From 1f6492a166cb543a7e5426c4dff7ef3449eb5cd5 Mon Sep 17 00:00:00 2001
From: Philip-Lynch <phil.lynch25@gmail.com>
Date: Mon, 17 Jul 2023 17:35:54 +0200
Subject: [PATCH] Simplified KerrGeoFourVelocity API by removing index option.
All components are returned in association.
---
Kernel/FourVelocity.m | 114 ++++++++++++++++++++++--------------------
1 file changed, 61 insertions(+), 53 deletions(-)
diff --git a/Kernel/FourVelocity.m b/Kernel/FourVelocity.m
index 88adc1e..dad7e0e 100644
--- a/Kernel/FourVelocity.m
+++ b/Kernel/FourVelocity.m
@@ -17,7 +17,7 @@
Begin["`Private`"];
-(* ::Subsection::Closed:: *)
+(* ::Subsection:: *)
(*Error messages*)
@@ -32,7 +32,7 @@
(*Circular, Equatorial*)
-KerrGeoVelocityMino[(0|0.),p_,(0|0.),x_,initPhases_,index_ ]:= Module[{En,L,Q,r,z,r1,r2,r3,r4,kr,zp,zm,kz, \[CapitalUpsilon]r, \[CapitalUpsilon]z,
+KerrGeoVelocityMino[(0|0.),p_,(0|0.),x_,initPhases_ ]:= Module[{En,L,Q,r,z,r1,r2,r3,r4,kr,zp,zm,kz, \[CapitalUpsilon]r, \[CapitalUpsilon]z,
qr, qz, \[Lambda]local ,qr0, qz0, rprime, zprime, \[CapitalDelta], \[CapitalSigma], \[Omega], utContra,urContra,u\[Theta]Contra,uzContra,u\[Phi]Contra, utCo, urCo, u\[Theta]Co, u\[Phi]Co},
(*Constants of Motion*)
@@ -44,24 +44,21 @@
qz[\[Lambda]_] := \[Lambda] \[CapitalUpsilon]z + qz0;
-If[index == "Contravariant",
+
utContra= Function[{Global`\[Lambda]},Evaluate[Sqrt[p/(-3+p)] ], Listable];
urContra:= Function[{Global`\[Lambda]},Evaluate[0],Listable];
u\[Theta]Contra = Function[{Global`\[Lambda]}, Evaluate[(Sqrt[((1-x^2)/(-3+p))] Sin[qz[Global`\[Lambda]]] )/(p Sqrt[1+(-1+x^2) Cos[qz[Global`\[Lambda]]]^2])],Listable];
-u\[Phi]Contra = Function[{Global`\[Lambda]},Evaluate[x/(Sqrt[-3+p] (p+p (-1+x^2) Cos[qz[Global`\[Lambda]]]^2))],Listable];
-
-<|"\!\(\*SuperscriptBox[\(u\), \(t\)]\)"->utContra, "\!\(\*SuperscriptBox[\(u\), \(r\)]\)"->urContra, "\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"-> u\[Theta]Contra, "\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)"-> u\[Phi]Contra|>,
-
-(*Else if Index \[Equal] Covariant*)
+u\[Phi]Contra = Function[{Global`\[Lambda]},Evaluate[x/(Sqrt[-3+p] (p+p (-1+x^2) Cos[qz[Global`\[Lambda]]]^2))],Listable];
utCo = Function[{Global`\[Lambda]},Evaluate[-En], Listable];
urCo= Function[{Global`\[Lambda]},Evaluate[0],Listable];
u\[Theta]Co= Function[{Global`\[Lambda]},Evaluate[(p Sqrt[(1-x^2)/(-3+p)] Sin[qz[Global`\[Lambda]]])/ Sqrt[1+(-1+x^2) Cos[qz[Global`\[Lambda]]]^2]],Listable];
u\[Phi]Co= Function[{Global`\[Lambda]},Evaluate[L],Listable];
-<|"\!\(\*SubscriptBox[\(u\), \(t\)]\)"->utCo, "\!\(\*SubscriptBox[\(u\), \(r\)]\)"->urCo, "\!\(\*SubscriptBox[\(u\), \(\[Theta]\)]\)"-> u\[Theta]Co, "\!\(\*SubscriptBox[\(u\), \(\[Phi]\)]\)"-> u\[Phi]Co|>
-]
+<|"\!\(\*SuperscriptBox[\(u\), \(t\)]\)"->utContra, "\!\(\*SuperscriptBox[\(u\), \(r\)]\)"->urContra, "\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"-> u\[Theta]Contra, "\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)"-> u\[Phi]Contra,
