HPC_YZ_gamma.wl

(* ::Package:: *)

(* ::Subsection:: *)
(*Setup:*)


ClearAll["`*"]


(* Arguements 1, 2 ,3 and 4 correspond to math -nopromt- script codename *) 
(* Every input after that is for code configuration *)


LPA=0;


inputs = {5, 6, 7, 8, 9, 10, 11}
{Ncores, Ns, dim, uor, yor, zsor} = Rationalize[Chop[$CommandLine[[#]]]]& /@ inputs
LaunchKernels[Ncores];
dims=$CommandLine[[7]];


(* Code below is for local implementation *)
(*ClearAll["`*"]
SetDirectory["/Users/gregoryjohnson/Desktop/Code/Projects/FRG_main"]
Ns=2; dim=3;
uor=5; yor=1; zsor=2;
dims=3;
Ncores=8;*)


(* ::Subsubsection::Closed:: *)
(*Generate File Names:*)


(* ::Input:: *)
(*(* Theory and Truncation String *)*)


TheoryString = StringJoin[ ToString /@ {"N_", N\[Phi]s, "_d_", dims, "_a_", as, "_Uor_", uor, "_Yor_", yor, "_Zsor_", zsor}];
TheoryString = StringReplace[ TheoryString, {"."->"p", "-"->"m"}];
TheoryString = StringJoin[ TheoryString, ".wl"];


FileNameImportRGeqns = StringJoin[{"RGeqns_",TheoryString}];
FileNameImport\[Phi]RGeqns = StringJoin[{"phi_RGeqns_",TheoryString}];
FileNameImportFPdata = StringJoin[{"FPdata_",TheoryString}];
FileNameOutputCryWF = StringJoin[{"WFCriticalDataYLE_",ToString[Ns],TheoryString}];


(* ::Subsubsection::Closed:: *)
(*Import FRG:*)


Print["Just before FRG Import"]


Import[FileNameJoin[{Directory[],"Packages/ONvars_YZ.wl"}]]
Import[FileNameJoin[{Directory[], "RGeqns/ON_YLE_flow/", FileNameImportRGeqns}]];
Import[FileNameJoin[{Directory[],"FPData/ON_YLE_flow/", FileNameImportFPdata}]];


FPIntNap5=Cases[FPIntNap5,{_Integer,__}] //NumericalSort;


apmsINTdata=Table[{i,1/2},{i,1,10}]
(* \[Eta]pms vs \[CapitalDelta]pms *)
(* Turn for \[CapitalDelta]pms - remove line for \[Eta]pms *)
(*apmsINTdata=apms\[CapitalDelta]Data*)
(* Turn for Hcpms - remove line for \[Eta]pms *)
(*apmsINTdata=HcPMSData*)


(* ::Subsection::Closed:: *)
(*Solvers:*)


Print["Just before Solvers"]


(* ::Subsubsection::Closed:: *)
(*IC Finder from FP:*)


(* ::Item:: *)
(*Construct fixed point solver. Use \[Alpha]=1/2 solution for initial conditions to recompute the solution for whatever \[Alpha] value the code may need.*)


(* ::Item:: *)
(*Detail the initial condition function*)


(* ::Item:: *)
(*Do i use fixed mass or fixed renormalized mass*)


WFSolver[uo_, zo_, yo_?NumericQ, Ms_, as_, wp_, prec_ ]:=Module[{(*Guess,*)VarInit,VarS}, 
VarInit=Drop[Table[{VarList[[i]],Guess[[i]]},{i,1,Length[VarList]}],{2}];
VarS=FindRoot[Table[(\[Beta]FYLE2[index,dim,VarList, \[Eta]Fys2[dim,VarList,Ms,as],Ms,as]/. Subscript[u, 1]->-2 \[Rho] Subscript[u, 2])==0,{index,1,Length[VarList]-1}], VarInit,
WorkingPrecision->wp,PrecisionGoal->prec,AccuracyGoal->prec,MaxIterations->1 10^3];
Guess=VarList /. VarS;
VarS
]


InitialConditionsFunc[\[Delta]t_?NumericQ,m2_?NumericQ, Ms_(*, as_*),wp_,prec_]:=
Module[{EqPrep,Rho0,InitialC,Initial,rhofp,EqPrepZs,EqPrepY,R,PotentialNearYLE,InitialZs, InitialY, VarS, as},

