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Cell["ABSTRACT", "Section", CellChangeTimes->{{3.7257199329223537`*^9, 3.725720005948655*^9}, { 3.72572008110417*^9, 3.725720088583918*^9}, {3.735906066467186*^9, 3.7359060766280823`*^9}, 3.781170294285297*^9},ExpressionUUID->"19833cfa-da84-4cef-8557-\ b850b6cb6842"], Cell["\<\ A lot of good code was written in FORTRAN in the days of punch cards. \ Unfortunately, a good deal of it was lost along with the boxes of cards. I \ recently had need of Akima\[CloseCurlyQuote]s spline method that we used a \ lot in those days, and reimplementing the algorithm from the original FORTRAN \ (still online at acm.org) in Wolfram Language was less than ideal. Since then \ I\[CloseCurlyQuote]ve had the opportunity to start fresh from the original \ math. This talk will describe the new implementation of both the spline and \ interpolation methods as CompiledFunction and InterpolatingFunction objects, \ and their deployment in the Wolfram Function Repository. Additionally, Akima \ had published a 2D interpolation algorithm, and I will describe how his \ method can be extended to n-dimensions and implemented efficiently with \ ListConvolve.\ \>", "Text", CellChangeTimes->{{3.725720132418301*^9, 3.7257201347705364`*^9}, 3.781170305602213*^9, {3.781170492744096*^9, 3.781170494584844*^9}},ExpressionUUID->"827fbb58-34f7-4856-a780-\ 6a3ac202a509"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"18890854-13ed-454b-9c41-1d64e7819121"], Cell[CellGroupData[{ Cell["Interpolation", "Section", CellChangeTimes->{{3.781170582197135*^9, 3.781170584836297*^9}},ExpressionUUID->"ae30f065-4ebc-4a56-8e24-\ d2d748020b4d"], Cell[CellGroupData[{ Cell[TextData[{ "From the ", ButtonBox["Meriam-Webster Dictionary", BaseStyle->"Hyperlink", ButtonData->{ URL["https://www.merriam-webster.com/dictionary/interpolation"], None}, ButtonNote->"https://www.merriam-webster.com/dictionary/interpolation"] }], "Subsection", CellChangeTimes->{{3.781180871750046*^9, 3.781180877499803*^9}, { 3.78118102061476*^9, 3.78118104788533*^9}},ExpressionUUID->"07740e94-ecbb-4f51-ba08-\ ef0b66c23490"], Cell["\<\ interpolation noun in\[CenterDot]\:200bter\[CenterDot]\:200bpo\[CenterDot]\:200bla\[CenterDot]\ \:200btion | \\ in-\:02cct\:0259r-p\:0259-\:02c8l\[ABar]-sh\:0259n\ \>", "Text", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, {3.781181071236558*^9, 3.781181073545506*^9}},ExpressionUUID->"f27ab454-d970-471c-a741-\ c98e0deb6db1"], Cell["", "ItemNumbered", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, {3.781181071236558*^9, 3.781181108945938*^9}},ExpressionUUID->"d5bb1ce7-112d-4759-8752-\ 2678da4f856c"], Cell[TextData[{ StyleBox["a", FontWeight->"Bold"], " : an act of interpolating something or the state of being interpolated : \ ", StyleBox["the introduction or insertion of something spurious or foreign", Background->RGBColor[1, 1, 0]] }], "Text", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, {3.781181071236558*^9, 3.78118110384511*^9}, { 3.781181147210878*^9, 3.781181150186872*^9}, 3.781181235205246*^9},ExpressionUUID->"9405d9ec-c8c1-4007-b8ba-\ 4db0362b09b3"], Cell[CellGroupData[{ Cell["\<\ \[Ellipsis] versions disfigured by the frequent and substantial interpolation \ of freely invented matter \[Ellipsis]\ \>", "ItemParagraph", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, {3.781181071236558*^9, 3.78118110384511*^9}, { 3.781181147210878*^9, 3.781181150186872*^9}, 3.781181240148643*^9},ExpressionUUID->"e8a25a90-e74d-41e8-beaf-\ b24980ecb610"], Cell["\[LongDash] Bernard Knox", "ItemParagraph", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, {3.781181071236558*^9, 3.78118110384511*^9}, { 3.781181147210878*^9, 3.781181150186872*^9}},ExpressionUUID->"2d064ec8-13e1-4d54-899a-\ c078ead201df"] }, Open ]], Cell[TextData[{ StyleBox["b", FontWeight->"Bold"], " : something that is introduced or inserted : an insertion or addition" }], "Text", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, {3.781181071236558*^9, 3.781181087937893*^9}, { 3.7811811604192953`*^9, 3.781181161106428*^9}, 3.781181267740046*^9},ExpressionUUID->"80dab1d7-9d53-4956-a2fd-\ 43e80fbf2a7b"], Cell[CellGroupData[{ Cell["\<\ How can such interpolations be identified, and what literary processes led to \ these additions?\ \>", "ItemParagraph", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, {3.781181071236558*^9, 3.781181087937893*^9}, { 3.7811811604192953`*^9, 3.781181161106428*^9}, 3.7811812697642593`*^9},ExpressionUUID->"8042a7ca-58c9-458c-996b-\ 7b2bf21da943"], Cell["\[LongDash] Jan Nattier", "ItemParagraph", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, {3.781181071236558*^9, 3.781181087937893*^9}, { 3.7811811604192953`*^9, 3.781181161106428*^9}},ExpressionUUID->"0a340f06-c0b3-4681-804a-\ 0ba69cac415d"], Cell[TextData[{ ": the ", StyleBox["process of calculating an approximate value based on values that \ are already known", Background->RGBColor[1, 1, 0]] }], "ItemNumbered", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, 3.781181071236558*^9, {3.781181177146509*^9, 3.781181182186965*^9}, 3.781181282005389*^9},ExpressionUUID->"367acab8-e595-4dcc-9f22-\ c6d783bad038"], Cell["\<\ The age of tephras that were not directly dated was estimated by linear \ interpolation from the calibrated date.\ \>", "ItemParagraph", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, 3.781181071236558*^9, {3.781181177146509*^9, 3.781181182186965*^9}, 3.7811812841574574`*^9},ExpressionUUID->"9033c4fb-61ca-469e-947d-\ ea64ac88a105"], Cell["\[LongDash] Richard J. Payne and Jeffrey J. Blackford", "ItemParagraph", CellChangeTimes->{{3.781180813675602*^9, 3.781180823697571*^9}, 3.781180999931273*^9, 3.781181071236558*^9, {3.781181177146509*^9, 3.781181182186965*^9}, {3.78118129801302*^9, 3.781181298364997*^9}},ExpressionUUID->"7f750031-1272-4aac-af78-\ 978ffcd6bea3"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "From ", ButtonBox["Wikipedia", BaseStyle->"Hyperlink", ButtonData->{ URL["https://en.wikipedia.org/wiki/Interpolation"], None}, ButtonNote->"https://en.wikipedia.org/wiki/Interpolation"] }], "Subsection", CellChangeTimes->{{3.781181345507379*^9, 3.781181366923875*^9}, { 3.78118393923411*^9, 3.78118396894414*^9}},ExpressionUUID->"99bc58be-4bd9-4d27-b51b-\ 4b024490d591"], Cell[TextData[{ "In the mathematical field of numerical analysis, interpolation is a type of \ estimation, a ", StyleBox["method of constructing new data points within the range of a \ discrete set of known data points", Background->RGBColor[1, 1, 0]], "." }], "Text", 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the function values \ \\!\\(\\*SubscriptBox[StyleBox[\\\"f\\\", \\\"TI\\\"], StyleBox[\\\"i\\\", \\\ \"TI\\\"]]\\) corresponding to \\!\\(\\*StyleBox[\\\"x\\\", \\\"TI\\\"]\\) \ values \\!\\(\\*SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], \ StyleBox[\\\"i\\\", \ \\\"TI\\\"]]\\).\\n\\!\\(\\*RowBox[{\\\"Interpolation\\\", \\\"[\\\", \ RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], StyleBox[\\\"1\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"y\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\ \"TR\\\"]}], \\\"}\\\"}], \\\",\\\", SubscriptBox[StyleBox[\\\"f\\\", \ \\\"TI\\\"], StyleBox[\\\"1\\\", \\\"TR\\\"]]}], \\\"}\\\"}], \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], StyleBox[\\\"2\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"y\\\", \\\"TI\\\"], \ 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constructs an interpolation that \ reproduces derivatives as well as function \ values.\\n\\!\\(\\*RowBox[{\\\"Interpolation\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"data\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"x\\\", \\\ \"TI\\\"]}], \\\"]\\\"}]\\) find an interpolation of \ \\!\\(\\*StyleBox[\\\"data\\\", \\\"TI\\\"]\\) at the point \ \\!\\(\\*StyleBox[\\\"x\\\", \\\"TI\\\"]\\).\"\>", "InformationUsageText", StripOnInput->False, LineSpacing->{1.5, 1.5, 3.}], FrameMargins->{{10, 10}, {8, 10}}], BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False], ItemBox["\<\"\"\>", BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False]}, { PaneBox[GridBox[{ { DynamicModuleBox[{System`InformationDump`open$$ = { False, False, False, False, False, False, False, False, False, False, False, False}}, StyleBox[GridBox[{ { TagBox[ TooltipBox[ StyleBox["\<\" Documentation\"\>", "InformationRowLabel", StripOnInput->False], "\"Documentation\"", TooltipStyle->"TextStyling"], Annotation[#, "Documentation", "Tooltip"]& ], TemplateBox[{ TemplateBox[{ "\"Local \[RightGuillemet]\"", "paclet:ref/Interpolation", "paclet:ref/Interpolation", "Link", { RGBColor[0.9686274509803922, 0.4666666666666667, 0.]}, BaseStyle -> { RGBColor[0.0784313725490196, 0.1568627450980392, 0.6]}}, "HyperlinkTemplate"],"\" \"",StyleBox[ "\"|\"", "InformationRowLabel", StripOnInput -> False], "\" \"",TemplateBox[{"\"Web \[RightGuillemet]\"", { URL[ "http://reference.wolfram.com/language/ref/Interpolation.\ html"], None}, "http://reference.wolfram.com/language/ref/Interpolation.html", "Hyperlink", { RGBColor[0.9686274509803922, 0.4666666666666667, 0.]