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authorJaron Kent-Dobias <jaron@kent-dobias.com>2021-10-06 17:13:58 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2021-10-06 17:13:58 +0200
commit4eae6a3b275df83426e97997d5dad9e7e05a06f9 (patch)
tree5cd3be86fed4165a0816cf6fb429d04dd4fb868b
parent5269fa0fb763e7193738b6ae7ba1c62288da8ff9 (diff)
downloadmma-4eae6a3b275df83426e97997d5dad9e7e05a06f9.tar.gz
mma-4eae6a3b275df83426e97997d5dad9e7e05a06f9.tar.bz2
mma-4eae6a3b275df83426e97997d5dad9e7e05a06f9.zip
Work.
Diffstat
-rw-r--r--m8.wl10
-rw-r--r--new_schofield.nb8437
-rw-r--r--schofield.wl60
3 files changed, 2575 insertions, 5932 deletions
diff --git a/m8.wl b/m8.wl
new file mode 100644
index 0000000..8875506
--- /dev/null
+++ b/m8.wl
@@ -0,0 +1,10 @@
+(* Created with the Wolfram Language : www.wolfram.com *)
+{10851.579671794501, {\[Theta]c -> 1.320598743540984,
+ \[Theta]0 -> 0.19670390350427933, AH -> -2.5259470863324207,
+ A[1] -> 1.6947480539779154, A[2] -> 0.5761725007964409,
+ gC[1] -> -0.2794780718284905, gC[2] -> -0.04009433554574842,
+ A[3] -> -0.1596671465481377, gC[3] -> 0.0043479399923616055,
+ gC[4] -> 0.006533076700974013, A[4] -> 0.0007744577414188262,
+ gC[5] -> -0.0019568496974147614, gC[6] -> 0.00022305717672714141,
+ A[5] -> 0.0024207206316697546, gC[7] -> -0.00002144977801064647,
+ gC[8] -> 3.9882468182738*^-6, A[6] -> 0.0000421977466132342}}
diff --git a/new_schofield.nb b/new_schofield.nb
index 47d3407..e80a47b 100644
--- a/new_schofield.nb
+++ b/new_schofield.nb
@@ -10,10 +10,10 @@
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
-NotebookDataLength[ 367963, 8506]
-NotebookOptionsPosition[ 283126, 7118]
-NotebookOutlinePosition[ 283524, 7134]
-CellTagsIndexPosition[ 283481, 7131]
+NotebookDataLength[ 229983, 5139]
+NotebookOptionsPosition[ 214867, 4911]
+NotebookOutlinePosition[ 215264, 4927]
+CellTagsIndexPosition[ 215221, 4924]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
@@ -31,8 +31,9 @@ Cell[BoxData[
3.839409661432328*^9, 3.839409662064075*^9}, {3.839479110706854*^9,
3.839479110850239*^9}, {3.839569665835891*^9, 3.839569666219857*^9}, {
3.83957102205329*^9, 3.8395710222207737`*^9}, {3.841389917784724*^9,
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- CellLabel->"In[1]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"],
+ 3.841389919112598*^9}, {3.8424227955510283`*^9, 3.842422804973724*^9}, {
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+ CellLabel->"In[13]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"],
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-Cell[232318, 5965, 214, 4, 18, "Print",ExpressionUUID->"675faf5b-4311-49e7-8b1a-fcd3f0834ef9"],
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-Cell[232754, 5977, 214, 4, 18, "Print",ExpressionUUID->"a759c179-7c48-4826-8457-6fda0b49f576"]
-}, Open ]],
