diff --git a/Data/notebooks/Ec.nb b/Data/notebooks/Ec.nb index af5ab2b..756446b 100644 --- a/Data/notebooks/Ec.nb +++ b/Data/notebooks/Ec.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 10108305, 188640] -NotebookOptionsPosition[ 10076594, 188110] -NotebookOutlinePosition[ 10076987, 188126] -CellTagsIndexPosition[ 10076944, 188123] +NotebookDataLength[ 10114646, 188765] +NotebookOptionsPosition[ 10082918, 188235] +NotebookOutlinePosition[ 10083312, 188251] +CellTagsIndexPosition[ 10083269, 188248] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -1256,7 +1256,7 @@ Cell[BoxData[ 3.8358426235399923`*^9, 3.835842647113277*^9}, {3.8358427468092012`*^9, 3.835842766149206*^9}, 3.835842872017395*^9, {3.8364826140299664`*^9, 3.836482689913847*^9}, {3.836723977584033*^9, 3.836723999892174*^9}}, - CellLabel->"In[94]:=",ExpressionUUID->"a67ae21a-c72d-4d67-abe2-1be3a36cc379"], + CellLabel->"In[5]:=",ExpressionUUID->"a67ae21a-c72d-4d67-abe2-1be3a36cc379"], Cell[BoxData[ RowBox[{ @@ -1638,7 +1638,7 @@ Cell[BoxData[ 3.835842735188808*^9}, {3.835842833547297*^9, 3.835842842539638*^9}, 3.8358428762049923`*^9, {3.8364826954520607`*^9, 3.8364827243067417`*^9}, { 3.836723984893615*^9, 3.836723992741331*^9}}, - CellLabel->"In[95]:=",ExpressionUUID->"9512555e-aa1a-4421-b857-cbdcec0bc190"] + CellLabel->"In[6]:=",ExpressionUUID->"9512555e-aa1a-4421-b857-cbdcec0bc190"] }, Closed]], Cell[CellGroupData[{ @@ -1676,8 +1676,8 @@ Cell[BoxData[ ",", "fitPT2OO", ",", "fitrPT2OO", ",", "\[IndentingNewLine]", RowBox[{"start", "=", "9"}], ",", RowBox[{"nfit", "=", "5"}], ",", "wPT2NO", ",", "wrPT2NO", ",", - "wPT2OO", ",", "wrPT2OO", ",", "TabPT2", ",", "TabrPT2", ",", "plot"}], - "}"}], ",", "\[IndentingNewLine]", + "wPT2OO", ",", "wrPT2OO", ",", "TabPT2", ",", "TabrPT2NO", ",", + "TabrPT2OO", ",", "plot"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"NO", "=", RowBox[{"Import", "[", @@ -1874,7 +1874,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Take", "[", RowBox[{"SCIrPT2NO", ",", - RowBox[{"-", "nfit"}]}], "]"}], ",", + RowBox[{"-", "nfit"}], ","}], "]"}], ",", RowBox[{"{", RowBox[{"1", ",", "x"}], "}"}], ",", "x"}], "]"}]}], ";", "\[IndentingNewLine]", @@ -2032,7 +2032,7 @@ $E_\\\\text{PT2}^\\\\text{OO}$}\>\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], "}"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{"TabrPT2", "=", + RowBox[{"TabrPT2OO", "=", RowBox[{"TableForm", "[", RowBox[{ RowBox[{"Table", "[", @@ -2063,7 +2063,7 @@ $E_\\\\text{PT2}^\\\\text{OO}$}\>\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], "}"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{"Print", "[", + RowBox[{"TabrPT2NO", "=", RowBox[{"TableForm", "[", RowBox[{ RowBox[{"Table", "[", @@ -2093,7 +2093,7 @@ $E_\\\\text{PT2}^\\\\text{OO}$}\>\"", ",", RowBox[{"None", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], - "}"}]}], "}"}]}]}], "]"}], "]"}], ";", "\[IndentingNewLine]", + "}"}]}], "}"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{"ExpFig", ",", RowBox[{"Export", "[", @@ -2102,11 +2102,145 @@ $E_\\\\text{PT2}^\\\\text{OO}$}\>\"", ",", RowBox[{"ToString", "[", "Mol", "]"}], "<>", "\"\<_EvsPT2.pdf\>\""}], ",", "plot"}], "]"}]}], "]"}], ";", "\[IndentingNewLine]", + RowBox[{"(*", + RowBox[{ + RowBox[{"Print", "[", "\[IndentingNewLine]", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"k", ",", + RowBox[{ + SuperscriptBox["10", "3"], + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"Last", "[", "NO", "]"}], "\[LeftDoubleBracket]", + "2", "\[RightDoubleBracket]"}], "+", + RowBox[{ + RowBox[{"Last", "[", "NO", "]"}], "\[LeftDoubleBracket]", + "5", "\[RightDoubleBracket]"}], "-", "HF"}], ")"}]}], ",", + RowBox[{ + RowBox[{"Evaluate", "[", + RowBox[{ + RowBox[{"LinearModelFit", "[", + RowBox[{ + RowBox[{"Take", "[", + RowBox[{"SCIrPT2NO", ",", + RowBox[{"-", "k"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "x"}], "}"}], ",", "x", ",", + RowBox[{"Weights", "\[Rule]", + RowBox[{"1", "/", + SuperscriptBox[ + RowBox[{"Take", "[", + RowBox[{"wrPT2NO", ",", + RowBox[{"-", "k"}]}], "]"}], "2"]}]}]}], "]"}], "//", + "Normal"}], "]"}], "/.", + RowBox[{"x", "\[Rule]", "0"}]}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{ + SuperscriptBox["10", "3"], + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"Last", "[", "NO", "]"}], "\[LeftDoubleBracket]", + "2", "\[RightDoubleBracket]"}], "+", + RowBox[{ + RowBox[{"Last", "[", "NO", "]"}], "\[LeftDoubleBracket]", + "5", "\[RightDoubleBracket]"}], "-", "HF"}], ")"}]}], "-", + + RowBox[{"Evaluate", "[", + RowBox[{ + RowBox[{"LinearModelFit", "[", + RowBox[{ + RowBox[{"Take", "[", + RowBox[{"SCIrPT2NO", ",", + RowBox[{"-", "k"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "x"}], "}"}], ",", "x", ",", + RowBox[{"Weights", "\[Rule]", + RowBox[{"1", "/", + SuperscriptBox[ + RowBox[{"Take", "[", + RowBox[{"wrPT2NO", ",", + RowBox[{"-", "k"}]}], "]"}], "2"]}]}]}], "]"}], "//", + "Normal"}], "]"}]}], "/.", + RowBox[{"x", "\[Rule]", "0"}]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"k", ",", "3", ",", "7"}], "}"}]}], "]"}], + "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", + RowBox[{"Print", "[", "\[IndentingNewLine]", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"k", ",", + RowBox[{ + SuperscriptBox["10", "3"], + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"Last", "[", "OO", "]"}], "\[LeftDoubleBracket]", + "2", "\[RightDoubleBracket]"}], "+", + RowBox[{ + RowBox[{"Last", "[", "OO", "]"}], "\[LeftDoubleBracket]", + "5", "\[RightDoubleBracket]"}], "-", "HF"}], ")"}]}], ",", + RowBox[{ + RowBox[{"Evaluate", "[", + RowBox[{ + RowBox[{"LinearModelFit", "[", + RowBox[{ + RowBox[{"Take", "[", + RowBox[{"SCIrPT2OO", ",", + RowBox[{"-", "k"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "x"}], "}"}], ",", "x", ",", + RowBox[{"Weights", "\[Rule]", + RowBox[{"1", "/", + SuperscriptBox[ + RowBox[{"Take", "[", + RowBox[{"wrPT2OO", ",", + RowBox[{"-", "k"}]}], "]"}], "2"]}]}]}], "]"}], "//", + "Normal"}], "]"}], "/.", + RowBox[{"x", "\[Rule]", "0"}]}], ",", + RowBox[{ + RowBox[{ + RowBox[{ + SuperscriptBox["10", "3"], + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"Last", "[", "OO", "]"}], "\[LeftDoubleBracket]", + "2", "\[RightDoubleBracket]"}], "+", + RowBox[{ + RowBox[{"Last", "[", "OO", "]"}], "\[LeftDoubleBracket]", + "5", "\[RightDoubleBracket]"}], "-", "HF"}], ")"}]}], "-", + + RowBox[{"Evaluate", "[", + RowBox[{ + RowBox[{"LinearModelFit", "[", + RowBox[{ + RowBox[{"Take", "[", + RowBox[{"SCIrPT2OO", ",", + RowBox[{"-", "k"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "x"}], "}"}], ",", "x", ",", + RowBox[{"Weights", "\[Rule]", + RowBox[{"1", "/", + SuperscriptBox[ + RowBox[{"Take", "[", + RowBox[{"wrPT2OO", ",", + RowBox[{"-", "k"}]}], "]"}], "2"]}]}]}], "]"}], "//", + "Normal"}], "]"}]}], "/.", + RowBox[{"x", "\[Rule]", "0"}]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"k", ",", "3", ",", "7"}], "}"}]}], "]"}], + "\[IndentingNewLine]", "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"Row", "[", RowBox[{"{", - RowBox[{"plot", ",", "TabrPT2"}], "}"}], "]"}], "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}]}], ";"}]], "Input", + RowBox[{"plot", ",", "TabrPT2NO", ",", "TabrPT2OO"}], "}"}], "]"}], + "]"}], ";"}]}], "\[IndentingNewLine]", "]"}]}], ";"}]], "Input", InitializationCell->True, CellChangeTimes->{{3.833872913742401*^9, 3.8338730957719507`*^9}, { 3.8338733404092293`*^9, 3.833873340478711*^9}, {3.833873702006819*^9, @@ -2147,8 +2281,14 @@ $E_\\\\text{PT2}^\\\\text{OO}$}\>\"", ",", 3.8364842469572287`*^9}, {3.8364844196301937`*^9, 3.836484427964044*^9}, { 3.836484530912304*^9, 3.836484538852857*^9}, {3.836484639047102*^9, 3.83648464079974*^9}, {3.836485316103344*^9, 3.836485320950551*^9}, - 3.836724011841918*^9}, - CellLabel->"In[96]:=",ExpressionUUID->"4a7754e0-f469-452a-aa2e-0612e3e61cc4"], + 3.836724011841918*^9, {3.838976495459361*^9, 3.8389767001375723`*^9}, { + 3.838976763100322*^9, 3.838976824600512*^9}, {3.838977052482436*^9, + 3.838977135684705*^9}, {3.838977189393663*^9, 3.838977252719028*^9}, { + 3.838979812899804*^9, 3.8389798637621603`*^9}, {3.8389799365275927`*^9, + 3.8389799413274612`*^9}, {3.8389960749806767`*^9, 3.838996107454554*^9}, + 3.838998541788493*^9}, + CellLabel-> + "In[102]:=",ExpressionUUID->"4a7754e0-f469-452a-aa2e-0612e3e61cc4"], Cell[BoxData[ RowBox[{ @@ -2724,7 +2864,7 @@ $E_\\\\text{PT2}^\\\\text{OO}$}\>\"", ",", 3.836484243031506*^9}, {3.8364844748044443`*^9, 3.836484523280661*^9}, { 3.8364853259191713`*^9, 3.83648532759412*^9}, {3.836724018391357*^9, 3.836724018623048*^9}}, - CellLabel->"In[97]:=",ExpressionUUID->"b067e9ee-682a-4525-bf90-091d95752712"] + CellLabel->"In[8]:=",ExpressionUUID->"b067e9ee-682a-4525-bf90-091d95752712"] }, Closed]], Cell[CellGroupData[{ @@ -2938,8 +3078,7 @@ $\\\\mathcal{O}(N^\\\\alpha)$}\>\"", ",", 3.8367245756763*^9, 3.836724576283485*^9}, {3.8367247850312443`*^9, 3.836724785396144*^9}, {3.8367248183237762`*^9, 3.836724821004279*^9}, { 3.836724852353944*^9, 3.836724914116791*^9}}, - CellLabel-> - "In[682]:=",ExpressionUUID->"6bf0d177-eada-4bc7-8e00-b86af49684f3"] + CellLabel->"In[9]:=",ExpressionUUID->"6bf0d177-eada-4bc7-8e00-b86af49684f3"] }, Closed]] }, Closed]], @@ -3046,8 +3185,7 @@ Cell[BoxData[{ 3.836296907216282*^9, 3.8362969192059727`*^9}, {3.836297937035616*^9, 3.8362979398974543`*^9}, {3.8363009800593*^9, 3.836301031335051*^9}, 3.836301087567992*^9, {3.836301632789894*^9, 3.8363016489496727`*^9}}, - CellLabel-> - "In[686]:=",ExpressionUUID->"895ab98c-f42b-4d20-8b55-5797a7b91a74"], + CellLabel->"In[10]:=",ExpressionUUID->"895ab98c-f42b-4d20-8b55-5797a7b91a74"], Cell[CellGroupData[{ @@ -18869,8 +19007,7 @@ Cell[BoxData[{ 3.8362968061020947`*^9, 3.836296834963818*^9}, {3.836296867998667*^9, 3.836296888609527*^9}, {3.836297947818438*^9, 3.836297948730022*^9}, 3.836301112509487*^9, {3.836301612621418*^9, 3.836301629706069*^9}}, - CellLabel-> - "In[701]:=",ExpressionUUID->"45aa8230-f7ee-467a-96ce-1c41bb98be6e"], + CellLabel->"In[16]:=",ExpressionUUID->"45aa8230-f7ee-467a-96ce-1c41bb98be6e"], Cell[CellGroupData[{ @@ -33512,8 +33649,7 @@ Cell[BoxData[{ 3.836035311203528*^9, 3.8360353248146667`*^9}, {3.8360353852901506`*^9, 3.83603538844252*^9}, {3.836296929074575*^9, 3.836296974259878*^9}, 3.8363011392344646`*^9, {3.836301591603333*^9, 3.8363016092564783`*^9}}, - CellLabel-> - "In[716]:=",ExpressionUUID->"0f6df49c-36bc-4f29-a06b-1e01f88c8af7"], + CellLabel->"In[22]:=",ExpressionUUID->"0f6df49c-36bc-4f29-a06b-1e01f88c8af7"], Cell[CellGroupData[{ @@ -48573,8 +48709,7 @@ Cell[BoxData[{ 3.836034078526534*^9}, {3.836035396252777*^9, 3.83603540661322*^9}, { 3.8362970151729794`*^9, 3.836297037844171*^9}, 3.836301168086928*^9, { 3.836301570355815*^9, 3.8363015884340067`*^9}}, - CellLabel-> - "In[731]:=",ExpressionUUID->"f11bb471-abb4-4b35-b78e-924d82295d82"], + CellLabel->"In[28]:=",ExpressionUUID->"f11bb471-abb4-4b35-b78e-924d82295d82"], Cell[CellGroupData[{ @@ -63364,8 +63499,7 @@ Cell[BoxData[{ 3.8360354136141863`*^9, 3.8360354240751534`*^9}, {3.8362970463191643`*^9, 3.836297051021658*^9}, {3.836297084405161*^9, 3.836297099367598*^9}, 3.836301188846321*^9, {3.8363015462780247`*^9, 3.836301565356069*^9}}, - CellLabel-> - "In[746]:=",ExpressionUUID->"fec12b1f-939b-432a-89a4-71b4992d614a"], + CellLabel->"In[34]:=",ExpressionUUID->"fec12b1f-939b-432a-89a4-71b4992d614a"], Cell[CellGroupData[{ @@ -78418,8 +78552,7 @@ Cell[BoxData[{ 3.836297113328833*^9, 3.83629711919875*^9}, {3.836297154299591*^9, 3.836297167405526*^9}, 3.836301217268993*^9, {3.836301512799171*^9, 3.836301530517323*^9}}, - CellLabel-> - "In[761]:=",ExpressionUUID->"00ce6a41-3340-4211-974d-333201273f2b"], + CellLabel->"In[40]:=",ExpressionUUID->"00ce6a41-3340-4211-974d-333201273f2b"], Cell[CellGroupData[{ @@ -97047,8 +97180,7 @@ Cell[BoxData[{ 3.8357983406389523`*^9, 3.835798352989449*^9}, {3.8360354519720507`*^9, 3.836035470534597*^9}, {3.8362971749655313`*^9, 3.836297224436997*^9}, 3.836301245448848*^9, {3.836301489295274*^9, 3.836301508110798*^9}}, - CellLabel-> - "In[777]:=",ExpressionUUID->"9d9cd269-5af2-4502-b5cf-01d155493236"], + CellLabel->"In[46]:=",ExpressionUUID->"9d9cd269-5af2-4502-b5cf-01d155493236"], Cell[CellGroupData[{ @@ -112025,8 +112157,7 @@ hmcCiA74En0MRG+R3g6mT/m6R5lMeePoVhkCpovuHU4B0Vt2rUkF0RYNk4xW AGmnUg0TEJ1U+otFY+obRzX/L+wg+l7/+V+aQNo0Ue43iF50rlxYC0gf/3RC FEQDAEH6qpc= "], - CellLabel-> - "In[792]:=",ExpressionUUID->"3f8c9a69-d755-4607-984f-39042c34f390"], + CellLabel->"In[52]:=",ExpressionUUID->"3f8c9a69-d755-4607-984f-39042c34f390"], Cell[CellGroupData[{ @@ -127293,8 +127424,7 @@ Cell[BoxData[{ 3.83603551479957*^9, 3.8360355293709373`*^9}, {3.8362972909106293`*^9, 3.8362972959719687`*^9}, {3.8362973457069817`*^9, 3.8362973591999826`*^9}, 3.836301297008564*^9, {3.8363014407066727`*^9, 3.836301458785242*^9}}, - CellLabel-> - "In[807]:=",ExpressionUUID->"4e96eaec-94cc-465a-be70-f93c6b2a6381"], + CellLabel->"In[58]:=",ExpressionUUID->"4e96eaec-94cc-465a-be70-f93c6b2a6381"], Cell[CellGroupData[{ @@ -142297,8 +142427,7 @@ Cell[BoxData[{ 3.8360355386694183`*^9, 3.8360355506360073`*^9}, {3.836297367030525*^9, 3.836297414235635*^9}, 3.8363013169757357`*^9, {3.836301413874866*^9, 3.836301436019479*^9}}, - CellLabel-> - "In[822]:=",ExpressionUUID->"5cdc98a8-ba9a-4309-8652-c42849243a3c"], + CellLabel->"In[64]:=",ExpressionUUID->"5cdc98a8-ba9a-4309-8652-c42849243a3c"], Cell[CellGroupData[{ @@ -157547,8 +157676,7 @@ Cell[BoxData[{ 3.836035559701003*^9, 3.836035568787516*^9}, {3.8362974576995993`*^9, 3.8362974802124567`*^9}, 3.836301337627151*^9, {3.8363013869039183`*^9, 3.836301407126546*^9}}, - CellLabel-> - "In[838]:=",ExpressionUUID->"bb79f009-b78a-42cd-a70b-1c427ab4c78f"], + CellLabel->"In[70]:=",ExpressionUUID->"bb79f009-b78a-42cd-a70b-1c427ab4c78f"], Cell[CellGroupData[{ @@ -172547,8 +172675,7 @@ XcaoBaI/qQTYguignGUeILruhHsUiN63TC8ZRG849nIWiD5v0D8XRHst8nUz mfLG8fHRFHcQ7bIitn85kBY7lQCmVwW22a8A0vuKLziA6HrlD4oaU984yk+w VQPRLxa5+oNort4jASD6lcJpVi0gLa49mQNEAwCtXZpC "], - CellLabel-> - "In[853]:=",ExpressionUUID->"52f42957-7028-4c6a-87b7-6d3cbef3d400"], + CellLabel->"In[76]:=",ExpressionUUID->"52f42957-7028-4c6a-87b7-6d3cbef3d400"], Cell[CellGroupData[{ @@ -187379,7 +187506,7 @@ Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.836724608692368*^9}, CellLabel-> "In[868]:=",ExpressionUUID->"18d02b6c-55e6-4a07-b179-52672bef5bee"] -}, Closed]] +}, Open ]] }, Closed]], Cell[CellGroupData[{ @@ -187402,8 +187529,7 @@ Cell[BoxData[ InitializationCell->True, CellChangeTimes->{{3.8360347495881863`*^9, 3.83603480144481*^9}, 3.836035039829109*^9}, - CellLabel-> - "In[281]:=",ExpressionUUID->"0fbf8e5b-2c67-467d-9b6a-fedb8d5dd48a"], + CellLabel->"In[82]:=",ExpressionUUID->"0fbf8e5b-2c67-467d-9b6a-fedb8d5dd48a"], Cell[BoxData[ RowBox[{ @@ -187445,8 +187571,7 @@ Cell[BoxData[ InitializationCell->True, CellChangeTimes->{{3.836034387912941*^9, 3.836034427303453*^9}, { 3.836034506514387*^9, 3.836034673274126*^9}, 3.8360350365709467`*^9}, - CellLabel-> - "In[282]:=",ExpressionUUID->"6f1d9e38-cf5a-407d-bce7-a920d10a6249"], + CellLabel->"In[83]:=",ExpressionUUID->"6f1d9e38-cf5a-407d-bce7-a920d10a6249"], Cell[BoxData[ RowBox[{ @@ -187489,8 +187614,7 @@ Cell[BoxData[ CellChangeTimes->{{3.836034387912941*^9, 3.836034427303453*^9}, { 3.836034506514387*^9, 3.836034673274126*^9}, {3.8360350365709467`*^9, 3.836035073909945*^9}}, - CellLabel-> - "In[283]:=",ExpressionUUID->"4d9c28a8-eb44-41db-82fb-4a6d1da18c91"], + CellLabel->"In[84]:=",ExpressionUUID->"4d9c28a8-eb44-41db-82fb-4a6d1da18c91"], Cell[BoxData[ RowBox[{ @@ -187533,8 +187657,7 @@ Cell[BoxData[ CellChangeTimes->{{3.836034387912941*^9, 3.836034427303453*^9}, { 3.836034506514387*^9, 3.836034673274126*^9}, {3.8360350365709467`*^9, 3.836035097115736*^9}}, - CellLabel-> - "In[284]:=",ExpressionUUID->"36f8d626-8fdc-4100-a29e-d47d0d0eabe1"], + CellLabel->"In[85]:=",ExpressionUUID->"36f8d626-8fdc-4100-a29e-d47d0d0eabe1"], Cell[BoxData[ RowBox[{ @@ -187587,8 +187710,7 @@ Cell[BoxData[ CellChangeTimes->{{3.836035221872222*^9, 3.836035265973969*^9}, { 3.836297879041025*^9, 3.836297896964918*^9}, {3.836297999204657*^9, 3.8362980183261433`*^9}}, - CellLabel-> - "In[285]:=",ExpressionUUID->"58e226a7-7689-4a2b-ac93-4db52cc1c5b0"], + CellLabel->"In[86]:=",ExpressionUUID->"58e226a7-7689-4a2b-ac93-4db52cc1c5b0"], Cell[CellGroupData[{ @@ -187785,8 +187907,7 @@ Cell[BoxData[{ 3.836035856072257*^9}, {3.836297872843511*^9, 3.83629790813723*^9}, { 3.836298030105542*^9, 3.836298210942573*^9}, {3.836301734262437*^9, 3.8363017682677593`*^9}}, - CellLabel-> - "In[286]:=",ExpressionUUID->"a0e1fe79-49fa-4da6-8302-31437c3bebf7"], + CellLabel->"In[87]:=",ExpressionUUID->"a0e1fe79-49fa-4da6-8302-31437c3bebf7"], Cell[BoxData[ TagBox[ @@ -187848,10 +187969,11 @@ Cell[BoxData[ 3.836298156505755*^9, 3.836298218799776*^9, {3.836301655712038*^9, 3.836301661865406*^9}, 3.8363017057264557`*^9, 3.8363017689680843`*^9, 3.836482680248103*^9, 3.83648433435258*^9, 3.8365748057543907`*^9, - 3.836722201802979*^9, 3.836724142957694*^9}, + 3.836722201802979*^9, 3.836724142957694*^9, 3.838976437662228*^9, + 3.8389961101981907`*^9}, CellLabel-> - "Out[286]//TableForm=",ExpressionUUID->"e5d6b0fa-9fec-4b23-820d-\ -595bbac55db7"], + "Out[87]//TableForm=",ExpressionUUID->"7554d460-cd50-4e0e-91c2-\ +398eaf4fe77a"], Cell[BoxData[ TagBox[ @@ -187907,10 +188029,11 @@ Cell[BoxData[ 3.836298156505755*^9, 3.836298218799776*^9, {3.836301655712038*^9, 3.836301661865406*^9}, 3.8363017057264557`*^9, 3.8363017689680843`*^9, 3.836482680248103*^9, 3.83648433435258*^9, 3.8365748057543907`*^9, - 3.836722201802979*^9, 3.836724143001705*^9}, + 3.836722201802979*^9, 3.836724142957694*^9, 3.838976437662228*^9, + 3.838996110199061*^9}, CellLabel-> - "Out[287]//TableForm=",ExpressionUUID->"82c7e22e-3948-44ae-b3d4-\ -3d479dac7bbf"], + "Out[88]//TableForm=",ExpressionUUID->"c87848c9-b0e5-4a49-9070-\ +f6d1016a80ab"], Cell[BoxData[ TagBox[ @@ -187966,10 +188089,11 @@ Cell[BoxData[ 3.836298156505755*^9, 3.836298218799776*^9, {3.836301655712038*^9, 3.836301661865406*^9}, 3.8363017057264557`*^9, 3.8363017689680843`*^9, 3.836482680248103*^9, 3.83648433435258*^9, 3.8365748057543907`*^9, - 3.836722201802979*^9, 3.836724143046979*^9}, + 3.836722201802979*^9, 3.836724142957694*^9, 3.838976437662228*^9, + 3.838996110201577*^9}, CellLabel-> - "Out[288]//TableForm=",ExpressionUUID->"a372f1e2-9d29-44bf-bf06-\ -f11269ea3b27"], + "Out[89]//TableForm=",ExpressionUUID->"adcc4f38-8ff4-4379-900f-\ +80132211bf31"], Cell[BoxData[ TagBox[ @@ -188101,14 +188225,15 @@ Cell[BoxData[ 3.836298156505755*^9, 3.836298218799776*^9, {3.836301655712038*^9, 3.836301661865406*^9}, 3.8363017057264557`*^9, 3.8363017689680843`*^9, 3.836482680248103*^9, 3.83648433435258*^9, 3.8365748057543907`*^9, - 3.836722201802979*^9, 3.8367241430553007`*^9}, + 3.836722201802979*^9, 3.836724142957694*^9, 3.838976437662228*^9, + 3.838996110203336*^9}, CellLabel-> - "Out[289]//TableForm=",ExpressionUUID->"31a87b69-6a19-4245-9b84-\ -148b5feb4296"] + "Out[90]//TableForm=",ExpressionUUID->"61e609dc-f220-4b62-ae3f-\ +c7d628d7115a"] }, Open ]] }, Closed]] }, -WindowSize->{1280, 755}, +WindowSize->{1280, 1392}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"12.1 for Mac OS X x86 (64-bit) (March 13, 2020)", StyleDefinitions->"Default.nb", @@ -188165,481 +188290,481 @@ Cell[CellGroupData[{ Cell[42714, 936, 152, 3, 72, "Title",ExpressionUUID->"e86ca219-ce50-41b6-9e1b-b19ff1ff4ecd"], Cell[CellGroupData[{ Cell[42891, 943, 433, 13, 54, "Subsection",ExpressionUUID->"f8195ea6-11f3-4cd9-bbc6-58b4f338894f"], -Cell[43327, 958, 13364, 300, 888, "Input",ExpressionUUID->"a67ae21a-c72d-4d67-abe2-1be3a36cc379", +Cell[43327, 958, 13363, 300, 888, "Input",ExpressionUUID->"a67ae21a-c72d-4d67-abe2-1be3a36cc379", InitializationCell->True], -Cell[56694, 1260, 16727, 380, 1020, "Input",ExpressionUUID->"9512555e-aa1a-4421-b857-cbdcec0bc190", +Cell[56693, 1260, 16726, 380, 1020, "Input",ExpressionUUID->"9512555e-aa1a-4421-b857-cbdcec0bc190", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ -Cell[73458, 1645, 435, 13, 38, "Subsection",ExpressionUUID->"2deee525-8033-41a7-81fa-8f54db8e8686"], -Cell[73896, 1660, 21291, 490, 1234, "Input",ExpressionUUID->"4a7754e0-f469-452a-aa2e-0612e3e61cc4", +Cell[73456, 1645, 435, 13, 38, "Subsection",ExpressionUUID->"2deee525-8033-41a7-81fa-8f54db8e8686"], +Cell[73894, 1660, 27507, 630, 1417, "Input",ExpressionUUID->"4a7754e0-f469-452a-aa2e-0612e3e61cc4", InitializationCell->True], -Cell[95190, 2152, 24487, 574, 1368, "Input",ExpressionUUID->"b067e9ee-682a-4525-bf90-091d95752712", +Cell[101404, 2292, 24486, 574, 1368, "Input",ExpressionUUID->"b067e9ee-682a-4525-bf90-091d95752712", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ -Cell[119714, 2731, 157, 3, 38, "Subsection",ExpressionUUID->"a2a915a7-a20f-44e2-9ca7-5cf5ea2da90c"], -Cell[119874, 2736, 10109, 205, 635, "Input",ExpressionUUID->"6bf0d177-eada-4bc7-8e00-b86af49684f3", +Cell[125927, 2871, 157, 3, 38, "Subsection",ExpressionUUID->"a2a915a7-a20f-44e2-9ca7-5cf5ea2da90c"], +Cell[126087, 2876, 10104, 204, 635, "Input",ExpressionUUID->"6bf0d177-eada-4bc7-8e00-b86af49684f3", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[130032, 2947, 209, 4, 72, "Title",ExpressionUUID->"65349f7e-5bc6-4eab-a848-be2c224ab83e"], +Cell[136240, 3086, 209, 4, 72, "Title",ExpressionUUID->"65349f7e-5bc6-4eab-a848-be2c224ab83e"], Cell[CellGroupData[{ -Cell[130266, 2955, 165, 3, 67, "Section",ExpressionUUID->"16a381ea-1b1c-49bc-af20-8f5dd32b688e"], -Cell[130434, 2960, 3494, 89, 194, "Input",ExpressionUUID->"895ab98c-f42b-4d20-8b55-5797a7b91a74", +Cell[136474, 3094, 165, 3, 67, "Section",ExpressionUUID->"16a381ea-1b1c-49bc-af20-8f5dd32b688e"], +Cell[136642, 3099, 3490, 88, 194, "Input",ExpressionUUID->"895ab98c-f42b-4d20-8b55-5797a7b91a74", InitializationCell->True], Cell[CellGroupData[{ -Cell[133953, 3053, 154, 3, 54, "Subsection",ExpressionUUID->"3bb0d721-e299-4b18-9417-d1e1c05fee25"], +Cell[140157, 3191, 154, 3, 54, "Subsection",ExpressionUUID->"3bb0d721-e299-4b18-9417-d1e1c05fee25"], Cell[CellGroupData[{ -Cell[134132, 3060, 1364, 35, 74, "Input",ExpressionUUID->"cdb434ce-1eaf-4f2d-9564-f363019aec44"], -Cell[135499, 3097, 638, 13, 70, "Output",ExpressionUUID->"a4074cce-e7e9-4d3d-98ec-50486a3851d7"], -Cell[136140, 3112, 558, 11, 70, "Output",ExpressionUUID->"2db4d6ea-42d8-427b-888a-c71e9fa1fff3"] +Cell[140336, 3198, 1364, 35, 74, "Input",ExpressionUUID->"cdb434ce-1eaf-4f2d-9564-f363019aec44"], +Cell[141703, 3235, 638, 13, 70, "Output",ExpressionUUID->"a4074cce-e7e9-4d3d-98ec-50486a3851d7"], +Cell[142344, 3250, 558, 11, 70, "Output",ExpressionUUID->"2db4d6ea-42d8-427b-888a-c71e9fa1fff3"] }, Open ]], Cell[CellGroupData[{ -Cell[136735, 3128, 1314, 34, 74, "Input",ExpressionUUID->"0db7e576-b902-4e92-a166-46319a6b0730"], -Cell[138052, 3164, 547, 11, 70, "Output",ExpressionUUID->"975f5360-76ce-4dd5-bc1f-5911c3c86692"], -Cell[138602, 3177, 447, 8, 70, "Output",ExpressionUUID->"75c9470e-f17e-4c74-9fc0-0f2f70c75e97"] +Cell[142939, 3266, 1314, 34, 74, "Input",ExpressionUUID->"0db7e576-b902-4e92-a166-46319a6b0730"], +Cell[144256, 3302, 547, 11, 70, "Output",ExpressionUUID->"975f5360-76ce-4dd5-bc1f-5911c3c86692"], +Cell[144806, 3315, 447, 8, 70, "Output",ExpressionUUID->"75c9470e-f17e-4c74-9fc0-0f2f70c75e97"] }, Open ]], Cell[CellGroupData[{ -Cell[139086, 3190, 1311, 34, 74, "Input",ExpressionUUID->"e3745875-1382-48d6-9233-a584c3ea6f23"], -Cell[140400, 3226, 575, 12, 70, "Output",ExpressionUUID->"f46e78f0-7a94-4720-9cde-16d7eab9242e"], -Cell[140978, 3240, 471, 9, 70, "Output",ExpressionUUID->"b9e3ff89-eadd-45d1-aea2-8038e3a78569"] +Cell[145290, 3328, 1311, 34, 74, "Input",ExpressionUUID->"e3745875-1382-48d6-9233-a584c3ea6f23"], +Cell[146604, 3364, 575, 12, 70, "Output",ExpressionUUID->"f46e78f0-7a94-4720-9cde-16d7eab9242e"], +Cell[147182, 3378, 471, 9, 70, "Output",ExpressionUUID->"b9e3ff89-eadd-45d1-aea2-8038e3a78569"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[141510, 3256, 164, 3, 53, "Section",ExpressionUUID->"1bb1c8f3-2f05-4c2c-a98d-e9900e55f10d"], +Cell[147714, 3394, 164, 3, 53, "Section",ExpressionUUID->"1bb1c8f3-2f05-4c2c-a98d-e9900e55f10d"], Cell[CellGroupData[{ -Cell[141699, 3263, 1320, 28, 73, "Input",ExpressionUUID->"5b87143c-454a-4069-aded-93ae6535f27a"], -Cell[143022, 3293, 283770, 5081, 70, "Output",ExpressionUUID->"b9a4fffa-ca7a-4cbd-bc96-77b9d523ec2c"], -Cell[426795, 8376, 310020, 5818, 70, "Output",ExpressionUUID->"67247965-2ddf-43b7-af75-4a4f39703426"], -Cell[736818, 14196, 6238, 146, 