(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 190623, 5959] NotebookOptionsPosition[ 128090, 4256] NotebookOutlinePosition[ 157278, 4994] CellTagsIndexPosition[ 157017, 4984] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["", "ZeroHeightSpacer", CellChangeTimes->{{3.572921955515625*^9, 3.572921958078125*^9}, { 3.572957338640625*^9, 3.572957339265625*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Programov\[AAcute]n\[IAcute]", " ", "II"}]], "Title", CellChangeTimes->{{3.572921945375*^9, 3.572921952453125*^9}}], Cell["Obsah", "OverviewSection", CellChangeTimes->{{3.572921960734375*^9, 3.572921963125*^9}}, CellTags->"Overview"], Cell[TextData[{ "V t\[EAcute]to \[CHacek]\[AAcute]sti \ roz\[SHacek]\[IAcute]\[RHacek]\[IAcute]me sv\[EAcute] znalosti o programov\ \[AAcute]n\[IAcute] v SW ", StyleBox["Mathematica.", FontSlant->"Italic"], " Zam\[EHacek]\[RHacek]\[IAcute]me se na n\[AAcute]sleduj\[IAcute]c\[IAcute]:" }], "Text", CellChangeTimes->{{3.5729219665*^9, 3.572922029890625*^9}}, CellTags->"Overview"], Cell[CellGroupData[{ Cell[TextData[{ "struktura a syntax jazyka ", StyleBox["Mathematica:", FontSlant->"Italic"], " v\[YAcute]razy, pravidla a zp\[URing]sob vyhodnocen\[IAcute]" }], "Item", CellChangeTimes->{{3.572922032375*^9, 3.572922066546875*^9}}, CellTags->"Overview"], Cell["\<\ tvorba funkc\[IAcute] s voliteln\[YAcute]mi parametry a varovn\[EAcute] zpr\ \[AAcute]vy\ \>", "Item", CellChangeTimes->{{3.572922075859375*^9, 3.572922108265625*^9}}, CellTags->"Overview"], Cell["\<\ funkcion\[AAcute]ln\[IAcute] programov\[AAcute]n\[IAcute], v\[CHacek]etn\ \[EHacek] anonymn\[IAcute] funkce, specifikaci \[UAcute]rovn\[EHacek] a srovn\ \[AAcute]n\[IAcute] s ostatn\[IAcute]mi styly\ \>", "Item", CellChangeTimes->{{3.572922112328125*^9, 3.57292216353125*^9}, { 3.572931240671875*^9, 3.57293125046875*^9}}, CellTags->"Overview"], Cell["\<\ ot\[AAcute]zky efektivity v\[YAcute]po\[CHacek]tu: odstran\[EHacek]n\[IAcute] \ redundance ve v\[YAcute]po\[CHacek]tu, pou\[ZHacek]it\[IAcute] funkc\[IAcute] \ vy\[SHacek]\[SHacek]\[IAcute] \[UAcute]rovn\[EHacek], p\[RHacek]esn\[EAcute] \ vs. nep\[RHacek]esn\[EAcute] v\[YAcute]po\[CHacek]ty\ \>", "Item", CellChangeTimes->{{3.57292217284375*^9, 3.572922235859375*^9}}, CellTags->"Overview"] }, Open ]], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Z\[AAcute]kladn\[IAcute] principy", "Section", CellChangeTimes->{{3.57292224340625*^9, 3.572922251609375*^9}}, CellTags->"Basic Principles"], Cell["Obsah", "OverviewSubsection", CellChangeTimes->{{3.57292225475*^9, 3.572922255578125*^9}}, CellTags->"Basic Principles"], Cell[CellGroupData[{ Cell["\<\ struktura atomick\[YAcute]ch a norm\[AAcute]ln\[IAcute]ch (slo\[ZHacek]en\ \[YAcute]ch) v\[YAcute]raz\[URing]\ \>", "Item", CellChangeTimes->{{3.5729255560625*^9, 3.5729255805*^9}}, CellTags->"Basic Principles"], Cell["\<\ vytvo\[RHacek]en\[IAcute] a pr\[AAcute]ce s v\[IAcute]ce pravidly definovan\ \[YAcute]mi pro jeden symbol\ \>", "Item", CellChangeTimes->{{3.5729255865*^9, 3.572925610203125*^9}}, CellTags->"Basic Principles"], Cell["\<\ vyhodnocen\[IAcute] pravidel, po\[RHacek]ad\[IAcute] vyhodnocen\[IAcute], \ nestandardn\[IAcute] vyhodnocen\[IAcute]\ \>", "Item", CellChangeTimes->{{3.57292561375*^9, 3.572925641515625*^9}}, CellTags->"Basic Principles"], Cell["atributy symbol\[URing]", "Item", CellChangeTimes->{{3.57292564409375*^9, 3.57292565184375*^9}}, CellTags->"Basic Principles"] }, Open ]], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Z\[AAcute]kladn\[IAcute] principy", "Color7", FontSlant->"Plain"]], "Subsection", CellChangeTimes->{{3.572922261421875*^9, 3.572922268609375*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "Programovac\[IAcute] jazyk SW ", StyleBox["Mathematica", FontSlant->"Italic"], " je zalo\[ZHacek]en na n\[EHacek]kolika jednoduch\[YAcute]ch prinicpech. \ Tyto prinicpy mohou b\[YAcute]t pou\[ZHacek]ity k zodpov\[EHacek]zen\[IAcute] \ v\[SHacek]ech z\[AAcute]kladn\[IAcute]ch ot\[AAcute]zek o programov\[AAcute]n\ \[IAcute] v SW ", StyleBox["Mathematica", FontSlant->"Italic"], ". " }], "Text", CellChangeTimes->{{3.572925658796875*^9, 3.5729257510625*^9}}, CellTags->"Basic Principles"], Cell[CellGroupData[{ Cell["V\[SHacek]e je v\[YAcute]raz.", "Item", CellChangeTimes->{{3.57292575334375*^9, 3.572925759515625*^9}}, CellTags->"Basic Principles"], Cell["\<\ Vyhodnocen\[IAcute] pracuje aplikov\[AAcute]n\[IAcute]m pravidel spojen\ \[YAcute]ch se symboly. \ \>", "Item", CellChangeTimes->{{3.572925765390625*^9, 3.57292578915625*^9}}, CellTags->"Basic Principles"], Cell["\<\ Pravidla jsou aplikov\[AAcute]na, dokud existuj\[IAcute] pravidla, kter\ \[AAcute] lze aplikovat.\ \>", "Item", CellChangeTimes->{{3.572925795046875*^9, 3.572925836390625*^9}}, CellTags->"Basic Principles"], Cell["\<\ \[CapitalCHacek]\[AAcute]sti v\[YAcute]raz\[URing] jsou vyhodnoceny v dan\ \[EAcute]m po\[RHacek]ad\[IAcute].\ \>", "Item", CellChangeTimes->{{3.572925841078125*^9, 3.572925870546875*^9}}, CellTags->"Basic Principles"] }, Open ]], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicpy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "V\[YAcute]razy" }], "Subsection", CellChangeTimes->{{3.5729222754375*^9, 3.572922285234375*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "Jak bylo uk\[AAcute]z\[AAcute]no v prvn\[IAcute] \[CHacek]\[AAcute]sti o \ programov\[AAcute]n\[IAcute], v\[SHacek]echny viditeln\[EAcute] informace v ", StyleBox["Mathematica", FontSlant->"Italic"], " jsou reprezentov\[AAcute]ny v\[YAcute]razy a ka\[ZHacek]d\[YAcute] v\ \[YAcute]raz je bu\[DHacek] atomick\[YAcute] v\[YAcute]raz \ (\[CHacek]\[IAcute]sla, \[RHacek]et\[EHacek]zce, symboly) nebo ve form\ \[EHacek] ", Cell[BoxData[ RowBox[{ StyleBox["h", "TI"], "[", RowBox[{ SubscriptBox[ StyleBox["e", "TI"], StyleBox["1", "TR"]], ",", SubscriptBox[ StyleBox["e", "TI"], StyleBox["2", "TR"]], ",", "\[Ellipsis]", ",", StyleBox[ SubscriptBox["e", "n"], "TI"]}], "]"}]]], ". , nap\[RHacek]\[IAcute]klad v\[YAcute]raz ", Cell[BoxData[ RowBox[{"f", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]]], " m\[AAcute] hlavu ", StyleBox["f", "MR"], " a 3 argumenty, kter\[EAcute] jsou atomy." }], "Text", CellChangeTimes->{{3.57292589325*^9, 3.572926058390625*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ Cell[BoxData[ RowBox[{"Head", "[", StyleBox["expr", "TI"], "]"}]]], " vr\[AAcute]t\[IAcute] hlavu v\[YAcute]razu" }], "MathCaption", CellChangeTimes->{{3.572926066203125*^9, 3.57292607578125*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Head", "[", RowBox[{"f", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ Cell[BoxData[ RowBox[{"Length", "[", StyleBox["expr", "TI"], "]"}]]], " vrac\[IAcute] po\[CAcute]et prvk\[URing] ve v\[YAcute]razu" }], "MathCaption", CellChangeTimes->{{3.57292607975*^9, 3.5729261003125*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Length", "[", RowBox[{"f", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "Tato struktura se vztahuje na v\[SHacek]echny v\[YAcute]razy v ", StyleBox["Mathematica", FontSlant->"Italic"], ", dokonce i na ty, kter\[EAcute] maj\[IAcute] na prvn\[IAcute] pohled odli\ \[SHacek]nou strukturu od uveden\[EAcute] z\[AAcute]kladn\[IAcute] struktury." }], "MathCaption", CellChangeTimes->{{3.57292610490625*^9, 3.57292618646875*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"FullForm", "[", RowBox[{"a", "+", "b", "+", "c"}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"FullForm", "[", RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "Tato jednotnost datov\[EAcute] struktury je z\[AAcute]kladn\[IAcute] rys SW \ ", StyleBox["Mathematica", FontSlant->"Italic"], ". S ohledem na tuto vlastnost m\[URing]\[ZHacek]e b\[YAcute]t \ v\[YAcute]sledek jak\[EAcute]hokoliv v\[YAcute]po\[CHacek]tu pou\[ZHacek]it \ jako vstup do dal\[SHacek]\[IAcute]ho v\[YAcute]po\[CHacek]tu. Nav\[IAcute]c \ znalost manipulace se strukturou z\[AAcute]kladn\[IAcute]ch v\[YAcute]raz\ \[URing] V\[AAcute]m umo\[ZHacek]\[NHacek]uje pracovat s jak\[YAcute]mkoliv \ objektem v ", StyleBox["Mathematica", FontSlant->"Italic"], "." }], "Text", CellChangeTimes->{{3.572926193453125*^9, 3.572926360921875*^9}}, CellTags->"Basic Principles"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicpy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], StyleBox["Pravidla vyhodnocen\[IAcute]", "Color7"], StyleBox[" ", "Color7", FontSlant->"Italic"] }], "Subsection", CellChangeTimes->{{3.572922290046875*^9, 3.5729223081875*^9}}, CellTags->"Basic Principles"], Cell["\<\ Dal\[SHacek]\[IAcute]m z\[AAcute]kladn\[IAcute]m prinicpem je spojen\[IAcute] \ vyhodnocovac\[IAcute]ch pravidel se symbolem a vyhodnocov\[AAcute]n\[IAcute] \ dle t\[EHacek]chto pravidel.\ \>", "Text", CellChangeTimes->{{3.572926377359375*^9, 3.57292642171875*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "N\[EHacek]kter\[EAcute] funkce maj\[IAcute] vestav\[EHacek]n\[EAcute] \ vyhodnocovac\[IAcute] pravidla. N\[AAcute]sleduje v\[YAcute]po\[CHacek]et, \ kter\[YAcute] pou\[ZHacek]\[IAcute]v\[AAcute] vestav\[EHacek]n\[EAcute] \ pravidlo pro vyhodnocen\[IAcute] funkce", Cell[BoxData[ ButtonBox[ RowBox[{" ", "Cos"}], BaseStyle->"Link", ButtonData->"paclet:ref/Cos"]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.57292642875*^9, 3.572926503109375*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Cos", "[", FractionBox["\[Pi]", "4"], "]"}]], "Input", CellTags->"Basic Principles"], Cell["\<\ Nov\[AAcute] pravidla vyhodnocen\[IAcute] jsou p\[RHacek]id\[AAcute]na pou\ \[ZHacek]it\[IAcute]m p\[RHacek]i\[RHacek]azen\[IAcute]. \ \>", "Text", CellChangeTimes->{{3.572926510671875*^9, 3.57292653690625*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad p\[RHacek]i\[RHacek]azen\[IAcute] ", Cell[BoxData[ RowBox[{"x", "=", "5"}]]], " zav\[AAcute]d\[IAcute] vyhodocovac\[IAcute] pravidlo, kter\[EAcute] symbol \ ", StyleBox["x", "MR"], " p\[RHacek]ep\[IAcute]\[SHacek]e hodnotou ", StyleBox["5,", "MR"], " kdykoliv je symbol vyhodnocen." }], "MathCaption", CellChangeTimes->{{3.57292654221875*^9, 3.572926624875*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"x", "=", "5"}]], "Input", CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{ RowBox[{"2", "x"}], "+", "1"}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "P\[RHacek]i\[RHacek]azen\[IAcute] ", Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{"Cos", "[", "x", "]"}]}]]], " zav\[AAcute]d\[IAcute] vyhodnocovac\[IAcute] pravidlo, kter\[EAcute] ka\ \[ZHacek]d\[YAcute] v\[YAcute]raz, kter\[YAcute] odpov\[IAcute]d\[AAcute] \ vzoru ", Cell[BoxData[ RowBox[{"f", "[", "x_", "]"}]]], " p\[RHacek]ep\[IAcute]\[SHacek]e v\[YAcute]razem ", Cell[BoxData[ RowBox[{"Cos", "[", "x", "]"}]]], "." }], "MathCaption", CellChangeTimes->{{3.572926650546875*^9, 3.57292671365625*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{"Cos", "[", "x", "]"}]}]], "Input", CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"f", "[", "1", "]"}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "Vy\[CHacek]isti