-Cell[232983, 5984, 1767, 43, 76, "Output",ExpressionUUID->"603ce513-d919-4a6a-aae2-e99140ba8fb2"]
-}, Open ]],
-Cell[CellGroupData[{
-Cell[234787, 6032, 1403, 36, 24, "Input",ExpressionUUID->"77feec13-1cdc-471d-8d45-49920b8c9c58"],
-Cell[236193, 6070, 229, 4, 25, "Output",ExpressionUUID->"362d644d-39b8-4815-95d9-a10f5c313532"]
-}, Open ]],
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-Cell[252278, 6433, 862, 16, 22, "Message",ExpressionUUID->"ba4bcc27-d9ad-4822-a182-dbfb6baf266b"]
-}, Open ]],
-Cell[253155, 6452, 11952, 233, 182, "Input",ExpressionUUID->"673ffefa-75f0-46ac-befd-c785b4bc3ce1"],
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-Cell[267706, 6771, 1396, 33, 41, "Input",ExpressionUUID->"0f44ea2f-bcb6-4b65-a37b-65515908d127"],
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}
diff --git a/schofield.wl b/schofield.wl
index f32d855..3f45f5d 100644
--- a/schofield.wl
+++ b/schofield.wl
@@ -96,9 +96,11 @@ dΦdηList[n_, h_][m_, θp_] := Module[
]
ruleB[g_] := B -> (2 * OverBar[s] / π) * (- g'[θc] / t[θc]^Δ[2])
-ruleθ0[g_] := Simplify[g[I θ0]/(-t[I θ0])^Δ[2]/I] - Around[0.18930, 0.00005]
+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))
+ruleθ0[g_] := ξYL[g] - Around[0.18930, 0.00005]
ruleAL[g_] := AL -> Exp[Δ[2] t[θc]^(Δ[2] - 1) t'[θc] / (2 OverBar[s] / π g'[θc]) - t[θc]^Δ[2] g''[θc] / (4 OverBar[s] / π g'[θc]^2)] t[θc]^(1/8) OverBar[s] / (2 π) * g'[θc]
-ruleAH[g_] := AH / ((g[I θ0]/ I)^(2 / Δ[2]) * (-η[g]'[I θ0] / (2 θ0 I))^(5/6)) + Around[1.37, 0.02]
+ruleAH[g_] := AYL[g] + Around[1.37, 0.02]
eqLowRHSReg[n_][m_] := dRFc[n][m]
@@ -144,9 +146,9 @@ Gls = {
Around[ 2.937665, 3.0 10^(-6)],
Around[-15.61, 1.0 10^(-2)],
Around[ 96.76, 1.0 10^(-2)],
- -6.79 10^2,
- 5.34 10^3,
- -4.66 10^4,
+ Around[-6.79 10^2, 1.0],
+ Around[5.34 10^3, 10.],
+ Around[-4.66 10^4, 0.01 10^4],
4.46 10^5,
-4.66 10^6
}
@@ -187,7 +189,7 @@ resLow[n_, g_, δ_][m_] := formResiduals[Gls[[;;m+1]], dGdξLowList[n, g][m], δ
resHigh[n_, g_, δ_][m_] := Rest[formResiduals[Ghs[[;;m+1]], dGdξList[n, g][m, 0], δ][[;;;;2]]]
-res[F_, g_, δ_][m_] := Join[resLow[F, g, δ][m], resHigh[F, g, δ][m], {ruleθ0[g] / 0.00005(*, ruleAH[g] / 0.02*)} /. Around[x_, _] :> x]
+res[F_, g_, δ_][m_] := Join[resLow[F, g, δ][m], resHigh[F, g, δ][m]]
chiSquared[F_, g_, δ_][m_] := Total[res[F, g, δ][m]^2]
newSol[eqs_, oldSol_, newVars_, δ_:0, γ_:0, opts___] := FindRoot[
@@ -205,8 +207,9 @@ levenbergMarquardtStep[M_, λ_, g_] := Quiet[
, LinearSolve::luc
]
-levenbergMarquardtAcceleration[M_, λ_, v_, J_, rold_, rf_, h_, β_, δ_] := Quiet[
- - Re[LinearSolve[M + λ DiagonalMatrix[Diagonal[M]], Transpose[J].(2/h((rf[Append[β[[All,2]] + h v, δ]] - rold) / h - J . v))] / 2]
+levenbergMarquardtAcceleration[M_, λ_, v_, J_, rold_, rf_, h_, β_] := Quiet[
+ δβ = β; δβ[[All, 2]] += h v;
+ - Re[LinearSolve[M + λ DiagonalMatrix[Diagonal[M]], Transpose[J].(2/h(((rf /. δβ) - rold) / h - J . v))] / 2]
, LinearSolve::luc
]
