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-rw-r--r--new_schofield.nb11976
-rw-r--r--schofield.wl90
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 @@
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-Cell[515563, 11790, 71, 0, 178, "Output",ExpressionUUID->"b7f39439-0c1d-40f8-af40-5fed6fd931de"],
-Cell[515637, 11792, 71, 0, 25, "Output",ExpressionUUID->"2b7f8ec2-0126-4787-92e3-a6d9dd600de2"]
}, Open ]]
-}, Closed]]
}
]
*)
diff --git a/schofield.wl b/schofield.wl
index 77dce96..40253d4 100644
--- a/schofield.wl
+++ b/schofield.wl
@@ -213,73 +213,101 @@ levenbergMarquardtStep[M_, λ_, g_] := Quiet[
, LinearSolve::luc
]
-levenbergMarquardtAcceleration[M_, λ_, v_, J_, rold_, rf_, h_, β_] := Quiet[
- - Re[LinearSolve[M + λ DiagonalMatrix[Diagonal[M]], Transpose[J].(2/h((rf[β[[All,2]] + 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[]