}, BaseStyle -> { RGBColor[0.0784313725490196, 0.1568627450980392, 0.6]}}, "HyperlinkTemplate"]}, "RowDefault"]}, { TagBox[ TooltipBox[ StyleBox["\<\" Options\"\>", "InformationRowLabel", StripOnInput->False], "\"Options\"", TooltipStyle->"TextStyling"], Annotation[#, "Options", "Tooltip"]& ], RowBox[{"{", RowBox[{ RowBox[{"InterpolationOrder", "\[Rule]", "3"}], ",", RowBox[{"Method", "\[Rule]", "Automatic"}], ",", RowBox[{"PeriodicInterpolation", "\[Rule]", "False"}]}], "}"}]}, { TagBox[ TooltipBox[ StyleBox["\<\" Attributes\"\>", "InformationRowLabel", StripOnInput->False], "\"Attributes\"", TooltipStyle->"TextStyling"], Annotation[#, "Attributes", "Tooltip"]& ], RowBox[{"{", "Protected", "}"}]}, { TagBox[ TooltipBox[ StyleBox["\<\" Full Name\"\>", "InformationRowLabel", StripOnInput->False], "\"FullName\"", TooltipStyle->"TextStyling"], Annotation[#, "FullName", "Tooltip"]& ], "\<\"System`Interpolation\"\>"} }, AutoDelete->False, GridBoxAlignment->{"Columns" -> {Right, Left}}, GridBoxDividers->None, GridBoxItemSize->{"Columns" -> {Automatic, Automatic}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.8]}, Offset[0.2]}}], "DialogStyle", StripOnInput->False], DynamicModuleValues:>{}]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxDividers->{"Columns" -> {{False}}, "Rows" -> {{False}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[3.6]}, Offset[0.2]}}], FrameMargins->6], ""}, { ItemBox[ TagBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "UpPointerOpener"]], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "UpPointerOpenerHot"]]}, Dynamic[ System`InformationDump`mouseOver$$]], Alignment->Left, Appearance->{"Default" -> None}, ButtonFunction:>FEPrivate`Set[ System`InformationDump`open$$, False], Evaluator->Automatic, FrameMargins->{{9, 0}, {0, 0}}, ImageMargins->0, ImageSize->Full, Method->"Preemptive"], EventHandlerTag[{ "MouseEntered" :> FEPrivate`Set[System`InformationDump`mouseOver$$, True], "MouseExited" :> FEPrivate`Set[System`InformationDump`mouseOver$$, False], Method -> "Preemptive", PassEventsDown -> Automatic, PassEventsUp -> True}]], BaseStyle->"InformationTitleBackground", StripOnInput->False], "\[SpanFromLeft]"} }, AutoDelete->False, FrameStyle->Directive[ GrayLevel[0.8], Thickness[Tiny]], GridBoxAlignment->{"Columns" -> {Left, Right}, "Rows" -> {{Center}}}, GridBoxDividers->{ "Columns" -> {{None}}, "Rows" -> {False, {True}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"], False-> TagBox[GridBox[{ { ItemBox[ PaneBox[ StyleBox["\<\" Symbol\"\>", "InformationTitleText", StripOnInput->False], FrameMargins->{{4, 0}, {-1, 1}}], BaseStyle->"InformationTitleBackground", StripOnInput->False], ItemBox[ PaneBox[ TooltipBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIcon"], ImageSizeCache->{13., {1., 12.}}], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIconHot"], ImageSizeCache->{13., {1., 12.}}]}, Dynamic[ CurrentValue["MouseOver"]]], Appearance->None, BaseStyle->"Link", ButtonData->"paclet:ref/Interpolation", ButtonNote->"paclet:ref/Interpolation"], "\"paclet:ref/Interpolation\""], FrameMargins->{{0, 4}, {0, 2}}], BaseStyle->"InformationTitleBackground", StripOnInput->False]}, { ItemBox[ PaneBox[ StyleBox["\<\"\\!\\(\\*RowBox[{\\\"Interpolation\\\", \\\"[\\\", \ RowBox[{\\\"{\\\", RowBox[{SubscriptBox[StyleBox[\\\"f\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"f\\\", \ \\\"TI\\\"], StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\ \[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\"}], \\\"]\\\"}]\\) constructs an \ interpolation of the function values \ \\!\\(\\*SubscriptBox[StyleBox[\\\"f\\\", \\\"TI\\\"], StyleBox[\\\"i\\\", \\\ \"TI\\\"]]\\), assumed to correspond to \\!\\(\\*StyleBox[\\\"x\\\", \\\"TI\\\ \"]\\) values 1, 2, \[Ellipsis] . \\n\\!\\(\\*RowBox[{\\\"Interpolation\\\", \ \\\"[\\\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], StyleBox[\\\"1\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"f\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]]}], \\\"}\\\"}], \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], \ StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"f\\\", \ \\\"TI\\\"], StyleBox[\\\"2\\\", \\\"TR\\\"]]}], \\\"}\\\"}], \\\",\\\", \ StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\"}], \\\"]\\\"}]\\) \ constructs an interpolation of the function values \ \\!\\(\\*SubscriptBox[StyleBox[\\\"f\\\", \\\"TI\\\"], StyleBox[\\\"i\\\", \\\ \"TI\\\"]]\\) corresponding to \\!\\(\\*StyleBox[\\\"x\\\", \\\"TI\\\"]\\) \ values \\!\\(\\*SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], \ StyleBox[\\\"i\\\", \ \\\"TI\\\"]]\\).\\n\\!\\(\\*RowBox[{\\\"Interpolation\\\", \\\"[\\\", \ RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], StyleBox[\\\"1\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"y\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\ \"TR\\\"]}], \\\"}\\\"}], \\\",\\\", SubscriptBox[StyleBox[\\\"f\\\", \ \\\"TI\\\"], StyleBox[\\\"1\\\", \\\"TR\\\"]]}], \\\"}\\\"}], \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], StyleBox[\\\"2\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"y\\\", \\\"TI\\\"], \ StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\ \"TR\\\"]}], \\\"}\\\"}], \\\",\\\", SubscriptBox[StyleBox[\\\"f\\\", \ \\\"TI\\\"], StyleBox[\\\"2\\\", \\\"TR\\\"]]}], \\\"}\\\"}], \\\",\\\", \ StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\"}], \\\"]\\\"}]\\) \ constructs an interpolation of multidimensional \ data.\\n\\!\\(\\*RowBox[{\\\"Interpolation\\\", \\\"[\\\", RowBox[{\\\"{\\\", \ RowBox[{RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], StyleBox[\\\"1\\\", \ \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\ \"}], \\\",\\\", SubscriptBox[StyleBox[\\\"f\\\", \\\"TI\\\"], StyleBox[\\\"1\ \\\", \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"df\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\ \"TR\\\"]}], \\\"}\\\"}], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \ \\\"TR\\\"]}], \\\"}\\\"}], \\\"]\\\"}]\\) constructs an interpolation that \ reproduces derivatives as well as function \ values.\\n\\!\\(\\*RowBox[{\\\"Interpolation\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"data\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"x\\\", \\\ \"TI\\\"]}], \\\"]\\\"}]\\) find an interpolation of \ \\!\\(\\*StyleBox[\\\"data\\\", \\\"TI\\\"]\\) at the point \ \\!\\(\\*StyleBox[\\\"x\\\", \\\"TI\\\"]\\).\"\>", "InformationUsageText", StripOnInput->False, LineSpacing->{1.5, 1.5, 3.}], FrameMargins->{{10, 10}, {8, 10}}], BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False], ItemBox["\<\"\"\>", BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False]}, { ItemBox[ TagBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpener"], ImageSizeCache->{10., {2., 8.}}], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpenerHot"], ImageSizeCache->{10., {2., 8.}}]}, Dynamic[ System`InformationDump`mouseOver$$]], Alignment->Left, Appearance->{"Default" -> None}, ButtonFunction:>FEPrivate`Set[ System`InformationDump`open$$, True], Evaluator->Automatic, FrameMargins->{{9, 0}, {0, 0}}, ImageMargins->0, ImageSize->Full, Method->"Preemptive"], EventHandlerTag[{ "MouseEntered" :> FEPrivate`Set[System`InformationDump`mouseOver$$, True], "MouseExited" :> FEPrivate`Set[System`InformationDump`mouseOver$$, False], Method -> "Preemptive", PassEventsDown -> Automatic, PassEventsUp -> True}]], BaseStyle->"InformationTitleBackground", StripOnInput->False], "\[SpanFromLeft]"} }, AutoDelete->False, FrameStyle->Directive[ GrayLevel[0.8], Thickness[Tiny]], GridBoxAlignment->{"Columns" -> {Left, Right}, "Rows" -> {{Center}}}, GridBoxDividers->{ "Columns" -> {{None}}, "Rows" -> {False, {True}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]}, Dynamic[System`InformationDump`open$$], BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], DynamicModuleValues:>{}], BaseStyle->"InformationGridFrame", StripOnInput->False], "InformationGridPlain", StripOnInput->False], InformationData[ Association[ "ObjectType" -> "Symbol", "Usage" -> "\!\(\*RowBox[{\"Interpolation\", \"[\", RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"1\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \"]\"}]\) constructs an \ interpolation of the function values \!\(\*SubscriptBox[StyleBox[\"f\", \ \"TI\"], StyleBox[\"i\", \"TI\"]]\), assumed to correspond to \!\(\*StyleBox[\ \"x\", \"TI\"]\) values 1, 2, \[Ellipsis] . \n\ \!\(\*RowBox[{\"Interpolation\", \"[\", RowBox[{\"{\", RowBox[{RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"1\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"1\", \"TR\"]]}], \ \"}\"}], \",\", RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], \ StyleBox[\"2\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"f\", \"TI\"], \ StyleBox[\"2\", \"TR\"]]}], \"}\"}], \",\", StyleBox[\"\[Ellipsis]\", \ \"TR\"]}], \"}\"}], \"]\"}]\) constructs an interpolation of the function \ values \!\(\*SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"i\", \"TI\"]]\) \ corresponding to \!\(\*StyleBox[\"x\", \"TI\"]\) values \ \!\(\*SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"i\", \"TI\"]]\).\n\!\(\ \*RowBox[{\"Interpolation\", \"[\", RowBox[{\"{\", RowBox[{RowBox[{\"{\", \ RowBox[{RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], \ StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"y\", \"TI\"], \ StyleBox[\"1\", \"TR\"]], \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}], \ \"}\"}], \",\", SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"1\", \ \"TR\"]]}], \"}\"}], \",\", RowBox[{\"{\", RowBox[{RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"2\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"y\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \",\", \ SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"2\", \"TR\"]]}], \"}\"}], \ \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \"]\"}]\) constructs an \ interpolation of multidimensional data.\n\!