {xx_?NumberQ,yy_,zz_,ww_}->{xx,yy,zz-(eqdatafitv2[[1,1]]/. \[Eta]->my\[Eta]/. S->spinparameter[my\[Eta],xx,yy]),ww};
+ If[0.25 -myd\[Eta]<my\[Eta]<0.25 +myd\[Eta],
+ dataq1Sym=dataq1/. {xx_?NumberQ,yy_,zz_,ww_}->{yy,xx,zz,ww};
+ dataq1=Join[dataq1,dataq1Sym];
+ ];
+ plot2 = myListPlot3D[dataq1[[All,1;;3]], AxesLabel->{Style["\[Chi]1",14],Style["\[Chi]2",14],""}, PlotRange->{{-1,1},{-1,1},All}, PlotLabel->Style["data(\[Chi]1,\[Chi]2) - fit(S)",14], ImageSize->250];
+
+ dataq1 = TakeColumn[mysel,{2,3,4,5}]/. {xx_?NumberQ,yy_,zz_,ww_}->{spinparameter[my\[Eta],xx,yy],xx-yy,zz-(eqdatafitv2[[1,1]]/. \[Eta]->my\[Eta]/. S->spinparameter[my\[Eta],xx,yy]),ww};
+ If[0.25 -myd\[Eta]<my\[Eta]<0.25+myd\[Eta],
+ dataq1Sym=dataq1/. {xx_?NumberQ,yy_,zz_,ww_}->{xx,-yy,zz,ww};
+ dataq1=Join[dataq1,dataq1Sym];
+ ];
+ plot3 = myListPlot3D[dataq1[[All,1;;3]], PlotStyle->Directive[RGBColor[0.880722, 0.611041, 0.142051],Opacity[0.7]], Lighting->{{"Ambient",RGBColor[0.880722, 0.611041, 0.142051]}},
+ AxesLabel->{Style["S",14],Style["\!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\)",14],""}, PlotRange->{{-1,1},{-2,2},All}, PlotLabel->Style["data(S,\!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\)) - fit(S)",14], ImageSize->250];
+ ];
+
+ Clear[a,b,c,\[Chi]1,\[Chi]2,\[Delta]\[Chi]];
+ dataq1a= TakeColumn[dataq1,{1,2,3}];
+
+ dataq1 = TakeColumn[mysel,{2,3,4,5}]/. {xx_?NumberQ,yy_,zz_,ww_}->{spindiffparameter[my\[Eta],xx,yy],zz-(eqdatafitv2[[1,1]]/. \[Eta]->my\[Eta]/. S->spinparameter[my\[Eta],xx,yy]),ww};
+ (*dataq1 = TakeColumn[mysel,{2,3,4,5}]/.\[VeryThinSpace]{xx_?NumberQ,yy_,zz_,ww_}\[Rule]{(xx-yy),zz-(eqdatafitv2[[1,1]]/.\[VeryThinSpace]\[Eta]\[Rule]my\[Eta]/.\[VeryThinSpace]S\[Rule]spinparameter[my\[Eta],xx,yy]),ww}*)
+
+
+ Print["data dimensionality: ",Length@dataq1];
+ If[0.25 -myd\[Eta]<my\[Eta]<0.25+myd\[Eta],
+ dataq1Sym = dataq1/. {xx_?NumberQ,zz_,ww_}->{-xx,zz,ww};
+ dataq1 = Join[dataq1,dataq1Sym];
+ If[perqVerbosity>0, tooltiptagsaux = Join[tooltiptagsaux,tooltiptagsaux];];
+ Print["data dimensionality (including symmetric duplicates): ",Length@dataq1];
+ ];
+
+ (*dataq1mixterm = TakeColumn[mysel,{2,3,4,5}]/.\[VeryThinSpace]{xx_?NumberQ,yy_,zz_,ww_}\[Rule]{xx-yy,spinparameter[my\[Eta],xx,yy]*(xx-yy),zz-(eqdatafitv2[[1,1]]/.\[VeryThinSpace]\[Eta]\[Rule]my\[Eta]/.\[VeryThinSpace]S\[Rule]spinparameter[my\[Eta],xx,yy]),ww};*)
+ dataq1mixterm = TakeColumn[mysel,{2,3,4,5}]/. {xx_?NumberQ,yy_,zz_,ww_}->{spindiffparameter[my\[Eta],xx,yy],spinparameter[my\[Eta],xx,yy]*spindiffparameter[my\[Eta],xx,yy],zz-(eqdatafitv2[[1,1]]/. \[Eta]->my\[Eta]/. S->spinparameter[my\[Eta],xx,yy]),ww};
+
+ myfit = DataFitFunction[dataq1, {{a \[Delta]\[Chi], {\[Delta]\[Chi]}}, {a \[Delta]\[Chi] + b \[Delta]\[Chi]^2,{\[Delta]\[Chi]}}}, "Verbose"->perqVerbosity, "AxesTag"->"Amplitude",
+ "StatisticalTest"->statisticaltest, "Sorted"->False, "Weights"->weights, "GetIntervals"->False];
+ myfitmixterm = DataFitFunction[dataq1mixterm, {{a \[Delta]\[Chi] + c y, {\[Delta]\[Chi],y}}, {a \[Delta]\[Chi] + c y +b \[Delta]\[Chi]^2,{\[Delta]\[Chi],y}}}, "Verbose"->perqVerbosity, "AxesTag"->"Amplitude",
+ "StatisticalTest"->statisticaltest, "Sorted"->False, "Weights"->weights, "GetIntervals"->False];
+
+ myfit = Join[myfit,myfitmixterm,{avgwgthperq}];
+ (* do NOT show mix-term fits here, as they tend to blow the scale, and are only projected down anyway *)
+ (* plot4=Show[Plot[{myfit[[1,1]],myfit[[2,1]]},{\[Delta]\[Chi],-0.1,0.1},PlotRange\[Rule]All,ImageSize\[Rule]250,
+ Frame\[Rule]True,FrameLabel\[Rule]{"Subscript[\[Chi], diff]","\[CapitalDelta](Subscript[\[Chi], diff])"},PlotLegends\[Rule]{"linear","lin+quad"}],
+ ListPlot[Table[Tooltip[dataq1[[i,1;;2]],If[ListQ@tooltiptags,tooltiptagsaux[[i]],ToString[{dataq1[[i,1]],dataq1[[i,2]]}]]],{i,Length@dataq1}],PlotStyle\[Rule]PointSize[Medium],PlotRange\[Rule]All,Frame->True]];
+ *)
+
+ dataq1a= Transpose[{dataq1a[[All,1]],dataq1a[[All,2]],dataq1a[[All,3]]-(myfit[[1,1]]/.\[Delta]\[Chi]->dataq1[[All,1]])}];
+ plot3a = myListPlot3D[dataq1a, PlotStyle->Directive[RGBColor[0.880722, 0.611041, 0.142051],Opacity[0.7]], Lighting->{{"Ambient",RGBColor[0.880722, 0.611041, 0.142051]}},
+ AxesLabel->{Style["S",14],Style["\!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\)",14],""}, PlotRange->{{-1,1},{-2,2},All}, PlotLabel->Style["data(S,\!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\)) - (fit(S) + f(\[Eta])\!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\))",14], ImageSize->250];
+
+ If[fitcase==4,
+ plot4a = ListPlot[Table[Tooltip[dataq1[[i,1;;2]],If[ListQ@tooltiptags,tooltiptagsaux[[i]],ToString[{dataq1[[i,1]],dataq1[[i,2]]}]]],{i,Length@dataq1}],
+ PlotStyle->PointSize[Medium], PlotRange->{{-2.,2.},All}, PlotLegends->{"NR data"}];
+ plot4b = Plot[{myfit[[1,1]],myfit[[2,1]]},{\[Delta]\[Chi],-2.,2.}, PlotLegends->{"linear","lin+quad"}, PlotRange->{{-2.,2.},All}];
+ If[0.25 -myd\[Eta]<my\[Eta]<0.25+myd\[Eta],
+ plot4mirror = ListPlot[Table[{dataq1[[i,1]],dataq1[[i,2]]},{i,Length@dataq1}], PlotStyle->{Gray,PointSize[Medium]}, PlotMarkers->\!\(\*
+StyleBox["\"\<\[FilledSquare]\>\"",
+StripOnInput->False,
+FontSize->8]\), PlotLegends->{"mirror NR data"}];
+ plot4 = Show[{plot4b,plot4a}, Frame->True, FrameLabel->{"\!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\)","\[CapitalDelta](\!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\))"}, ImageSize->250];
+ ,
+ plot4 = Show[{plot4b,plot4a}, Frame->True, FrameLabel->{"\!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\)","\[CapitalDelta](\!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\))"}, ImageSize->250];
+ ];
+ Print[{plot1,plot2,plot3,plot3a,plot4}];
+ ];
+
+ myfit, {i,massratiounequalfits}]; (* this line finishes the tabfits list *)
+
+(*Print[tabfits[[All,-1]]];*)
+
+Print["-----------"];
+Print[Style["\[Eta] dependence of \!\(\*SubscriptBox[\(\[Chi]\), \(diff\)]\) terms",Blue]];
+
+extrawght=Join[tabfits[[All,-1]],{1.}];
+
+If[fastanalysis,
+
+If[Length@addspindifflinansatz>0,
+ ansatzchidifflinear = addspindifflinansatz[[1,1]];
+ ,
+ ansatzchidifflinear = (ToExpression["a10"] \[Eta]^Abs[ToExpression["a11"]] Sqrt[1-4 \[Eta]]^Abs[ToExpression["a12"]] ) /. spindifferencerules;
+];
+
+If[Length@addspindiffquadansatz>0,
+ ansatzchidiffquadratic = addspindiffquadansatz[[1,1]];
+ ,
+ ansatzchidiffquadratic = ((ToExpression["a20"] \[Eta]^Abs[ToExpression["a21"]] Sqrt[1-4 \[Eta]]^Abs[ToExpression["a22"]] )) /. spindifferencerules;
+];
+ansatzFinal\[Delta]\[Chi]2 = (ansatzFinal /. S->spinparameter[\[Eta],\[Chi]1,\[Chi]2]) + ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffquadratic spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]^2;
+
+If[Length@addspindiffmixansatz>0,
+ ansatzchidiffmix = addspindiffmixansatz[[1,1]];
+ ,
+ ansatzchidiffmix = ((ToExpression["a30"] \[Eta]^Abs[ToExpression["a31"]] Sqrt[1-4 \[Eta]]^Abs[ToExpression["a32"]] )) /. spindifferencerules;
+];
+
+ansatzS\[Delta]\[Chi]\[Chi]2raw = ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffmix S spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffquadratic spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]^2; (* needed to extract the coefficients later on *)
+ansatzFinalS\[Delta]\[Chi]\[Chi]2 = ( ansatzFinal + ansatzS\[Delta]\[Chi]\[Chi]2raw )/.S->spinparameter[\[Eta],\[Chi]1,\[Chi]2]; (* this is the form passed to DataFitFunction[] *)
+
+Print[Style["full 3D fit to all "<>ToString@Length@dataunconstr<>" data points without 1D regions... (see results at the end after plots)",Blue]];
+
+uneqfit2 = DataFitFunction[dataunconstr, {{ansatzFinalS\[Delta]\[Chi]\[Chi]2,{\[Eta],\[Chi]1,\[Chi]2}}},
+ "Verbose"->0, "AxesTag"->"Amplitude", "StatisticalTest"->statisticaltest, "Sorted"->False, "Weights"->weights, "GetIntervals"->getintervals];
+
+
+Print["Done"];
+Return[{uneqfit2 ,extraStuff, nsfits, q1fits, spinpart}];
+
+,
+
+linearparerr=Flatten@TakeColumn[tabfits,1][[All,9,1]];
+linearparerr=Join[linearparerr,{10^-9}];
+linearpar=Transpose[{Join[massratiounequalfits,{0}],Join[a/.TakeColumn[tabfits,1][[All,2]],{0}],extrawght/linearparerr^2}];
+linearpar[[1]]={0.25,0,extrawght[[1]]/(10^(-9))^2};
+linearparerr[[1]]={10^-9};
+
+linearpar2err=Flatten@TakeColumn[tabfits,2][[All,9,1]];
+linearpar2err=Join[linearpar2err,{10^-9}];
+linearpar2=Transpose[{Join[massratiounequalfits,{0}],Join[a/.TakeColumn[tabfits,2][[All,2]],{0}],extrawght/linearpar2err^2}];
+linearpar2[[1]]={0.25,0,extrawght[[1]]/(10^(-9))^2};
+linearpar2err[[1]]={10^-9};
+
+quadparerr=Flatten@TakeColumn[tabfits,2][[All,9,2]];
+quadparerr=Join[quadparerr,{10^-9}];
+quadpar=Transpose[{Join[massratiounequalfits,{0}],Join[b/.TakeColumn[tabfits,2][[All,2]],{0}],extrawght/quadparerr^2}];
+
+linearpar3err=Flatten@TakeColumn[tabfits,3][[All,9,1]];
+linearpar3err=Join[linearpar3err,{10^-9}];
+linearpar3=Transpose[{Join[massratiounequalfits,{0}],Join[a/.TakeColumn[tabfits,3][[All,2]],{0}],extrawght/linearpar2err^2}];
+linearpar3[[1]]={0.25,0,extrawght[[1]]/(10^(-9))^2};
+linearpar3err[[1]]={10^-9};
+
+mixparerr=Flatten@TakeColumn[tabfits,3][[All,9,2]];
+mixparerr=Join[mixparerr,{10^-9}];
+mixpar=Transpose[{Join[massratiounequalfits,{0}],Join[c/.TakeColumn[tabfits,3][[All,2]],{0}],extrawght/mixparerr^2}];
+mixpar[[1]]={0.25,0,extrawght[[1]]/(10^(-9))^2};
+mixparerr[[1]]={10^-9};
+
+linearpar4err=Flatten@TakeColumn[tabfits,4][[All,9,1]];
+linearpar4err=Join[linearpar4err,{10^-9}];
+linearpar4=Transpose[{Join[massratiounequalfits,{0}],Join[a/.TakeColumn[tabfits,4][[All,2]],{0}],extrawght/linearpar4err^2}];
+linearpar4[[1]]={0.25,0,extrawght[[1]]/(10^(-9))^2};
+linearpar4err[[1]]={10^-9};
+
+mixparerr2=Flatten@TakeColumn[tabfits,4][[All,9,2]];
+mixparerr2=Join[mixparerr2,{10^-9}];
+mixpar2=Transpose[{Join[massratiounequalfits,{0}],Join[c/.TakeColumn[tabfits,4][[All,2]],{0}],extrawght/mixparerr2^2}];
+mixpar2[[1]]={0.25,0,extrawght[[1]]/(10^(-9))^2};
+mixparerr2[[1]]={10^-9};
+
+quadparerr2=Flatten@TakeColumn[tabfits,4][[All,9,2]];
+quadparerr2=Join[quadparerr2,{10^-9}];
+quadpar2=Transpose[{Join[massratiounequalfits,{0}],Join[b/.TakeColumn[tabfits,4][[All,2]],{0}],extrawght/quadparerr2^2}];
+
+(*ansatz\[Eta]1=a0 \[Eta]^Abs[a1] N[1-4 \[Eta]]^0.7;*)
+(*ansatz\[Eta]1=a0 \[Eta]^Abs[a1] N[1-4 \[Eta]]^Abs[a2];*)
+(*ansatz\[Eta]1=a0 \[Eta] N[1-4 \[Eta]]^Abs[a2];*)
+
+If[Length@addspindifflinansatz>0,
+ ansatzchidifflinear = addspindifflinansatz[[1,1]];
+ ,
+ ansatzchidifflinear = (ToExpression["a10"] \[Eta]^Abs[ToExpression["a11"]] Sqrt[1-4 \[Eta]]^Abs[ToExpression["a12"]] ) /. spindifferencerules;
+];
+(*ansatzFinal\[Delta]\[Chi]=(ansatzFinal/. S\[Rule] spinparameter[\[Eta],\[Chi]1,\[Chi]2])+ansatzchidifflinear (\[Chi]1-\[Chi]2);*)
+
+
+ansatzFinal\[Delta]\[Chi] = (ansatzFinal /. S->spinparameter[\[Eta],\[Chi]1,\[Chi]2]) + ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2];
+
+If[Length@addspindiffquadansatz>0,
+ ansatzchidiffquadratic = addspindiffquadansatz[[1,1]];
+ ,
+ ansatzchidiffquadratic = ((ToExpression["a20"] \[Eta]^Abs[ToExpression["a21"]] Sqrt[1-4 \[Eta]]^Abs[ToExpression["a22"]] )) /. spindifferencerules;
+];
+ansatzFinal\[Delta]\[Chi]2 = (ansatzFinal /. S->spinparameter[\[Eta],\[Chi]1,\[Chi]2]) + ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffquadratic spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]^2;
+
+If[Length@addspindiffmixansatz>0,
+ ansatzchidiffmix = addspindiffmixansatz[[1,1]];
+ ,
+ ansatzchidiffmix = ((ToExpression["a30"] \[Eta]^Abs[ToExpression["a31"]] Sqrt[1-4 \[Eta]]^Abs[ToExpression["a32"]] )) /. spindifferencerules;
+];
+ansatzS\[Delta]\[Chi]raw = ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffmix S spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]; (* needed to extract the coefficients later on *)
+ansatzFinalS\[Delta]\[Chi] = ( ansatzFinal + ansatzS\[Delta]\[Chi]raw ) /. S->spinparameter[\[Eta],\[Chi]1,\[Chi]2]; (* this is the form passed to DataFitFunction[] *)
+
+ansatzS\[Delta]\[Chi]\[Chi]2raw = ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffmix S spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffquadratic spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]^2; (* needed to extract the coefficients later on *)
+ansatzFinalS\[Delta]\[Chi]\[Chi]2 = ( ansatzFinal + ansatzS\[Delta]\[Chi]\[Chi]2raw ) /. S->spinparameter[\[Eta],\[Chi]1,\[Chi]2]; (* this is the form passed to DataFitFunction[] *)
+
+Print["Fitting ansaetze to per-q slopes, linear only:"];
+linearfit1 = DataFitFunction[linearpar, {{ansatzchidifflinear,{\[Eta]}}}, "Verbose"->1, "Weights"->weights];
+Print["linear+quadratic:"];
+linearfit2 = DataFitFunction[linearpar2, {{ansatzchidifflinear,{\[Eta]}}}, "Verbose"->1, "Weights"->weights];
+quadfit = DataFitFunction[quadpar, {{ansatzchidiffquadratic,{\[Eta]}}}, "Verbose"->1, "Weights"->weights];
+Print["linear+mixture:"];
+linearfit3 = DataFitFunction[linearpar3, {{ansatzchidifflinear,{\[Eta]}}}, "Verbose"->1, "Weights"->weights];
+mixfit = DataFitFunction[mixpar, {{ansatzchidiffmix,{\[Eta]}}}, "Verbose"->1, "Weights"->weights];
+Print["linear+mixture+quadratic:"];
+linearfit4 = DataFitFunction[linearpar4, {{ansatzchidifflinear,{\[Eta]}}}, "Verbose"->1, "Weights"->weights];
+mixfit2 = DataFitFunction[mixpar2, {{ansatzchidiffmix,{\[Eta]}}}, "Verbose"->1, "Weights"->weights];
+quadfit2 = DataFitFunction[quadpar2, {{ansatzchidiffquadratic,{\[Eta]}}}, "Verbose"->1, "Weights"->weights];
+
+Clear[a10,a11,a12,a20,a21,a22,a30,a31,a32,a1,a2,a0];
+
+(*If[Length@addgenansatz>0,ansatz=addgenansatz[[1]];];*)
+(*ansatzFinal=Table[AnsatzRestrictions[ansatzAll[[i,1]],ansatzAll[[i,2]],ansatzAll[[i,3]]],{i,Length@ansatzAll}];*)
+
+(* this will only differ from uneqfit2 in the width of the error bars, not in the results, and is not needed anymore, but let's keep it here commented-out to have it handy for sanity checks *)
+(*
+Print[Style["full 3D fit to all "<>ToString@Length@data<>" data points...",Blue]];
+uneqfit = DataFitFunction[data, {{ansatzFinal\[Delta]\[Chi],{\[Eta],\[Chi]1,\[Chi]2}},{ansatzFinal\[Delta]\[Chi]2,{\[Eta],\[Chi]1,\[Chi]2}},{ansatzFinalS\[Delta]\[Chi],{\[Eta],\[Chi]1,\[Chi]2}},{ansatzFinalS\[Delta]\[Chi]\[Chi]2,{\[Eta],\[Chi]1,\[Chi]2}}},
+ "Verbose"\[Rule]0, "AxesTag"\[Rule]"Amplitude", "StatisticalTest"\[Rule]statisticaltest, "Sorted"\[Rule]False, "Weights"\[Rule] weights, "GetIntervals"\[Rule]getintervals];
