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authorJaron Kent-Dobias <jaron@kent-dobias.com>2021-10-19 17:44:20 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2021-10-19 17:44:20 +0200
commit96caec0cfcd5b6aaed53676062bd91932c7a0b35 (patch)
tree4fbb752452fa9f97f50c799dc4fcaba08037d816
parent4eae6a3b275df83426e97997d5dad9e7e05a06f9 (diff)
downloadmma-96caec0cfcd5b6aaed53676062bd91932c7a0b35.tar.gz
mma-96caec0cfcd5b6aaed53676062bd91932c7a0b35.tar.bz2
mma-96caec0cfcd5b6aaed53676062bd91932c7a0b35.zip
Work.
Diffstat
-rw-r--r--m11-2.wl10
-rw-r--r--m11.wl11
-rw-r--r--m8.wl18
-rw-r--r--new_schofield.nb33432
-rw-r--r--s11.wl11
-rw-r--r--schofield.wl109
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}}
diff --git a/m11.wl b/m11.wl
new file mode 100644
index 0000000..ff7185a
--- /dev/null
+++ b/m11.wl
@@ -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}}
diff --git a/m8.wl b/m8.wl
index 8875506..a313ad9 100644
--- a/m8.wl
+++ b/m8.wl
@@ -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\>\"",
+ "]"}]}], ";"}]], "Input",
+ CellChangeTimes->{{3.8425246889199257`*^9, 3.8425247111111097`*^9}},
+ CellLabel->"In[5]:=",ExpressionUUID->"8f4d55d2-f559-4382-a0b2-1a4eb0ce0b9a"],
+
Cell[CellGroupData[{
Cell["Match ends", "Section",
@@ -82,7 +91,7 @@ Cell[BoxData[
RowBox[{
RowBox[{"nAs", "=", "2"}], ";"}]], "Input",
CellChangeTimes->{{3.841213645969795*^9, 3.841213648302487*^9}},
- CellLabel->"In[5]:=",ExpressionUUID->"c2736e8b-b9a2-44e3-be7a-35f424888e11"],
+ CellLabel->"In[33]:=",ExpressionUUID->"c2736e8b-b9a2-44e3-be7a-35f424888e11"],
Cell[CellGroupData[{
@@ -144,20 +153,21 @@ Cell[BoxData[
3.841994430388618*^9, 3.8419944408046093`*^9}, {3.841994755179496*^9,
3.841994755346443*^9}, {3.841994896941716*^9, 3.841994926998374*^9}, {
3.841994983607177*^9, 3.8419950242243156`*^9}, {3.841995200194737*^9,
- 3.8419952057475653`*^9}},
- CellLabel->"In[6]:=",ExpressionUUID->"a326d1ad-f5a3-49d5-9b86-3a79e4cb291c"],
+ 3.8419952057475653`*^9}, {3.842688660466323*^9, 3.842688668562681*^9}, {
+ 3.842688747500245*^9, 3.842688751827346*^9}},
+ CellLabel->"In[34]:=",ExpressionUUID->"a326d1ad-f5a3-49d5-9b86-3a79e4cb291c"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
- RowBox[{"\[Theta]c", "\[Rule]", "1.140880712736358`"}], ",",
- RowBox[{"\[Theta]0", "\[Rule]", "0.19739663849533437`"}], ",",
+ RowBox[{"\[Theta]c", "\[Rule]", "1.1601426664504497`"}], ",",
+ RowBox[{"\[Theta]0", "\[Rule]", "0.1976347222403779`"}], ",",
RowBox[{"AH", "\[Rule]",
- RowBox[{"-", "2.448385445073114`"}]}], ",",
+ RowBox[{"-", "2.4223780247586535`"}]}], ",",
RowBox[{
- RowBox[{"A", "[", "1", "]"}], "\[Rule]", "1.6244482861491158`"}], ",",
+ RowBox[{"A", "[", "1", "]"}], "\[Rule]", "1.5808792797213091`"}], ",",
RowBox[{
- RowBox[{"A", "[", "2", "]"}], "\[Rule]", "0.5400156139770322`"}]}],
+ RowBox[{"A", "[", "2", "]"}], "\[Rule]", "0.5226041775708052`"}]}],
"}"}]], "Output",
CellChangeTimes->{{3.841213667298201*^9, 3.841213680834222*^9}, {
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@@ -176,8 +186,17 @@ Cell[BoxData[
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@@ -200,20 +219,18 @@ Cell[BoxData[
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Cell[BoxData[
RowBox[{"{",
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@@ -242,10 +267,11 @@ Cell[BoxData[
RowBox[{
RowBox[{"dGd\[Xi]LowList", "[",