\(\*RowBox[{\"Interpolation\", \"[\ \", RowBox[{\"{\", RowBox[{RowBox[{\"{\", RowBox[{RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"1\", \"TR\"]], \ \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \",\", \ SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"1\", \"TR\"]], \",\", \ SubscriptBox[StyleBox[\"df\", \"TI\"], StyleBox[\"1\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \"]\"}]\) constructs an \ interpolation that reproduces derivatives as well as function values.\n\ \!\(\*RowBox[{\"Interpolation\", \"[\", RowBox[{StyleBox[\"data\", \"TI\"], \ \",\", StyleBox[\"x\", \"TI\"]}], \"]\"}]\) find an interpolation of \ \!\(\*StyleBox[\"data\", \"TI\"]\) at the point \!\(\*StyleBox[\"x\", \"TI\"]\ \).", "Documentation" -> Association[ "Local" -> "paclet:ref/Interpolation", "Web" -> "http://reference.wolfram.com/language/ref/Interpolation.html"], "OwnValues" -> None, "UpValues" -> None, "DownValues" -> None, "SubValues" -> None, "DefaultValues" -> None, "NValues" -> None, "FormatValues" -> None, "Options" -> { InterpolationOrder -> 3, Method -> Automatic, PeriodicInterpolation -> False}, "Attributes" -> {Protected}, "FullName" -> "System`Interpolation"], False]]], "Output", CellChangeTimes->{3.7813117933260727`*^9, 3.781339557476709*^9, 3.781351079091052*^9, 3.781351440398525*^9}, CellLabel->"Out[8]=",ExpressionUUID->"3e31cb4f-0d88-4f23-9c6b-5db81d6b2ac5"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ ButtonBox["\[KernelIcon]", Active->True, Background->RGBColor[0.88, 1, 0.88], BaseStyle->"EvaluateCell", ButtonFunction:> Module[{nb = InputNotebook[]}, SelectionMove[nb, All, ButtonCell]; SelectionEvaluate[nb]; Null], Evaluator->Automatic], ";", RowBox[{"?", "FindFit"}]}]], "Input", CellChangeTimes->{{3.781184197958398*^9, 3.781184199825899*^9}, 3.781311783419883*^9}, CellLabel->"In[9]:=",ExpressionUUID->"4d603c91-6639-487b-af0a-1472ea5a4692"], Cell[BoxData[ InterpretationBox[ StyleBox[ FrameBox[ DynamicModuleBox[{System`InformationDump`open$$ = False, System`InformationDump`mouseOver$$ = False}, PaneSelectorBox[{True-> TagBox[GridBox[{ { ItemBox[ PaneBox[ StyleBox["\<\" Symbol\"\>", "InformationTitleText", StripOnInput->False, BaseStyle -> None], FrameMargins->{{4, 0}, {-1, 1}}], BaseStyle->"InformationTitleBackground", StripOnInput->False], ItemBox[ PaneBox[ TooltipBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIcon"]], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIconHot"]]}, Dynamic[ CurrentValue["MouseOver"]]], Appearance->None, BaseStyle->"Link", ButtonData->"paclet:ref/FindFit", ButtonNote->"paclet:ref/FindFit"], "\"paclet:ref/FindFit\""], FrameMargins->{{0, 4}, {0, 2}}], BaseStyle->"InformationTitleBackground", StripOnInput->False]}, { ItemBox[ PaneBox[ StyleBox["\<\"\\!\\(\\*RowBox[{\\\"FindFit\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"data\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"expr\\\", \ \\\"TI\\\"], \\\",\\\", StyleBox[\\\"pars\\\", \\\"TI\\\"], \\\",\\\", \ StyleBox[\\\"vars\\\", \\\"TI\\\"]}], \\\"]\\\"}]\\) finds numerical values \ of the parameters \\!\\(\\*StyleBox[\\\"pars\\\", \\\"TI\\\"]\\) that make \ \\!\\(\\*StyleBox[\\\"expr\\\", \\\"TI\\\"]\\) give a best fit to \ \\!\\(\\*StyleBox[\\\"data\\\", \\\"TI\\\"]\\) as a function of \ \\!\\(\\*StyleBox[\\\"vars\\\", \\\"TI\\\"]\\). \ \\n\\!\\(\\*RowBox[{\\\"FindFit\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"data\\\", \\\"TI\\\"], \\\",\\\", RowBox[{\\\"{\\\", \ RowBox[{StyleBox[\\\"expr\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"cons\\\", \ \\\"TI\\\"]}], \\\"}\\\"}], \\\",\\\", StyleBox[\\\"pars\\\", \\\"TI\\\"], \\\ \",\\\", StyleBox[\\\"vars\\\", \\\"TI\\\"]}], \\\"]\\\"}]\\) finds a best \ fit subject to the parameter constraints \\!\\(\\*StyleBox[\\\"cons\\\", \ \\\"TI\\\"]\\).\"\>", "InformationUsageText", StripOnInput->False, LineSpacing->{1.5, 1.5, 3.}], FrameMargins->{{10, 10}, {8, 10}}], BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False], ItemBox["\<\"\"\>", BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False]}, { PaneBox[GridBox[{ { DynamicModuleBox[{System`InformationDump`open$$ = { False, False, False, False, False, False, False, False, False, False, False, False}}, StyleBox[GridBox[{ { TagBox[ TooltipBox[ StyleBox["\<\" Documentation\"\>", "InformationRowLabel", StripOnInput->False], "\"Documentation\"", TooltipStyle->"TextStyling"], Annotation[#, "Documentation", "Tooltip"]& ], TemplateBox[{ TemplateBox[{ "\"Local \[RightGuillemet]\"", "paclet:ref/FindFit", "paclet:ref/FindFit", "Link", { RGBColor[0.9686274509803922, 0.4666666666666667, 0.]}, BaseStyle -> { RGBColor[0.0784313725490196, 0.1568627450980392, 0.6]}}, "HyperlinkTemplate"],"\" \"",StyleBox[ "\"|\"", "InformationRowLabel", StripOnInput -> False], "\" \"",TemplateBox[{"\"Web \[RightGuillemet]\"", { URL[ "http://reference.wolfram.com/language/ref/FindFit.html"], None}, "http://reference.wolfram.com/language/ref/FindFit.html", "Hyperlink", { RGBColor[0.9686274509803922, 0.4666666666666667, 0.]}, BaseStyle -> { RGBColor[0.0784313725490196, 0.1568627450980392, 0.6]}}, "HyperlinkTemplate"]}, "RowDefault"]}, { PaneSelectorBox[{True-> ButtonBox[ PaneSelectorBox[{False-> TemplateBox[{ "\[ThickSpace]","\"\[ThickSpace]\"",StyleBox[ "\"Options\"", "InformationRowLabel", StripOnInput -> False],DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpener"]]}, "RowWithSeparators"], True-> TemplateBox[{ "\[ThickSpace]","\"\[ThickSpace]\"",StyleBox[ "\"Options\"", "InformationRowLabel", StripOnInput -> False],DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpenerHot"]]}, "RowWithSeparators"]}, Dynamic[ CurrentValue["MouseOver"]], FrameMargins->0, ImageSize->Automatic], Appearance->None, BaseStyle->None, ButtonFunction:>(Part[System`InformationDump`open$$, 9] = False), Evaluator->Automatic, FrameMargins->0, ImageMargins->0, 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ACM, VOL. 15, NO. 10,\\nC P. 914.\\n \ SUBROUTINE INTRPL(IU,L,X,Y,N,U,V) INTR \ 10\\nC INTERPOLATION OF A SINGLE-VALUED FUNCTION\\nC THIS SUBROUTINE \ INTERPOLATES, FROM VALUES OF THE FUNCTION\\nC GIVEN AS ORDINATES OF INPUT \ DATA POINTS IN AN X-Y PLANE\\nC AND FOR A GIVEN SET OF X VALUES (ABSCISSAS), \ THE VALUES OF\\nC A SINGLE-VALUED FUNCTION Y = Y(X).\\nC THE INPUT PARAMETERS \ ARE\\nC IU = LOGICAL UNIT NUMBER OF STANDARD OUTPUT UNIT\\nC L = \ NUMBER OF INPUT DATA POINTS\\nC (MUST BE 2 OR GREATER)\\nC X = \ ARRAY OF DIMENSION L STORING THE X VALUES\\nC (ABSCISSAS) OF INPUT \ DATA POINTS\\nC (IN ASCENDING ORDER)\\nC Y = ARRAY OF DIMENSION \ L STORING THE Y VALUES\\nC (ORDINATES) OF INPUT DATA POINTS\\nC \ N = NUMBER OF POINTS AT WHICH INTERPOLATION OF THE\\nC Y VALUE \ (ORDINATE) IS DESIRED\\nC (MUST BE 1 OR GREATER)\\nC U = ARRAY \ OF DIMENSION N STORING THE X VALUES\\nC (ABSCISSAS) OF DESIRED \ POINTS\\nC THE OUTPUT PARAMETER IS\\nC V = ARRAY OF DIMENSION N WHERE \ THE INTERPOLATED Y\\nC VALUES (ORDINATES) ARE TO BE DISPLAYED\\nC \ DECLARATION STATEMENTS\\n DIMENSION X(L),Y(L),U(N),V(N)\\n \ EQUIVALENCE (P0,X3),(Q0,Y3),(Q1,T3)\\n REAL M1,M2,M3,M4,M5\\n \ EQUIVALENCE (UK,DX),(IMN,X2,A1,M1),(IMX,X5,A5,M5),\\n 1 \ (J,SW,SA),(Y2,W2,W4,Q2),(Y5,W3,Q3)\\nC PRELIMINARY PROCESSING\\n 10 L0=L\\n \ LM1=L0-1\\n LM2=LM1-1\\n LP1=L0+1\\n N0=N\\n \ IF(LM2.LT.0) GO TO 90\\n IF(N0.LE.0) GO TO 91\\n DO \ 11 I=2,L0\\n IF(X(I-1)-X(I)) 11,95,96\\n 11 CONTINUE\\n \ IPV=0\\nC MAIN DO-LOOP\\n DO 80 K=1,N0\\n UK=U(K)\\nC ROUTINE TO \ LOCATE THE DESIRED POINT\\n 20 IF(LM2.EQ.0) GO TO 27\\n \ IF(UK.GE.X(L0)) GO TO 26\\n IF(UK.LT.X(1)) GO TO 25\\n \ IMN=2\\n IMX=L0\\n 21 I=(IMN+IMX)/2\\n IF(UK.GE.X(I)) GO \ TO 23\\n 22 IMX=I\\n GO TO 24\\n 23 IMN=I+1\\n 24 \ IF(IMX.GT.IMN) GO TO 21\\n I=IMX\\n GO TO 30\\n 25 \ I=1\\n GO TO 30\\n 26 I=LP1\\n GO TO 30\\n 27 I=2\\nC \ CHECK IF I = IPV\\n 30 IF(I.EQ.IPV) GO TO 70\\n IPV=I\\nC \ ROUTINES TO PICK UP NECESSARY X AND Y VALUES AND\\nC TO ESTIMATE \ THEM IF NECESSARY\\n 40 J=I\\n IF(J.EQ.1) J=2\\n \ IF(J.EQ.LP1) J=L0\\n X3=X(J-1)\\n Y3=Y(J-1)\\n \ X4=X(J)\\n Y4=Y(J)\\n A3=X4-X3\\n M3=(Y4-Y3)/A3\\n \ IF(LM2.EQ.0) GO TO 43\\n IF(J.EQ.2) GO TO 41\\n \ X2=X(J-2)\\n Y2=Y(J-2)\\n A2=X3-X2\\n M2=(Y3-Y2)/A2\\n \ IF(J.EQ.L0) GO TO 42\\n 41 X5=X(J+1)\\n Y5=Y(J+1)\\n \ A4=X5-X4\\n M4=(Y5-Y4)/A4\\n IF(J.EQ.2) \ M2=M3+M3-M4\\n GO TO 45\\n 42 M4=M3+M3-M2\\n GO TO 45\\n \ 43 M2=M3\\n M4=M3\\n 45 IF(J.LE.3) GO TO 46\\n \ A1=X2-X(J-3)\\n M1=(Y2-Y(J-3))/A1\\n GO TO 47\\n 46 \ M1=M2+M2-M3\\n 47 IF(J.GE.LM1) GO TO 48\\n A5=X(J+2)-X5\\n \ M5=(Y(J+2)-Y5)/A5\\n GO TO 50\\n 48 M5=M4+M4-M3\\nC NUMERICAL \ DIFFERENTIATION\\n 50 IF(I.EQ.LP1) GO TO 52\\n \ W2=ABS(M4-M3)\\n W3=ABS(M2-M1)\\n SW=W2+W3\\n \ IF(SW.NE.0.0) GO TO 51\\n W2=0.5\\n W3=0.5\\n SW=1.0\ \\n 51 T3=(W2*M2+W3*M3)/SW\\n IF(I.EQ.1) GO TO 54\\n 52 \ W3=ABS(M5-M4)\\n W4=ABS(M3-M2)\\n SW=W3+W4\\n \ IF(SW.NE.0.0) GO TO 53\\n W3=0.5\\n W4=0.5\\n SW=1.0\ \\n 53 T4=(W3*M3+W4*M4)/SW\\n IF(I.NE.LP1) GO TO 60\\n \ T3=T4\\n SA=A2+A3\\n \ T4=0.5*(M4+M5-A2*(A2-A3)*(M2-M3)/(SA*SA))\\n X3=X4\\n Y3=Y4\\n \ A3=A2\\n M3=M4\\n GO TO 60\\n 54 T4=T3\\n \ SA=A3+A4\\n T3=0.5*(M1+M2-A4*(A3-A4)*(M3-M4)/(SA*SA))\\n \ X3=X3-A4\\n Y3=Y3-M2*A4\\n A3=A4\\n M3=M2\\nC \ DETERMINATION OF THE COEFFICIENTS\\n 60 Q2=(2.0*(M3-T3)+M3-T4)/A3\\n \ Q3=(-M3-M3+T3+T4)/(A3*A3)\\nC COMPUTATION OF THE POLYNOMIAL\\n 70 \ DX=UK-P0\\n 80 V(K)=Q0+DX*(Q1+DX*(Q2+DX*Q3))\\n RETURN\\nC ERROR \ EXIT\\n 90 WRITE (IU,2090)\\n GO TO 99\\n 91 WRITE (IU,2091)\\n \ GO TO 99\\n 95 WRITE (IU,2095)\\n GO TO 97\\n 96 WRITE (IU,2096)\\n \ 97 WRITE (IU,2097) I,X(I)\\n 99 WRITE (IU,2099) L0,N0\\n RETURN\\nC \ FORMAT STATEMENTS\\n 2090 FORMAT(1X/22H *** L = 1 OR LESS./)\\n 2091 \ FORMAT(1X/22H *** N = 0 OR LESS./)\\n 2095 FORMAT(1X/27H *** IDENTICAL \ X VALUES./)\\n 2096 FORMAT(1X/33H *** X VALUES OUT OF SEQUENCE./)\\n 2097 \ FORMAT(6H I =,I7,10X,6HX(I) =,E12.3)\\n 2099 FORMAT(6H L =,I7,10X,3HN \ =,I7/\\n 1 36H ERROR DETECTED IN ROUTINE INTRPL)\\n END\\n \ SUBROUTINE CRVFIT(IU,MD,L,X,Y,M,N,U,V) \ CRVF1670\\nC SMOOTH CURVE FITTING\\nC THIS SUBROUTINE FITS A SMOOTH CURVE TO \ A GIVEN SET OF IN-\\nC PUT DATA POINTS IN AN X-Y PLANE. IT INTERPOLATES \ POINTS\\nC IN EACH INTERVAL BETWEEN A PAIR OF DATA POINTS AND GENER-\\nC ATES \ A SET OF OUTPUT POINTS CONSISTING OF THE INPUT DATA\\nC POINTS AND THE \ INTERPOLATED POINTS. IT CAN PROCESS EITHER\\nC A SINGLE-VALUED FUNCTION OR A \ MULTIPLE-VALUED FUNCTION.