diff options
| -rw-r--r-- | m11-2.wl | 10 | ||||
| -rw-r--r-- | m11.wl | 11 | ||||
| -rw-r--r-- | m8.wl | 18 | ||||
| -rw-r--r-- | new_schofield.nb | 33432 | ||||
| -rw-r--r-- | s11.wl | 11 | ||||
| -rw-r--r-- | schofield.wl | 109 |
6 files changed, 30709 insertions, 2882 deletions
diff --git a/m11-2.wl b/m11-2.wl new file mode 100644 index 0000000..8fd2334 --- /dev/null +++ b/m11-2.wl @@ -0,0 +1,10 @@ +(* Created with the Wolfram Language : www.wolfram.com *) +{44.1455365446347, {\[Theta]c -> 1.3996678273044187, + \[Theta]0 -> 0.19657716689868718, AH -> -2.5496048635470787, + A[1] -> 1.7293729017965527, A[2] -> 0.5922884824663168, + gC[1] -> -0.36979238667656467, gC[2] -> 0.002968078845974853, + A[3] -> -0.2916655943110614, gC[3] -> 0.0527958256144447, + gC[4] -> -0.02010289010025246, A[4] -> 0.07506575034449132, + gC[5] -> 0.003409047702842989, gC[6] -> -0.0002344412816387626, + A[5] -> -0.007116812172949844, gC[7] -> -0.000018352846229494057, + gC[8] -> 2.8743650612586413*^-6, A[6] -> -0.00004059955187474823}} @@ -0,0 +1,11 @@ +(* Created with the Wolfram Language : www.wolfram.com *) +{46.09717221309653, {\[Theta]c -> 1.3946138306670082, + \[Theta]0 -> 0.19657199819072152, AH -> -2.549884341329218, + A[1] -> 1.729824822954169, A[2] -> 0.5936422729924692, + gC[1] -> -0.3668176862190405, gC[2] -> 0.0017034014515813535, + A[3] -> -0.2907234499611062, gC[3] -> 0.0527244497325125, + gC[4] -> -0.019930276510068432, A[4] -> 0.07443664599491684, + gC[5] -> 0.0034547342987311437, gC[6] -> -0.00023454445562759953, + A[5] -> -0.007132897669965838, gC[7] -> -0.000029009558483817375, + gC[8] -> 6.858876270903605*^-6, A[6] -> 0.000023324292969831963, + gC[9] -> -4.5663240630002894*^-7}} @@ -1,10 +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}} +{477.8872720993887, {\[Theta]c -> 1.3945095399721226, + \[Theta]0 -> 0.19657331402448114, AH -> -2.540815351266595, + A[1] -> 1.7168304596304513, A[2] -> 0.58914437918972, + gC[1] -> -0.3578933157155564, gC[2] -> -0.0002471276399885635, + A[3] -> -0.28467214257786666, gC[3] -> 0.05289863457865093, + gC[4] -> -0.0201090322678147, A[4] -> 0.073168474426385, + gC[5] -> 0.0034486104788930307, gC[6] -> -0.00021837125394706086, + A[5] -> -0.007098620515609658, gC[7] -> -0.000025781921631023817, + gC[8] -> 3.737427990965571*^-6, A[6] -> 0.000017492654253389754}} diff --git a/new_schofield.nb b/new_schofield.nb index e80a47b..5e541df 100644 --- a/new_schofield.nb +++ b/new_schofield.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 229983, 5139] -NotebookOptionsPosition[ 214867, 4911] -NotebookOutlinePosition[ 215264, 4927] -CellTagsIndexPosition[ 215221, 4924] +NotebookDataLength[ 1895487, 32889] +NotebookOptionsPosition[ 1880585, 32654] +NotebookOutlinePosition[ 1880983, 32670] +CellTagsIndexPosition[ 1880940, 32667] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -33,7 +33,7 @@ Cell[BoxData[ 3.83957102205329*^9, 3.8395710222207737`*^9}, {3.841389917784724*^9, 3.841389919112598*^9}, {3.8424227955510283`*^9, 3.842422804973724*^9}, { 3.8425181034802094`*^9, 3.8425181185428543`*^9}}, - CellLabel->"In[13]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"], + CellLabel->"In[1]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"], Cell[BoxData[{ RowBox[{ @@ -63,6 +63,15 @@ Cell[BoxData[ CellChangeTimes->{{3.840877914184023*^9, 3.840877925544536*^9}}, CellLabel->"In[4]:=",ExpressionUUID->"2fdffe9d-9220-4c97-866d-0a1f5e3200a1"], +Cell[BoxData[ + RowBox[{ + RowBox[{"$DefaultRemoteKernel", "=", + RowBox[{ + "RemoteKernelObject", "[", "\"\<ssh://math@sident.lassp.cornell.edu\>\"", + 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"Input",ExpressionUUID->"cdb9b75d-4c04-4ef5-9969-9e72079c5d58"], +Cell[1863259, 32207, 1671, 39, 89, "Input",ExpressionUUID->"e7739266-4bd1-4804-846a-5133bf45bfe6"], +Cell[1864933, 32248, 1740, 42, 105, "Input",ExpressionUUID->"e0c29aa2-30dd-4eb9-990b-b4abf8865eeb"], +Cell[1866676, 32292, 1946, 49, 105, "Input",ExpressionUUID->"80a3d021-bc5a-410c-8e70-089bc45d33bc"], +Cell[1868625, 32343, 2035, 50, 105, "Input",ExpressionUUID->"1d95a4fa-b7b4-4d6f-9695-22a28602846c"], +Cell[1870663, 32395, 2280, 55, 121, "Input",ExpressionUUID->"f3f292b7-6741-4c30-b2ac-b80cd82a3eaa"], +Cell[1872946, 32452, 2423, 60, 121, "Input",ExpressionUUID->"b6e4cc8e-edfb-44a9-a3e6-a4d9a234eb0c"], +Cell[1875372, 32514, 2451, 62, 137, "Input",ExpressionUUID->"2f0f517e-a884-4fb5-aa03-33b1e6e8e890"], Cell[CellGroupData[{ -Cell[212492, 4852, 1821, 41, 41, "Input",ExpressionUUID->"b9ab51e0-9b64-4dfa-80a9-3047d72051b1"], -Cell[214316, 4895, 511, 11, 20, "Message",ExpressionUUID->"edaad5f4-5205-486f-b107-406316036f3a"] +Cell[1877848, 32580, 782, 21, 72, "Input",ExpressionUUID->"990c0156-b917-447b-8ea2-39f8d0d504d1"], +Cell[1878633, 32603, 1912, 46, 60, "Output",ExpressionUUID->"81cdba28-d0b6-47a3-9244-3d7e31ecea11"] }, Open ]] }, Open ]] }, Open ]] @@ -0,0 +1,11 @@ +(* Created with the Wolfram Language : www.wolfram.com *) +{1156.5563282982414, {\[Theta]c -> 1.3913474674915387, + \[Theta]0 -> 0.19655731479519636, AH -> -2.543160499630645, + A[1] -> 1.7202774828753598, A[2] -> 0.5931379821475696, + gC[1] -> -0.3590042949089068, gC[2] -> -0.0020294361484579516, + A[3] -> -0.28632916219030613, gC[3] -> 0.05284520770144243, + gC[4] -> -0.0200782236788562, A[4] -> 0.07340497669659873, + gC[5] -> 0.0034133036368888883, gC[6] -> -0.00021383325303668766, + A[5] -> -0.007299574480334138, gC[7] -> -0.00002495169711421392, + gC[8] -> 3.6299187273213372*^-6, A[6] -> 0.0000294160793005649, + gC[9] -> -1.2350236293412953*^-8}} diff --git a/schofield.wl b/schofield.wl index 3f45f5d..98f9721 100644 --- a/schofield.wl +++ b/schofield.wl @@ -32,7 +32,7 @@ $Assumptions = {θc > 0, θc > 1, gC[_] ∈ Reals, B > 0} Δ[D_:2] := β[D] δ[D] -OverBar[s] := 2^(1/12) Exp[-1/8] Glaisher^(3/2) +os := 2^(1/12) Exp[-1/8] Glaisher^(3/2) t[θ_] := ((θ/1)^2 - 1) h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2*i+1), {i, 0, n}] @@ -95,11 +95,11 @@ dΦdηList[n_, h_][m_, θp_] := Module[ Table[Sum[df[[k+1]] BellY[j, k, ds[[;; j - k + 1]]], {k, 0, j}]/(j!), {j, 0, m}] ] -ruleB[g_] := B -> (2 * OverBar[s] / π) * (- g'[θc] / t[θc]^Δ[2]) +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)) 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] +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] eqLowRHSReg[n_][m_] := dRFc[n][m] @@ -137,8 +137,8 @@ eqMid[F_, h_][m_] := D[ Gls = { 0, - -OverBar[s], - −1.000960328725262189480934955172097320572505951770117 Sqrt[2]/((2 )^(-7/8) (2^(3/16)/OverBar[s])^2)/2/(12 \[Pi]), + -os, + −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)], @@ -156,7 +156,7 @@ Gls = { Ghs = { 0, 0, - -1.000815260440212647119476363047210236937534925597789 Sqrt[2]/((2 )^(-7/8) (2^(3/16)/OverBar[s])^2)/2, + -1.000815260440212647119476363047210236937534925597789 Sqrt[2]/((2 )^(-7/8) (2^(3/16)/os)^2)/2, 0, Around[ 8.333711750, 5.0 10^(-9)], 0, @@ -189,7 +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]] +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] newSol[eqs_, oldSol_, newVars_, δ_:0, γ_:0, opts___] := FindRoot[ @@ -203,13 +203,12 @@ newSol[eqs_, oldSol_, newVars_, δ_:0, γ_:0, opts___] := FindRoot[ ] levenbergMarquardtStep[M_, λ_, g_] := Quiet[ - - LinearSolve[M + λ DiagonalMatrix[Diagonal[M]], g] + - LinearSolve[M + λ DiagonalMatrix[Max[10^-5, #] & /@Diagonal[M]], g] , LinearSolve::luc ] 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] + - Re[LinearSolve[M + λ DiagonalMatrix[Max[10^-5, #] & /@Diagonal[M]], Transpose[J].