hodnoty ", StyleBox["f", "MR"], " a ", StyleBox["x", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.57292672296875*^9, 3.57292673565625*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"f", ",", "x"}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicpy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], StyleBox["Pravidla vyhodnocen\[IAcute] symbol\[URing]", "Color7"] }], "Subsection", CellChangeTimes->{{3.5729223266875*^9, 3.5729223891875*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "S jedn\[IAcute]m symbolem m\[URing]\[ZHacek]e b\[YAcute]t sv\[AAcute]z\ \[AAcute]no mnoho pravidel. N\[AAcute]sleduj\[IAcute]c\[IAcute] 3 p\[RHacek]i\ \[RHacek]azen\[IAcute] jsou sv\[AAcute]z\[AAcute]na s jedn\[IAcute]m symbolem \ ", StyleBox["f", "MR"], "." }], "Text", CellChangeTimes->{{3.572926796171875*^9, 3.572926845265625*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_Integer", "]"}], ":=", RowBox[{"x", "+", "1"}]}]], "Input", CellChangeTimes->{{3.4930538992513437`*^9, 3.49305390954187*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_Real", "]"}], ":=", RowBox[{"x", "+", "2"}]}]], "Input", CellChangeTimes->{{3.4930539127794313`*^9, 3.493053920979134*^9}, { 3.493053957374555*^9, 3.493053958628446*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", SuperscriptBox["x", "2"]}]], "Input", CellChangeTimes->{{3.4930539240330753`*^9, 3.493053928516325*^9}, { 3.493053963028613*^9, 3.493053964791621*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"f", "[", "2", "]"}], ",", RowBox[{"f", "[", "2.0", "]"}], ",", RowBox[{"f", "[", "\[Alpha]", "]"}]}], "}"}]], "Input", CellChangeTimes->{{3.493053968002602*^9, 3.493053979641224*^9}}], Cell[TextData[{ "V\[SHacek]imn\[EHacek]te si, \[ZHacek]e obecn\[EAcute] pravidlo ", Cell[BoxData[ RowBox[{"f", "[", "x_", "]"}]]], " je aplikov\[AAcute]no ve v\[SHacek]ech p\[RHacek]\[IAcute]padech, kdy \ nejsou aplikov\[AAcute]na prvn\[IAcute] dv\[EHacek] pravidla." }], "Text", CellChangeTimes->{{3.57292685240625*^9, 3.572926898109375*^9}}], Cell["\<\ Nav\[IAcute]c je mo\[ZHacek]n\[EAcute] pomoc\[IAcute] vstupn\[IAcute]ch vzor\ \[URing] rozli\[SHacek]it pou\[ZHacek]it\[IAcute] pravidel pro r\[URing]zn\ \[EAcute] vstupy. Je mo\[ZHacek]n\[EAcute] pou\[ZHacek]\[IAcute]t i \ strukturovan\[EAcute] argumenty, kter\[EAcute] ur\[CHacek]\[IAcute] chov\ \[AAcute]n\[IAcute] funkce.\ \>", "Text", CellChangeTimes->{{3.4930540499903727`*^9, 3.493054120989654*^9}, { 3.57292692990625*^9, 3.572927004671875*^9}}], Cell[TextData[{ "P\[RHacek]\[IAcute]kladem jsou dv\[EHacek] pravidla pro funkci ", StyleBox["log", "MR"], " kter\[EAcute] ur\[CHacek]\[UAcute]j\[IAcute] dv\[EHacek] vlastnosti funkce \ logaritmus neboli pravidla pro po\[CHacek]\[IAcute]t\[AAcute]n\[IAcute] ve v\ \[YAcute]razech s logaritmy." }], "MathCaption", CellChangeTimes->{{3.57292701196875*^9, 3.57292710290625*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"log", "[", RowBox[{"a_", "*", "b_"}], "]"}], ":=", RowBox[{ RowBox[{"log", "[", "a", "]"}], "+", RowBox[{"log", "[", "b", "]"}]}]}]], "Input", CellChangeTimes->{{3.493053860067251*^9, 3.4930538744037046`*^9}, { 3.4930541542049103`*^9, 3.493054159679598*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{ RowBox[{"log", "[", SuperscriptBox["a_", "n_"], "]"}], ":=", RowBox[{"n", " ", RowBox[{"log", "[", "a", "]"}]}]}]], "Input", CellChangeTimes->{{3.493053887129361*^9, 3.4930538874160624`*^9}, { 3.493054163468995*^9, 3.493054179554201*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"log", "[", RowBox[{"x", " ", "y", " ", SuperscriptBox["z", "5"]}], "]"}]], "Input", CellChangeTimes->{{3.4930542528898087`*^9, 3.4930542642919073`*^9}}], Cell[TextData[{ "Pro zru\[SHacek]en\[IAcute] po\[ZHacek]adovan\[EAcute]ho pravidla je mo\ \[ZHacek]n\[EAcute] pou\[ZHacek]\[IAcute]t p\[RHacek]i\[RHacek]azen\[IAcute] ", Cell[BoxData[ RowBox[{ RowBox[{"log", "[", RowBox[{"a_", " ", "b_"}], "]"}], "=."}]]], " " }], "MathCaption", CellChangeTimes->{{3.572927134796875*^9, 3.572927181375*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{ RowBox[{"log", "[", RowBox[{"a_", " ", "b_"}], "]"}], "=."}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "V\[SHacek]imn\[EHacek]te si, \[ZHacek]e pravidlo pro ", Cell[BoxData[ RowBox[{"log", "[", RowBox[{"a_", " ", "b_"}], "]"}]]], " bylo odstran\[EHacek]no." }], "MathCaption", CellChangeTimes->{{3.572927188140625*^9, 3.572927208140625*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"?", "log"}]], "Input", CellChangeTimes->{{3.493054348368479*^9, 3.4930543486426163`*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ StyleBox["Clear", "MR"], " zru\[SHacek]te v\[SHacek]echna pravidla sv\[AAcute]zan\[AAcute] s pou\ \[ZHacek]it\[YAcute]mi symboly." }], "MathCaption", CellChangeTimes->{{3.572927228453125*^9, 3.57292725171875*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"f", ",", "log"}], "]"}]], "Input", CellChangeTimes->{{3.493054362561411*^9, 3.493054363204483*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "V\[SHacek]echna vyhodnocovac\[IAcute] pravidla sv\[AAcute]zan\[AAcute] s ", StyleBox["f", "MR"], " byla nyn\[IAcute] odstran\[EHacek]na." }], "MathCaption", CellChangeTimes->{{3.572927261390625*^9, 3.57292728628125*^9}, { 3.57292743503125*^9, 3.572927439640625*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"?", "f"}]], "Input", CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"?", "log"}]], "Input", CellChangeTimes->{{3.493054401413012*^9, 3.493054402141638*^9}}], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicp:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "Nekone\[CHacek]n\[EAcute] vyhodnocen\[IAcute]" }], "Subsection", CellChangeTimes->{{3.57292240228125*^9, 3.572922424625*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "Dal\[SHacek]\[IAcute] z\[AAcute]kladn\[IAcute] prinicp SW ", StyleBox["Mathematica", FontSlant->"Italic"], " pou\[ZHacek]\[IAcute]v\[AAcute] vyhodnocovac\[IAcute] strategii naz\ \[YAcute]vanou \[OpenCurlyDoubleQuote]nekone\[CHacek]n\[EAcute]\ \[CloseCurlyDoubleQuote] vyhodnocov\[AAcute]n\[IAcute]. Nekone\[CHacek]n\ \[EAcute] vyhodnocov\[AAcute]n\[IAcute] znamen\[AAcute], \[ZHacek]e pravidla \ jsou aplikov\[AAcute]na, dokud existuje jak\[EAcute]koliv pravidlo, \ aplikovateln\[EAcute] na vyhodnocov\[AAcute]n\[YAcute] v\[YAcute]raz." }], "Text", CellChangeTimes->{{3.5729274575625*^9, 3.5729275921875*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad p\[RHacek]i\[RHacek]azen\[IAcute] ", Cell[BoxData[ RowBox[{"x1", "=", "x2"}]]], " zav\[AAcute]d\[IAcute] vyhodnocovac\[IAcute] pravidlo, kter\[EAcute] \ nahrad\[IAcute] ", StyleBox["x1", "MR"], " symbolem ", StyleBox["x2", "MR"], ", p\[RHacek]i\[RHacek]azen\[IAcute] ", Cell[BoxData[ RowBox[{"x2", "=", "x3"}]]], " zav\[AAcute]d\[IAcute] pravidlo, kter\[EAcute] nahrad\[IAcute] ", StyleBox["x2", "MR"], " symbolem ", StyleBox["x3", "MR"], ", atd." }], "MathCaption", CellChangeTimes->{{3.57292759590625*^9, 3.572927685140625*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"x1", "=", "x2"}]], "Input", CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"x2", "=", "x3"}]], "Input", CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"x3", "=", "4"}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "V\[SHacek]echna tato pravidla jsou aplikov\[AAcute]na p\[RHacek]i evaluaci ", StyleBox["x1", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.572927697375*^9, 3.572927718890625*^9}}, CellTags->"Basic Principles"], Cell[BoxData["x1"], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "Odstra\[NHacek]te v\[SHacek]echna pravidlo pro ", StyleBox["x1", "MR"], ", ", StyleBox["x2", "MR"], ", a ", StyleBox["x3", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.57292776253125*^9, 3.572927779875*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"x1", ",", "x2", ",", "x3", ",", "x"}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicpy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "Po\[RHacek]ad\[IAcute] vyhodnocen\[IAcute]" }], "Subsection", CellChangeTimes->{{3.572922430375*^9, 3.572922450328125*^9}, 3.57292778521875*^9}, CellTags->"Basic Principles"], Cell["\<\ Nakonec n\[EHacek]kolik jednoduch\[YAcute]ch prinicp\[URing], kter\[EAcute] \ ur\[CHacek]uj\[IAcute] po\[RHacek]ad\[IAcute] vyhodnocen\[IAcute] \ v\[YAcute]raz\[URing] a prvk\[URing] ve v\[YAcute]razech.\ \>", "Text", CellChangeTimes->{{3.5729277935625*^9, 3.572927837296875*^9}}, CellTags->"Basic Principles"], Cell["\<\ Obecn\[EHacek] jsou argumenty funkce vyhodnoceny p\[RHacek]ed t\[IAcute]m, ne\ \[ZHacek] jsou vlo\[ZHacek]eny do funkce. T\[IAcute]mto \ po\[RHacek]ad\[IAcute]m vyhodnocen\[IAcute] se \[RHacek]\[IAcute]d\[IAcute] v\ \[EHacek]t\[SHacek]ina programovac\[IAcute]ch jazyk\[URing].\ \>", "Text", CellChangeTimes->{{3.57292784575*^9, 3.5729279136875*^9}}, CellTags->"Basic Principles"], Cell["\<\ Existuje n\[EHacek]kolik d\[URing]le\[ZHacek]it\[YAcute]ch vyj\[IAcute]mek, \ ve kter\[YAcute]ch argumenty funkce jsou posl\[AAcute]ny do funkce bez \ vyhodnocen\[IAcute]. \ \>", "Text", CellChangeTimes->{{3.572927921734375*^9, 3.5729279708125*^9}, { 3.572957379296875*^9, 3.572957379859375*^9}}, CellTags->"Basic Principles"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicpy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "Standardn\[IAcute] vyhodnocen\[IAcute]" }], "Subsection", CellChangeTimes->{{3.57292245653125*^9, 3.572922475390625*^9}}, CellTags->"Basic Principles"], Cell["\<\ Dle standardn\[IAcute]ho po\[RHacek]ad\[IAcute] vyhodnocen\[IAcute] jsou \ argumenty funkce vyhodnoceny p\[RHacek]ed t\[IAcute]m, ne\[ZHacek] jsou vlo\ \[ZHacek]eny do volan\[EAcute] funkce.\ \>", "Text", CellChangeTimes->{{3.572927982828125*^9, 3.572928028953125*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad v\[YAcute]raz ", Cell[BoxData[ RowBox[{"Head", "[", RowBox[{"x", "+", "x"}], "]"}]]], " vrac\[IAcute] ", Cell[BoxData[ ButtonBox["Times", BaseStyle->"Link", ButtonData->"paclet:ref/Times"]], "InlineFormula"], ", a\[CHacek]koli bychom o\[CHacek]ek\[AAcute]vali ", Cell[BoxData[ ButtonBox["", BaseStyle->"Link", ButtonData->"paclet:ref/Times"]], "InlineFormula"], Cell[BoxData[ ButtonBox["Plus", BaseStyle->"Link", ButtonData->"paclet:ref/Plus"]]] }], "MathCaption", CellChangeTimes->{{3.572928031140625*^9, 3.572928122171875*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Head", "[", RowBox[{"x", "+", "x"}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "A\[CHacek]koliv hlava ", Cell[BoxData[ RowBox[{"x", "+", "x"}]]], " je ", Cell[BoxData[ ButtonBox["Plus", BaseStyle->"Link", ButtonData->"paclet:ref/Plus"]], "InlineFormula"], ", ", Cell[BoxData[ RowBox[{"x", "+", "x"}]]], " je nejd\[RHacek]\[IAcute]ve vyhodnoceno jako ", Cell[BoxData[ RowBox[{"2", " ", "x"}]]], " a potom je zavol\[AAcute]na funkce ", Cell[BoxData[ ButtonBox["Head", BaseStyle->"Link", ButtonData->"paclet:ref/Head"]], "InlineFormula"], "." }], "Text", CellChangeTimes->{{3.572928095359375*^9, 3.572928159609375*^9}}, CellTags->"Basic Principles"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicpy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "Nesdandardn\[IAcute] vyhodnocen\[IAcute]" }], "Subsection", CellChangeTimes->{{3.572922478109375*^9, 3.572922507578125*^9}}, CellTags->"Basic Principles"], Cell["\<\ Existuje mnoho funkc\[IAcute], u kter\[AAcute]ch je u\[ZHacek]ite\[CHacek]n\ \[EAcute] a n\[EHacek]kdy nutn\[EAcute] poru\[SHacek]it standardn\[IAcute] po\ \[RHacek]ad\[IAcute] vyhodnocen\[IAcute] a vkl\[AAcute]dat argumenty do \ funkce bez jejich vyhodnocen\[IAcute].