\\nC THE INPUT PARAMETERS ARE\\nC IU = LOGICAL \ UNIT NUMBER OF STANDARD OUTPUT UNIT\\nC MD = MODE OF THE CURVE (MUST BE 1 \ OR 2)\\nC = 1 FOR A SINGLE-VALUED FUNCTION\\nC = 2 FOR A \ MULTIPLE-VALUED FUNCTION\\nC L = NUMBER OF INPUT DATA POINTS\\nC \ (MUST BE 2 OR GREATER)\\nC X = ARRAY OF DIMENSION L STORING THE \ ABSCISSAS OF\\nC INPUT DATA POINTS (IN ASCENDING OR DESCENDING\\nC \ ORDER FOR MD = 1)\\nC Y = ARRAY OF DIMENSION L STORING THE \ ORDINATES OF\\nC INPUT DATA POINTS\\nC M = NUMBER OF \ SUBINTERVALS BETWEEN EACH PAIR OF\\nC INPUT DATA POINTS (MUST BE 2 \ OR GREATER)\\nC N = NUMBER OF OUTPUT POINTS\\nC = (L-1)*M+1\\nC \ THE OUTPUT PARAMETERS ARE\\nC U = ARRAY OF DIMENSION N WHERE THE \ ABSCISSAS OF\\nC OUTPUT POINTS ARE TO BE DISPLAYED\\nC V = \ ARRAY OF DIMENSION N WHERE THE ORDINATES OF\\nC OUTPUT POINTS ARE TO \ BE DISPLAYED\\nC DECLARATION STATEMENTS\\n DIMENSION \ X(L),Y(L),U(N),V(N)\\n EQUIVALENCE (M1,B1),(M2,B2),(M3,B3),(M4,B4),\\n \ 1 (X2,P0),(Y2,Q0),(T2,Q1)\\n REAL M1,M2,M3,M4\\n \ EQUIVALENCE (W2,Q2),(W3,Q3),(A1,P2),(B1,P3),\\n 1 \ (A2,DZ),(SW,R,Z)\\nC PRELIMINARY PROCESSING\\n 10 MD0=MD\\n MDM1=MD0-1\ \\n L0=L\\n LM1=L0-1\\n M0=M\\n MM1=M0-1\\n N0=N\\n \ IF(MD0.LE.0) GO TO 90\\n IF(MD0.GE.3) GO TO 90\\n \ IF(LM1.LE.0) GO TO 91\\n IF(MM1.LE.0) GO TO 92\\n \ IF(N0.NE.LM1*M0+1) GO TO 93\\n GO TO (11,16), MD0\\n 11 I=2\\n \ IF(X(1)-X(2)) 12,95,14\\n 12 DO 13 I=3,L0\\n IF(X(I-1)-X(I)) \ 13,95,96\\n 13 CONTINUE\\n GO TO 18\\n 14 DO 15 I=3,L0\\n \ IF(X(I-1)-X(I)) 96,95,15\\n 15 CONTINUE\\n GO TO 18\\n 16 DO 17 \ I=2,L0\\n IF(X(I-1).NE.X(I)) GO TO 17\\n IF(Y(I-1).EQ.Y(I)) \ GO TO 97\\n 17 CONTINUE\\n 18 K=N0+M0\\n I=L0+1\\n DO 19 \ J=1,L0\\n K=K-M0\\n I=I-1\\n U(K)=X(I)\\n 19 \ V(K)=Y(I)\\n RM=M0\\n RM=1.0/RM\\nC MAIN DO-LOOP\\n 20 K5=M0+1\\n \ DO 80 I=1,L0\\nC ROUTINES TO PICK UP NECESSARY X AND Y VALUES AND\\nC \ TO ESTIMATE THEM IF NECESSARY\\n IF(I.GT.1) GO TO 40\\n \ 30 X3=U(1)\\n Y3=V(1)\\n X4=U(M0+1)\\n Y4=V(M0+1)\\n \ A3=X4-X3\\n B3=Y4-Y3\\n IF(MDM1.EQ.0) M3=B3/A3\\n \ IF(L0.NE.2) GO TO 41\\n A4=A3\\n B4=B3\\n 31 GO TO \ (33,32), MD0\\n 32 A2=A3+A3-A4\\n A1=A2+A2-A3\\n 33 \ B2=B3+B3-B4\\n B1=B2+B2-B3\\n GO TO (51,56), MD0\\n 40 \ X2=X3\\n Y2=Y3\\n X3=X4\\n Y3=Y4\\n X4=X5\\n \ Y4=Y5\\n A1=A2\\n B1=B2\\n A2=A3\\n B2=B3\\n \ A3=A4\\n B3=B4\\n IF(I.GE.LM1) GO TO 42\\n 41 \ K5=K5+M0\\n X5=U(K5)\\n Y5=V(K5)\\n A4=X5-X4\\n \ B4=Y5-Y4\\n IF(MDM1.EQ.0) M4=B4/A4\\n GO TO 43\\n 42 \ IF(MDM1.NE.0) A4=A3+A3-A2\\n B4=B3+B3-B2\\n 43 IF(I.EQ.1) \ GO TO 31\\n GO TO (50,55), MD0\\nC NUMERICAL DIFFERENTIATION\\n 50 \ T2=T3\\n 51 W2=ABS(M4-M3)\\n W3=ABS(M2-M1)\\n SW=W2+W3\\n \ IF(SW.NE.0.0) GO TO 52\\n W2=0.5\\n W3=0.5\\n \ SW=1.0\\n 52 T3=(W2*M2+W3*M3)/SW\\n IF(I-1) 80,80,60\\n 55 \ COS2=COS3\\n SIN2=SIN3\\n 56 W2=ABS(A3*B4-A4*B3)\\n \ W3=ABS(A1*B2-A2*B1)\\n IF(W2+W3.NE.0.0) GO TO 57\\n \ W2=SQRT(A3*A3+B3*B3)\\n W3=SQRT(A2*A2+B2*B2)\\n 57 \ COS3=W2*A2+W3*A3\\n SIN3=W2*B2+W3*B3\\n \ R=COS3*COS3+SIN3*SIN3\\n IF(R.EQ.0.0) GO TO 58\\n \ R=SQRT(R)\\n COS3=COS3/R\\n SIN3=SIN3/R\\n 58 IF(I-1) \ 80,80,65\\nC DETERMINATION OF THE COEFFICIENTS\\n 60 \ Q2=(2.0*(M2-T2)+M2-T3)/A2\\n Q3=(-M2-M2+T2+T3)/(A2*A2)\\n GO TO \ 70\\n 65 R=SQRT(A2*A2+B2*B2)\\n P1=R*COS2\\n \ P2=3.0*A2-R*(COS2+COS2+COS3)\\n P3=A2-P1-P2\\n Q1=R*SIN2\\n \ Q2=3.0*B2-R*(SIN2+SIN2+SIN3)\\n Q3=B2-Q1-Q2\\n GO TO 75\\nC \ COMPUTATION OF THE POLYNOMIALS\\n 70 DZ=A2*RM\\n Z=0.0\\n \ DO 71 J=1,MM1\\n K=K+1\\n Z=Z+DZ\\n U(K)=P0+Z\\n \ 71 V(K)=Q0+Z*(Q1+Z*(Q2+Z*Q3))\\n GO TO 79\\n 75 Z=0.0\\n \ DO 76 J=1,MM1\\n K=K+1\\n Z=Z+RM\\n \ U(K)=P0+Z*(P1+Z*(P2+Z*P3))\\n 76 V(K)=Q0+Z*(Q1+Z*(Q2+Z*Q3))\\n 79 \ K=K+1\\n 80 CONTINUE\\n RETURN\\nC ERROR EXIT\\n 90 WRITE \ (IU,2090)\\n GO TO 99\\n 91 WRITE (IU,2091)\\n GO TO 99\\n 92 \ WRITE (IU,2092)\\n GO TO 99\\n 93 WRITE (IU,2093)\\n GO TO 99\\n \ 95 WRITE (IU,2095)\\n GO TO 98\\n 96 WRITE (IU,2096)\\n GO TO 98\ \\n 97 WRITE (IU,2097)\\n 98 WRITE (IU,2098) I,X(I),Y(I)\\n 99 WRITE \ (IU,2099) MD0,L0,M0,N0\\n RETURN\\nC FORMAT STATEMENTS\\n 2090 \ FORMAT(1X/31H *** MD OUT OF PROPER RANGE./)\\n 2091 FORMAT(1X/22H *** L \ = 1 OR LESS./)\\n 2092 FORMAT(1X/22H *** M = 1 OR LESS./)\\n 2093 \ FORMAT(1X/25H *** IMPROPER N VALUE./)\\n 2095 FORMAT(1X/27H *** \ IDENTICAL X VALUES./)\\n 2096 FORMAT(1X/33H *** X VALUES OUT OF \ SEQUENCE./)\\n 2097 FORMAT(1X/33H *** IDENTICAL X AND Y VALUES./)\\n 2098 \ FORMAT(7H I =,I4,10X,6HX(I) =,E12.3,\\n 1 \ 10X,6HY(I) =,E12.3)\\n 2099 FORMAT(7H MD =,I4,8X,3HL =,I5,8X,\\n 1 \ 3HM =,I5,8X,3HN =,I5/\\n 2 36H ERROR DETECTED IN ROUTINE \ CRVFIT)\\n END\\n\"\>", StripOnInput->False, FontSize->14], ImageSize->{720, 432}, Scrollbars->{False, Automatic}]], "Output", CellChangeTimes->{3.781311947284322*^9, 3.781339561512866*^9, 3.781351083890724*^9, 3.7813514442651653`*^9}, CellLabel->"Out[13]=",ExpressionUUID->"2720dba2-457b-4974-a83a-10f30c4f4414"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ One of the drawbacks of the original algorithm was that the user had to \ provide the points at which the interpolation was desired\ \>", "Item", CellChangeTimes->{{3.7811985286256247`*^9, 3.781198579966035*^9}},ExpressionUUID->"d7b2e278-e03f-4df6-b643-\ 5646eea0cb7e"], Cell["Sometimes this led to plots that did not appear smooth", "Subitem", CellChangeTimes->{{3.7811985286256247`*^9, 3.781198569450787*^9}, { 3.781198609338243*^9, 3.781198650409029*^9}, {3.781215848266911*^9, 3.781215865713146*^9}},ExpressionUUID->"f907e329-c241-4b5f-9e18-\ 999cb883952c"] }, Open ]], Cell["", "Text",ExpressionUUID->"55b3c6c9-24f6-4825-bac5-708f6ab7f8a3"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"dac57df2-e631-46e4-be82-115389a965bf"], Cell[CellGroupData[{ Cell["Long story short", "Section", CellChangeTimes->{{3.7811707334151707`*^9, 3.781170736087763*^9}, 3.781197707013215*^9},ExpressionUUID->"111124bd-3513-47d9-b810-\ 570e9dffa966"], 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AspectRatio -> 1, Axes -> {False, False}, AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :> Identity, Epilog -> { RGBColor[1, 0, 0], PointSize[0.02], PointBox[{{0, 0}, {1, 0}, {2, 0}, {3, 0}, {4, 0}, {5, 1}, {6, 10}, {7, 80}, {8, 100}, {9, 150}}]}, Frame -> {{True, True}, {True, True}}, FrameLabel -> {{None, None}, {None, None}}, FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, GridLines -> {None, None}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& )}}, PlotRange -> {{0, 9}, {-1.0924607066202, 149.99998806122514`}}, PlotRangeClipping -> True, PlotRangePadding -> {{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[ FormBox[ TemplateBox[{"\"Hermite\"", "\"Spline\"", "\"Akima\""}, "LineLegend", DisplayFunction -> (FormBox[ StyleBox[ StyleBox[ PaneBox[ TagBox[ GridBox[{{ TagBox[ GridBox[{{ GraphicsBox[{{ Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6]], { LineBox[{{0, 10}, {20, 10}}]}}, { Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, ImageSize -> {20, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { GraphicsBox[{{ Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6]], { LineBox[{{0, 10}, {20, 10}}]}}, { Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, ImageSize -> {20, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { GraphicsBox[{{ Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], RGBColor[0.560181, 0.691569, 0.194885], AbsoluteThickness[1.6]], { LineBox[{{0, 10}, {20, 10}}]}}, { Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], RGBColor[0.560181, 0.691569, 0.194885], AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, ImageSize -> {20, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, GridBoxAlignment -> { "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, AutoDelete -> False, GridBoxDividers -> { "Columns" -> {{False}}, "Rows" -> {{False}}}, GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, GridBoxSpacings -> { "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], "Grid"], Alignment -> Left, AppearanceElements -> None, ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> False], TraditionalForm]& ), InterpretationFunction :> (RowBox[{"LineLegend", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Directive", "[", RowBox[{ RowBox[{"Opacity", "[", "1.`", "]"}], ",", InterpretationBox[ ButtonBox[ TooltipBox[ GraphicsBox[{{ GrayLevel[0], RectangleBox[{0, 0}]}, { GrayLevel[0], RectangleBox[{1, -1}]}, { RGBColor[0.368417, 0.506779, 0.709798], RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, FrameStyle -> RGBColor[ 0.24561133333333335`, 0.3378526666666667, 0.4731986666666667], FrameTicks -> None, PlotRangePadding -> None, ImageSize -> Dynamic[{ Automatic, 1.35 CurrentValue["FontCapHeight"]/ AbsoluteCurrentValue[Magnification]}]], StyleBox[ RowBox[{"RGBColor", "[", RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}], "]"}], NumberMarks -> False]], Appearance -> None, BaseStyle -> {}, BaselinePosition -> Baseline, DefaultBaseStyle -> {}, ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, If[ Not[ AbsoluteCurrentValue["Deployed"]], SelectionMove[Typeset`box$, All, Expression]; FrontEnd`Private`$ColorSelectorInitialAlpha = 1; FrontEnd`Private`$ColorSelectorInitialColor = RGBColor[0.368417, 0.506779, 0.709798]; FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; MathLink`CallFrontEnd[ FrontEnd`AttachCell[Typeset`box$, FrontEndResource["RGBColorValueSelector"], { 0, {Left, Bottom}}, {Left, Top}, "ClosingActions" -> { "SelectionDeparture", "ParentChanged", "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> Automatic, Method -> "Preemptive"], RGBColor[0.368417, 0.506779, 0.709798], Editable -> False, Selectable -> False], ",", RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], ",", RowBox[{"Directive", "[", RowBox[{ RowBox[{"Opacity", "[", "1.