70, "Print",ExpressionUUID->"d30bb5d0-c1a0-4989-84ef-4cd3566f9cf2"], -Cell[743059, 14344, 243914, 4424, 70, "Output",ExpressionUUID->"918eea83-7fd6-4535-b9f3-1005c8b50d42"] +Cell[147903, 3401, 1320, 28, 73, "Input",ExpressionUUID->"5b87143c-454a-4069-aded-93ae6535f27a"], +Cell[149226, 3431, 283770, 5081, 429, "Output",ExpressionUUID->"b9a4fffa-ca7a-4cbd-bc96-77b9d523ec2c"], +Cell[432999, 8514, 310020, 5818, 374, "Output",ExpressionUUID->"67247965-2ddf-43b7-af75-4a4f39703426"], +Cell[743022, 14334, 6238, 146, 292, "Print",ExpressionUUID->"d30bb5d0-c1a0-4989-84ef-4cd3566f9cf2"], +Cell[749263, 14482, 243914, 4424, 380, "Output",ExpressionUUID->"918eea83-7fd6-4535-b9f3-1005c8b50d42"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[987034, 18775, 150, 3, 72, "Title",ExpressionUUID->"c8ea3a71-bf82-42b1-8ca9-bd2f3ea9c623"], +Cell[993238, 18913, 150, 3, 72, "Title",ExpressionUUID->"c8ea3a71-bf82-42b1-8ca9-bd2f3ea9c623"], Cell[CellGroupData[{ -Cell[987209, 18782, 165, 3, 67, "Section",ExpressionUUID->"c53c0e7c-8d76-4b78-ab46-cee8483f7a76"], -Cell[987377, 18787, 3146, 85, 173, "Input",ExpressionUUID->"45aa8230-f7ee-467a-96ce-1c41bb98be6e", +Cell[993413, 18920, 165, 3, 67, "Section",ExpressionUUID->"c53c0e7c-8d76-4b78-ab46-cee8483f7a76"], +Cell[993581, 18925, 3142, 84, 173, "Input",ExpressionUUID->"45aa8230-f7ee-467a-96ce-1c41bb98be6e", InitializationCell->True], Cell[CellGroupData[{ -Cell[990548, 18876, 154, 3, 54, "Subsection",ExpressionUUID->"6ed9e07a-b697-4c5b-9c64-02e7d7193dd9"], +Cell[996748, 19013, 154, 3, 54, "Subsection",ExpressionUUID->"6ed9e07a-b697-4c5b-9c64-02e7d7193dd9"], Cell[CellGroupData[{ -Cell[990727, 18883, 1328, 34, 74, "Input",ExpressionUUID->"faeee6a1-27da-4747-bba6-385c63127336"], -Cell[992058, 18919, 735, 14, 70, "Output",ExpressionUUID->"87cc956e-729d-4004-8c6e-7c3dfd0ace10"], -Cell[992796, 18935, 654, 12, 70, "Output",ExpressionUUID->"22df4c29-74ee-4858-a450-5124c34ec4b2"] +Cell[996927, 19020, 1328, 34, 74, "Input",ExpressionUUID->"faeee6a1-27da-4747-bba6-385c63127336"], +Cell[998258, 19056, 735, 14, 70, "Output",ExpressionUUID->"87cc956e-729d-4004-8c6e-7c3dfd0ace10"], +Cell[998996, 19072, 654, 12, 70, "Output",ExpressionUUID->"22df4c29-74ee-4858-a450-5124c34ec4b2"] }, Open ]], Cell[CellGroupData[{ -Cell[993487, 18952, 1305, 34, 74, "Input",ExpressionUUID->"a1e6c246-a9cb-4349-925b-42f5dafd15c2"], -Cell[994795, 18988, 669, 13, 70, "Output",ExpressionUUID->"520b8a98-39fe-478f-946e-79dcb834118f"], -Cell[995467, 19003, 569, 10, 70, "Output",ExpressionUUID->"a5a61a06-c447-4cce-a927-78e3e05cdd05"] +Cell[999687, 19089, 1305, 34, 74, "Input",ExpressionUUID->"a1e6c246-a9cb-4349-925b-42f5dafd15c2"], +Cell[1000995, 19125, 669, 13, 70, "Output",ExpressionUUID->"520b8a98-39fe-478f-946e-79dcb834118f"], +Cell[1001667, 19140, 569, 10, 70, "Output",ExpressionUUID->"a5a61a06-c447-4cce-a927-78e3e05cdd05"] }, Open ]], Cell[CellGroupData[{ -Cell[996073, 19018, 1302, 34, 74, "Input",ExpressionUUID->"3ea592cd-abcc-42c2-a4cd-02387a54ba6b"], -Cell[997378, 19054, 717, 14, 70, "Output",ExpressionUUID->"f4421658-e242-44a4-befb-e382e3cd14a9"], -Cell[998098, 19070, 617, 11, 70, "Output",ExpressionUUID->"624d1058-3f8b-4df7-9892-2397ecc368d4"] +Cell[1002273, 19155, 1302, 34, 74, "Input",ExpressionUUID->"3ea592cd-abcc-42c2-a4cd-02387a54ba6b"], +Cell[1003578, 19191, 717, 14, 70, "Output",ExpressionUUID->"f4421658-e242-44a4-befb-e382e3cd14a9"], +Cell[1004298, 19207, 617, 11, 70, "Output",ExpressionUUID->"624d1058-3f8b-4df7-9892-2397ecc368d4"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[998776, 19088, 164, 3, 53, "Section",ExpressionUUID->"285c7b18-4488-4051-b69c-1c735933f199"], +Cell[1004976, 19225, 164, 3, 53, "Section",ExpressionUUID->"285c7b18-4488-4051-b69c-1c735933f199"], Cell[CellGroupData[{ -Cell[998965, 19095, 1340, 28, 73, "Input",ExpressionUUID->"f97d8f09-09e2-4eb1-8f8e-49bb58119b51"], -Cell[1000308, 19125, 260153, 4691, 70, "Output",ExpressionUUID->"76e48df5-969c-4ad3-8ff2-fa54963ba5d7"], -Cell[1260464, 23818, 286493, 5427, 70, "Output",ExpressionUUID->"76360ed1-483a-4e75-b57e-e0315394e4b1"], -Cell[1546960, 29247, 6101, 143, 70, "Print",ExpressionUUID->"6f0ec506-bd77-4d8a-87d3-7bb77464d9ef"], -Cell[1553064, 29392, 219646, 4019, 70, "Output",ExpressionUUID->"e6018275-bcbb-4eac-be15-bcdd11d3e9ad"] +Cell[1005165, 19232, 1340, 28, 73, "Input",ExpressionUUID->"f97d8f09-09e2-4eb1-8f8e-49bb58119b51"], +Cell[1006508, 19262, 260153, 4691, 70, "Output",ExpressionUUID->"76e48df5-969c-4ad3-8ff2-fa54963ba5d7"], +Cell[1266664, 23955, 286493, 5427, 70, "Output",ExpressionUUID->"76360ed1-483a-4e75-b57e-e0315394e4b1"], +Cell[1553160, 29384, 6101, 143, 70, "Print",ExpressionUUID->"6f0ec506-bd77-4d8a-87d3-7bb77464d9ef"], +Cell[1559264, 29529, 219646, 4019, 70, "Output",ExpressionUUID->"e6018275-bcbb-4eac-be15-bcdd11d3e9ad"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ -Cell[1772771, 33418, 156, 3, 72, "Title",ExpressionUUID->"0860c22a-77ea-459e-9e4f-ab8d06aad316"], +Cell[1778971, 33555, 156, 3, 72, "Title",ExpressionUUID->"0860c22a-77ea-459e-9e4f-ab8d06aad316"], Cell[CellGroupData[{ -Cell[1772952, 33425, 165, 3, 67, "Section",ExpressionUUID->"86c38d97-2176-4491-bd1b-14fcbf3c9de6"], -Cell[1773120, 33430, 3175, 85, 173, "Input",ExpressionUUID->"0f6df49c-36bc-4f29-a06b-1e01f88c8af7", +Cell[1779152, 33562, 165, 3, 67, "Section",ExpressionUUID->"86c38d97-2176-4491-bd1b-14fcbf3c9de6"], +Cell[1779320, 33567, 3171, 84, 173, "Input",ExpressionUUID->"0f6df49c-36bc-4f29-a06b-1e01f88c8af7", InitializationCell->True], Cell[CellGroupData[{ -Cell[1776320, 33519, 154, 3, 54, "Subsection",ExpressionUUID->"09abf152-a5b7-441a-b5b5-f9ac1c555a3e"], +Cell[1782516, 33655, 154, 3, 54, "Subsection",ExpressionUUID->"09abf152-a5b7-441a-b5b5-f9ac1c555a3e"], Cell[CellGroupData[{ -Cell[1776499, 33526, 1358, 35, 74, "Input",ExpressionUUID->"fc3b72f7-0f23-4ab8-b2f7-31cf8d6afb6a"], -Cell[1777860, 33563, 709, 14, 70, "Output",ExpressionUUID->"88a770fc-a2c4-4647-a8fa-4e0f5b796b5a"], -Cell[1778572, 33579, 631, 12, 70, "Output",ExpressionUUID->"01564634-6538-4b61-83f2-18970d07aadc"] +Cell[1782695, 33662, 1358, 35, 74, "Input",ExpressionUUID->"fc3b72f7-0f23-4ab8-b2f7-31cf8d6afb6a"], +Cell[1784056, 33699, 709, 14, 70, "Output",ExpressionUUID->"88a770fc-a2c4-4647-a8fa-4e0f5b796b5a"], +Cell[1784768, 33715, 631, 12, 70, "Output",ExpressionUUID->"01564634-6538-4b61-83f2-18970d07aadc"] }, Open ]], Cell[CellGroupData[{ -Cell[1779240, 33596, 1331, 34, 74, "Input",ExpressionUUID->"7a91f090-8b86-423b-a3b3-e111116f8a39"], -Cell[1780574, 33632, 648, 13, 70, "Output",ExpressionUUID->"b1cda7fc-a48c-484f-b35c-f59abd0bf2c8"], -Cell[1781225, 33647, 548, 10, 70, "Output",ExpressionUUID->"600e5ca3-6992-4690-8e58-6dd1bafdf3a7"] +Cell[1785436, 33732, 1331, 34, 74, "Input",ExpressionUUID->"7a91f090-8b86-423b-a3b3-e111116f8a39"], +Cell[1786770, 33768, 648, 13, 70, "Output",ExpressionUUID->"b1cda7fc-a48c-484f-b35c-f59abd0bf2c8"], +Cell[1787421, 33783, 548, 10, 70, "Output",ExpressionUUID->"600e5ca3-6992-4690-8e58-6dd1bafdf3a7"] }, Open ]], Cell[CellGroupData[{ -Cell[1781810, 33662, 1328, 34, 74, "Input",ExpressionUUID->"42c1fc2d-3b30-4c28-8611-511d1f3a6e37"], -Cell[1783141, 33698, 690, 13, 70, "Output",ExpressionUUID->"10de2993-f607-4fb8-99ea-22f9bc00a56c"], -Cell[1783834, 33713, 589, 10, 70, "Output",ExpressionUUID->"1116cec2-16a7-4d8c-80d0-0f2425ac8311"] +Cell[1788006, 33798, 1328, 34, 74, "Input",ExpressionUUID->"42c1fc2d-3b30-4c28-8611-511d1f3a6e37"], +Cell[1789337, 33834, 690, 13, 70, "Output",ExpressionUUID->"10de2993-f607-4fb8-99ea-22f9bc00a56c"], +Cell[1790030, 33849, 589, 10, 70, "Output",ExpressionUUID->"1116cec2-16a7-4d8c-80d0-0f2425ac8311"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[1784484, 33730, 164, 3, 53, "Section",ExpressionUUID->"e555d041-c954-4d42-975d-189c29eecbf7"], +Cell[1790680, 33866, 164, 3, 53, "Section",ExpressionUUID->"e555d041-c954-4d42-975d-189c29eecbf7"], Cell[CellGroupData[{ -Cell[1784673, 33737, 1110, 24, 73, "Input",ExpressionUUID->"877d2c8b-2c78-4762-8177-a1dc684f1b5e"], -Cell[1785786, 33763, 268848, 4831, 70, "Output",ExpressionUUID->"325a7ae0-61e2-4072-a249-9cf84e60ecca"], -Cell[2054637, 38596, 295033, 5563, 70, "Output",ExpressionUUID->"df588ab9-adbb-47d9-9fd7-e6aeda24f065"], -Cell[2349673, 44161, 6103, 143, 70, "Print",ExpressionUUID->"4ac5d8b4-1e94-43ce-8e5f-4e0413397cab"], -Cell[2355779, 44306, 228586, 4165, 70, "Output",ExpressionUUID->"87d3d886-4c5c-4030-9f2b-21f28fb87bda"] +Cell[1790869, 33873, 1110, 24, 73, "Input",ExpressionUUID->"877d2c8b-2c78-4762-8177-a1dc684f1b5e"], +Cell[1791982, 33899, 268848, 4831, 70, "Output",ExpressionUUID->"325a7ae0-61e2-4072-a249-9cf84e60ecca"], +Cell[2060833, 38732, 295033, 5563, 70, "Output",ExpressionUUID->"df588ab9-adbb-47d9-9fd7-e6aeda24f065"], +Cell[2355869, 44297, 6103, 143, 70, "Print",ExpressionUUID->"4ac5d8b4-1e94-43ce-8e5f-4e0413397cab"], +Cell[2361975, 44442, 228586, 4165, 70, "Output",ExpressionUUID->"87d3d886-4c5c-4030-9f2b-21f28fb87bda"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[2584426, 48478, 150, 3, 72, "Title",ExpressionUUID->"d9294d8a-4355-4e8d-bbd5-410646cba2c4"], +Cell[2590622, 48614, 150, 3, 72, "Title",ExpressionUUID->"d9294d8a-4355-4e8d-bbd5-410646cba2c4"], Cell[CellGroupData[{ -Cell[2584601, 48485, 165, 3, 67, "Section",ExpressionUUID->"ba4a26a0-d628-45e2-bb2e-6d6478a5b973"], -Cell[2584769, 48490, 3210, 86, 173, "Input",ExpressionUUID->"f11bb471-abb4-4b35-b78e-924d82295d82", +Cell[2590797, 48621, 165, 3, 67, "Section",ExpressionUUID->"ba4a26a0-d628-45e2-bb2e-6d6478a5b973"], +Cell[2590965, 48626, 3206, 85, 173, "Input",ExpressionUUID->"f11bb471-abb4-4b35-b78e-924d82295d82", InitializationCell->True], Cell[CellGroupData[{ -Cell[2588004, 48580, 154, 3, 54, "Subsection",ExpressionUUID->"e9c42ce3-0b52-4370-bf57-f8c7c204b085"], +Cell[2594196, 48715, 154, 3, 54, "Subsection",ExpressionUUID->"e9c42ce3-0b52-4370-bf57-f8c7c204b085"], Cell[CellGroupData[{ -Cell[2588183, 48587, 1378, 35, 74, "Input",ExpressionUUID->"68b92834-2cb8-4602-8e77-8c84f6a33562"], -Cell[2589564, 48624, 708, 14, 70, "Output",ExpressionUUID->"a0428871-b39a-4843-aa47-46668275b37d"], -Cell[2590275, 48640, 626, 12, 70, "Output",ExpressionUUID->"a8883b70-cfae-475f-b6a7-7aad966b3f6a"] +Cell[2594375, 48722, 1378, 35, 74, "Input",ExpressionUUID->"68b92834-2cb8-4602-8e77-8c84f6a33562"], +Cell[2595756, 48759, 708, 14, 70, "Output",ExpressionUUID->"a0428871-b39a-4843-aa47-46668275b37d"], +Cell[2596467, 48775, 626, 12, 70, "Output",ExpressionUUID->"a8883b70-cfae-475f-b6a7-7aad966b3f6a"] }, Open ]], Cell[CellGroupData[{ -Cell[2590938, 48657, 1355, 35, 74, "Input",ExpressionUUID->"4ead6903-964a-4732-82a1-349ed005a7a0"], -Cell[2592296, 48694, 646, 13, 70, "Output",ExpressionUUID->"af6cad2e-3c6d-4040-904b-15f640ee7c05"], -Cell[2592945, 48709, 547, 10, 70, "Output",ExpressionUUID->"6659bd43-c6b8-41e3-a594-0bbdac7d6a09"] +Cell[2597130, 48792, 1355, 35, 74, "Input",ExpressionUUID->"4ead6903-964a-4732-82a1-349ed005a7a0"], +Cell[2598488, 48829, 646, 13, 70, "Output",ExpressionUUID->"af6cad2e-3c6d-4040-904b-15f640ee7c05"], +Cell[2599137, 48844, 547, 10, 70, "Output",ExpressionUUID->"6659bd43-c6b8-41e3-a594-0bbdac7d6a09"] }, Open ]], Cell[CellGroupData[{ -Cell[2593529, 48724, 1402, 35, 74, "Input",ExpressionUUID->"b7abe509-152d-4b0a-acfa-9f50e03d419a"], -Cell[2594934, 48761, 688, 13, 70, "Output",ExpressionUUID->"0ce788d7-1e34-43e1-a3f7-dd84234bc97d"], -Cell[2595625, 48776, 582, 10, 70, "Output",ExpressionUUID->"bedfd7d2-8b23-49f4-98cb-93b2103f38af"] +Cell[2599721, 48859, 1402, 35, 74, "Input",ExpressionUUID->"b7abe509-152d-4b0a-acfa-9f50e03d419a"], +Cell[2601126, 48896, 688, 13, 70, "Output",ExpressionUUID->"0ce788d7-1e34-43e1-a3f7-dd84234bc97d"], +Cell[2601817, 48911, 582, 10, 70, "Output",ExpressionUUID->"bedfd7d2-8b23-49f4-98cb-93b2103f38af"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[2596268, 48793, 164, 3, 53, "Section",ExpressionUUID->"0ce9737a-03fc-4a26-a86f-c789f03e34bc"], +Cell[2602460, 48928, 164, 3, 53, "Section",ExpressionUUID->"0ce9737a-03fc-4a26-a86f-c789f03e34bc"], Cell[CellGroupData[{ -Cell[2596457, 48800, 955, 22, 73, "Input",ExpressionUUID->"5c19bfec-9035-4e97-b29e-a7411588e829"], -Cell[2597415, 48824, 262879, 4739, 70, "Output",ExpressionUUID->"35bcc544-514d-424e-85e1-36382658454a"], -Cell[2860297, 53565, 