\ \>", "Text", CellChangeTimes->{{3.572928166671875*^9, 3.57292823403125*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]lad ", Cell[BoxData[ ButtonBox["If", BaseStyle->"Link", ButtonData->"paclet:ref/If"]], "InlineFormula"], " funkce pracuje pouze, kdy\[ZHacek] jeden argument z\[URing]st\[AAcute]v\ \[AAcute] nevyhodnocen, nebo\[THacek] \[UAcute]kolem funkce je vyhodnotit pr\ \[AAcute]v\[EHacek] jeden argument." }], "MathCaption", CellChangeTimes->{{3.572928244375*^9, 3.572928333140625*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"If", "[", RowBox[{ RowBox[{"x", ">", "y"}], ",", RowBox[{"Print", "[", RowBox[{"1", "+", "1"}], "]"}], ",", RowBox[{"Print", "[", RowBox[{"2", "+", "2"}], "]"}]}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "V\[EHacek]t\[SHacek]ina numerick\[YAcute]ch funkc\[IAcute] jako je nap\ \[RHacek]. ", Cell[BoxData[ ButtonBox["NIntegrate", BaseStyle->"Link", ButtonData->"paclet:ref/NIntegrate"]], "InlineFormula"], ", nech\[AAcute]v\[AAcute] tak\[EAcute] sv\[EAcute] argumenty nevyhodnocen\ \[EAcute]. Integrand je do funkce ", Cell[BoxData[ ButtonBox["NIntegrate", BaseStyle->"Link", ButtonData->"paclet:ref/NIntegrate"]], "InlineFormula"], " vlo\[ZHacek]en jako nevyhodnocen\[YAcute] a je vyhodnocen a\[ZHacek] por p\ \[RHacek]i\[RHacek]azen\[IAcute] \[CHacek]\[IAcute]seln\[EAcute] hodnoty \ argumentu ", StyleBox["x", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.57292834671875*^9, 3.572928456734375*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}]}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicpy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "Atributy vyhodnocen\[IAcute]" }], "Subsection", CellChangeTimes->{{3.572922523234375*^9, 3.572922546890625*^9}}, CellTags->"Basic Principles"], Cell["\<\ Atributy ur\[CHacek]uj\[IAcute] vlastnosti symbolu.\ \>", "Text", CellChangeTimes->{{3.572928480515625*^9, 3.57292849271875*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "Nestandardn\[IAcute] vyhodnocen\[IAcute] je kontrolov\[AAcute]no \ n\[AAcute]sleduj\[IAcute]c\[IAcute]mi atributy ", Cell[BoxData[ ButtonBox["HoldAll", BaseStyle->"Link", ButtonData->"paclet:ref/HoldAll"]], "InlineFormula"], ", ", Cell[BoxData[ ButtonBox["HoldFirst", BaseStyle->"Link", ButtonData->"paclet:ref/HoldFirst"]], "InlineFormula"], ", ", Cell[BoxData[ ButtonBox["HoldRest", BaseStyle->"Link", ButtonData->"paclet:ref/HoldRest"]], "InlineFormula"], ", a ", Cell[BoxData[ ButtonBox["HoldAllComplete", BaseStyle->"Link", ButtonData->"paclet:ref/HoldAllComplete"]], "InlineFormula"], ". Funkce ", Cell[BoxData[ ButtonBox["Attributes", BaseStyle->"Link", ButtonData->"paclet:ref/Attributes"]], "InlineFormula"], " vrac\[IAcute] seznam v\[SHacek]ech atribut\[URing] symbolu." }], "Text", CellChangeTimes->{{3.572928494796875*^9, 3.572928553234375*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad, ", Cell[BoxData[ ButtonBox["NIntegrate", BaseStyle->"Link", ButtonData->"paclet:ref/NIntegrate"]], "InlineFormula"], " a ", Cell[BoxData[ ButtonBox["Plot", BaseStyle->"Link", ButtonData->"paclet:ref/Plot"]], "InlineFormula"], " maj\[IAcute] atribbut ", Cell[BoxData[ ButtonBox["HoldAll", BaseStyle->"Link", ButtonData->"paclet:ref/HoldAll"]], "InlineFormula"], ", tak\[ZHacek]e ob\[EHacek] funkce v\[SHacek]echny sv\[EAcute] argumenty \ nech\[AAcute]vaj\[IAcute] bez vyhodnocen\[IAcute]." }], "MathCaption", CellChangeTimes->{{3.57292855796875*^9, 3.572928626359375*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Attributes", "[", "NIntegrate", "]"}]], "Input", CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Attributes", "[", "Plot", "]"}]], "Input", CellTags->"Basic Principles"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicpy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "Kontrola po\[RHacek]ad\[IAcute] vyhodnocen\[IAcute]" }], "Subsection", CellChangeTimes->{{3.572922552796875*^9, 3.572922574734375*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "N\[EHacek]kdy je u\[ZHacek]ite\[CHacek]n\[EAcute] aktivovat vyhodnocen\ \[IAcute] argument\[URing], kter\[EAcute] by jinak s ohledem na nastaven\ \[IAcute] atribut\[URing] z\[URing]staly nevyhodnoceny. Toto provedeme pomoc\ \[IAcute] ", Cell[BoxData[ ButtonBox["Evaluate", BaseStyle->"Link", ButtonData->"paclet:ref/Evaluate"]], "InlineFormula"], "." }], "Text", CellChangeTimes->{{3.572928637796875*^9, 3.5729287163125*^9}}, CellTags->"Basic Principles"], Cell["\<\ Nap\[RHacek]\[IAcute]klad uva\[ZHacek]ujem vykreslen\[IAcute] seznamu 8 \ Legendrov\[YAcute]ch polynom\[URing].\ \>", "MathCaption", CellChangeTimes->{{3.57292872015625*^9, 3.5729287645*^9}}, CellTags->"Basic Principles"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"LegendreP", "[", RowBox[{"n", ",", "x"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "8"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.57292898853125*^9, 3.5729289986875*^9}, { 3.5729290308125*^9, 3.572929032046875*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"3", " ", SuperscriptBox["x", "2"]}]}], ")"}]}], ",", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", "x"}], "+", RowBox[{"5", " ", SuperscriptBox["x", "3"]}]}], ")"}]}], ",", RowBox[{ FractionBox["1", "8"], " ", RowBox[{"(", RowBox[{"3", "-", RowBox[{"30", " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"35", " ", SuperscriptBox["x", "4"]}]}], ")"}]}], ",", RowBox[{ FractionBox["1", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{"15", " ", "x"}], "-", RowBox[{"70", " ", SuperscriptBox["x", "3"]}], "+", RowBox[{"63", " ", SuperscriptBox["x", "5"]}]}], ")"}]}], ",", RowBox[{ FractionBox["1", "16"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "5"}], "+", RowBox[{"105", " ", SuperscriptBox["x", "2"]}], "-", RowBox[{"315", " ", SuperscriptBox["x", "4"]}], "+", RowBox[{"231", " ", SuperscriptBox["x", "6"]}]}], ")"}]}], ",", RowBox[{ FractionBox["1", "16"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "35"}], " ", "x"}], "+", RowBox[{"315", " ", SuperscriptBox["x", "3"]}], "-", RowBox[{"693", " ", SuperscriptBox["x", "5"]}], "+", RowBox[{"429", " ", SuperscriptBox["x", "7"]}]}], ")"}]}], ",", RowBox[{ FractionBox["1", "128"], " ", RowBox[{"(", RowBox[{"35", "-", RowBox[{"1260", " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"6930", " ", SuperscriptBox["x", "4"]}], "-", RowBox[{"12012", " ", SuperscriptBox["x", "6"]}], "+", RowBox[{"6435", " ", SuperscriptBox["x", "8"]}]}], ")"}]}]}], "}"}]], "Output", CellChangeTimes->{{3.572928985859375*^9, 3.572929000890625*^9}}, CellTags->"Basic Principles"] }, Open ]], Cell[TextData[{ "Pokud jednodu\[SHacek]e pou\[ZHacek]ijeme seznam polynom\[URing] jako prvn\ \[IAcute] argument funkce ", Cell[BoxData[ ButtonBox["Plot", BaseStyle->"Link", ButtonData->"paclet:ref/Plot"]], "InlineFormula"], ", v\[YAcute]po\[CHacek]et spot\[RHacek]ebuje v\[IAcute]ce \[CHacek]asu, \ nebo\[THacek] \[OpenCurlyDoubleQuote]nevyhodnocen\[AAcute]\ \[CloseCurlyDoubleQuote] tabulka polynom\[URing] se bude znovu vyhodnocovat \ pro ka\[ZHacek]dou hodnotu ", StyleBox["x", "MR"], ". V\[SHacek]imn\[EHacek]te si tak\[EAcute], \[ZHacek]e v tomto p\[RHacek]\ \[IAcute]pad\[EHacek] ", StyleBox["Mathematica", FontSlant->"Italic"], " bere v\[SHacek]echny polynomy jako jednu funkci a vykresl\[IAcute] je \ jednou barvou." }], "MathCaption", CellChangeTimes->{{3.57292877934375*^9, 3.572928983015625*^9}, { 3.572929038328125*^9, 3.572929039046875*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"LegendreP", "[", RowBox[{"n", ",", "x"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "8"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[TextData[{ "Vlo\[ZHacek]en\[IAcute]m ", Cell[BoxData[ ButtonBox["Table", BaseStyle->"Link", ButtonData->"paclet:ref/Table"]], "InlineFormula"], " do ", Cell[BoxData[ ButtonBox["Evaluate", BaseStyle->"Link", ButtonData->"paclet:ref/Evaluate"]], "InlineFormula"], " iniciujeme vyhodnocen\[IAcute] seznamu polynomu, jeho\[ZHacek] \ v\[YAcute]sledkem je seznam jednotliv\[YAcute]ch polynom\[URing], kter\ \[EAcute] jsou pot\[EAcute] rychleji vykresleny jako jednotliv\[EAcute] \ funkce. " }], "MathCaption", CellChangeTimes->{{3.57292904975*^9, 3.57292910071875*^9}, { 3.5729291525625*^9, 3.572929241921875*^9}}, CellTags->"Basic Principles"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"LegendreP", "[", RowBox[{"n", ",", "x"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "8"}], "}"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Basic Principles"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Z\[AAcute]kladn\[IAcute] prinicpy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "Souhrn" }], "Subsection", CellChangeTimes->{{3.572922582671875*^9, 3.572922590296875*^9}}, CellTags->"Basic Principles"], Cell[TextData[{ "V\[EHacek]t\[SHacek]ina z\[AAcute]kladn\[IAcute]ch ot\[AAcute]zek o \ programov\[AAcute]n\[IAcute] v ", StyleBox["Mathematica", FontSlant->"Italic"], " m\[URing]\[ZHacek]e b\[YAcute]t zodpov\[EHacek]zeno s pou\[ZHacek]it\ \[IAcute]m n\[EHacek]kolika jednoduch\[YAcute]ch princip\[URing]." }], "Text", CellChangeTimes->{{3.572929267375*^9, 3.572929312171875*^9}}, CellTags->"Basic Principles"], Cell[CellGroupData[{ Cell["V\[SHacek]e je v\[YAcute]raz.", "Item", CellChangeTimes->{{3.5729293153125*^9, 3.5729293204375*^9}}, CellTags->"Basic Principles"], Cell["\<\ Vyhodnocen\[IAcute] symbolu prob\[IAcute]h\[AAcute] aplikac\[IAcute] pravidel \ sv\[AAcute]zan\[YAcute]ch se symbolem.\ \>", "Item", CellChangeTimes->{{3.5729293248125*^9, 3.57292936390625*^9}}, CellTags->"Basic Principles"], Cell["\<\ Pravidla jsou aplikov\[AAcute]na, dokud lze aplikovat jak\[EAcute]koliv \ pravidlo sv\[AAcute]zan\[EAcute] se symbolem.\ \>", "Item", CellChangeTimes->{{3.57292976046875*^9, 3.572929791921875*^9}}, CellTags->"Basic Principles"], Cell["\<\ \[CapitalCHacek]\[AAcute]sti v\[YAcute]raz\[URing] jsou vyhodnocov\[AAcute]ny \ v dan\[EAcute]m po\[RHacek]ad\[IAcute].