`", "]"}], ",", InterpretationBox[ ButtonBox[ TooltipBox[ GraphicsBox[{{ GrayLevel[0], RectangleBox[{0, 0}]}, { GrayLevel[0], RectangleBox[{1, -1}]}, { RGBColor[0.880722, 0.611041, 0.142051], RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, FrameStyle -> RGBColor[ 0.587148, 0.40736066666666665`, 0.09470066666666668], FrameTicks -> None, PlotRangePadding -> None, ImageSize -> Dynamic[{ Automatic, 1.35 CurrentValue["FontCapHeight"]/ AbsoluteCurrentValue[Magnification]}]], StyleBox[ RowBox[{"RGBColor", "[", RowBox[{"0.880722`", ",", "0.611041`", ",", "0.142051`"}], "]"}], NumberMarks -> False]], Appearance -> None, BaseStyle -> {}, BaselinePosition -> Baseline, DefaultBaseStyle -> {}, ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, If[ Not[ AbsoluteCurrentValue["Deployed"]], SelectionMove[Typeset`box$, All, Expression]; FrontEnd`Private`$ColorSelectorInitialAlpha = 1; FrontEnd`Private`$ColorSelectorInitialColor = RGBColor[0.880722, 0.611041, 0.142051]; FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; MathLink`CallFrontEnd[ FrontEnd`AttachCell[Typeset`box$, FrontEndResource["RGBColorValueSelector"], { 0, {Left, Bottom}}, {Left, Top}, "ClosingActions" -> { "SelectionDeparture", "ParentChanged", "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> Automatic, Method -> "Preemptive"], RGBColor[0.880722, 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Alternatives[False, True], Alternatives[False, True]}, Akima`Private`periodic, Blank[], Message[ MessageName[Akima`AkimaInterpolation2D, "opttf"], PeriodicInterpolation, Akima`Private`periodic]; Throw[$Failed]]]; Akima`Private`dataRange = OptionValue[DataRange]; If[ MatchQ[Akima`Private`dataRange, Automatic], Akima`Private`dataRange = { Akima`Private`dataRange, Akima`Private`dataRange}]; Akima`Private`ok = True; Akima`Private`debugEcho["check number levels"]; MapThread[If[# < #2, Akima`Private`ok = False; Message[ MessageName[ Akima`AkimaInterpolation2D, "npts"], #, #3, #2]]& , { Dimensions[Akima`Private`array], Map[If[#, 3, 2]& , Akima`Private`periodic], {"y", "x"}}]; If[ Not[Akima`Private`ok], Throw[$Failed]]; Akima`Private`debugEcho["check data periodic"]; MapThread[If[ And[#, #2 != #3], Akima`Private`ok = False; Message[ MessageName[Akima`AkimaInterpolation2D, "per"]]; Null]& , { Akima`Private`periodic, { Part[Akima`Private`array, All, 1], Part[Akima`Private`array, 1, All]}, { Part[Akima`Private`array, All, -1], Part[Akima`Private`array, -1, All]}}]; If[ Not[Akima`Private`ok], Throw[$Failed]]; Akima`Private`debugEcho["check ordinates"]; Akima`Private`dataRange = MapThread[Switch[#, Automatic, Range[#2], Condition[{ PatternTest[ Pattern[Akima`Private`a, Blank[]], NumberQ], PatternTest[ Pattern[Akima`Private`b, Blank[]], NumberQ]}, Akima`Private`a < Akima`Private`b], Akima`Private`debugEcho[ Range[ Apply[Sequence, #], Apply[Subtract, Reverse[#]]/(#2 - 1)]], Condition[ Pattern[Akima`Private`l, { PatternTest[ BlankSequence[], NumberQ]}], Length[Akima`Private`l] == #2], #, Blank[], Message[ MessageName[ Akima`AkimaInterpolation2D, "drange"]]; $Failed]& , { Akima`Private`dataRange, Reverse[ Dimensions[Akima`Private`array]]}]; If[ MemberQ[Akima`Private`dataRange, $Failed], Throw[$Failed]]; Akima`Private`debugEcho["sort"]; Akima`Private`zIn = MapThread[Prepend, { Prepend[Akima`Private`array, First[Akima`Private`dataRange]], Prepend[ Last[Akima`Private`dataRange], Null]}]; Akima`Private`zIn = N[ Transpose[ RotateRight[ SortBy[ Transpose[ RotateRight[ SortBy[Akima`Private`zIn, First]]], First]]]]; If[Length[Akima`Private`zIn] == 3, Akima`Private`zIn = Insert[Akima`Private`zIn, Mean[ Rest[Akima`Private`zIn]], 3]]; If[Length[ First[Akima`Private`zIn]] == 3, Akima`Private`zIn = Map[Insert[#, Mean[ Rest[#]], 3]& , Akima`Private`zIn]]; Akima`Private`debugEcho["extract"]; Akima`Private`xIn = Part[Akima`Private`zIn, 1, Span[2, All]]; Akima`Private`yIn = Part[Akima`Private`zIn, Span[2, All], 1]; Akima`Private`zIn = Part[Akima`Private`zIn, Span[2, All], Span[2, All]]; Akima`Private`debugEcho["extrapolate"]; Akima`Private`x = Join[ Reverse[ Akima`Private`extrapolateOrdinate[ Reverse[ Part[Akima`Private`xIn, Span[1, 3]]]]], Akima`Private`xIn, Akima`Private`extrapolateOrdinate[ Part[Akima`Private`xIn, Span[-3, All]]]]; Akima`Private`y = Join[ Reverse[ Akima`Private`extrapolateOrdinate[ Reverse[ Part[Akima`Private`yIn, Span[1, 3]]]]], Akima`Private`yIn, Akima`Private`extrapolateOrdinate[ Part[Akima`Private`yIn, Span[-3, All]]]]; Akima`Private`z = Map[Join[ Reverse[ Akima`Private`extrapolateAbscissa[ Reverse[ Part[Akima`Private`yIn, Span[1, 3]]], Reverse[ Part[#, Span[1, 3]]]]], #, Akima`Private`extrapolateAbscissa[ Part[Akima`Private`yIn, Span[-3, All]], Part[#, Span[-3, All]]]]& , Akima`Private`zIn]; Akima`Private`z = Transpose[ Map[Join[ Reverse[ Akima`Private`extrapolateAbscissa[ Reverse[ Part[Akima`Private`xIn, Span[1, 3]]], Reverse[ Part[#, Span[1, 3]]]]], #, Akima`Private`extrapolateAbscissa[ Part[Akima`Private`xIn, Span[-3, All]], Part[#, Span[-3, All]]]]& , Transpose[Akima`Private`z]]]; Akima`Private`debugEcho["interval gradients"]; Akima`Private`c = Transpose[ MapThread[Divide, { Apply[Subtract, Partition[ Transpose[Akima`Private`z], 2, 1], {1}], Apply[Subtract, Partition[Akima`Private`x, 2, 1], {1}]}]]; Akima`Private`debugEcho[Akima`Private`c, "c", MatrixForm]; Akima`Private`d = MapThread[Divide, { Apply[Subtract, 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Partition[Akima`Private`cj, 4, 1], {1}]], Part[Akima`Private`c, Span[3, -3]]]; Akima`Private`debugEcho[Akima`Private`zx, "zx", MatrixForm]; Akima`Private`zy = Transpose[ Map[ Function[Akima`Private`di, Apply[ With[{Akima`Private`w2 = Abs[#4 - #3], Akima`Private`w3 = Abs[#2 - #]}, If[ Akima`Private`w2 + Akima`Private`w3 != 0, (Akima`Private`w2 #2 + Akima`Private`w3 #3)/( Akima`Private`w2 + Akima`Private`w3), (#2 + #3)/2]]& , Partition[Akima`Private`di, 4, 1], {1}]], Part[ Transpose[Akima`Private`d], Span[3, -3]]]]; Akima`Private`debugEcho[Akima`Private`zy, "zy", MatrixForm]; Akima`Private`zxy = Table[(Part[Akima`Private`wx, Akima`Private`i, Akima`Private`j] ( Part[Akima`Private`wy, Akima`Private`i, Akima`Private`j] Part[Akima`Private`e, Akima`Private`i - 1, Akima`Private`j - 1] + Part[ Akima`Private`wy, Akima`Private`i - 2, Akima`Private`j] Part[Akima`Private`e, Akima`Private`i, Akima`Private`j - 1]) + Part[Akima`Private`wx, Akima`Private`i, Akima`Private`j - 2] ( Part[Akima`Private`wy, 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2-D cases, the method for the interval slopes, or \ divided differences, is the same, as are the first derivatives ", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"\[DifferentialD]", "y"}], RowBox[{"\[DifferentialD]", "x"}]], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "1d0bf034-f984-4f73-b5fa-acfe14d58abf"], " and ", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"\[DifferentialD]", "y"}], RowBox[{"\[DifferentialD]", "x"}]], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "5dde2be0-2184-4ddb-a6ab-d11c0c6da1a9"] }], "Item", CellChangeTimes->{{3.7812569151543837`*^9, 3.7812569645989428`*^9}, { 3.781257024751794*^9, 3.7812570310148697`*^9}, {3.781257102838397*^9, 3.7812571513517637`*^9}},ExpressionUUID->"19433a3b-05d2-4deb-b89a-\ 204e62b53156"], Cell[TextData[{ "Second order divided differences are computed from first order divided \ differences, and second derivatives ", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{ SuperscriptBox["\[DifferentialD]", 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TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["String", "IconizedItem"]}]}, { RowBox[{ TagBox["\"String length: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["10338", "IconizedItem"]}]}, { RowBox[{ TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["11272", "IconizedItem"]}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle -> "Column", GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],Dynamic[ Typeset`open]}, "IconizedObject"]], "C ALGORITHM 433 COLLECTED ALGORITHMS FROM ACM.\nC ALGORITHM \ APPEARED IN COMM. ACM, VOL. 15, NO. 10,\nC P. 914.\n SUBROUTINE \ INTRPL(IU,L,X,Y,N,U,V) INTR 10\nC \ INTERPOLATION OF A SINGLE-VALUED FUNCTION\nC THIS SUBROUTINE INTERPOLATES, \ FROM VALUES OF THE FUNCTION\nC GIVEN AS ORDINATES OF INPUT DATA POINTS IN AN \ X-Y PLANE\nC AND FOR A GIVEN SET OF X VALUES (ABSCISSAS), THE VALUES OF\nC A \ SINGLE-VALUED FUNCTION Y = Y(X).