+*)
+
+Print[Style["full 3D fit to all "<>ToString@Length@dataunconstr<>" data points without 1D regions... (see results at the end after plots)",Blue]];
+uneqfit2 = DataFitFunction[dataunconstr, {{ansatzFinal\[Delta]\[Chi],{\[Eta],\[Chi]1,\[Chi]2}},{ansatzFinal\[Delta]\[Chi]2,{\[Eta],\[Chi]1,\[Chi]2}},{ansatzFinalS\[Delta]\[Chi],{\[Eta],\[Chi]1,\[Chi]2}},{ansatzFinalS\[Delta]\[Chi]\[Chi]2,{\[Eta],\[Chi]1,\[Chi]2}}},
+ "Verbose"->0, "AxesTag"->"Amplitude", "StatisticalTest"->statisticaltest, "Sorted"->False, "Weights"->weights, "GetIntervals"->getintervals];
+
+
+Print[Style["spin-diff fit to "<>ToString@Length@datauneqs<>" unequal-spin data points...",Blue]];
+uneqfit3 = DataFitFunction[TakeColumn[datauneqs,{1,2,3,4,5}]/. {\[Eta]\[Eta]_,c1_,c2_,res_,ww_}->{\[Eta]\[Eta],c1,c2,res-(eqdatafitv2[[1,1]]/. \[Eta]->\[Eta]\[Eta]/. S->spinparameter[\[Eta]\[Eta],c1,c2]),ww},
+ {{ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2], {\[Eta],\[Chi]1,\[Chi]2}},
+ {ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffquadratic spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]^2, {\[Eta],\[Chi]1,\[Chi]2}},
+ {ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffmix spinparameter[\[Eta],\[Chi]1,\[Chi]2] spindiffparameter[\[Eta],\[Chi]1,\[Chi]2], {\[Eta],\[Chi]1,\[Chi]2}},
+ {ansatzchidifflinear spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffmix spinparameter[\[Eta],\[Chi]1,\[Chi]2] spindiffparameter[\[Eta],\[Chi]1,\[Chi]2] + ansatzchidiffquadratic spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]^2, {\[Eta],\[Chi]1,\[Chi]2}}},
+ "Verbose"->1, "AxesTag"->"Amplitude", "StatisticalTest"->statisticaltest, "Sorted"->False, "Weights"->weights, "GetIntervals"->getintervals];
+
+(*
+Print[Style["full 3D fit to "<>ToString@Length@datauneqs<>" unequal-spin data points...",Blue]];
+uneqfit3 = DataFitFunction[datauneqs, {{ansatzFinal\[Delta]\[Chi],{\[Eta],\[Chi]1,\[Chi]2}},{ansatzFinal\[Delta]\[Chi]2,{\[Eta],\[Chi]1,\[Chi]2}},{ansatzFinalS\[Delta]\[Chi],{\[Eta],\[Chi]1,\[Chi]2}},{ansatzFinalS\[Delta]\[Chi]\[Chi]2,{\[Eta],\[Chi]1,\[Chi]2}}},
+ "Verbose"\[Rule]0, "AxesTag"\[Rule]"Amplitude", "StatisticalTest"\[Rule]statisticaltest, "Sorted"\[Rule]False, "Weights"\[Rule] weights, "GetIntervals"\[Rule]getintervals];
+*)
+
+(* eta-dependence for direct 3D fit over all non-1D data *)
+spindiffterm = CoefficientList[uneqfit2[[1,1]]/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[2]];
+spindiffterm21 = CoefficientList[uneqfit2[[2,1]]/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[2]];
+spindiffterm22 = CoefficientList[uneqfit2[[2,1]]/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[3]];
+spindiffterm31 = CoefficientList[ansatzS\[Delta]\[Chi]raw/.uneqfit2[[3,2]]/.S->0/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[2]];
+spindiffterm32 = CoefficientList[ansatzS\[Delta]\[Chi]raw/.uneqfit2[[3,2]]/.S*spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->y,y][[2]];
+spindiffterm41 = CoefficientList[ansatzS\[Delta]\[Chi]\[Chi]2raw/.uneqfit2[[4,2]]/.S->0/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[2]];
+spindiffterm42 = CoefficientList[ansatzS\[Delta]\[Chi]\[Chi]2raw/.uneqfit2[[4,2]]/.S spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->y,y][[2]];
+spindiffterm43 = CoefficientList[ansatzS\[Delta]\[Chi]\[Chi]2raw/.uneqfit2[[4,2]]/.S->0/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[3]];
+
+(* eta-dependence for residuals-only spin-diff fit over all uneqS data *)
+dfitspindiffterm = CoefficientList[uneqfit3[[1,1]]/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[2]];
+dfitspindiffterm21 = CoefficientList[uneqfit3[[2,1]]/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[2]];
+dfitspindiffterm22 = CoefficientList[uneqfit3[[2,1]]/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[3]];
+dfitspindiffterm31 = CoefficientList[ansatzS\[Delta]\[Chi]raw/.uneqfit3[[3,2]]/.S->0/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[2]];
+dfitspindiffterm32 = CoefficientList[ansatzS\[Delta]\[Chi]raw/.uneqfit3[[3,2]]/.S*spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->y,y][[2]];
+dfitspindiffterm41 = CoefficientList[ansatzS\[Delta]\[Chi]\[Chi]2raw/.uneqfit3[[4,2]]/.S->0/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[2]];
+dfitspindiffterm42 = CoefficientList[ansatzS\[Delta]\[Chi]\[Chi]2raw/.uneqfit3[[4,2]]/.S spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->y,y][[2]];
+dfitspindiffterm43 = CoefficientList[ansatzS\[Delta]\[Chi]\[Chi]2raw/.uneqfit3[[4,2]]/.S->0/.spindiffparameter[\[Eta],\[Chi]1,\[Chi]2]->\[Chi]diff,\[Chi]diff][[3]];
+
+lplot=Show[{Plot[{spindiffterm,dfitspindiffterm,linearfit1[[1,1]]}, {\[Eta],0,0.25}, PlotLegends->{"direct 3D fit","fit to residuals","per-q res. fits"}, PlotStyle->{{Orange},{Magenta,Dotted},{Blue,Dashed}}],
+ ErrorListPlot[Table[{linearpar[[i,1;;2]], ErrorBar[1/Sqrt[linearpar[[i,-1]]]]}, {i,Length@linearparerr}], PlotStyle->Red],
+ ErrorListPlot[Table[{linearpar[[i,1;;2]], ErrorBar[linearparerr[[i]]]}, {i,Length@linearparerr}], PlotLegends->{"per-q fit results"}]},
+ PlotRange->{{0,0.25},{Min@linearpar[[All,2]]-0.001,Max@linearpar[[All,2]]+0.001}}, ImageSize->330, Frame->True, FrameLabel->{Style["\[Eta]",14],Style["\!\(\*SubscriptBox[\(f\), \(a\)]\)(\[Eta])",14]}, PlotLabel->{"linear fit, \!\(\*SubscriptBox[\(f\), \(a\)]\)(\[Eta])="{ansatzchidifflinear}}];
+
+lqplotl=Show[{Plot[{spindiffterm21,dfitspindiffterm21,linearfit2[[1,1]]}, {\[Eta],0,0.25}, PlotLegends->{"direct 3D fit","fit to residuals","per-q res. fits"}, PlotStyle->{{Orange},{Magenta,Dotted},{Blue,Dashed}}],
+ ErrorListPlot[Table[{linearpar2[[i,1;;2]], ErrorBar[1/Sqrt[linearpar2[[i,-1]]]]}, {i,Length@linearpar2err}], PlotStyle->Red],
+ ErrorListPlot[Table[{linearpar2[[i,1;;2]], ErrorBar[linearpar2err[[i]]]}, {i,Length@linearpar2err}], PlotLegends->{"per-q fit results"}]},
+ PlotRange->{{0,0.25},{Min@linearpar2[[All,2]]-0.001,Max@linearpar2[[All,2]]+0.001}}, ImageSize->330, Frame->True, FrameLabel->{Style["\[Eta]",14],Style["\!\(\*SubscriptBox[\(f\), \(a\)]\)(\[Eta])",14]}, PlotLabel->{"lin+quad fit, lin term, \!\(\*SubscriptBox[\(f\), \(a\)]\)(\[Eta])="{ansatzchidifflinear}}];
+
+lqplotq=Show[{Plot[{spindiffterm22,dfitspindiffterm22,quadfit[[1,1]]}, {\[Eta],0,0.25}, PlotLegends->{"direct 3D fit","fit to residuals","per-q res. fits"}, PlotStyle->{{Orange},{Magenta,Dotted},{Blue,Dashed}}],
+ ErrorListPlot[Table[{quadpar[[i,1;;2]],ErrorBar[1/Sqrt[quadpar[[i,-1]]]]},{i,Length@quadparerr}], PlotStyle->Red],
+ ErrorListPlot[Table[{quadpar[[i,1;;2]],ErrorBar[quadparerr[[i]]]},{i,Length@quadparerr}], PlotLegends->{"per-q fit results"}]},
+ PlotRange->{{0,0.25},{Min@quadpar[[All,2]]-0.001,Max@quadpar[[All,2]]+0.001}}, ImageSize->330, Frame->True, FrameLabel->{Style["\[Eta]",14],Style["\!\(\*SubscriptBox[\(f\), \(b\)]\)(\[Eta])",14]}, PlotLabel->{"lin+quad fit, quad term, \!\(\*SubscriptBox[\(f\), \(b\)]\)(\[Eta])="{ansatzchidiffquadratic}}];
+
+lmplotl=Show[{Plot[{spindiffterm31,dfitspindiffterm31,linearfit3[[1,1]]},{\[Eta],0,0.25},PlotLegends->{"direct 3D fit","fit to residuals","per-q res. fits"}, PlotStyle->{{Orange},{Magenta,Dotted},{Blue,Dashed}}],
+ ErrorListPlot[Table[{linearpar3[[i,1;;2]],ErrorBar[1/Sqrt[linearpar3[[i,-1]]]]},{i,Length@linearpar3err}], PlotStyle->Red],
+ ErrorListPlot[Table[{linearpar3[[i,1;;2]],ErrorBar[linearpar3err[[i]]]},{i,Length@linearpar3err}], PlotLegends->{"per-q fit results"}]},
+ PlotRange->{{0,0.25},{Min@linearpar3[[All,2]]-0.001,Max@linearpar3[[All,2]]+0.001}}, ImageSize->330, Frame->True, FrameLabel->{Style["\[Eta]",14],Style["\!\(\*SubscriptBox[\(f\), \(a\)]\)(\[Eta])",14]}, PlotLabel->{"lin+mix fit, lin term, \!\(\*SubscriptBox[\(f\), \(a\)]\)(\[Eta])="{ansatzchidifflinear}}];
+
+lmplotm=Show[{Plot[{spindiffterm32,dfitspindiffterm32,mixfit[[1,1]]},{\[Eta],0,0.25},PlotLegends->{"direct 3D fit","fit to residuals","per-q res. fits"}, PlotStyle->{{Orange},{Magenta,Dotted},{Blue,Dashed}}],
+ ErrorListPlot[Table[{mixpar[[i,1;;2]],ErrorBar[1/Sqrt[mixpar[[i,-1]]]]},{i,Length@mixparerr}], PlotStyle->Red],
+ ErrorListPlot[Table[{mixpar[[i,1;;2]],ErrorBar[mixparerr[[i]]]},{i,Length@mixparerr}], PlotLegends->{"per-q fit results"}]},
+ PlotRange->{{0,0.25},{Min@mixpar[[All,2]]-0.001,Max@mixpar[[All,2]]+0.001}}, ImageSize->330, Frame->True, FrameLabel->{Style["\[Eta]",14],Style["\!\(\*SubscriptBox[\(f\), \(c\)]\)(\[Eta])",14]}, PlotLabel->{"lin+mix fit, mix term, \!\(\*SubscriptBox[\(f\), \(c\)]\)(\[Eta])="{ansatzchidiffmix}}];
+
+
+lmqplotl=Show[{Plot[{spindiffterm41,dfitspindiffterm41,linearfit4[[1,1]]},{\[Eta],0,0.25},PlotLegends->{"direct 3D fit","fit to residuals","per-q res. fits"}, PlotStyle->{{Orange},{Magenta,Dotted},{Blue,Dashed}}],
+ ErrorListPlot[Table[{linearpar4[[i,1;;2]],ErrorBar[1/Sqrt[linearpar4[[i,-1]]]]},{i,Length@linearpar4err}], PlotStyle->Red],
+ ErrorListPlot[Table[{linearpar4[[i,1;;2]],ErrorBar[linearpar4err[[i]]]},{i,Length@linearpar4err}], PlotLegends->{"per-q fit results"}]},
+ PlotRange->{{0,0.25},{Min@linearpar4[[All,2]]-0.001,Max@linearpar4[[All,2]]+0.001}}, ImageSize->330, Frame->True, FrameLabel->{Style["\[Eta]",14],Style["\!\(\*SubscriptBox[\(f\), \(a\)]\)(\[Eta])",14]}, PlotLabel->{"lin+mix+quad fit, lin term, \!\(\*SubscriptBox[\(f\), \(a\)]\)(\[Eta])="{ansatzchidifflinear}}];
+
+lmqplotq=Show[{Plot[{spindiffterm43,dfitspindiffterm43,quadfit2[[1,1]]},{\[Eta],0,0.25},PlotLegends->{"direct 3D fit","fit to residuals","per-q res. fits"}, PlotStyle->{{Orange},{Magenta,Dotted},{Blue,Dashed}}],
+ ErrorListPlot[Table[{quadpar2[[i,1;;2]],ErrorBar[1/Sqrt[quadpar2[[i,-1]]]]},{i,Length@quadparerr2}], PlotStyle->Red],
+ ErrorListPlot[Table[{quadpar2[[i,1;;2]],ErrorBar[quadparerr2[[i]]]},{i,Length@quadparerr2}], PlotLegends->{"per-q fit results"}]},
+ PlotRange->{{0,0.25},{Min@quadpar2[[All,2]]-0.001,Max@quadpar2[[All,2]]+0.001}}, ImageSize->330, Frame->True, FrameLabel->{Style["\[Eta]",14],Style["\!\(\*SubscriptBox[\(f\), \(b\)]\)(\[Eta])",14]}, PlotLabel->{"lin+mix+quad fit, quad term, \!\(\*SubscriptBox[\(f\), \(b\)]\)(\[Eta])="{ansatzchidiffquadratic}}];
+
+lmqplotm=Show[{Plot[{spindiffterm42,dfitspindiffterm42,mixfit2[[1,1]]},{\[Eta],0,0.25},PlotLegends->{"direct 3D fit","fit to residuals","per-q res. fits"}, PlotStyle->{{Orange},{Magenta,Dotted},{Blue,Dashed}}],
+ ErrorListPlot[Table[{mixpar2[[i,1;;2]],ErrorBar[1/Sqrt[mixpar2[[i,-1]]]]},{i,Length@mixparerr2}], PlotStyle->Red],
+ ErrorListPlot[Table[{mixpar2[[i,1;;2]],ErrorBar[mixparerr2[[i]]]},{i,Length@mixparerr2}], PlotLegends->{"per-q fit results"}]},
+ PlotRange->{{0,0.25},{Min@mixpar2[[All,2]]-0.001,Max@mixpar2[[All,2]]+0.001}}, ImageSize->330, Frame->True, FrameLabel->{Style["\[Eta]",14],Style["\!\(\*SubscriptBox[\(f\), \(c\)]\)(\[Eta])",14]}, PlotLabel->{"lin+mix+quad fit, mix term, \!\(\*SubscriptBox[\(f\), \(c\)]\)(\[Eta])="{ansatzchidifflinear}}];
+
+Print[{lplot,lqplotl}]
+Print[{lmplotl,lmqplotl}];
+Print[{lqplotq,lmqplotq,Show[lmqplotq,PlotRange->{{0.0,0.25},Automatic}]}];
+Print[{lmplotm,lmqplotm,Show[lmqplotm,PlotRange->{{0.0,0.25},Automatic}]}];
+
+(* rewrite fit and ansatz output in terms of (\[Eta],S.\[Chi]1,\[Chi]2) and not as the expanded (\[Eta],\[Chi]1,\[Chi]2) version processed by DataFitFunction *)
+uneqfit2[[1,1]] = ( ansatzFinal + ansatzchidifflinear (\[Chi]1-\[Chi]2) )/.uneqfit2[[1,2]];
+uneqfit2[[1,15]] = ansatzFinal + ansatzchidifflinear (\[Chi]1-\[Chi]2);
+uneqfit2[[2,1]] = ( ansatzFinal + ansatzchidifflinear (\[Chi]1-\[Chi]2) + ansatzchidiffquadratic (\[Chi]1-\[Chi]2)^2 )/.uneqfit2[[2,2]];
+uneqfit2[[2,15]] = ansatzFinal + ansatzchidifflinear (\[Chi]1-\[Chi]2) + ansatzchidiffquadratic (\[Chi]1-\[Chi]2)^2;
+uneqfit2[[3,1]] = ( ansatzFinal + ansatzchidifflinear (\[Chi]1-\[Chi]2) + ansatzchidiffmix S (\[Chi]1-\[Chi]2) )/.uneqfit2[[3,2]];
+uneqfit2[[3,15]] = ansatzFinal + ansatzchidifflinear (\[Chi]1-\[Chi]2) + ansatzchidiffmix S (\[Chi]1-\[Chi]2);
+uneqfit2[[4,1]] = ( ansatzFinal + ansatzchidifflinear (\[Chi]1-\[Chi]2) + ansatzchidiffmix S (\[Chi]1-\[Chi]2) + ansatzchidiffquadratic (\[Chi]1-\[Chi]2)^2 )/.uneqfit2[[4,2]];
+uneqfit2[[4,15]] = ansatzFinal + ansatzchidifflinear (\[Chi]1-\[Chi]2) + ansatzchidiffmix S (\[Chi]1-\[Chi]2) + ansatzchidiffquadratic (\[Chi]1-\[Chi]2)^2;
+
+Print[Style["total fit (linear in spindiff) to all data:",Blue]];
+Print[uneqfit2[[1,1;;8]]];
+Print[Style["total fit (linear+ quadratic in spindiff) to all data:",Blue]];
+Print[uneqfit2[[2,1;;8]]];
+Print[Style["total fit (linear in spindiff + spineff*spindiff) to all data:",Blue]];
+Print[uneqfit2[[3,1;;8]]];
+Print[Style["total fit (linear+quadratic in spindiff + spineff*spindiff) to all data:",Blue]];
+Print[uneqfit2[[4,1;;8]]];
+
+Print[Style["----------------", Blue]];
+(* 2DeqS 2Dall 3Dlin 3Dlinquad 3Dlinmix 3Dlinquadmix 1D2Dparts 1Deta 1DS 2DSansatz *)
+Return[{eqdatafitv2, alldataeqfitv2, uneqfit2[[1;;1]], uneqfit2[[2;;2]], uneqfit2[[3;;3]], uneqfit2[[4;;4]], extraStuff, nsfits, q1fits, spinpart}];];
+]
+
+
+AnsatzRestrictions[q1fit_,ansatzGen_,var_,varval_,OptionsPattern[{"Parameters"->False}]]:=Module[{ansatz,nsdegree,q1degree,expans,coeffs1,coeffs2,q1var,coeff\[Eta],expns,coeffS,sys,
+coeffs,solveVars,solNS,ansatzS,solq1,ansatzFinal,parameters},
+
+parameters=OptionValue["Parameters"];
+
+ansatz=ansatzGen;
+q1var=Variables[q1fit][[1]];
+
+expans= Exponent[ansatz,q1var];
+expns = Exponent[q1fit, q1var];
+
+coeffs1= CoefficientList[Collect[ansatz,S],q1var];
+solveVars= CoefficientList[#,var]&/@ coeffs1;
+solveVars = Last/@\[NonBreakingSpace]Select[solveVars, Length@# > 0 &];
+
+solveVars =Select[AtomsList[solveVars],!NumberQ[#1]&];
+Print["solveVars: ", solveVars];
+
+Print["q1fit: ", q1fit];
+coeffs1=Select[CoefficientList[Collect[ansatz,S],q1var]/. var->varval,Not@NumberQ@#&];
+coeffs2 = Drop[CoefficientList[q1fit,q1var],1]; (* this won't always work *)
+
+(*
+Print["coeffs1: ", coeffs1];
+Print["coeffs2: ", coeffs2];
+*)
+sys=Table[coeffs1[[i]]==coeffs2[[i]],{i,Min[Length@coeffs1,Length@coeffs2]}];
+(*
+Print["sys: ",sys];
+*)
+
+coeffs=Drop[Select[AtomsList[ansatz/.var-> varval],!NumberQ[#1]&],-1];
+(*
+Print["coeffs:", coeffs[[1;;Min[expans+1,expns+1]]]];
+*)
+solq1=Simplify@First[Solve[sys,solveVars]];
+ansatzFinal=ansatz/. solq1;