\ \>", "Item", CellChangeTimes->{{3.572929795640625*^9, 3.572929816046875*^9}}, CellTags->"Basic Principles"] }, Open ]], Cell["", "Text", CellChangeTimes->{3.572929820453125*^9}, CellTags->"Basic Principles"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Funkcion\[AAcute]ln\[IAcute] programov\[AAcute]n\[IAcute]", "Section", CellChangeTimes->{{3.572922598140625*^9, 3.572922602703125*^9}}, CellTags->"Functional Programming"], Cell["Obsah", "OverviewSubsection", CellChangeTimes->{{3.572922606546875*^9, 3.57292260890625*^9}}, CellTags->"Functional Programming"], Cell[CellGroupData[{ Cell["\<\ anonymn\[IAcute] funkce, syntaxe a z\[AAcute]pis\ \>", "Item", CellChangeTimes->{{3.572930341203125*^9, 3.57293035753125*^9}, { 3.57293127340625*^9, 3.5729312770625*^9}}, CellTags->"Functional Programming"], Cell["\<\ tvorba a pr\[AAcute]ce s anonymn\[IAcute]mi fukcemi\ \>", "Item", CellChangeTimes->{{3.572930361890625*^9, 3.57293037734375*^9}, { 3.57293128175*^9, 3.57293129253125*^9}}, CellTags->"Functional Programming"], Cell["\<\ specifikace \[UAcute]rovn\[EHacek] v\[YAcute]po\[CHacek]tu pro funkcion\ \[AAcute]ln\[IAcute] konstrukty\ \>", "Item", CellChangeTimes->{{3.5729303949375*^9, 3.572930419046875*^9}}, CellTags->"Functional Programming"], Cell["\<\ p\[RHacek]\[IAcute]klady funkcion\[AAcute]ln\[IAcute]ho programov\[AAcute]n\ \[IAcute]\ \>", "Item", CellChangeTimes->{{3.57293042365625*^9, 3.5729304378125*^9}}, CellTags->"Functional Programming"] }, Open ]], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Funkcion\[AAcute]ln\[IAcute] programov\[AAcute]n\[IAcute]:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], StyleBox["Anonymn\[IAcute]", "Color7"], " funkce" }], "Subsection", CellChangeTimes->{{3.5729304470625*^9, 3.57293046046875*^9}, { 3.572931333328125*^9, 3.572931336359375*^9}}, CellTags->"Functional Programming"], Cell[TextData[{ "Anonymn\[IAcute] funkce jsou funkce, kter\[EAcute] jsou \ implementov\[AAcute]ny beze jm\[EAcute]na. Tytp funkce jsou \ konstruov\[AAcute]ny s pou\[ZHacek]it\[IAcute]m ", Cell[BoxData[ ButtonBox["Function", BaseStyle->"Link", ButtonData->"paclet:ref/Function"]], "InlineFormula"], "." }], "Text", CellChangeTimes->{{3.5729313070625*^9, 3.572931329875*^9}, { 3.572931471984375*^9, 3.572931505671875*^9}}, CellTags->"Functional Programming"], Cell["\<\ N\[AAcute]sleduj\[IAcute]c\[IAcute] anonymn\[IAcute] funkce n\[AAcute]sob\ \[IAcute] sv\[URing]j argument konstantou.\ \>", "MathCaption", CellChangeTimes->{{3.572931515953125*^9, 3.57293154325*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Function", "[", RowBox[{"x", ",", RowBox[{"10", "x"}]}], "]"}]], "Input", CellTags->"Functional Programming"], Cell["\<\ Anonymn\[IAcute] funkce je pou\[ZHacek]ita jako hlava v\[YAcute]razu stejn\ \[YAcute]m zp\[URing]sobem jako se pracuje s ostatn\[IAcute]mi funkcemi.\ \>", "MathCaption", CellChangeTimes->{{3.57293266703125*^9, 3.572932681046875*^9}, { 3.572932711125*^9, 3.5729327490625*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{ RowBox[{"Function", "[", RowBox[{"x", ",", RowBox[{"10", "x"}]}], "]"}], "[", "3", "]"}]], "Input", CellTags->"Functional Programming"], Cell["\<\ Tato anonymn\[IAcute] funkce pracuje stejn\[EHacek] jako n\[AAcute]sleduj\ \[IAcute]c\[IAcute] funkce, ale bez nutnosti jej\[IAcute] explicitn\[IAcute] \ definice.\ \>", "MathCaption", CellChangeTimes->{{3.57293275625*^9, 3.572932765015625*^9}, { 3.5729328038125*^9, 3.572932827046875*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{"10", " ", "x"}]}]], "Input", CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"f", "[", "3", "]"}]], "Input", CellTags->"Functional Programming"], Cell[TextData[{ "Odstra\[NHacek] definici ", StyleBox["f", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.572932835984375*^9, 3.572932842453125*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Clear", "[", "f", "]"}]], "Input", CellTags->"Functional Programming"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Funkcion\[AAcute]ln\[IAcute] programov\[AAcute]n\[IAcute]:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "Z\[AAcute]pis anonymn\[IAcute] funkce" }], "Subsection", CellChangeTimes->{{3.572932869*^9, 3.572932912734375*^9}}, CellTags->"Functional Programming"], Cell[TextData[{ "P\[RHacek]i pr\[AAcute]ci s anonymn\[IAcute]mi funkcemi je mo\[ZHacek]n\ \[EAcute] pou\[ZHacek]\[IAcute]t ", StyleBox["#", "MR"], " k ozna\[CHacek]en\[IAcute] hodnoty argumentu funkce a ", StyleBox["&", "MR"], " jako indikaci, \[ZHacek]e v\[YAcute]raz je anonymn\[IAcute] funkce." }], "Text", CellChangeTimes->{{3.57293291859375*^9, 3.572932979625*^9}}, CellTags->"Functional Programming"], Cell["\<\ N\[AAcute]sleduj\[IAcute]c\[IAcute] v\[YAcute]raz reprezentuje anoanymn\ \[IAcute] funkci, kter\[AAcute] n\[AAcute]sob\[IAcute] sv\[URing]j argument \ konstantou.\ \>", "MathCaption", CellChangeTimes->{{3.572932986375*^9, 3.57293305078125*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{ RowBox[{"10", " ", "#"}], "&"}]], "Input", CellTags->"Functional Programming"], Cell["\<\ Toto je ekvivalentn\[IAcute] z\[AAcute]pis, ve kter\[EAcute]m je \ prom\[EHacek]nn\[AAcute] pojmenov\[AAcute]na.\ \>", "MathCaption", CellChangeTimes->{{3.5729330656875*^9, 3.572933094765625*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Function", "[", RowBox[{"x", ",", RowBox[{"10", " ", "x"}]}], "]"}]], "Input", CellTags->"Functional Programming"], Cell["\<\ Ob\[EHacek] definice anonzmn\[IAcute] funkce pracuj\[IAcute] stejn\[EHacek]. \ Z\[AAcute]vorky zde nejsou nutn\[EAcute], ale zv\[YAcute]raz\[NHacek]uj\ \[IAcute] a zp\[RHacek]ehled\[NHacek]uj\[IAcute] definici funkce.\ \>", "MathCaption", CellChangeTimes->{{3.5729331073125*^9, 3.572933168453125*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"10", " ", "#"}], "&"}], ")"}], "[", "3", "]"}]], "Input", CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{ RowBox[{"Function", "[", RowBox[{"x", ",", RowBox[{"10", " ", "x"}]}], "]"}], "[", "3", "]"}]], "Input", CellTags->"Functional Programming"], Cell[TextData[{ "Z\[AAcute]pis ", StyleBox["#1", "MR"], ", ", StyleBox["#2", "MR"], ", \[Ellipsis] je pou\[ZHacek]it u anonymn\[IAcute]ch funkc\[IAcute] s v\ \[IAcute]ce ne\[ZHacek] jedn\[IAcute]m argumentem." }], "MathCaption", CellChangeTimes->{{3.57293317340625*^9, 3.572933207734375*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#1", "+", RowBox[{"#2", " ", "#3"}]}], "&"}], ")"}], "[", RowBox[{"x", ",", "y", ",", "z"}], "]"}]], "Input", CellTags->"Functional Programming"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Funkcion\[AAcute]ln\[IAcute] programov\[AAcute]n\[IAcute]: ", "Color7", FontSlant->"Plain"], "P\[RHacek]\[IAcute]klad" }], "Subsection", CellChangeTimes->{{3.572933220390625*^9, 3.572933238265625*^9}}, CellTags->"Functional Programming"], Cell[TextData[{ StyleBox["Demonstrace", FontWeight->"Bold", FontSlant->"Italic"], ": p\[RHacek]ed dal\[SHacek]\[IAcute]m v\[YAcute]kladem vytvo\[RHacek]te n\ \[AAcute]sleduj\[IAcute]c\[IAcute] anonymn\[IAcute] funkce:" }], "Text", CellChangeTimes->{{3.572943484734375*^9, 3.57294351425*^9}}, CellTags->"Functional Programming"], Cell["\<\ funkce p\[RHacek]i\[CHacek]te 5 kectverci sv\[EAcute]ho argumentu\ \>", "Item", CellChangeTimes->{{3.572943518625*^9, 3.572943534546875*^9}}, CellTags->"Functional Programming"], Cell[BoxData[""], "NonPrintButton", CellChangeTimes->{3.57294353659375*^9}], Cell["\<\ funkce ode\[CHacek]te t\[RHacek]et\[IAcute] mocninu argumentu od \ \[CHacek]tverce sv\[EAcute]ho argumentu\ \>", "Item", CellChangeTimes->{{3.572943543671875*^9, 3.572943576203125*^9}}, CellTags->"Functional Programming"], Cell[BoxData[""], "NonPrintButton", CellChangeTimes->{3.57294357821875*^9}], Cell["\<\ funkce vrac\[IAcute] \[CHacek]tverec rozd\[IAcute]lu sv\[YAcute]ch dvou \ argument\[URing]\ \>", "Item", CellChangeTimes->{{3.572943587953125*^9, 3.572943611234375*^9}}, CellTags->"Functional Programming"], Cell[BoxData[""], "NonPrintButton", CellChangeTimes->{3.5729435810625*^9}], Cell[TextData[{ "funkce vrac\[IAcute] ", Cell[BoxData[ ButtonBox["True", BaseStyle->"Link", ButtonData->"paclet:ref/True"]], "InlineFormula"], " jestli\[ZHacek]e jej\[IAcute] argument je mezi ", Cell[BoxData[ FormBox[ RowBox[{"-", "0.1"}], TraditionalForm]]], " a ", Cell[BoxData[ FormBox["0.1", TraditionalForm]]] }], "Item", CellChangeTimes->{{3.5729436136875*^9, 3.572943635921875*^9}}, CellTags->"Functional Programming"], Cell[BoxData[""], "NonPrintButton", CellChangeTimes->{3.572943583171875*^9}], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Funkcion\[AAcute]ln\[IAcute] programov\[AAcute]n\[IAcute]:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "U\[ZHacek]it\[IAcute] anonymn\[IAcute]ch funkc\[IAcute]" }], "Subsection", CellChangeTimes->{{3.572943641609375*^9, 3.572943665125*^9}}, CellTags->"Functional Programming"], Cell[TextData[{ "Anonymn\[IAcute] funkcejsou \[CAcute]asto vyu\[ZHacek]\[IAcute]v\[AAcute]ny \ ve spojen\[IAcute] s ostatn\[IAcute]mi funkcemi jako jsou ", Cell[BoxData[ ButtonBox["Map", BaseStyle->"Link", ButtonData->"paclet:ref/Map"]], "InlineFormula"], " a ", Cell[BoxData[ ButtonBox["Apply", BaseStyle->"Link", ButtonData->"paclet:ref/Apply"]], "InlineFormula"], "." }], "Text", CellChangeTimes->{{3.572943667421875*^9, 3.572943701859375*^9}}, CellTags->"Functional Programming"], Cell["\<\ N\[AAcute]sleduj\[IAcute]c\[IAcute] mapuje anoanymn\[IAcute] funkci, kter\ \[AAcute] vrac\[IAcute] \[CHacek]tverec sv\[EAcute]ho argumentu na prvky \ seznamu.\ \>", "MathCaption", CellChangeTimes->{{3.572943705203125*^9, 3.57294375178125*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"#", "^", "2"}], "&"}], ",", RowBox[{"{", RowBox[{"2", ",", "a", ",", "\[Pi]", ",", ".001"}], "}"}]}], "]"}]], "Input", CellTags->"Functional Programming"], Cell[TextData[{ "Anonymn\[IAcute] funkce umocn\[IAcute] druhou mocninu ty prvky seznamu, \ kter\[EAcute] jsou v intervalu ", Cell[BoxData[ FormBox[ RowBox[{"-", "1"}], TraditionalForm]]], " a 1." }], "MathCaption", CellChangeTimes->{{3.57294376940625*^9, 3.572943810609375*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"If", "[", 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Zkuste zm\[EHacek]nit ", StyleBox["#3", "MR"], " na ", StyleBox["#1", "MR"], " nebo ", StyleBox["#2", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.57294484859375*^9, 3.572944907640625*^9}}], Cell[BoxData[ RowBox[{"Plot3D", "[", RowBox[{ SuperscriptBox["E", RowBox[{ RowBox[{"-", SuperscriptBox["x", "2"]}], "-", SuperscriptBox["y", "2"]}]], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"ColorFunction", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"Hue", "[", "#3", "]"}], "&"}], ")"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.57294495903125*^9, 3.572944974*^9}}], Cell[TextData[{ "Hodnota parametru ", Cell[BoxData[ ButtonBox["RegionFunction", BaseStyle->"Link", ButtonData->"paclet:ref/RegionFunction"]], "InlineFormula"], " je anonymn\[IAcute] funkce, kter\[AAcute] omez\[IAcute] oblast vykreslen\ \[IAcute] na plochu definovanou ", Cell[BoxData[ FormBox[ RowBox[{"1", "<", RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]}], "<", "8"}], TraditionalForm]]], ". 