Permalink
Cannot retrieve contributors at this time
Name already in use
A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
crlb-bos/sensitivity_analysis_crlb.nb
Go to fileThis commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
executable file
636 lines (574 sloc)
20.9 KB
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
(* Content-type: application/vnd.wolfram.mathematica *) | |
(*** Wolfram Notebook File ***) | |
(* http://www.wolfram.com/nb *) | |
(* CreatedBy='Mathematica 11.2' *) | |
(*CacheID: 234*) | |
(* Internal cache information: | |
NotebookFileLineBreakTest | |
NotebookFileLineBreakTest | |
NotebookDataPosition[ 158, 7] | |
NotebookDataLength[ 21250, 628] | |
NotebookOptionsPosition[ 16380, 533] | |
NotebookOutlinePosition[ 17072, 556] | |
CellTagsIndexPosition[ 16985, 551] | |
WindowFrame->Normal*) | |
(* Beginning of Notebook Content *) | |
Notebook[{ | |
Cell[BoxData[ | |
RowBox[{"Clear", "[", "\"\<Global`*\>\"", "]"}]], "Input", | |
CellChangeTimes->{{3.7887095877477093`*^9, | |
3.7887095877485332`*^9}},ExpressionUUID->"4f6bc103-8f1c-44c2-990d-\ | |
71251ebaa813"], | |
Cell[CellGroupData[{ | |
Cell["\<\ | |
Define CRLB equation for which sensitivity analysis is to be performed\ | |
\>", "Subsubsection", | |
CellChangeTimes->{ | |
3.788697464606394*^9},ExpressionUUID->"2e5c9027-a1b7-4fc8-9601-\ | |
a3cd599c5786"], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{"$Assumptions", " ", "=", " ", | |
RowBox[{ | |
RowBox[{"sn", " ", ">", " ", "0"}], " ", "&&", " ", | |
RowBox[{"gamm", " ", ">", " ", "0"}], " ", "&&", " ", | |
RowBox[{"dr", " ", ">", " ", "0"}], " ", "&&", " ", | |
RowBox[{"alphao", " ", ">", " ", "0"}], " ", "&&", " ", | |
RowBox[{"etax", " ", ">", " ", "0"}], " ", "&&", " ", | |
RowBox[{"etay", " ", ">", " ", "0"}], " ", "&&", " ", | |
RowBox[{"R", "\[Element]", "Reals"}]}]}]], "Input", | |
CellChangeTimes->{{3.788609692781907*^9, 3.788609768782737*^9}, { | |
3.788695569734687*^9, | |
3.7886955701499043`*^9}},ExpressionUUID->"b392b2d0-fc56-4c4d-aef3-\ | |
66ed719906ed"], | |
Cell[BoxData[ | |
RowBox[{ | |
RowBox[{"sn", ">", "0"}], "&&", | |
RowBox[{"gamm", ">", "0"}], "&&", | |
RowBox[{"dr", ">", "0"}], "&&", | |
RowBox[{"alphao", ">", "0"}], "&&", | |
RowBox[{"etax", ">", "0"}], "&&", | |
RowBox[{"etay", ">", "0"}], "&&", | |
RowBox[{"R", "\[Element]", | |
TemplateBox[{}, | |
"Reals"]}]}]], "Output", | |
CellChangeTimes->{3.78860977408088*^9, 3.7886955748007812`*^9, | |
3.788711126326688*^9, | |
3.7887118675502567`*^9},ExpressionUUID->"723699e7-29b4-46eb-9b15-\ | |
b1979e94b38c"] | |
}, Open ]], | |
Cell[BoxData[ | |
RowBox[{ | |
RowBox[{"sx", "[", | |
RowBox[{ | |
"sn_", ",", " ", "alphao_", ",", " ", "etax_", ",", " ", "etay_", ",", " ", | |
"R_"}], "]"}], ":=", " ", | |
RowBox[{"2", | |