+
+Print["Applying q=1 restriction : ",solq1 ];
+(*Print["Applying q=1 restriction : ",solq1//TableForm ];*)
+
+If[parameters,solq1,ansatzFinal]
+];
+
+
+AnsatzRestrictions[q1fit_,ansatzGen_,OptionsPattern[{"Parameters"->False}]]:=Module[{ansatz,nsdegree,q1degree,expans,coeffs1,coeffs2,q1var,coeff\[Eta],expns,coeffS,sys,coeffs,solveVars,
+solNS,ansatzS,solq1,ansatzFinal,parameters},
+
+parameters=OptionValue["Parameters"];
+
+ansatz=ansatzGen;
+q1var=Variables[q1fit][[1]];
+
+expans= Exponent[ansatz,q1var];
+expns = Exponent[q1fit, q1var];
+
+coeffs1= CoefficientList[Collect[ansatz,S],q1var];
+solveVars= CoefficientList[#,\[Eta]]&/@ coeffs1;
+solveVars = Last/@\[NonBreakingSpace]Select[solveVars, Length@# > 0 &];
+
+solveVars =Select[AtomsList[solveVars],!NumberQ[#1]&];
+Print["solveVars: ", solveVars];
+
+Print["q1fit: ", q1fit];
+
+coeffs1 = Select[CoefficientList[Collect[ansatz,S],q1var],Not@NumberQ@#&]/. \[Eta]->0.25;
+(* coeffs2 = Take[CoefficientList[q1fit,q1var],-Length@coeffs1] (* won't always work *); *)
+coeffs2 = Coefficient[q1fit,q1var^Sort@Select[Exponent[MonomialList[ansatz,q1var],q1var],#>0& ] ]; (* this should work more generally, unless maybe for non-exact S-independent constant coefficients...? *)
+Print["coeffs1: ", coeffs1];
+Print["coeffs2: ", coeffs2];
+
+sys=Table[coeffs1[[i]]==coeffs2[[i]],{i,Min[Length@coeffs1,Length@coeffs2]}];
+
+Print["sys: ",sys];
+
+
+coeffs=Drop[Select[AtomsList[ansatz/. \[Eta]->0.25],!NumberQ[#1]&],-1];
+(*
+Print["coeffs:", coeffs[[1;;Min[expans+1,expns+1]]]];
+*)
+solq1=Simplify@First[Solve[sys,solveVars]];
+ansatzFinal=ansatz/. solq1;
+
+Print["Applying q=1 restriction : ",solq1//TableForm ];
+
+If[parameters,solq1,ansatzFinal]
+];
+
+
+AnsatzRestrictions[nsfit_,q1fit_,ansatzGen_,OptionsPattern[{"Parameters"->False}]]:=Module[{ansatz,nsdegree,q1degree,expans,expns,nsvar,q1var,coeff\[Eta],coeffS,sys,coeffs,solNS,ansatzS,
+solq1,ansatzFinal,parameters},
+
+parameters=OptionValue["Parameters"];
+
+ansatz=ansatzGen;
+nsvar=Variables[nsfit][[1]];
+q1var=Variables[q1fit][[1]];
+
+Print["nsvar: ", nsvar];
+Print["q1var: ", q1var];
+
+expans= Exponent[ansatz,nsvar];
+expns = Exponent[nsfit, nsvar];
+
+Print["expans: ", expans];
+Print["expns: ", expns];
+
+sys=Table[CoefficientList[Collect[ansatz/. q1var->0,nsvar],nsvar][[i]]==CoefficientList[nsfit,nsvar][[i]],{i,Min[expans+1,expns+1]}];
+
+Print["sys: ",sys];
+
+If[Length@Select[sys,Not@TrueQ]==0,
+ ansatzS=ansatz,
+ Print[Style["Something is wrong with the restrictions",Red]]
+];
+
+Print["Applying non-spinning restriction : ", ansatz//TableForm ];
+
+expans= Exponent[ansatz,q1var];
+expns = Exponent[q1fit, q1var];
+
+Print["expans: ", expans];
+Print["expns: ", expns];
+
+
+sys=Table[CoefficientList[Collect[ansatzS/. nsvar->0.25,S],q1var][[i]]==CoefficientList[q1fit,q1var][[i]],{i,Min[expans+1,expns+1]}];
+
+Print["sys: ",sys];
+
+
+coeffs=Drop[Select[AtomsList[ansatzS/. nsvar->0.25],!NumberQ[#1]&],-1];
+
+
+Print["coeffs: ",coeffs];
+
+solq1=First[Solve[sys,coeffs[[1;;Min[expans+1,expns+1]]]]];
+ansatzFinal=ansatzS/. solq1;
+
+Print["Applying q=1 restriction : ",solq1//TableForm ];
+
+If[parameters,solq1,ansatzFinal]
+];
+
+
+Plot2DFits[data_?ListQ,fitlist_?ListQ,fitvars_?ListQ,OptionsPattern[{"PlotRange"->Automatic,"ShowLegend"->True,"zLabel"->"","ToolTipTags"->"","Outliers"->0.005}]]:=Module[{myfitlist,fitdata,myresidual,styles,plotrange,pos,myvar1,myvar2,
+myminvar1,mymaxvar2,mymaxvar1,myminvar2,myfitlistfunc,plot1,plot2,plot3,plottab,showlegend,zlabel,tooltiptags,myresidualhist,posoutliers,outliers,mylegend},
+
+plotrange=OptionValue["PlotRange"];
+showlegend=OptionValue["ShowLegend"];
+zlabel=OptionValue["zLabel"];
+tooltiptags=OptionValue["ToolTipTags"];
+outliers=OptionValue["Outliers"];
+
+myfitlist=Flatten[TakeColumn[#,1]&/@fitlist,1];
+
+myvar1=Evaluate@Symbol@ToString@fitvars[[1]];
+myvar2=Evaluate@Symbol@ToString@fitvars[[2]];
+
+If[ListQ@plotrange,
+myminvar1=plotrange[[1,1]];
+mymaxvar1=plotrange[[1,2]];
+myminvar2=plotrange[[2,1]];
+mymaxvar2=plotrange[[2,2]];
+,
+myminvar1=Min[data[[All,1]]];
+mymaxvar1=Max[data[[All,1]]];
+myminvar2=Min[data[[All,2]]];
+mymaxvar2=Max[data[[All,2]]];
+];
+
+myfitlist=(#/.myvar1->x/.myvar2->y)&/@myfitlist;
+
+Print[Length[data]," data points, variables plotted -> ",{myvar1, myvar2}];
+If[showlegend,
+
+mylegend=(myfitlist/.x->myvar1/.y->myvar2);
+Print[plot1=Show[{Plot3D[myfitlist,{x,myminvar1,mymaxvar1},{y,myminvar2,mymaxvar2},PlotStyle->Drop[ColorData[3,"ColorList"],1],PlotLabel->Style[ToString[zlabel],14,Black],PlotLegends->mylegend,Lighting->Automatic,PlotRange->plotrange,
+AxesLabel->{Style[ToString@myvar1,14,Black],Style[ToString@myvar2,14,Black],""}],ListPointPlot3D[data,PlotStyle->PointSize[0.025]]}]],
+Print[plot1=Show[{Plot3D[myfitlist,{x,myminvar1,mymaxvar1},{y,myminvar2,mymaxvar2},PlotStyle->Drop[ColorData[3,"ColorList"],1],PlotLabel->Style[ToString[zlabel],14,Black],Lighting->Automatic,PlotRange->plotrange,
+AxesLabel->{Style[ToString@myvar1,14,Black],Style[ToString@myvar2,14,Black],""}],ListPointPlot3D[data,PlotStyle->PointSize[0.025]]}]]
+];
+
+plottab=Table[
+Print[myfitlist[[j]]/.x->myvar1/.y->myvar2];
+
+fitdata=Transpose[{data[[All,1]],data[[All,2]],Table[myfitlist[[j]]/.x->data[[i,1]]/.y->data[[i,2]],{i,Length@data}]}];
+myresidual=Transpose[{data[[All,1]],data[[All,2]],fitdata[[All,3]]-data[[All,3]]}];
+myresidualhist=myresidual[[All,3]]/fitdata[[All,3]];
+
+
+Print[{plot2=Show[ListPointPlot3D[data,PlotStyle->PointSize[0.025],PlotRange->All],
+ Plot3D[myfitlist[[j]],{x,myminvar1,mymaxvar1},{y,myminvar2,mymaxvar2},PlotLabel->Style[ToString[zlabel],14,Black],
+ AxesLabel->{Style[ToString@myvar1,14,Black],Style[ToString@myvar2,14,Black],""},ImageSize->350,
+ PlotStyle->Drop[ColorData[3,"ColorList"],1][[j]],Lighting->Automatic,PlotRange->plotrange],AxesLabel->{Style[ToString@myvar1,14,Black],
+ Style[ToString@myvar2,14,Black],""}],
+ plot3=myListPlot3D[myresidual,PlotLabel->Style[ToString["residual"],14,Black],PlotRange->plotrange,ImageSize->350,AxesLabel->{Style[ToString@myvar1,14,Black],
+ Style[ToString@myvar2,14,Black],""},PlotStyle->Drop[ColorData[3,"ColorList"],1][[j]]],
+ If[Length@fitlist[[j,1]]==1,"No stats. available",fitlist[[j,1,3]]],Show[Histogram[myresidualhist,100],Frame->True,FrameLabel -> {"1-data/fit", "#"}],
+ ListPlot[Table[Tooltip[myresidualhist[[i]],If[ListQ@tooltiptags,tooltiptags[[i]],ToString[{data[[i,1]],data[[i,2]]}]]],{i,Length@myresidualhist}],PlotRange->All,Frame->True,FrameLabel -> {"#","1-data/fit"}],
+ Sqrt@Mean[myresidual[[All,3]]^2],
+ Select[(Reverse@SortBy[Transpose[{Abs@myresidualhist,If[ListQ@tooltiptags,tooltiptags,data[[All,1;;2]]]}],First]),#[[1]]>outliers&][[All,2]]//TableForm
+ }];
+
+{plot2,plot3}
+
+,{j,Length@myfitlist}];
+Return[{plot1,plottab}]
+]
+
+
+(* ::Code::Initialization:: *)
+End[];
+EndPackage[];
diff --git a/code/GRTensor.m b/code/GRTensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..44c78cc0d76a36adc28fdd5aa946ab392c3e0c7f
--- /dev/null
+++ b/code/GRTensor.m
@@ -0,0 +1,1334 @@
+(* ::Package:: *)
+
+(************************************************************************)
+(* This file was generated automatically by the Mathematica front end. *)
+(* It contains Initialization cells from a Notebook file, which *)
+(* typically will have the same name as this file except ending in *)
+(* ".nb" instead of ".m". *)
+(* *)
+(* This file is intended to be loaded into the Mathematica kernel using *)
+(* the package loading commands Get or Needs. Doing so is equivalent *)
+(* to using the Evaluate Initialization Cells menu command in the front *)
+(* end. *)
+(* *)
+(* DO NOT EDIT THIS FILE. This entire file is regenerated *)
+(* automatically each time the parent Notebook file is saved in the *)
+(* Mathematica front end. Any changes you make to this file will be *)
+(* overwritten. *)
+(************************************************************************)
+
+
+
+
+(* Probably not all the extra packages are really needed *)
+BeginPackage["GRTensor`"];
+
+
+MetDet::usage="MetDet[g_]. Compute the determinant of the metric";
+InverseMetric::usage="InverseMetric[g_]. Compute the inverse of the metric";
+
+
+ChristoffelSymbol::usage="ChristoffelSymbol[coords_,g_,pert_:0]. Compute Christoffel symbols. Default for perturbation variabel pert is 0.";
+WeylTensor::usage="WeylTensor[coords_,g_,pert_:0]. Compute Weyl tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1. Default for perturbation variabel pert is 0. ";
+RiemannTensor::usage="RiemannTensor[coords_,g_,pert_:0]. Compute Riemann tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 .Default for perturbation variabel pert is 0. ";
+RicciTensor::usage="RicciTensor[coords_,g_,pert_:0]. Compute Riemann tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1. Default for perturbation variabel pert is 0. ";
+RicciScalar::usage="RicciScalar[coords_,g_,pert_:0]. Compute RicciScalar scalar. Default for perturbation variabel pert is 0. ";
+KrScalar::usage="KrScalar[coords_,g_]. Compute Kretschmann scalar";
+WeylTrace::usage"WeylTrace[coords_,g_]: Compute Weyl Tensor trace";
+Einstein::usage="Einstein[coords_,g_,\[Epsilon]p:]. Compute Einstein tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 with perturbation index \[Epsilon]p";
+ETensor::usage="ETensor[coords_,g_,\[Epsilon]p_]. Compute the energy momentum tensor with perturbation index \[Epsilon]p.";
+
+
+DAlembert::usage="DAlembert[coords_,g_,func_]. Compute D'Alembert operator for func[coords]";
+CovDer::usage="CovDer[coords_,metric_,tensor_,comps_]. Compute the covariant derivative (default covariant version) for scalar and 1-2 forms. The components are given in a list as: {a},{a,b},{a,b,c}";
+NonZeroChristoffel::usage="NonZeroChristoffel[\[CapitalGamma]]. Show the nonzero Christoffel components.";
+NonZeroMetricComp::usage="NonZeroMetricComp[g]. Show the nonzero metric components.";
+NonZeroTensorComp::usage="NonZeroTensorComp[T]. Show the nonzero Tensor components. It works with any symmetric m xmxmxmx... tensor";
+LeviCivitaTensorCurv::usage="LeviCivitaTensorCurv[coords_,g_]. Compute the Levi-Civita antisymmetric tensor for curvilinear coordinates. For cartesian xx recovers the usual \[Epsilon]_(abc).";
+CheckTetrad::usage="[gab_,nullv_]. Check whether the 4 null tetrad vectors satisfy orthonormality conditions.";
+
+
+EinsteinfR::usage="EinsteinfR[coords_,g_,fR_]. Compute fR Einstein equations following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 ";
+EinsteinST::usage="EinsteinST[coords_,g_,v\[Phi]_]. Compute scalar-tensor Einstein equations following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 ";
+STensorT\[Psi]::usage="STensorT\[Psi][coords_,g_,v\[Phi]_]. Compute scalar-tensor Energy momentum tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 ";
+TeffFR::usage="TeffFR[coords_,g_,fR_]. Compute fR Teff tensor such Gab=8\[Pi]/f'[R](Tab + Teff) following the convention of Misner et al., that is, [S2] = 1, [S3] = 1";
+TeffST::usage="TeffST[coords_,g_,{V\[CurlyPhi],\[CurlyPhi]}]. Compute ST-EF/JF Teff tensor such Gab=8\[Pi] (Tab + Teff) following the convention of Misner et al., that is, [S2] = 1, [S3] = 1. Allowed options for the Frame are Einstein, Jordan";
+FRTOV::usage="FRTOV[coords_,g_,fR_,vars_]. Compute fR TOV eqs such Gab=8\[Pi]/f'[R](Tab + Teff) following the convention of Misner et al., that is, [S2] = 1, [S3] = 1";
+STTOV::usage="STTOV[coords_,g_,{V\[CurlyPhi]_,var\[CurlyPhi]_},vars_]. Compute ST-EF/JF TOV eqs such Gab=8\[Pi](Tab + Teff) following the convention of Misner et al., that is, [S2] = 1, [S3] = 1";
+fR2Pot::usage="fR2UJF[fR_]. From fR model to the ST potential U(\[Phi])-V(\[Phi])";
+CurlCurvilinear::usage"CurlCurvilinear[xx,g,vec]. It computes the curl tensor in curvilinear coordinates";
+ElectricTensor3p1Dev::usage="ElectricTensor3p1Dev[xx_,g_,Kt_,pert_:0,OptionsPattern[]]";
+MagneticTensor3p1Dev::usage="MagneticTensor3p1Dev[xx_,g_,Kt_,pert_:0,OptionsPattern[]]"
+
+
+EoSCallParsBSks::usage="EoSCallParsBSks[model_]: Parameters for BSK1-3 EOS for the matter density.";
+EoSCallParsSly::usage="EoSCallParsSly[model_]: Parameters for SLy1 EOS for the matter density.";
+EoSBSks::usage="EoSBSks[model_]: Analytic EOS for BSK1-3for BSK1-3 EOS for the matter density.";
+EoSSly::usage="EoSSly[model_]: Analytic EOS for SLy1 EOS for the matter density.";
+SlyInner::usage="";
+SlyLCore::usage="";
+SlyLCoreAll::usage="";
+SlyInnerAll::usage="";
+EoSFitsPars::usage="EoSFitsPars[model_,verbose_:False]. Parameters for the JRead(arxiv:0812.2163) parameters.";
+EoSSlyCrust::usage="EoSSlyCrust[\[Rho]_]. Crust model for the NS of JRead(arxiv:0812.2163)";
+EoSFits::usage="EoSFits[model_,OptionsPattern[]]. NS EOS of JRead(arxiv:0812.2163)";
+EoSPol::usage="EoSPol[model_]. NS EOS for a non-relativistic (NR) and relativistic (R, default) NS respectively";
+EoSPol\[Epsilon]::usage="EoSPol\[Epsilon][model_]. NS EOS for a non-relativistic (NR) and relativistic (R, default) NS respectively";
+From\[Rho]To\[Epsilon]Fits::usage"From\[Rho]To\[Epsilon]Fits[eos_]. NS EOS of JRead(arxiv:0812.2163) for the energy density.";
+
+
+ShootingNStars::usage="ShootingNStars[eqs_,eqsRg_,rvar_,vars_,shtdInd_,varshtdRg_]. Shooting function of the index var shtdInd for a set of eqs integrated in eqsRg on the variables vars ;";
+BracketingSTNStars::usage="BracketingSTNStars[eqs_,eqsRg_,rvar_,vars_,shtdInd_,varshtdRg_]. Shooting function of the index var shtdInd for a set of eqs integrated in eqsRg on the variables vars ;";
+
+
+RK4::usage="RK4[func_?ListQ,vars_?ListQ,ivals_?ListQ,pars_?ListQ,step_]";
+TestCode::usage"TestCode[eqs_,vars_,icond_,rlst_,drlst_]";
+
+
+AtomsList::usage="Take the coefficients out";
+InterpolationDomain::usage="InterpolationDomain[interpolatedfunction]. It outputs the domain in a format {tmin,tmax}";
+TakeColumn::usage="TakeColumn[list1_,list2_] extracts columns list2 from list1, i.e. it gives the functionality of the pre-Mathematica 6 Column function.";
+
+
+(* All here below are dev. versions. Replace them when they are sufficiently tested. *)
+ChristoffelSymbolDev::usage="ChristoffelSymbolDev[coords_,g_,pert_:0]. Compute Christoffel symbols. Default for perturbation variabel pert is 0."