(* Finding fixed point PMS solution for N at given truncation using PMS alpha values*)
Guess=SetPrecision[VarList /.FPIntNap5[[Ms,3]], 100]; 
as=SetPrecision[apmsINTdata[[Ms,2]],150];
VarS=WFSolver[uor, yor, zsor, Ms, as, 100, 100];

(* Add in thermal perturbation and re-expand functions about field value with fixed mass of m2 *)
(* Return the set of initial conditions for the flows *)
PotentialNearYLE=Sum[((R-\[Rho])^i Subscript[u, i])/i!,{i,1,uor}]//.Subscript[u, 1]->-2 \[Rho] Subscript[u, 2]/.VarS//Expand;
rhofp=\[Rho]/.VarS;
EqPrep=PotentialNearYLE + \[Delta]t R;
EqPrepY=Sum[Subscript[y, i](R-\[Rho])^i/(i!),{i,0,yor}] /.VarS;
EqPrepZs=Sum[Subscript[zs, i](R-\[Rho])^i/(i!),{i,0,zsor}] /.VarS;
Rho0=R/.NSolve[D[EqPrep,R]+2 R D[EqPrep,{R,2}]==m2 && rhofp/5<R<rhofp*5, R, Reals, WorkingPrecision->wp][[1]];
InitialC=Table[Subscript[u, i][0]==D[EqPrep,{R,i}]/.R->Rho0,{i,2,uor}];
InitialY=Table[Subscript[y, i][0]==D[EqPrepY,{R,i}]/.R->Rho0,{i,0,yor}];
InitialZs=Table[Subscript[zs, i][0]==D[EqPrepZs,{R,i}]/.R->Rho0,{i,1,zsor}];
Initial=If[LPA==1,
	Flatten[Join[{\[Rho][0]==Rho0}, InitialC ]],
	Flatten[Join[{\[Rho][0]==Rho0}, InitialC, InitialY, InitialZs]]];
Initial
]


(* ::Subsubsection::Closed:: *)
(*YLE Solver 2 WF:*)


YLESolver2[t0_, rin_, m_, dim_, wp_, prec_, Ms_]:=Module[{d,Vars, Varsoft,ReducedVars,ReducedVarsoft,SetVariables, BSOE,IV,tm, as},

(* t0 is IR cutoff, rin is thermal perturbation, m is mass perturbation m=Subscript[m, s]^2, dim is dimension, wp and prec are precisions, Ms is Number of field components *)

Off[NIntegrate::precw]; Off[NDSolve::precw];
Vars=VarList;
Varsoft=Table[VarList[[i]][t],{i,1,Length[VarList]}] ;
SetVariables=Table[Vars[[i]]-> Varsoft[[i]],{i,1,Length[Vars]}];
d=dim;

ReducedVars=Drop[Vars,{2}];
ReducedVarsoft=Drop[Varsoft,{2}];

BSOE=Join[Table[D[ ReducedVarsoft[[i]],t]==(\[Beta]FYLE2[i,d, Vars, \[Eta]Fys2[d,Vars,Ms,as],Ms,as] /. SetVariables),{i,1,Length[ReducedVarsoft]}],
{Z'[t]==-(\[Eta]Fys2[d,Vars,Ms,as]/. SetVariables) Z[t]}] /. {Subscript[u, 1][t] -> m Exp[-2t] -2 \[Rho][t] Subscript[u, 2][t]};

If[Ms==1, If[LPA==0, BSOE=Drop[BSOE,{uor+1,uor+1+yor}]]]; (* At N=1, flows for Y decople. So, drops these flows as they are unneeded *)

(*If[LPA==1,ReducedVars=ReducedVars, 
ReducedVars=Drop[ReducedVars,{-1-(yor)}];
BSOE=Drop[BSOE,{-1-(yor+1)}];];
ReducedVarsoft=Table[ReducedVars[[i]][t],{i,1,Length[ReducedVars]}];*)

tm=0;
as=SetPrecision[apmsINTdata[[Ms,2]],150];
IV=Join[InitialConditionsFunc[rin,m, Ms, 100, 100],{Z[tm]==1}];
Broken=NDSolve[ {BSOE, IV}, 
Join[ReducedVars,{Z}], {t, tm, t0} ,WorkingPrecision->wp,PrecisionGoal-> prec, AccuracyGoal->prec, Method->{"StiffnessSwitching" ,"EquationSimplification"->"Solve"} ,
MaxSteps-> 2 10^3
]
];