289224, 5476, 70, "Output",ExpressionUUID->"fd65dcce-71ff-4d18-925e-cab0bbc447aa"], -Cell[3149524, 59043, 6109, 143, 70, "Print",ExpressionUUID->"b4eac94b-d90c-4a74-aced-c62e53f57578"], -Cell[3155636, 59188, 222520, 4073, 70, "Output",ExpressionUUID->"d1aeef46-aab9-4fef-a49e-abcf142972bd"] +Cell[2602649, 48935, 955, 22, 73, "Input",ExpressionUUID->"5c19bfec-9035-4e97-b29e-a7411588e829"], +Cell[2603607, 48959, 262879, 4739, 70, "Output",ExpressionUUID->"35bcc544-514d-424e-85e1-36382658454a"], +Cell[2866489, 53700, 289224, 5476, 70, "Output",ExpressionUUID->"fd65dcce-71ff-4d18-925e-cab0bbc447aa"], +Cell[3155716, 59178, 6109, 143, 70, "Print",ExpressionUUID->"b4eac94b-d90c-4a74-aced-c62e53f57578"], +Cell[3161828, 59323, 222520, 4073, 70, "Output",ExpressionUUID->"d1aeef46-aab9-4fef-a49e-abcf142972bd"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ -Cell[3378217, 63268, 154, 3, 72, "Title",ExpressionUUID->"3504afb6-6eb1-48f6-9495-ed3dc6c532d7"], +Cell[3384409, 63403, 154, 3, 72, "Title",ExpressionUUID->"3504afb6-6eb1-48f6-9495-ed3dc6c532d7"], Cell[CellGroupData[{ -Cell[3378396, 63275, 165, 3, 67, "Section",ExpressionUUID->"a5f2404f-9967-45e0-8a61-25658fb37a23"], -Cell[3378564, 63280, 3325, 87, 173, "Input",ExpressionUUID->"fec12b1f-939b-432a-89a4-71b4992d614a", +Cell[3384588, 63410, 165, 3, 67, "Section",ExpressionUUID->"a5f2404f-9967-45e0-8a61-25658fb37a23"], +Cell[3384756, 63415, 3321, 86, 173, "Input",ExpressionUUID->"fec12b1f-939b-432a-89a4-71b4992d614a", InitializationCell->True], Cell[CellGroupData[{ -Cell[3381914, 63371, 154, 3, 54, "Subsection",ExpressionUUID->"c46e08d4-b6ba-46f0-9c89-b288880426ce"], +Cell[3388102, 63505, 154, 3, 54, "Subsection",ExpressionUUID->"c46e08d4-b6ba-46f0-9c89-b288880426ce"], Cell[CellGroupData[{ -Cell[3382093, 63378, 1402, 35, 74, "Input",ExpressionUUID->"11d7747b-9e15-426e-81f8-ba79899ac511"], -Cell[3383498, 63415, 762, 15, 70, "Output",ExpressionUUID->"4d2477a2-9c9f-42a2-8328-d60afdf261f9"], -Cell[3384263, 63432, 682, 13, 70, "Output",ExpressionUUID->"f5325e0d-8bfb-45c5-876f-4b5717772804"] +Cell[3388281, 63512, 1402, 35, 74, "Input",ExpressionUUID->"11d7747b-9e15-426e-81f8-ba79899ac511"], +Cell[3389686, 63549, 762, 15, 70, "Output",ExpressionUUID->"4d2477a2-9c9f-42a2-8328-d60afdf261f9"], +Cell[3390451, 63566, 682, 13, 70, "Output",ExpressionUUID->"f5325e0d-8bfb-45c5-876f-4b5717772804"] }, Open ]], Cell[CellGroupData[{ -Cell[3384982, 63450, 1381, 35, 74, "Input",ExpressionUUID->"626d5c14-7754-47d2-bc07-efbaf7f4fd74"], -Cell[3386366, 63487, 691, 13, 70, "Output",ExpressionUUID->"e58d1d22-1931-4975-8224-1a6da589a3fe"], -Cell[3387060, 63502, 590, 10, 70, "Output",ExpressionUUID->"7c3ae9a9-9880-4948-bc3c-34eeac5cd1f0"] +Cell[3391170, 63584, 1381, 35, 74, "Input",ExpressionUUID->"626d5c14-7754-47d2-bc07-efbaf7f4fd74"], +Cell[3392554, 63621, 691, 13, 70, "Output",ExpressionUUID->"e58d1d22-1931-4975-8224-1a6da589a3fe"], +Cell[3393248, 63636, 590, 10, 70, "Output",ExpressionUUID->"7c3ae9a9-9880-4948-bc3c-34eeac5cd1f0"] }, Open ]], Cell[CellGroupData[{ -Cell[3387687, 63517, 1432, 36, 74, "Input",ExpressionUUID->"7b995c40-5cad-4bf5-9772-3e40edc3fe66"], -Cell[3389122, 63555, 737, 14, 70, "Output",ExpressionUUID->"406645d2-5186-41c7-87c0-6b13960073b0"], -Cell[3389862, 63571, 636, 11, 70, "Output",ExpressionUUID->"5c36da4a-6c5a-4eac-a082-8ad6f5e6a2a6"] +Cell[3393875, 63651, 1432, 36, 74, "Input",ExpressionUUID->"7b995c40-5cad-4bf5-9772-3e40edc3fe66"], +Cell[3395310, 63689, 737, 14, 70, "Output",ExpressionUUID->"406645d2-5186-41c7-87c0-6b13960073b0"], +Cell[3396050, 63705, 636, 11, 70, "Output",ExpressionUUID->"5c36da4a-6c5a-4eac-a082-8ad6f5e6a2a6"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[3390559, 63589, 164, 3, 53, "Section",ExpressionUUID->"a49527a9-f9ad-46c4-84b7-e9dc0ea5c2fb"], +Cell[3396747, 63723, 164, 3, 53, "Section",ExpressionUUID->"a49527a9-f9ad-46c4-84b7-e9dc0ea5c2fb"], Cell[CellGroupData[{ -Cell[3390748, 63596, 1023, 23, 73, "Input",ExpressionUUID->"498a55fb-15c8-491a-86db-9027ef3a57f0"], -Cell[3391774, 63621, 268275, 4823, 70, "Output",ExpressionUUID->"b74c66fb-dce1-472c-bbf2-c4e4e345a52c"], -Cell[3660052, 68446, 294604, 5560, 70, "Output",ExpressionUUID->"f48d437c-baa0-456d-ac40-87d36f646ca3"], -Cell[3954659, 74008, 6109, 143, 70, "Print",ExpressionUUID->"24595696-2ad2-4bcb-bbfd-218cdb44c694"], -Cell[3960771, 74153, 228281, 4162, 70, "Output",ExpressionUUID->"60690fc1-c300-4bc0-b282-50c5cbabaae3"] +Cell[3396936, 63730, 1023, 23, 73, "Input",ExpressionUUID->"498a55fb-15c8-491a-86db-9027ef3a57f0"], +Cell[3397962, 63755, 268275, 4823, 70, "Output",ExpressionUUID->"b74c66fb-dce1-472c-bbf2-c4e4e345a52c"], +Cell[3666240, 68580, 294604, 5560, 70, "Output",ExpressionUUID->"f48d437c-baa0-456d-ac40-87d36f646ca3"], +Cell[3960847, 74142, 6109, 143, 70, "Print",ExpressionUUID->"24595696-2ad2-4bcb-bbfd-218cdb44c694"], +Cell[3966959, 74287, 228281, 4162, 70, "Output",ExpressionUUID->"60690fc1-c300-4bc0-b282-50c5cbabaae3"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ -Cell[4189113, 78322, 200, 4, 72, "Title",ExpressionUUID->"0d0d68ed-d033-407d-8b39-64222dce8392"], +Cell[4195301, 78456, 200, 4, 72, "Title",ExpressionUUID->"0d0d68ed-d033-407d-8b39-64222dce8392"], Cell[CellGroupData[{ -Cell[4189338, 78330, 165, 3, 67, "Section",ExpressionUUID->"837a9e8f-f906-41ee-adc6-0d92540acac3"], -Cell[4189506, 78335, 3181, 86, 173, "Input",ExpressionUUID->"00ce6a41-3340-4211-974d-333201273f2b", +Cell[4195526, 78464, 165, 3, 67, "Section",ExpressionUUID->"837a9e8f-f906-41ee-adc6-0d92540acac3"], +Cell[4195694, 78469, 3177, 85, 173, "Input",ExpressionUUID->"00ce6a41-3340-4211-974d-333201273f2b", InitializationCell->True], Cell[CellGroupData[{ -Cell[4192712, 78425, 154, 3, 54, "Subsection",ExpressionUUID->"ed1ad587-16f2-416d-bd92-ebf8eeda035b"], +Cell[4198896, 78558, 154, 3, 54, "Subsection",ExpressionUUID->"ed1ad587-16f2-416d-bd92-ebf8eeda035b"], Cell[CellGroupData[{ -Cell[4192891, 78432, 1284, 34, 74, "Input",ExpressionUUID->"6d7742c9-df65-4590-b3f1-0fd9e52bb881"], -Cell[4194178, 78468, 684, 14, 70, "Output",ExpressionUUID->"02cea764-cd08-410e-aea3-165753600c14"], -Cell[4194865, 78484, 606, 12, 70, "Output",ExpressionUUID->"5b2bc7f4-971c-4106-a91a-b3ac368cc328"] +Cell[4199075, 78565, 1284, 34, 74, "Input",ExpressionUUID->"6d7742c9-df65-4590-b3f1-0fd9e52bb881"], +Cell[4200362, 78601, 684, 14, 70, "Output",ExpressionUUID->"02cea764-cd08-410e-aea3-165753600c14"], +Cell[4201049, 78617, 606, 12, 70, "Output",ExpressionUUID->"5b2bc7f4-971c-4106-a91a-b3ac368cc328"] }, Open ]], Cell[CellGroupData[{ -Cell[4195508, 78501, 1285, 34, 74, "Input",ExpressionUUID->"4c80c160-37f9-438f-9852-a500b1652816"], -Cell[4196796, 78537, 622, 12, 70, "Output",ExpressionUUID->"25153302-02d3-4f65-8e52-006dd06591e7"], -Cell[4197421, 78551, 522, 9, 70, "Output",ExpressionUUID->"2a8cc2ca-af06-4824-aa2f-ca4c67e6dd3e"] +Cell[4201692, 78634, 1285, 34, 74, "Input",ExpressionUUID->"4c80c160-37f9-438f-9852-a500b1652816"], +Cell[4202980, 78670, 622, 12, 70, "Output",ExpressionUUID->"25153302-02d3-4f65-8e52-006dd06591e7"], +Cell[4203605, 78684, 522, 9, 70, "Output",ExpressionUUID->"2a8cc2ca-af06-4824-aa2f-ca4c67e6dd3e"] }, Open ]], Cell[CellGroupData[{ -Cell[4197980, 78565, 1282, 34, 74, "Input",ExpressionUUID->"384d7e0c-6f6e-475f-8857-b08cec2b998b"], -Cell[4199265, 78601, 645, 13, 70, "Output",ExpressionUUID->"68f6640f-6100-4d44-9507-8c686f5c30c8"], -Cell[4199913, 78616, 546, 10, 70, "Output",ExpressionUUID->"93d585fa-96ca-4402-8065-3857447338e8"] +Cell[4204164, 78698, 1282, 34, 74, "Input",ExpressionUUID->"384d7e0c-6f6e-475f-8857-b08cec2b998b"], +Cell[4205449, 78734, 645, 13, 70, "Output",ExpressionUUID->"68f6640f-6100-4d44-9507-8c686f5c30c8"], +Cell[4206097, 78749, 546, 10, 70, "Output",ExpressionUUID->"93d585fa-96ca-4402-8065-3857447338e8"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[4200520, 78633, 164, 3, 53, "Section",ExpressionUUID->"5968a8e7-7690-4c56-89df-d2afe069402b"], +Cell[4206704, 78766, 164, 3, 53, "Section",ExpressionUUID->"5968a8e7-7690-4c56-89df-d2afe069402b"], Cell[CellGroupData[{ -Cell[4200709, 78640, 936, 22, 73, "Input",ExpressionUUID->"e0024c13-0d48-40c7-8c74-741cc42a624f"], -Cell[4201648, 78664, 264658, 4760, 70, "Output",ExpressionUUID->"236edc6c-20be-49e0-a2f6-9fc71dec8046"], -Cell[4466309, 83426, 290961, 5499, 70, "Output",ExpressionUUID->"3b64b462-0650-49a6-9525-c758b3fdf73d"], -Cell[4757273, 88927, 6109, 143, 70, "Print",ExpressionUUID->"09558e91-23e6-413b-a4c8-53e0f00a2a4c"], -Cell[4763385, 89072, 224151, 4095, 70, "Output",ExpressionUUID->"9935d306-9e36-4037-97df-937a975c4381"] +Cell[4206893, 78773, 936, 22, 73, "Input",ExpressionUUID->"e0024c13-0d48-40c7-8c74-741cc42a624f"], +Cell[4207832, 78797, 264658, 4760, 70, "Output",ExpressionUUID->"236edc6c-20be-49e0-a2f6-9fc71dec8046"], +Cell[4472493, 83559, 290961, 5499, 70, "Output",ExpressionUUID->"3b64b462-0650-49a6-9525-c758b3fdf73d"], +Cell[4763457, 89060, 6109, 143, 70, "Print",ExpressionUUID->"09558e91-23e6-413b-a4c8-53e0f00a2a4c"], +Cell[4769569, 89205, 224151, 4095, 70, "Output",ExpressionUUID->"9935d306-9e36-4037-97df-937a975c4381"] }, Open ]], Cell[CellGroupData[{ -Cell[4987573, 93172, 356, 9, 30, "Input",ExpressionUUID->"f44f880c-c881-45fc-8c3e-fcbb555d8e37"], -Cell[4987932, 93183, 195176, 3761, 70, "Output",ExpressionUUID->"198ae4f7-8356-40e3-b594-a34ee809159b"] +Cell[4993757, 93305, 356, 9, 30, "Input",ExpressionUUID->"f44f880c-c881-45fc-8c3e-fcbb555d8e37"], +Cell[4994116, 93316, 195176, 3761, 70, "Output",ExpressionUUID->"198ae4f7-8356-40e3-b594-a34ee809159b"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[5183169, 96951, 174, 3, 72, "Title",ExpressionUUID->"89ceb3e6-e8ed-48f9-ad54-8f55b765da3d"], +Cell[5189353, 97084, 174, 3, 72, "Title",ExpressionUUID->"89ceb3e6-e8ed-48f9-ad54-8f55b765da3d"], Cell[CellGroupData[{ -Cell[5183368, 96958, 165, 3, 67, "Section",ExpressionUUID->"a672ed73-4892-4c6f-94df-45113bd9185d"], -Cell[5183536, 96963, 3316, 87, 173, "Input",ExpressionUUID->"9d9cd269-5af2-4502-b5cf-01d155493236", +Cell[5189552, 97091, 165, 3, 67, "Section",ExpressionUUID->"a672ed73-4892-4c6f-94df-45113bd9185d"], +Cell[5189720, 97096, 3312, 86, 173, "Input",ExpressionUUID->"9d9cd269-5af2-4502-b5cf-01d155493236", InitializationCell->True], Cell[CellGroupData[{ -Cell[5186877, 97054, 154, 3, 54, "Subsection",ExpressionUUID->"6843b2aa-bfe0-4330-85ec-c12a4533f092"], +Cell[5193057, 97186, 154, 3, 54, "Subsection",ExpressionUUID->"6843b2aa-bfe0-4330-85ec-c12a4533f092"], Cell[CellGroupData[{ -Cell[5187056, 97061, 1427, 36, 74, "Input",ExpressionUUID->"c2fd0978-56ec-4bdb-a941-8830e1cddb0d"], -Cell[5188486, 97099, 788, 15, 70, "Output",ExpressionUUID->"c9bbcbea-6c45-4cde-8600-8fb59142fac2"], -Cell[5189277, 97116, 707, 13, 70, "Output",ExpressionUUID->"edbc56a1-e5e4-495d-b394-be5ac69601d1"] +Cell[5193236, 97193, 1427, 36, 74, "Input",ExpressionUUID->"c2fd0978-56ec-4bdb-a941-8830e1cddb0d"], +Cell[5194666, 97231, 788, 15, 70, "Output",ExpressionUUID->"c9bbcbea-6c45-4cde-8600-8fb59142fac2"], +Cell[5195457, 97248, 707, 13, 70, "Output",ExpressionUUID->"edbc56a1-e5e4-495d-b394-be5ac69601d1"] }, Open ]], Cell[CellGroupData[{ -Cell[5190021, 97134, 1404, 35, 74, "Input",ExpressionUUID->"35a4401d-efa7-45ac-a9f9-662b80ee42c4"], -Cell[5191428, 97171, 717, 14, 70, "Output",ExpressionUUID->"2145f38b-0ff6-495d-b0b2-201f0ff9b118"], -Cell[5192148, 97187, 618, 11, 70, "Output",ExpressionUUID->"f5314b7f-da7f-4ffa-919f-edbce64ce103"] +Cell[5196201, 97266, 1404, 35, 74, "Input",ExpressionUUID->"35a4401d-efa7-45ac-a9f9-662b80ee42c4"], +Cell[5197608, 97303, 717, 14, 70, "Output",ExpressionUUID->"2145f38b-0ff6-495d-b0b2-201f0ff9b118"], +Cell[5198328, 97319, 618, 11, 70, "Output",ExpressionUUID->"f5314b7f-da7f-4ffa-919f-edbce64ce103"] }, Open ]], Cell[CellGroupData[{ -Cell[5192803, 97203, 1453, 36, 74, "Input",ExpressionUUID->"d9bc890c-a92c-4bf9-b971-2b0ab8a0ebfa"], -Cell[5194259, 97241, 759, 14, 70, "Output",ExpressionUUID->"f12e910b-2356-4b78-bf08-0e9ad6bd7197"], -Cell[5195021, 97257, 658, 11, 70, "Output",ExpressionUUID->"7988ee08-4a2b-4806-8a88-1c86e667784b"] +Cell[5198983, 97335, 1453, 36, 74, "Input",ExpressionUUID->"d9bc890c-a92c-4bf9-b971-2b0ab8a0ebfa"], +Cell[5200439, 97373, 759, 14, 70, "Output",ExpressionUUID->"f12e910b-2356-4b78-bf08-0e9ad6bd7197"], +Cell[5201201, 