\nC THE INPUT PARAMETERS ARE\nC IU = \ LOGICAL UNIT NUMBER OF STANDARD OUTPUT UNIT\nC L = NUMBER OF INPUT DATA \ POINTS\nC (MUST BE 2 OR GREATER)\nC X = ARRAY OF DIMENSION L \ STORING THE X VALUES\nC (ABSCISSAS) OF INPUT DATA POINTS\nC \ (IN ASCENDING ORDER)\nC Y = ARRAY OF DIMENSION L STORING THE Y VALUES\nC \ (ORDINATES) OF INPUT DATA POINTS\nC N = NUMBER OF POINTS AT \ WHICH INTERPOLATION OF THE\nC Y VALUE (ORDINATE) IS DESIRED\nC \ (MUST BE 1 OR GREATER)\nC U = ARRAY OF DIMENSION N STORING THE X \ VALUES\nC (ABSCISSAS) OF DESIRED POINTS\nC THE OUTPUT PARAMETER IS\n\ C V = ARRAY OF DIMENSION N WHERE THE INTERPOLATED Y\nC VALUES \ (ORDINATES) ARE TO BE DISPLAYED\nC DECLARATION STATEMENTS\n DIMENSION \ X(L),Y(L),U(N),V(N)\n EQUIVALENCE (P0,X3),(Q0,Y3),(Q1,T3)\n REAL \ M1,M2,M3,M4,M5\n EQUIVALENCE \ (UK,DX),(IMN,X2,A1,M1),(IMX,X5,A5,M5),\n 1 \ (J,SW,SA),(Y2,W2,W4,Q2),(Y5,W3,Q3)\nC PRELIMINARY PROCESSING\n 10 L0=L\n \ LM1=L0-1\n LM2=LM1-1\n LP1=L0+1\n N0=N\n IF(LM2.LT.0) \ GO TO 90\n IF(N0.LE.0) GO TO 91\n DO 11 I=2,L0\n \ IF(X(I-1)-X(I)) 11,95,96\n 11 CONTINUE\n IPV=0\nC MAIN DO-LOOP\n \ DO 80 K=1,N0\n UK=U(K)\nC ROUTINE TO LOCATE THE DESIRED POINT\n \ 20 IF(LM2.EQ.0) GO TO 27\n IF(UK.GE.X(L0)) GO TO 26\n \ IF(UK.LT.X(1)) GO TO 25\n IMN=2\n IMX=L0\n 21 \ I=(IMN+IMX)/2\n IF(UK.GE.X(I)) GO TO 23\n 22 IMX=I\n GO \ TO 24\n 23 IMN=I+1\n 24 IF(IMX.GT.IMN) GO TO 21\n I=IMX\n \ GO TO 30\n 25 I=1\n GO TO 30\n 26 I=LP1\n GO TO 30\ \n 27 I=2\nC CHECK IF I = IPV\n 30 IF(I.EQ.IPV) GO TO 70\n \ IPV=I\nC ROUTINES TO PICK UP NECESSARY X AND Y VALUES AND\nC TO \ ESTIMATE THEM IF NECESSARY\n 40 J=I\n IF(J.EQ.1) J=2\n \ IF(J.EQ.LP1) J=L0\n X3=X(J-1)\n Y3=Y(J-1)\n \ X4=X(J)\n Y4=Y(J)\n A3=X4-X3\n M3=(Y4-Y3)/A3\n \ IF(LM2.EQ.0) GO TO 43\n IF(J.EQ.2) GO TO 41\n \ X2=X(J-2)\n Y2=Y(J-2)\n A2=X3-X2\n M2=(Y3-Y2)/A2\n \ IF(J.EQ.L0) GO TO 42\n 41 X5=X(J+1)\n Y5=Y(J+1)\n \ A4=X5-X4\n M4=(Y5-Y4)/A4\n IF(J.EQ.2) M2=M3+M3-M4\n \ GO TO 45\n 42 M4=M3+M3-M2\n GO TO 45\n 43 M2=M3\n \ M4=M3\n 45 IF(J.LE.3) GO TO 46\n A1=X2-X(J-3)\n \ M1=(Y2-Y(J-3))/A1\n GO TO 47\n 46 M1=M2+M2-M3\n 47 \ IF(J.GE.LM1) GO TO 48\n A5=X(J+2)-X5\n M5=(Y(J+2)-Y5)/A5\n \ GO TO 50\n 48 M5=M4+M4-M3\nC NUMERICAL DIFFERENTIATION\n 50 \ IF(I.EQ.LP1) GO TO 52\n W2=ABS(M4-M3)\n W3=ABS(M2-M1)\n \ SW=W2+W3\n IF(SW.NE.0.0) GO TO 51\n W2=0.5\n \ W3=0.5\n SW=1.0\n 51 T3=(W2*M2+W3*M3)/SW\n IF(I.EQ.1) \ GO TO 54\n 52 W3=ABS(M5-M4)\n W4=ABS(M3-M2)\n SW=W3+W4\n \ IF(SW.NE.0.0) GO TO 53\n W3=0.5\n W4=0.5\n \ SW=1.0\n 53 T4=(W3*M3+W4*M4)/SW\n IF(I.NE.LP1) GO TO 60\n \ T3=T4\n SA=A2+A3\n T4=0.5*(M4+M5-A2*(A2-A3)*(M2-M3)/(SA*SA))\ \n X3=X4\n Y3=Y4\n A3=A2\n M3=M4\n GO TO \ 60\n 54 T4=T3\n SA=A3+A4\n \ T3=0.5*(M1+M2-A4*(A3-A4)*(M3-M4)/(SA*SA))\n X3=X3-A4\n \ Y3=Y3-M2*A4\n A3=A4\n M3=M2\nC DETERMINATION OF THE \ COEFFICIENTS\n 60 Q2=(2.0*(M3-T3)+M3-T4)/A3\n \ Q3=(-M3-M3+T3+T4)/(A3*A3)\nC COMPUTATION OF THE POLYNOMIAL\n 70 DX=UK-P0\n\ 80 V(K)=Q0+DX*(Q1+DX*(Q2+DX*Q3))\n RETURN\nC ERROR EXIT\n 90 \ WRITE (IU,2090)\n GO TO 99\n 91 WRITE (IU,2091)\n GO TO 99\n 95 \ WRITE (IU,2095)\n GO TO 97\n 96 WRITE (IU,2096)\n 97 WRITE (IU,2097) \ I,X(I)\n 99 WRITE (IU,2099) L0,N0\n RETURN\nC FORMAT STATEMENTS\n \ 2090 FORMAT(1X/22H *** L = 1 OR LESS./)\n 2091 FORMAT(1X/22H *** N = 0 \ OR LESS./)\n 2095 FORMAT(1X/27H *** IDENTICAL X VALUES./)\n 2096 \ FORMAT(1X/33H *** X VALUES OUT OF SEQUENCE./)\n 2097 FORMAT(6H I \ =,I7,10X,6HX(I) =,E12.3)\n 2099 FORMAT(6H L =,I7,10X,3HN =,I7/\n 1 \ 36H ERROR DETECTED IN ROUTINE INTRPL)\n END\n SUBROUTINE \ CRVFIT(IU,MD,L,X,Y,M,N,U,V) CRVF1670\nC SMOOTH \ CURVE FITTING\nC THIS SUBROUTINE FITS A SMOOTH CURVE TO A GIVEN SET OF IN-\nC \ PUT DATA POINTS IN AN X-Y PLANE. IT INTERPOLATES POINTS\nC IN EACH INTERVAL \ BETWEEN A PAIR OF DATA POINTS AND GENER-\nC ATES A SET OF OUTPUT POINTS \ CONSISTING OF THE INPUT DATA\nC POINTS AND THE INTERPOLATED POINTS. IT CAN \ PROCESS EITHER\nC A SINGLE-VALUED FUNCTION OR A MULTIPLE-VALUED FUNCTION.\nC \ THE INPUT PARAMETERS ARE\nC IU = LOGICAL UNIT NUMBER OF STANDARD OUTPUT \ UNIT\nC MD = MODE OF THE CURVE (MUST BE 1 OR 2)\nC = 1 FOR A \ SINGLE-VALUED FUNCTION\nC = 2 FOR A MULTIPLE-VALUED FUNCTION\nC L \ = NUMBER OF INPUT DATA POINTS\nC (MUST BE 2 OR GREATER)\nC X = \ ARRAY OF DIMENSION L STORING THE ABSCISSAS OF\nC INPUT DATA POINTS \ (IN ASCENDING OR DESCENDING\nC ORDER FOR MD = 1)\nC Y = ARRAY \ OF DIMENSION L STORING THE ORDINATES OF\nC INPUT DATA POINTS\nC \ M = NUMBER OF SUBINTERVALS BETWEEN EACH PAIR OF\nC INPUT DATA \ POINTS (MUST BE 2 OR GREATER)\nC N = NUMBER OF OUTPUT POINTS\nC = \ (L-1)*M+1\nC THE OUTPUT PARAMETERS ARE\nC U = ARRAY OF DIMENSION N WHERE \ THE ABSCISSAS OF\nC OUTPUT POINTS ARE TO BE DISPLAYED\nC V = \ ARRAY OF DIMENSION N WHERE THE ORDINATES OF\nC OUTPUT POINTS ARE TO \ BE DISPLAYED\nC DECLARATION STATEMENTS\n DIMENSION \ X(L),Y(L),U(N),V(N)\n EQUIVALENCE (M1,B1),(M2,B2),(M3,B3),(M4,B4),\n \ 1 (X2,P0),(Y2,Q0),(T2,Q1)\n REAL M1,M2,M3,M4\n \ EQUIVALENCE (W2,Q2),(W3,Q3),(A1,P2),(B1,P3),\n 1 \ (A2,DZ),(SW,R,Z)\nC PRELIMINARY PROCESSING\n 10 MD0=MD\n MDM1=MD0-1\n \ L0=L\n LM1=L0-1\n M0=M\n MM1=M0-1\n N0=N\n \ IF(MD0.LE.0) GO TO 90\n IF(MD0.GE.3) GO TO 90\n \ IF(LM1.LE.0) GO TO 91\n IF(MM1.LE.0) GO TO 92\n \ IF(N0.NE.LM1*M0+1) GO TO 93\n GO TO (11,16), MD0\n 11 I=2\n \ IF(X(1)-X(2)) 12,95,14\n 12 DO 13 I=3,L0\n IF(X(I-1)-X(I)) \ 13,95,96\n 13 CONTINUE\n GO TO 18\n 14 DO 15 I=3,L0\n \ IF(X(I-1)-X(I)) 96,95,15\n 15 CONTINUE\n GO TO 18\n 16 DO 17 \ I=2,L0\n IF(X(I-1).NE.X(I)) GO TO 17\n IF(Y(I-1).EQ.Y(I)) GO \ TO 97\n 17 CONTINUE\n 18 K=N0+M0\n I=L0+1\n DO 19 J=1,L0\n \ K=K-M0\n I=I-1\n U(K)=X(I)\n 19 V(K)=Y(I)\n RM=M0\ \n RM=1.0/RM\nC MAIN DO-LOOP\n 20 K5=M0+1\n DO 80 I=1,L0\nC \ ROUTINES TO PICK UP NECESSARY X AND Y VALUES AND\nC TO ESTIMATE THEM \ IF NECESSARY\n IF(I.GT.1) GO TO 40\n 30 X3=U(1)\n \ Y3=V(1)\n X4=U(M0+1)\n Y4=V(M0+1)\n A3=X4-X3\n \ B3=Y4-Y3\n IF(MDM1.EQ.0) M3=B3/A3\n IF(L0.NE.2) GO TO \ 41\n A4=A3\n B4=B3\n 31 GO TO (33,32), MD0\n 32 \ A2=A3+A3-A4\n A1=A2+A2-A3\n 33 B2=B3+B3-B4\n B1=B2+B2-B3\n \ GO TO (51,56), MD0\n 40 X2=X3\n Y2=Y3\n X3=X4\n \ Y3=Y4\n X4=X5\n Y4=Y5\n A1=A2\n B1=B2\n \ A2=A3\n B2=B3\n A3=A4\n B3=B4\n IF(I.GE.LM1) \ GO TO 42\n 41 K5=K5+M0\n X5=U(K5)\n Y5=V(K5)\n \ A4=X5-X4\n B4=Y5-Y4\n IF(MDM1.EQ.0) M4=B4/A4\n GO TO \ 43\n 42 IF(MDM1.NE.0) A4=A3+A3-A2\n B4=B3+B3-B2\n 43 \ IF(I.EQ.1) GO TO 31\n GO TO (50,55), MD0\nC NUMERICAL \ DIFFERENTIATION\n 50 T2=T3\n 51 W2=ABS(M4-M3)\n W3=ABS(M2-M1)\n\ SW=W2+W3\n IF(SW.NE.0.0) GO TO 52\n W2=0.5\n \ W3=0.5\n SW=1.0\n 52 T3=(W2*M2+W3*M3)/SW\n IF(I-1) 80,80,60\ \n 55 COS2=COS3\n SIN2=SIN3\n 56 W2=ABS(A3*B4-A4*B3)\n \ W3=ABS(A1*B2-A2*B1)\n IF(W2+W3.NE.0.0) GO TO 57\n \ W2=SQRT(A3*A3+B3*B3)\n W3=SQRT(A2*A2+B2*B2)\n 57 COS3=W2*A2+W3*A3\n\ SIN3=W2*B2+W3*B3\n R=COS3*COS3+SIN3*SIN3\n IF(R.EQ.0.0) \ GO TO 58\n R=SQRT(R)\n COS3=COS3/R\n SIN3=SIN3/R\n \ 58 IF(I-1) 80,80,65\nC DETERMINATION OF THE COEFFICIENTS\n 60 \ Q2=(2.0*(M2-T2)+M2-T3)/A2\n Q3=(-M2-M2+T2+T3)/(A2*A2)\n GO TO \ 70\n 65 R=SQRT(A2*A2+B2*B2)\n P1=R*COS2\n \ P2=3.0*A2-R*(COS2+COS2+COS3)\n P3=A2-P1-P2\n Q1=R*SIN2\n \ Q2=3.0*B2-R*(SIN2+SIN2+SIN3)\n Q3=B2-Q1-Q2\n GO TO 75\nC \ COMPUTATION OF THE POLYNOMIALS\n 70 DZ=A2*RM\n Z=0.0\n DO \ 71 J=1,MM1\n K=K+1\n Z=Z+DZ\n U(K)=P0+Z\n 71 \ V(K)=Q0+Z*(Q1+Z*(Q2+Z*Q3))\n GO TO 79\n 75 Z=0.0\n DO 76 \ J=1,MM1\n K=K+1\n Z=Z+RM\n \ U(K)=P0+Z*(P1+Z*(P2+Z*P3))\n 76 V(K)=Q0+Z*(Q1+Z*(Q2+Z*Q3))\n 79 \ K=K+1\n 80 CONTINUE\n RETURN\nC ERROR EXIT\n 90 WRITE (IU,2090)\n \ GO TO 99\n 91 WRITE (IU,2091)\n GO TO 99\n 92 WRITE (IU,2092)\n \ GO TO 99\n 93 WRITE (IU,2093)\n GO TO 99\n 95 WRITE (IU,2095)\n \ GO TO 98\n 96 WRITE (IU,2096)\n GO TO 98\n 97 WRITE (IU,2097)\n \ 98 WRITE (IU,2098) I,X(I),Y(I)\n 99 WRITE (IU,2099) MD0,L0,M0,N0\n \ RETURN\nC FORMAT STATEMENTS\n 2090 FORMAT(1X/31H *** MD OUT OF PROPER \ RANGE./)\n 2091 FORMAT(1X/22H *** L = 1 OR 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"Slideshow Presentation", StyleDefinitions -> StyleData["Text", "Slideshow Working"]]], Cell[ StyleData[ "Text", "Scrolling Presentation", StyleDefinitions -> StyleData["Text", "Slideshow Working"]]], Cell[ StyleData["Text", "Printout"], CellMargins -> {{49, Inherited}, {Inherited, Inherited}}, Hyphenation -> True]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SmallText"], CellMargins -> {{66, 10}, {6, 6}}, LineSpacing -> {1, 3}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "SmallText", MenuSortingValue -> 1750, StyleMenuListing -> None, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 13, FontColor -> Dynamic[ FEPrivate`If[ ColorQ[ FrontEnd`CurrentValue["Background"]], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1Reverse"}], FrontEnd`CurrentValue[{StyleHints, "ColorSet", "Text1"}]]]], Cell[ StyleData["SmallText", "SlideShow"], CellMargins -> {{ 0.135 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {9, 9}}, FontSize -> 18], Cell[ StyleData["SmallText", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.12 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.08 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {9, 9}}], FontSize -> Dynamic[0.018 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "SmallText", "Slideshow Presentation", StyleDefinitions -> StyleData["SmallText", "Slideshow Working"]]], Cell[ StyleData[ "SmallText", "Scrolling Presentation", StyleDefinitions -> StyleData["SmallText", "Slideshow Working"]]], Cell[ StyleData["SmallText", "Printout"], CellMargins -> {{33, Inherited}, {Inherited, Inherited}}, Hyphenation -> True]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Display", "Subsection"], Cell[ CellGroupData[{ Cell["Lists", "Subsubsection"], Cell[ CellGroupData[{ Cell["Bulleted", "Subsubsubsection"], Cell[ CellGroupData[{ Cell[ StyleData["Item"], CellDingbat -> StyleBox[ AdjustmentBox[ "\[FilledSmallCircle]", BoxBaselineShift -> -0.3], Alignment -> Top, FontColor -> Dynamic[ CurrentValue[{StyleHints, "ColorSet", "Dingbat"}]], Magnification -> 0.7], CellMargins -> {{81, 10}, {4, 8}}, ReturnCreatesNewCell -> True, StyleKeyMapping -> {"Tab" -> "Subitem", "*" -> "Subitem"}, CellGroupingRules -> { "GroupTogetherNestedGrouping", 15000}, CellFrameLabelMargins -> 