+RiemannTensorDev::usage="RiemannTensor[coords_,g_,pert_:0]. Compute Riemann tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 .Default for perturbation variabel pert is 0. "
+RicciTensorDev::usage="RicciTensorDev[coords_,g_,pert_:0]. Compute Riemann tensor following the convention of Misner et al., that is, [S2] = 1, [S3] = 1 .Default for perturbation variabel pert is 0. ";
+
+
+Begin["`Private`"];
+
+
+Options[MetDet]={"PerturbationIndex"->1,"SimplifyFunction"->Identity};
+MetDet[g_,OptionsPattern[]]:=Block[{simpl},simpl=OptionValue["SimplifyFunction"]; simpl@Det[g]];
+
+Options[InverseMetric]={"PerturbationIndex"->1,"SimplifyFunction"->Identity};
+InverseMetric[g_,OptionsPattern[]]:=Block[{simpl},simpl=OptionValue["SimplifyFunction"]; simpl@Inverse[g]]
+
+
+Options[ChristoffelSymbol]={"Verbose"->False,"PerturbationIndex"->1,"SimplifyFunction"->Identity};
+ChristoffelSymbol[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{n,ig,res,perti,simpl,verbose},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+verbose=OptionValue["Verbose"];
+
+n=Length@xx;
+ig=InverseMetric[g];
+res=Table[(1/2)*If[NumericQ[pert],Sum[ig[[i,s]]*(-D[g[[j,k]],xx[[s]]]+D[g[[j,s]],xx[[k]]]+D[g[[s,k]],xx[[j]]]),{s,1,n}],
+ Normal@Series[Sum[ig[[i,s]]*(-D[g[[j,k]],xx[[s]]]+D[g[[j,s]],xx[[k]]]+D[g[[s,k]],xx[[j]]]),{s,1,n}],{pert,0,perti}]],{i,1,n},{j,1,n},{k,1,n}];
+simpl@res]
+
+Options[RiemannTensor]=Options[ChristoffelSymbol];
+RiemannTensor[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{n,Chr,res,perti,simpl,verbose},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+verbose=OptionValue["Verbose"];
+
+n=Length@xx;
+If[verbose,Print["Starting with Christoffel symbols..."]];
+Chr=ChristoffelSymbol[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+If[verbose,Print["Christoffel symbols computed. Starting with Riemann..."]];
+res=Table[If[NumericQ[pert],D[Chr[[i,k,m]],xx[[l]]]-D[Chr[[i,k,l]],xx[[m]]]+Sum[Chr[[i,s,l]]*Chr[[s,k,m]],{s,1,n}]-Sum[Chr[[i,s,m]]*Chr[[s,k,l]],{s,1,n}],
+ Normal@Series[D[Chr[[i,k,m]],xx[[l]]]-D[Chr[[i,k,l]],xx[[m]]]+Sum[Chr[[i,s,l]]*Chr[[s,k,m]],{s,1,n}]-Sum[Chr[[i,s,m]]*Chr[[s,k,l]],{s,1,n}],{pert,0,perti}]],{i,1,n},{k,1,n},{l,1,n},{m,1,n}];
+If[verbose,Print["...Riemann computed"]];
+simpl@res];
+
+Options[WeylTensor]=Options[ChristoffelSymbol];
+WeylTensor[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{n,Chr,riemann,riemanndown,ricciS,ricciT,res,perti,simpl,verbose},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+verbose=OptionValue["Verbose"];
+n=Length@xx;
+
+If[verbose,Print["Starting with RicciScalar..."]];
+ricciS=RicciScalar[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+If[verbose,Print["Following with RicciTensor..."]];
+ricciT=RicciTensor[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+If[verbose,Print["Following with Riemann..."]];
+riemann=RiemannTensor[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+riemanndown=Table[Sum[g[[a,\[Alpha]]]riemann[[\[Alpha],b,c,d]],{\[Alpha],4}],{a,n},{b,n},{c,n},{d,n}];
+
+res=Table[If[NumericQ[pert],riemanndown[[i,k,l,m]]+1/(n-2)(ricciT[[i,m]]g[[k,l]]-ricciT[[i,l]]g[[k,m]]+ricciT[[k,l]]g[[i,m]]-ricciT[[k,m]]g[[i,l]])+1/((n-1)(n-2))ricciS(g[[i,l]]g[[k,m]]-g[[i,m]]g[[k,l]]),
+ Normal@Series[riemanndown[[i,k,l,m]]+1/(n-2)(ricciT[[i,m]]g[[k,l]]-ricciT[[i,l]]g[[k,m]]+ricciT[[k,l]]g[[i,m]]-ricciT[[k,m]]g[[i,l]])+1/((n-1)(n-2))ricciS(g[[i,l]]g[[k,m]]-g[[i,m]]g[[k,l]]),{pert,0,perti}]],{i,1,n},{k,1,n},{l,1,n},{m,1,n}];
+(*Simplify[res]*)
+simpl@res];
+
+
+Options[RicciTensor]=Options[ChristoffelSymbol];
+RicciTensor[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{Rie,res,n,perti,simpl},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+
+n=Length@xx;
+Rie=RiemannTensor[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+res=Table[If[NumericQ[pert],Sum[Rie[[s,i,s,j]],{s,1,n}],
+ Normal@Series[Sum[Rie[[s,i,s,j]],{s,1,n}],{pert,0,perti}]],{i,1,n},{j,1,n}];
+(*Simplify[res]*)
+simpl@res]
+
+Options[RicciScalar]=Options[ChristoffelSymbol];
+RicciScalar[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{Ricc,ig,res,n,perti,simpl},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+n=Length@xx;
+
+Ricc=RicciTensor[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+ig=InverseMetric[g,"SimplifyFunction"->simpl];
+res=If[NumericQ[pert],Sum[ig[[s,i]] Ricc[[s,i]],{s,1,n},{i,1,n}],
+ Normal@Series[Sum[ig[[s,i]] Ricc[[s,i]],{s,1,n},{i,1,n}],{pert,0,perti}]];
+simpl@res]
+
+Options[KrScalar]=Options[ChristoffelSymbol];
+KrScalar[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{Rie,res,n,Ried,Rieup,gup,perti,simpl},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+n=Length@xx;
+
+Rie=RiemannTensor[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+gup=Inverse@g;
+Ried=Table[Sum[g[[i,k]] Rie[[i,j,m,l]],{i,1,n}],{k,1,n},{j,1,n},{m,1,n},{l,1,n}];
+Rieup=Table[Sum[gup[[j,k]]gup[[m,\[Mu]]] gup[[l,\[Nu]]] Rie[[i,j,m,l]],{j,1,n},{m,1,n},{l,1,n}],{i,1,n},{k,1,n},{\[Mu],1,n},{\[Nu],1,n}];
+res=Sum[Ried[[i,j,m,l]] Rieup[[i,j,m,l]],{i,1,n},{j,1,n},{m,1,n},{l,1,n}];
+
+If[NumericQ[pert],simpl@res,Normal@Series[simpl@res,{pert,0,perti}]]];
+
+Options[WeylTrace]=Options[ChristoffelSymbol];
+WeylTrace[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{Chr,ig,n,riemann,Rieup,ricciS,ricciT,res,perti,simpl,weylT,weylTup},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+n=Length@xx;
+ig=InverseMetric[g,"SimplifyFunction"->simpl];
+
+weylT=WeylTensor[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+weylTup=Table[Sum[ig[[a,\[Alpha]]] ig[[b,\[Beta]]] ig[[c,\[Gamma]]] ig[[d,\[Delta]]] weylT[[\[Alpha],\[Beta],\[Gamma],\[Delta]]],{\[Alpha],n},{\[Beta],n},{\[Gamma],n},{\[Delta],n}],{a,n},{b,n},{c,n},{d,n}];
+res=If[NumericQ[pert],Sum[weylT[[i,k,l,m]]weylTup[[i,k,l,m]],{i,n},{k,n},{l,n},{m,n}],
+ Normal@Series[Sum[weylT[[i,k,l,m]]weylTup[[i,k,l,m]],{i,n},{k,n},{l,n},{m,n}],{pert,0,perti}]];
+
+simpl@res];
+
+Options[Einstein]=Options[ChristoffelSymbol];
+Einstein[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{res,perti,simpl},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+res=RicciTensor[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl]-1/2 RicciScalar[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl] g;
+If[NumericQ[pert],simpl@res,Normal@Series[simpl@res,{pert,0,perti}]]
+]
+
+
+DAlembert[xx_,metric_,scalfun_]:=Block[{metdet,dal,metup,sqrtdet},
+
+metup=Inverse[metric];
+metdet=MetDet[metric];
+sqrtdet=Sqrt[-metdet];
+
+dal=FullSimplify[(1/sqrtdet) Sum[
+D[sqrtdet metup[[\[Nu],\[Mu]]] D[scalfun,xx[[\[Mu]]]],xx[[\[Nu]]]],{\[Nu],4},{\[Mu],4}]]
+]
+
+
+Options[ETensor]=Join[{"Signature"->1},Options[ChristoffelSymbol]];
+
+ETensor[coors_,met_,pert_:0,OptionsPattern[]]:=Block[{g,gup,Global`\[Rho],\[Rho]c,Global`p,perti,pc,riscal,riscalvars,sign,simpl,T\[Mu]\[Nu],T\[Mu]\[Nu]up,u,udown,\[CapitalOmega]},
+perti=OptionValue["PerturbationIndex"];
+sign=OptionValue["Signature"];
+simpl=OptionValue["SimplifyFunction"];
+
+g=met;
+riscal=RicciScalar[coors,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+riscalvars=Complement[coors,Complement[coors,AtomsList[riscal]]];
+gup=Inverse[g];
+pc=Global`p@@riscalvars;
+\[Rho]c=Global`\[Rho]@@riscalvars;
+
+u=If[sign==1,{1/Sqrt[-g[[1,1]]],0,0,pert \[CapitalOmega]/Sqrt[-g[[1,1]]]},{1/Sqrt[g[[1,1]]],0,0,pert \[CapitalOmega]/Sqrt[g[[1,1]]]}];
+u=Normal@Series[u,{pert,0,perti}];
+udown=Table[Sum[u[[i]]g[[i,l]],{i,Length@coors}],{l,Length@coors}];
+udown=Normal@Series[udown,{pert,0,perti}];
+
+If[Simplify[Normal@Series[u.udown,{pert,0,1}]]!=-1,Return["Wrong normalization"]];
+
+T\[Mu]\[Nu]up=If[sign==1,Normal@Series[Table[(pc+\[Rho]c) u[[i]] u[[j]]+pc gup[[i,j]],{i,Length@coors},{j,Length@coors}],{pert,0,perti}],
+ Normal@Series[Table[(pc+\[Rho]c) u[[i]] u[[j]]-pc gup[[i,j]],{i,Length@coors},{j,Length@coors}],{pert,0,perti}]]//Simplify;
+T\[Mu]\[Nu]=Normal@Series[g(T\[Mu]\[Nu]up.g),{pert,0,1}]
+]
+
+
+Options[NonZeroTensorComp]={"Verbose"->True,"TensorString"->"T"};
+NonZeroTensorComp[gamma_,OptionsPattern[]]:=Module[{dimension,ii,nonzerpos,tstring,verbose,
+allpos,zerpos},
+
+tstring=OptionValue["TensorString"];
+verbose=OptionValue["Verbose"];
+
+(* set dimensions and total number or elements *)
+dimension=Dimensions[gamma];
+(*allpos=Flatten[Table[{i,j,k},{i,dimension[[1]]},{j,dimension[[1]]},{k,dimension[[1]]}],1];*)
+allpos=Tuples[Table[i,{i,dimension[[1]]}],Length@dimension];
+
+zerpos=Position[gamma,_?(#== 0 &)];
+nonzerpos=Complement[allpos,zerpos];
+
+If[verbose,Do[Print[ToString[Subscript[tstring, StringJoin[ToString/@(nonzerpos[[i,1;;Length@dimension]]-1)]],StandardForm]<>" = "<>ToString[Extract[gamma,nonzerpos[[i]]],StandardForm]],{i,Length@nonzerpos}]];
+nonzerpos
+]
+
+
+Options[NonZeroMetricComp]={"Verbose"->True,"TensorString"->"T"};
+NonZeroMetricComp[gamma_,OptionsPattern[]]:=Module[{allpos,dimension,
+n,nonzerpos,tstring,verbose,zerpos},
+
+verbose=OptionValue["Verbose"];
+tstring=OptionValue["TensorString"];
+
+n=Length@gamma;
+
+(* set dimensions and total number or elements *)
+dimension=Dimensions[gamma][[1]];
+allpos=Flatten[Table[{i,j},{i,dimension},{j,dimension}],1];
+
+zerpos=Position[gamma,_?(#== 0 &)];
+nonzerpos=Complement[allpos,zerpos];
+
+If[verbose,Do[Print[ToString[tstring,StandardForm]<>" = "<>ToString[gamma[[nonzerpos[[i,1]],nonzerpos[[i,2]]]],StandardForm]],{i,Length@nonzerpos}]];
+nonzerpos
+]
+
+
+CovDer[coords_,metric_,tensor_,index_,OptionsPattern[{"Valence"->"Covariant","Verbose"->False}]]:=Block[{Crhistoffel,g,xx,n,h\[Eta]\[Nu],rank,cov,valence,verbose,c,b,a},
+(*Print[Style["It is wrong!",Red]];*)
+valence=OptionValue["Valence"];
+verbose=OptionValue["Verbose"];
+n=Length@coords;
+g=metric;
+h\[Eta]\[Nu]=tensor;
+xx=coords;
+If[ListQ[h\[Eta]\[Nu]],
+ rank=Length@Dimensions@tensor;
+ Crhistoffel=ChristoffelSymbol[xx,g],
+ rank=0;
+ ];
+
+Which[rank==0, If[verbose,Print["Scalar , "];Print[valence];];
+ {a}=index;
+ cov=D[h\[Eta]\[Nu],xx[[index]]]; ,
+ rank==1, If[verbose,Print["Vector , "];Print[valence];];
+ {a,b}=index;
+ Which[valence=="Covariant",
+ cov=D[h\[Eta]\[Nu][[b]],xx[[a]]]-Sum[Crhistoffel[[\[Rho],a,b]]h\[Eta]\[Nu][[\[Rho]]],{\[Rho],Length@xx}];,
+ valence=="Contravariant",
+ cov=D[h\[Eta]\[Nu][[b]],xx[[a]]]+Sum[Crhistoffel[[\[Rho],a,b]]h\[Eta]\[Nu][[\[Rho]]],{\[Rho],Length@xx}];
+ ];,
+ rank==2, If[verbose,Print["Tensor , "];Print[valence];];
+ {a,b,c}=index;
+ Which[valence=="Covariant",
+ cov=D[h\[Eta]\[Nu][[b,c]],xx[[a]]]-Sum[Crhistoffel[[d,a,b]]h\[Eta]\[Nu][[c,d]]+Crhistoffel[[d,a,c]]h\[Eta]\[Nu][[b,d]],{d,n}];,
+ valence=="Contravariant",
+ cov=D[h\[Eta]\[Nu][[b,c]],xx[[a]]]+Sum[Crhistoffel[[b,a,d]]h\[Eta]\[Nu][[c,d]]+Crhistoffel[[c,a,d]]h\[Eta]\[Nu][[d,b]],{d,n}];,
+ valence=="Mixed",
+ cov=D[h\[Eta]\[Nu][[b,c]],xx[[a]]]+Sum[Crhistoffel[[b,a,d]]h\[Eta]\[Nu][[c,d]]-Crhistoffel[[c,a,d]]h\[Eta]\[Nu][[d,b]],{d,n}];];,
+ True, If[verbose,Print["Rank not recognised"]];
+ Return[];
+];
+Simplify@cov
+]
+
+
+LeviCivitaTensorCurv[xx_,g_]:=Module[{dim},
+dim=Length@xx;
+Sqrt[Det[g]]LeviCivitaTensor[dim,List]
+]
+
+
+CurlCurvilinear[xx_,g_,vec_]:=Module[{lv,vecb,DCov,lvup,gup,vecn},
+lv=LeviCivitaTensorCurv[xx,g];
+vecb=Sqrt[Diagonal[g]];
+vecn=vec*vecb;
+DCov=Table[CovDer[xx,g,vecn,{a,b}],{a,Length@xx},{b,Length@xx}];
+gup=InverseMetric[g];
+lvup=Simplify[Table[Sum[gup[[i,a]]gup[[j,b]] gup[[k,c]] lv[[a,b,c]],{a,Length@xx},{b,Length@xx},{c,Length@xx}],{i,Length@xx},{j,Length@xx},{k,Length@xx}]];
+
+Table[Simplify[Sum[lvup[[i,e,d]]DCov[[e,d]],{e,Length@xx},{d,Length@xx}]]vecb[[i]],{i,Length@xx}]
+]
+
+
+Options[CheckTetrad]=Options[ChristoffelSymbol];
+CheckTetrad[gab_,nullv_,OptionsPattern[]]:=Block[{l,n,m,mb,test,verbose},
+{l,n,m,mb}=nullv;
+verbose=OptionValue["Verbose"];
+
+test=Chop@Simplify@{l.gab.l,
+n.gab.n,
+m.gab.m,
+mb.gab.mb,
+l.gab.m,
+l.gab.mb,
+n.gab.m,
+n.gab.mb,
+l.gab.n,
+m.gab.mb};
+
+If[verbose,Print["{l.l,n.n,m.m,mb.mb,l.m,l.mb,n.m,n.mb,l.n,m.mb} = ",test]];
+
+If[Total@test[[1;;8]]==0&&test[[9]]*test[[10]]==-1,Print[Style["Your tetrad satisfies the properties of orthonormality",Blue]];,Print[Style["Your tetrad has some troubles",Blue]]]];
+
+
+Options[ChristoffelSymbolDev]={"Verbose"->False,"PerturbationIndex"->1,"SimplifyFunction"->Identity,"Compile"->False,"CompileCoordinateIndex"->{1,2,3,4}};
+ChristoffelSymbolDev[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{n,ig,compile,compilecind,coords,res,perti,simpl,verbose},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+verbose=OptionValue["Verbose"];
+compile=OptionValue["Compile"];
+compilecind=OptionValue["CompileCoordinateIndex"];
+
+
+n=Length@xx;
+ig=InverseMetric[g];
+res=ConstantArray[0,{n,n,n}];
+If[NumericQ[pert], Do[res[[i,j,k]]=Sum[ig[[i,s]]*(-D[g[[j,k]],xx[[s]]]+D[g[[j,s]],xx[[k]]]+D[g[[s,k]],xx[[j]]]),{s,n}],{i,n},{j,n},{k,j,n}];,
+ Do[res[[i,j,n]]=Normal@Series[Sum[ig[[i,s]]*(-D[g[[j,k]],xx[[s]]]+D[g[[j,s]],xx[[k]]]+D[g[[s,k]],xx[[j]]]),{s,n}],{pert,0,perti}],{i,n},{j,n},{k,j,n}]];
+res=simpl[1/2 res];
+
+(* Compile *)
+If[compile, Do[res[[i,j,k]]=If[NumberQ[res[[i,j,k]]],res[[i,j,k]],Compile[Evaluate@({#,_Real}&/@(xx[[compilecind]])),Evaluate[res[[i,j,k]]],CompilationTarget->"C",CompilationOptions->"InlineExternalDefinitions"->True]],{i,n},{j,n},{k,j,n}];];