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Zm\ \[EHacek]nou hodnoty ", Cell[BoxData[ ButtonBox["MeshFunctions", BaseStyle->"Link", ButtonData->"paclet:ref/MeshFunctions"]], "InlineFormula"], " z ", StyleBox["#3", "MR"], " na ", StyleBox["#2", "MR"], " vykresl\[IAcute] k\[RHacek]\[IAcute]vky pod\[EAcute]l osy ", Cell[BoxData[ FormBox["y", TraditionalForm]]], "; zm\[EHacek]nou na ", StyleBox["#1", "MR"], " z\[IAcute]sk\[AAcute]me k\[RHacek]ivky pod\[EAcute]l osy x (", StyleBox["#4", "MR"], " poskytne radi\[AAcute]ln\[IAcute] k\[RHacek]ivky). 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N\[AAcute]sleduj\[IAcute]c\[IAcute] \[RHacek]e\:015ben\[IAcute] je pomoc\ \[IAcute] procedur\[AAcute]ln\[IAcute]ho p\[RHacek]\[IAcute]stupu.\ \>", "MathCaption", CellChangeTimes->{{3.5729457764375*^9, 3.5729457925625*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"m", "[", RowBox[{"[", RowBox[{"k", ",", "2"}], "]"}], "]"}], ",", RowBox[{"m", "[", RowBox[{"[", RowBox[{"k", ",", "1"}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}]}], "]"}]], "Input", CellTags->"Functional Programming"], Cell[TextData[{ "Toto je funkcion\[AAcute]ln\[IAcute] program. Proto\[ZHacek]e ", Cell[BoxData[ ButtonBox["Map", BaseStyle->"Link", ButtonData->"paclet:ref/Map"]], "InlineFormula"], " operuje na prvc\[IAcute]ch seznamu tj. na dvojic\[IAcute]ch, \ ka\[ZHacek]dou z t\[EHacek]chto dvojic obr\[AAcute]t\[IAcute]." }], "MathCaption", CellChangeTimes->{{3.5729458139375*^9, 3.5729458705625*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Map", "[", RowBox[{"Reverse", ",", "m"}], "]"}]], "Input", CellTags->"Functional Programming"], Cell["\<\ a nakonec \[RHacek]e\[SHacek]en\[IAcute] pomoc\[IAcute] aplikace substitu\ \[CHacek]n\[IAcute]ch pravidel.\ \>", "MathCaption", CellChangeTimes->{{3.572945876078125*^9, 3.572945894671875*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"m", "/.", RowBox[{ RowBox[{"{", RowBox[{"p_", ",", "q_"}], "}"}], "\[Rule]", RowBox[{"{", RowBox[{"q", ",", "p"}], "}"}]}]}]], "Input", CellTags->"Functional Programming"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", 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\>", "MathCaption", CellChangeTimes->{{3.57294598725*^9, 3.572946003859375*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"m", "[", RowBox[{"[", RowBox[{"k", ",", "1"}], "]"}], "]"}], "==", RowBox[{"m", "[", RowBox[{"[", RowBox[{"k", ",", "2"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "3"}], "}"}]}], "]"}]], "Input", CellTags->"Functional Programming"], Cell["\<\ Funkcion\[AAcute]ln\[IAcute] program generuje stejn\[YAcute] v\[YAcute]sledek\ \>", "MathCaption", CellChangeTimes->{{3.572946026890625*^9, 3.572946068765625*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Apply", "[", RowBox[{"Equal", ",", "m", ",", RowBox[{"{", "1", "}"}]}], "]"}]], "Input", CellTags->"Functional Programming"], Cell["\<\ Pou\[ZHacek]it\[IAcute] substitu\[CHacek]n\[IAcute]ho pravidla je velmi \ srozumiteln\[EAcute].\ \>", "MathCaption", CellChangeTimes->{{3.572946261046875*^9, 3.572946307703125*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"m", "/.", RowBox[{ RowBox[{"{", RowBox[{"p_", ",", "q_"}], "}"}], "\[Rule]", " ", RowBox[{"p", "\[Equal]", "q"}]}]}]], "Input", CellTags->"Functional Programming"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Funkcion\[AAcute]ln\[IAcute] programov\[AAcute]n\[IAcute]: ", "Color7", FontSlant->"Plain"], "P\[RHacek]\[IAcute]klad\[LongDash]konverze dvou seznam\[URing] na seznam \ pravidel" }], "Subsection", CellChangeTimes->{{3.57294631240625*^9, 3.572946340046875*^9}}, CellTags->"Functional Programming"], Cell[TextData[{ "P\[RHacek]edpokl\[AAcute]dejme, \[ZHacek]e m\[AAcute]me seznam \ prom\[EHacek]nn\[YAcute]ch a odpov\[IAcute]daj\[IAcute]c\[IAcute] seznam \ hodnot \[UAcute]kolem je vytvo\[RHacek]it seznam pravidel ve form\[EHacek] ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox[ StyleBox["var", 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Co se stane, \ pokud aplikujeme funkci Rule pomoc\[IAcute] Map ?" }], "MathCaption", CellChangeTimes->{{3.5729464451875*^9, 3.572946479140625*^9}, { 3.572946633953125*^9, 3.572946673125*^9}}, CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Apply", "[", RowBox[{"Rule", ",", "data", ",", RowBox[{"{", "1", "}"}]}], "]"}]], "Input", CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Map", "[", RowBox[{"Rule", ",", "data"}], "]"}]], "Input", CellChangeTimes->{{3.57294649665625*^9, 3.572946514234375*^9}, { 3.5729465545625*^9, 3.572946587546875*^9}, 3.5729466840625*^9}], Cell[TextData[{ "There is a more direct way to do this, using ", Cell[BoxData[ ButtonBox["Thread", BaseStyle->"Link", ButtonData->"paclet:ref/Thread"]], "InlineFormula"], "." }], "MathCaption", CellTags->"Functional Programming"], Cell[BoxData[ RowBox[{"Thread", "[", RowBox[{"Rule", "[", RowBox[{"vars", ",", "vals"}], "]"}], "]"}]], "Input", CellTags->"Functional Programming"], Cell[TextData[{ "Je mo\[ZHacek]n\[EAcute] pou\[ZHacek]\[IAcute]t i funkci ", Cell[BoxData[ ButtonBox["MapThread", BaseStyle->"Link", ButtonData->"paclet:ref/MapThread"]], "InlineFormula"], " s odli\[SHacek]nou syntax\[IAcute]." }], "MathCaption", CellChangeTimes->{{3.5729467215*^9, 3.572946742625*^9}}], Cell[BoxData[ RowBox[{"MapThread", "[", RowBox[{"Rule", ",", RowBox[{"{", RowBox[{"vars", ",", "vals"}], "}"}]}], "]"}]], "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Parametry a zpr\[AAcute]vy", "Section", CellChangeTimes->{{3.572946785484375*^9, 3.57294679625*^9}, { 3.5729470149375*^9, 3.572947044140625*^9}}, CellTags->"Options and Messages"], Cell["Obsah", "OverviewSubsection", CellChangeTimes->{{3.572946800390625*^9, 3.57294680109375*^9}}, CellTags->"Options and Messages"], Cell[CellGroupData[{ Cell["\<\ pou\[ZHacek]it\[IAcute] voliteln\[YAcute]ch argument\[URing] ve \ funkc\[IAcute]ch\ \>", "Item", CellChangeTimes->{{3.572946814953125*^9, 3.572946827796875*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "p\[RHacek]id\[AAcute]n\[IAcute] parametr\[URing] do u\[ZHacek]ivatelsky \ definovan\[YAcute]ch funkc\[IAcute] \[LongDash]", Cell[BoxData[ ButtonBox["OptionsPattern", BaseStyle->"Link", ButtonData->"paclet:ref/OptionsPattern"]]], " a ", Cell[BoxData[ ButtonBox["OptionValue", BaseStyle->"Link", ButtonData->"paclet:ref/OptionValue"]]] }], "Item", CellChangeTimes->{{3.57294683215625*^9, 3.572946866*^9}}, CellTags->"Options and Messages"], Cell["p\[RHacek]\[IAcute]klad \[LongDash]n\[AAcute]hodn\[AAcute] proch\ \[AAcute]zka", "Item", CellChangeTimes->{{3.572946868296875*^9, 3.572946878578125*^9}}, CellTags->"Options and Messages"], Cell["vytvo\[RHacek]en\[IAcute] varovn\[YAcute]ch zpr\[AAcute]v", "Item", CellChangeTimes->{{3.572946881734375*^9, 3.572946891828125*^9}}, CellTags->"Options and Messages"], Cell["pou\[ZHacek]it\[IAcute] zpr\[AAcute]v", "Item", CellChangeTimes->{{3.5729468949375*^9, 3.572946901390625*^9}}, CellTags->"Options and Messages"] }, Open ]], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[StyleBox[" Parametry a zpr\[AAcute]vy: Parametry", "Color7", FontSlant->"Plain"]], "Subsection", CellChangeTimes->{{3.5729470085625*^9, 3.572947050390625*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "Mnoho funkc\[IAcute] v ", StyleBox["Mathematica", FontSlant->"Italic"], " maj\[IAcute] voliteln\[EAcute] argumenty (parametry), kter\[EAcute] lze \ nastavit . Pokud je nenapln\[IAcute]me, SW ", StyleBox["Mathematica", FontSlant->"Italic"], " pou\[ZHacek]ije p\[RHacek]ednastaven\[EAcute] hodnoty." }], "Text", CellChangeTimes->{{3.572949105796875*^9, 3.5729491725*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad nastaven\[AAcute] hodnota pro ", Cell[BoxData[ ButtonBox["Mesh", BaseStyle->"Link", ButtonData->"paclet:ref/Mesh"]], "InlineFormula"], " ve funkci ", Cell[BoxData[ ButtonBox["Plot", BaseStyle->"Link", ButtonData->"paclet:ref/Plot"]], "InlineFormula"], " je ", Cell[BoxData[ ButtonBox["None", BaseStyle->"Link", ButtonData->"paclet:ref/None"]], "InlineFormula"], ". Tato hodnota je pou\[ZHacek]ita, pokud ji explicitn\[EHacek] \ nezm\[EHacek]n\[IAcute]me." }], "MathCaption", CellChangeTimes->{{3.5729491741875*^9, 3.57294921978125*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"Options", "[", RowBox[{"Plot", ",", "Mesh"}], "]"}]], "Input", CellChangeTimes->{{3.5729492379375*^9, 3.572949244296875*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "Nastaven\[IAcute] hodnoty ", Cell[BoxData[ ButtonBox["Mesh", BaseStyle->"Link", ButtonData->"paclet:ref/Mesh"]], "InlineFormula"], " p\[RHacek]ep\[IAcute]\[SHacek]e implicitn\[IAcute] chov\[AAcute]n\[IAcute] \ funkce. V n\[AAcute]sleduj\[IAcute]c\[IAcute]m \ p\[RHacek]\[IAcute]pad\[EHacek] hodnota ", Cell[BoxData[ ButtonBox["All", BaseStyle->"Link", ButtonData->"paclet:ref/All"]], "InlineFormula"], " zobraz\[IAcute] v\[SHacek]echny body pou\[ZHacek]it\[EAcute] p\[RHacek]i v\ \[YAcute]po\[CHacek]tu nakreslen\[EAcute] k\[RHacek]ivky." }], "MathCaption", CellChangeTimes->{{3.572949256484375*^9, 3.5729493224375*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Sin", "[", RowBox[{"x", "+", RowBox[{ SqrtBox["2"], RowBox[{"Sin", "[", "x", "]"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"2", "\[Pi]"}]}], "}"}], ",", RowBox[{"Mesh", "\[Rule]", "All"}]}], "]"}]], "Input", CellTags->"Options and Messages"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Parametry a zpr\[AAcute]vy: ", "Color7", FontSlant->"Plain"], "P\[RHacek]id\[AAcute]n\[IAcute] parametr\[URing]" }], "Subsection", CellChangeTimes->{{3.572949346265625*^9, 3.57294935271875*^9}}, CellTags->"Options and Messages"], Cell["\<\ P\[RHacek]i konstrukci sv\[EAcute] funkce j\[IAcute] m\[URing]\[ZHacek]eme \ definovat libovoln\[EAcute] mno\[ZHacek]stv\[IAcute] parametr\[URing]. Nejd\ \[RHacek]\[IAcute]ve definujeme jm\[EAcute]no nov\[EAcute]ho parametru a pot\ \[EAcute] jeho implicitn\[IAcute] nastavenou hodnotu. \ \>", "Text", CellChangeTimes->{{3.57294935509375*^9, 3.57294942284375*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad n\[AAcute]sleduj\[IAcute]c\[IAcute] definuje dva \ parametry ", StyleBox["opt1", "MR"], " a ", StyleBox["opt2", "MR"], " pro funkci ", StyleBox["f", "MR"], ", a nastav\[IAcute] jejich implicitn\[IAcute] hodnoty." }], "MathCaption", CellChangeTimes->{{3.57294942575*^9, 3.572949467828125*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{"Options", "[", "f", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"opt1", "\[Rule]", "a"}], ",", RowBox[{"opt2", "\[Rule]", "b"}]}], "}"}]}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "Pomoc\[IAcute] ", Cell[BoxData[ ButtonBox["OptionsPattern", BaseStyle->"Link", ButtonData->"paclet:ref/OptionsPattern"]], "InlineFormula"], ", je mo\[ZHacek]n\[EAcute] v dan\[EAcute] funkci ", StyleBox["f", "MR"], " voliteln\[EAcute] parametry pou\[ZHacek]\[IAcute]t. Hodnotu parametru z\ \[IAcute]sk\[AAcute]me pomoc\[IAcute] funkce ", Cell[BoxData[ ButtonBox["OptionValue", BaseStyle->"Link", ButtonData->"paclet:ref/OptionValue"]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.57294948440625*^9, 3.572949541546875*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", RowBox[{"x_", ",", RowBox[{"OptionsPattern", "[", "]"}]}], "]"}], ":=", RowBox[{ SuperscriptBox["x", "2"], "+", FractionBox[ RowBox[{"OptionValue", "[", "opt1", "]"}], RowBox[{"OptionValue", "[", "opt2", "]"}]]}]}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "First, try out ", StyleBox["f", "MR"], " with one argument. In this case, the default value of the options are used." }], "MathCaption", CellTags->"Options and Messages"], Cell["\<\ Pokud chceme hodnoty parametr\[URing] nastavit explicitn\[EHacek], vlo\ \[ZHacek]\[IAcute]me je p\[RHacek]i vol\[AAcute]n\[IAcute] funkce pomoc\ \[IAcute] substitu\[CHacek]n\[IAcute]ch pravidel, kter\[AAcute] nastav\ \[IAcute] parametry na po\[ZHacek]adovan\[EAcute] hodnoty.