From 49799190a6d089ba58758c76b7a2194934af2de5 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 6 Feb 2023 17:05:47 +0100
Subject: Added an inverse coordinate function.

---
 IsingScalingFunction.wl | 20 ++++++++++++++------
 1 file changed, 14 insertions(+), 6 deletions(-)

diff --git a/IsingScalingFunction.wl b/IsingScalingFunction.wl
index 29370eb..b119b9f 100644
--- a/IsingScalingFunction.wl
+++ b/IsingScalingFunction.wl
@@ -99,7 +99,7 @@ Ghs := {
   Around[-1.04 10^7, 0.01 10^7]
 }
 
-Data[2] = <|
+Data[2] = Rationalize[#, 10^-20] & /@ <|
   "θ0"  -> 1.148407773492004`,
   "θYL" -> 0.9896669889911205`,
   "CYL" -> -0.172823989504767`,
@@ -107,7 +107,7 @@ Data[2] = <|
   "gs"  -> {0.37369093055254343`, -0.021636313152585823`}
 |>
 
-Data[3] = <|
+Data[3] = Rationalize[#, 10^-20] & /@ <|
   "θ0"  -> 1.2542120477507488`,
   "θYL" -> 0.6020557328641167`,
   "CYL" -> -0.38566364361428684`,
@@ -115,7 +115,7 @@ Data[3] = <|
   "gs"  -> {0.4483788209731592`, -0.022032295172535358`, 0.00022200608228654115`}
 |>
 
-Data[4] = <|
+Data[4] = Rationalize[#, 10^-20] & /@ <|
   "θ0"  -> 1.3164928721109121`,
   "θYL" -> 0.6400189996493497`,
   "CYL" -> -0.3563974694580203`,
@@ -123,7 +123,7 @@ Data[4] = <|
   "gs"  -> {0.4410742751152714`, -0.034817777358116885`, 0.000678172648789985`, -0.00004305140578834467`}
 |>
 
-Data[5] = <|
+Data[5] = Rationalize[#, 10^-20] & /@ <|
   "θ0"  -> 1.3403205742656135`,
   "θYL" -> 0.6238113973493433`,
   "CYL" -> -0.38002950945224295`,
@@ -131,7 +131,7 @@ Data[5] = <|
   "gs"  -> {0.44371885415894785`, -0.04609943321005163`, -0.0007458341071947777`, 0.00005966875622885447`, -4.403083529955303`*^-6}
 |>
 
-Data[6] = <|
+Data[6] = Rationalize[#, 10^-20] & /@ <|
   "θ0"  -> 1.3626103817690176`,
   "θYL" -> 0.6462147447024515`,
   "CYL" -> -0.35576386594103865`,
@@ -163,6 +163,14 @@ ut[R_, θ_] := R t[θ]
 
 uh[θ0_, gs_][R_, θ_] := R^Δ g[θ0, gs][θ]
 
+InverseCoordinates[\[Theta]0_, gs_, wp_:20][tn_, hn_] :=
+ ({Exp[logR], \[Theta]0 Tanh[x]} /.
+    FindRoot[{
+      Rationalize[tn, 10^-30] == ut[Exp[logR], \[Theta]0 Tanh[x]],
+      Rationalize[hn, 10^-30] == uh[\[Theta]0, gs][Exp[logR], \[Theta]0 Tanh[x]]
+     }, {{logR, 2}, {x, Sign[hn]/2}}, WorkingPrecision -> wp]) /;
+  NumericQ[tn] && NumericQ[hn]
+
 η[θ0_, gs_][θ_] := t[θ] / RealAbs[g[θ0, gs][θ]]^(1 / Δ)
 
 ξ[θ0_, gs_][θ_] := g[θ0, gs][θ] / RealAbs[t[θ]]^Δ
@@ -198,7 +206,7 @@ InverseDerivativeList[n_][f_][x_] := Module[
         fp'[xp] D[Pm, xp] - (2 m - 1) fp''[xp] Pm], 1, Range[n - 1]] /.
     Derivative[m_][fp][xp] :> dfs[[m]];
   MapIndexed[{Pn, i} \[Function] Pn/dfs[[1]]^(2 i[[1]] - 1), Pns]
-  ]
+]
 
 CompositeFunctionDerivativeList[G_, F_, X_, FSupp_:(0&)][m_, θ_] := Module[
   { ds, dF, df, fp },
-- 
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