(* 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[ 142174, 4360] NotebookOptionsPosition[ 99280, 3131] NotebookOutlinePosition[ 119261, 3671] CellTagsIndexPosition[ 119049, 3662] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["Numerick\[EAcute] v\[YAcute]po\[CHacek]ty", "Title", CellChangeTimes->{{3.5783805415*^9, 3.578380558875*^9}}, TextAlignment->Center], Cell["Obsah", "Text", CellChangeTimes->{{3.578380822953125*^9, 3.578380823609375*^9}}], Cell["", "OverviewSection", CellChangeTimes->{{3.578380653390625*^9, 3.5783806556875*^9}, { 3.578380812609375*^9, 3.578380814578125*^9}}, CellTags->"Overview"], Cell["\<\ Tato kapitola 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Adres\[AAcute]\ \[RHacek]e, ve kter\[YAcute]ch le\[ZHacek]\[IAcute] datov\[YAcute] adres\ \[AAcute]\[RHacek] DataFiles je nutn\[EAcute] p\[RHacek]izp\[URing]sobit aktu\ \[AAcute]ln\[IAcute]mu nastaven\[IAcute].\ \>", "MathCaption", CellChangeTimes->{{3.578381877453125*^9, 3.5783819265*^9}, { 3.578381990640625*^9, 3.578382026640625*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"filedata", "=", RowBox[{"FileNameJoin", "[", RowBox[{"{", RowBox[{ "$HomeDirectory", ",", "\"\\"", ",", "\"\\"", ",", "\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}], "]"}]}]], "Input", CellChangeTimes->{{3.578381936171875*^9, 3.578381984953125*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"data", "=", RowBox[{"Import", "[", RowBox[{"filedata", ",", "\"\\""}], "]"}]}]], "Input", CellTags->"Functions"], Cell[BoxData[ RowBox[{"dataplot", "=", RowBox[{"ListPlot", "[", "data", "]"}]}]], "Input", CellTags->"Functions"], Cell[TextData[{ "N\[AAcute]sleduj\[IAcute]c\[IAcute] p\[RHacek]\[IAcute]kaz vytvo\[RHacek]\ \[IAcute] interpola\[CHacek]n\[IAcute] funkci, kterou je \ mo\[ZHacek]n\[EAcute] pou\[ZHacek]\[IAcute]t jako kteroukoliv jinou funkci v ", StyleBox["Mathematica", FontSlant->"Italic"], "." }], "MathCaption", CellChangeTimes->{{3.578382058859375*^9, 3.5783820985*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"f", "=", RowBox[{"Interpolation", "[", "data", "]"}]}]], "Input", CellTags->"Functions"], Cell["\<\ Na obr\[AAcute]zku je nakreslen graf interpola\[CHacek]n\[IAcute] funkce \ spolu s p\[URing]vodn\[IAcute]mi daty.\ \>", "MathCaption", CellChangeTimes->{{3.57838212659375*^9, 3.578382156890625*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"{", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"f", "[", "x", "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "4"}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", "Red"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", "dataplot"}], "}"}], "]"}]], "Input", CellTags->"Functions"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"f", ",", "data", ",", "dataplot", ",", "filedata"}], "]"}]], "Input", CellTags->"Functions"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Funkce pro numerick\[EAcute] v\[YAcute]po\[CHacek]ty:", "Color7", FontSlant->"Plain"], StyleBox[" ", FontSlant->"Plain"], "Integrov\[AAcute]n\[IAcute]" }], "Subsection", CellChangeTimes->{{3.578822848955375*^9, 3.5788228725031548`*^9}}, CellTags->"Functions"], Cell[TextData[{ "N\[AAcute]sleduj\[IAcute]c\[IAcute] vrac\[IAcute] \[CHacek]\[IAcute]seln\ \[YAcute] integr\[AAcute]lfunkce ", Cell[BoxData[ RowBox[{"Exp", "[", "x", "]"}]]], " dle x pro ", StyleBox["x", "MR"], " od 0 do 1." }], "Text", CellChangeTimes->{{3.578822883159814*^9, 3.5788229269271193`*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{"Exp", "[", "x", "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Functions"], Cell[TextData[{ "P\[RHacek]i integrov\[AAcute]n\[IAcute] mnoha funkc\[IAcute] mohou nastat \ probl\[EAcute]my p\[RHacek]i pou\[ZHacek]it\[IAcute] numerick\[YAcute]ch \ postup\[URing] v ", Cell[BoxData[ ButtonBox["NIntegrate", BaseStyle->"Link", ButtonData->"paclet:ref/NIntegrate"]], "InlineFormula"], ". V takov\[YAcute]ch p\[RHacek]\[IAcute]padech je obvykle d\[URing]le\ \[ZHacek]it\[EAcute] takovou funkci analyzovat a odpov\[IAcute]daj\[IAcute]c\ \[IAcute]m zp\[URing]sobem upravit argumenty nebo podm\[IAcute]nky pro \ integrov\[AAcute]n\[IAcute] ru\[CHacek]n\[EHacek]." }], "Text", CellChangeTimes->{{3.5788229454590807`*^9, 3.5788230936366453`*^9}}, CellTags->"Functions"], Cell["\<\ Zde je p\[RHacek]\[IAcute]klad funkce, ve kter\[EAcute] na dan\[EAcute]m \ oboru integrov\[AAcute]n\[IAcute] existuje cel\[AAcute] \[RHacek]ada \ nespojitost\[IAcute].\ \>", "MathCaption", CellChangeTimes->{{3.5788230969961495`*^9, 3.5788231430916696`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ FractionBox["1", SqrtBox[ RowBox[{"Sin", "[", "x", "]"}]]], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"10.303166074630907`", "\[VeryThinSpace]", "-", RowBox[{"6.742554183083223`", " ", "\[ImaginaryI]"}]}]], "Output", CellChangeTimes->{3.578823281893874*^9}] }, Open ]], Cell[TextData[{ "Pokud pou\[ZHacek]ijeme podm\[IAcute]nku ", Cell[BoxData[ ButtonBox["Exclusions", BaseStyle->"Link", ButtonData->"paclet:ref/Exclusions"]], "InlineFormula"], ", m\[URing]\[ZHacek]eme specifikovat tyto nespojitosti a vylou\[CHacek]it \ je z v\[YAcute]po\[CHacek]tu." }], "MathCaption", CellChangeTimes->{{3.578823166561321*^9, 3.5788232145787897`*^9}}], Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ FractionBox["1", SqrtBox[ RowBox[{"Sin", "[", "x", "]"}]]], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"Exclusions", "\[Rule]", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "\[Equal]", "0"}]}]}], "]"}]], "Input"], Cell[TextData[{ "Pop\[RHacek]. je mo\[ZHacek]n\[EAcute] nastavit v\[EHacek]t\[SHacek]\ \[IAcute] po\[CHacek]et rekurz\[IAcute] ", Cell[BoxData[ ButtonBox["MaxRecursion", BaseStyle->"Link", ButtonData->"paclet:ref/MaxRecursion"]], "InlineFormula"], " tak, abychom z\[IAcute]skali p\[RHacek]esn\[EAcute]j\[SHacek]\[IAcute] v\ \[YAcute]sledek." }], "MathCaption", CellChangeTimes->{{3.578823235845231*^9, 3.5788232778937206`*^9}}, CellID->416954400], Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ FractionBox["1", SqrtBox[ RowBox[{"Sin", "[", "x", "]"}]]], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"MaxRecursion", "\[Rule]", "100"}]}], "]"}]], "Input", CellID->682978387], Cell["\<\ V takov\[EAcute]m p\[RHacek]\[IAcute]pad\[EHacek] je efektivn\[EHacek]j\ \[SHacek]\[IAcute] explicitn\[EHacek] specifikovat nespojitosti na dan\ \[EAcute]m intervalu..\ \>", "MathCaption", CellChangeTimes->{{3.5788233304738646`*^9, 3.578823363397004*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ FractionBox["1", SqrtBox[ RowBox[{"Sin", "[", "x", "]"}]]], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "\[Pi]", ",", RowBox[{"2", " ", "\[Pi]"}], ",", RowBox[{"3", " ", "\[Pi]"}], ",", "10"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{3.5788233793976183`*^9}, CellTags->"Functions"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Funkce pro numerick\[EAcute] v\[YAcute]po\[CHacek]ty:", "Color7", FontSlant->"Plain"], StyleBox[" \[CapitalRHacek]e\[SHacek]en\[IAcute] rovnic", FontSlant->"Plain"] }], "Subsection", CellChangeTimes->{{3.578823395007593*^9, 3.578823414539549*^9}}, CellTags->"Functions"], Cell[TextData[{ "Funkci ", Cell[BoxData[ ButtonBox["FindRoot", BaseStyle->"Link", ButtonData->"paclet:ref/FindRoot"]], "InlineFormula"], " je mo\[ZHacek]n\[EAcute] pou\[ZHacek]\[IAcute]t pro \ v\[YAcute]po\[CHacek]et \[CHacek]\[IAcute]seln\[EAcute]ho \ \[RHacek]e\[SHacek]en\[IAcute] rovnice nebo soustavy rovnic." }], "Text", CellChangeTimes->{{3.5788234179771595`*^9, 3.578823475713382*^9}}, CellTags->"Functions"], Cell[TextData[{ "N\[AAcute]sleduje