+"\!\(\*SubscriptBox[\(u\), \(t\)]\)"->utCo, "\!\(\*SubscriptBox[\(u\), \(r\)]\)"->urCo, "\!\(\*SubscriptBox[\(u\), \(\[Theta]\)]\)"-> u\[Theta]Co, "\!\(\*SubscriptBox[\(u\), \(\[Phi]\)]\)"-> u\[Phi]Co|>
+
]
@@ -75,13 +72,13 @@
(*Generic (Mino)*)
-KerrGeoVelocityMino[a_,p_,e_,x_,initPhases_,index_ ]:= Module[{En,L,Q,r,z,r1,r2,r3,r4,kr,zp,zm,kz, \[CapitalUpsilon]r, \[CapitalUpsilon]z,
+KerrGeoVelocityMino[a_,p_,e_,x_,initPhases_]:= Module[{En,L,Q,r,z,r1,r2,r3,r4,kr,zp,zm,kz, \[CapitalUpsilon]r, \[CapitalUpsilon]z,
qr, qz, \[Lambda]local ,qr0, qz0, rprime, zprime, \[CapitalDelta], \[CapitalSigma], \[Omega], utContra,urContra,u\[Theta]Contra,uzContra,u\[Phi]Contra, utCo, urCo, u\[Theta]Co, u\[Phi]Co},
(*Constants of Motion*)
{En,L,Q}= {"\[ScriptCapitalE]","\[ScriptCapitalL]","\[ScriptCapitalQ]"}/.KerrGeoConstantsOfMotion[a,p,e,x];
-{r1,r2,r3,r4}=KerrGeodesics`OrbitalFrequencies`Private`KerrGeoRadialRoots[a, p, e, x];
+{r1,r2,r3,r4}=KerrGeodesics`OrbitalFrequencies`Private`KerrGeoRadialRoots[a, p, e, x,En,Q];
{zp,zm}= KerrGeodesics`OrbitalFrequencies`Private`KerrGeoPolarRoots[a, p, e, x];
@@ -113,52 +110,59 @@
\[Omega][qr_] := Sqrt[r[qr]^2+ a^2];
\[CapitalSigma][qr_,qz_] := r[qr]^2 + a^2 z[qz]^2;
-If[index == "Contravariant",
utContra= Function[{Global`\[Lambda]},Evaluate[1/\[CapitalSigma][qr[Global`\[Lambda]],qz[Global`\[Lambda]]] (\[Omega][qr[Global`\[Lambda]]]^2/\[CapitalDelta][qr[Global`\[Lambda]]] ( \[Omega][qr[Global`\[Lambda] ]]^2 En - a L) - a^2 (1-z[qz[Global`\[Lambda]]]^2)En + a L)], Listable];
urContra:= Function[{Global`\[Lambda]},Evaluate[( rprime[qr[Global`\[Lambda]]] \[CapitalUpsilon]r)/\[CapitalSigma][qr[Global`\[Lambda]],qz[Global`\[Lambda]]]],Listable];
u\[Theta]Contra = Function[{Global`\[Lambda]}, Evaluate[-(\[CapitalUpsilon]z zprime[qz[Global`\[Lambda]]])/(\[CapitalSigma][qr[Global`\[Lambda]],qz[Global`\[Lambda]]]Sqrt[1-z[qz[Global`\[Lambda]]]^2])],Listable];
u\[Phi]Contra = Function[{Global`\[Lambda]},Evaluate[1/\[CapitalSigma][qr[Global`\[Lambda]],qz[Global`\[Lambda]]] (a/\[CapitalDelta][qr[Global`\[Lambda]]] ( \[Omega][qr[Global`\[Lambda]]]^2 En - a L) - a En + L/(1-z[qz[Global`\[Lambda]]]^2))],Listable];
-<|"\!\(\*SuperscriptBox[\(u\), \(t\)]\)"->utContra, "\!\(\*SuperscriptBox[\(u\), \(r\)]\)"->urContra, "\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"-> u\[Theta]Contra, "\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)"-> u\[Phi]Contra|>,
-
-(*Else if Index \[Equal] Covariant*)
utCo = Function[{Global`\[Lambda]},Evaluate[-En], Listable];
urCo= Function[{Global`\[Lambda]},Evaluate[( rprime[qr[Global`\[Lambda]]] \[CapitalUpsilon]r)/\[CapitalDelta][qr[Global`\[Lambda]]]],Listable];
u\[Theta]Co= Function[{Global`\[Lambda]},Evaluate[-((\[CapitalUpsilon]z zprime[qz[Global`\[Lambda]]])/Sqrt[1-z[qz[Global`\[Lambda]]]^2])],Listable];