\ \>", "MathCaption", CellChangeTimes->{{3.5729495868125*^9, 3.572949655609375*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"f", "[", RowBox[{"z", ",", RowBox[{"opt1", "\[Rule]", "\[Alpha]"}], ",", RowBox[{"opt2", "\[Rule]", "\[Beta]"}]}], "]"}]], "Input", CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"ClearAll", "[", "f", "]"}]], "Input", CellChangeTimes->{{3.57295281884375*^9, 3.572952838296875*^9}, { 3.5729528756875*^9, 3.572952876015625*^9}}], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Parametry a zpr\[AAcute]vy:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7", FontSlant->"Italic"], "P\[RHacek]\[IAcute]klad\[LongDash]N\[AAcute]hodn\[AAcute] proch\[AAcute]zka" }], "Subsection", CellChangeTimes->{{3.572949671890625*^9, 3.572949683859375*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "N\[AAcute]sleduj\[IAcute]c\[IAcute] p\[RHacek]\[IAcute]klad vytv\[AAcute]\ \[RHacek]\[IAcute] funkci, ", StyleBox["RandomWalk", "MR"], ", kter\[AAcute] generuje n\[AAcute]hodnou proch\[AAcute]zku v jedn\[EAcute] \ nebo dvou dimen\[IAcute]ch. U\[ZHacek]ivatel nastav\[IAcute] dimenzi jako \ hodnotu voliteln\[EAcute]ho parametru ", StyleBox["Dimension", "MR"], "." }], "Text", CellChangeTimes->{{3.572949685640625*^9, 3.57294975571875*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "Nejd\[RHacek]\[IAcute]ve vytvo\[RHacek]\[IAcute]me dv\[EHacek] funkce. \ Jednu pro jednodimenzion\[AAcute]ln\[IAcute] p\[RHacek]\[IAcute]pad a druhou \ pro dvoudimenzion\[AAcute]ln\[IAcute]. Seznam ", Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}]]], " ukazuje sm\[EHacek]r krok\[URing] (sever, jih, v\[YAcute]chod, \ z\[AAcute]pad) pro dvoudimenzion\[AAcute]ln\[IAcute]ho chodce." }], "MathCaption", CellChangeTimes->{{3.572949765421875*^9, 3.57294985809375*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{"walk1D", "[", "t_", "]"}], ":=", RowBox[{"Accumulate", "[", RowBox[{"RandomChoice", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", "t"}], "]"}], "]"}]}]], "Input", CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{"walk2D", "[", "t_", "]"}], ":=", RowBox[{"Accumulate", "[", RowBox[{"RandomChoice", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}], ",", "t"}], "]"}], "]"}]}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "Jednoduch\[EAcute] p\[RHacek]\[IAcute]klady ukazuj\[IAcute] chov\[AAcute]n\ \[IAcute] funkce. N\[AAcute]sleduj\[IAcute]c\[IAcute] vybere n\[AAcute]hodn\ \[EHacek] 5 prvk\[URing] ze seznamu ", Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]]], "." }], "MathCaption", CellChangeTimes->{{3.57294988071875*^9, 3.57294992603125*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"RandomChoice", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", "5"}], "]"}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "Funkce ", Cell[BoxData[ ButtonBox["Accumulate", BaseStyle->"Link", ButtonData->"paclet:ref/Accumulate"]], "InlineFormula"], " vytvo\[RHacek]\[IAcute] celkov\[YAcute] po\[CHacek]et krok\[URing] v dan\ \[EAcute]m sm\[EHacek]ru." }], "MathCaption", CellChangeTimes->{{3.572949956140625*^9, 3.5729499775*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"Accumulate", "[", "%", "]"}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "Funkce ", StyleBox["RandomWalk", "MR"], " jednodu\[SHacek]e vol\[AAcute] ob\[EHacek] funkce v z\[AAcute]vislosti na \ nastaven\[IAcute] voliteln\[EAcute]ho parametru ", StyleBox["Dimension", "MR"], ". " }], "MathCaption", CellChangeTimes->{{3.572949986078125*^9, 3.572950046578125*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Options", "[", "RandomWalk", "]"}], "=", RowBox[{"{", RowBox[{"Dimension", "\[Rule]", "2"}], "}"}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"RandomWalk", "[", RowBox[{"t_Integer", ",", RowBox[{"OptionsPattern", "[", "]"}]}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"OptionValue", "[", "Dimension", "]"}], "==", "1"}], ",", RowBox[{"walk1D", "[", "t", "]"}], ",", RowBox[{"walk2D", "[", "t", "]"}]}], "]"}]}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "N\[AAcute]sleduj\[IAcute]c\[IAcute] ukazuje n\[AAcute]hodnou \ proch\[AAcute]zku o 10 kroc\[IAcute]ch s implicitn\[IAcute] hodnotou \ parametru ", StyleBox["Dimension", "MR"] }], "MathCaption", CellChangeTimes->{{3.57295005303125*^9, 3.5729500979375*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"RandomWalk", "[", "10", "]"}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "Tento p\[RHacek]\[IAcute]klad pou\[ZHacek]\[IAcute]v\[AAcute] ", StyleBox["RandomWalk", "MR"], " s explicitn\[IAcute]m nastaven\[IAcute]m parametru ", StyleBox["Dimension", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.572950155296875*^9, 3.572950185453125*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"RandomWalk", "[", RowBox[{"10", ",", RowBox[{"Dimension", "\[Rule]", "1"}]}], "]"}]], "Input", CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"ListLinePlot", "[", RowBox[{ RowBox[{"RandomWalk", "[", "10000", "]"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]], "Input", CellTags->"Options and Messages"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Parametry a zpr\[AAcute]vy: ", "Color7", FontSlant->"Plain"], "Varovn\[EAcute] zpr\[AAcute]vy" }], "Subsection", CellChangeTimes->{{3.572950249765625*^9, 3.572950269796875*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ StyleBox["RandomWalk", "MR"], " byl nastaven tak, \[ZHacek]e hodnota parametru ", StyleBox["Dimension", "MR"], " vol\[AAcute] bu\[DHacek] funkci ", StyleBox["walk1D", "MR"], " nebo ", StyleBox["walk2D", "MR"], ". Takto to bude pracovat bez chyb, pokud u\[ZHacek]ivatel zad\[AAcute] \ explicitn\[EHacek] pouze hodnoty 1 nebo 2. V p\[RHacek]\[IAcute]pad\[EHacek] \ jin\[EAcute] zadan\[EAcute] hodnoty parametru ", StyleBox["Dimension", "MR"], " p\[RHacek]\[IAcute]kaz ", Cell[BoxData[ ButtonBox["If", BaseStyle->"Link", ButtonData->"paclet:ref/If"]], "InlineFormula"], " aktivuje ELSE v\[EHacek]tev." }], "Text", CellChangeTimes->{{3.572950277734375*^9, 3.5729504095625*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"RandomWalk", "[", RowBox[{"5", ",", RowBox[{"Dimension", "\[Rule]", "3"}]}], "]"}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "Nam\[IAcute]sto toho by m\[EHacek]la b\[YAcute]t iniciov\[AAcute]na zpr\ \[AAcute]va, \[ZHacek]e byla zad\[AAcute]na \[SHacek]patn\[AAcute] hodnota \ parametru ", StyleBox["Dimension", "MR"], ". Toto je mo\[ZHacek]n\[EAcute] impemlentovat zad\[AAcute]n\[IAcute]m \ varovn\[EAcute] zpr\[AAcute]vy a jej\[IAcute] vyvol\[AAcute]n\[IAcute] v t\ \[EHacek]le funkce ", StyleBox["RandomWalk", "MR"], " ve chv\[IAcute]li, kdy nastane takov\[AAcute] situace. " }], "Text", CellChangeTimes->{{3.572950415234375*^9, 3.572950528265625*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "N\[AAcute]sleduje definice funkce ", StyleBox["RandomWalk", "MR"], " z p\[RHacek]edch\[AAcute]zej\[IAcute]c\[IAcute] \[CAcute]\[AAcute]sti " }], "MathCaption", CellChangeTimes->{{3.57295054140625*^9, 3.572950565515625*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{"walk1D", "[", "t_", "]"}], ":=", RowBox[{"Accumulate", "[", RowBox[{"RandomChoice", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", "t"}], "]"}], "]"}]}]], "Input", CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{"walk2D", "[", "t_", "]"}], ":=", RowBox[{"Accumulate", "[", RowBox[{"RandomChoice", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}], ",", "t"}], "]"}], "]"}]}]], "Input", CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Options", "[", "RandomWalk", "]"}], "=", RowBox[{"{", RowBox[{"Dimension", "\[Rule]", "2"}], "}"}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"RandomWalk", "[", RowBox[{"t_Integer", ",", RowBox[{"OptionsPattern", "[", "]"}]}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"OptionValue", "[", "Dimension", "]"}], "==", "1"}], ",", RowBox[{"walk1D", "[", "t", "]"}], ",", RowBox[{"walk2D", "[", "t", "]"}]}], "]"}]}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "Njed\[RHacek]\[IAcute]ve odstran\[IAcute]me definici funkce ", StyleBox["RandomWalk", "MR"], ". ", Cell[BoxData[ ButtonBox["Clear", BaseStyle->"Link", ButtonData->"paclet:ref/Clear"]], "InlineFormula"], " by v tomto p\[RHacek]\[IAcute]pad\[EHacek] vymazala pouze hodnoty sv\ \[AAcute]zan\[EAcute] se symbolem funkce. Pou\[ZHacek]it\[AAcute] funkce ", Cell[BoxData[ ButtonBox["ClearAll", BaseStyle->"Link", ButtonData->"paclet:ref/ClearAll"]], "InlineFormula"], " odstran\[IAcute] tak\[EAcute] v\:015bechny atributy a parametry. " }], "MathCaption", CellChangeTimes->{{3.572950587265625*^9, 3.5729506715625*^9}}], Cell[BoxData[ RowBox[{"ClearAll", "[", "RandomWalk", "]"}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "V dal\[SHacek]\[IAcute]m vytvo\[RHacek]\[IAcute]me zpr\[AAcute]vu, kter\ \[AAcute] je zobrazena kdykoliv je nastavena \[SHacek]patn\[AAcute] hodnota \ parametru ", StyleBox["Dimension", "MR"], ". N\[AAcute]zev zpr\[AAcute]vy je ", StyleBox["baddim", "MR"], ". Zpr\[AAcute]va je sv\[AAcute]z\[AAcute]na s funkc\[IAcute] ", StyleBox["RandomWalk", "MR"], ". " }], "MathCaption", CellChangeTimes->{{3.57295068009375*^9, 3.5729507513125*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"RandomWalk", "::", "baddim"}], "=", "\"\\""}], ";"}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "M\[IAcute]sto pou\[ZHacek]it\[IAcute] funkce ", Cell[BoxData[ ButtonBox["If", BaseStyle->"Link", ButtonData->"paclet:ref/If"]], "InlineFormula"], " function, kter\[AAcute] m\[AAcute] pouze dv\[EHacek] v\[EHacek]tve, pou\ \[ZHacek]ijeme funkci ", Cell[BoxData[ ButtonBox["Which", BaseStyle->"Link", ButtonData->"paclet:ref/Which"]], "InlineFormula"], ", kter\[AAcute] vybere odpov\[IAcute]daj\[IAcute]c\[IAcute] v\[EHacek]tev z \ v\[IAcute]ce mo\[ZHacek]nost\[IAcute]. a vyol\[AAcute] jednu z funkc\[IAcute] \ ", StyleBox["walk1D", "MR"], ", ", StyleBox["walk2D", "MR"], ", nebo aktivuje varovnou zpr\[AAcute]vu." }], "MathCaption", CellChangeTimes->{{3.572950767*^9, 3.572950774609375*^9}, { 3.57295086746875*^9, 