typick\[YAcute] v\[YAcute]po\[CHacek]et s pou\[ZHacek]it\ \[IAcute]m ", Cell[BoxData[ ButtonBox["FindRoot", BaseStyle->"Link", ButtonData->"paclet:ref/FindRoot"]], "InlineFormula"], ". Po\[CHacek]\[AAcute]te\[CHacek]n\[IAcute] (startovac\[IAcute]) hodnota \ hledan\[EAcute]ho \[RHacek]e\[SHacek]en\[IAcute] je \ vy\[ZHacek]adov\[AAcute]na pou\[ZHacek]it\[YAcute]m itera\[CHacek]n\[IAcute]m \ algoritmem (Newtonova metoda). \[CapitalRHacek]e\[SHacek]en\[IAcute] je vr\ \[AAcute]ceno jako seznam substitu\[CHacek]n\[IAcute]ch pravidel (", ButtonBox["Demonstrace Newtonovy metody", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/TwoGeometricViewsOfNewtonsMethod/"]\ , None}, ButtonNote-> "http://demonstrations.wolfram.com/TwoGeometricViewsOfNewtonsMethod/"], ")." }], "MathCaption", CellChangeTimes->{{3.578823483244873*^9, 3.5788236497033243`*^9}, { 3.578823680798069*^9, 3.5788236869545164`*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "\[Equal]", RowBox[{"Exp", "[", RowBox[{"-", "x"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Functions"], Cell["\<\ Velmi u\[ZHacek]ite\[CHacek]n\[YAcute]m n\[AAcute]strojem k stanoven\[IAcute] \ startovac\[IAcute]ch hodnot je vykreslen\[IAcute] grafu rozd\[IAcute]lu obou \ lev\[EAcute] a prav\[EAcute] strany rovnice.\ \>", "MathCaption", CellChangeTimes->{{3.578823660797429*^9, 3.5788237357217016`*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "-", RowBox[{"Exp", "[", RowBox[{"-", "x"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "6"}], "}"}]}], "]"}]], "Input", CellTags->"Functions"], Cell[TextData[{ "\[CapitalRHacek]e\[SHacek]en\[IAcute] pro ", StyleBox["x", "MR"], " pobl\[IAcute]\[ZHacek] 3 m\[URing]\[ZHacek]e b\[YAcute]t nalezeno u\ \[ZHacek]it\[IAcute]m startovac\[IAcute] hodnoty bl\[IAcute]zko \[RHacek]e\ \[SHacek]en\[IAcute]." }], "MathCaption", CellChangeTimes->{{3.5788237725353794`*^9, 3.578823823865147*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "\[Equal]", RowBox[{"Exp", "[", RowBox[{"-", "x"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "3"}], "}"}]}], "]"}]], "Input", CellTags->"Functions"], Cell[TextData[{ Cell[BoxData[ ButtonBox["FindRoot", BaseStyle->"Link", ButtonData->"paclet:ref/FindRoot"]], "InlineFormula"], " m\[URing]\[ZHacek]e b\[YAcute]t pou\[ZHacek]ita i k \[CHacek]\[IAcute]seln\ \[EAcute]mu \[RHacek]e\[SHacek]en\[IAcute] soustavy rovnic." }], "MathCaption", CellChangeTimes->{{3.578823831271634*^9, 3.578823856991207*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]}], "\[Equal]", "1"}], ",", RowBox[{"y", "\[Equal]", SuperscriptBox["x", "2"]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Functions"], Cell[TextData[{ Cell[BoxData[ ButtonBox["NSolve", BaseStyle->"Link", ButtonData->"paclet:ref/NSolve"]], "InlineFormula"], " je dal\[SHacek]\[IAcute] funkc\[IAcute], kter\[AAcute] nalezne \ v\[SHacek]echna \[CHacek]\[IAcute]seln\[AAcute] \ \[RHacek]e\[SHacek]en\[IAcute]." }], "MathCaption", CellChangeTimes->{{3.57882386941348*^9, 3.578823894133021*^9}}], Cell[BoxData[ RowBox[{"NSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]}], "\[Equal]", "1"}], ",", RowBox[{"y", "\[Equal]", SuperscriptBox["x", "2"]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5788239134148874`*^9, 3.578823927571591*^9}}], Cell[TextData[{ "Jako pom\[URing]cku je mo\[ZHacek]n\[EAcute] pou\[ZHacek]\[IAcute]t funkci ", Cell[BoxData[ ButtonBox["ContourPlot", BaseStyle->"Link", ButtonData->"paclet:ref/ContourPlot"]], "InlineFormula"], " k vytvo\[RHacek]en\[IAcute] graf\[URing] implicitn\[EHacek] definovan\ \[YAcute]ch funkc\[IAcute]." }], "MathCaption", CellChangeTimes->{{3.5788239686822815`*^9, 