(* ::Subsection::Closed:: *)
(*Computing critical data related to gamma scaling form:*)


Off[Precision::precsm,FittedModel::precw,NonlinearModelFit::precw,FindRoot::precw, NDSolve::ndsz]
ParallelEvaluate[Off[Precision::precsm,FittedModel::precw,NonlinearModelFit::precw,FindRoot::precw,NDSolve::ndsz]];


Off[N::precsm,NumericalMath`LowerPrecision::precsm]


(* ::Subsubsection::Closed:: *)
(*Computing \[Gamma] Flows:*)


(* ::Item:: *)
(*import delta scaling parameters as they are needed for associated corrections to scaling*)


(* ::Item:: *)
(*import mdata (mc data) from relevant file - needed to compute flows which determine \[Gamma] and SuperPlus[Subscript[C, 2]].*)


(* ::Item:: *)
(*Computes higher order amplitudes SuperPlus[Subscript[C, 2n]] for later use. Not used further here though.*)


Print["Importing mc Data"]


(*Import[FileNameJoin[{Directory[], "CritData_eta/", FileNameOutputCryWF}]];*)
Import[FileNameJoin[{Directory[], "CritData_delta/", FileNameOutputCryWF}]];
(*Import[FileNameJoin[{Directory[], "CritData_Hc/", FileNameOutputCryWF}]];*)


Print["Just before gamma data"]


si=If[Ns==2, -9, -10]; sf=-8; ss=(sf-si)/((*2*) Ncores-1);
srange=Table[i,{i,si,sf,ss}];
t0=-40;


wp=60; prec=wp/2;
(*wp=100; prec=wp/2;*)
$MinPrecision=prec;
ParallelEvaluate[$MinPrecision=prec];
v=0;


(*mcTestTot=SetPrecision[McColl[[-1,-1]],wp]*)
(*mcTestTot=If[Length[McColl]>1, SetPrecision[McColl[[-1,-1]],wp],SetPrecision[McColl[[-1]],wp]]*)
mcTestTot=SetPrecision[McColl[[-1]],wp] (*//Reverse*)


t\[Eta]=-5;
mdata=Table[(*m /.*) mcTestTot[[i,2]],{i,1,Length[mcTestTot]}];
mdata=SetPrecision[mdata,wp]


{time,\[Nu]\[Gamma]Data}=ParallelTable[{si+i ss,Log[E^t0 Sqrt[Subscript[u, 1][t0]+2 \[Rho][t0] Subscript[u, 2][t0]]]/Log[10],
Log[E^(2 t0) Z[t0] (Subscript[u, 1][t0]+2 \[Rho][t0] Subscript[u, 2][t0])]/Log[10],
Log[(3 (E^t0)^(-4-dim) Subscript[u, 2][t0])/(Z[t0]^2 Subscript[u, 1][t0]^4)]/Log[10],
Log[((E^t0)^(-6-2 dim) (90 Subscript[u, 2][t0]^2-15 Subscript[u, 1][t0] Subscript[u, 3][t0]))/(Z[t0]^3 Subscript[u, 1][t0]^7)]/Log[10],
Log[(105 (E^t0)^(-8-3 dim) (72 Subscript[u, 2][t0]^3-24 Subscript[u, 1][t0] Subscript[u, 2][t0] Subscript[u, 3][t0]+Subscript[u, 1][t0]^2 Subscript[u, 4][t0]))/(Z[t0]^4 Subscript[u, 1][t0]^10)]/Log[10],
Log[(945 (E^t0)^(-10-4 dim) (1320 Subscript[u, 2][t0]^4-660 Subscript[u, 1][t0] Subscript[u, 2][t0]^2 Subscript[u, 3][t0]+40 Subscript[u, 1][t0]^2 Subscript[u, 2][t0] Subscript[u, 4][t0]+Subscript[u, 1][t0]^2 (30 Subscript[u, 3][t0]^2-Subscript[u, 1][t0] Subscript[u, 5][t0])))/(Z[t0]^5 Subscript[u, 1][t0]^13)]/Log[10],
-Z'[t\[Eta]]/Z[t\[Eta]],
Sqrt[2] E^(1/2 (2+dim) t0) Sqrt[Z[t0]] Sqrt[\[Rho][t0]] Subscript[u, 1][t0]}
/. Subscript[u, 1][t_]->(E^(-2 t) mdata[[i+1]])(*/Z[t]*)-2 \[Rho][t] Subscript[u, 2][t]  
/. YLESolver2[t0, 10^(si+i ss), mdata[[i+1]], dim, wp, prec, Ns][[1]],{i,0,Length[srange]-1} ] //AbsoluteTiming;
Print["nutime=",time]