RowBox[{"Sqrt", "[", | |
RowBox[{"2", "Pi"}], "]"}], | |
RowBox[{"sn", "/", | |
RowBox[{"(", "alphao", ")"}]}], " ", "*", " ", | |
SuperscriptBox[ | |
RowBox[{"(", "etax", ")"}], | |
RowBox[{"3", "/", "2"}]], | |
SuperscriptBox[ | |
RowBox[{"(", "etay", ")"}], | |
RowBox[{"1", "/", "2"}]], | |
SuperscriptBox[ | |
RowBox[{"(", | |
RowBox[{"1", "-", | |
SuperscriptBox["R", "2"]}], ")"}], | |
RowBox[{"1", "/", "4"}]]}]}]], "Input", | |
CellChangeTimes->{{3.788609780565538*^9, 3.7886098828837233`*^9}, { | |
3.7886955829502363`*^9, 3.788695636284691*^9}, {3.788695745666543*^9, | |
3.7886957609695187`*^9}},ExpressionUUID->"068b16b8-c23c-4eb6-bcdf-\ | |
2c5e3c98f9cc"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell["Derive relations for sensitivity coefficients", "Subsubsection", | |
CellChangeTimes->{{3.788697332016361*^9, | |
3.788697348328342*^9}},ExpressionUUID->"4151b887-106f-4e96-b29f-\ | |
bae328eb1c6c"], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{ | |
RowBox[{"Asn", "[", | |
RowBox[{"sn", ",", "alphao", ",", "etax", ",", "etay", ",", "R"}], "]"}], | |
"=", | |
RowBox[{"D", "[", | |
RowBox[{ | |
RowBox[{"sx", "[", | |
RowBox[{"sn", ",", "alphao", ",", "etax", ",", "etay", ",", "R"}], "]"}], | |
",", " ", "sn"}], "]"}]}]], "Input", | |
CellChangeTimes->{{3.7886957699557056`*^9, 3.7886958010271797`*^9}, { | |
3.788709326586474*^9, 3.7887093453130903`*^9}, {3.788711181333144*^9, | |
3.7887111827325277`*^9}, {3.7887112338823233`*^9, 3.788711238451427*^9}, { | |
3.78871137130622*^9, 3.788711372490965*^9}, {3.7887118477916613`*^9, | |
3.788711887069859*^9}},ExpressionUUID->"5b08c282-54bf-4e18-b50d-\ | |
05671b878166"], | |
Cell[BoxData[ | |
FractionBox[ | |
RowBox[{"2", " ", | |
SuperscriptBox["etax", | |
RowBox[{"3", "/", "2"}]], " ", | |
SqrtBox["etay"], " ", | |
SqrtBox[ | |
RowBox[{"2", " ", "\[Pi]"}]], " ", | |
SuperscriptBox[ | |
RowBox[{"(", | |
RowBox[{"1", "-", | |
SuperscriptBox["R", "2"]}], ")"}], | |
RowBox[{"1", "/", "4"}]]}], "alphao"]], "Output", | |
CellChangeTimes->{ | |
3.788711887529258*^9, {3.7887122474066677`*^9, 3.788712259090316*^9}, { | |
3.788716651088558*^9, 3.788716657137838*^9}, | |
3.788716710231514*^9},ExpressionUUID->"6c57b853-0306-4aef-aa38-\ | |
1aebc42ff3f5"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{"Aalphao", "=", | |
RowBox[{"D", "[", | |
RowBox[{ | |
RowBox[{"sx", "[", | |
RowBox[{"sn", ",", "alphao", ",", "etax", ",", "etay", ",", "R"}], "]"}], | |
",", "alphao"}], "]"}]}]], "Input", | |
CellChangeTimes->{{3.7886958104526167`*^9, | |
3.788695821495409*^9}},ExpressionUUID->"a39b0fde-c652-4479-9ad1-\ | |
b8e3838dfa86"], | |
Cell[BoxData[ | |
RowBox[{"-", | |
FractionBox[ | |
RowBox[{"2", " ", | |
SuperscriptBox["etax", | |
RowBox[{"3", "/", "2"}]], " ", | |
SqrtBox["etay"], " ", | |
SqrtBox[ | |