+(* Applying symmetries *)
+Do[res[[i,j+1,k]]=res[[i,k,j+1]];,{i,n},{j,n-1},{k,j}];
+
+res
+]
+
+
+Options[RiemannTensorDev]=Join[Options[ChristoffelSymbolDev],{"IndexDown"->False}];
+RiemannTensorDev[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{caux,n,Chr,compile,compilecind,index,res,perti,simpl,time,verbose},
+index=OptionValue["IndexDown"];
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+compile=OptionValue["Compile"];
+compilecind=OptionValue["CompileCoordinateIndex"];
+verbose=OptionValue["Verbose"];
+
+n=Length@xx;
+If[verbose,Print["Starting with Christoffel symbols..."]];
+Chr=ChristoffelSymbolDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl,"Compile"->False];
+If[verbose,Print["Christoffel symbols computed. Starting with Riemann..."]];
+
+res=ConstantArray[0,{n,n,n,n}];
+If[index,
+ If[NumericQ[pert], Do[res[[i,k,l,m]]=Sum[g[[i,p]](D[Chr[[p,k,m]],xx[[l]]]-D[Chr[[p,k,l]],xx[[m]]]+Sum[Chr[[p,s,l]]*Chr[[s,k,m]]-Chr[[p,s,m]]*Chr[[s,k,l]],{s,n}]),{p,n}],{i,n},{k,i,n},{l,n},{m,l,n}],
+ Do[res[[i,k,l,m]]=Sum[g[[i,p]](Normal@Series[D[Chr[[p,k,m]],xx[[l]]]-D[Chr[[p,k,l]],xx[[m]]]+Sum[Chr[[p,s,l]]*Chr[[s,k,m]],{s,n}]-Sum[Chr[[p,s,m]]*Chr[[s,k,l]],{s,n}],{pert,0,perti}]),{p,n}],{i,n},{k,n},{l,n},{m,n}]];
+
+ (* Applying simmetries *)
+ (*Do[res[[i+1,k,l,m]]=res[[l,k,i+1,m]],{i,n-1},{k,n},{l,i},{m,n}];*)
+ Do[res[[i,k,l+1,m]]=-res[[i,k,m,l+1]],{i,n},{k,n},{l,n-1},{m,l}];
+ Do[res[[i+1,k,l,m]]=-res[[k,i+1,l,m]],{i,n-1},{k,i},{l,n},{m,n}];
+ If[compile,caux=0; Do[time=Timing[res[[i,k,l,m]]=Compile[Evaluate@({#,_Real}&/@(xx[[compilecind]])),Evaluate[res[[i,k,l,m]]],RuntimeOptions->"Speed"]][[1]];If[verbose,Print["compiling: ",{i,k,l,m}," ",time," s"]];,{i,n},{k,n},{l,n},{m,n}];]
+ ,
+ If[NumericQ[pert], Do[res[[i,k,l,m]]=(D[Chr[[i,k,m]],xx[[l]]]-D[Chr[[i,k,l]],xx[[m]]]+Sum[Chr[[i,s,l]]*Chr[[s,k,m]]-Chr[[i,s,m]]*Chr[[s,k,l]],{s,n}]),{i,n},{k,n},{l,n},{m,n}],
+ Do[res[[i,k,l,m]]=(Normal@Series[D[Chr[[i,k,m]],xx[[l]]]-D[Chr[[i,k,l]],xx[[m]]]+Sum[Chr[[i,s,l]]*Chr[[s,k,m]],{s,n}]-Sum[Chr[[i,s,m]]*Chr[[s,k,l]],{s,n}],{pert,0,perti}]),{i,n},{k,n},{l,n},{m,n}]];
+ ];
+
+
+If[verbose,Print["...Riemann computed"]];
+simpl@res];
+
+
+Options[RicciTensorDev]=Options[ChristoffelSymbolDev];
+RicciTensorDev[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{compile,Rie,res,n,perti,simpl},
+perti=OptionValue["PerturbationIndex"];
+compile=OptionValue["Compile"];
+simpl=OptionValue["SimplifyFunction"];
+
+n=Length@xx;
+Rie=RiemannTensorDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+
+res=ConstantArray[0,{n,n}];
+If[NumericQ[pert], Do[res[[i,j]]=Sum[Rie[[s,i,s,j]],{s,n}],{i,n},{j,n}],
+ Do[res[[i,j]]=Normal@Series[Sum[Rie[[s,i,s,j]],{s,n}],{pert,0,perti}],{i,n},{j,i,n}]];
+
+If[compile, Do[res[[i,j]]=If[NumberQ[res[[i,j]]],res[[i,j]],Compile[Evaluate@({#,_Real}&/@xx),Evaluate[res[[i,j]]],CompilationTarget->"C",CompilationOptions->"InlineExternalDefinitions"->True]],{i,n},{j,i,n}];] ;
+(* Applying symmetries *)
+Do[res[[i+1,j]]=res[[j,i+1]];,{i,n-1},{j,i}];
+
+simpl@res]
+
+
+Options[ElectricTensor3p1Dev]=Options[ChristoffelSymbolDev];
+ElectricTensor3p1Dev[xx_,g_,Kt_,pert_:0,OptionsPattern[]]:=Block[{compile,gup,Ks,Ktup,Ric,res,n,perti,simpl},
+perti=OptionValue["PerturbationIndex"];
+compile=OptionValue["Compile"];
+simpl=OptionValue["SimplifyFunction"];
+
+n=Length@xx;
+Ric=RicciTensorDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+gup=InverseMetric[g];
+Ktup=(gup.gup.Kt);
+Ks=(Sum[gup[[a,b]]Kt[[a,b]],{a,n},{b,n}]);
+
+res=ConstantArray[0,{n,n}];
+If[NumericQ[pert], Do[res[[i,j]]=Ric[[i,j]]+Ks Kt[[i,j]]-Sum[Kt[[i,m]]Ktup[[m,j]],{m,n}],{i,n},{j,i,n}],
+ Do[res[[i,j]]=Normal@Series[Ric[[i,j]]+Ks Kt[[i,j]]-Sum[Kt[[i,m]]Ktup[[m,j]],{m,n}],{pert,0,perti}],{i,n},{j,i,n}]];
+
+If[compile, Do[res[[i,j]]=If[NumberQ[res[[i,j]]],res[[i,j]],Compile[Evaluate@({#,_Real}&/@xx),Evaluate[res[[i,j]]],CompilationTarget->"C",CompilationOptions->"InlineExternalDefinitions"->True]],{i,n},{j,i,n}];];
+(* Applying symmetries *)
+Do[res[[i+1,j]]=res[[j,i+1]];,{i,n-1},{j,i}];
+
+simpl@res]
+
+
+Options[MagneticTensor3p1Dev]=Options[ChristoffelSymbolDev];
+MagneticTensor3p1Dev[xx_,g_,Kt_,pert_:0,OptionsPattern[]]:=Block[{compile,gup,Ks,Ktup,Ric,res,rescov,n,perti,simpl,\[Epsilon]},
+perti=OptionValue["PerturbationIndex"];
+compile=OptionValue["Compile"];
+simpl=OptionValue["SimplifyFunction"];
+
+n=Length@xx;
+Ric=RicciTensorDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+gup=InverseMetric[g];
+\[Epsilon]=Det[gup]^(-1/2)LeviCivitaTensor[n];
+\[Epsilon]=Table[Sum[g[[s,i]]\[Epsilon][[s,j,k]],{s,n}],{i,n},{j,n},{k,n}];
+
+rescov=ConstantArray[0,{n,n,n}];
+Do[rescov[[k,i,j]]=CovDer[xx,g,Kt,{k,i,j},"Valence"->"Covariant"],{k,n},{i,n},{j,i,n}];
+Do[rescov[[k,i+1,j]]=rescov[[k,j,i+1]];,{k,n},{i,n-1},{j,i}];
+
+res=ConstantArray[0,{n,n}];
+If[NumericQ[pert], Do[res[[i,j]]=Sum[\[Epsilon][[i,m,k]]rescov[[m,k,j]],{m,n},{k,n}],{i,n},{j,i,n}],
+ Do[res[[i,j]]=Normal@Series[Sum[\[Epsilon][[i,m,k]]rescov[[m,k,j]],{m,n},{k,n}],{pert,0,perti}],{i,n},{j,i,n}]];
+
+If[compile, Do[res[[i,j]]=If[NumberQ[res[[i,j]]],res[[i,j]],Compile[Evaluate@({#,_Real}&/@xx),Evaluate[res[[i,j]]],CompilationTarget->"C",CompilationOptions->"InlineExternalDefinitions"->True]],{i,n},{j,i,n}];];
+(* Applying symmetries *)
+Do[res[[i+1,j]]=res[[j,i+1]];,{i,n-1},{j,i}];
+
+simpl@res]
+
+
+Options[RicciScalarDev]=Options[ChristoffelSymbolDev];
+RicciScalarDev[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{Ricc,ig,res,n,perti,simpl},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+n=Length@xx;
+
+Ricc=RicciTensorDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+ig=InverseMetric[g,"SimplifyFunction"->simpl];
+res=If[NumericQ[pert],Sum[If[i==s,ig[[s,i]] Ricc[[s,i]],2 ig[[s,i]] Ricc[[s,i]]],{s,n},{i,s}],
+ Normal@Series[Sum[ig[[s,i]] Ricc[[s,i]],{s,1,n},{i,1,n}],{pert,0,perti}]];
+simpl@res]
+
+
+Options[WeylTensorDev]=Options[ChristoffelSymbolDev];
+WeylTensorDev[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{n,Chr,riemann,riemanndown,ricciS,ricciT,res,perti,simpl,verbose},
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+verbose=OptionValue["Verbose"];
+n=Length@xx;
+
+If[verbose,Print["Starting with RicciScalar..."]];
+ricciS=RicciScalarDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+If[verbose,Print["Following with RicciTensor..."]];
+ricciT=RicciTensorDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+If[verbose,Print["Following with Riemann..."]];
+riemann=RiemannTensorDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl,"IndexDown"->False];
+
+res=Table[If[NumericQ[pert],riemann[[i,k,l,m]]+1/(n-2)(ricciT[[i,m]]g[[k,l]]-ricciT[[i,l]]g[[k,m]]+ricciT[[k,l]]g[[i,m]]-ricciT[[k,m]]g[[i,l]])+1/((n-1)(n-2))ricciS(g[[i,l]]g[[k,m]]-g[[i,m]]g[[k,l]]),
+ Normal@Series[riemann[[i,k,l,m]]+1/(n-2)(ricciT[[i,m]]g[[k,l]]-ricciT[[i,l]]g[[k,m]]+ricciT[[k,l]]g[[i,m]]-ricciT[[k,m]]g[[i,l]])+1/((n-1)(n-2))ricciS(g[[i,l]]g[[k,m]]-g[[i,m]]g[[k,l]]),{pert,0,perti}]],{i,1,n},{k,1,n},{l,1,n},{m,1,n}];
+(*Simplify[res]*)
+simpl@res];
+
+
+Options[EinsteinfR]={{"Metric"->True},Join[Options[ChristoffelSymbol]]};
+EinsteinfR[xx_,g_,fR_,OptionsPattern[]]:=Block[{res,fRterm1,fRterm2,dalem,Global`R,riscal,riscalvars,simpl,Rc,fRc,dfRc,covterm1,covterm2,metric},
+
+metric=OptionValue["Metric"];
+simpl=OptionValue["SimplifyFunction"];
+
+riscal=simpl@RicciScalar[xx,g];
+riscalvars=Complement[xx,Complement[xx,AtomsList[riscal]]];
+Rc=Global`R@@riscalvars;
+fRc=fR/.Global`R->Rc;
+dfRc=D[fRc,Rc];
+dalem=DAlembert[xx,g,dfRc];
+fRterm1=Simplify[dfRc RicciTensor[xx,g]-1/2 g fRc];
+If[metric,
+ covterm1=Table[CovDer[xx,g,dfRc,{i},"Valence"->"Covariant","Verbose"->False],{i,Length@xx}];
+ covterm2=Table[CovDer[xx,g,covterm1,{i,j},"Valence"->"Covariant","Verbose"->False],{i,Length@xx},{j,Length@xx}];
+ fRterm2=covterm2-g*dalem;
+ res=(fRterm1-fRterm2);
+ Return[{covterm1}];
+ ,
+ res=(fRterm1);
+];
+
+Simplify@res
+]
+
+
+STensorT\[Psi][coor_,met_,\[Psi]potl_]:=Module[{a,b,l,m,g,xx,\[Psi],pot,gup},
+xx=coor;
+g=met;
+pot=\[Psi]potl[[2]];
+\[Psi]=\[Psi]potl[[1]];
+gup=Inverse@g;
+
+Table[D[\[Psi],xx[[a]]]D[\[Psi],xx[[b]]]-1/2g[[a,b]]Sum[gup[[l,m]]D[\[Psi],xx[[l]]]D[\[Psi],xx[[m]]],{l,4},{m,4}]-g[[a,b]] pot ,{a,Length@xx},{b,Length@xx}]
+]
+
+
+Options[TeffFR]=Join[{"Metric"->True},Options[ChristoffelSymbol]];
+TeffFR[xx_,g_,fR_,pert_:0,OptionsPattern[]]:=Block[{res,fRterm1,fRterm2,dalem,Global`R,riscal,riscalvars,Rc,fRc,dfRc,simpl,covterm1,covterm2,metric,perti},
+metric=OptionValue["Metric"];
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+
+riscal=simpl@RicciScalar[xx,g,pert,"PerturbationIndex"->perti];
+riscalvars=Complement[xx,Complement[xx,AtomsList[riscal]]];
+Rc=Global`R@@riscalvars;
+fRc=fR/.Global`R->Rc;
+dfRc=D[fRc,Rc];
+dalem=DAlembert[xx,g,dfRc];
+
+If[metric,
+ covterm1=Table[CovDer[xx,g,dfRc,{i},"Valence"->"Covariant","Verbose"->False],{i,Length@xx}];
+ covterm2=Table[CovDer[xx,g,covterm1,{i,j},"Valence"->"Covariant","Verbose"->False],{i,Length@xx},{j,Length@xx}];
+ fRterm2=covterm2-g*dalem;
+ res=If[Not@NumericQ@pert,Normal@Series[1/(8\[Pi])(fRterm2-dfRc/2 Rc g + 1/2 fRc g),{pert,0,perti}],1/(8\[Pi])(fRterm2-dfRc/2 Rc g + 1/2 fRc g)];
+ ,
+ res=If[Not@NumericQ@pert,Normal@Series[(fRterm1),{pert,0,perti}],(fRterm1)];
+];
+
+Simplify@res
+]
+
+
+Options[TeffST]=Join[{"Frame"->"Einstein"},Options[ChristoffelSymbol]];
+TeffST[xx_,g_,{V\[CurlyPhi]_,var\[CurlyPhi]_},pert_:0,OptionsPattern[]]:=Block[{covterm1,covterm2,dalem,der,gup,frame,perti,res,riscal,riscalvars,simpl,sumder,V\[CurlyPhi]c,\[CurlyPhi]c,\[Phi]term2},
+perti=OptionValue["PerturbationIndex"];
+frame=OptionValue["Frame"];
+simpl=OptionValue["SimplifyFunction"];
+
+riscal=simpl@RicciScalar[xx,g,pert,"PerturbationIndex"->perti];
+riscalvars=Complement[xx,Complement[xx,AtomsList[riscal]]];
+gup=Inverse[g];
+\[CurlyPhi]c=var\[CurlyPhi]@@riscalvars;
+V\[CurlyPhi]c=V\[CurlyPhi]/.var\[CurlyPhi]->\[CurlyPhi]c;
+
+Which[frame=="Einstein",
+ der=Table[D[\[CurlyPhi]c,xx[[a]]]D[\[CurlyPhi]c,xx[[b]]],{a,Length@xx},{b,Length@xx}];
+ sumder=Sum[ gup[[a,b]](der[[a,b]]),{a,Length@xx},{b,Length@xx}];
+ res=1/(8\[Pi]) (2 der-g sumder -1/2 g V\[CurlyPhi]c);,
+ frame=="Jordan",
+ dalem=DAlembert[xx,g,\[CurlyPhi]c];
+ covterm1=Table[CovDer[xx,g,\[CurlyPhi]c,{i},"Valence"->"Covariant","Verbose"->False],{i,Length@xx}];
+ covterm2=Table[CovDer[xx,g,covterm1,{i,j},"Valence"->"Covariant","Verbose"->False],{i,Length@xx},{j,Length@xx}];
+ \[Phi]term2=covterm2-g*dalem;
+ res=If[Not@NumericQ@pert,Normal@Series[1/(8\[Pi])(\[Phi]term2-V\[CurlyPhi]c/2 g),{pert,0,perti}],1/(8\[Pi])(\[Phi]term2-V\[CurlyPhi]c/2 g)];,
+ True,
+ Print["Wrong option for Frame"];Return[];
+];
+If[NumberQ@pert,Simplify@res,Simplify@Normal@Series[res,{pert,0,perti}]]
+]
+
+
+(* Are you sure this is right??? *)
+EinsteinST[xx_,g_,V\[Phi]_]:=Block[{res,fRterm1,fRterm2,dalem,R,riscal,riscalvars,\[Phi]c,fRc,dfRc,covterm1,covterm2},
+
+riscal=Simplify@RicciScalar[xx,g];
+riscalvars=Complement[xx,Complement[xx,AtomsList[V\[Phi]]]];
+
+\[Phi]c=\[Phi]@@riscalvars;
+dalem=DAlembert[xx,g,\[Phi]c];
+fRterm1=Simplify[RicciTensor[xx,g]-1/2 g D[V\[Phi],\[Phi]c]+ 1/2 g V\[Phi]/(2 \[Phi]c )];
+
+covterm1=Table[CovDer[xx,g,dfRc,{i},"Valence"->"Covariant","Verbose"->False],{i,Length@xx}];
+covterm2=Table[CovDer[xx,g,covterm1,{i,j},"Valence"->"Covariant","Verbose"->False],{i,Length@xx},{j,Length@xx}];
+fRterm2=-(1/\[Phi]c) (covterm2-g*dalem);
+
+res=(fRterm1-fRterm2);
+
+Simplify@res
+]
+
+
+Options[STTOV]=Join[{"Signature"->1},Options[TeffST]];
+STTOV[coors_,met_,{V\[CurlyPhi]_,var\[CurlyPhi]_},metvars_,pert_:0,OptionsPattern[]]:=Block[{Global`x,Aa,\[Alpha]a,dV\[CurlyPhi]c,dpc,d\[Phi]c,d\[Phi]\[CurlyPhi]c,eq,eqaux,eqKG,eqp,eval,ET,eq2,frame,g,gup,perti,riscal,riscalvars,sign,simpl,T,TEF,Teff,Ttot,T\[Mu]\[Nu],T\[Mu]\[Nu]up,V\[CurlyPhi]c,\[CurlyPhi]c,\[CurlyPhi]2c,Global`r,Global`\[Rho],\[Rho]c,Global`p,pc,Global`\[Phi],\[Phi]c,\[Phi]\[CurlyPhi]c,Global`\[CurlyPhi]},
+sign=OptionValue["Signature"];
+frame=OptionValue["Frame"];
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+Which[frame!= "Einstein" && frame!="Jordan",Return[];];
+
+Print["Variables must be given as: {p,Var_gtt,Var_grr,\[CurlyPhi]}"];
+g=met;
+gup=Inverse[g];
+riscal=simpl@RicciScalar[coors,g,pert,"PerturbationIndex"->perti];
+
+riscalvars=Complement[coors,Complement[coors,AtomsList[riscal]]];
+\[CurlyPhi]c=var\[CurlyPhi]@@riscalvars;
+V\[CurlyPhi]c=V\[CurlyPhi]/.var\[CurlyPhi]->\[CurlyPhi]c;
+dV\[CurlyPhi]c=D[V\[CurlyPhi]c,\[CurlyPhi]c];
+\[CurlyPhi]2c=(var\[CurlyPhi]'')@@riscalvars;
+pc=Global`p@@riscalvars;
+\[Rho]c=Global`\[Rho]@@riscalvars;
+\[Phi]c=Global`\[Phi]@@riscalvars;
+dpc=D[pc,riscalvars];
+d\[Phi]c=D[\[Phi]c,riscalvars];
+(* Define the coupling of the scalar field with matter *)
+\[Phi]\[CurlyPhi]c[\[CurlyPhi]_]:=Exp[2/Sqrt[3]\[CurlyPhi]];
+d\[Phi]\[CurlyPhi]c=D[\[Phi]\[CurlyPhi]c,Global`r];
+
+eval[x_]:=Evaluate[x];
+(* Computation of the matter energy-momentum tensor *)
+T\[Mu]\[Nu]=ETensor[coors,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+T\[Mu]\[Nu]up=Normal@Series[(gup.T\[Mu]\[Nu])gup,{pert,0,perti}];