hData=Table[\[Nu]\[Gamma]Data[[i,9]],{i,1,Length[\[Nu]\[Gamma]Data]}];
\[Nu]Data=Table[{\[Nu]\[Gamma]Data[[i,1]],\[Nu]\[Gamma]Data[[i,2]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
\[Gamma]Data=Table[{\[Nu]\[Gamma]Data[[i,1]],\[Nu]\[Gamma]Data[[i,3]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
\[Gamma]4Data=Table[{\[Nu]\[Gamma]Data[[i,1]],\[Nu]\[Gamma]Data[[i,4]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
\[Gamma]6Data=Table[{\[Nu]\[Gamma]Data[[i,1]],\[Nu]\[Gamma]Data[[i,5]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
\[Gamma]8Data=Table[{\[Nu]\[Gamma]Data[[i,1]],\[Nu]\[Gamma]Data[[i,6]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
\[Gamma]10Data=Table[{\[Nu]\[Gamma]Data[[i,1]],\[Nu]\[Gamma]Data[[i,7]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
\[Eta]FData=Table[{\[Nu]\[Gamma]Data[[i,8]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
\[Eta]f=\[Eta]FData[[1]];


ErrorTab=(ParallelTable[10^(2 s),{s,si,sf,ss}] -Abs[hData])/ParallelTable[10^(2 s),{s,si,sf,ss}] // Log10[Abs[#]]&;
Print[ErrorTab ]


Corr\[Gamma]Data=Table[{\[Nu]\[Gamma]Data[[i,1]],Log10[Abs[\[Nu]\[Gamma]Data[[i,9]]]], \[Nu]\[Gamma]Data[[i,3]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
Corr\[Nu]Data=Table[{\[Nu]\[Gamma]Data[[i,1]],Log10[Abs[\[Nu]\[Gamma]Data[[i,9]]]], \[Nu]\[Gamma]Data[[i,2]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
Corr\[Gamma]4Data=Table[{\[Nu]\[Gamma]Data[[i,1]],Log10[Abs[\[Nu]\[Gamma]Data[[i,9]]]],\[Nu]\[Gamma]Data[[i,4]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
Corr\[Gamma]6Data=Table[{\[Nu]\[Gamma]Data[[i,1]],Log10[Abs[\[Nu]\[Gamma]Data[[i,9]]]],\[Nu]\[Gamma]Data[[i,5]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
Corr\[Gamma]8Data=Table[{\[Nu]\[Gamma]Data[[i,1]],Log10[Abs[\[Nu]\[Gamma]Data[[i,9]]]],\[Nu]\[Gamma]Data[[i,6]]},{i,1,Length[\[Nu]\[Gamma]Data]}];
Corr\[Gamma]10Data=Table[{\[Nu]\[Gamma]Data[[i,1]],Log10[Abs[\[Nu]\[Gamma]Data[[i,9]]]],\[Nu]\[Gamma]Data[[i,7]]},{i,1,Length[\[Nu]\[Gamma]Data]}];


(* ::Subsubsection::Closed:: *)
(*Gamma:*)


Off[N::precsm,NumericalMath`LowerPrecision::precsm]


Clear[\[Gamma],Cp0];
FitG2=NonlinearModelFit[(*({#[[1]],-Abs[#[[2]]]}&/@ \[Gamma]Data[[1;;-1]])*)\[Gamma]Data[[1;;-1]],\[Gamma]0*x-Log10[Cp0],{\[Gamma]0,{Cp0,10^-4}},x,
PrecisionGoal->prec, AccuracyGoal->prec, WorkingPrecision->wp, MaxIterations->10000];
(*Export["gammaplot.jpg",Show[Plot[FitG[x],{x,si-1,sf+1}], ListPlot[\[Gamma]Data] ] ];*)
(*FitG2["ParameterConfidenceIntervalTable"]*)
\[Gamma]=\[Gamma]0/.FitG2["BestFitParameters"];
Cp=Cp0/.FitG2["BestFitParameters"];


\[Beta]=SetPrecision[\[Gamma]/(\[Delta]-1),wp] /. \[Delta]->5;
\[CapitalDelta]=SetPrecision[\[Beta] \[Delta],wp]/. \[Delta]->5;