97389, 658, 11, 70, "Output",ExpressionUUID->"7988ee08-4a2b-4806-8a88-1c86e667784b"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[5195740, 97275, 164, 3, 53, "Section",ExpressionUUID->"9f8745cf-1727-417a-b067-8d71d31bea6e"], +Cell[5201920, 97407, 164, 3, 53, "Section",ExpressionUUID->"9f8745cf-1727-417a-b067-8d71d31bea6e"], Cell[CellGroupData[{ -Cell[5195929, 97282, 841, 21, 73, "Input",ExpressionUUID->"1af3a898-a964-44d7-86a6-b01d3c2bd890"], -Cell[5196773, 97305, 266610, 4797, 70, "Output",ExpressionUUID->"a1a5e406-ccd0-4c8c-97a9-61a4171e2f60"], -Cell[5463386, 102104, 292907, 5534, 70, "Output",ExpressionUUID->"eb751853-de87-4ae4-b5dd-b5efad43ff54"], -Cell[5756296, 107640, 6109, 143, 70, "Print",ExpressionUUID->"e0e2fea4-292b-46ec-a12b-d0136608d847"], -Cell[5762408, 107785, 226132, 4139, 70, "Output",ExpressionUUID->"319b574b-2e35-403c-b78e-23fbca44a24c"] +Cell[5202109, 97414, 841, 21, 73, "Input",ExpressionUUID->"1af3a898-a964-44d7-86a6-b01d3c2bd890"], +Cell[5202953, 97437, 266610, 4797, 70, "Output",ExpressionUUID->"a1a5e406-ccd0-4c8c-97a9-61a4171e2f60"], +Cell[5469566, 102236, 292907, 5534, 70, "Output",ExpressionUUID->"eb751853-de87-4ae4-b5dd-b5efad43ff54"], +Cell[5762476, 107772, 6109, 143, 70, "Print",ExpressionUUID->"e0e2fea4-292b-46ec-a12b-d0136608d847"], +Cell[5768588, 107917, 226132, 4139, 70, "Output",ExpressionUUID->"319b574b-2e35-403c-b78e-23fbca44a24c"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[5988601, 111931, 202, 4, 72, "Title",ExpressionUUID->"0191a663-bf30-4a43-b8c7-edce09d2361b"], +Cell[5994781, 112063, 202, 4, 72, "Title",ExpressionUUID->"0191a663-bf30-4a43-b8c7-edce09d2361b"], Cell[CellGroupData[{ -Cell[5988828, 111939, 165, 3, 67, "Section",ExpressionUUID->"17e4dd54-73a6-4cfc-948f-3b2a0a2d0174"], -Cell[5988996, 111944, 2863, 84, 173, "Input",ExpressionUUID->"3f8c9a69-d755-4607-984f-39042c34f390", +Cell[5995008, 112071, 165, 3, 67, "Section",ExpressionUUID->"17e4dd54-73a6-4cfc-948f-3b2a0a2d0174"], +Cell[5995176, 112076, 2859, 83, 173, "Input",ExpressionUUID->"3f8c9a69-d755-4607-984f-39042c34f390", InitializationCell->True], Cell[CellGroupData[{ -Cell[5991884, 112032, 154, 3, 54, "Subsection",ExpressionUUID->"d815ea12-04a1-462c-b37f-a002453aac90"], +Cell[5998060, 112163, 154, 3, 54, "Subsection",ExpressionUUID->"d815ea12-04a1-462c-b37f-a002453aac90"], Cell[CellGroupData[{ -Cell[5992063, 112039, 1475, 36, 74, "Input",ExpressionUUID->"dfd2825c-abed-47ff-b89d-1d580bdf5592"], -Cell[5993541, 112077, 780, 15, 70, "Output",ExpressionUUID->"b353e07a-2814-4e72-b840-9054e9410006"], -Cell[5994324, 112094, 699, 13, 70, "Output",ExpressionUUID->"1ec92fc3-cfe8-4908-814f-0f603fff2731"] +Cell[5998239, 112170, 1475, 36, 74, "Input",ExpressionUUID->"dfd2825c-abed-47ff-b89d-1d580bdf5592"], +Cell[5999717, 112208, 780, 15, 70, "Output",ExpressionUUID->"b353e07a-2814-4e72-b840-9054e9410006"], +Cell[6000500, 112225, 699, 13, 70, "Output",ExpressionUUID->"1ec92fc3-cfe8-4908-814f-0f603fff2731"] }, Open ]], Cell[CellGroupData[{ -Cell[5995060, 112112, 1455, 36, 74, "Input",ExpressionUUID->"ed9510f5-93cb-4fe6-971b-e392ed5691d9"], -Cell[5996518, 112150, 713, 14, 70, "Output",ExpressionUUID->"797798ba-0f7f-4bde-a079-f2f5fc3011a6"], -Cell[5997234, 112166, 616, 11, 70, "Output",ExpressionUUID->"474bd8e9-c3a8-436e-b334-bdcf89c9b411"] +Cell[6001236, 112243, 1455, 36, 74, "Input",ExpressionUUID->"ed9510f5-93cb-4fe6-971b-e392ed5691d9"], +Cell[6002694, 112281, 713, 14, 70, "Output",ExpressionUUID->"797798ba-0f7f-4bde-a079-f2f5fc3011a6"], +Cell[6003410, 112297, 616, 11, 70, "Output",ExpressionUUID->"474bd8e9-c3a8-436e-b334-bdcf89c9b411"] }, Open ]], Cell[CellGroupData[{ -Cell[5997887, 112182, 1509, 37, 74, "Input",ExpressionUUID->"12f033be-f0a6-4fff-8219-81a8819e3850"], -Cell[5999399, 112221, 754, 14, 70, "Output",ExpressionUUID->"682d3ee6-d022-45e2-939f-62e44aa827ce"], -Cell[6000156, 112237, 652, 11, 70, "Output",ExpressionUUID->"c893beb8-f016-469f-a675-02a99f0942ad"] +Cell[6004063, 112313, 1509, 37, 74, "Input",ExpressionUUID->"12f033be-f0a6-4fff-8219-81a8819e3850"], +Cell[6005575, 112352, 754, 14, 70, "Output",ExpressionUUID->"682d3ee6-d022-45e2-939f-62e44aa827ce"], +Cell[6006332, 112368, 652, 11, 70, "Output",ExpressionUUID->"c893beb8-f016-469f-a675-02a99f0942ad"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[6000869, 112255, 164, 3, 53, "Section",ExpressionUUID->"ad009b44-9684-4d7a-816a-3d7e17470d67"], +Cell[6007045, 112386, 164, 3, 53, "Section",ExpressionUUID->"ad009b44-9684-4d7a-816a-3d7e17470d67"], Cell[CellGroupData[{ -Cell[6001058, 112262, 820, 20, 73, "Input",ExpressionUUID->"0f1c98a3-43fd-4540-aefb-564369a4b97b"], -Cell[6001881, 112284, 272259, 4891, 70, "Output",ExpressionUUID->"deba1a09-af28-42d1-a387-898ce4c59db1"], -Cell[6274143, 117177, 298624, 5631, 70, "Output",ExpressionUUID->"974ab132-a109-49ba-b0ff-ca98f94bf287"], -Cell[6572770, 122810, 6095, 143, 70, "Print",ExpressionUUID->"cafa3aab-55ec-4c14-ad39-52b2b49c9313"], -Cell[6578868, 122955, 231918, 4233, 70, "Output",ExpressionUUID->"aa0423c2-ef79-4650-9884-917509c455cb"] +Cell[6007234, 112393, 820, 20, 73, "Input",ExpressionUUID->"0f1c98a3-43fd-4540-aefb-564369a4b97b"], +Cell[6008057, 112415, 272259, 4891, 70, "Output",ExpressionUUID->"deba1a09-af28-42d1-a387-898ce4c59db1"], +Cell[6280319, 117308, 298624, 5631, 70, "Output",ExpressionUUID->"974ab132-a109-49ba-b0ff-ca98f94bf287"], +Cell[6578946, 122941, 6095, 143, 70, "Print",ExpressionUUID->"cafa3aab-55ec-4c14-ad39-52b2b49c9313"], +Cell[6585044, 123086, 231918, 4233, 70, "Output",ExpressionUUID->"aa0423c2-ef79-4650-9884-917509c455cb"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[6810847, 127195, 151, 3, 72, "Title",ExpressionUUID->"b573437c-89db-4f4d-a3b8-3ca447533bd8"], +Cell[6817023, 127326, 151, 3, 72, "Title",ExpressionUUID->"b573437c-89db-4f4d-a3b8-3ca447533bd8"], Cell[CellGroupData[{ -Cell[6811023, 127202, 165, 3, 67, "Section",ExpressionUUID->"4bafd2ed-5d5e-49ff-af2c-b66598cb80d1"], -Cell[6811191, 127207, 3466, 89, 173, "Input",ExpressionUUID->"4e96eaec-94cc-465a-be70-f93c6b2a6381", +Cell[6817199, 127333, 165, 3, 67, "Section",ExpressionUUID->"4bafd2ed-5d5e-49ff-af2c-b66598cb80d1"], +Cell[6817367, 127338, 3462, 88, 173, "Input",ExpressionUUID->"4e96eaec-94cc-465a-be70-f93c6b2a6381", InitializationCell->True], Cell[CellGroupData[{ -Cell[6814682, 127300, 154, 3, 54, "Subsection",ExpressionUUID->"9107415c-fdc8-4f7d-89f9-b49684ad3106"], +Cell[6820854, 127430, 154, 3, 54, "Subsection",ExpressionUUID->"9107415c-fdc8-4f7d-89f9-b49684ad3106"], Cell[CellGroupData[{ -Cell[6814861, 127307, 1427, 36, 74, "Input",ExpressionUUID->"4600701a-7489-4aeb-8a2c-e1011a80c2b3"], -Cell[6816291, 127345, 801, 15, 70, "Output",ExpressionUUID->"cff2728a-3862-4eae-b848-af83912c2ded"], -Cell[6817095, 127362, 722, 13, 70, "Output",ExpressionUUID->"707d5265-1b6c-4222-9aa1-4fa042dff0b9"] +Cell[6821033, 127437, 1427, 36, 74, "Input",ExpressionUUID->"4600701a-7489-4aeb-8a2c-e1011a80c2b3"], +Cell[6822463, 127475, 801, 15, 70, "Output",ExpressionUUID->"cff2728a-3862-4eae-b848-af83912c2ded"], +Cell[6823267, 127492, 722, 13, 70, "Output",ExpressionUUID->"707d5265-1b6c-4222-9aa1-4fa042dff0b9"] }, Open ]], Cell[CellGroupData[{ -Cell[6817854, 127380, 1402, 35, 74, "Input",ExpressionUUID->"1c3f2e72-9de5-45ee-a0ca-7a44639c025a"], -Cell[6819259, 127417, 739, 14, 70, "Output",ExpressionUUID->"ce798fe4-95c5-4c40-ab44-fa61599cda3d"], -Cell[6820001, 127433, 640, 11, 70, "Output",ExpressionUUID->"1e4c932c-1e6a-4f4d-8ce1-7e2c957b58a0"] +Cell[6824026, 127510, 1402, 35, 74, "Input",ExpressionUUID->"1c3f2e72-9de5-45ee-a0ca-7a44639c025a"], +Cell[6825431, 127547, 739, 14, 70, "Output",ExpressionUUID->"ce798fe4-95c5-4c40-ab44-fa61599cda3d"], +Cell[6826173, 127563, 640, 11, 70, "Output",ExpressionUUID->"1e4c932c-1e6a-4f4d-8ce1-7e2c957b58a0"] }, Open ]], Cell[CellGroupData[{ -Cell[6820678, 127449, 1453, 36, 74, "Input",ExpressionUUID->"0da9c2ab-13b6-49bf-acbb-14c13d6c25b7"], -Cell[6822134, 127487, 786, 15, 70, "Output",ExpressionUUID->"36fcfbf2-b44c-49e1-9fd6-d8c80863e28e"], -Cell[6822923, 127504, 685, 12, 70, "Output",ExpressionUUID->"2c37243b-2199-481b-9bb0-9d235a1b26ba"] +Cell[6826850, 127579, 1453, 36, 74, "Input",ExpressionUUID->"0da9c2ab-13b6-49bf-acbb-14c13d6c25b7"], +Cell[6828306, 127617, 786, 15, 70, "Output",ExpressionUUID->"36fcfbf2-b44c-49e1-9fd6-d8c80863e28e"], +Cell[6829095, 127634, 685, 12, 70, "Output",ExpressionUUID->"2c37243b-2199-481b-9bb0-9d235a1b26ba"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[6823669, 127523, 164, 3, 53, "Section",ExpressionUUID->"0e1e9409-cd66-4922-a1ed-71fe5827c12e"], +Cell[6829841, 127653, 164, 3, 53, "Section",ExpressionUUID->"0e1e9409-cd66-4922-a1ed-71fe5827c12e"], Cell[CellGroupData[{ -Cell[6823858, 127530, 813, 20, 73, "Input",ExpressionUUID->"1a55c1f0-9585-4e5a-a2e3-f739cfe0ceb8"], -Cell[6824674, 127552, 267247, 4809, 70, "Output",ExpressionUUID->"ef246109-ddfc-4cb8-a744-b880e0b28819"], -Cell[7091924, 132363, 293421, 5542, 70, "Output",ExpressionUUID->"9ffb02c2-c0bd-40d0-99dd-dc37a563b6f0"], -Cell[7385348, 137907, 6118, 144, 70, "Print",ExpressionUUID->"bd2bf63b-05f8-49ba-a3fc-f02a2b6c983b"], -Cell[7391469, 138053, 226758, 4138, 70, "Output",ExpressionUUID->"948cc031-538e-47c9-86d7-12e6971fd03c"] +Cell[6830030, 127660, 813, 20, 73, "Input",ExpressionUUID->"1a55c1f0-9585-4e5a-a2e3-f739cfe0ceb8"], +Cell[6830846, 127682, 267247, 4809, 70, "Output",ExpressionUUID->"ef246109-ddfc-4cb8-a744-b880e0b28819"], +Cell[7098096, 132493, 293421, 5542, 70, "Output",ExpressionUUID->"9ffb02c2-c0bd-40d0-99dd-dc37a563b6f0"], +Cell[7391520, 138037, 6118, 144, 70, "Print",ExpressionUUID->"bd2bf63b-05f8-49ba-a3fc-f02a2b6c983b"], +Cell[7397641, 138183, 226758, 4138, 70, "Output",ExpressionUUID->"948cc031-538e-47c9-86d7-12e6971fd03c"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[7618288, 142198, 153, 3, 72, "Title",ExpressionUUID->"8a4ffb97-273c-457a-86b2-f36b838038c3"], +Cell[7624460, 142328, 153, 3, 72, "Title",ExpressionUUID->"8a4ffb97-273c-457a-86b2-f36b838038c3"], Cell[CellGroupData[{ -Cell[7618466, 142205, 165, 3, 67, "Section",ExpressionUUID->"410ead3f-69f8-455a-b141-b8c6bb31b59e"], -Cell[7618634, 142210, 3507, 90, 173, "Input",ExpressionUUID->"5cdc98a8-ba9a-4309-8652-c42849243a3c", +Cell[7624638, 142335, 165, 3, 67, "Section",ExpressionUUID->"410ead3f-69f8-455a-b141-b8c6bb31b59e"], +Cell[7624806, 142340, 3503, 89, 173, "Input",ExpressionUUID->"5cdc98a8-ba9a-4309-8652-c42849243a3c", InitializationCell->True], Cell[CellGroupData[{ -Cell[7622166, 142304, 154, 3, 54, "Subsection",ExpressionUUID->"129935a0-86a7-4051-bdca-a2a54da66afe"], +Cell[7628334, 142433, 154, 3, 54, "Subsection",ExpressionUUID->"129935a0-86a7-4051-bdca-a2a54da66afe"], Cell[CellGroupData[{ -Cell[7622345, 142311, 1428, 36, 74, "Input",ExpressionUUID->"c7e5d329-77b0-4dd0-88db-00aa2b589947"], -Cell[7623776, 142349, 783, 15, 70, "Output",ExpressionUUID->"12176d01-0c70-4e70-806f-1a9d742705f6"], -Cell[7624562, 142366, 705, 13, 70, "Output",ExpressionUUID->"119b1726-85a1-4dec-9db1-a4e1adee2b6e"] +Cell[7628513, 142440, 1428, 36, 74, "Input",ExpressionUUID->"c7e5d329-77b0-4dd0-88db-00aa2b589947"], +Cell[7629944, 142478, 783, 15, 70, "Output",ExpressionUUID->"12176d01-0c70-4e70-806f-1a9d742705f6"], +Cell[7630730, 142495, 705, 13, 70, "Output",ExpressionUUID->"119b1726-85a1-4dec-9db1-a4e1adee2b6e"] }, Open ]], Cell[CellGroupData[{ -Cell[7625304, 142384, 1404, 35, 74, "Input",ExpressionUUID->"a70de1ce-8526-4071-a1eb-123213e8a509"], -Cell[7626711, 142421, 714, 14, 70, "Output",ExpressionUUID->"4e1a6578-b711-4343-9587-dbc8c31cfe61"], -Cell[7627428, 142437, 615, 11, 70, "Output",ExpressionUUID->"719bae9f-4e65-4dbb-a32b-94f50fc847f3"] +Cell[7631472, 142513, 1404, 35, 74, "Input",ExpressionUUID->"a70de1ce-8526-4071-a1eb-123213e8a509"], +Cell[7632879, 142550, 714, 14, 70, "Output",ExpressionUUID->"4e1a6578-b711-4343-9587-dbc8c31cfe61"], +Cell[7633596, 142566, 615, 11, 70, "Output",ExpressionUUID->"719bae9f-4e65-4dbb-a32b-94f50fc847f3"] }, Open ]], Cell[CellGroupData[{ -Cell[7628080, 142453, 1455, 36, 74, "Input",ExpressionUUID->"edc830ee-5ccd-4b26-8a91-1e951afe5bc6"], -Cell[7629538, 142491, 756, 14, 70, "Output",ExpressionUUID->"58240990-71ea-445c-89f7-9f55faec3cd4"], -Cell[7630297, 142507, 654, 11, 