SetDirectory["~/doc/research/first_order_singularities/paper"];

<<IsingScalingFunction`

PrepareArgument[Data[2]]

Data[2]["θ0"]

data2={θ0->1.14841,θYL->0.989667,CYL->-0.172824,G[1]->-0.310183,G[2]->0.247454,g[0]->0.373691,g[1]->-0.0216363}

prep2={θ0,θYL,ruleB[θ0,{g[0],g[1]}],ruleAL[θ0,{g[0],g[1]}],CYL,{G[1],G[2]},{g[0],g[1]}}/.data2

Plot[Evaluate@Last[(DScriptF0DηList@@PrepareArgument[Data[6]])[6,θ]],{θ,0,1.1483}]

Solve[{tt==R((θ^2)-1),h==(R^(15/8))g[Data[2]["θ0"],Data[2]["gs"]][θ]},{R,h}]

InverseCoordinates[θ0_,gs_][ut_,uh_]:=FindRoot[{ut==R((θ^2)-1),-uh==((Abs[R])^(15/8))g[θ0,gs][θ]},{{R,1,0,(10^8)},{θ,Sign[uh]1,-Data[2]["θ0"],Data[2]["θ0"]}}]

InverseCoordinates[Data[2]["θ0"],Data[2]["gs"]][6/10,0.2]

Solve[{tt==R((θ^2)-1),h==(R^Δ)g[θ]},{R,θ}]

Plot[Evaluate[g[θ0,{g[0],g[1]}][θ]/.data2],{θ,0,1.148}]

Plot[(uf@@Most[prep2])[1,θ],{θ,-1.148,1.148}]

dat=Flatten[Table[{ut[R,θ],uh[θ0,{g[0],g[1]}][R,θ],-(DufDuh@@prep2)[1][R,θ]}/.data2,{R,0.05,2,0.05},{θ,-1.14841,1.14841,0.05}],1];

ListPlot3D[dat]

Plot[Evaluate[(DufDut@@prep2)[2][R,0.1]],{R,0,2}]

ParametricPlot[{θ,Evaluate[(DufDut@@prep2)[2][.1,θ]]},{θ,-1.148,1.148},AspectRatio->1]

dGdξ

(dΦdηList@@prep2)[0,1]

ListLogPlot[Abs[(DScriptFPlusMinusDξθ0List@@prep2)[10]]]

ListLogPlot[Abs[(DScriptF0DηList@@prep2)[10,0.5]]]