RowBox[{"2", ",",
- RowBox[{"h", "[", "0", "]"}]}], "]"}], "[", "6", "]"}], "]"}], "//.",
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- RowBox[{"h", "[", "0", "]"}], "]"}]}], "/.", "s0"}], "]"}]}],
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+ RowBox[{"h", "[", "0", "]"}], "]"}]}], "/.",
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RowBox[{"h", "[", "0", "]"}]}], "]"}], "[",
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RowBox[{"rules", "[",
- RowBox[{"h", "[", "0", "]"}], "]"}]}], "/.", "s0"}], "]"}]}],
- "\[IndentingNewLine]", "}"}], "]"}]], "Input",
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}, Open ]],
-Cell[136054, 3060, 2031, 51, 76, "Output",ExpressionUUID->"95a89ed3-1405-46fd-84e6-4e39c6d0115c"]
+Cell[CellGroupData[{
+Cell[328029, 6825, 2206, 52, 62, "Input",ExpressionUUID->"997c9c3d-3291-4f27-afcd-2a3c02bfd3fd"],
+Cell[330238, 6879, 23560, 404, 253, "Output",ExpressionUUID->"b89ead09-4dd2-4e82-9f4f-7394478ce32f"]
}, Open ]],
Cell[CellGroupData[{
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}, Open ]],
-Cell[140472, 3173, 12251, 241, 198, "Input",ExpressionUUID->"673ffefa-75f0-46ac-befd-c785b4bc3ce1"],
Cell[CellGroupData[{
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+Cell[1484232, 25855, 1176, 30, 41, "Input",ExpressionUUID->"626e933d-cd37-4a52-851f-6473bebeff53"],
+Cell[1485411, 25887, 163730, 2704, 317, "Output",ExpressionUUID->"df893735-eb2f-4fa8-937b-dbb343a52a39"]
}, Open ]],
Cell[CellGroupData[{
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-Cell[170735, 3828, 15720, 365, 347, "Output",ExpressionUUID->"c05b3224-88e5-4816-869c-4737a893ff59"]
+Cell[1649178, 28596, 1906, 42, 75, "Input",ExpressionUUID->"9985bed4-dad9-41a8-a4a0-bf515be7111c"],
+Cell[1651087, 28640, 199193, 3283, 362, "Output",ExpressionUUID->"7ad32301-6347-4a43-8055-9158b827767a"]
}, Open ]],
-Cell[186470, 4196, 154, 3, 22, "Input",ExpressionUUID->"a1f6b25c-0873-4498-a93d-113565ed896c"],
Cell[CellGroupData[{
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-Cell[188365, 4247, 10185, 224, 339, "Output",ExpressionUUID->"cb1c4020-ab43-4766-b2c6-457ac2e5298a"]
+Cell[1850317, 31928, 1018, 27, 24, "Input",ExpressionUUID->"95c3ad10-59a3-4496-bbd9-ec9966e153e1"],
+Cell[1851338, 31957, 8989, 170, 163, "Output",ExpressionUUID->"a3028a35-bb3d-4af0-9cec-08135dfa52fc"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
-Cell[198599, 4477, 159, 3, 41, "Subsection",ExpressionUUID->"36c7685a-f47a-40aa-a737-8c7f6f4317c1"],
-Cell[198761, 4482, 791, 22, 89, InheritFromParent,ExpressionUUID->"afc540ea-ef9a-493b-9583-ed901e3ac580"],
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-Cell[210447, 4794, 2020, 54, 137, InheritFromParent,ExpressionUUID->"a5a4b4cf-3264-415e-9912-fe5941040891"],
+Cell[1860376, 32133, 159, 3, 41, "Subsection",ExpressionUUID->"36c7685a-f47a-40aa-a737-8c7f6f4317c1"],
+Cell[1860538, 32138, 1301, 31, 72, "Input",ExpressionUUID->"afc540ea-ef9a-493b-9583-ed901e3ac580"],
+Cell[1861842, 32171, 1414, 34, 89, "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"],
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+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 ]]
diff --git a/s11.wl b/s11.wl
new file mode 100644
index 0000000..e6293c8
--- /dev/null
+++ b/s11.wl
@@ -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_] :=