3.572950931125*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Options", "[", "RandomWalk", "]"}], "=", RowBox[{"{", RowBox[{"Dimension", "\[Rule]", "2"}], "}"}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"RandomWalk", "[", RowBox[{"t_Integer", ",", RowBox[{"OptionsPattern", "[", "]"}]}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"dim", "=", RowBox[{"OptionValue", "[", "Dimension", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Which", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"dim", "\[Equal]", "1"}], ",", RowBox[{"walk1D", "[", "t", "]"}], ",", "\[IndentingNewLine]", RowBox[{"dim", "\[Equal]", "2"}], ",", RowBox[{"walk2D", "[", "t", "]"}], ",", "\[IndentingNewLine]", "True", ",", RowBox[{"Message", "[", RowBox[{ RowBox[{"RandomWalk", "::", "\"\\""}], ",", "dim"}], "]"}]}], "\[IndentingNewLine]", "]"}]}], "]"}]}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "Zde je popis pou\[ZHacek]it\[IAcute] funkce ", Cell[BoxData[ ButtonBox["Which", BaseStyle->"Link", ButtonData->"paclet:ref/Which"]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.572950942515625*^9, 3.57295095528125*^9}}], Cell[BoxData[ RowBox[{"?", "Which"}]], "Input", CellTags->"Options and Messages"], Cell[TextData[{ "Uvedn\[EAcute] p\[RHacek]\[IAcute]klady ukazuj\[IAcute] pou\[ZHacek]it\ \[IAcute] funkce ", StyleBox["RandomWalk", "MR"], " bez parametru a s nastavenou hodnotou parametru ", StyleBox["Dimension", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.572951015828125*^9, 3.57295105546875*^9}}], Cell[BoxData[ RowBox[{"RandomWalk", "[", "8", "]"}]], "Input", CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"RandomWalk", "[", RowBox[{"10", ",", RowBox[{"Dimension", "\[Rule]", "4.5"}]}], "]"}]], "Input", CellTags->"Options and Messages"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Parametry a zpr\[AAcute]vy: ", "Color7", FontSlant->"Plain"], "Popis pou\[ZHacek]it\[IAcute] funkce - n\[AAcute]vod" }], "Subsection", CellChangeTimes->{{3.572951344640625*^9, 3.57295136396875*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "Ka\[ZHacek]d\[AAcute] vestav\[EHacek]n\[AAcute] funkce v ", StyleBox["Mathematica", FontSlant->"Italic"], " m\[AAcute] popis pou\[ZHacek]it\[IAcute] (zpr\[AAcute]vu o pou\[ZHacek]it\ \[IAcute]), kter\[YAcute] snadno vyvol\[AAcute]me zad\[AAcute]n\[IAcute]m ", StyleBox["?", "MR"], StyleBox["FunctionName", "IT"], "." }], "Text", CellChangeTimes->{{3.572951365828125*^9, 3.5729514366875*^9}}, CellTags->"Options and Messages"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad pou\[ZHacek]it\[IAcute] funkce ", Cell[BoxData[ ButtonBox["RandomChoice", BaseStyle->"Link", ButtonData->"paclet:ref/RandomChoice"]], "InlineFormula"], ". zjist\[IAcute]me" }], "MathCaption", CellChangeTimes->{{3.572951405859375*^9, 3.5729514221875*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"?", "RandomChoice"}]], "Input", CellTags->"Options and Messages"], Cell["\<\ Takov\[YAcute] n\[AAcute]vod \[CHacek]i popis pou\[ZHacek]it\[IAcute] je mo\ \[ZHacek]n\[EAcute] p\[RHacek]idat ke ka\[ZHacek]d\[EAcute] funkci, kterou \ vytvo\[RHacek]\[IAcute]me. N\[AAcute]sleduje vzor, dle kter\[EAcute]ho lze \ zpr\[AAcute]vu vytov\[RHacek]it. \ \>", "MathCaption", CellChangeTimes->{{3.572951447671875*^9, 3.572951511*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"RandomWalk", "::", "usage"}], "=", "\"\\""}], ";"}]], "Input", CellChangeTimes->{{3.5729515196875*^9, 3.572951633703125*^9}, 3.57295171840625*^9}, CellTags->"Options and Messages"], Cell[TextData[{ "Nyn\[IAcute] je ji\[ZHacek] mo\[ZHacek]n\[EAcute] obdr\[ZHacek]et informace \ o funkci ", StyleBox["RandomWalk", "MR"], " stejn\[YAcute]m zp\[URing]sobem jako u jin\[YAcute]ch vestav\[EHacek]n\ \[YAcute]ch funkc\[IAcute] v ", StyleBox["Mathematica", FontSlant->"Italic"], "." }], "MathCaption", CellChangeTimes->{{3.572951650125*^9, 3.572951704453125*^9}}, CellTags->"Options and Messages"], Cell[BoxData[ RowBox[{"?", "RandomWalk"}]], "Input", CellTags->"Options and Messages"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Efektivnost v\[YAcute]po\[CHacek]t\[URing]", "Section", CellChangeTimes->{{3.572951757765625*^9, 3.572951760984375*^9}, { 3.57295718446875*^9, 3.572957186109375*^9}}, CellTags->"Efficiency"], Cell["Obsah", "OverviewSection", CellChangeTimes->{{3.572951764796875*^9, 3.57295176546875*^9}}, CellTags->"Efficiency"], Cell[TextData[{ "Neju\[ZHacek]ite\[CHacek]n\[EHacek]j\[SHacek]\[IAcute] principy efektivn\ \[IAcute]ho programov\[AAcute]n\[IAcute] jsou v SW ", StyleBox["Mathematica", FontSlant->"Italic"], " stejn\[EAcute] jako v kter\[EAcute]mkoliv jin\[EAcute]m programovac\ \[IAcute]m jazyce." }], "Text", CellChangeTimes->{{3.5729518261875*^9, 3.572951876328125*^9}}, CellTags->"Efficiency"], Cell[CellGroupData[{ Cell["odstranit redundantn\[IAcute] v\[YAcute]po\[CHacek]ty", "Item", CellChangeTimes->{{3.572951884171875*^9, 3.572951900234375*^9}}, CellTags->"Efficiency"], Cell["\<\ v\[YAcute]b\[EHacek]r efektivn\[IAcute]ho p\[RHacek]\[IAcute]stupu k \ \[RHacek]e\[SHacek]en\[IAcute] probl\[EAcute]mu - pou\[ZHacek]it\[IAcute] vy\ \[SHacek]\[SHacek]\[IAcute]ch funkc\[IAcute] \ \>", "Item", CellChangeTimes->{{3.572951903453125*^9, 3.572951948109375*^9}}, CellTags->"Efficiency"], Cell["\<\ rozd\[EHacek]lit v\[EHacek]t\[SHacek]\[IAcute] programy do men\[SHacek]\ \[IAcute]ch snadn\[EHacek]ji \[RHacek]iditeln\[YAcute]ch \[CHacek]\[AAcute]st\ \[IAcute]\ \>", "Item", CellChangeTimes->{{3.5729519538125*^9, 3.572951994953125*^9}, { 3.572957225921875*^9, 3.572957238078125*^9}}, CellTags->"Efficiency"] }, Open ]], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Efektivnost: ", "Color7", FontSlant->"Plain"], "Redundantn\[IAcute] v\[YAcute]po\[CHacek]ty" }], "Subsection", CellChangeTimes->{{3.5729520014375*^9, 3.572952014546875*^9}, { 3.57295719171875*^9, 3.572957193296875*^9}}, CellTags->"Efficiency"], Cell["\<\ Zde je p\[RHacek]\[IAcute]klad v\[YAcute]po\[CHacek]tu, kter\[YAcute] je \ relativn\[EHacek] neefektivn\[IAcute], proto\[ZHacek]e zahrnuje redundantn\ \[IAcute] v\[YAcute]po\[CHacek]ty.\ \>", "Text", CellChangeTimes->{{3.572952016421875*^9, 3.5729520551875*^9}}, CellTags->"Efficiency"], Cell[TextData[{ "Symbolick\[YAcute] ur\[CHacek]it\[YAcute] integr\[AAcute]l v tomto p\ \[RHacek]\[IAcute]kladu je integrov\[AAcute]n pro ka\[ZHacek]d\[YAcute] bod \ na vykreslovan\[EAcute] k\[RHacek]ivce. Rychlost v\[YAcute]po\[CHacek]tu je \ ur\[CHacek]ena obaluj\[IAcute]c\[IAcute] funkc\[IAcute] ", Cell[BoxData[ ButtonBox["AbsoluteTiming", BaseStyle->"Link", ButtonData->"paclet:ref/AbsoluteTiming"]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.57295206184375*^9, 3.572952099265625*^9}, { 3.572952130515625*^9, 3.57295216271875*^9}, {3.572952326984375*^9, 3.572952331140625*^9}}, CellTags->"Efficiency"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"x", " ", RowBox[{"Cos", "[", "x", "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "t"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "10"}], "}"}]}], "]"}], "\[IndentingNewLine]", "]"}]], "Input", CellTags->"Efficiency"], Cell[BoxData["$Aborted"], "Output", CellChangeTimes->{3.572952343890625*^9}, CellTags->"Efficiency"] }, Open ]], Cell["\<\ V\[YAcute]po\[CHacek]ty jsou mnohem rychlej\[SHacek]\[IAcute], pokud je \ integr\[AAcute]l nejd\[RHacek]\[IAcute]ve vyhodnocen a pouze jednou. \ \>", "MathCaption", CellChangeTimes->{{3.57295216975*^9, 3.572952233203125*^9}, { 3.572952311875*^9, 3.572952312765625*^9}}, CellTags->"Efficiency"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"int", "=", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"x", " ", RowBox[{"Cos", "[", "x", "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "t"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{"int", ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "10"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "]"}]], "Input", CellTags->"Efficiency"], Cell[TextData[{ "Stejn\[YAcute] v\[YAcute]sledek obdr\[ZHacek]\[IAcute]me, pokud integr\ \[AAcute]l nejd\[RHacek]\[IAcute]ve vyhodnot\[IAcute]me pomoc\[IAcute] funkce \ ", Cell[BoxData[ ButtonBox["Evaluate", BaseStyle->"Link", ButtonData->"paclet:ref/Evaluate"]], "InlineFormula"], ", proto\[ZHacek]e argumenty funkce ", Cell[BoxData[ ButtonBox["Plot", BaseStyle->"Link", ButtonData->"paclet:ref/Plot"]], "InlineFormula"], " nejsou implicitn\[EHacek] vyhodnocov\[AAcute]ny." }], "MathCaption", CellChangeTimes->{{3.572952357140625*^9, 3.5729524234375*^9}}, CellTags->"Efficiency"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{"Integrate", "[", RowBox[{ RowBox[{"x", " ", RowBox[{"Cos", "[", "x", "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "t"}], "}"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "10"}], "}"}]}], "]"}], "\[IndentingNewLine]", "]"}]], "Input", CellTags->"Efficiency"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Efektivnost: ", "Color7", FontSlant->"Plain"], "Dal\[SHacek]\[IAcute] principy" }], "Subsection", CellChangeTimes->{{3.572952444921875*^9, 3.572952451171875*^9}, { 3.5729572015*^9, 3.572957202953125*^9}}, CellTags->"Efficiency"], Cell[TextData[{ "Existuje n\[EHacek]kolik dal\[SHacek]\[IAcute]ch prinicp\[URing] efektivn\ \[IAcute]ho programov\[AAcute]n\[IAcute], kter\[EAcute] jsou \ aplikov\[AAcute]ny zejm\[EAcute]na na programovac\[IAcute] jazyky vy\[SHacek]\ \[SHacek]\[IAcute] \[UAcute]rovn\[EHacek], kter\[YAcute]m je i SW ", StyleBox["Mathematica", FontSlant->"Italic"], "." }], "Text", CellChangeTimes->{{3.572952494265625*^9, 3.5729525669375*^9}}, CellTags->"Efficiency"], Cell[CellGroupData[{ Cell["\<\ Funkce vy\[SHacek]\[SHacek]\[IAcute] \[UAcute]rovn\[EHacek], kter\[EAcute] \ operuj\[IAcute] na cel\[YAcute]ch vektorech, matic\[IAcute]ch nebo jin\ \[YAcute]ch v\[YAcute]razech, kter\[EAcute] jsou v\[ZHacek]dy efektivn\ \[EHacek]j\[SHacek]\[IAcute] ne\[ZHacek] programy, kter\[EAcute] pracuj\ \[IAcute] s jednotliv\[YAcute]mi prvky v\[YAcute]raz\[URing]. \ \>", "Item", CellChangeTimes->{{3.572952574984375*^9, 3.57295265615625*^9}}, CellTags->"Efficiency"], Cell["\<\ Zva\[ZHacek]te pe\[CHacek]liv\[EHacek], kdy je t\[RHacek]eba pou\[ZHacek]\ \[IAcute]t p\[RHacek]esnou (symbolickou) a kdy nep\[RHacek]esnou (\[CHacek]\ \[IAcute]selnou) metodu v\[YAcute]po\[CHacek]tu.\ \>", "Item", CellChangeTimes->{{3.57295266634375*^9, 3.57295272425*^9}}, CellTags->"Efficiency"] }, Open ]], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Efektivnost: ", "Color7", FontSlant->"Plain"], "Pou\[ZHacek]it\[IAcute] funkc\[IAcute] vy\[SHacek]\[SHacek]\[IAcute] \ \[UAcute]rovn\[EHacek]" }], "Subsection", CellChangeTimes->{{3.572952459796875*^9, 3.57295247634375*^9}, { 3.572957254171875*^9, 3.572957255703125*^9}}, CellTags->"Efficiency"], Cell["\<\ Uva\[ZHacek]ujte \[UAcute]lohu, ve kt\[EAcute]r\[EAcute] m\[AAcute]te z\ \[IAcute]skat dvou prvn\[IAcute]ch sloupc\[URing] matice.