RowBox[{"2", " ", "\[Pi]"}]], " ", | |
SuperscriptBox[ | |
RowBox[{"(", | |
RowBox[{"1", "-", | |
SuperscriptBox["R", "2"]}], ")"}], | |
RowBox[{"1", "/", "4"}]], " ", "sn"}], | |
SuperscriptBox["alphao", "2"]]}]], "Output", | |
CellChangeTimes->{ | |
3.788695822108262*^9, 3.7887092188405743`*^9, {3.788711152092145*^9, | |
3.7887111642421217`*^9}, 3.788711877638749*^9, 3.788716713045144*^9, | |
3.788716759018573*^9},ExpressionUUID->"0a6398e1-ecf5-49bc-88ed-\ | |
3567d332748c"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{"Aetax", "=", | |
RowBox[{"D", "[", | |
RowBox[{ | |
RowBox[{"sx", "[", | |
RowBox[{"sn", ",", "alphao", ",", "etax", ",", "etay", ",", "R"}], "]"}], | |
",", "etax"}], "]"}]}]], "Input", | |
CellChangeTimes->{{3.78869583311373*^9, | |
3.788695843591093*^9}},ExpressionUUID->"1be9d087-d261-49f5-98c2-\ | |
06ec9d187492"], | |
Cell[BoxData[ | |
FractionBox[ | |
RowBox[{"3", " ", | |
SqrtBox["etax"], " ", | |
SqrtBox["etay"], " ", | |
SqrtBox[ | |
RowBox[{"2", " ", "\[Pi]"}]], " ", | |
SuperscriptBox[ | |
RowBox[{"(", | |
RowBox[{"1", "-", | |
SuperscriptBox["R", "2"]}], ")"}], | |
RowBox[{"1", "/", "4"}]], " ", "sn"}], "alphao"]], "Output", | |
CellChangeTimes->{3.7887118776684933`*^9, 3.788716775828722*^9, | |
3.7887168203242207`*^9},ExpressionUUID->"ea309666-29aa-4a0d-8a07-\ | |
74b3311301b6"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{"Aetay", "=", | |
RowBox[{"D", "[", | |
RowBox[{ | |
RowBox[{"sx", "[", | |
RowBox[{"sn", ",", "alphao", ",", "etax", ",", "etay", ",", "R"}], "]"}], | |
",", "etay"}], "]"}]}]], "Input", | |
CellChangeTimes->{{3.7886958540216513`*^9, 3.788695857279518*^9}, { | |
3.78869606898783*^9, | |
3.788696070058886*^9}},ExpressionUUID->"28e4a6a9-3734-4d2a-91a5-\ | |
24efe8a82a53"], | |
Cell[BoxData[ | |
FractionBox[ | |
RowBox[{ | |
SuperscriptBox["etax", | |
RowBox[{"3", "/", "2"}]], " ", | |
SqrtBox[ | |
RowBox[{"2", " ", "\[Pi]"}]], " ", | |
SuperscriptBox[ | |
RowBox[{"(", | |
RowBox[{"1", "-", | |
SuperscriptBox["R", "2"]}], ")"}], | |
RowBox[{"1", "/", "4"}]], " ", "sn"}], | |
RowBox[{"alphao", " ", | |
SqrtBox["etay"]}]]], "Output", | |
CellChangeTimes->{3.7887118779767237`*^9, 3.788716824211328*^9, | |
3.788716951290682*^9},ExpressionUUID->"b284d347-c7e0-4eff-be81-\ | |
da3a2efc7a9d"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{"AR", " ", "=", " ", | |
RowBox[{"D", "[", | |
RowBox[{ | |
RowBox[{"sx", "[", | |
RowBox[{"sn", ",", "alphao", ",", "etax", ",", "etay", ",", "R"}], "]"}], | |
",", "R"}], "]"}]}]], "Input", | |
CellChangeTimes->{{3.788716953352599*^9, | |
3.788716966650041*^9}},ExpressionUUID->"195685a8-411d-4d83-8741-\ | |
f0595c7a4762"], | |
Cell[BoxData[ | |
RowBox[{"-", | |
RowBox[{"(", | |
RowBox[{ | |
RowBox[{"(", | |
RowBox[{ | |
RowBox[{"etax", "^", | |