u\[Phi]Co= Function[{Global`\[Lambda]},Evaluate[L],Listable];
-<|"\!\(\*SubscriptBox[\(u\), \(t\)]\)"->utCo, "\!\(\*SubscriptBox[\(u\), \(r\)]\)"->urCo, "\!\(\*SubscriptBox[\(u\), \(\[Theta]\)]\)"-> u\[Theta]Co, "\!\(\*SubscriptBox[\(u\), \(\[Phi]\)]\)"-> u\[Phi]Co|>
+<|"\!\(\*SuperscriptBox[\(u\), \(t\)]\)"->utContra, "\!\(\*SuperscriptBox[\(u\), \(r\)]\)"->urContra,
+"\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"-> u\[Theta]Contra, "\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)"-> u\[Phi]Contra,
+"\!\(\*SubscriptBox[\(u\), \(t\)]\)"->utCo, "\!\(\*SubscriptBox[\(u\), \(r\)]\)"->urCo,
+"\!\(\*SubscriptBox[\(u\), \(\[Theta]\)]\)"-> u\[Theta]Co, "\!\(\*SubscriptBox[\(u\), \(\[Phi]\)]\)"-> u\[Phi]Co|>
]
-]
-
(* ::Subsection:: *)
(*Equatorial (Darwin)*)
-(* ::Subsubsection::Closed:: *)
+(* ::Subsubsection:: *)
(*Circular Case*)
-KerrGeoVelocityDarwin[a_,p_,(0|0.),x_,initPhases_,index_ ]:= Module[{ut,ur,u\[Theta],u\[Phi], MinoVelocities,ut1,ur1,u\[Theta]1,u\[Phi]1},
+KerrGeoVelocityDarwin[a_,p_,(0|0.),x_,initPhases_]:= Module[{ut,ur,u\[Theta],u\[Phi], MinoVelocities,utContra,urContra,u\[Theta]Contra,u\[Phi]Contra,
+utCo,urCo,u\[Theta]Co,u\[Phi]Co,utUp,urUp,u\[Theta]Up,u\[Phi]Up, utDown,urDown,u\[Theta]Down,u\[Phi]Down},
+
+MinoVelocities = KerrGeoVelocityMino[a,p,0,x,{0,0}];
-MinoVelocities = KerrGeoVelocityMino[a,p,0,x,{0,0}, index];
+utUp="\!\(\*SuperscriptBox[\(u\), \(t\)]\)"; urUp="\!\(\*SuperscriptBox[\(u\), \(r\)]\)";
+u\[Theta]Up="\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"; u\[Phi]Up="\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)";
+utDown="\!\(\*SubscriptBox[\(u\), \(t\)]\)"; urDown="\!\(\*SubscriptBox[\(u\), \(r\)]\)";
+u\[Theta]Down="\!\(\*SubscriptBox[\(u\), \(\[Theta]\)]\)"; u\[Phi]Down="\!\(\*SubscriptBox[\(u\), \(\[Phi]\)]\)";
-If[index == "Contravariant",
- ut1="\!\(\*SuperscriptBox[\(u\), \(t\)]\)"; ur1="\!\(\*SuperscriptBox[\(u\), \(r\)]\)"; u\[Theta]1="\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"; u\[Phi]1="\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)";,
- ut1="\!\(\*SubscriptBox[\(u\), \(t\)]\)"; ur1="\!\(\*SubscriptBox[\(u\), \(r\)]\)"; u\[Theta]1="\!\(\*SubscriptBox[\(u\), \(\[Theta]\)]\)"; u\[Phi]1="\!\(\*SubscriptBox[\(u\), \(\[Phi]\)]\)";
-];
(*All components are Constants*)
-ut = Function[{Global`\[Chi]},Evaluate[MinoVelocities [ut1][Global`\[Chi]]], Listable];
-ur = Function[{Global`\[Chi]},Evaluate[0],Listable];
-u\[Theta]= Function[{Global`\[Chi]},Evaluate[0],Listable];
-u\[Phi]= Function[{Global`\[Chi]},Evaluate[MinoVelocities [u\[Phi]1][Global`\[Chi]]],Listable];
+utContra = Function[{Global`\[Chi]},Evaluate[MinoVelocities [utUp][Global`\[Chi]]],Listable];
+urContra = Function[{Global`\[Chi]},Evaluate[0],Listable];
+u\[Theta]Contra = Function[{Global`\[Chi]}, Evaluate[0],Listable];
+u\[Phi]Contra = Function[{Global`\[Chi]}, Evaluate[MinoVelocities [u\[Phi]Up][Global`\[Chi]]],Listable];