+T=Normal@Series[Sum[(g.T\[Mu]\[Nu]up)[[i,i]],{i,Length@coors}],{pert,0,perti}];
+If[frame=="Einstein",
+ TEF=(T* Exp[-4/Sqrt[3]\[CurlyPhi]c]);,
+ TEF=(T)];
+
+(* Computation of the effective energy-momentum tensor. Aa converts matter quantities to the Jordan-Frame. *)
+Teff=TeffST[coors,g,{V\[CurlyPhi],var\[CurlyPhi]},pert,"Frame"->frame,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+If[frame=="Einstein",
+ Aa[\[CurlyPhi]_]:=Exp[-\[CurlyPhi]/Sqrt[3]];
+ \[Alpha]a[\[CurlyPhi]_]:=D[Log[Aa[\[CurlyPhi]]],\[CurlyPhi]];
+ Ttot=FullSimplify[8\[Pi](T\[Mu]\[Nu] Aa[\[CurlyPhi]c]^4 +Teff)];
+ ;,
+ Aa[\[CurlyPhi]_]:=1;
+ \[Alpha]a[\[CurlyPhi]_]:=1;
+ Ttot=FullSimplify[8\[Pi]/\[CurlyPhi]c(T\[Mu]\[Nu] +Teff)];];
+
+(* Einstein tensor *)
+ET=Einstein[coors,g,pert,"PerturbationIndex"->perti];
+
+(* Solving the equations *)
+eq=ET-Ttot;
+eq2=Simplify[{Solve[eq[[1]]==0,metvars[[3]]'@@riscalvars][[1,1]],Solve[eq[[2]]==0,metvars[[2]]'@@riscalvars][[1,1]]}];
+
+(* Continuity equation and conversion to EF if frame\[Rule]Einstein *)
+eqp=Flatten[Solve[Table[Sum[CovDer[coors,g,T\[Mu]\[Nu]up,{i,i,j},"Valence"->"Contravariant"],{i,Length@coors}],{j,Length@coors}]=={0,0,0,0},metvars[[1]]'@@riscalvars]];
+If[frame=="Einstein",
+ eqaux=Table[T*\[Alpha]a[\[CurlyPhi]c] Sum[gup[[a,b]]D[\[CurlyPhi]c,coors[[a]]],{a,4}],{b,4}];
+ eqp=Equal@@@Flatten[Solve[Table[Sum[CovDer[coors,g,T\[Mu]\[Nu]up,{i,i,j},"Valence"->"Contravariant"],{i,Length@coors}],{j,Length@coors}]==eqaux,dpc]];
+ eqp=Simplify@Solve[eqp/.metvars[[1]]->Function[r,Global`\[Phi][r]^(-2)*metvars[[1]][r]]/.\[Rho]c->(\[Rho]c \[Phi]c^(-2))/.Global`\[Phi]->Function[r,Evaluate[\[Phi]\[CurlyPhi]c[Global`\[CurlyPhi][r]]]],dpc];
+ eqp=Simplify@Normal@Series[Flatten[eqp],{pert,0,perti}];,
+
+ eqp=Simplify[eqp];];
+
+(* KG equation *)
+If[frame=="Einstein",
+ eqKG=Solve[DAlembert[coors,g,\[CurlyPhi]c]==-4\[Pi] \[Alpha]a[\[CurlyPhi]c]TEF+1/4 dV\[CurlyPhi]c, \[CurlyPhi]2c];,
+ eqKG=Solve[3DAlembert[coors,g,\[CurlyPhi]c]==8\[Pi] \[Alpha]a[\[CurlyPhi]c]TEF+ \[CurlyPhi]c dV\[CurlyPhi]c -2 V\[CurlyPhi]c, \[CurlyPhi]2c];];
+
+Normal@Series[Equal@@@Flatten[Join[eqp,eq2,eqKG]],{pert,0,perti}]
+]
+
+
+Options[FRTOV]=Join[{"Signature"->1},Options[TeffST]];
+FRTOV[coors_,met_,fR_,metvars_,pert_,OptionsPattern[]]:=Block[{Global`R,teff,perti,sign,u,udown,g,gup,simpl,T\[Mu]\[Nu]up,T\[Mu]\[Nu],T,Teff,Ttot,ET,riscal,riscalvars,Rc,fRc,dfRc,eq,eq2,eqp,eqKG,R2c},
+sign=OptionValue["Signature"];
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+
+Print["Variables must be given as: {p,Var_gtt,Var_grr,R}"];
+g=met;
+gup=Inverse[g];
+riscal=RicciScalar[coors,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+riscalvars=Complement[coors,Complement[coors,AtomsList[riscal]]];
+Rc=Global`R@@riscalvars;
+R2c=(Global`R'')@@riscalvars;
+fRc=fR/.Global`R->Rc;
+dfRc=D[fRc,Rc];
+
+(* Computation of the matter energy-momentum tensor *)
+T\[Mu]\[Nu]=ETensor[coors,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+T\[Mu]\[Nu]up=(gup.T\[Mu]\[Nu])gup;
+T=Sum[(g.T\[Mu]\[Nu]up)[[i,i]],{i,Length@coors}];
+
+(* Computation of the effective energy-momentum tensor *)
+Teff=TeffFR[coors,g,fR,pert,"PerturbationIndex"->perti];
+Ttot=FullSimplify[8\[Pi]/dfRc(T\[Mu]\[Nu]+Teff)];
+
+(* Einstein tensor *)
+ET=Einstein[coors,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+
+(* Solving the equations *)
+eq=ET-Ttot;
+eq2=Simplify[{Solve[eq[[1]]==0,metvars[[3]]'@@riscalvars][[1,1]],Solve[eq[[2]]==0,metvars[[2]]'@@riscalvars][[1,1]]}];
+
+(* Continuity equation *)
+eqp=Flatten[Solve[Table[Sum[CovDer[coors,g,T\[Mu]\[Nu]up,{i,i,j},"Valence"->"Contravariant"],{i,Length@coors}],{j,Length@coors}]=={0,0,0,0},metvars[[1]]'@@riscalvars]];
+
+(* KG equation *)
+eqKG=Solve[(3DAlembert[coors,g,dfRc]+dfRc Rc-2fRc)==8\[Pi] T,R2c];
+
+Equal@@@Flatten[Join[eqp,eq2,eqKG]]
+]
+
+
+fR2Pot[fR_,\[Phi]\[CurlyPhi]_:1]:=Block[{dfRc,fRc,fun,Rc,uc,Global`R,Global`\[Phi],\[Phi]c,Rc\[Phi]},
+
+Rc=Global`R;
+\[Phi]c=Global`\[Phi];
+fRc=fR/.Global`R->Rc;
+dfRc=D[fRc,Rc];
+
+Rc\[Phi]=(Rc/.Solve[\[Phi]c==dfRc,Rc]);
+uc=Simplify[Rc\[Phi] \[Phi]c - (fRc/.Rc->Rc\[Phi])];
+(* pot=1 gives the JF potential else gives the SF *)
+$Assumptions = _ \[Element] Reals;
+If[NumericQ@\[Phi]\[CurlyPhi],fun=uc,fun=FullSimplify[(uc/\[Phi]c^2)/.\[Phi]c->\[Phi]\[CurlyPhi]];];
+fun
+];
+
+
+Pot2fR[V\[CurlyPhi]_,\[Phi]\[CurlyPhi]_]:=Block[{dfRc,fRc,fun,Rc,uc,Global`R,Global`\[Phi],Global`\[CurlyPhi],\[Phi]c,Rc\[Phi],\[CurlyPhi]c},
+
+
+
+Rc=Global`R;
+\[Phi]c=Global`\[Phi];
+\[CurlyPhi]c=Global`\[CurlyPhi];
+fRc=fR/.Global`R->Rc;
+dfRc=D[fRc,Rc];
+
+Return[Solve[\[Phi]\[CurlyPhi]==\[Phi]c,\[CurlyPhi]c]];
+
+Rc\[Phi]=(Rc/.Solve[\[Phi]c==dfRc,Rc])[[1]];
+uc=Simplify[Rc\[Phi] \[Phi]c - (fRc/.Rc->Rc\[Phi])];
+(* pot=1 gives the JF potential else gives the SF *)
+$Assumptions = _ \[Element] Reals;
+If[NumericQ@\[Phi]\[CurlyPhi],fun=uc,fun=FullSimplify[(uc/\[Phi]c^2)/.\[Phi]c->\[Phi]\[CurlyPhi]];];
+fun
+];
+
+
+EoSCallParsBSks[model_]:=
+Block[{a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15,a16,a17,a18,a19,a20,a21,a22,a23,a24,table,pars},
+
+table={{a1,3.916`,4.078`,4.857`},{a2,7.701`,7.587`,6.981`},{a3,0.00858`,0.00839`,0.00706`},{a4,0.22114`,0.21695`,0.19351`},{a5,3.269`,3.614`,4.085`},{a6,11.964`,11.942`,12.065`},{a7,13.349`,13.751`,10.521`},{a8,1.3683`,1.3373`,1.5905`},{a9,3.254`,3.606`,4.104`},{a10,-12.953`,-22.996`,-28.726`},{a11,0.9237`,1.6229`,2.0845`},{a12,6.2`,4.88`,4.89`},{a13,14.383`,14.274`,14.302`},{a14,16.693`,23.56`,22.881`},{a15,-1.0514`,-1.5564`,-1.769`},{a16,2.486`,2.095`,0.989`},{a17,15.362`,15.294`,15.313`},{a18,0.085`,0.084`,0.091`},{a19,6.23`,6.36`,4.68`},{a20,11.68`,11.67`,11.65`},{a21,-0.029`,-0.042`,-0.086`},{a22,20.1`,14.8`,10.`},{a23,14.19`,14.18`,14.15`}};
+
+pars=Table[table[[i,1]]->table[[i,model+1]],{i,Length@table}]
+]
+
+
+EoSCallParsSly[model_]:=
+Block[{a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15,a16,a17,a18,a19,a20,a21,a22,a23,a24,table,pars},
+
+table={{a1, 6.22},{a10,11.4950},
+{a2,6.121},{a11,-22.775},
+{a3,0.005925},{a12,1.5707},
+{a4,0.16326},{a13,4.3 },
+{a5,6.48},{a14,14.08 },
+{a6,11.4971},{a15,27.80 },
+{a7,19.105},{a16,-1.653},
+{a8,0.8938},{a17,1.50},
+{a9,6.54},{a18,14.67}};
+
+pars=Table[table[[i,1]]->table[[i,model+1]],{i,Length@table}]
+]
+
+
+EoSBSks[model_]:=Block[{\[Zeta],\[Rho],pars},
+pars=EoSCallParsBSks[model];
+
+\[Zeta]=(a1+a2 \[Rho] +a3 \[Rho]^3)/(1+a4 \[Rho]) (Exp[a5(\[Rho]-a6)]+1)^(-1)+(a7+a8 \[Rho])(Exp[a9(a6-\[Rho])]+1)^(-1)
++(a10+a11 \[Rho])(Exp[a12(a13-\[Rho])]+1)^(-1)+(a14+a15 \[Rho])(Exp[a16(a17-\[Rho])]+1)^(-1)
++a18/(1+(a19(\[Rho]-a20))^2)+a21/(1+(a22(\[Rho]-a20))^2);
+\[Zeta]/.pars
+
+]
+
+
+EoSSly[model_]:=Block[{\[Zeta],\[Rho],pars,x,f0},
+
+pars=EoSCallParsSly[model];
+f0[x_]:=1/(Exp[x]+1);
+
+\[Zeta]=(a1+a2 \[Rho] +a3 \[Rho]^3)/(1+a4 \[Rho]) f0[a5(\[Rho]-a6)]+
+(a7+a8 \[Rho])f0[(a9(a10-\[Rho]))]+
+(a11+a12 \[Rho])f0[(a13(a14-\[Rho]))]+
+(a15+a16 \[Rho])f0[(a17(a18-\[Rho]))];
+\[Zeta]/.pars
+
+]
+
+
+SlyInner={{0.00020905`,3.4951`*^11,6.214999999999999`*^29,1.177`,0.0099795`,1.6774`*^13,3.072`*^31,1.342`},{0.00022059000000000003`,3.6883`*^11,6.4304`*^29,0.527`,0.012513000000000002`,2.1042`*^13,4.1574`*^31,1.332`},{0.00023114`,3.865`*^11,6.5813`*^29,0.476`,0.016547`,2.7844000000000004`*^13,6.023399999999999`*^31,1.322`},{0.00026426`,4.4199`*^11,6.9945`*^29,0.447`,0.021405`,3.6043`*^13,8.461299999999999`*^31,1.32`},{0.00030533000000000003`,5.1079999999999994`*^11,7.4685`*^29,0.466`,0.024157`,4.068800000000001`*^13,9.928599999999999`*^31,1.325`},{0.00035331`,5.9119`*^11,8.0149`*^29,0.504`,0.027894000000000002`,4.7001`*^13,1.2022999999999999`*^32,1.338`},{0.00040763999999999997`,6.8224`*^11,8.644299999999999`*^29,0.554`,0.031941000000000004`,5.3843`*^13,1.4430000000000001`*^32,1.358`},{0.000468`,7.8339`*^11,9.3667`*^29,0.61`,0.036264`,6.115300000000001`*^13,1.7175`*^32,1.387`},{0.00053414`,8.9426`*^11,1.0190999999999999`*^30,0.668`,0.039888`,6.7284`*^13,1.9626`*^32,1.416`},{0.00060594`,1.0146`*^12,1.1128`*^30,0.726`,0.044578`,7.5224`*^13,2.3024`*^32,1.458`},{0.00076608`,1.2831`*^12,1.337`*^30,0.84`,0.048425`,8.1738`*^13,2.6018`*^32,1.496`},{0.0010471`,1.7543`*^12,1.7792`*^30,0.987`,0.052327000000000005`,8.835000000000002`*^13,2.9261000000000002`*^32,1.536`},{0.0012616`,2.1141`*^12,2.1547000000000002`*^30,1.067`,0.056264`,9.5022`*^13,3.2756`*^32,1.576`},{0.0016246000000000001`,2.7232`*^12,2.8565000000000003`*^30,1.16`,0.060218999999999995`,1.0173000000000002`*^14,3.6505000000000004`*^32,1.615`},{0.0020384`,3.4178`*^12,3.7461000000000004`*^30,1.227`,0.064183`,1.0845`*^14,4.0509000000000005`*^32,1.65`},{0.0026726000000000002`,4.4827`*^12,5.2679`*^30,1.286`,0.067163`,1.1351`*^14,4.3681`*^32,1.672`},{0.0034064`,5.7153`*^12,7.230400000000001`*^30,1.322`,0.070154`,1.1859`*^14,4.6998`*^32,1.686`},{0.0044746`,7.5106`*^12,1.0404999999999999`*^31,1.344`,0.073174`,1.2372`*^14,5.0462`*^32,1.685`},{0.005726`,9.6148`*^12,1.4513`*^31,1.353`,0.075226`,1.272`*^14,5.2856`*^32,1.662`},{0.0074963`,1.2593`*^13,2.0894`*^31,1.351`,0.075959`,1.2845`*^14,5.3739`*^32,1.644`}};
+
+
+SlyLCore={{0.0771`,1.3038`*^14,5.3739`*^32,2.159`,0.49`,8.850899999999999`*^14,1.0315`*^35,2.953`},{0.08`,1.3531`*^14,5.8259999999999996`*^32,2.217`,0.52`,9.4695`*^14,1.2289`*^35,2.943`},{0.085`,1.4381`*^14,6.6828`*^32,2.309`,0.55`,1.0102`*^15,1.4491`*^35,2.933`},{0.09`,1.5232`*^14,7.6443`*^32,2.394`,0.58`,1.0748`*^15,1.693`*^35,2.924`},{0.1`,1.6935`*^14,9.9146`*^32,2.539`,0.61`,1.1408`*^15,1.9616`*^35,2.916`},{0.11`,1.8641`*^14,1.2700999999999999`*^33,2.655`,0.64`,1.2085`*^15,2.2558999999999998`*^35,2.908`},{0.12`,2.035`*^14,1.6063`*^33,2.708`,0.67`,1.2777`*^15,2.5769`*^35,2.9`},{0.13`,2.2063`*^14,1.9971`*^33,2.746`,0.7`,1.3486`*^15,2.9255`*^35,2.893`},{0.16`,2.7223000000000003`*^14,3.5926999999999995`*^33,2.905`,0.75`,1.4706`*^15,3.5702`*^35,2.881`},{0.19`,3.2424`*^14,5.9667`*^33,2.99`,0.8`,1.5977`*^15,4.2981`*^35,2.869`},{0.22`,3.7675`*^14,9.2766`*^33,3.025`,0.85`,1.7302`*^15,5.1128999999999996`*^35,2.858`},{0.25`,4.2983`*^14,1.3668`*^34,3.035`,0.9`,1.8683`*^15,6.0183`*^35,2.847`},{0.28`,4.8358`*^14,1.9276999999999999`*^34,3.032`,0.95`,2.0123000000000002`*^15,7.0176`*^35,2.836`},{0.31`,5.3808`*^14,2.6234999999999996`*^34,3.023`,1.`,2.1624`*^15,8.113899999999998`*^35,2.824`},{0.34`,5.934`*^14,3.467`*^34,3.012`,1.1`,2.482`*^15,1.0609`*^36,2.801`},{0.37`,6.4963`*^14,4.4702`*^34,2.999`,1.2`,2.8289`*^15,1.3524`*^36,2.778`},{0.4`,7.0684`*^14,5.6451`*^34,2.987`,1.3`,3.2048`*^15,1.6876`*^36,2.754`},{0.43`,7.651`*^14,7.0033`*^34,2.975`,1.4`,3.6113`*^15,2.0678999999999998`*^36,2.731`},{0.46`,8.244999999999999`*^14,8.5561`*^34,2.964`,1.5`,4.0498000000000005`*^15,2.4947`*^36,2.708`}};
+
+
+SlyLCoreAll=Join[TakeColumn[SlyLCore,{2,3}],TakeColumn[SlyLCore,{6,7}]]/.{zz_,yy_}->{Log[10,zz],Log[10,yy]};
+
+
+SlyInnerAll=Join[TakeColumn[SlyInner,{2,3}],TakeColumn[SlyInner,{6,7}]]/.{zz_,yy_}->{Log[10,zz],Log[10,yy]};
+
+
+EoSFitsPars[model_,verbose_:False]:=Module[{eostable},
+eostable={{"PAL6",34.38`,2.227`,2.189`,2.159`,0.0011`,0.693`,1.37`,1.477`,-0.47`,0.374`,-0.51`,1660,-0.97`,1.051`,-2.03`,10.547`,-0.54`},{"SLy",34.384`,3.005`,2.988`,2.851`,0.002`,0.989`,1.41`,2.049`,0.02`,0.592`,0.81`,1810,0.1`,1.288`,-0.08`,11.736`,-0.21`},{"APR1",33.943`,2.442`,3.256`,2.908`,0.019`,0.924`,9.94`,1.683`,-1.6`,0.581`,2.79`,2240,1.05`,0.908`,-2.57`,9.361`,-1.85`},{"APR2",34.126`,2.643`,3.014`,2.945`,0.0089`,1.032`,0.42`,1.808`,-1.5`,0.605`,0.33`,2110,-0.02`,1.024`,-2.34`,10.179`,-1.57`},{"APR3",34.392`,3.166`,3.573`,3.281`,0.0091`,1.134`,2.72`,2.39`,-1.`,0.704`,0.57`,1810,-0.14`,1.375`,-1.59`,12.094`,-0.96`},{"APR4",34.269`,2.83`,3.445`,3.348`,0.0068`,1.16`,1.45`,2.213`,-1.08`,0.696`,0.22`,1940,0.05`,1.243`,-1.36`,11.428`,-0.9`},{"FPS",34.283`,2.985`,2.863`,2.6`,0.005`,0.883`,2.29`,1.799`,-0.03`,0.53`,0.67`,1880,0.11`,1.137`,0.03`,10.85`,0.12`},{"WFF1",34.031`,2.519`,3.791`,3.66`,0.018`,1.185`,7.86`,2.133`,-0.29`,0.739`,2.21`,2040,0.3`,1.085`,0.1`,10.414`,0.02`},{"WFF2",34.233`,2.888`,3.475`,3.517`,0.017`,1.139`,7.93`,2.198`,-0.14`,0.717`,0.71`,1990,0.03`,1.204`,-0.59`,11.159`,-0.28`},{"WFF3",34.283`,3.329`,2.952`,2.589`,0.017`,0.835`,8.11`,1.844`,-0.48`,0.53`,2.26`,1860,0.59`,1.16`,-0.25`,10.926`,-0.12`},{"BBB2",34.331`,3.418`,2.835`,2.832`,0.0055`,0.914`,7.75`,1.918`,0.1`,0.574`,0.97`,1900,0.47`,1.188`,0.17`,11.139`,-0.29`},{"BPAL12",34.358`,2.209`,2.201`,2.176`,0.001`,0.708`,1.03`,1.452`,-0.18`,0.382`,-0.29`,1700,-1.03`,0.974`,0.2`,10.024`,0.67`},{"ENG",34.437`,3.514`,3.13`,3.168`,0.015`,1.`,10.71`,2.24`,-0.05`,0.654`,0.39`,1820,-0.44`,1.372`,-0.97`,12.059`,-0.69`},{"MPA1",34.495`,3.446`,3.572`,2.887`,0.0081`,0.994`,4.91`,2.461`,-0.16`,0.67`,-0.05`,1700,-0.18`,1.455`,-0.41`,12.473`,-0.26`},{"MS1",34.858`,3.224`,3.033`,1.325`,0.019`,0.888`,12.44`,2.767`,-0.54`,0.606`,-0.52`,1400,1.67`,1.944`,-0.09`,14.918`,0.06`},{"MS2",34.605`,2.447`,2.184`,1.855`,0.003`,0.582`,3.96`,1.806`,-0.42`,0.343`,2.57`,1250,2.25`,1.658`,0.46`,14.464`,-2.69`},{"MS1b",34.855`,3.456`,3.011`,1.425`,0.015`,0.889`,11.38`,2.776`,-1.03`,0.614`,-0.56`,1420,1.38`,1.888`,-0.64`,14.583`,-0.32`},{"PS",34.671`,2.216`,1.64`,2.365`,0.028`,0.691`,7.36`,1.755`,-1.53`,0.355`,-1.45`,1300,-2.39`,2.067`,-3.06`,15.472`,3.72`},{"GS1",34.504`,2.35`,1.267`,2.421`,0.018`,0.695`,0.49`,1.382`,-1.