RowBox[{"(", | |
RowBox[{"3", "/", "2"}], ")"}]}], "*", | |
RowBox[{"Sqrt", "[", "etay", "]"}], "*", | |
RowBox[{"Sqrt", "[", | |
RowBox[{"2", "*", "Pi"}], "]"}], "*", "R", "*", "sn"}], ")"}], "/", | |
RowBox[{"(", | |
RowBox[{"alphao", "*", | |
RowBox[{ | |
RowBox[{"(", | |
RowBox[{"1", " ", "-", " ", | |
RowBox[{"R", "^", "2"}]}], ")"}], "^", | |
RowBox[{"(", | |
RowBox[{"3", "/", "4"}], ")"}]}]}], ")"}]}], ")"}]}]], "Output", | |
CellChangeTimes->{{3.788716968140864*^9, 3.788716973382186*^9}}, | |
FormatType-> | |
"InputForm",ExpressionUUID->"a8d32950-fc82-4855-83b5-52e8cbd3abb7"] | |
}, Open ]] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell["Monte Carlo simulation", "Subsubsection", | |
CellChangeTimes->{{3.788706350351022*^9, | |
3.788706354342181*^9}},ExpressionUUID->"b3bcef90-0562-4e25-b1b0-\ | |
c71c118e0a4a"], | |
Cell["set number of trials", "Text", | |
CellChangeTimes->{{3.78870690401836*^9, | |
3.78870690613902*^9}},ExpressionUUID->"b6397522-ed01-45c7-8217-\ | |
6e13b51c7c32"], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{"num_trials", "=", "10"}]], "Input", | |
CellChangeTimes->{{3.788706907837167*^9, | |
3.788706913874902*^9}},ExpressionUUID->"7ece7b8d-de35-4910-9384-\ | |
cf70c6035a2c"], | |
Cell[BoxData["10"], "Output", | |
CellChangeTimes->{ | |
3.788706914420368*^9},ExpressionUUID->"d1d17996-cc9e-4eb3-8588-\ | |
1e48a8eda874"] | |
}, Open ]], | |
Cell["set expected value for each parameter", "Text", | |
CellChangeTimes->{{3.788706780989581*^9, | |
3.788706789525426*^9}},ExpressionUUID->"38ebf141-4ef7-4711-8259-\ | |
c4644ccf1afb"], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{ | |
RowBox[{"{", | |
RowBox[{ | |
"snc", ",", " ", "alphaoc", ",", " ", "etaxc", ",", " ", "etayc", ",", " ", | |
"Rc"}], "}"}], " ", "=", " ", | |
RowBox[{"{", | |
RowBox[{"5", ",", "1000", ",", "5", ",", "3", ",", "0"}], "}"}]}]], "Input",\ | |
CellChangeTimes->{{3.788706794783381*^9, | |
3.78870682797292*^9}},ExpressionUUID->"7c5a9752-3d0f-40a0-8c10-\ | |
a789920ddcb5"], | |
Cell[BoxData[ | |
RowBox[{"{", | |
RowBox[{"5", ",", "1000", ",", "5", ",", "3", ",", "0"}], "}"}]], "Output", | |
CellChangeTimes->{ | |
3.788706848490223*^9},ExpressionUUID->"7ae3c19c-a66f-4002-84a8-\ | |
478b1ac71408"] | |
}, Open ]], | |
Cell["set data range for each parameter", "Text", | |
CellChangeTimes->{{3.7887066011140203`*^9, 3.788706628258456*^9}, { | |
3.788706689048242*^9, | |
3.7887066935197678`*^9}},ExpressionUUID->"4d2f67c6-ce0e-4aad-add0-\ | |
4df1fa08beab"], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{ | |
RowBox[{"{", | |
RowBox[{ | |
"dsn", ",", " ", "dalapha0", ",", " ", "detax", ",", " ", "detay", ",", | |
" ", "dR"}], "}"}], " ", "=", " ", | |
RowBox[{"{", | |
RowBox[{ | |
"3", ",", " ", "100", ",", " ", "2", ",", " ", "2", ",", " ", "1"}], | |