3.5788240472160444`*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"ContourPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]}], "\[Equal]", "1"}], ",", RowBox[{"y", "\[Equal]", SuperscriptBox["x", "2"]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Functions"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Funkce pro numerick\[EAcute] v\[YAcute]po\[CHacek]ty: ", "Color7", FontSlant->"Plain"], "Optimalizace" }], "Subsection", CellChangeTimes->{{3.5788241153275986`*^9, 3.5788241301874495`*^9}}, CellTags->"Functions"], Cell[TextData[{ "Funkci ", Cell[BoxData[ ButtonBox["FindMinimum", BaseStyle->"Link", ButtonData->"paclet:ref/FindMinimum"]], "InlineFormula"], " je mo\[ZHacek]n\[EAcute] pou\[ZHacek]\[IAcute]t k v\[YAcute]po\[CHacek]tu \ \[CHacek]\[IAcute]seln\[EAcute] hodnoty minima pro jednu nebo v\[IAcute]ce \ prom\[EHacek]nn\[YAcute]ch." }], "Text", CellChangeTimes->{{3.5788241463129654`*^9, 3.5788242120338182`*^9}}, CellTags->"Functions"], Cell["\<\ Nejd\[RHacek]\[IAcute]ve vykresl\[IAcute]me graf funkce, \ jej\[IAcute]\[ZHacek] minimum hled\[AAcute]me.\ \>", "MathCaption", CellChangeTimes->{{3.5788242179871335`*^9, 3.578824242941057*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Exp", "[", "x", "]"}], RowBox[{"Cos", "[", "x", "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}]}], "]"}]], "Input", CellTags->"Functions"], Cell[CellGroupData[{ Cell[TextData[{ "N\[AAcute]sleduj\[IAcute]c\[IAcute] p\[RHacek]\[IAcute]kaz ukazuje pou\ \[ZHacek]it\[IAcute] ", Cell[BoxData[ 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V\ \[YAcute]sledkem je seznam dvou prvk\[URing]. Prvn\[IAcute] prvek je hodnota \ funkce v dan\[EAcute]m lok\[AAcute]ln\[IAcute]m minimu a druh\[YAcute] prvek \ je seznam substitu\[CHacek]n\[IAcute]ch pravidel, kter\[AAcute] obsahuj\ \[IAcute] hodnotu prom\[EHacek]nn\[EAcute] pro dan\[EAcute] minimum." }], "MathCaption", CellGroupingRules->{Global`GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.578824278832831*^9, 3.578824437666001*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"s", " ", "=", " ", RowBox[{"FindMinimum", "[", RowBox[{ RowBox[{ RowBox[{"Exp", "[", "x", "]"}], RowBox[{"Cos", "[", "x", "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "4"}], "}"}]}], "]"}]}]], "Input", CellGroupingRules->{Global`GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.5788245868416944`*^9, 3.5788245873573327`*^9}}, CellTags->"Functions"] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "35.888511369222115`"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", "3.9269908169180185`"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.5788244498538127`*^9, 3.578824588451111*^9}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"x", "/.", RowBox[{"Last", "[", "s", "]"}]}], ",", RowBox[{"First", "[", "s", "]"}]}], "}"}], "]"}]], "Input", CellChangeTimes->{3.5788246769533763`*^9}], Cell[BoxData[ RowBox[{"Show", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Exp", "[", "x", "]"}], RowBox[{"Cos", "[", "x", "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}]}], "]"}], ",", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"PointSize", "[", "0.02", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"x", "/.", RowBox[{"Last", "[", "s", "]"}]}], ",", RowBox[{"First", "[", "s", "]"}]}], "}"}], "]"}]}], "}"}], "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.578824543387457*^9, 3.5788246287646427`*^9}, { 3.578824741314399*^9, 3.5788247805966544`*^9}}], Cell[TextData[{ "Mathematica nab\[IAcute]z\[IAcute] i n\[EHacek]kolik funkc\[IAcute] pro \ \[RHacek]e\[SHacek]en\[IAcute] glob\[AAcute]ln\[IAcute]ch \ optimaliza\[CHacek]n\[IAcute]ch probl\[EAcute]m\[URing]. \ Nap\[RHacek]\[IAcute]klad na\:015bleduj\[IAcute]c\[IAcute] minimum funkce ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{"y", "-", FractionBox["1", "2"]}], ")"}], "2"]}], TraditionalForm]], "InlineFormula"], " s ohledem na omezen\[IAcute] ", Cell[BoxData[ FormBox[ RowBox[{"y", "\[GreaterEqual]", "0"}], TraditionalForm]], "InlineFormula"], " a ", Cell[BoxData[ FormBox[ RowBox[{"y", "\[GreaterEqual]", RowBox[{"x", "+", "1"}]}], TraditionalForm]], "InlineFormula"], ". 