-<|ut1-> ut, ur1-> ur, u\[Theta]1-> u\[Theta], u\[Phi]1-> u\[Phi] |>
+utCo = Function[{Global`\[Chi]},Evaluate[MinoVelocities [utDown][Global`\[Chi]]],Listable];
+urCo = Function[{Global`\[Chi]},Evaluate[0],Listable];
+u\[Theta]Co = Function[{Global`\[Chi]}, Evaluate[0],Listable];
+u\[Phi]Co = Function[{Global`\[Chi]}, Evaluate[MinoVelocities [u\[Phi]Down][Global`\[Chi]]],Listable];
+
+<|utUp ->utContra, urUp ->urContra,
+u\[Theta]Up-> u\[Theta]Contra, u\[Phi]Up-> u\[Phi]Contra,
+utDown->utCo, urDown->urCo,
+u\[Theta]Down-> u\[Theta]Co, u\[Phi]Down-> u\[Phi]Co|>
]
@@ -167,14 +171,15 @@
(*Eccentric Case*)
-KerrGeoVelocityDarwin[a_,p_,e_,x_/;x^2==1,initPhases_,index_ ]:= Module[{En,L,Q,r,z,r1,r2,r3,r4,kr, \[CapitalUpsilon]r, \[CapitalLambda]r,yr,\[Lambda]0r,r01,\[CapitalLambda]r1,\[Lambda],
-\[Chi]0,\[Nu], \[Chi]local ,qr0, qz0, rprime, zprime, \[CapitalDelta], \[CapitalSigma], \[Omega], ut,ur,u\[Theta],u\[Phi], MinoVelocities,ut1,ur1,u\[Theta]1,u\[Phi]1},
+KerrGeoVelocityDarwin[a_,p_,e_,x_/;x^2==1,initPhases_]:= Module[{En,L,Q,r,z,r1,r2,r3,r4,kr, \[CapitalUpsilon]r, \[CapitalLambda]r,yr,\[Lambda]0r,r01,\[CapitalLambda]r1,\[Lambda],
+\[Chi]0,\[Nu], \[Chi]local ,qr0, qz0, rprime, zprime, \[CapitalDelta], \[CapitalSigma], \[Omega], ut,ur,u\[Theta],u\[Phi], MinoVelocities,utContra,urContra,u\[Theta]Contra,u\[Phi]Contra,
+utCo,urCo,u\[Theta]Co,u\[Phi]Co,utUp,urUp,u\[Theta]Up,u\[Phi]Up, utDown,urDown,u\[Theta]Down,u\[Phi]Down},
(*Constants of Motion*)
{En,L,Q}= {"\[ScriptCapitalE]","\[ScriptCapitalL]","\[ScriptCapitalQ]"}/.KerrGeoConstantsOfMotion[a,p,e,x];
(*Roots*)
-{r1,r2,r3,r4}=KerrGeodesics`OrbitalFrequencies`Private`KerrGeoRadialRoots[a, p, e, x];
+{r1,r2,r3,r4}=KerrGeodesics`OrbitalFrequencies`Private`KerrGeoRadialRoots[a, p, e, x,En,Q];
kr = ((r1-r2)(r3-r4))/((r1-r3)(r2-r4));
@@ -197,47 +202,50 @@
\[Lambda][\[Nu]_]:=\[CapitalLambda]r Floor[\[Nu]/(2\[Pi])]+If[Mod[\[Nu],2\[Pi]]<=\[Pi], \[Lambda]0r[r[\[Nu]]]-\[CapitalLambda]r1,\[CapitalLambda]r-\[Lambda]0r[r[\[Nu]]]];
-MinoVelocities = KerrGeoVelocityMino[a,p,e,x,{0,0}, index];
+MinoVelocities = KerrGeoVelocityMino[a,p,e,x,{0,0}];
-If[index == "Contravariant",
- ut1="\!\(\*SuperscriptBox[\(u\), \(t\)]\)"; ur1="\!\(\*SuperscriptBox[\(u\), \(r\)]\)"; u\[Theta]1="\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"; u\[Phi]1="\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)";,
- ut1="\!\(\*SubscriptBox[\(u\), \(t\)]\)"; ur1="\!\(\*SubscriptBox[\(u\), \(r\)]\)"; u\[Theta]1="\!\(\*SubscriptBox[\(u\), \(\[Theta]\)]\)"; u\[Phi]1="\!\(\*SubscriptBox[\(u\), \(\[Phi]\)]\)";
-];
+utUp="\!\(\*SuperscriptBox[\(u\), \(t\)]\)"; urUp="\!\(\*SuperscriptBox[\(u\), \(r\)]\)";
+u\[Theta]Up="\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"; u\[Phi]Up="\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)";