"}"}]}]], "Input", | |
CellChangeTimes->{{3.78870669527411*^9, | |
3.7887067702942667`*^9}},ExpressionUUID->"bb227087-a539-4c1c-b66d-\ | |
2e9008a3824c"], | |
Cell[BoxData[ | |
RowBox[{"{", | |
RowBox[{"3", ",", "100", ",", "2", ",", "2", ",", "1"}], "}"}]], "Output", | |
CellChangeTimes->{ | |
3.78870677415338*^9},ExpressionUUID->"283ad75e-0800-49d0-934b-6f56d37ccf16"] | |
}, Open ]], | |
Cell["generate random numbers", "Text", | |
CellChangeTimes->{{3.7887069336453238`*^9, 3.788706965130254*^9}, { | |
3.788709137718569*^9, | |
3.788709141775077*^9}},ExpressionUUID->"bba5fb7c-756f-4ebf-8f72-\ | |
5f89788f1b0c"], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{"rnorms1", "=", | |
RowBox[{"RandomVariate", "[", | |
RowBox[{ | |
RowBox[{"UniformDistribution", "[", | |
RowBox[{"{", | |
RowBox[{ | |
RowBox[{"-", "0.5"}], ",", "0.5"}], "}"}], "]"}], ",", "5"}], | |
"]"}]}]], "Input", | |
CellChangeTimes->{{3.788709152695319*^9, | |
3.788709152696102*^9}},ExpressionUUID->"8ebc405b-0413-4e60-8484-\ | |
edcbcf81209f"], | |
Cell[BoxData[ | |
RowBox[{"{", | |
RowBox[{ | |
RowBox[{"-", "0.24829098386724957`"}], ",", | |
RowBox[{"-", "0.15237929059732291`"}], ",", | |
RowBox[{"-", "0.17400348301328616`"}], ",", "0.19496388055883673`", ",", | |
"0.39610789105561306`"}], "}"}]], "Output", | |
CellChangeTimes->{3.788706967541407*^9, | |
3.788709154610853*^9},ExpressionUUID->"ebdc0188-ec96-41fd-8933-\ | |
8070f0ba4a06"] | |
}, Open ]], | |
Cell["assign random values to parameters", "Text", | |
CellChangeTimes->{{3.788706549002582*^9, | |
3.788706560602734*^9}},ExpressionUUID->"35a4eb9e-3557-4c10-b39d-\ | |
bc3150da13bb"], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{ | |
RowBox[{"{", | |
RowBox[{"snt", ",", "alphaot", ",", "etaxt", ",", "etayt", ",", "Rt"}], | |
"}"}], " ", "=", " ", | |
RowBox[{ | |
RowBox[{"{", | |
RowBox[{"snc", ",", "alphaoc", ",", "etaxc", ",", "etayc", ",", "Rc"}], | |
"}"}], " ", "+", " ", | |
RowBox[{"rnorms1", " ", "*", " ", | |
RowBox[{"{", | |
RowBox[{"dsn", ",", "dalapha0", ",", "detax", ",", "detay", ",", "dR"}], | |
"}"}]}]}]}]], "Input", | |
CellChangeTimes->{{3.7887071169564466`*^9, 3.788707188141527*^9}, { | |
3.7887094242804527`*^9, | |
3.788709429055529*^9}},ExpressionUUID->"51ef0ff0-cf40-40c0-a631-\ | |
113dbf8d5710"], | |
Cell[BoxData[ | |
RowBox[{"{", | |
RowBox[{ | |
"4.2551270483982515`", ",", "984.7620709402677`", ",", "4.651993033973428`", | |
",", "3.3899277611176735`", ",", "0.39610789105561306`"}], | |
"}"}]], "Output", | |
CellChangeTimes->{3.788707156183552*^9, 3.7887071923004417`*^9, | |
3.788709429761714*^9},ExpressionUUID->"7d9a9bb3-5f6f-4dc8-a31c-\ | |
1d290f0f2045"] | |
}, Open ]], | |
Cell["evaluate sensitivity coefficients for each trial", "Text", | |