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Um\[IAcute] \ \[RHacek]e\[SHacek]it probl\[EAcute]m inicializa\[CHacek]n\[IAcute]ch hodnot, \ probl\[EAcute]m hrani\[CHacek]n\[IAcute]ch hodnot line\[AAcute]rn\[IAcute]ch \ rovnic a parci\[AAcute]ln\[IAcute] diferenci\[AAcute]ln\[IAcute] rovnice dvou \ prom\[EHacek]nn\[YAcute]ch." }], "Text", CellChangeTimes->{{3.5788261603774676`*^9, 3.578826323161843*^9}}, CellTags->"Functions"], Cell[TextData[{ "N\[AAcute]sleduj\[IAcute]c\[IAcute] ukazuje pou\[ZHacek]it\[IAcute] ", Cell[BoxData[ ButtonBox["NDSolve", BaseStyle->"Link", ButtonData->"paclet:ref/NDSolve"]], "InlineFormula"], " k \[RHacek]e\[SHacek]en\[IAcute] probl\[EAcute]mu inicializa\[CHacek]n\ \[IAcute]ch hodnot.." }], "MathCaption", CellChangeTimes->{{3.578826327974435*^9, 3.578826366209544*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"soln", "=", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"f", "''"}], "[", "x", "]"}], "+", RowBox[{ RowBox[{"f", "'"}], "[", "x", "]"}], "+", RowBox[{"f", "[", "x", "]"}]}], "\[Equal]", "0"}], ",", RowBox[{ RowBox[{"f", "[", "0", "]"}], "\[Equal]", "1"}], ",", RowBox[{ RowBox[{ RowBox[{"f", "'"}], "[", "0", "]"}], "\[Equal]", "1"}]}], "}"}], ",", "f", ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "10"}], "}"}]}], "]"}]}]], "Input", CellTags->"Functions"], Cell[TextData[{ "V\[YAcute]sledek vrac\[IAcute] ", Cell[BoxData[ ButtonBox["NDSolve", BaseStyle->"Link", ButtonData->"paclet:ref/NDSolve"]], "InlineFormula"], " ve stejn\[EAcute]m form\[AAcute]tu jako funkce ", Cell[BoxData[ ButtonBox["Solve", BaseStyle->"Link", ButtonData->"paclet:ref/Solve"]], "InlineFormula"], " a ", Cell[BoxData[ ButtonBox["DSolve", BaseStyle->"Link", ButtonData->"paclet:ref/DSolve"]], "InlineFormula"], ", a pracujeme s n\[IAcute]m stejn\[YAcute]m zp\[URing]sobem." }], "Text", CellChangeTimes->{{3.5788263806473217`*^9, 3.578826408835363*^9}, { 3.5788264752272625`*^9, 3.578826511384207*^9}}, CellTags->"Functions"], Cell[TextData[{ "\[CapitalRHacek]e\[SHacek]en\[IAcute] jsou reprezentovana s pou\[ZHacek]it\ \[IAcute]m objektu ", Cell[BoxData[ ButtonBox["InterpolatingFunction", BaseStyle->"Link", ButtonData->"paclet:ref/InterpolatingFunction"]], "InlineFormula"], ", kter\[YAcute] vyu\[ZHacek]\[IAcute]v\[AAcute] obvykl\[YAcute] \ zp\[URing]sob interpolace mezi body, kter\[EAcute] byly vypo\[CHacek]teny \ \[RHacek]e\[SHacek]itelem diferenci\[AAcute]ln\[IAcute] rovnice." }], "Text", CellChangeTimes->{{3.5788265163218017`*^9, 3.578826634230315*^9}}, CellTags->"Functions"], Cell[TextData[{ "Hodnotu \[RHacek]e\[SHacek]en\[IAcute] v bodu ", StyleBox["x", "MR"], " obdr\[ZHacek]\[IAcute]me pou\[ZHacek]it\[IAcute]m \[RHacek]e\[SHacek]en\ \[IAcute] k substituci ", StyleBox["f", "MR"], " v ", Cell[BoxData[ RowBox[{"f", "[", "x", "]"}]]], ". N\[AAcute]p\[RHacek]\[IAcute]klad n\[AAcute]sleduj\[IAcute]c\[IAcute] \ vstup hodnotu \[RHacek]e\[SHacek]en\[IAcute] pro ", Cell[BoxData[ RowBox[{"f", "[", "2", "]"}]]], "." }], "MathCaption", CellChangeTimes->{{3.5788266535275607`*^9, 3.578826757092049*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "2", "]"}], "/.", "soln"}]], "Input", CellTags->"Functions"], Cell["\<\ N\[AAcute]sleduj\[IAcute]c\[IAcute] generuje graf \[RHacek]e\[SHacek]en\ \[IAcute].