@@ -229,7 +232,7 @@ levenbergMarquardt[r_, β0_, λ0_ : 1, ν_ : 2, ε_ : 10^-15] :=
]
-levenbergMarquardtHelper[Δ_, rf_, Jf_, β0_, λ0_ : 1, ν_ : 2, ε_ : 10^-15, accOff_ : False] :=
+levenbergMarquardtHelper[r_, J_, β0_, λ0_ : 1, ν_ : 2, ε_ : 10^-15] :=
Module[
{
n = Length[β0],
@@ -240,66 +243,63 @@ levenbergMarquardtHelper[Δ_, rf_, Jf_, β0_, λ0_ : 1, ν_ : 2, ε_ : 10^-15, a
h = 0.1, fvv, α = 0.1, a, v, U, nSteps = 0, reject, μ =3
},
PrintTemporary["Beginning the algorithm."];
- oldr = rf[Append[β[[All, 2]], Δ]];
- oldJ = Jf[Append[β[[All, 2]], Δ]];
+ oldr = r /. β;
+ oldJ = J /. β;
U = First[SingularValueDecomposition[oldJ]];
oldC = Re[Total[oldr^2]];
newC = oldC;
g = Re[Transpose[oldJ] . oldr];
M = Re[Transpose[oldJ] . oldJ];
v = levenbergMarquardtStep[M, λ, g];
- a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, rf, h, β, Δ];
- δ = v + If[accOff, 0, a];
+ a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, r, h, β];
+ δ = v + a;
vlast = v;
PrintTemporary["Current cost value: ", Dynamic[oldC]];
While[Norm[δ] > ε,
newβ[[All, 2]] += δ;
- newr = rf[Append[newβ[[All, 2]], Δ]];
+ newr = r /. newβ;
newC = Re[Total[newr^2]];
While[((1 - v . vlast / Norm[v] / Norm[vlast])newC > oldC) || (2 Norm[a] / Norm[v] > α),
λ *= ν;
v = levenbergMarquardtStep[M, λ, g];
- a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, rf, h, β, Δ];
- δ = v + If[accOff, 0, a];
+ a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, r, h, β];
+ δ = v + a;
newβ = β;
newβ[[All, 2]] += δ;
- newr = rf[Append[newβ[[All, 2]], Δ]];
+ newr = r /. newβ;
newC = Re[Total[newr^2]];
];
oldC = newC;
oldr = newr;
β = newβ;
- oldJ = Jf[Append[β[[All, 2]], Δ]];
+ oldJ = J /. β;
U = First[SingularValueDecomposition[oldJ]];
g = Re[Transpose[oldJ] . oldr];
M = Re[Transpose[oldJ] . oldJ];
vlast = v;
λ /= μ;
v = levenbergMarquardtStep[M, λ, g];
- a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, rf, h, β, Δ];
- δ = v + If[accOff, 0, a];
+ a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, r, h, β];
+ δ = v + a;
nSteps += 1;
];
{newC, β}
]
annealFit[r_, Δ_, β0_, δ0_ : 10^-5, δ1_ : 10^-13, δδ_ : 100, λ0_ : 1, ν_ : 2, ε_: 10^-15] :=
-Module[ {lastfit = {1,β0}, rf, Jf, δ = δ0, n = Length[β0]},
- Quiet[
- rf = Compile[{{x, _Real, 1}},
- Evaluate[r /. Thread[Rule[Append[First /@ β0, Δ], Part[x, #] & /@ Range[n + 1]]]]
- ];
- Jf = Compile[{{x, _Real, 1}},
- Evaluate[D[r, {First /@ β0}] /. Thread[Rule[Append[First /@ β0, Δ], Part[x, #] & /@ Range[n + 1]]]]
- ];
- , Part::partd];
+Module[ {lastfit = {1, β0}, dr, δ = δ0},
+ dr = D[r, {First /@ β0}];
While[δ >= δ1,
- lastfit = levenbergMarquardtHelper[δ, rf, Jf, lastfit[[2]]];
+ lastfit = levenbergMarquardtHelper[r /. Δ -> δ, dr /. Δ -> δ, lastfit[[2]], λ0, ν, ε];
Print[lastfit[[1]]];
δ /= δδ;
];
lastfit
]
+fitCov[res_, s_] :=
+ With[{J = D[res, {s[[All, 1]]}]},
+ Symmetrize[Inverse[SetPrecision[Transpose[J] . J /. s, 60]]]]
+
EndPackage[]