CellChangeTimes->{{3.7887065644821167`*^9, | |
3.788706572402727*^9}},ExpressionUUID->"3681cae8-7a88-4e2c-b75e-\ | |
de880fb5cf3e"], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{"D", "[", | |
RowBox[{ | |
RowBox[{"sx", "[", | |
RowBox[{"sn", ",", "alphao", ",", "etax", ",", "etay", ",", "R"}], "]"}], | |
",", "sn"}], "]"}]], "Input", | |
CellChangeTimes->{{3.788709184390418*^9, 3.7887091979791613`*^9}, { | |
3.7887094049221287`*^9, | |
3.788709446287531*^9}},ExpressionUUID->"3edd6b4e-91ca-489d-a877-\ | |
45a0ad85d9d6"], | |
Cell[BoxData[ | |
RowBox[{ | |
SubscriptBox["\[PartialD]", "4.528607897120084`"], | |
"0.5106556807280463`"}]], "Output", | |
CellChangeTimes->{3.7887092050003653`*^9, 3.7887092798947687`*^9, | |
3.788709446824635*^9},ExpressionUUID->"ac44d2d3-2c9c-4fb9-9d3f-\ | |
63f93c6792a7"] | |
}, Open ]], | |
Cell["plot pdf of sensitivity coefficients for all parameters", "Text", | |
CellChangeTimes->{{3.788706575683323*^9, | |
3.788706583106167*^9}},ExpressionUUID->"e20670d3-f3b9-4408-b420-\ | |
c743686e365a"], | |
Cell[CellGroupData[{ | |
Cell[BoxData[ | |
RowBox[{"?", "etax"}]], "Input", | |
CellChangeTimes->{{3.788709510746142*^9, | |
3.7887095382376003`*^9}},ExpressionUUID->"139db136-da36-4a73-ad2d-\ | |
44507aec56c0"], | |
Cell[CellGroupData[{ | |
Cell["Global`etax", "Print", "PrintUsage", | |
CellChangeTimes->{3.7887095387748632`*^9}, | |
CellTags-> | |
"Info953788691538-8261937",ExpressionUUID->"e33571c0-1cf7-46f8-8cb9-\ | |
59181a1a74f9"], | |
Cell[BoxData[ | |
InterpretationBox[GridBox[{ | |
{GridBox[{ | |
{ | |
RowBox[{ | |
RowBox[{"etax", "[", | |
RowBox[{ | |
"eta_", ",", "gd_", ",", "no_", ",", "M_", ",", "zd_", ",", "fn_", | |
",", "delz_", ",", "del2rho_"}], "]"}], ":=", | |
SqrtBox[ | |
RowBox[{ | |
SuperscriptBox["eta", "2"], "+", | |
RowBox[{ | |
FractionBox["1", "12"], " ", | |
SuperscriptBox[ | |
RowBox[{"(", | |
FractionBox["gd", "no"], ")"}], "2"], " ", | |
SuperscriptBox[ | |
RowBox[{"(", | |
FractionBox[ | |
RowBox[{ | |
SuperscriptBox["M", "2"], " ", | |
SuperscriptBox["zd", "2"]}], | |
RowBox[{ | |
RowBox[{"(", | |
RowBox[{"M", "+", "1"}], ")"}], " ", "fn"}]], ")"}], "2"], | |
" ", | |
SuperscriptBox[ | |
RowBox[{"(", | |
RowBox[{"del2rho", " ", "delz"}], ")"}], "2"]}]}]]}]} | |
}, | |
BaselinePosition->{Baseline, {1, 1}}, | |
GridBoxAlignment->{ | |
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, | |
"RowsIndexed" -> {}}, | |
GridBoxItemSize->{"Columns" -> {{ | |
Scaled[0.999]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, | |
"RowsIndexed" -> {}}]} | |
}, | |
BaselinePosition->{Baseline, {1, 1}}, | |
GridBoxAlignment->{ | |
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, | |
"RowsIndexed" -> {}}], | |
Definition[$CellContext`etax], | |
Editable->False]], "Print", | |
CellChangeTimes->{3.7887095387948503`*^9}, | |