4, CounterIncrements -> "Item", CounterAssignments -> {{"Subitem", 0}, {"Subsubitem", 0}}, MenuSortingValue -> 1600, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 14, FontColor -> Dynamic[ FEPrivate`If[ ColorQ[ FrontEnd`CurrentValue["Background"]], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1Reverse"}], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1"}]]]], Cell[ StyleData["Item", "SlideShow"], CellMargins -> {{ 0.17 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 10}}, CellFrameLabelMargins -> 8, FontSize -> 22], Cell[ StyleData["Item", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.17 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, { 0.012 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.01 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}}], CellFrameLabelMargins -> 8, FontSize -> Dynamic[ 0.022 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "Item", "Slideshow Presentation", StyleDefinitions -> StyleData["Item", "Slideshow Working"]]], Cell[ StyleData[ "Item", "Scrolling Presentation", StyleDefinitions -> StyleData["Item", "Slideshow Working"]]], Cell[ StyleData["Item", "Printout"], CellDingbat -> StyleBox["\[FilledSmallCircle]", Alignment -> Baseline, GrayLevel[0.2]], CellMargins -> {{65, Inherited}, {Inherited, Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ItemParagraph"], CellMargins -> {{81, 10}, {4, 1}}, ReturnCreatesNewCell -> True, StyleKeyMapping -> {"Tab" -> "SubitemParagraph"}, CellGroupingRules -> { "GroupTogetherNestedGrouping", 15000}, DefaultNewCellStyle -> "Item", MenuSortingValue -> 1600, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 14, FontColor -> Dynamic[ FEPrivate`If[ ColorQ[ FrontEnd`CurrentValue["Background"]], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1Reverse"}], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1"}]]]], Cell[ StyleData["ItemParagraph", "SlideShow"], ShowGroupOpener -> False, CellMargins -> {{ 0.17 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 2}}, FontSize -> 22], Cell[ StyleData["ItemParagraph", "Slideshow Working"], ShowGroupOpener -> False, CellMargins -> Dynamic[{{ 0.17 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, { 0.0122 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.00248148 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}}], FontSize -> Dynamic[ 0.022 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "ItemParagraph", "Slideshow Presentation", StyleDefinitions -> StyleData["ItemParagraph", "Slideshow Working"]]], Cell[ StyleData[ "ItemParagraph", "Scrolling Presentation", StyleDefinitions -> StyleData["ItemParagraph", "Slideshow Working"]]], Cell[ StyleData["ItemParagraph", "Printout"], CellMargins -> {{65, Inherited}, { Inherited, 0.5 Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Subitem"], CellDingbat -> StyleBox[ AdjustmentBox[ "\[FilledSmallCircle]", BoxBaselineShift -> -0.3], Alignment -> Top, FontColor -> Dynamic[ CurrentValue[{StyleHints, "ColorSet", "Dingbat"}]], Magnification -> 0.7], CellMargins -> {{105, 12}, {4, 4}}, ReturnCreatesNewCell -> True, StyleKeyMapping -> { "Tab" -> "Subsubitem", "*" -> "Subsubitem", "Backspace" -> "Item", KeyEvent["Tab", Modifiers -> {Shift}] -> "Item"}, CellGroupingRules -> { "GroupTogetherNestedGrouping", 15100}, CellFrameLabelMargins -> 4, DefaultNewCellStyle -> "Item", CounterIncrements -> "Subitem", CounterAssignments -> {{"Subsubitem", 0}}, MenuSortingValue -> 1610, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 13.5, FontColor -> Dynamic[ FEPrivate`If[ ColorQ[ FrontEnd`CurrentValue["Background"]], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1Reverse"}], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1"}]]]], Cell[ StyleData["Subitem", "SlideShow"], CellMargins -> {{ 0.2 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 10}}, CellFrameLabelMargins -> 8, FontSize -> 22], Cell[ StyleData["Subitem", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.2 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, { 0.0124074 FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}], 0.0124074 FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}]}}], CellFrameLabelMargins -> 8, FontSize -> Dynamic[ 0.022 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "Subitem", "Slideshow Presentation", StyleDefinitions -> StyleData["Subitem", "Slideshow Working"]]], Cell[ StyleData[ "Subitem", "Scrolling Presentation", StyleDefinitions -> StyleData["Subitem", "Slideshow Working"]]], Cell[ StyleData["Subitem", "Printout"], CellDingbat -> StyleBox["\[FilledSmallCircle]", Alignment -> Baseline, GrayLevel[0.3]], CellMargins -> {{92, Inherited}, {Inherited, Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubitemParagraph"], CellMargins -> {{105, 12}, {4, 1}}, ReturnCreatesNewCell -> True, StyleKeyMapping -> { "Tab" -> "SubsubitemParagraph", "Backspace" -> "ItemParagraph", KeyEvent["Tab", Modifiers -> {Shift}] -> "ItemParagraph"}, CellGroupingRules -> { "GroupTogetherNestedGrouping", 15100}, CellFrameLabelMargins -> 4, DefaultNewCellStyle -> "Subitem", MenuSortingValue -> 1610, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 13.5, FontColor -> Dynamic[ FEPrivate`If[ ColorQ[ FrontEnd`CurrentValue["Background"]], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1Reverse"}], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1"}]]]], Cell[ StyleData["SubitemParagraph", "SlideShow"], CellMargins -> {{ 0.2 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 2}}, FontSize -> 22], Cell[ StyleData["SubitemParagraph", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.2 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, { 0.0124074 FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}], 0.00248 FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}]}}], FontSize -> Dynamic[ 0.022 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "SubitemParagraph", "Slideshow Presentation", StyleDefinitions -> StyleData["SubitemParagraph", "Slideshow Working"]]], Cell[ StyleData[ "SubitemParagraph", "Scrolling Presentation", StyleDefinitions -> StyleData["SubitemParagraph", "Slideshow Working"]]], Cell[ StyleData["SubitemParagraph", "Printout"], CellMargins -> {{92, Inherited}, { Inherited, 0.1 Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Subsubitem"], CellDingbat -> StyleBox[ AdjustmentBox[ "\[FilledSmallCircle]", BoxBaselineShift -> -0.3], Alignment -> Top, FontColor -> Dynamic[ CurrentValue[{StyleHints, "ColorSet", "Dingbat"}]], Magnification -> 0.7], CellMargins -> {{129, 12}, {4, 4}}, ReturnCreatesNewCell -> True, StyleKeyMapping -> { "Backspace" -> "Subitem", KeyEvent["Tab", Modifiers -> {Shift}] -> "Subitem"}, CellGroupingRules -> { "GroupTogetherNestedGrouping", 15200}, CellFrameLabelMargins -> 4, DefaultNewCellStyle -> "Subsubitem", CounterIncrements -> "Subsubitem", MenuSortingValue -> 1620, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 13, FontColor -> Dynamic[ FEPrivate`If[ ColorQ[ FrontEnd`CurrentValue["Background"]], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1Reverse"}], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1"}]]]], Cell[ StyleData["Subsubitem", "SlideShow"], CellMargins -> {{ 0.176 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 10}}, CellFrameLabelMargins -> 8, FontSize -> 22], Cell[ StyleData["Subsubitem", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.23 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, { 0.0124074 FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}], 0.0124074 FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}]}}], CellFrameLabelMargins -> 8, FontSize -> Dynamic[ 0.02 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "Subsubitem", "Slideshow Presentation", StyleDefinitions -> StyleData["Subsubitem", "Slideshow Working"]]], Cell[ StyleData[ "Subsubitem", "Scrolling Presentation", StyleDefinitions -> StyleData["Subsubitem", "Slideshow Working"]]], Cell[ StyleData["Subsubitem", "Printout"], CellDingbat -> StyleBox["\[FilledSmallCircle]", Alignment -> Baseline, GrayLevel[0.4]], CellMargins -> {{119, Inherited}, { Inherited, Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsubitemParagraph"], CellMargins -> {{129, 12}, {4, 1}}, ReturnCreatesNewCell -> True, StyleKeyMapping -> { "Backspace" -> "SubitemParagraph", KeyEvent["Tab", Modifiers -> {Shift}] -> "SubitemParagraph"}, CellGroupingRules -> { "GroupTogetherNestedGrouping", 15200}, CellFrameLabelMargins -> 4, DefaultNewCellStyle -> "Subsubitem", CounterIncrements -> "Subsubitem", MenuSortingValue -> 1625, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 13, FontColor -> Dynamic[ FEPrivate`If[ ColorQ[ FrontEnd`CurrentValue["Background"]], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1Reverse"}], FrontEnd`CurrentValue[{ StyleHints, "ColorSet", "Text1"}]]]], Cell[ StyleData["SubsubitemParagraph", "SlideShow"], CellMargins -> {{ 0.176 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 2}}, FontSize -> 22], Cell[ StyleData["SubsubitemParagraph", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.23 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, { 0.0124074 FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}], 0.00248 FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}]}}], FontSize -> Dynamic[ 0.02 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "SubsubitemParagraph", "Slideshow Presentation", StyleDefinitions -> StyleData["SubsubitemParagraph", "Slideshow Working"]]], Cell[ StyleData[ "SubsubitemParagraph", "Scrolling Presentation", StyleDefinitions -> StyleData["SubsubitemParagraph", "Slideshow Working"]]], Cell[ StyleData["SubsubitemParagraph", "Printout"], CellMargins -> {{119, Inherited}, { Inherited, 0.1 Inherited}}]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Numbered", "Subsubsubsection"], Cell[ CellGroupData[{ Cell[ StyleData["ItemNumbered"], CellDingbat -> Cell[ TextData[{ CounterBox["ItemNumbered"], "."