`,0.395`,-0.64`,1660,9.05`,0.766`,-3.13`,Null},{"GS2",34.642`,2.519`,1.571`,2.314`,0.026`,0.592`,16.1`,1.653`,-0.3`,0.339`,7.71`,1340,3.77`,1.795`,-3.33`,14.299`,0.07`},{"BGN1H1",34.623`,3.258`,1.472`,2.464`,0.029`,0.878`,-7.42`,1.628`,0.39`,0.437`,-3.55`,1670,-2.08`,1.504`,0.56`,12.901`,-1.96`},{"GNH3",34.648`,2.664`,2.194`,2.304`,0.0045`,0.75`,2.04`,1.962`,0.13`,0.427`,0.37`,1410,-0.04`,1.713`,0.38`,14.203`,-0.28`},{"H1",34.564`,2.595`,1.845`,1.897`,0.0019`,0.561`,2.81`,1.555`,-0.92`,0.311`,-1.47`,1320,-1.46`,1.488`,-1.45`,12.861`,-0.03`},{"H2",34.617`,2.775`,1.855`,1.858`,0.0028`,0.565`,1.38`,1.666`,-0.77`,0.322`,-0.55`,1280,-1.29`,1.623`,-0.82`,13.479`,0.29`},{"H3",34.646`,2.787`,1.951`,1.901`,0.007`,0.564`,7.05`,1.788`,-0.79`,0.343`,1.07`,1290,-0.88`,1.702`,-1.18`,13.84`,0.31`},{"H4",34.669`,2.909`,2.246`,2.144`,0.0028`,0.685`,4.52`,2.032`,-0.85`,0.428`,-1.01`,1400,-1.28`,1.729`,-1.18`,13.774`,1.34`},{"H5",34.609`,2.793`,1.974`,1.915`,0.005`,0.596`,1.65`,1.727`,-1.`,0.347`,-0.82`,1340,-1.55`,1.615`,-1.31`,13.348`,0.68`},{"H6",34.593`,2.637`,2.121`,2.064`,0.0087`,0.598`,11.71`,1.778`,0.07`,0.346`,8.65`,1310,5.33`,1.623`,-2.19`,13.463`,0.37`},{"H7",34.559`,2.621`,2.048`,2.006`,0.0046`,0.63`,1.82`,1.683`,-1.12`,0.357`,-0.57`,1410,-1.52`,1.527`,-2.33`,12.992`,0.23`},{"PCL2",34.507`,2.554`,1.88`,1.977`,0.0069`,0.6`,1.74`,1.482`,-0.79`,0.326`,-2.25`,1440,-1.87`,1.291`,-3.27`,11.761`,-1.15`},{"ALF1",34.055`,2.013`,3.389`,2.033`,0.04`,0.565`,18.59`,1.495`,-0.53`,0.386`,3.52`,1730,2.44`,0.987`,-0.4`,9.896`,-0.22`},{"ALF2",34.616`,4.07`,2.411`,1.89`,0.043`,0.642`,1.5`,2.086`,-5.26`,0.436`,-0.62`,1440,1.01`,1.638`,-6.94`,13.188`,-3.66`},{"ALF3",34.283`,2.883`,2.653`,1.952`,0.017`,0.565`,11.29`,1.473`,-0.06`,0.358`,2.46`,1620,1.79`,1.041`,0.76`,10.314`,-0.25`},{"ALF4",34.314`,3.009`,3.438`,1.803`,0.023`,0.685`,14.78`,1.943`,-0.93`,0.454`,0.59`,1590,0.52`,1.297`,-2.38`,11.667`,-1.2`}};
+If[verbose,eostable[[All,1]],Flatten@Select[eostable,#[[1]]==model&]]
+]
+
+
+EoSSlyCrust[\[Rho]_]:=Module[{pol1,pol2,pol3,pol4,\[Rho]l1,\[Rho]l2,\[Rho]l3,k1,k2,k3,k4,\[CapitalGamma]1,\[CapitalGamma]2,\[CapitalGamma]3,\[CapitalGamma]4,c},
+
+c=2.99792458 10^10;
+\[Rho]l1=Log[10,2.44034 10^(07)];
+\[Rho]l2=Log[10,3.78358 10^(11)];
+\[Rho]l3=Log[10,2.62780 10^(12)];
+
+k1=Log[10,(6.80110 10^(-9))*c^2];
+k2=Log[10,(1.06186 10^(-6))*c^2];
+k3=Log[10,(5.32697 10)*c^2];
+k4=Log[10,(3.99874 10^(-8))*c^2];
+
+\[CapitalGamma]1=1.58425;
+\[CapitalGamma]2=1.28733;
+\[CapitalGamma]3=0.62223;
+\[CapitalGamma]4=1.35692;
+
+pol1=k1+ \[CapitalGamma]1 \[Rho];
+pol2=k2+ \[CapitalGamma]2 \[Rho];
+pol3=k3+ \[CapitalGamma]3 \[Rho];
+pol4=k4+ \[CapitalGamma]4 \[Rho];
+
+Piecewise[{{pol1,\[Rho]<=\[Rho]l1},{pol2,\[Rho]l1<\[Rho]<=\[Rho]l2},{pol3,\[Rho]l2<\[Rho]<=\[Rho]l3},{pol4,\[Rho]>\[Rho]l3}}]
+
+];
+
+
+EoSPol[model_:"PolR"]:=Block[{k,\[CapitalGamma],pol,Global`\[Rho],c,pol1,pol2,k2},
+
+If[ListQ[model],k=Log10[model[[1]]];\[CapitalGamma]=model[[2]];pol=k+ \[CapitalGamma] Global`\[Rho],
+
+Which[model=="PolNR",k=Log[10,(3.3)];\[CapitalGamma]=2; pol=k+ \[CapitalGamma] Global`\[Rho];,
+ model=="PolR",k=Log[10,(1.98183*10^-6)];\[CapitalGamma]=2.75; pol=k+ \[CapitalGamma] Global`\[Rho];,
+ model=="PolMS",k=Log[10,3.849119840037`*^14];\[CapitalGamma]=4/3; pol= k +\[CapitalGamma] Global`\[Rho];,
+ model=="PolMSMix",k=Log[10,3.849119840037`*^14]; pol1=k+ 4/3 Global`\[Rho];k2=Log[10,1.2392481667219052`*^15];pol2= k2+ 5/3 Global`\[Rho]; pol=Piecewise[{{pol1,Global`\[Rho]>Log10[0.029964]},{pol2,Global`\[Rho]<=Log10[0.029964]}}];,
+ True,Return[]];
+ ];
+pol
+]
+
+
+EoSPol\[Epsilon][model_:"PolR"]:=Block[{k,\[CapitalGamma],pol,Global`\[Rho],c,pol1,pol2,k2},
+c=2.99792458 10^10;
+
+If[ListQ[model],k=Log10[model[[1]]];\[CapitalGamma]=model[[2]];pol=k+ \[CapitalGamma] Global`\[Rho],
+
+Which[model=="PolNR",k=Log[10,(3.3)];\[CapitalGamma]=2; pol=k+ \[CapitalGamma] Global`\[Rho],
+ model=="PolR",k=Log[10,(1.98183*10^-6)];\[CapitalGamma]=2.75; pol=k+ \[CapitalGamma] Global`\[Rho],
+ model=="PolMS",k=Log[10,3.849119840037`*^14];\[CapitalGamma]=4/3; pol=k+ \[CapitalGamma] Global`\[Rho];];
+ ];
+Global`\[Rho] +10^k/(c^2(\[CapitalGamma]-1))Global`\[Rho]^(\[CapitalGamma])
+]
+
+
+Options[EoSFits]:={"PhysUnits"->False,"Verbose"->False}
+EoSFits[model_,OptionsPattern[]]:=Block[{P0Sly=Log[10,5.37*10^(32)],\[Rho]0Sly=Log[10,1.2845 10^14],\[CapitalGamma]0=4/3,\[Rho]1=Log[10,10^(14.7)],\[Rho]2=Log[10,10^(15.)],fit0,fit1,fit2,
+fit3,Global`\[Rho],p,pars,p1, \[CapitalGamma]1,\[CapitalGamma]2,\[CapitalGamma]3,K0,K1,K2,K3,\[Rho]0c,p2,verbose,picore,res,\[Rho]1c,\[Rho]2c,\[Rho]3c,k1c,k2c,k3c,k4c,\[CapitalGamma]1c,\[CapitalGamma]2c,\[CapitalGamma]3c,\[CapitalGamma]4c,fit1c,fit2c,fit3c,fit4c,physuns,c},
+verbose=OptionValue["Verbose"];
+physuns=OptionValue["PhysUnits"];
+If[verbose,Print[" EoS available "];Return[EoSFitsPars[model,True]]];
+
+c=2.99792458 10^10;
+(* values for the crust taken from SLy crust model *)
+\[Rho]1c=Log[10,2.44034 10^(07)];
+\[Rho]2c=Log[10,3.78358 10^(11)];
+\[Rho]3c=Log[10,2.62780 10^(12)];
+
+k1c=Log[10,(6.80110 10^(-9))*c^2];
+k2c=Log[10,(1.06186 10^(-6))*c^2];
+k3c=Log[10,(5.32697 10)*c^2];
+k4c=Log[10,(3.99874 10^(-8))*c^2];
+
+\[CapitalGamma]1c=1.58425;
+\[CapitalGamma]2c=1.28733;
+\[CapitalGamma]3c=0.62223;
+\[CapitalGamma]4c=1.35692;
+
+fit1c=k1c+ \[CapitalGamma]1c Global`\[Rho];
+fit2c=k2c+ \[CapitalGamma]2c Global`\[Rho];
+fit3c=k3c+ \[CapitalGamma]3c Global`\[Rho];
+fit4c=k4c+ \[CapitalGamma]4c Global`\[Rho];
+
+
+(* p1, \[CapitalGamma]1,\[CapitalGamma]2,\[CapitalGamma]3*)
+{p1, \[CapitalGamma]1,\[CapitalGamma]2,\[CapitalGamma]3}=EoSFitsPars[model][[2;;5]];
+
+(* Using a polytropic SLy for the crust *)
+K1=(p1-(\[CapitalGamma]1 \[Rho]1));
+fit0=Piecewise[{{fit1c,Global`\[Rho]<=\[Rho]1c},{fit2c,\[Rho]1c<Global`\[Rho]<=\[Rho]2c},{fit3c,\[Rho]2c<Global`\[Rho]<=\[Rho]3c},{fit4c,Global`\[Rho]>\[Rho]3c}}];
+fit1=K1+(\[CapitalGamma]1 Global`\[Rho]);
+\[Rho]0c=(Global`\[Rho]/.Solve[fit0==K1+\[CapitalGamma]1 Global`\[Rho],Global`\[Rho]])[[1]];
+
+K2=p1-(\[CapitalGamma]2 \[Rho]1);
+fit2=K2+(\[CapitalGamma]2 Global`\[Rho]);
+p2=K2+(\[CapitalGamma]2 \[Rho]2);
+
+K3=p2-(\[CapitalGamma]3 \[Rho]2);
+fit3=K3+(\[CapitalGamma]3 Global`\[Rho]);
+If[Not@physuns,
+res=Piecewise[{{fit1c,Global`\[Rho]<=\[Rho]1c},{fit2c,\[Rho]1c<Global`\[Rho]<=\[Rho]2c},{fit3c,\[Rho]2c<Global`\[Rho]<=\[Rho]3c},{fit4c,\[Rho]3c<Global`\[Rho]<=\[Rho]0c},{fit1,\[Rho]0c<Global`\[Rho]<=\[Rho]1},{fit2,\[Rho]1<Global`\[Rho]<=\[Rho]2},{fit3,Global`\[Rho]>\[Rho]2}}];,
+res=Piecewise[{{10^(fit1c/.Global`\[Rho]->Log[10,Global`\[Rho]]),Global`\[Rho]<=10^\[Rho]1c},{10^(fit2c/.Global`\[Rho]->Log[10,Global`\[Rho]]),10^\[Rho]1c<Global`\[Rho]<=10^\[Rho]2c},{10^(fit3c/.Global`\[Rho]->Log[10,Global`\[Rho]]),10^\[Rho]2c<Global`\[Rho]<=10^\[Rho]3c},{10^(fit4c/.Global`\[Rho]->Log[10,Global`\[Rho]]),10^\[Rho]3c<Global`\[Rho]<=10^\[Rho]0c},{10^(fit1/.Global`\[Rho]->Log[10,Global`\[Rho]]),10^\[Rho]0c<Global`\[Rho]<=10^\[Rho]1},{10^(fit2/.Global`\[Rho]->Log[10,Global`\[Rho]]),10^\[Rho]1<Global`\[Rho]<=10^\[Rho]2},{10^(fit3/.Global`\[Rho]->Log[10,Global`\[Rho]]),Global`\[Rho]>10^\[Rho]2}}];
+];
+res
+]
+
+
+From\[Rho]To\[Epsilon]Fits[eos_]:=Block[{Global`\[Rho],ks,\[Gamma]s,pols,polsd,a,\[Rho]s,\[Epsilon],tab,k,k1,\[Gamma],\[Gamma]1,\[Rho]v,c},
+c=2.99792458 10^10;
+If[eos=="PolMSMix",pols=EoSPol[eos][[1]],pols=EoSFits[eos][[1]]];
+{ks,\[Gamma]s}=Transpose[CoefficientList[#,Global`\[Rho]]&/@pols[[All,1]]];
+polsd=pols[[All,2]];
+\[Rho]s=DeleteDuplicates@polsd[[All,-1]];
+a=0;
+\[Epsilon][Global`\[Rho]_,a_,k_,\[Gamma]_]:=(1+a)Global`\[Rho] + k/(c^2(\[Gamma]-1))Global`\[Rho]^(\[Gamma]);
+polsd=Table[10^\[Rho]s[[i]]<Global`\[Rho]<=10^\[Rho]s[[i+1]],{i,Length@\[Rho]s-1}];
+polsd=Join[{Global`\[Rho]<=10^\[Rho]s[[1]]},polsd,{Global`\[Rho]>10^\[Rho]s[[-1]]}];
+
+tab=Table[k=10^ks[[i]];\[Gamma]=\[Gamma]s[[i]];\[Rho]v=10^\[Rho]s[[i]];k1=10^ks[[i+1]];\[Gamma]1=\[Gamma]s[[i+1]];
+ a=\[Epsilon][\[Rho]v,a,k,\[Gamma]]/\[Rho]v-1- k1/(c^2(\[Gamma]1-1))\[Rho]v^(\[Gamma]1-1);
+ {\[Epsilon][Global`\[Rho],a,k1,\[Gamma]1],polsd[[i+1]]}
+,{i,1,Length@\[Rho]s}];
+
+Simplify@Piecewise[Join[{{\[Epsilon][Global`\[Rho],0,10^ks[[1]],\[Gamma]s[[1]]],polsd[[1]]}},tab]]
+]
+
+
+RK4[func_?ListQ,vars_?ListQ,ivals_?ListQ,pars_?ListQ,step_]:=Module[{k1,k2,k3,k4,x2,f1,f2,x3,f3,x4,f4,dx,x,x0,sol},
+
+dx=step;
+{x,x0}={pars[[1]],pars[[2]]};
+
+k1=dx ((func/.x->(x0))/.MapThread[Rule, {vars,ivals}]);
+k2=dx ((func/.x->(x0+dx/2))/.MapThread[Rule, {vars,ivals +1/2 k1}]);
+k3=dx ((func/.x->(x0+dx/2))/.MapThread[Rule, {vars,ivals +1/2 k2}]);
+k4=dx ((func/.x->(x0+dx))/.MapThread[Rule, {vars,ivals + k3}]);
+
+ivals+1/6(k1+2k2+2k3+k4)
+]
+
+
+TestCode[eqs_,vars_,icond_,rlst_,drlst_]:=Module[{R1,R,v1,v,w1,w,\[Lambda]1,\[Lambda],p1,p,eqsrules,atomlst,atomlstaux,solvevars,varsp1,rvar,rval,drvar,drval},
+{rvar,rval}=rlst;
+{drvar,drval}=drlst;
+eqsrules=(Flatten[eqs/.MapThread[Rule, {vars,icond}]])/.drvar->drval/.rvar->rval;
+varsp1=Flatten[eqs][[All,1]];
+eqsrules=Flatten@Solve[eqsrules,varsp1];
+
+Return[varsp1/.eqsrules];
+]
+
+
+Options[BracketingSTNStars]={"Tolerance"->10^(-8),"Verbose"->False,"MaxIteraton"->100,"NPoints"->1000,"AssymptoticMatch"->None,"AssymptoticValue"->10^-8};
+BracketingSTNStars[eqs_,eqsRg_,Global`r_,vars_,shtdInd_,varshtdRg_,OptionsPattern[]]:=Module[{dom,eqsht,
+Sh0,Sh0m,posref,mean,tol,Sh\[Infinity],Sh\[Infinity]m,Sh\[Infinity]m2,Sh0m2,Sh0ref,
+a,posreftest,verbose,begin,eqsRga,brack,varshtdRga,varsa,varshta,varshtalw,dvarshta,out,ShtStr,raux,np,i,amax,assymptotic,
+Rs,r,datab,datfit,a0,m,y1,y2,A3,assval,threshold,Sh\[Infinity]maux},
+
+(* Loading options *)
+tol=OptionValue["Tolerance"];
+verbose=OptionValue["Verbose"];
+amax=OptionValue["MaxIteraton"];
+assymptotic=OptionValue["AssymptoticMatch"];
+np=OptionValue["NPoints"];
+assval=OptionValue["AssymptoticValue"];
+
+(* Some auxiliary variables *)
+eqsRga=eqsRg;
+varshtdRga=varshtdRg;
+varsa=ToExpression[(ToString[#]<>"a")&/@vars];
+varshta=Join[varshtdRga,{Mean[varshtdRga]}];
+ShtStr=ToString[varsa[[shtdInd]]];
+a=0 (* auxiliary counter *) ;
+i=0 (* auxiliary counter *) ;
+dvarshta=(varshta[[2]]-varshta[[1]])/np;
+(* In case 'bracketing' is activated, we split [varshta[[1]], varshta[[2]]] in np points *)
+
+ Sh\[Infinity]m=1.1;
+ If[assval>=1,threshold=assval,threshold=0];
+ While[Sh\[Infinity]m>threshold&&i< np,
+ i=i+1;
+ Sh\[Infinity]maux=Sh\[Infinity]m;
+ varshtalw=varshtdRg[[2]] - i*dvarshta;
+ If[verbose, Print["n: ",i," Redefining upper limit as: ",varshtalw]];
+ eqsht={vars[[shtdInd]][eqsRga[[1]]]==varshtalw};
+ eqsht=Join[eqs,eqsht];
+ varsa=vars/.Flatten[NDSolve[eqsht,vars,{Global`r,eqsRga[[1]],eqsRga[[2]]},AccuracyGoal->15,PrecisionGoal->15,WorkingPrecision->30,MaxSteps->Infinity]];
+ dom=InterpolationDomain[varsa[[1]]];
+ Sh\[Infinity]m=varsa[[shtdInd]]@dom[[2]];
+ ];
+
+ Return[{varshtalw,varshtalw + dvarshta,i}]
+ (* The - is to avoid varshta[[1]]=varshta[[2]] *)
+ (*varshta[[2]]=varshtalw + dvarshta;
+ If[verbose, Print[" New upper limit: ",varshta[[2]]]];
+ Sh\[Infinity]m=-0.1;
+ i=0;
+ varshtalw=varshta[[1]];
+ If[assval\[GreaterEqual]1,threshold=assval,threshold=0];
+ While[Sh\[Infinity]m<threshold && i<np,
+ i=i+1;
+ varshtalw=varshtdRg[[1]] +i*dvarshta;
+ eqsht={vars[[shtdInd]][eqsRga[[1]]]\[Equal]varshtalw};
+ eqsht=Join[eqs,eqsht];
+ varsa=vars/.Flatten[NDSolve[eqsht,vars,{Global`r,eqsRga[[1]],eqsRga[[2]]},AccuracyGoal\[Rule]15,PrecisionGoal\[Rule]15,WorkingPrecision\[Rule]30,MaxSteps->Infinity]];
+ dom=InterpolationDomain[varsa[[1]]];
+ Sh\[Infinity]m=varsa[[shtdInd]]@dom[[2]];
+ varshta[[1]]=varshtalw;
+ If[verbose, Print["n: ",i,". Redefining lower limit as: ",varshta[[1]]]];
+ ];
+ varshta[[1]]=varshtalw - dvarshta;
+ Return[Flatten[Join[varshta[[1;;2]],{i}]]];
+*)];
+
+
+Options[ShootingNStars]={"Tolerance"->10^(-8),"Verbose"->True,"Bracketing"->False,"MaxIteraton"->100,"NPoints"->1000,"AssymptoticMatch"->None,"AssymptoticValue"->10^-8};
+ShootingNStars[eqs_,eqsRg_,Global`r_,vars_,shtdInd_,varshtdRg_,optNDS__,OptionsPattern[]]:=Module[{dom,eqsht,
+Sh0,Sh0m,posref,mean,tol,Sh\[Infinity],Sh\[Infinity]m,Sh\[Infinity]m2,Sh0m2,Sh0ref,
+a,posreftest,verbose,begin,eqsRga,brack,varshtdRga,varsa,varshta,varshtalw,dvarshta,out,ShtStr,raux,np,i,amax,assymptotic,
+Rs,r,datab,datfit,a0,m,y1,y2,A3,assval,threshold},
+
+(* Loading options *)
+tol=OptionValue["Tolerance"];
+verbose=OptionValue["Verbose"];
+brack=OptionValue["Bracketing"];
+amax=OptionValue["MaxIteraton"];
+assymptotic=OptionValue["AssymptoticMatch"];
+np=OptionValue["NPoints"];
+assval=OptionValue["AssymptoticValue"];
+
+(* Some auxiliary variables *)
+eqsRga=eqsRg;
+varshtdRga=varshtdRg;
+varsa=ToExpression[(ToString[#]<>"a")&/@vars];
+varshta=Join[varshtdRga,{Mean[varshtdRga]}];
+ShtStr=ToString[varsa[[shtdInd]]];
+a=0 (* auxiliary counter *) ;
+i=0 (* auxiliary counter *) ;
+dvarshta=(varshta[[2]]-varshta[[1]])/np;(* In case 'bracketing' is activated, we split [varshta[[1]], varshta[[2]]] in np points *)
+