\ \>", "MathCaption", CellChangeTimes->{{3.5788267735611153`*^9, 3.578826789889554*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"f", "[", "x", "]"}], "/.", "soln"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input", CellTags->"Functions"], Cell["\<\ V\[YAcute]hodou pr\[AAcute]ce s interpola\[CHacek]n\[IAcute] funkc\[IAcute] \ je jej\[IAcute] spojitost, kter\[AAcute] umo\[ZHacek]\[NHacek]uje jednodu\ \[SHacek]e prov\[AAcute]d\[EHacek]t mnoho z\[AAcute]kladn\[IAcute]ch v\ \[YAcute]po\[CHacek]t\[URing]. N\[AAcute]sleduje p\[RHacek]\[IAcute]klad \ vykreslen\[IAcute] grafu derivace \[RHacek]e\[SHacek]en\[IAcute].\ \>", "MathCaption", CellChangeTimes->{{3.578826811593096*^9, 3.578826917392002*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"f", "'"}], "[", "x", "]"}], "/.", "soln"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input", CellTags->"Functions"], Cell[TextData[{ "Pokud chceme vid\[EHacek]t jednotliv\[EAcute] diskr\[EAcute]tn\[IAcute] \ body, ze kter\[YAcute]ch se ", "interpola\[CHacek]n\[IAcute] funkce ", "skl\[AAcute]d\[AAcute], m\[URing]\[ZHacek]eme tyto hodnoty z\[IAcute]skat s \ pou\[ZHacek]it\[IAcute]m funkce ", Cell[BoxData[ ButtonBox["EvaluationMonitor", BaseStyle->"Link", ButtonData->"paclet:ref/EvaluationMonitor"]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.5788269611584673`*^9, 3.578827028175379*^9}, { 3.578827135396188*^9, 3.57882717355317*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"soln", "=", RowBox[{"Reap", "[", "\[IndentingNewLine]", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"f", "''"}], "[", "x", "]"}], "+", RowBox[{ RowBox[{"f", "'"}], "[", "x", "]"}], "+", RowBox[{"f", "[", "x", "]"}]}], "\[Equal]", "0"}], ",", RowBox[{ RowBox[{"f", "[", "0", "]"}], "\[Equal]", "1"}], ",", RowBox[{ RowBox[{ RowBox[{"f", "'"}], "[", "0", "]"}], "\[Equal]", "1"}]}], "}"}], ",", "f", ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"EvaluationMonitor", "\[RuleDelayed]", RowBox[{"Sow", "[", RowBox[{"{", RowBox[{"x", ",", RowBox[{"f", "[", "x", "]"}]}], "}"}], "]"}]}]}], "]"}], "\[IndentingNewLine]", "]"}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{"Short", "[", RowBox[{ RowBox[{"Last", "[", "soln", "]"}], ",", "12"}], "]"}]], "Input"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Funkce pro numerick\[EAcute] v\[YAcute]po\[CHacek]ty:", "Color7", FontSlant->"Plain"], StyleBox[" ", "Color7"], "\[CapitalRHacek]e\[SHacek]en\[IAcute] soustavy line\[AAcute]rn\[IAcute]ch \ rovnic" }], "Subsection", CellChangeTimes->{{3.579243955109375*^9, 3.579243978*^9}}, CellTags->"Functions"], Cell[TextData[{ "\[CapitalRHacek]e\[SHacek]en\[IAcute] soustav rovnic pomoc\[IAcute] maticov\ \[YAcute]ch metod je jednou z nejstar\[SHacek]\[IAcute]ch a nejobvyklej\ \[SHacek]\[IAcute]ch \[UAcute]loh p\[RHacek]i pr\[AAcute]ci s velk\[YAcute]m \ objemem dat. Pokud m\[AAcute]me d\[AAcute]nu matici ", Cell[BoxData[ FormBox["A", TraditionalForm]]], " avektor ", Cell[BoxData[ FormBox["b", TraditionalForm]]], ", \[RHacek]e\[SHacek]en\[IAcute] rovnice ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"A", ".", "x"}], "=", "b"}], TraditionalForm]]], " m\[URing]\[ZHacek]e b\[YAcute]t dosa\[ZHacek]eno r\[URing]zn\[YAcute]mi \ postupy. P\[RHacek]esto\[ZHacek]e je mo\[ZHacek]n\[EAcute] za\[CHacek]\ \[IAcute]t \[RHacek]e\[SHacek]en\[IAcute] hled\[AAcute]n\[IAcute]m inverzn\ \[IAcute] matice ", Cell[BoxData[ FormBox[ SuperscriptBox["A", RowBox[{"-", "1"}]], TraditionalForm]]], ", v ", StyleBox["Mathematica", FontSlant->"Italic"], " existuj\[IAcute] vhodn\[EHacek]j\[SHacek]\[IAcute] a efektivn\[EHacek]j\ \[SHacek]\[IAcute] postupy \[RHacek]e\[SHacek]en\[IAcute]." }], "Text", CellChangeTimes->{{3.579243983890625*^9, 3.579244223234375*^9}}, CellTags->"Functions"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad m\[AAcute]me d\[AAcute]nu jednoduchou matici ", Cell[BoxData[ FormBox["A", TraditionalForm]]], " a vektor ", Cell[BoxData[ FormBox["b", TraditionalForm]]], "." }], "MathCaption", CellChangeTimes->{{3.579244225234375*^9, 3.579244244421875*^9}}, CellTags->"Functions"], Cell[BoxData[{ RowBox[{ RowBox[{"A", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1.", ",", " ", "2."