CellTags-> | |
"Info953788691538-8261937",ExpressionUUID->"aa68078a-9cc7-4dba-ae40-\ | |
f5944c37746e"] | |
}, Open ]] | |
}, Open ]] | |
}, Open ]] | |
}, | |
WindowSize->{1280, 778}, | |
WindowMargins->{{0, Automatic}, {Automatic, 22}}, | |
FrontEndVersion->"11.2 for Linux x86 (64-bit) (September 10, 2017)", | |
StyleDefinitions->"Default.nb" | |
] | |
(* End of Notebook Content *) | |
(* Internal cache information *) | |
(*CellTagsOutline | |
CellTagsIndex->{ | |
"Info953788691538-8261937"->{ | |
Cell[14444, 474, 185, 4, 46, "Print",ExpressionUUID->"e33571c0-1cf7-46f8-8cb9-59181a1a74f9", | |
CellTags->"Info953788691538-8261937"], | |
Cell[14632, 480, 1708, 48, 51, "Print",ExpressionUUID->"aa68078a-9cc7-4dba-ae40-f5944c37746e", | |
CellTags->"Info953788691538-8261937"]} | |
} | |
*) | |
(*CellTagsIndex | |
CellTagsIndex->{ | |
{"Info953788691538-8261937", 16685, 543} | |
} | |
*) | |
(*NotebookFileOutline | |
Notebook[{ | |
Cell[558, 20, 203, 4, 31, "Input",ExpressionUUID->"4f6bc103-8f1c-44c2-990d-71251ebaa813"], | |
Cell[CellGroupData[{ | |
Cell[786, 28, 205, 5, 47, "Subsubsection",ExpressionUUID->"2e5c9027-a1b7-4fc8-9601-a3cd599c5786"], | |
Cell[CellGroupData[{ | |
Cell[1016, 37, 643, 13, 31, "Input",ExpressionUUID->"b392b2d0-fc56-4c4d-aef3-66ed719906ed"], | |
Cell[1662, 52, 495, 14, 35, "Output",ExpressionUUID->"723699e7-29b4-46eb-9b15-b1979e94b38c"] | |
}, Open ]], | |
Cell[2172, 69, 857, 25, 37, "Input",ExpressionUUID->"068b16b8-c23c-4eb6-bcdf-2c5e3c98f9cc"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[3066, 99, 196, 3, 47, "Subsubsection",ExpressionUUID->"4151b887-106f-4e96-b29f-bae328eb1c6c"], | |
Cell[CellGroupData[{ | |
Cell[3287, 106, 686, 15, 31, "Input",ExpressionUUID->"5b08c282-54bf-4e18-b50d-05671b878166"], | |
Cell[3976, 123, 572, 17, 64, "Output",ExpressionUUID->"6c57b853-0306-4aef-aa38-1aebc42ff3f5"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[4585, 145, 344, 9, 31, "Input",ExpressionUUID->"a39b0fde-c652-4479-9ad1-b8e3838dfa86"], | |
Cell[4932, 156, 659, 19, 65, "Output",ExpressionUUID->"0a6398e1-ecf5-49bc-88ed-3567d332748c"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[5628, 180, 337, 9, 31, "Input",ExpressionUUID->"1be9d087-d261-49f5-98c2-06ec9d187492"], | |
Cell[5968, 191, 470, 14, 64, "Output",ExpressionUUID->"ea309666-29aa-4a0d-8a07-74b3311301b6"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[6475, 210, 388, 10, 31, "Input",ExpressionUUID->"28e4a6a9-3734-4d2a-91a5-24efe8a82a53"], | |
Cell[6866, 222, 508, 16, 67, "Output",ExpressionUUID->"b284d347-c7e0-4eff-be81-da3a2efc7a9d"] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[7411, 243, 342, 9, 31, "Input",ExpressionUUID->"195685a8-411d-4d83-8741-f0595c7a4762"], | |
Cell[7756, 254, 750, 22, 68, "Output",ExpressionUUID->"a8d32950-fc82-4855-83b5-52e8cbd3abb7"] | |