+(* In case shooting is not required *)
+If[Length@varshtdRga==1,
+eqsht={vars[[shtdInd]][eqsRga[[1]]]==(varshta[[1]])};
+eqsht=Join[eqs,eqsht];
+varsa=vars/.Flatten[NDSolve[Chop[eqsht],vars,{Global`r,eqsRga[[1]],eqsRga[[2]]},AccuracyGoal->15,PrecisionGoal->15,WorkingPrecision->30,MaxSteps->Infinity]];
+out=Join[varsa,{a,Rationalize[varsa[[shtdInd]]@eqsRga[[1]]],0}];
+Return[out];
+];
+(* We also include provide a 'bracketing' option in case the bracketing on the shooting variable is required *)
+If[brack,
+ varshtalw=Chop[varshta[[2]]];
+ eqsht={vars[[shtdInd]][eqsRga[[1]]]==varshtalw};
+ eqsht=Join[eqs,eqsht];
+
+ varsa=vars/.Flatten[NDSolve[Chop[eqsht],vars,{Global`r,eqsRga[[1]],eqsRga[[2]]},AccuracyGoal->15,PrecisionGoal->15,WorkingPrecision->30,MaxSteps->Infinity]];
+ dom=InterpolationDomain[varsa[[1]]][[1]];
+ (*If[dom[[2]]<eqsRga[[2]],eqsRga[[2]]=Rationalize[0.9*eqsRga[[2]],1];If[verbose,Print[Style[" Breakup found. Changing rfin to ",Red],eqsRga[[2]]] ];Goto[begin];];*)
+ Which[Sh\[Infinity]m<0&&assval<= 1, Print[Style[" Upper value of the shooted variable is not positive at rmax: Redefine the brackets !",Red]]; Return[];,
+ Sh\[Infinity]m<1&&assval>= 1, Print[Style[" Upper value of the shooted variable is <1 at rmax: Redefine the brackets !",Red]]; Return[];];
+
+ Sh\[Infinity]m=-0.1;
+ i=0;
+ If[assval>=1,threshold=assval,threshold=0];
+ While[Sh\[Infinity]m<threshold && i< np,
+ i=i+1;
+ varshtalw=varshtdRg[[1]] +i*dvarshta;
+ eqsht={vars[[shtdInd]][eqsRga[[1]]]==varshtalw};
+ eqsht=Join[eqs,eqsht];
+ varsa=vars/.Flatten[NDSolve[eqsht,vars,{Global`r,eqsRga[[1]],eqsRga[[2]]},AccuracyGoal->15,PrecisionGoal->15,WorkingPrecision->30,MaxSteps->Infinity]];
+ dom=InterpolationDomain[varsa[[1]]][[1]];
+ Sh\[Infinity]m=Chop[varsa[[shtdInd]]@dom[[2]]];
+ varshta[[1]]=Chop[varshtalw];
+ If[verbose, Print["n: ",i,". Redefining lower limit as: ",varshta[[1]]]];
+ ];
+ Return[Flatten[Join[varshta[[1;;2]],{i}]]];
+];
+
+(* First estimates on the value of the shooted variable at eqsRg1[[2]]. There is a goto to correct possible breakups on the equations. We also include provide a 'bracketing' option in case the bracketing on the unknown variable is needed*)
+Label[begin];
+ Sh\[Infinity]=Table[
+ eqsht={vars[[shtdInd]][eqsRga[[1]]]==(varshta[[i]])};
+ eqsht=Join[eqs,eqsht];
+ varsa=vars/.Flatten[NDSolve[eqsht,vars,{Global`r,eqsRga[[1]],eqsRga[[2]]},AccuracyGoal->15,PrecisionGoal->15,WorkingPrecision->30,MaxSteps->Infinity]];
+ dom=InterpolationDomain[varsa[[1]]][[1]];
+ (*If[dom[[2]]<eqsRga[[2]],eqsRga[[2]]=Rationalize[0.9*eqsRga[[2]],1];If[verbose,Print[Style[" Breakup found. Changing rfin to ",Red],eqsRga[[2]]] ];Goto[begin];];*)
+ Sh\[Infinity]m=varsa[[shtdInd]]@dom[[2]]
+ ,{i,3}];
+Sh\[Infinity]m=Sh\[Infinity][[3]];
+Sh0m=varshta[[3]];
+posref=Position[{Abs[Sh\[Infinity][[1]]],Abs[Sh\[Infinity][[2]]]},_?(#==Min[{Abs[Sh\[Infinity][[1]]],Abs[Sh\[Infinity][[2]]]}] &)][[1]];
+Sh\[Infinity]m2=Sh\[Infinity][[posref]][[1]];
+Sh0m2=varshtdRga[[posref]];
+Sh0ref=Flatten[{Sh0m,Sh0m2}];
+mean=Mean[Sh0ref];
+
+(* Starts the shooting loop. *)
+If[verbose,Print["Output: vars, a, "<>ShtStr<>" variable at \[Infinity], Error"]];
+If[verbose,Print["Intermediate prints: iteration, "<>ShtStr<>" at \[Infinity], Error"]];
+
+While[ Abs[Sh\[Infinity]m]>assval &&Abs[1-Sh\[Infinity]m/Sh\[Infinity]m2]>tol && Length@posref>0 && a<= amax,
+a=a+1;
+If[verbose,Print[{a,Round[mean,10^-16],varsa[[shtdInd]]@dom[[2]],Abs[1-Sh\[Infinity]m/Sh\[Infinity]m2]}]];
+eqsht={vars[[shtdInd]][eqsRga[[1]]]==mean};
+eqsht=Join[eqs,eqsht];
+varsa=vars/.Flatten[NDSolve[eqsht,vars,{Global`r,eqsRga[[1]],eqsRga[[2]]},
+AccuracyGoal->15,PrecisionGoal->15,WorkingPrecision->30,MaxSteps->Infinity]];
+(*If[dom[[2]]<eqsRga[[2]],eqsRga[[2]]=Rationalize[0.9*eqsRga[[2]],1];If[verbose,Print[Style[" Breakup found. Changing rfin to ",Red],eqsRga[[2]] ]];Goto[begin];];*)
+dom=InterpolationDomain[varsa[[1]]][[1]];
+Which[assymptotic=="Exponential"&&dom[[2]]==eqsRga[[2]],
+ Rs=0.95(r/.FindRoot[varsa[[1]]@r,{r,6}]);datab=Table[{r,varsa[[shtdInd]]@r},{r,Rs,dom[[2]],0.01}];
+ y1=varsa[[shtdInd]]@Rs;y2=(D[varsa[[shtdInd]]@r,r]/.r->Rs);m=(-y1-Rs^2 y2)/(Rs y1);a0= y1;
+ datfit=NonlinearModelFit[datab,A3 + a0 Exp[-r m],{A3},r];Print[{a0,m,datfit["BestFitParameters"]}]];
+
+posreftest=Quiet@Position[{Abs[Sh\[Infinity]m],Abs[varsa[[shtdInd]]@dom[[2]]]},_?(#==Min[{Abs@Sh\[Infinity]m,Abs[varsa[[shtdInd]]@dom[[2]]]}] &)];
+If[Length@posreftest>0,posref=posreftest[[1]],posref={};];
+Sh0ref={mean,Sh0ref[[posref]][[1]]};
+mean=Mean[Sh0ref];
+Sh\[Infinity]m2={Sh\[Infinity]m,Sh\[Infinity]m2}[[posref[[1]]]];
+Sh\[Infinity]m=varsa[[shtdInd]]@dom[[2]];
+];
+If[verbose,Print["Output: vars, a, Shooted variable at \[Infinity]"]];
+out=Join[varsa,{a,Round[mean,10^-8],Sh\[Infinity]m}];
+Return[out]
+]
+
+
+ComputeEdges[pts_]:=Module[{ptsx,auxvar,auxvar2,nears,i},
+ptsx=SortBy[pts,First];
+auxvar={};
+i=1;
+AppendTo[auxvar,{ptsx[[i]]}];
+While[i<= Length@ptsx-1,
+If[ptsx[[i+1,1]]==ptsx[[i,1]],i=i+1,AppendTo[auxvar,{ptsx[[i]]}];i=i+1]
+];
+AppendTo[auxvar,{ptsx[[i]]}];
+auxvar=Flatten[auxvar,1];
+
+i=Length@ptsx-1;
+While[i> 1,
+If[ptsx[[i+1,1]]==ptsx[[i,1]],i=i-1,AppendTo[auxvar,ptsx[[i+1]]];i=i-1]
+];
+AppendTo[auxvar,ptsx[[i]]];
+Do[auxvar=AppendTo[auxvar,0.5auxvar[[1]]+0.5auxvar[[-1]]],{i,3}];
+auxvar
+]
+
+
+CredibleRegion[data_,level_]:=Module[{datasrt,prob,cumprob,pbound},
+(* Last column must be the PDF *)
+datasrt=SortBy[data,Last];
+prob=TakeColumn[datasrt,-1];
+cumprob=Accumulate[prob];
+
+pbound=Quiet@Position[cumprob,_?(#>= (1-level) cumprob[[-1]]& ),1][[1,1]];
+
+ComputeEdges[datasrt[[pbound-1;;-1]]][[All,1;;-2]]
+]
+
+
+LoveNumber[eos_,mtot_]:=Module[{y,r,p,\[Epsilon],m,eqy,\[CapitalGamma],eqsGR,listeos,yy,zz,eqEoS,\[Rho]int,pint,rin,\[Rho]c,pc,eqsIC,rMax,alleqs,alleqsnd,Pr,mr,yr,Rm,Mm,Cc,G,c,m0,rg,P0,\[Rho]0,R0},
+
+G=6.67428 10^-8;
+c=2.99792458 10^10;
+m0=1.989 10^33;
+rg= G m0/c^2;
+P0=m0 c^2/rg^3;
+\[Rho]0=m0/rg^3;
+R0=1/rg^2;
+
+eqEoS={p[r]==(10^EoSFits[eos]/.\[Rho]->Log[10,\[Rho]0 \[Rho][r]])/P0};
+listeos=Table[{(EoSFits[eos]/.\[Rho]->x),(From\[Rho]To\[Epsilon]Fits[eos]/.\[Rho]->10^x)},{x,1,16,0.01}];
+\[Rho]int=Interpolation[listeos/.{yy_,zz_}->{(10^yy)/P0,(zz)/( \[Rho]0)}];
+pint=Interpolation[listeos/.{yy_,zz_}->{(zz)/( \[Rho]0),(10^yy)/P0}];
+
+(* Equations 1-2 GR ToVs. Equation 3 k2 eq. *)
+eqsGR={((m[r]+4 \[Pi] r^3 p[r]) (p[r]+\[Rho][r]))/(r^2-2 r m[r])+Derivative[1][p][r]==0,4 \[Pi] r^2 \[Rho][r]-Derivative[1][m][r]==0};
+eqy={y'[r]==-(y[r]^2/r)-(r+4\[Pi] r^3 (p[r]-\[Rho][r]))/(r(r-2m[r])) y[r]+(4(m[r] +4\[Pi] r^3 p[r])^2)/(r(r-2m[r]))+6/(r-2m[r])-(4\[Pi] r^2)/(r-2m[r]) (5\[Rho][r]+9p[r]+(\[Rho][r] +p[r])/D[pint@\[Rho][r],\[Rho][r]])};
+alleqs=Join[eqsGR,eqy];
+
+(* --------*)
+
+(* Solve the system *)
+\[Rho]c=\[Rho]max[[1]]0.76;
+rin=10^-5;
+pc=eqEoS[[1,2]]/.\[Rho][r]->\[Rho]c;
+
+eqsIC={p[rin]==pc,m[rin]==0,y[rin]==2,WhenEvent[p[r]/pc<10^(-12),rMax=r;"StopIntegration"]};
+alleqsnd=alleqs/.\[Rho][r]->\[Rho]int[p[r]]/.p[r]->Max[p[r],0];
+{Pr,mr,yr}={p,m,y}/.Flatten[NDSolve[Flatten@Join[alleqsnd,Join[eqsIC]],{p,m,y},{r,rin,100},Method->{"ExplicitRungeKutta","DifferenceOrder"->8},AccuracyGoal->16,PrecisionGoal->13]];
+Rm=InterpolationDomain[Pr][[2]];
+Mm=(mr@Rm);
+Cc=Mm/(Rm);
+
+(2/3((c^2/G)(rg Rm)/(Mm*m0))^5)k2[Cc,yr[Rm]]
+
+];
+
+
+k2[c_,y_]:=(8 c^5)/5 (1-2c)^2(2+2c(y-1)-y)(2c(6-3y +3c(5y-8))+4c^3(13-11y+c(3y-2)+2c^2(1+y))
++3(1-2c)^2(2-y+2c(y-1))Log[1-2c])^(-1)
+
+
+(* ::Code::Initialization:: *)
+AtomsList[expr_]:=Union@Select[Level[expr,{0,Infinity}],AtomQ];
+InterpolationDomain[fun_]:=Module[{min,max},fun[[1]]];
+TakeColumn[list1_?ListQ,list2_?ListQ]:=Map[Part[#,list2]&,list1];
+TakeColumn[list1_?ListQ,n_?IntegerQ]:=(list1//Transpose)[[n]];
+
+
+(* ::Code::Initialization:: *)
+End[];
+EndPackage[];
+
+
+Options[RiemannTensorDev2]=Join[Options[ChristoffelSymbolDev],{"IndexDown"->False}];
+RiemannTensorDev2[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{n,Chr,compile,index,res,perti,simpl,verbose},
+index=OptionValue["IndexDown"];
+perti=OptionValue["PerturbationIndex"];
+simpl=OptionValue["SimplifyFunction"];
+compile=OptionValue["Compile"];
+verbose=OptionValue["Verbose"];
+
+n=Length@xx;
+If[verbose,Print["Starting with Christoffel symbols..."]];
+Chr=ChristoffelSymbolDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl,"Compile"->False];
+If[verbose,Print["Christoffel symbols computed. Starting with Riemann..."]];
+
+res=ConstantArray[0,{n,n,n,n}];
+If[index,
+ If[NumericQ[pert], Do[res[[i,k,l,m]]=Sum[g[[i,p]](D[Chr[[p,k,m]],xx[[l]]]-D[Chr[[p,k,l]],xx[[m]]]+Sum[Chr[[p,s,l]]*Chr[[s,k,m]]-Chr[[p,s,m]]*Chr[[s,k,l]],{s,n}]),{p,n}],{i,n},{k,n},{l,n},{m,n}],
+ Do[res[[i,k,l,m]]=Sum[g[[i,p]](Normal@Series[D[Chr[[p,k,m]],xx[[l]]]-D[Chr[[p,k,l]],xx[[m]]]+Sum[Chr[[p,s,l]]*Chr[[s,k,m]],{s,n}]-Sum[Chr[[p,s,m]]*Chr[[s,k,l]],{s,n}],{pert,0,perti}]),{p,n}],{i,n},{k,n},{l,n},{m,n}]];
+
+ If[compile, Do[res[[i,k,l,m]]=If[NumberQ[res[[i,k,l,m]]],res[[i,k,l,m]],Compile[Evaluate@({#,_Real}&/@xx),Evaluate[res[[i,k,l,m]]],CompilationTarget->"C",CompilationOptions->"InlineExternalDefinitions"->True]],{i,n},{k,n},{l,n},{m,n}];];
+ (* Applying simmetries *)
+ ,
+ If[NumericQ[pert], Do[res[[i,k,l,m]]=(D[Chr[[i,k,m]],xx[[l]]]-D[Chr[[i,k,l]],xx[[m]]]+Sum[Chr[[i,s,l]]*Chr[[s,k,m]]-Chr[[i,s,m]]*Chr[[s,k,l]],{s,n}]),{i,n},{k,n},{l,n},{m,n}],
+ Do[res[[i,k,l,m]]=(Normal@Series[D[Chr[[i,k,m]],xx[[l]]]-D[Chr[[i,k,l]],xx[[m]]]+Sum[Chr[[i,s,l]]*Chr[[s,k,m]],{s,n}]-Sum[Chr[[i,s,m]]*Chr[[s,k,l]],{s,n}],{pert,0,perti}]),{i,n},{k,n},{l,n},{m,n}]];
+ ];
+
+
+If[verbose,Print["...Riemann computed"]];
+simpl@res];
+
+
+Options[RicciTensorDev]=Options[ChristoffelSymbolDev];
+RicciTensorDev[xx_,g_,pert_:0,OptionsPattern[]]:=Block[{compile,Rie,res,n,perti,simpl},
+perti=OptionValue["PerturbationIndex"];
+compile=OptionValue["Compile"];
+simpl=OptionValue["SimplifyFunction"];
+
+n=Length@xx;
+Rie=RiemannTensorDev[xx,g,pert,"PerturbationIndex"->perti,"SimplifyFunction"->simpl];
+
+res=ConstantArray[0,{n,n}];
+If[NumericQ[pert], Do[res[[i,j]]=Sum[Rie[[s,i,s,j]],{s,n}],{i,n},{j,n}],
+ Do[res[[i,j]]=Normal@Series[Sum[Rie[[s,i,s,j]],{s,n}],{pert,0,perti}],{i,n},{j,i,n}]];
+
+If[compile, Do[res[[i,j]]=If[NumberQ[res[[i,j]]],res[[i,j]],Compile[Evaluate@({#,_Real}&/@xx),Evaluate[res[[i,j]]],CompilationTarget->"C",CompilationOptions->"InlineExternalDefinitions"->True]],{i,n},{j,i,n}];] ;
+(* Applying symmetries *)
+Do[res[[i+1,j]]=res[[j,i+1]];,{i,n-1},{j,i}];
+
+simpl@res]
+
+
+
diff --git a/code/GRTensor.nb b/code/GRTensor.nb
new file mode 100644
index 0000000000000000000000000000000000000000..b5af1945cfdfa497fb3b32e629809fcea8fcaf02
--- /dev/null
+++ b/code/GRTensor.nb
@@ -0,0 +1,41811 @@
+(* Content-type: application/vnd.wolfram.mathematica *)
+
+(*** Wolfram Notebook File ***)
+(* http://www.wolfram.com/nb *)
+
+(* CreatedBy='Mathematica 11.3' *)
+
+(*CacheID: 234*)
+(* Internal cache information:
+NotebookFileLineBreakTest
+NotebookFileLineBreakTest
+NotebookDataPosition[ 158, 7]
+NotebookDataLength[ 1798327, 41803]
+NotebookOptionsPosition[ 1718831, 40553]
+NotebookOutlinePosition[ 1719426, 40575]
+CellTagsIndexPosition[ 1719335, 40570]
+WindowFrame->Normal*)
+
+(* Beginning of Notebook Content *)
+Notebook[{
+
+Cell[CellGroupData[{
+Cell["BGR Tensor", "Title",
+ CellChangeTimes->{{3.747969475841448*^9, 3.747969478495125*^9},
+ 3.7479695552006407`*^9},ExpressionUUID->"412e446d-949d-4a39-ab8f-\
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+Cell["XJ 2018", "Subtitle",
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+
+Cell["\<\
+Provide functions to compute tensor-related quantities in GR and BGR:\
+\>", "Subsubtitle",
+ CellChangeTimes->{{3.5230204030134068`*^9, 3.523020425030308*^9}, {
+ 3.5230265395509644`*^9, 3.523026547108094*^9}, {3.747969524970929*^9,
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+Cell[CellGroupData[{
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+Cell["Compute Christoffel, Riemann,Ricci, KrScalar.. ", "Item",
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+Cell["Equations for FR and scalar-tensor.", "Item",
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+Cell["TODO: Improve and improve", "Text",
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+Cell[CellGroupData[{
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+Cell["\<\
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+\>", "Item",
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+ RowBox[{
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+ "\"\<WeylTensor[coords_,g_,pert_:0]. Compute Weyl tensor following the \
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+ RowBox[{
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+ RowBox[{
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+ "\"\<Einstein[coords_,g_,\[Epsilon]p:]. Compute Einstein tensor following \
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+ "\"\<CovDer[coords_,metric_,tensor_,comps_]. Compute the covariant \
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+ "\"\<LeviCivitaTensorCurv[coords_,g_]. Compute the Levi-Civita \
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