From 07531dcf8fce5ffc2401794e65c3813e86090228 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 27 Oct 2021 19:05:59 +0200 Subject: Work. --- caselle_compare.nb | 580 +- new_schofield.nb | 57523 +++++++++++++++++++++++++++------------------------ schofield.wl | 24 +- 3 files changed, 31186 insertions(+), 26941 deletions(-) diff --git a/caselle_compare.nb b/caselle_compare.nb index 7932af0..a64a48c 100644 --- a/caselle_compare.nb +++ b/caselle_compare.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 201218, 4506] -NotebookOptionsPosition[ 190375, 4317] -NotebookOutlinePosition[ 190816, 4334] -CellTagsIndexPosition[ 190773, 4331] +NotebookDataLength[ 204728, 4608] +NotebookOptionsPosition[ 193637, 4413] +NotebookOutlinePosition[ 194074, 4430] +CellTagsIndexPosition[ 194031, 4427] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -96,23 +96,23 @@ Cell[BoxData[{ 3.8438061646410103`*^9}, 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Baseline)], #5}, { + GraphicsBox[{{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.772079, 0.431554, 0.102387], + AbsoluteThickness[1.6]], { + LineBox[{{0, 10}, {20, 10}}]}}, { + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.772079, 0.431554, 0.102387], + AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, + ImageSize -> {20, 10}, PlotRangePadding -> None, + ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #6}, { + GraphicsBox[{{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.363898, 0.618501, 0.782349], + AbsoluteThickness[1.6]], { + LineBox[{{0, 10}, {20, 10}}]}}, { + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.363898, 0.618501, 0.782349], + AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, + ImageSize -> {20, 10}, PlotRangePadding -> None, + ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #7}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, + GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"PointLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.368417, 0.506779, 0.709798], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.24561133333333335`, 0.3378526666666667, + 0.4731986666666667], FrameTicks -> None, PlotRangePadding -> + None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.368417, 0.506779, 0.709798]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.368417, 0.506779, 0.709798], Editable -> False, + Selectable -> False], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.880722, 0.611041, 0.142051], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.587148, 0.40736066666666665`, 0.09470066666666668], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.880722`", ",", "0.611041`", ",", "0.142051`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.880722, 0.611041, 0.142051]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.880722, 0.611041, 0.142051], Editable -> False, + Selectable -> False], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.560181, 0.691569, 0.194885], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.37345400000000006`, 0.461046, 0.12992333333333334`], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.560181`", ",", "0.691569`", ",", "0.194885`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.560181, 0.691569, 0.194885]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.560181, 0.691569, 0.194885], Editable -> False, + Selectable -> False], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.922526, 0.385626, 0.209179], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.6150173333333333, 0.25708400000000003`, + 0.13945266666666667`], FrameTicks -> None, + PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.922526`", ",", "0.385626`", ",", "0.209179`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.922526, 0.385626, 0.209179]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.922526, 0.385626, 0.209179], Editable -> False, + Selectable -> False], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.528488, 0.470624, 0.701351], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.3523253333333333, 0.3137493333333333, + 0.46756733333333333`], FrameTicks -> None, + PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.528488`", ",", "0.470624`", ",", "0.701351`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.528488, 0.470624, 0.701351]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.528488, 0.470624, 0.701351], Editable -> False, + Selectable -> False], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.772079, 0.431554, 0.102387], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.5147193333333333, 0.28770266666666666`, + 0.06825800000000001], FrameTicks -> None, + PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.772079`", ",", "0.431554`", ",", "0.102387`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.772079, 0.431554, 0.102387]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + 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θc_][θ_] := (θc Exp[1/(B θc)] ExpIntegralEi[-1/(B θc)] + (θ - θc) Exp[-1/(B (θ - θc))] ExpIntegralEi[1/(B (θ - θc))]) / π RFLow[B_, θc_][θ_] := fLow[B, θc][θ] + fLow[B, θc][-θ] -RFHigh[ξ0_][ξ_] := (ξ^2+ξ0^2)^(5/6) - (ξ0^2)^(5/6) - +RFHigh[ξ0_][ξ_] := (-I ξ+ ξ0)^(5/6) + (I ξ+ ξ0)^(5/6) - 2 ξ0^(5/6) RFReg[n_][θ_] := AL fLow[B, θc][-θ] + AH RFHigh[θ0][θ] + Sum[A[i] θ^(2 i), {i, 1, n}] RF[n_][θ_] := RFReg[n][θ] + AL fLow[B, θc][θ] dfLow[AL_, B_][m_] := Piecewise[{{AL m! Gamma[m - 1] B^(m - 1) / π, m > 1}, {AL θc Exp[1/(B θc)] ExpIntegralEi[-1/(B θc)] / π, m == 0}, {0, True}}] @@ -97,7 +96,7 @@ dΦdηList[n_, h_, params_:{}][m_, θp_] := Module[ ruleB[g_] := B -> (2 * os / π) * (- g'[θc] / t[θc]^Δ[2]) ξYL[g_] := g[I θ0]/(-t[I θ0])^Δ[2]/I -AYL[g_] := AH / ((g[I θ0]/ I)^(2 / Δ[2]) * (-η[g]'[I θ0] / (2 θ0 I))^(5/6)) +AYL[g_] := AH / ((g[I θ0]/ I)^(2 / Δ[2]) * (-η[g]'[I θ0] / (I))^(5/6)) ruleθ0[g_] := ξYL[g] - Around[0.18930, 0.00005] ruleAL[g_] := AL -> Exp[Δ[2] t[θc]^(Δ[2] - 1) t'[θc] / (2 os / π g'[θc]) - t[θc]^Δ[2] g''[θc] / (4 os / π g'[θc]^2)] t[θc]^(1/8) os / (2 π) * g'[θc] ruleAH[g_] := AYL[g] + Around[1.37, 0.02] @@ -137,12 +136,12 @@ eqMid[F_, h_][m_] := D[ ]], *) Around[0.110886196683, 2.0 10^-12], - Around[0.01642689465, 1.0 10^-11], + Around[0.01642689465, 2.0 10^-11], Around[-2.639978 10^-4, 1.0 10^-10], Around[-5.140526 10^-4, 1.0 10^-10], Around[2.08865 10^-4, 1.0 10^-9], Around[-4.4819 10^-5, 1.0 10^-9], - Around[3.194 10^-7, 1.0 10^-9], + Around[3.16 10^-7, 1.0 10^-9], Around[4.31 10^-6, 0.01 10^-6], Around[-1.99 10^-6, 0.01 10^-6] } @@ -153,15 +152,15 @@ Gls = { −1.000960328725262189480934955172097320572505951770117 Sqrt[2]/((2 )^(-7/8) (2^(3/16)/os)^2)/2/(12 \[Pi]), Around[ 0.038863932, 3.0 10^(-9)], Around[−0.068362119, 2.0 10^(-9)], - Around[ 0.18388371, 1.0 10^(-8)], - Around[-0.659170, 1.0 10^(-6)], + Around[ 0.18388370, 1.0 10^(-8)], + Around[-0.6591714, 1.0 10^(-7)], Around[ 2.937665, 3.0 10^(-6)], Around[-15.61, 1.0 10^(-2)], Around[ 96.76, 1.0 10^(-2)], Around[-6.79 10^2, 1.0], - Around[5.34 10^3, 10.], + Around[ 5.34 10^3, 10.], Around[-4.66 10^4, 0.01 10^4], - Around[4.46 10^5, 0.01 10^5], + Around[ 4.46 10^5, 0.01 10^5], Around[-4.66 10^6, 0.01 10^6] } @@ -172,7 +171,7 @@ Ghs = { 0, Around[ 8.333711750, 5.0 10^(-9)], 0, - Around[-95.16897, 3.0 10^(-5)], + Around[-95.16896, 1.0 10^(-5)], 0, Around[1457.62, 3.0 10^(-2)], 0, @@ -189,7 +188,7 @@ dRule[sym_][f_, i_] := Derivative[i[[1]] - 1][sym][0] -> f (i[[1]] - 1)! GlRules = MapIndexed[dRule[Gl], Gls]; GhRules = MapIndexed[dRule[Gh], Ghs]; -rules[g_] := Join[ΦRules, GlRules, GhRules, {ruleAL[g], ruleB[g], gC[0] -> 1}] +rules[g_] := Join[ΦRules, GlRules, GhRules, {ruleAL[g], ruleB[g]}] eqAround[n_, g_][m_, p_, q_] := Flatten[Join[{ruleAH[g], ruleθ0[g]}, eqLow[n, g][#] & /@ Range[0, m],eqMid[RF[n], g][#] & /@ Range[0, p], eqHigh[n, g] /@ Range[2, q, 2]]] //. rules[g] @@ -206,6 +205,7 @@ resMid[n_, g_, δ_][m_] := formResiduals[Φs[[;;m+1]], dΦdηList[n, g][m, 1], res[F_, g_, δ_][m_] := Join[resLow[F, g, δ][m], resHigh[F, g, δ][m]] //. rules[g] chiSquared[F_, g_, δ_][m_] := Total[res[F, g, δ][m]^2] resAll[F_, g_, δ_][m_] := Join[resLow[F, g, δ][m], resHigh[F, g, δ][m], (*resMid[F, g, δ][m],*) {ruleθ0[g] / 0.00005, ruleAH[g] / 0.02} /. Around[x_, _] :> x] //. rules[g] +resHighAll[F_, g_, δ_][m_] := Join[resLow[F, g, δ][m][[{1}]], resHigh[F, g, δ][m], (*resMid[F, g, δ][m],*) {ruleθ0[g] / 0.00005, ruleAH[g] / 0.02} /. Around[x_, _] :> x] //. rules[g] newSol[eqs_, oldSol_, newVars_, δ_:0, γ_:0, opts___] := FindRoot[ eqs, @@ -296,7 +296,7 @@ levenbergMarquardtHelper[Δ_, rf_, Jf_, β0_, λ0_ : 1, ν_ : 1.5, ε_ : 10^-15] {newC, β} ] -annealFit[r_, β0_, γ_ : 0, λ0_ : 1, ν_ : 2, μ_ : 3, ε_: 10^-14, h_ : 0.1, α_ : 0.1] := +annealFit[r_, β0_, γ_ : 0, λ0_ : 1, ν_ : 2, μ_ : 3, ε_: 10^-15, h_ : 0.1, α_ : 0.1] := Module[ { rf, Jf, n = Length[β0], -- cgit v1.2.3-54-g00ecf