FitG2=NonlinearModelFit[\[Gamma]Data[[1;;-1]],\[Gamma]1*x-Log10[Cp0]-Log10[1 + g 10^(t x)],{{\[Gamma]1,\[Gamma]},{Cp0,Cp},{g,0},{t,1/2}},x,
PrecisionGoal->prec, AccuracyGoal->prec, WorkingPrecision->wp, MaxIterations->10000];
(*Export["gammaplot.jpg",Show[Plot[FitG[x],{x,si-1,sf+1}], ListPlot[\[Gamma]Data] ] ];*)
(*FitG2["ParameterConfidenceIntervalTable"]*)
\[Gamma]=\[Gamma]1/.FitG2["BestFitParameters"];
Cp=Cp0/.FitG2["BestFitParameters"];
\[Theta]\[Gamma]=t/.FitG2["BestFitParameters"];
g2=g/.FitG2["BestFitParameters"];


FitG2=NonlinearModelFit[(*Corr*)\[Gamma]Data,\[Gamma]1*x - Log10[Cp0]-Log10[1 + g 10^(t x)+g1 10^(2 t x)],{{\[Gamma]1,\[Gamma]},{Cp0,Cp},{g,0},{t,4/10},{g1,0}},x, 
PrecisionGoal->prec, AccuracyGoal->prec, WorkingPrecision->wp, MaxIterations->10^5];
(*FitG2["ParameterConfidenceIntervalTable"]*)
\[Gamma]=\[Gamma]1/.FitG2["BestFitParameters"];
Cp=Cp0/.FitG2["BestFitParameters"];
\[Theta]\[Gamma]=t/.FitG2["BestFitParameters"];
g2=g/.FitG2["BestFitParameters"];
g4=g1/.FitG2["BestFitParameters"];


(*FitG2["ParameterConfidenceIntervalTable"]*)


(*FitG2=NonlinearModelFit[Corr\[Gamma]Data[[2;;-1]],\[Gamma]1*x - Log10[Cp0]-Log10[1+f (10^ y 10^(- \[CapitalDelta]0 x))^2+ g2 10^(t x)],{{\[Gamma]1,\[Gamma]},{Cp0,Cp},{g,g2},{t,\[Theta]\[Gamma]},{f,0}, {\[CapitalDelta]0,\[CapitalDelta]}},{x,y}, 
PrecisionGoal->prec, AccuracyGoal->prec, WorkingPrecision->wp, MaxIterations->10^4];
FitG2["ParameterConfidenceIntervalTable"]
\[Gamma]=\[Gamma]1/.FitG2["BestFitParameters"];
Cp=Cp0/.FitG2["BestFitParameters"];
\[Theta]\[Gamma]=t/.FitG2["BestFitParameters"];
g2=g/.FitG2["BestFitParameters"];
f0=f/.FitG2["BestFitParameters"];
f20=f2 /.FitG2["BestFitParameters"];
NumberForm[dt Hc^((1-\[Delta])/(\[Gamma] \[Delta])) (Bc/Cp)^(1/\[Gamma]),5]*)


(* ::Subsection::Closed:: *)
(*Saving:*)


FileNameOutputCryWF


aspms=apmsINTdata[[Ns,2]];
Print[aspms]


DataColl={wp, time, aspms, mdata, ErrorTab, \[Nu]\[Gamma]Data};


(*Save[FileNameJoin[{Directory[], "CritData_eta/", FileNameOutputCryWF}], DataColl]
Save[FileNameJoin[{Directory[], "CritData_eta/", FileNameOutputCryWF}], {\[Gamma], Cp, \[Theta]\[Gamma], g2, g4}]*)


Save[FileNameJoin[{Directory[], "CritData_delta/", FileNameOutputCryWF}], DataColl]
Save[FileNameJoin[{Directory[], "CritData_delta/", FileNameOutputCryWF}], {\[Gamma], Cp, \[Theta]\[Gamma], g2, g4}]


(*Save[FileNameJoin[{Directory[], "CritData_Hc/", FileNameOutputCryWF}], DataColl]
Save[FileNameJoin[{Directory[], "CritData_Hc/", FileNameOutputCryWF}], {\[Gamma], Cp, \[Theta]\[Gamma], g2, g4}]*)