(2/h((rf[β[[All,2]] + h v] - rold) / h - J . v))] / 2] , LinearSolve::luc ] @@ -232,7 +231,7 @@ levenbergMarquardt[r_, β0_, λ0_ : 1, ν_ : 2, ε_ : 10^-15] := ] -levenbergMarquardtHelper[r_, J_, β0_, λ0_ : 1, ν_ : 2, ε_ : 10^-15] := +levenbergMarquardtHelper[Δ_, rf_, Jf_, β0_, λ0_ : 1, ν_ : 1.5, ε_ : 10^-15] := Module[ { n = Length[β0], @@ -240,61 +239,107 @@ levenbergMarquardtHelper[r_, J_, β0_, λ0_ : 1, ν_ : 2, ε_ : 10^-15] := λ = λ0, newβ = β0, x, oldJ, oldr, newr, M, g, δ, oldC, newC, vlast, - h = 0.1, fvv, α = 0.1, a, v, U, nSteps = 0, reject, μ =3 + h = 0.1, α = 0.1, a, v, μ = 5 }, - PrintTemporary["Beginning the algorithm."]; - oldr = r /. β; - oldJ = J /. β; - U = First[SingularValueDecomposition[oldJ]]; + oldr = rf[Append[β[[All, 2]], Δ]]; + oldJ = Jf[Append[β[[All, 2]], Δ]]; 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, r, h, β]; + a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, rf, h, β, Δ]; δ = v + a; vlast = v; PrintTemporary["Current cost value: ", Dynamic[oldC]]; While[Norm[δ] > ε, newβ[[All, 2]] += δ; - newr = r /. newβ; + newr = rf[Append[newβ[[All, 2]], Δ]]; 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, r, h, β]; + a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, rf, h, β, Δ]; δ = v + a; newβ = β; newβ[[All, 2]] += δ; - newr = r /. newβ; + newr = rf[Append[newβ[[All, 2]], Δ]]; newC = Re[Total[newr^2]]; ]; oldC = newC; oldr = newr; β = newβ; - oldJ = J /. β; - U = First[SingularValueDecomposition[oldJ]]; + oldJ = Jf[Append[β[[All, 2]], Δ]]; 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, r, h, β]; + a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, rf, h, β, Δ]; 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}, dr, δ = δ0}, - dr = D[r, {First /@ β0}]; - While[δ >= δ1, - lastfit = levenbergMarquardtHelper[r /. Δ -> δ, dr /. Δ -> δ, lastfit[[2]], λ0, ν, ε]; - Print[lastfit[[1]]]; - δ /= δδ; +annealFit[r_, β0_, γ_ : 0, λ0_ : 1, ν_ : 2, μ_ : 3, ε_: 10^-14, h_ : 0.1, α_ : 0.1] := +Module[ { + rf, Jf, + n = Length[β0], + β = β0, + λ = λ0, + newβ = β0, + x, oldJ, oldr, newr, M, g, δβ, oldC, newC, vlast, + a, v + }, + Quiet[ + rf = Compile[{{x, _Real, 1}}, + Evaluate[r /. Thread[Rule[First /@ β0, Part[x, #] & /@ Range[n]]]] + ]; + Jf = Compile[{{x, _Real, 1}}, + Evaluate[D[r, {First /@ β0}] /. Thread[Rule[First /@ β0, Part[x, #] & /@ Range[n]]]] + ]; + , Part::partd]; + If[γ > 0, + β[[All, 2]] += RandomVariate[NormalDistribution[0, γ], n]]; + newβ = β; + λ = λ0; + oldr = rf[β[[All, 2]]]; + oldJ = Jf[β[[All, 2]]]; + 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]; + δβ = v + a; + vlast = v; + While[Norm[δβ] > ε, + newβ[[All, 2]] += δβ; + newr = rf[newβ[[All, 2]]]; + 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]; + δβ = v + a; + newβ = β; + newβ[[All, 2]] += δβ; + newr = rf[newβ[[All, 2]]]; + newC = Re[Total[newr^2]]; + ]; + oldC = newC; + oldr = newr; + β = newβ; + oldJ = Jf[β[[All, 2]]]; + 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]; + δβ = v + a; ]; - lastfit + {oldC, β} ] fitCov[res_, s_] := |