}, Open ]] | |
}, Open ]], | |
Cell[CellGroupData[{ | |
Cell[8555, 282, 173, 3, 47, "Subsubsection",ExpressionUUID->"b3bcef90-0562-4e25-b1b0-c71c118e0a4a"], | |
Cell[8731, 287, 160, 3, 37, "Text",ExpressionUUID->"b6397522-ed01-45c7-8217-6e13b51c7c32"], | |
Cell[CellGroupData[{ | |
Cell[8916, 294, 185, 4, 31, "Input",ExpressionUUID->"7ece7b8d-de35-4910-9384-cf70c6035a2c"], | |
Cell[9104, 300, 131, 3, 35, "Output",ExpressionUUID->"d1d17996-cc9e-4eb3-8588-1e48a8eda874"] | |
}, Open ]], | |
Cell[9250, 306, 179, 3, 37, "Text",ExpressionUUID->"38ebf141-4ef7-4711-8259-c4644ccf1afb"], | |
Cell[CellGroupData[{ | |
Cell[9454, 313, 389, 11, 31, "Input",ExpressionUUID->"7c5a9752-3d0f-40a0-8c10-a789920ddcb5"], | |
Cell[9846, 326, 208, 5, 35, "Output",ExpressionUUID->"7ae3c19c-a66f-4002-84a8-478b1ac71408"] | |
}, Open ]], | |
Cell[10069, 334, 228, 4, 37, "Text",ExpressionUUID->"4d2f67c6-ce0e-4aad-add0-4df1fa08beab"], | |
Cell[CellGroupData[{ | |
Cell[10322, 342, 417, 12, 31, "Input",ExpressionUUID->"bb227087-a539-4c1c-b66d-2e9008a3824c"], | |
Cell[10742, 356, 204, 4, 35, "Output",ExpressionUUID->"283ad75e-0800-49d0-934b-6f56d37ccf16"] | |
}, Open ]], | |
Cell[10961, 363, 216, 4, 37, "Text",ExpressionUUID->"bba5fb7c-756f-4ebf-8f72-5f89788f1b0c"], | |
Cell[CellGroupData[{ | |
Cell[11202, 371, 377, 11, 31, "Input",ExpressionUUID->"8ebc405b-0413-4e60-8484-edcbcf81209f"], | |
Cell[11582, 384, 383, 9, 35, "Output",ExpressionUUID->"ebdc0188-ec96-41fd-8933-8070f0ba4a06"] | |
}, Open ]], | |
Cell[11980, 396, 176, 3, 37, "Text",ExpressionUUID->"35a4eb9e-3557-4c10-b39d-bc3150da13bb"], | |
Cell[CellGroupData[{ | |
Cell[12181, 403, 615, 16, 31, "Input",ExpressionUUID->"51ef0ff0-cf40-40c0-a631-113dbf8d5710"], | |
Cell[12799, 421, 350, 8, 35, "Output",ExpressionUUID->"7d9a9bb3-5f6f-4dc8-a31c-1d290f0f2045"] | |
}, Open ]], | |
Cell[13164, 432, 192, 3, 37, "Text",ExpressionUUID->"3681cae8-7a88-4e2c-b75e-de880fb5cf3e"], | |
Cell[CellGroupData[{ | |
Cell[13381, 439, 358, 9, 31, "Input",ExpressionUUID->"3edd6b4e-91ca-489d-a877-45a0ad85d9d6"], | |
Cell[13742, 450, 265, 6, 35, "Output",ExpressionUUID->"ac44d2d3-2c9c-4fb9-9d3f-63f93c6792a7"] | |
}, Open ]], | |
Cell[14022, 459, 197, 3, 37, "Text",ExpressionUUID->"e20670d3-f3b9-4408-b420-c743686e365a"], | |
Cell[CellGroupData[{ | |
Cell[14244, 466, 175, 4, 31, "Input",ExpressionUUID->"139db136-da36-4a73-ad2d-44507aec56c0"], | |
Cell[CellGroupData[{ | |
Cell[14444, 474, 185, 4, 46, "Print",ExpressionUUID->"e33571c0-1cf7-46f8-8cb9-59181a1a74f9", | |
CellTags->"Info953788691538-8261937"], | |
Cell[14632, 480, 1708, 48, 51, "Print",ExpressionUUID->"aa68078a-9cc7-4dba-ae40-f5944c37746e", | |
CellTags->"Info953788691538-8261937"] | |
}, Open ]] | |
}, Open ]] | |
}, Open ]] | |
} | |
] | |
*) | |