\ \>", "Text", CellChangeTimes->{{3.57295273865625*^9, 3.572952782078125*^9}}, CellTags->"Efficiency"], Cell["Zadejte matici", "MathCaption", CellChangeTimes->{{3.572952789859375*^9, 3.5729527945625*^9}}, CellTags->"Efficiency"], Cell[BoxData[{ RowBox[{ RowBox[{"mat", "=", RowBox[{"(", GridBox[{ {"a", "b", "c"}, {"d", "e", "f"}, {"g", "h", "i"} }], ")"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "mat", "]"}]}], "Input", CellTags->"Efficiency"], Cell[TextData[{ "Tento program pou\[ZHacek]\[IAcute]v\[AAcute] ", Cell[BoxData[ ButtonBox["Table", BaseStyle->"Link", ButtonData->"paclet:ref/Table"]], "InlineFormula"], ". Tento program explicitn\[EHacek] vyb\[IAcute]r\[AAcute] z matice ka\ \[ZHacek]d\[YAcute] prvek v po\[ZHacek]adovan\[YAcute]ch sloupc\[IAcute]ch." }], "MathCaption", CellChangeTimes->{{3.572952892109375*^9, 3.572952970328125*^9}}, CellTags->"Efficiency"], Cell[BoxData[{ RowBox[{ RowBox[{"result", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"mat", "[", RowBox[{"[", RowBox[{"k", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"Length", "[", "mat", "]"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "result", "]"}]}], "Input", CellTags->"Efficiency"], Cell[TextData[{ "Tento program pou\[ZHacek]\[IAcute]v\[AAcute] vy\[SHacek]\[SHacek]\[IAcute] \ funkci ", Cell[BoxData[ ButtonBox["Take", BaseStyle->"Link", ButtonData->"paclet:ref/Take"]], "InlineFormula"], " a ", Cell[BoxData[ ButtonBox["All", BaseStyle->"Link", ButtonData->"paclet:ref/All"]], "InlineFormula"], " k dosa\[ZHacek]en\[IAcute] t\[EAcute]ho\[ZHacek]. Toto vyb\[IAcute]r\ \[AAcute] v\[SHacek]echny \[RHacek]\[AAcute]dky a prvn\[IAcute] dva sloupce." }], "MathCaption", CellChangeTimes->{{3.572952978859375*^9, 3.572953052109375*^9}}, CellTags->"Efficiency"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"result", "=", RowBox[{"Take", "[", RowBox[{"mat", ",", "All", ",", "2"}], "]"}]}], ";"}], " "}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "result", "]"}]}], "Input", CellTags->"Efficiency"], Cell["\<\ \:015arovnejte rychlost obou program\[URing] na v\[EHacek]t\:015b\[IAcute] \ matici. \ \>", "MathCaption", CellChangeTimes->{{3.572953058171875*^9, 3.57295308446875*^9}}, CellTags->"Efficiency"], Cell[BoxData[ RowBox[{ RowBox[{"mat", "=", RowBox[{"RandomReal", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ SuperscriptBox["10", "6"], ",", "10"}], "}"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.498909282931975*^9, 3.498909284379458*^9}}, CellTags->"Efficiency"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"mat", "[", RowBox[{"[", RowBox[{"k", ",", RowBox[{"1", ";;", "2"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"Length", "[", "mat", "]"}]}], "}"}]}], "]"}], ";"}], "\[IndentingNewLine]", "]"}]], "Input", CellTags->"Efficiency"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Take", "[", RowBox[{"mat", ",", "All", ",", "2"}], "]"}], ";"}], "\[IndentingNewLine]", "]"}]], "Input", CellTags->"Efficiency"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Part", "[", RowBox[{"mat", ",", "All", ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "]"}], ";"}], "\[IndentingNewLine]", "]"}]], "Input", CellTags->"Efficiency"], Cell["\<\ Existuje mnoho zp\[URing]sob\[URing] jak \[RHacek]e\[SHacek]it tento probl\ \[EAcute]m. V\[EHacek]t\[SHacek]ina z nich pou\[ZHacek]\[IAcute]v\[AAcute] vy\ \[SHacek]\[SHacek]\[IAcute] funkce, kter\[EAcute] jsou rychlej\[SHacek]\ \[IAcute], ne\[ZHacek] vytvo\[RHacek]en\[YAcute] procedur\[AAcute]ln\[IAcute] \ program.\ \>", "Text", CellChangeTimes->{{3.572953127625*^9, 3.57295319471875*^9}}, CellTags->"Efficiency"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad toto je procedur\[AAcute]ln\[IAcute] program vyu\ \[ZHacek]\[IAcute]vaj\[IAcute]c\[IAcute] ", Cell[BoxData[ ButtonBox["Do", BaseStyle->"Link", ButtonData->"paclet:ref/Do"]], "InlineFormula"], " cyklus k v\[YAcute]b\[EHacek]ru prvn\[IAcute]ch dvou sloupc\[URing] v \ matici ", StyleBox["m", "MR"], ". V tomto p\[RHacek]\[IAcute]kladu je pou\[ZHacek]ita mnohem men\[SHacek]\ \[IAcute] matice." }], "MathCaption", CellChangeTimes->{{3.572953198484375*^9, 3.572953281625*^9}, { 3.57295337746875*^9, 3.57295337840625*^9}}, CellTags->"Efficiency"], Cell[BoxData[{ RowBox[{ RowBox[{"mat", "=", RowBox[{"RandomReal", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ SuperscriptBox["10", "4"], ",", "3"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"AbsoluteTiming", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"result", "=", RowBox[{"Table", "[", RowBox[{"Null", ",", RowBox[{"{", RowBox[{"Length", "[", "mat", "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Do", "[", RowBox[{ RowBox[{ RowBox[{"result", "[", RowBox[{"[", "k", "]"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"mat", "[", RowBox[{"[", RowBox[{"k", ",", "1"}], "]"}], "]"}], ",", RowBox[{"mat", "[", RowBox[{"[", RowBox[{"k", ",", "2"}], "]"}], "]"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"Length", "[", "mat", "]"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "]"}]}], "Input", CellTags->"Efficiency"], Cell[TextData[{ "Uvolni hodnoty ", StyleBox["mat", "MR"], " a ", StyleBox["result", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.57295340428125*^9, 3.5729534094375*^9}}, CellTags->"Efficiency"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"mat", ",", "result"}], "]"}]], "Input", CellTags->"Efficiency"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Efektivnost: Operace s vektory", "Color7", FontSlant->"Plain"]], "Subsection", CellChangeTimes->{{3.572953424265625*^9, 3.572953432828125*^9}, { 3.57295726471875*^9, 3.5729572661875*^9}}, CellTags->"Efficiency"], Cell[TextData[{ "Vektorov\[EAcute] operace jsou v ", StyleBox["Mathematica", FontSlant->"Italic"], " rychl\[EAcute] kdykoliv je mo\[ZHacek]n\[EAcute] redukovat \[CHacek]i \ transformovat probl\[EAcute]m na operace s vektory, sn\[IAcute]\[ZHacek]\ \[IAcute]me i \[CHacek]asovou n\[AAcute]ro\[CHacek]nost cel\[EAcute]ho v\ \[YAcute]po\[CHacek]tu. " }], "Text", CellChangeTimes->{{3.57295344975*^9, 3.57295353478125*^9}}], Cell[TextData[{ "N\[AAcute]sleduj\[IAcute]c\[IAcute] p\[RHacek]\[IAcute]klad vezme matici se \ dv\[EHacek]ma sloupci a vytvo\[RHacek]\[IAcute] 3-sloupcovou matici, ve kter\ \[EAcute] se 3. sloupec skl\[AAcute]d\[AAcute] z ", Cell[BoxData[ FormBox[ SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]}]], TraditionalForm]]], " kde {", Cell[BoxData[ FormBox["x", TraditionalForm]]], ",", Cell[BoxData[ FormBox["y", TraditionalForm]]], "} je p\[URing]vodn\[IAcute] \[RHacek]\[AAcute]dkov\[YAcute] vektor." }], "Text", CellChangeTimes->{{3.5729535388125*^9, 3.572953619421875*^9}}], Cell["\<\ Zde je mal\[AAcute] matice se dv\[EHacek]ma sloupci. k otestov\[AAcute]n\ \[IAcute] \[RHacek]e\:015ben\[IAcute].\ \>", "MathCaption", CellChangeTimes->{{3.57295362490625*^9, 3.572953666671875*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"mat", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ SubscriptBox["x", "1"], 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\[RHacek]\ \[AAcute]dkov\[EAcute] vektory. \ \>", "MathCaption", CellChangeTimes->{{3.572953693234375*^9, 3.57295374925*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", RowBox[{"{", RowBox[{"a_", ",", "b_"}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{"a", ",", "b", ",", SqrtBox[ RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]}]]}], "}"}]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Map", "[", RowBox[{"f", ",", "mat"}], "]"}], "//", "MatrixForm"}]], "Input"], Cell[TextData[{ "T\[RHacek]et\[IAcute] zp\[URing]sob \[RHacek]e\[SHacek]en\[IAcute] nejd\ \[RHacek]\[IAcute]ve vybere jednotliv\[EAcute] sloupce a pot\[EAcute] je spoj\ \[IAcute] dohromady pomoc\[IAcute] ", Cell[BoxData[ ButtonBox["Transpose", BaseStyle->"Link", ButtonData->"paclet:ref/Transpose"]], "InlineFormula"], " do v\[YAcute]sledn\[EAcute] matice." }], "MathCaption", CellChangeTimes->{{3.57295615053125*^9, 3.57295621671875*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"c1", "=", RowBox[{"mat", "[", RowBox[{"[", 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RowBox[{ RowBox[{"bigmat", "/.", RowBox[{ RowBox[{"{", RowBox[{"a_", ",", "b_"}], "}"}], "\[RuleDelayed]", RowBox[{"{", RowBox[{"a", ",", "b", ",", SqrtBox[ RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]}]]}], "}"}]}]}], ";"}], "//", "AbsoluteTiming"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"4.046875`6.6277197033769895", ",", "Null"}], "}"}]], "Output", CellChangeTimes->{3.57295625865625*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Map", "[", RowBox[{"f", ",", "bigmat"}], "]"}], ";"}], "//", "AbsoluteTiming"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"0.59375`5.794203535912547", ",", "Null"}], "}"}]], "Output", CellChangeTimes->{3.572956263921875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"c1", "=", RowBox[{"bigmat", "[", RowBox[{"[", RowBox[{"All", ",", "1"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"c2", "=", RowBox[{"bigmat", 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"Subsection", CellChangeTimes->{{3.57295634984375*^9, 3.572956363296875*^9}, { 3.572956833828125*^9, 3.572956838265625*^9}, {3.572957271984375*^9, 3.57295727346875*^9}}, CellTags->"Efficiency"], Cell["\<\ N\[EHacek]kdy je d\[URing]le\[ZHacek]it\[EAcute] zvolit spr\[AAcute]vn\ \[EHacek] p\[RHacek]esn\[YAcute] nebo p\[RHacek]ibli\[ZHacek]n\[YAcute] zp\ \[URing]sob v\[YAcute]po\[CHacek]tu. Toto rozhodnut\[IAcute] m\[URing]\ \[ZHacek]e m\[IAcute]t velk\[YAcute] vliv na \[UAcute]\[CHacek]innost v\ \[YAcute]po\[CHacek]tu.\ \>", "Text", CellChangeTimes->{{3.5729563685*^9, 3.572956425125*^9}, { 3.572956843890625*^9, 3.572956851734375*^9}, {3.57295727815625*^9, 3.572957281953125*^9}}, CellTags->"Efficiency"], Cell["\<\ Uva\[ZHacek]ujme n\[AAcute]sleduj\[IAcute]c\[IAcute] probl\[EAcute]m, \ \[RHacek]e\[SHacek]\[IAcute]c\[IAcute] sumu vyrazu. Uveden\[YAcute] \ p\[RHacek]esn\[YAcute] v\[YAcute]po\[CHacek]et eliminuje mo\[ZHacek]nost \ numerick\[YAcute]ch chyb, na druh\[EAcute] stran\[EHacek] m\[URing]\[ZHacek]e \ b\[YAcute]t v\[YAcute]sledek velmi objemn\[YAcute] a \ ne\[CHacek]iteln\[YAcute].\ \>", "MathCaption", CellChangeTimes->{{3.572956429421875*^9, 3.5729565055*^9}, { 3.572956560015625*^9, 3.5729565666875*^9}, {3.572956667109375*^9, 3.57295667709375*^9}}, CellTags->"Efficiency"], Cell[BoxData[ RowBox[{"result", "=", RowBox[{"Sum", "[", RowBox[{ SuperscriptBox[ RowBox[{"(", FractionBox[ RowBox[{"3", "/", "4"}], "k"], ")"}], FractionBox["k", RowBox[{"3", "/", "4"}]]], ",", RowBox[{"{", RowBox[{"k", ",", "5"}], "}"}]}], "]"}]}]], "Input", CellTags->"Efficiency"], Cell["\<\ \[CapitalCHacek]\[IAcute]seln\[AAcute] aproximace je nutn\[AAcute] s ohledem \ na zji\[SHacek]t\[EHacek]n\[IAcute] odpov\[EHacek]di na ot\[AAcute]zku, zda \ je v\[YAcute]sledek men\[SHacek]\[IAcute] nebo v\[EHacek]t\:015b\[IAcute] ne\ \[ZHacek] 1.\ \>", "MathCaption", CellChangeTimes->{{3.57295657384375*^9, 3.572956625453125*^9}, 3.5729568705625*^9}, CellTags->"Efficiency"], Cell[BoxData[ RowBox[{"N", "[", "result", "]"}]], "Input", CellTags->"Efficiency"], Cell["\<\ Odpov\[IAcute]daj\[IAcute]c\[IAcute] p\[RHacek]ibli\[ZHacek]n\[YAcute] v\ \[YAcute]sledek je mnohem kompaktn\[EHacek]j\[SHacek]\[IAcute]. 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