}], FontWeight -> "Bold"], CellMargins -> {{81, 10}, {4, 8}}, ReturnCreatesNewCell -> True, StyleKeyMapping -> {"Tab" -> "SubitemNumbered"}, CellGroupingRules -> { "GroupTogetherNestedGrouping", 15000}, CellFrameLabelMargins -> 4, CounterIncrements -> "ItemNumbered", CounterAssignments -> {{"SubitemNumbered", 0}, { "SubsubitemNumbered", 0}}, MenuSortingValue -> 1630, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 15], Cell[ StyleData["ItemNumbered", "SlideShow"], CellMargins -> {{ 0.135 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 10}}, CellFrameLabelMargins -> 6, FontSize -> 22], Cell[ StyleData["ItemNumbered", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.135 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 10}}], CellFrameLabelMargins -> 6, FontSize -> Dynamic[ 0.022 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "ItemNumbered", "Slideshow Presentation", StyleDefinitions -> StyleData["ItemNumbered", "Slideshow Working"]]], Cell[ StyleData[ "ItemNumbered", "Scrolling Presentation", StyleDefinitions -> StyleData["ItemNumbered", "Slideshow Working"]]], Cell[ StyleData["ItemNumbered", "Printout"], CellMargins -> {{65, Inherited}, {Inherited, Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubitemNumbered"], CellDingbat -> Cell[ TextData[{ CounterBox["ItemNumbered"], ".", CounterBox["SubitemNumbered"], "."}], FontWeight -> "Bold"], CellMargins -> {{105, 12}, {4, 4}}, ReturnCreatesNewCell -> True, StyleKeyMapping -> { "Tab" -> "SubsubitemNumbered", "Backspace" -> "ItemNumbered", KeyEvent["Tab", Modifiers -> {Shift}] -> "ItemNumbered"}, CellGroupingRules -> { "GroupTogetherNestedGrouping", 15100}, CellFrameLabelMargins -> 4, DefaultNewCellStyle -> "Item", CounterIncrements -> "SubitemNumbered", CounterAssignments -> {{"SubsubitemNumbered", 0}}, MenuSortingValue -> 1640, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 13.5], Cell[ StyleData["SubitemNumbered", "SlideShow"], CellMargins -> {{ 0.155 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 10}}, CellFrameLabelMargins -> 6, FontSize -> 22], Cell[ StyleData["SubitemNumbered", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.155 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 10}}], CellFrameLabelMargins -> 6, FontSize -> Dynamic[ 0.022 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "SubitemNumbered", "Slideshow Presentation", StyleDefinitions -> StyleData["SubitemNumbered", "Slideshow Working"]]], Cell[ StyleData[ "SubitemNumbered", "Scrolling Presentation", StyleDefinitions -> StyleData["SubitemNumbered", "Slideshow Working"]]], Cell[ StyleData["SubitemNumbered", "Printout"], CellMargins -> {{92, Inherited}, {Inherited, Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsubitemNumbered"], CellDingbat -> Cell[ TextData[{ CounterBox["ItemNumbered"], ".", CounterBox["SubitemNumbered"], ".", CounterBox["SubsubitemNumbered"], "."}], FontWeight -> "Bold"], CellMargins -> {{129, 12}, {4, 4}}, ReturnCreatesNewCell -> True, StyleKeyMapping -> { "Backspace" -> "SubitemNumbered", KeyEvent["Tab", Modifiers -> {Shift}] -> "SubitemNumbered"}, CellGroupingRules -> { "GroupTogetherNestedGrouping", 15200}, CellFrameLabelMargins -> 4, DefaultNewCellStyle -> "SubitemNumbered", CounterIncrements -> "SubsubitemNumbered", MenuSortingValue -> 1645, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "FontSet", "Text1"}]], FontSize -> 13], Cell[ StyleData["SubsubitemNumbered", "SlideShow"], CellMargins -> {{ 0.176 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 10}}, CellFrameLabelMargins -> 6, FontSize -> 22], Cell[ StyleData["SubsubitemNumbered", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.176 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {10, 10}}], CellFrameLabelMargins -> 6, FontSize -> Dynamic[ 0.022 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "SubsubitemNumbered", "Slideshow Presentation", StyleDefinitions -> StyleData["SubsubitemNumbered", "Slideshow Working"]]], Cell[ StyleData[ "SubsubitemNumbered", "Scrolling Presentation", StyleDefinitions -> StyleData["SubsubitemNumbered", "Slideshow Working"]]], Cell[ StyleData["SubsubitemNumbered", "Printout"], CellMargins -> {{119, Inherited}, { Inherited, Inherited}}]}, Closed]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Templates", "Subsubsection"], Cell[ CellGroupData[{ Cell[ StyleData[ "SideCaptionArray", StyleDefinitions -> StyleData["Text"]], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {Left}, "Rows" -> {Center}}, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}}], Cell[ StyleData["SideCaptionArray", "SlideShow"]], Cell[ StyleData["SideCaptionArray", "Slideshow Working"]], Cell[ StyleData[ "SideCaptionArray", "Slideshow Presentation", StyleDefinitions -> StyleData["SideCaptionArray", "Slideshow Working"]]], Cell[ StyleData[ "SideCaptionArray", "Scrolling Presentation", StyleDefinitions -> StyleData["SideCaptionArray", "Slideshow Working"]]], Cell[ StyleData["SideCaptionArray", "Printout"], CellMargins -> {{49, Inherited}, {Inherited, Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "SideCaption", StyleDefinitions -> StyleData["SmallText"]]], Cell[ StyleData["SideCaption", "SlideShow"]], Cell[ StyleData["SideCaption", "Slideshow Working"]], Cell[ StyleData[ "SideCaption", "Slideshow Presentation", StyleDefinitions -> StyleData["SideCaption", "Slideshow Working"]]], Cell[ StyleData[ "SideCaption", "Scrolling Presentation", StyleDefinitions -> StyleData["SideCaption", "Slideshow Working"]]], Cell[ StyleData["SideCaption", "Printout"]]}, Closed]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Hyperlinks", "Subsection"], Cell[ StyleData["Hyperlink"], MenuSortingValue -> None, FontColor -> Dynamic[ CurrentValue[{StyleHints, "ColorSet", "Display1"}]]], Cell[ StyleData["HyperlinkActive"], MenuSortingValue -> None, FontColor -> Dynamic[ CurrentValue[{StyleHints, "ColorSet", "Display2"}]]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Styles for Input and Output Cells", "Section"], Cell[ "The cells in this section define styles used for input and output to \ the kernel. Be careful when modifying, renaming, or removing these styles, \ because the front end associates special meanings with these style names. \ Some attributes for these styles are actually set in FormatType Styles (in \ the last section of this stylesheet). ", "Text"], Cell[ CellGroupData[{ Cell[ StyleData["Input"], StyleKeyMapping -> {"=" -> "WolframAlphaShort", "*" -> "Item"}, FontFamily -> Dynamic[ CurrentValue[{StyleHints, "CodeFont"}]], FontSize -> 13], Cell[ StyleData["Input", "SlideShow"], CellMargins -> {{ 0.135 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, {8, 15}}, LinebreakAdjustments -> {1, 2., 12., 1., 1.}, FontSize -> 20], Cell[ StyleData["Input", "Slideshow Working"], CellMargins -> Dynamic[{{ 0.16 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.12 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, { 0.00992593 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.0186111 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}}], LinebreakAdjustments -> {1, 2., 12., 1., 1.}, FontSize -> Dynamic[0.019 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]]], Cell[ StyleData[ "Input", "Slideshow Presentation", StyleDefinitions -> StyleData["Input", "Slideshow Working"]], CellEventActions -> {"LeftArrowKeyDown" :> FrontEndExecute[ FrontEndToken[ EvaluationNotebook[], "MovePrevious"]], "RightArrowKeyDown" :> FrontEndExecute[ FrontEndToken[ EvaluationNotebook[], "MoveNext"]]}], Cell[ StyleData[ "Input", "Scrolling Presentation", StyleDefinitions -> StyleData["Input", "Slideshow Working"]]], Cell[ StyleData["Input", "Printout"], CellMargins -> {{49, Inherited}, {Inherited, 8}}, LinebreakAdjustments -> {0.85, 2, 10, 1, 1}]}, Closed]], Cell[ StyleData["WolframAlphaShort", StyleDefinitions -> StyleData["Input"]], StyleKeyMapping -> { "=" -> "WolframAlphaLong", "Backspace" -> "Input"}, EvaluationMode -> "WolframAlphaShort", CellEventActions -> {"ReturnKeyDown" :> FrontEndTokenExecute[ EvaluationNotebook[], "HandleShiftReturn"]}, CellFrameLabels -> {{ Cell[ BoxData[ StyleBox[ "\[FreeformPrompt]", FontColor -> RGBColor[0.96875, 0.433594, 0.00390625]]]], None}, {None, None}}, DefaultFormatType -> TextForm, ShowCodeAssist -> False, FormatType -> TextForm, FontFamily -> "Helvetica"], Cell[ StyleData[ "WolframAlphaShortInput", StyleDefinitions -> StyleData["Input"]], EvaluationMode -> "WolframAlphaShort", CellEventActions -> {"ReturnKeyDown" :> FrontEndTokenExecute[ EvaluationNotebook[], "HandleShiftReturn"]}, CellFrameLabels -> {{ Cell[ BoxData[ StyleBox[ "\[FreeformPrompt]", FontColor -> RGBColor[0.96875, 0.433594, 0.00390625]]], CellBaseline -> Baseline], None}, {None, None}}, ShowCodeAssist -> False, FormatType -> TextForm, FontFamily -> "Helvetica"], Cell[ StyleData["WolframAlphaLong", StyleDefinitions -> StyleData["Input"]], StyleKeyMapping -> { "=" -> "Input", "Backspace" -> "WolframAlphaShort"}, EvaluationMode -> "WolframAlphaLong", CellEventActions -> {"ReturnKeyDown" :> FrontEndTokenExecute[ EvaluationNotebook[], "HandleShiftReturn"]}, CellFrameLabels -> {{ Cell[ BoxData[ StyleBox[ "\[WolframAlphaPrompt]", FontColor -> RGBColor[0.949219, 0.4375, 0.128906]]]], None}, {None, None}}, DefaultFormatType -> TextForm, ShowCodeAssist -> False, FormatType -> 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