+utDown="\!\(\*SubscriptBox[\(u\), \(t\)]\)"; urDown="\!\(\*SubscriptBox[\(u\), \(r\)]\)";
+u\[Theta]Down="\!\(\*SubscriptBox[\(u\), \(\[Theta]\)]\)"; u\[Phi]Down="\!\(\*SubscriptBox[\(u\), \(\[Phi]\)]\)";
-ut = Function[{Global`\[Chi]},Evaluate[MinoVelocities [ut1][\[Lambda][Global`\[Chi]-\[Chi]0]]],Listable];
-ur = Function[{Global`\[Chi]},Evaluate[MinoVelocities [ur1][\[Lambda][Global`\[Chi]-\[Chi]0]]],Listable];
-u\[Theta] = Function[{Global`\[Chi]}, Evaluate[0],Listable];
-u\[Phi] = Function[{Global`\[Chi]}, Evaluate[MinoVelocities [u\[Phi]1][\[Lambda][Global`\[Chi]-\[Chi]0]]],Listable];
+utContra = Function[{Global`\[Chi]},Evaluate[MinoVelocities [utUp][\[Lambda][Global`\[Chi]-\[Chi]0]]],Listable];
+urContra = Function[{Global`\[Chi]},Evaluate[MinoVelocities [urUp][\[Lambda][Global`\[Chi]-\[Chi]0]]],Listable];
+u\[Theta]Contra = Function[{Global`\[Chi]}, Evaluate[0],Listable];
+u\[Phi]Contra = Function[{Global`\[Chi]}, Evaluate[MinoVelocities [u\[Phi]Up][\[Lambda][Global`\[Chi]-\[Chi]0]]],Listable];
-<|ut1-> ut, ur1-> ur, u\[Theta]1-> u\[Theta], u\[Phi]1-> u\[Phi] |>
+utCo = Function[{Global`\[Chi]},Evaluate[MinoVelocities [utDown][\[Lambda][Global`\[Chi]-\[Chi]0]]],Listable];
+urCo = Function[{Global`\[Chi]},Evaluate[MinoVelocities [urDown][\[Lambda][Global`\[Chi]-\[Chi]0]]],Listable];
+u\[Theta]Co = Function[{Global`\[Chi]}, Evaluate[0],Listable];
+u\[Phi]Co = Function[{Global`\[Chi]}, Evaluate[MinoVelocities [u\[Phi]Down][\[Lambda][Global`\[Chi]-\[Chi]0]]],Listable];
+<|utUp ->utContra, urUp ->urContra,
+u\[Theta]Up-> u\[Theta]Contra, u\[Phi]Up-> u\[Phi]Contra,
+utDown->utCo, urDown->urCo,
+u\[Theta]Down-> u\[Theta]Co, u\[Phi]Down-> u\[Phi]Co|>
]
-(* ::Section::Closed:: *)
+(* ::Section:: *)
(*KerrGeoFourVelocity Wrapper*)
-Options[KerrGeoFourVelocity] = {"Covariant" -> False, "Parametrization"-> "Mino"}
+Options[KerrGeoFourVelocity] = {"Parametrization"-> "Mino"}
SyntaxInformation[KerrGeoFourVelocity] = {"ArgumentsPattern"->{_,_,_,_,OptionsPattern[]}};
-KerrGeoFourVelocity[a_,p_,e_,x_,initPhases:{_,_}:{0,0}, OptionsPattern[]]:= Module[{param, index},
+KerrGeoFourVelocity[a_,p_,e_,x_,initPhases:{_,_}:{0,0}, OptionsPattern[]]:= Module[{param},
param = OptionValue["Parametrization"];
-
-If[OptionValue["Covariant"], index = "Covariant" , index="Contravariant", Message[KerrGeoFourVelocity::opttf,"Covariant",OptionValue["Covariant"]]; Return[] ];
-
-
If[param == "Darwin",
If[ Abs[x]!=1,
Message[KerrGeoFourVelocity::parametrization, "Darwin parameterization only valid for equatorial motion"];
Return[];,
- Return[KerrGeoVelocityDarwin[a,p,e,x,initPhases, index]]]];
+ Return[KerrGeoVelocityDarwin[a,p,e,x,initPhases]]]];
- If[param == "Mino", Return[KerrGeoVelocityMino[a,p,e,x,initPhases, index]]];
+ If[param == "Mino", Return[KerrGeoVelocityMino[a,p,e,x,initPhases]]];
Message[KerrGeoFourVelocity::parametrization, "Unrecognized Paramaterization: " <> param];