70, "Output",ExpressionUUID->"d386d0f3-4094-4c1e-8a7f-346c36196a2c"] +Cell[7634248, 142582, 1455, 36, 74, "Input",ExpressionUUID->"edc830ee-5ccd-4b26-8a91-1e951afe5bc6"], +Cell[7635706, 142620, 756, 14, 70, "Output",ExpressionUUID->"58240990-71ea-445c-89f7-9f55faec3cd4"], +Cell[7636465, 142636, 654, 11, 70, "Output",ExpressionUUID->"d386d0f3-4094-4c1e-8a7f-346c36196a2c"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[7631012, 142525, 164, 3, 53, "Section",ExpressionUUID->"74affff8-cb32-47ad-9136-4b7cf83078b4"], +Cell[7637180, 142654, 164, 3, 53, "Section",ExpressionUUID->"74affff8-cb32-47ad-9136-4b7cf83078b4"], Cell[CellGroupData[{ -Cell[7631201, 142532, 821, 20, 73, "Input",ExpressionUUID->"2ca76e5a-82f7-4b88-9690-3ef64b3edef6"], -Cell[7632025, 142554, 271737, 4884, 70, "Output",ExpressionUUID->"c406bb2d-fcb7-4762-a484-ad3114907aba"], -Cell[7903765, 147440, 298115, 5623, 70, "Output",ExpressionUUID->"7b00676b-e93c-448a-9c0e-21c75766e599"], -Cell[8201883, 153065, 6101, 143, 70, "Print",ExpressionUUID->"25e22c1b-0284-4a2b-9f3f-c404ac0c0df6"], -Cell[8207987, 153210, 231272, 4227, 70, "Output",ExpressionUUID->"cd6795ad-7e8b-4a96-b2c2-18bf61544509"] +Cell[7637369, 142661, 821, 20, 73, "Input",ExpressionUUID->"2ca76e5a-82f7-4b88-9690-3ef64b3edef6"], +Cell[7638193, 142683, 271737, 4884, 70, "Output",ExpressionUUID->"c406bb2d-fcb7-4762-a484-ad3114907aba"], +Cell[7909933, 147569, 298115, 5623, 70, "Output",ExpressionUUID->"7b00676b-e93c-448a-9c0e-21c75766e599"], +Cell[8208051, 153194, 6101, 143, 70, "Print",ExpressionUUID->"25e22c1b-0284-4a2b-9f3f-c404ac0c0df6"], +Cell[8214155, 153339, 231272, 4227, 70, "Output",ExpressionUUID->"cd6795ad-7e8b-4a96-b2c2-18bf61544509"] }, Open ]], -Cell[8439274, 157440, 170, 3, 52, "Input",ExpressionUUID->"66210fa5-9b17-401b-bd16-13f154bc7b0a"] +Cell[8445442, 157569, 170, 3, 52, "Input",ExpressionUUID->"66210fa5-9b17-401b-bd16-13f154bc7b0a"] }, Open ]] }, Closed]], Cell[CellGroupData[{ -Cell[8439493, 157449, 151, 3, 72, "Title",ExpressionUUID->"3aa4c3c7-fc6f-42ef-aa94-929bb1c5aa0a"], +Cell[8445661, 157578, 151, 3, 72, "Title",ExpressionUUID->"3aa4c3c7-fc6f-42ef-aa94-929bb1c5aa0a"], Cell[CellGroupData[{ -Cell[8439669, 157456, 165, 3, 67, "Section",ExpressionUUID->"b03eb6df-71b5-4406-a539-f8a9bb649f41"], -Cell[8439837, 157461, 3422, 89, 173, "Input",ExpressionUUID->"bb79f009-b78a-42cd-a70b-1c427ab4c78f", +Cell[8445837, 157585, 165, 3, 67, "Section",ExpressionUUID->"b03eb6df-71b5-4406-a539-f8a9bb649f41"], +Cell[8446005, 157590, 3418, 88, 173, "Input",ExpressionUUID->"bb79f009-b78a-42cd-a70b-1c427ab4c78f", InitializationCell->True], Cell[CellGroupData[{ -Cell[8443284, 157554, 154, 3, 54, "Subsection",ExpressionUUID->"405e8c59-70fc-417a-adb3-16717ec9ddcc"], +Cell[8449448, 157682, 154, 3, 54, "Subsection",ExpressionUUID->"405e8c59-70fc-417a-adb3-16717ec9ddcc"], Cell[CellGroupData[{ -Cell[8443463, 157561, 1430, 36, 74, "Input",ExpressionUUID->"efaa24f1-ad32-4652-afa8-24a855b34924"], -Cell[8444896, 157599, 784, 15, 70, "Output",ExpressionUUID->"58a57da2-3eb5-4d21-901d-9662e578e771"], -Cell[8445683, 157616, 706, 13, 70, "Output",ExpressionUUID->"480406a4-ff94-418b-a27e-f294636e4284"] +Cell[8449627, 157689, 1430, 36, 74, "Input",ExpressionUUID->"efaa24f1-ad32-4652-afa8-24a855b34924"], +Cell[8451060, 157727, 784, 15, 70, "Output",ExpressionUUID->"58a57da2-3eb5-4d21-901d-9662e578e771"], +Cell[8451847, 157744, 706, 13, 70, "Output",ExpressionUUID->"480406a4-ff94-418b-a27e-f294636e4284"] }, Open ]], Cell[CellGroupData[{ -Cell[8446426, 157634, 1405, 35, 74, "Input",ExpressionUUID->"bd3953bd-1678-4443-b5d6-53b1ca3214af"], -Cell[8447834, 157671, 722, 14, 70, "Output",ExpressionUUID->"d9b1a949-6c41-4551-b2c5-ad314e51a960"], -Cell[8448559, 157687, 624, 11, 70, "Output",ExpressionUUID->"5a702cba-fc76-42f4-8890-e2cbb8a48a64"] +Cell[8452590, 157762, 1405, 35, 74, "Input",ExpressionUUID->"bd3953bd-1678-4443-b5d6-53b1ca3214af"], +Cell[8453998, 157799, 722, 14, 70, "Output",ExpressionUUID->"d9b1a949-6c41-4551-b2c5-ad314e51a960"], +Cell[8454723, 157815, 624, 11, 70, "Output",ExpressionUUID->"5a702cba-fc76-42f4-8890-e2cbb8a48a64"] }, Open ]], Cell[CellGroupData[{ -Cell[8449220, 157703, 1454, 36, 74, "Input",ExpressionUUID->"ec71f8b9-3a2f-4d82-9674-291fd3dcb70b"], -Cell[8450677, 157741, 753, 14, 70, "Output",ExpressionUUID->"7b4a7b90-25bf-4d81-be93-a726703c90ee"], -Cell[8451433, 157757, 651, 11, 70, "Output",ExpressionUUID->"de0d47d7-d0ca-46de-bc81-737682fd9292"] +Cell[8455384, 157831, 1454, 36, 74, "Input",ExpressionUUID->"ec71f8b9-3a2f-4d82-9674-291fd3dcb70b"], +Cell[8456841, 157869, 753, 14, 70, "Output",ExpressionUUID->"7b4a7b90-25bf-4d81-be93-a726703c90ee"], +Cell[8457597, 157885, 651, 11, 70, "Output",ExpressionUUID->"de0d47d7-d0ca-46de-bc81-737682fd9292"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[8452145, 157775, 164, 3, 53, "Section",ExpressionUUID->"310e5587-f9ab-4373-b92e-8e87daed147b"], +Cell[8458309, 157903, 164, 3, 53, "Section",ExpressionUUID->"310e5587-f9ab-4373-b92e-8e87daed147b"], Cell[CellGroupData[{ -Cell[8452334, 157782, 814, 20, 73, "Input",ExpressionUUID->"84daa51b-01a0-4d42-8143-288ce54cb6c0"], -Cell[8453151, 157804, 266983, 4809, 70, "Output",ExpressionUUID->"82363da1-960c-4497-8498-e423d6553d8b"], -Cell[8720137, 162615, 293397, 5549, 70, "Output",ExpressionUUID->"842518c1-9bb8-44f4-b519-2dfbe934f9c0"], -Cell[9013537, 168166, 6133, 144, 70, "Print",ExpressionUUID->"0257c2b2-28c1-488b-aaa9-6c58abd307da"], -Cell[9019673, 168312, 226251, 4136, 70, "Output",ExpressionUUID->"e27f3a84-c0ee-4745-9028-a1b2f20f3836"] +Cell[8458498, 157910, 814, 20, 73, "Input",ExpressionUUID->"84daa51b-01a0-4d42-8143-288ce54cb6c0"], +Cell[8459315, 157932, 266983, 4809, 70, "Output",ExpressionUUID->"82363da1-960c-4497-8498-e423d6553d8b"], +Cell[8726301, 162743, 293397, 5549, 70, "Output",ExpressionUUID->"842518c1-9bb8-44f4-b519-2dfbe934f9c0"], +Cell[9019701, 168294, 6133, 144, 70, "Print",ExpressionUUID->"0257c2b2-28c1-488b-aaa9-6c58abd307da"], +Cell[9025837, 168440, 226251, 4136, 70, "Output",ExpressionUUID->"e27f3a84-c0ee-4745-9028-a1b2f20f3836"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ -Cell[9245985, 172455, 151, 3, 72, "Title",ExpressionUUID->"3f1c5daa-9204-4fa2-aff4-6501ee71088b"], +Cell[9252149, 172583, 151, 3, 72, "Title",ExpressionUUID->"3f1c5daa-9204-4fa2-aff4-6501ee71088b"], Cell[CellGroupData[{ -Cell[9246161, 172462, 165, 3, 67, "Section",ExpressionUUID->"8f74d292-59d5-45cb-a51d-f25b4743cd6f"], -Cell[9246329, 172467, 2822, 83, 173, "Input",ExpressionUUID->"52f42957-7028-4c6a-87b7-6d3cbef3d400", +Cell[9252325, 172590, 165, 3, 67, "Section",ExpressionUUID->"8f74d292-59d5-45cb-a51d-f25b4743cd6f"], +Cell[9252493, 172595, 2818, 82, 173, "Input",ExpressionUUID->"52f42957-7028-4c6a-87b7-6d3cbef3d400", InitializationCell->True], Cell[CellGroupData[{ -Cell[9249176, 172554, 154, 3, 54, "Subsection",ExpressionUUID->"80951159-85f4-4b2a-b4e4-386ff0b4b2ed"], +Cell[9255336, 172681, 154, 3, 54, "Subsection",ExpressionUUID->"80951159-85f4-4b2a-b4e4-386ff0b4b2ed"], Cell[CellGroupData[{ -Cell[9249355, 172561, 1427, 36, 74, "Input",ExpressionUUID->"e557ec2c-a2fe-4826-972c-21055ce691c0"], -Cell[9250785, 172599, 785, 15, 70, "Output",ExpressionUUID->"3e3dd757-99a8-4f0d-8c3f-6381e35c1beb"], -Cell[9251573, 172616, 705, 13, 70, "Output",ExpressionUUID->"984547bb-dee9-4114-b7b7-0ddaa869f829"] +Cell[9255515, 172688, 1427, 36, 74, "Input",ExpressionUUID->"e557ec2c-a2fe-4826-972c-21055ce691c0"], +Cell[9256945, 172726, 785, 15, 70, "Output",ExpressionUUID->"3e3dd757-99a8-4f0d-8c3f-6381e35c1beb"], +Cell[9257733, 172743, 705, 13, 70, "Output",ExpressionUUID->"984547bb-dee9-4114-b7b7-0ddaa869f829"] }, Open ]], Cell[CellGroupData[{ -Cell[9252315, 172634, 1404, 35, 74, "Input",ExpressionUUID->"7968e064-d590-43d4-899b-e2830156ec83"], -Cell[9253722, 172671, 720, 14, 70, "Output",ExpressionUUID->"6e0e1613-f495-4eef-931e-512633bf1343"], -Cell[9254445, 172687, 620, 11, 70, "Output",ExpressionUUID->"fe885fb2-a7f1-4840-a984-13e021d08bc1"] +Cell[9258475, 172761, 1404, 35, 74, "Input",ExpressionUUID->"7968e064-d590-43d4-899b-e2830156ec83"], +Cell[9259882, 172798, 720, 14, 70, "Output",ExpressionUUID->"6e0e1613-f495-4eef-931e-512633bf1343"], +Cell[9260605, 172814, 620, 11, 70, "Output",ExpressionUUID->"fe885fb2-a7f1-4840-a984-13e021d08bc1"] }, Open ]], Cell[CellGroupData[{ -Cell[9255102, 172703, 1455, 36, 74, "Input",ExpressionUUID->"9a668e93-ff40-4858-83e4-377dc9a38be5"], -Cell[9256560, 172741, 758, 14, 70, "Output",ExpressionUUID->"dce1ccc9-5af5-40ce-bc48-9f9106740a73"], -Cell[9257321, 172757, 654, 11, 70, "Output",ExpressionUUID->"df09b653-b2f7-4153-953a-33191b323741"] +Cell[9261262, 172830, 1455, 36, 74, "Input",ExpressionUUID->"9a668e93-ff40-4858-83e4-377dc9a38be5"], +Cell[9262720, 172868, 758, 14, 70, "Output",ExpressionUUID->"dce1ccc9-5af5-40ce-bc48-9f9106740a73"], +Cell[9263481, 172884, 654, 11, 70, "Output",ExpressionUUID->"df09b653-b2f7-4153-953a-33191b323741"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ -Cell[9258036, 172775, 164, 3, 53, "Section",ExpressionUUID->"9d03b122-a5b6-4976-ad57-942073f6d9d0"], +Cell[9264196, 172902, 164, 3, 53, "Section",ExpressionUUID->"9d03b122-a5b6-4976-ad57-942073f6d9d0"], Cell[CellGroupData[{ -Cell[9258225, 172782, 912, 22, 73, "Input",ExpressionUUID->"22c90b4e-fec5-4cae-9b3f-6054fc1e0e89"], -Cell[9259140, 172806, 265621, 4782, 70, "Output",ExpressionUUID->"f2a25678-7bf2-4439-bd2d-b14a7956dffb"], -Cell[9524764, 177590, 291985, 5522, 70, "Output",ExpressionUUID->"80d1628e-838c-44b5-b954-2588295e7f39"], -Cell[9816752, 183114, 6185, 145, 70, "Print",ExpressionUUID->"a9e42da7-4826-4303-9682-a84f0f17df79"], -Cell[9822940, 183261, 225032, 4113, 70, "Output",ExpressionUUID->"35fe9a75-1ba9-4033-aa4a-91609c07298f"] +Cell[9264385, 172909, 912, 22, 73, "Input",ExpressionUUID->"22c90b4e-fec5-4cae-9b3f-6054fc1e0e89"], +Cell[9265300, 172933, 265621, 4782, 424, "Output",ExpressionUUID->"f2a25678-7bf2-4439-bd2d-b14a7956dffb"], +Cell[9530924, 177717, 291985, 5522, 374, "Output",ExpressionUUID->"80d1628e-838c-44b5-b954-2588295e7f39"], +Cell[9822912, 183241, 6185, 145, 292, "Print",ExpressionUUID->"a9e42da7-4826-4303-9682-a84f0f17df79"], +Cell[9829100, 183388, 225032, 4113, 380, "Output",ExpressionUUID->"35fe9a75-1ba9-4033-aa4a-91609c07298f"] }, Open ]], -Cell[10047987, 187377, 170, 3, 52, "Input",ExpressionUUID->"18d02b6c-55e6-4a07-b179-52672bef5bee"] -}, Closed]] +Cell[10054147, 187504, 170, 3, 52, "Input",ExpressionUUID->"18d02b6c-55e6-4a07-b179-52672bef5bee"] +}, Open ]] }, Closed]], Cell[CellGroupData[{ -Cell[10048206, 187386, 154, 3, 72, "Title",ExpressionUUID->"ab0b0e4e-65b0-4609-8a28-bc277f2c4504"], -Cell[10048363, 187391, 625, 14, 89, "Input",ExpressionUUID->"0fbf8e5b-2c67-467d-9b6a-fedb8d5dd48a", +Cell[10054366, 187513, 154, 3, 72, "Title",ExpressionUUID->"ab0b0e4e-65b0-4609-8a28-bc277f2c4504"], +Cell[10054523, 187518, 621, 13, 89, "Input",ExpressionUUID->"0fbf8e5b-2c67-467d-9b6a-fedb8d5dd48a", InitializationCell->True], -Cell[10048991, 187407, 2051, 41, 110, "Input",ExpressionUUID->"6f1d9e38-cf5a-407d-bce7-a920d10a6249", +Cell[10055147, 187533, 2047, 40, 110, "Input",ExpressionUUID->"6f1d9e38-cf5a-407d-bce7-a920d10a6249", InitializationCell->True], -Cell[10051045, 187450, 2091, 42, 110, "Input",ExpressionUUID->"4d9c28a8-eb44-41db-82fb-4a6d1da18c91", +Cell[10057197, 187575, 2087, 41, 110, "Input",ExpressionUUID->"4d9c28a8-eb44-41db-82fb-4a6d1da18c91", InitializationCell->True], -Cell[10053139, 187494, 2077, 42, 110, "Input",ExpressionUUID->"36f8d626-8fdc-4100-a29e-d47d0d0eabe1", +Cell[10059287, 187618, 2073, 41, 110, "Input",ExpressionUUID->"36f8d626-8fdc-4100-a29e-d47d0d0eabe1", InitializationCell->True], -Cell[10055219, 187538, 1925, 52, 110, "Input",ExpressionUUID->"58e226a7-7689-4a2b-ac93-4db52cc1c5b0", +Cell[10061363, 187661, 1921, 51, 110, "Input",ExpressionUUID->"58e226a7-7689-4a2b-ac93-4db52cc1c5b0", InitializationCell->True], Cell[CellGroupData[{ -Cell[10057169, 187594, 7230, 194, 320, "Input",ExpressionUUID->"a0e1fe79-49fa-4da6-8302-31437c3bebf7", +Cell[10063309, 187716, 7226, 193, 320, "Input",ExpressionUUID->"a0e1fe79-49fa-4da6-8302-31437c3bebf7", InitializationCell->True], -Cell[10064402, 187790, 2395, 63, 70, "Output",ExpressionUUID->"e5d6b0fa-9fec-4b23-820d-595bbac55db7"], -Cell[10066800, 187855, 2126, 57, 70, "Output",ExpressionUUID->"82c7e22e-3948-44ae-b3d4-3d479dac7bbf"], -Cell[10068929, 187914, 2137, 57, 70, "Output",ExpressionUUID->"a372f1e2-9d29-44bf-bf06-f11269ea3b27"], -Cell[10071069, 187973, 5497, 133, 70, "Output",ExpressionUUID->"31a87b69-6a19-4245-9b84-148b5feb4296"] +Cell[10070538, 187911, 2444, 64, 70, "Output",ExpressionUUID->"7554d460-cd50-4e0e-91c2-398eaf4fe77a"], +Cell[10072985, 187977, 2173, 58, 70, "Output",ExpressionUUID->"c87848c9-b0e5-4a49-9070-f6d1016a80ab"], +Cell[10075161, 188037, 2184, 58, 70, "Output",ExpressionUUID->"adcc4f38-8ff4-4379-900f-80132211bf31"], +Cell[10077348, 188097, 5542, 134, 70, "Output",ExpressionUUID->"61e609dc-f220-4b62-ae3f-c7d628d7115a"] }, Open ]] }, Closed]] } diff --git a/Manuscript/Ec.tex b/Manuscript/Ec.tex index a3882ea..537d73a 100644 --- a/Manuscript/Ec.tex +++ b/Manuscript/Ec.tex @@ -4,7 +4,7 @@ \newcommand{\ie}{\textit{i.e.