diff options
| -rw-r--r-- | new_schofield.nb | 11976 | ||||
| -rw-r--r-- | schofield.wl | 90 |
2 files changed, 2207 insertions, 9859 deletions
diff --git a/new_schofield.nb b/new_schofield.nb index a5a5d1e..5ad1c12 100644 --- a/new_schofield.nb +++ b/new_schofield.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 653051, 14042] -NotebookOptionsPosition[ 515736, 11796] -NotebookOutlinePosition[ 516134, 11812] -CellTagsIndexPosition[ 516091, 11809] +NotebookDataLength[ 275314, 6362] +NotebookOptionsPosition[ 198348, 5099] +NotebookOutlinePosition[ 198747, 5115] +CellTagsIndexPosition[ 198704, 5112] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -32,7 +32,7 @@ Cell[BoxData[ 3.839479110850239*^9}, {3.839569665835891*^9, 3.839569666219857*^9}, { 3.83957102205329*^9, 3.8395710222207737`*^9}, {3.841389917784724*^9, 3.841389919112598*^9}}, - CellLabel->"In[1]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"], + CellLabel->"In[97]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"], Cell[BoxData[{ RowBox[{ @@ -2117,14 +2117,14 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"{", RowBox[{ - 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+ h v] - rold) / h - J . v))] / 2] +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] , LinearSolve::luc ] +levenbergMarquardt[r_, β0_, λ0_ : 1, ν_ : 2, ε_ : 10^-15] := + Module[ + { + n = Length[β0], + rf, Jf + }, + PrintTemporary["Compiling the Jacobian..."]; + 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]; + levenbergMarquardtHelper[1, rf, Jf, β0, λ0, ν, ε] + ] + -levenburgMarquardt[r_, β0_, λ0_ : 1, ν_ : 2, ε_ : 10^-15] := +levenbergMarquardtHelper[Δ_, rf_, Jf_, β0_, λ0_ : 1, ν_ : 1.5, ε_ : 10^-15, accOff_ : False] := Module[ { n = Length[β0], β = β0, λ = λ0, newβ = β0, - x, rf, Jf, oldJ, oldr, newr, M, g, δ, oldC, newC, δlast, - h = 0.1, fvv, α = 0.75, a, v, U, nSteps = 0 + x, oldJ, oldr, newr, M, g, δ, oldC, newC, vlast, + h = 0.1, fvv, α = 0.75, a, v, U, nSteps = 0, reject, μ =3 }, - PrintTemporary["Compiling the Jacobian..."]; - rf = Quiet[Compile[{{x, _Real, 1}}, - Evaluate[r /. Thread[Rule[First /@ β, Part[x, #] & /@ Range[n]]]] - ], Part::partd]; - Jf = Quiet[Compile[{{x, _Real, 1}}, - Evaluate[D[r, {First /@ β}] /. Thread[Rule[First /@ β, Part[x, #] & /@ Range[n]]]] - ], Part::partd]; PrintTemporary["Beginning the algorithm."]; - oldr = rf[β[[All, 2]]]; - oldJ = Jf[β[[All, 2]]]; + oldr = rf[Append[β[[All, 2]], Δ]]; + oldJ = Jf[Append[β[[All, 2]], Δ]]; 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 / ν, g]; - a = levenbergMarquardtAcceleration[M, λ / ν, v, oldJ, oldr, rf, h, β]; - δ = v + a; - δlast = δ; + v = levenbergMarquardtStep[M, λ, g]; + a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, rf, h, β, Δ]; + δ = v + If[accOff, 0, a]; + vlast = v; PrintTemporary["Current cost value: ", Dynamic[oldC]]; While[Norm[δ] > ε, newβ[[All, 2]] += δ; - newr = rf[newβ[[All, 2]]]; + newr = rf[Append[newβ[[All, 2]], Δ]]; newC = Re[Total[newr^2]]; - While[((1 - δ . δlast / Norm[δ] / Norm[δlast])newC > oldC) || (2 Norm[a] / Norm[v] > α), + 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 = v + a; + a = levenbergMarquardtAcceleration[M, λ, v, oldJ, oldr, rf, h, β, Δ]; + δ = v + If[accOff, 0, a]; newβ = β; newβ[[All, 2]] += δ; - newr = rf[newβ[[All, 2]]]; + newr = rf[Append[newβ[[All, 2]], Δ]]; newC = Re[Total[newr^2]]; - λ *= ν; ]; - λ /= ν; oldC = newC; oldr = newr; β = newβ; - oldJ = Jf[β[[All, 2]]]; + oldJ = Jf[Append[β[[All, 2]], Δ]]; U = First[SingularValueDecomposition[oldJ]]; g = Re[Transpose[oldJ] . oldr]; M = Re[Transpose[oldJ] . oldJ]; - v = levenbergMarquardtStep[M, λ / ν, g]; - a = levenbergMarquardtAcceleration[M, λ / ν, v, oldJ, oldr, rf, h, β]; - δlast = δ; - δ = v + a; + 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]; nSteps += 1; ]; - Print[nSteps]; {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]; + While[δ >= δ1, + lastfit = levenbergMarquardtHelper[δ, rf, Jf, lastfit[[2]]]; + Print[lastfit[[1]]]; + δ /= δδ; + ]; + lastfit +] + EndPackage[] |