}} \newcommand{\eg}{\textit{e.g.}} -\newcommand{\alert}[1]{\textcolor{black}{#1}} +\newcommand{\alert}[1]{\textcolor{red}{#1}} \usepackage[normalem]{ulem} \newcommand{\titou}[1]{\textcolor{red}{#1}} \newcommand{\denis}[1]{\textcolor{blue}{#1}} @@ -55,7 +55,9 @@ \newcommand{\EHF}{E_\text{HF}} \newcommand{\Ec}{E_\text{c}} \newcommand{\Evar}{E_\text{var}} +\newcommand{\Efinal}{E_\text{final}} \newcommand{\Eextrap}{E_\text{extrap}} +\newcommand{\Edist}{E_\text{dist}} \newcommand{\EPT}{E_\text{PT2}} \newcommand{\ECIPSI}{E_\text{CIPSI}} @@ -167,6 +169,7 @@ This set of molecular systems corresponds to Hilbert spaces with sizes ranging f In addition to CIPSI, the performance and convergence properties of several series of methods are investigated. In particular, we study i) the MP perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), ii) the CC2, CC3, and CC4 approximate series, and ii) the ``complete'' CC series up to quadruples (\ie, CCSD, CCSDT, and CCSDTQ). The performance of the ground-state gold standard CCSD(T) as well as the completely renormalized (CR) CC model, CR-CC(2,3), \cite{Kowalski_2000a,Kowalski_2000b,Piecuch_2002a,Piecuch_2002b,Piecuch_2005} are also investigated. +\alert{From a theoretical point of view, one would expect the following ranking: MP2 $<$ CC2 $<$ MP3 $<$ CCSD $<$ MP4 $<$ CCSD(T) $<$ CR-CC(2,3) $<$ CC3 $<$ CCSDT $<$ MP5 $<$ CC4 $<$ CCSDTQ. But, as we shall see below, this ranking is slightly altered for the present systems.} The present manuscript is organized as follows. In Sec.~\ref{sec:OO-CIPSI}, we provide theoretical details about the CIPSI algorithm and the orbital optimization procedure employed here. @@ -441,93 +444,94 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}. %%% TABLE III %%% \begin{squeezetable} -\begin{table} +\begin{table*} \caption{ - Extrapolated correlation energies $\Delta \Eextrap$ (in \si{\milli\hartree}) computed in the cc-pVDZ basis for the twelve cyclic molecules represented in Fig.~\ref{fig:mol} and their associated fitting errors (in \si{\milli\hartree}) obtained via weighted linear fits with a varying number of points. + \alert{Extrapolation distance $\Delta \Edist$ (in \si{\milli\hartree}) defined as the difference between the final computed energy $\Delta \Efinal$ (in \si{\milli\hartree}) and the extrapolated correlation energies $\Delta \Eextrap$ (in \si{\milli\hartree}) computed in the cc-pVDZ basis for the twelve cyclic molecules represented in Fig.~\ref{fig:mol} and their associated fitting errors (in \si{\milli\hartree}) obtained via weighted linear fits with a varying number of points.} Two sets of orbitals are considered: natural orbitals and optimized orbitals. The weights are taken as the inverse square of the perturbative corrections. For a $m$-point fit, the $m$ largest variational wave functions are used. \label{tab:fit}} \begin{ruledtabular} - \begin{tabular}{lccccc} - Molecule & Number of & \mc{2}{c}{Natural orbitals} & \mc{2}{c}{Optimized orbitals} \\ - \cline{3-4}\cline{5-6} - & fitting points & $\Delta \Eextrap$ & Fitting error & $\Delta \Eextrap$ & Fitting error \\ + \begin{tabular}{lccccccccc} + Molecule & Number of & \mc{4}{c}{Natural orbitals} & \mc{4}{c}{Optimized orbitals} \\ + \cline{3-6}\cline{7-10} + & fitting points & $\Delta \Efinal$ & $\Delta \Eextrap$ & $\Delta \Edist$ & Fitting error + & $\Delta \Efinal$ & $\Delta \Eextrap$ & $\Delta \Edist$ & Fitting error \\ \hline - Cyclopentadiene & 3 & $-740.639$ & $0.273$ & $-739.295$ & $0.199$ \\ - & 4 & $-740.243$ & $0.306$ & $-739.309$ & $0.088$ \\ - &\bf5 & $-740.047$ & $0.242$ & $\bf-739.230$& $\bf0.074$ \\ - & 6 & $-739.952$ & $0.187$ & $-739.304$ & $0.072$ \\ - & 7 & $-739.761$ & $0.204$ & $-739.292$ & $0.055$ \\ + Cyclopentadiene & 3 & $-728.941$ & $-740.639$ & $11.699$ & $0.273$ & $-731.987$ & $-739.295$ & $7.308$ & $0.199$ \\ + & 4 & $-728.941$ & $-740.243$ & $11.303$ & $0.306$ & $-731.987$ & $-739.309$ & $7.322$ & $0.088$ \\ + &\bf5 & $-728.941$ & $-740.047$ & $11.106$ & $0.242$ &$\bf-731.987$ &$\bf-739.230$ &$\bf7.243$ &$\bf0.074$ \\ + & 6 & $-728.941$ & $-739.952$ & $11.011$ & $0.187$ & $-731.987$ & $-739.304$ & $7.317$ & $0.072$ \\ + & 7 & $-728.941$ & $-739.761$ & $10.820$ & $0.204$ & $-731.987$ & $-739.292$ & $7.305$ & $0.055$ \\ \hline - Furan & 3 & $-766.090$ & $0.729$ & $-767.790$ & $0.064$ \\ - & 4 & $-766.445$ & $0.459$ & $-768.104$ & $0.196$ \\ - &\bf5 & $-766.582$ & $0.318$ & $\bf-768.194$ &$\bf0.135$ \\ - & 6 & $-766.366$ & $0.288$ & $-768.060$ & $0.131$ \\ - & 7 & $-766.507$ & $0.254$ & $-768.086$ & $0.101$ \\ + Furan & 3 & $-758.946$ & $-766.090$ & $7.144$ & $0.729$ & $-761.715$ & $-767.790$ & $6.076$ & $0.064$ \\ + & 4 & $-758.946$ & $-766.445$ & $7.499$ & $0.459$ & $-761.715$ & $-768.104$ & $6.389$ & $0.196$ \\ + &\bf5 & $-758.946$ & $-766.582$ & $7.636$ & $0.318$ &$\bf-761.715$ &$\bf-768.194$ &$\bf6.479$ &$\bf0.135$ \\ + & 6 & $-758.946$ & $-766.366$ & $7.420$ & $0.288$ & $-761.715$ & $-768.060$ & $6.345$ & $0.131$ \\ + & 7 & $-758.946$ & $-766.507$ & $7.561$ & $0.254$ & $-761.715$ & $-768.086$ & $6.372$ & $0.101$ \\ \hline - Imidazole & 3 & $-778.148$ & $2.197$ & $-778.295$ & $0.356$ \\ - & 4 & $-777.436$ & $1.107$ & $-778.270$ & $0.150$ \\ - &\bf5 & $-776.300$ & $0.996$ & $\bf-778.178$ &$\bf0.105$ \\ - & 6 & $-776.104$ & $0.712$ & $-778.174$ & $0.072$ \\ - & 7 & $-776.098$ & $0.541$ & $-778.051$ & $0.099$ \\ + Imidazole & 3 & $-767.314$ & $-778.148$ & $10.833$ & $2.197$ & $-771.362$ & $-778.295$ & $6.932$ & $0.356$ \\ + & 4 & $-767.314$ & $-777.436$ & $10.122$ & $1.107$ & $-771.362$ & $-778.270$ & $6.908$ & $0.150$ \\ + &\bf5 & $-767.314$ & $-776.300$ & $8.986$ & $0.996$ &$\bf-771.362$ &$\bf-778.178$ &$\bf6.816$ &$\bf0.105$ \\ + & 6 & $-767.314$ & $-776.104$ & $8.789$ & $0.712$ & $-771.362$ & $-778.174$ & $6.812$ & $0.072$ \\ + & 7 & $-767.314$ & $-776.098$ & $8.784$ & $0.541$ & $-771.362$ & $-778.051$ & $6.689$ & $0.099$ \\ \hline - Pyrrole & 3 & $-758.309$ & $0.447$ & $-758.650$ & $0.321$ \\ - & 4 & $-758.749$ & $0.393$ & $-758.389$ & $0.174$ \\ - &\bf5 & $-758.405$ & $0.359$ & $\bf-758.460$ &$\bf0.110$ \\ - & 6 & $-758.136$ & $0.334$ & $-758.352$ & $0.100$ \\ - & 7 & $-757.990$ & $0.283$ & $-758.347$ & $0.075$ \\ + Pyrrole & 3 & $-748.961$ & $-758.309$ & $9.348$ & $0.447$ & $-751.862$ & $-758.650$ & $6.788$ & $0.321$ \\ + & 4 & $-748.961$ & $-758.749$ & $9.788$ & $0.393$ & $-751.862$ & $-758.389$ & $6.527$ & $0.174$ \\ + &\bf5 & $-748.961$ & $-758.405$ & $9.444$ & $0.359$ &$\bf-751.862$ &$\bf-758.460$ &$\bf6.598$ &$\bf0.110$ \\ + & 6 & $-748.961$ & $-758.136$ & $9.175$ & $0.334$ & $-751.862$ & $-758.352$ & $6.490$ & $0.100$ \\ + & 7 & $-748.961$ & $-757.990$ & $9.029$ & $0.283$ & $-751.862$ & $-758.347$ & $6.485$ & $0.075$ \\ \hline - Thiophene & 3 & $-728.054$ & $0.134$ & $-728.744$ & $0.691$ \\ - & 4 & $-728.240$ & $0.139$ & $-729.052$ & $0.331$ \\ - &\bf5 & $-728.243$ & $0.087$ & $\bf-728.948$ &$\bf0.203$ \\ - & 6 & $-728.242$ & $0.062$ & $-728.987$ & $0.140$ \\ - & 7 & $-728.420$ & $0.144$ & $-729.067$ & $0.117$ \\ + Thiophene & 3 & $-718.769$ & $-728.054$ & $9.285$ & $0.134$ & $-721.757$ & $-728.744$ & $6.987$ & $0.691$ \\ + & 4 & $-718.769$ & $-728.240$ & $9.471$ & $0.139$ & $-721.757$ & $-729.052$ & $7.295$ & $0.331$ \\ + &\bf5 & $-718.769$ & $-728.243$ & $9.474$ & $0.087$ &$\bf-721.757$ &$\bf-728.948$ &$\bf7.191$ &$\bf0.203$ \\ + & 6 & $-718.769$ & $-728.242$ & $9.472$ & $0.062$ & $-721.757$ & $-728.987$ & $7.230$ & $0.140$ \\ + & 7 & $-718.769$ & $-728.420$ & $9.651$ & $0.144$ & $-721.757$ & $-729.067$ & $7.310$ & $0.117$ \\ \hline - Benzene & 3 & $-860.350$ & $0.496$ & $-862.325$ & $0.279$ \\ - & 4 & $-861.949$ & $0.811$ & $-863.024$ & $0.424$ \\ - &\bf5 & $-861.807$ & $0.474$ & $\bf-862.890$ &$\bf0.266$ \\ - & 6 & $-861.110$ & $0.539$ & $-862.360$ & $0.383$ \\ - & 7 & $-861.410$ & $0.444$ & $-862.083$ & $0.339$ \\ + Benzene & 3 & $-841.030$ & $-860.350$ & $19.3197$ & $0.496$ & $-848.540$ & $-862.325$ & $13.7847$ & $0.279$ \\ + & 4 & $-841.030$ & $-861.949$ & $20.9186$ & $0.811$ & $-848.540$ & $-863.024$ & $14.4842$ & $0.424$ \\ + &\bf5 & $-841.030$ & $-861.807$ & $20.7772$ & $0.474$ &$\bf-848.540$ &$\bf-862.890$ &$\bf14.3496$ &$\bf0.266$ \\ + & 6 & $-841.030$ & $-861.110$ & $20.0803$ & $0.539$ & $-848.540$ & $-862.360$ & $13.8202$ & $0.383$ \\ + & 7 & $-841.030$ & $-861.410$ & $20.3794$ & $0.444$ & $-848.540$ & $-862.083$ & $13.5435$ & $0.339$ \\ \hline - Pyrazine & 3 & $-904.148$ & $0.035$ & $-904.867$ & $1.420$ \\ - & 4 & $-904.726$ & $0.377$ & $-904.588$ & $0.650$ \\ - &\bf5 & $-904.274$ & $0.383$ & $\bf-904.550$ &$\bf0.385$ \\ - & 6 & $-903.980$ & $0.341$ & $-903.982$ & $0.439$ \\ - & 7 & $-903.621$ & $0.370$ & $-903.746$ & $0.359$ \\ + Pyrazine & 3 & $-887.414$ & $-904.148$ & $16.734$ & $0.035$ & $-891.249$ & $-904.867$ & $13.619$ & $1.420$ \\ + & 4 & $-887.414$ & $-904.726$ & $17.312$ & $0.377$ & $-891.249$ & $-904.588$ & $13.340$ & $0.650$ \\ + &\bf5 & $-887.414$ & $-904.274$ & $16.859$ & $0.383$ &$\bf-891.249$ &$\bf-904.550$ &$\bf13.301$ &$\bf0.385$ \\ + & 6 & $-887.414$ & $-903.980$ & $16.566$ & $0.341$ & $-891.249$ & $-903.982$ & $12.734$ & $0.439$ \\ + & 7 & $-887.414$ & $-903.621$ & $16.206$ & $0.370$ & $-891.249$ & $-903.746$ & $12.497$ & $0.359$ \\ \hline - Pyridazine & 3 & $-910.856$ & $3.053$ & $-909.292$ & $0.024$ \\ - & 4 & $-908.222$ & $1.834$ & $-908.808$ & $0.230$ \\ - &\bf5 & $-909.282$ & $1.191$ & $\bf-908.820$ &$\bf0.133$ \\ - & 6 & $-912.566$ & $1.727$ & $-908.342$ & $0.303$ \\ - & 7 & $-910.694$ & $2.210$ & $-908.368$ & $0.224$ \\ + Pyridazine & 3 & $-887.410$ & $-910.856$ & $23.446$ & $3.053$ & $-895.565$ & $-909.292$ & $13.726$ & $0.024$ \\ + & 4 & $-887.410$ & $-908.222$ & $20.811$ & $1.834$ & $-895.565$ & $-908.808$ & $13.243$ & $0.230$ \\ + &\bf5 & $-887.410$ & $-909.282$ & $21.871$ & $1.191$ &$\bf-895.565$ &$\bf-908.820$ &$\bf13.255$ &$\bf0.133$ \\ + & 6 & $-887.410$ & $-912.566$ & $25.156$ & $1.727$ & $-895.565$ & $-908.342$ & $12.777$ & $0.303$ \\ + & 7 & $-887.410$ & $-910.694$ & $23.283$ & $2.210$ & $-895.565$ & $-908.368$ & $12.802$ & $0.224$ \\ \hline - Pyridine & 3 & $-883.025$ & $3.919$ & $-883.363$ & $0.047$ \\ - & 4 & $-883.862$ & $1.869$ & $-883.413$ & $0.029$ \\ - &\bf5 & $-881.664$ & $1.760$ & $\bf-882.700$ &$\bf0.405$ \\ - & 6 & $-880.422$ & $1.456$ & $-882.361$ & $0.341$ \\ - & 7 & $-880.191$ & $1.084$ & $-882.023$ & $0.330$ \\ + Pyridine & 3 & $-861.424$ & $-883.025$ & $21.601$ & $3.919$ & $-868.803$ & $-883.363$ & $14.560$ & $0.047$ \\ + & 4 & $-861.424$ & $-883.862$ & $22.438$ & $1.869$ & $-868.803$ & $-883.413$ & $14.610$ & $0.029$ \\ + &\bf5 & $-861.424$ & $-881.664$ & $20.240$ & $1.760$ &$\bf-868.803$ &$\bf-882.700$ &$\bf13.897$ &$\bf0.405$ \\ + & 6 & $-861.424$ & $-880.422$ & $18.998$ & $1.456$ & $-868.803$ & $-882.361$ & $13.558$ & $0.341$ \\ + & 7 & $-861.424$ & $-880.191$ & $18.768$ & $1.084$ & $-868.803$ & $-882.023$ & $13.221$ & $0.330$ \\ \hline - Pyrimidine & 3 & $-900.386$ & $1.884$ & $-900.817$ & $0.726$ \\ - & 4 & $-901.441$ & $0.991$ & $-900.383$ & $0.356$ \\ - &\bf5 & $-900.354$ & $0.865$ & $\bf-900.496$ &$\bf0.214$ \\ - & 6 & $-900.240$ & $0.594$ & $-900.698$ & $0.190$ \\ - & 7 & $-899.689$ & $0.565$ & $-900.464$ & $0.206$ \\ + Pyrimidine & 3 & $-879.958$ & $-900.386$ & $20.428$ & $1.884$ & $-887.009$ & $-900.817$ & $13.808$ & $0.726$ \\ + & 4 & $-879.958$ & $-901.441$ & $21.483$ & $0.991$ & $-887.009$ & $-900.383$ & $13.374$ & $0.356$ \\ + &\bf5 & $-879.958$ & $-900.354$ & $20.396$ & $0.865$ &$\bf-887.009$ &$\bf-900.496$ &$\bf13.487$ &$\bf0.214$ \\ + & 6 & $-879.958$ & $-900.240$ & $20.283$ & $0.594$ & $-887.009$ & $-900.698$ & $13.689$ & $0.190$ \\ + & 7 & $-879.958$ & $-899.689$ & $19.732$ & $0.565$ & $-887.009$ & $-900.464$ & $13.455$ & $0.206$ \\ \hline - s-Tetrazine & 3 & $-958.736$ & $0.320$ & $-957.559$ & $0.246$ \\ - & 4 & $-958.727$ & $0.148$ & $-957.299$ & $0.160$ \\ - &\bf5 & $-958.500$ & $0.172$ & $\bf-957.869$ &$\bf0.349$ \\ - & 6 & $-958.162$ & $0.260$ & $-957.744$ & $0.247$ \\ - & 7 & $-958.161$ & $0.198$ & $-957.709$ & $0.183$ \\ + s-Tetrazine & 3 & $-942.162$ & $-958.736$ & $16.574$ & $0.320$ & $-944.077$ & $-957.559$ & $13.4815$ & $0.246$ \\ + & 4 & $-942.162$ & $-958.727$ & $16.564$ & $0.148$ & $-944.077$ & $-957.299$ & $13.2221$ & $0.160$ \\ + &\bf5 & $-942.162$ & $-958.500$ & $16.337$ & $0.172$ &$\bf-944.077$ &$\bf-957.869$ &$\bf13.7916$ &$\bf0.349$ \\ + & 6 & $-942.162$ & $-958.162$ & $16.000$ & $0.260$ & $-944.077$ & $-957.744$ & $13.6665$ & $0.247$ \\ + & 7 & $-942.162$ & $-958.161$ & $15.999$ & $0.198$ & $-944.077$ & $-957.709$ & $13.6319$ & $0.183$ \\ \hline - s-Triazine & 3 & $-917.221$ & $0.693$ & $-919.596$ & $0.105$ \\ - & 4 & $-918.723$ & $0.913$ & $-918.457$ & $0.538$ \\ - &\bf5 & $-917.402$ & $0.956$ & $\bf-918.355$ &$\bf0.312$ \\ - & 6 & $-916.517$ & $0.862$ & $-918.206$ & $0.226$ \\ - & 7 & $-916.544$ & $0.643$ & $-917.876$ & $0.267$ \\ + s-Triazine & 3 & $-898.283$ & $-917.221$ & $18.938$ & $0.693$ & $-905.180$ & $-919.596$ & $14.4152$ & $0.105$ \\ + & 4 & $-898.283$ & $-918.723$ & $20.440$ & $0.913$ & $-905.180$ & $-918.457$ & $13.2768$ & $0.538$ \\ + &\bf5 & $-898.283$ & $-917.402$ & $19.119$ & $0.956$ &$\bf-905.180$ &$\bf-918.355$ &$\bf13.1745$ &$\bf0.312$ \\ + & 6 & $-898.283$ & $-916.517$ & $18.233$ & $0.862$ & $-905.180$ & $-918.206$ & $13.0251$ & $0.226$ \\ + & 7 & $-898.283$ & $-916.544$ & $18.261$ & $0.643$ & $-905.180$ & $-917.876$ & $12.6956$ & $0.267$ \\ \end{tabular} \end{ruledtabular} -\end{table} +\end{table*} \end{squeezetable} %%% %%% %%% @@ -647,7 +651,7 @@ As compared to natural orbitals (solid red lines), one can see that, for a given Adding the perturbative correction $\EPT$ yields very similar curves for both sets of orbitals (dashed lines). This indicates that, for a given number of determinants, $\EPT$ (which, we recall, provides a qualitative idea to the distance to the FCI limit) is much smaller for optimized orbitals than for natural orbitals. This is further evidenced in Fig.~\ref{fig:vsEPT2} where we show the behavior of $\Delta \Evar$ as a function of $\EPT$ for both sets of orbitals. -From Fig.~\ref{fig:vsEPT2}, it is clear that the behavior of $\Delta \Evar$ is much more linear and produces smaller $\EPT$ values when optimized orbitals are selected, hence facilitating the extrapolation procedure to the FCI limit (see below). +From Fig.~\ref{fig:vsEPT2}, \alert{it is clear one produces smaller $\EPT$ values when optimized orbitals are selected, hence facilitating the extrapolation procedure to the FCI limit (see below).} The five-point weighted linear fit using the five largest variational wave functions are also represented (dashed black lines), while the FCI estimate of the correlation energy (solid black line) is reported for reference in Figs.~\ref{fig:vsNdet} and \ref{fig:vsEPT2}. Figure \ref{fig:BenzenevsNdet} compares the convergence of $\Delta \Evar$ for natural, localized, and optimized orbitals for benzene. @@ -660,12 +664,14 @@ To this end, we have extrapolated the orbital-optimized variational CIPSI correl The fitting weights have been taken as the inverse square of the perturbative corrections. Our final FCI correlation energy estimates are reported in Tables \ref{tab:Tab5-VDZ} and \ref{tab:Tab6-VDZ} for the five- and six-membered rings, respectively, alongside their corresponding fitting error. The stability of these estimates are illustrated by the results gathered in Table \ref{tab:fit}, where we list the extrapolated correlation energies $\Delta \Eextrap$ and their associated fitting errors obtained via weighted linear fits varying the number of fitting points from $3$ to $7$. -Although we cannot provide a mathematically rigorous error bar, the data provided by Table \ref{tab:fit} show that the extrapolation procedure is robust and that our FCI estimates are very likely accurate to a few tenths of a millihartree. +\alert{The extrapolation distance $\Delta \Edist$ defined as the difference between the final computed energy $\Delta \Efinal$ and $\Delta \Eextrap$ is also reported.} +Although we cannot provide a mathematically rigorous error bar, the data provided by Table \ref{tab:fit} show that the extrapolation procedure is robust and that our FCI estimates \alert{carry an error of the order of one millihartree}. Logically, the FCI estimates for the five-membered rings seem slightly more accurate than for the (larger) six-membered rings. It is pleasing to see that, although different geometries are considered, our present estimate of the frozen-core correlation energy of the benzene molecule in the cc-pVDZ basis (\SI{-862.9}{\milli\hartree}) is very close to the one reported in Ref.~\onlinecite{Loos_2020e} (\SI{-863.4}{\milli\hartree}). Table \ref{tab:fit} does report extrapolated correlation energies and fitting errors for both natural and optimized orbitals. Again, the superiority of the latter set is clear as both the variation in extrapolated values and the fitting error are much larger with the natural set. +\alert{Moreover, the extrapolation distance $\Delta \Edist$ is systematically decreases by several \si{\milli\hartree}.} Taking cyclopentadiene as an example, the extrapolated values vary by almost \SI{1}{\milli\hartree} with natural orbitals and less than \SI{0.1}{\milli\hartree} with the optimized set. The fitting errors follow the same trend. @@ -702,14 +708,17 @@ Importantly here, one notices that MP4 [which scales as $\order*{N^7}$] is syste \label{sec:ccl} %%%%%%%%%%%%%%%%%%%%%%%%% Using the SCI algorithm named \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI), we have produced FCI-quality frozen-core correlation energies for twelve cyclic molecules (see Fig.~\ref{fig:mol}) in the correlation-consistent double-$\zeta$ Dunning basis set (cc-pVDZ). -These estimates, which are likely accurate to a few tenths of a millihartree, have been obtained by extrapolating CIPSI energies to the FCI limit based on a set of orbitals obtained by minimizing the CIPSI variational energy. +These estimates, which \alert{probably carry an error of the order of one millihartree}, have been obtained by extrapolating CIPSI energies to the FCI limit based on a set of orbitals obtained by minimizing the CIPSI variational energy. Using energetically optimized orbitals, one can reduce the size of the variational space by one order of magnitude for the same variational energy as compared to natural orbitals. Thanks to these reference FCI energies, we have then benchmarked three families of popular electronic structure methods: i) the MP perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), ii) the approximate CC series CC2, CC3, and CC4, and iii) the ``complete'' CC series CCSD, CCSDT, and CCSDTQ. With a $\order*{N^7}$ scaling, MP4 provides an interesting accuracy/cost ratio for this particular set of weakly correlated systems, while MP5 systematically worsen the perturbative estimates of the correlation energy. In addition, CC3 (where the triples are computed iteratively) outperforms the perturbative-triples CCSD(T) method with the same $\order*{N^7}$ scaling, its completely renormalized version CR-CC(2,3), as well as its more expensive parent, CCSDT. A similar trend is observed for the methods including quadruple excitations, where the $\order*{N^9}$ CC4 model has been shown to be slightly more accurate than CCSDTQ [which scales as $\order*{N^{10}}$], both methods providing correlation energies within \SI{2}{\milli\hartree} of the FCI limit. -Of course, the present trends are only valid for this particular class of (weakly-correlated) molecules and it would be desirable to have a broader variety of systems in the future by including more challenging systems such as, for example, transition metal compounds. +\alert{These observations slightly alter the method ranking provided in Sec.~\ref{sec:intro}. +Of course, the present trends are only valid for this particular class of (weakly-correlated) molecules. +For example, the performance of CC3 might decline for larger systems.} +Thus, it would be desirable to have a broader variety of systems in the future by including more challenging systems such as, for example, transition metal compounds. Some work along this line is currently being performed. As perspectives, we are currently investigating the performance of the present approach for excited states in order to expand the QUEST database of vertical excitation energies. \cite{Veril_2021} @@ -728,8 +737,6 @@ This project has received funding from the European Research Council (ERC) under %%%%%%%%%%%%%%%%%%%%%%%%% The data that support the findings of this study are openly available in Zenodo at \url{http://doi.org/10.5281/zenodo.5150663}. -\clearpage - %%%%%%%%%%%%%%%%%%%%%%%%% \bibliography{Ec} %%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/Manuscript/Response_Letter/Response_Letter.tex b/Manuscript/Response_Letter/Response_Letter.tex index 7188503..6cb6901 100644 --- a/Manuscript/Response_Letter/Response_Letter.tex +++ b/Manuscript/Response_Letter/Response_Letter.tex @@ -44,20 +44,31 @@ I have a few comments in the following before publication.} CR-CC(2,3) would be similar to CCSD(T) but I am not sure if it is a size-extensive model.} \\ \alert{ +We have mentioned this theoretical ranking at the end of the Introduction. +CR-CC(2,3) is indeed a size-extensive model and its theoretical accuracy should be slightly better than CCSD(T). } \item {It seems that the results of NO are more linear than those of OO in Fig 3. This contradicts the discussion in the right column of page 7. } \\ -\alert{ +\alert{Indeed, for relatively large PT2 corrections, the NO curves look more linear. +However, if one considers the last four or five points, the OO curves are also very linear. +The main point here is that OOs produce much smaller PT2 values than NOs. +To avoid confusions, we have removed our comment on the linearity of the curves, mentioning only that OOs yield much smaller PT2 values then NOs. } \item -{It is claimed that the FCI estimates in Table III are likely accurate to less than 1mEh. I think this is too optimistic as some results in the table range by 1-2 mEh with different number of ftting points. I also think the extrapolation distances need to be listed for comparison to the error-bar. +{It is claimed that the FCI estimates in Table III are likely accurate to less than 1mEh. +I think this is too optimistic as some results in the table range by 1-2 mEh with different number of fitting points. +I also think the extrapolation distances need to be listed for comparison to the error-bar. } \\ \alert{ +We strongly believe that our correlation energy estimates are accurate to a few tenths of a millihartree. +However, the error might be slightly larger for the six-membered rings. +To be conservative, we have decided to state, in the revised manuscript, that the present estimates carry an error of the order of one millihartreee. +Morevoer, we now list the extrapolation distances in Table III alongside other useful information and show that OOs systematically decrease the extrapolation distance by several millihartree as compared to NOs. } \item @@ -65,7 +76,10 @@ CR-CC(2,3) would be similar to CCSD(T) but I am not sure if it is a size-extensi } \\ \alert{ -} +We have mentioned these points in the concluding section of the manuscript. +This is indeed not always the case. +The performance of the MP series can be quite hard to predict. +Moreover, the performance of CC3 may depend on the size of the systems considered and is known to work best for relatively small systems.} \end{enumerate}