}], "}"}], ",", RowBox[{"{", RowBox[{"3.", ",", 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\>", "Text", CellChangeTimes->{{3.579244314078125*^9, 3.57924434103125*^9}}, CellTags->"Functions"], Cell[TextData[{ "N\[AAcute]sleduje definice matice ", Cell[BoxData[ FormBox[ RowBox[{"1000", "\[Cross]", "1000"}], TraditionalForm]]], " n\[AAcute]hodn\[YAcute]ch \[CHacek]\[IAcute]sel a odpov\[IAcute]daj\ \[IAcute]c\[IAcute] vektor." }], "MathCaption", CellChangeTimes->{{3.57924434659375*^9, 3.579244370703125*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{ RowBox[{"mat", "=", RowBox[{"RandomReal", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1000", ",", "1000"}], "}"}]}], "]"}]}], ";"}]], "Input", CellTags->"Functions"], Cell[BoxData[ RowBox[{ RowBox[{"b", "=", RowBox[{"RandomReal", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"Length", "[", "mat", "]"}], "}"}]}], "]"}]}], ";"}]], "Input", CellTags->"Functions"], Cell["\<\ N\[AAcute]sleduj\[IAcute]c\[IAcute] p\[RHacek]\[IAcute]kaz \ \[RHacek]e\[SHacek]\[IAcute] maticovou rovnici a \ zm\[EHacek]\[RHacek]\[IAcute] dobu \[RHacek]e\[SHacek]en\[IAcute].\ \>", "MathCaption", CellChangeTimes->{{3.5792443831875*^9, 3.579244412984375*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", RowBox[{ RowBox[{"x", "=", RowBox[{"LinearSolve", "[", RowBox[{"mat", ",", "b"}], "]"}]}], ";"}], "]"}]], "Input", CellTags->"Functions"], Cell[TextData[{ "Podobn\[EHacek] to lze ud\[EHacek]lat te\[CHacek]kov\[YAcute]m \ sou\[CAcute]inem a pou\[ZHacek]it\[IAcute]m funkce ", Cell[BoxData[ ButtonBox["Chop", BaseStyle->"Link", ButtonData->"paclet:ref/Chop"]], "InlineFormula"], ", kter\[AAcute] nahrad\[IAcute] \[CHacek]\[IAcute]sla \ bl\[IAcute]zk\[AAcute] nule hodnotou 0." }], "MathCaption", CellChangeTimes->{{3.57924442525*^9, 3.57924451875*^9}}, CellTags->"Functions"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"mat", ".", "x"}], "-", "b"}], "//", "Chop"}], "//", "Short"}]], "Input", CellTags->"Functions"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"A", ",", "x", ",", "mat", ",", "b", ",", "vals", ",", "soln"}], "]"}]], "Input", CellTags->"Functions"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Pr\[AAcute]ce s \[CHacek]\[IAcute]sly", "Section", CellChangeTimes->{{3.579245319859375*^9, 3.57924532496875*^9}}, CellTags->"Working with Numbers"], Cell["Obsah", "OverviewSubsection", CellChangeTimes->{{3.579245437015625*^9, 3.57924543909375*^9}}, CellTags->"Working with Numbers"], Cell[CellGroupData[{ Cell["p\[RHacek]esn\[AAcute] a nep\[RHacek]esn\[AAcute] \ \[CHacek]\[IAcute]sla", "Item", CellChangeTimes->{{3.579245328625*^9, 3.579245336296875*^9}}, CellTags->"Working with Numbers"], Cell["\<\ pr\[AAcute]ce s \[CHacek]\[IAcute]sly s vysokou m\[IAcute]rou \ p\[RHacek]esnosti\ \>", "Item", CellChangeTimes->{{3.57924535703125*^9, 3.579245375015625*^9}}, CellTags->"Working with Numbers"], Cell["\<\ v\[YAcute]po\[CHacek]ty, zahrnuj\[IAcute]c\[IAcute] \[CHacek]\[IAcute]sla s \ vysokou m\[IAcute]rou p\[RHacek]esnosti\ \>", "Item", CellChangeTimes->{{3.579245380515625*^9, 3.57924540184375*^9}}, CellTags->"Working with Numbers"], Cell[TextData[{ "kontrola p\[RHacek]esnosti p\[RHacek]i pou\[ZHacek]it\[IAcute] numerick\ \[YAcute]ch funkc\[IAcute]\[LongDash]", Cell[BoxData[ ButtonBox["WorkingPrecision", BaseStyle->"Link", ButtonData->"paclet:ref/WorkingPrecision"]]], ", ", Cell[BoxData[ ButtonBox["PrecisionGoal", BaseStyle->"Link", ButtonData->"paclet:ref/PrecisionGoal"]]] }], "Item", CellChangeTimes->{{3.579245447421875*^9, 3.579245477078125*^9}}, CellTags->"Working with Numbers"] }, Open ]], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Pr\[AAcute]ce s \[CHacek]\[IAcute]sly: P\[RHacek]esn\ \[AAcute] a nep\[RHacek]esn\[AAcute] \[CHacek]\[IAcute]sla", "Color7", FontSlant->"Plain"]], "Subsection", CellChangeTimes->{{3.5792454824375*^9, 3.57924550628125*^9}}, CellTags->"Working with Numbers"], Cell[TextData[{ "Na rozd\[IAcute]l od kapesn\[IAcute]ho kalkul\[AAcute]toru um\[IAcute] ", StyleBox["Mathematica", FontSlant->"Italic"], " pracovat s p\[RHacek]esn\[YAcute]mi \[CHacek]\[IAcute]sly stejn\[EHacek] \ tak jako s nep\[RHacek]esn\[YAcute]mi \[CHacek]\[IAcute]sly. Ve \ skute\[CHacek]nosti syst\[EAcute]m pou\[ZHacek]\[IAcute]v\[AAcute] \ t\[RHacek]i rozd\[IAcute]ln\[EAcute] druhy aritmetiky \[LongDash] \ p\[RHacek]esn\[AAcute], IEEE, a aritmetika s libovolnou nastavitelnou p\ \[RHacek]esnost\[IAcute]. IEEE aritmetika je velmi rychl\[AAcute], ale jej\ \[IAcute] p\[RHacek]esnost je pevn\[EHacek] d\[AAcute]na p\[RHacek]esnost\ \[IAcute] s pohyblivou desetinou \[CHacek]\[AAcute]rkou \ po\[CHacek]\[IAcute]ta\[CHacek]e (CPU). Aritmetika s libovolnou \ p\[RHacek]esnost\[IAcute] je pomalej\[SHacek]\[IAcute], ale ", StyleBox["Mathematica", FontSlant->"Italic"], " pracuje s danou p\[RHacek]esnost\[IAcute] ve v\[SHacek]ech v\[YAcute]po\ \[CHacek]tech a t\[IAcute]m je mo\[ZHacek]n\[EAcute] l\[EAcute]pe kontrolovat \ celkovou p\[RHacek]esnost v\[YAcute]sledku. Volba pou\[ZHacek]it\[EAcute] \ aritmetiky z\[AAcute]vis\[IAcute] na vstupech a povaze v\[YAcute]po\[CHacek]t\ \[URing] tak jak to ukazuj\[IAcute] n\[AAcute]sleduj\[IAcute]c\[IAcute] p\ \[RHacek]\[IAcute]klady." }], "Text", CellChangeTimes->{{3.579245511421875*^9, 3.5792456229375*^9}, { 3.57924569040625*^9, 3.5792458206875*^9}, {3.57924586853125*^9, 3.579245974671875*^9}, {3.579246038875*^9, 3.5792460454375*^9}}, CellTags->"Working with Numbers"], Cell["\<\ P\[RHacek]esn\[AAcute] \[CHacek]\[IAcute]sla zahrnuj\[IAcute] cel\[AAcute] \ \[CHacek]\[IAcute]sla (integers), zlomky a symbolick\[EAcute] konstanty, kter\ \[EAcute] jsou reprezentov\[AAcute]ny p\[RHacek]esn\[EHacek].\ \>", "MathCaption", CellChangeTimes->{{3.579245983578125*^9, 3.579246051390625*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"Map", "[", RowBox[{"Precision", ",", RowBox[{"{", RowBox[{"3", ",", FractionBox["22", "7"], ",", "\[Pi]"}], "}"}]}], "]"}]], "Input", CellTags->"Working with Numbers"], Cell["\<\ Nep\[RHacek]esn\[AAcute] \[CHacek]\[IAcute]sla jako nap\[RHacek]. 3.14159 \ jsou reprezentov\[AAcute]ny kone\[CHacek]n\[YAcute]m po\[CAcute]tem \[CHacek]\ \[IAcute]slic.\ \>", "MathCaption", CellChangeTimes->{{3.57924605440625*^9, 3.579246091453125*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"Precision", "[", "3.1415926535897932384626433832795", "]"}]], "Input"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Pr\[AAcute]ce s \[CHacek]\[IAcute]sly: ", "Color7", FontSlant->"Plain"], "V\[YAcute]po\[CHacek]ty" }], "Subsection", CellChangeTimes->{{3.579246100484375*^9, 3.57924611471875*^9}}, CellTags->"Working with Numbers"], Cell[TextData[{ "P\[RHacek]i v\[YAcute]po\[CHacek]tech ", StyleBox["Mathematica", FontSlant->"Italic"], " vrac\[IAcute] \[CHacek]\[IAcute]sla s takovou p\[RHacek]esnost\[IAcute], \ kter\[AAcute] je d\[AAcute]na p\[RHacek]esnost\[IAcute] vstup\[URing]." }], "Text", CellChangeTimes->{{3.5792461204375*^9, 3.57924619796875*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"P\[RHacek]esn\[EAcute] vstupy\"\>", "\<\"\[LongRightArrow]\"\>", RowBox[{"P\[RHacek]esn\[EAcute]", " ", "v\[YAcute]sledky"}]}, {"\<\"Nep\[RHacek]esn\[EAcute] vstupy\"\>", "\<\"\[LongRightArrow]\"\>", \ "\<\"Nep\[RHacek]esn\[EAcute] v\[YAcute]sledky\"\>"} }, AutoDelete->False, BaseStyle->{"SR"}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Center}}}, GridBoxBackground->{"Columns" -> {{ RGBColor[1, 1, 0.85]}}}, GridBoxDividers->{ "ColumnsIndexed" -> {1 -> GrayLevel[0.5]}, "RowsIndexed" -> {2 -> GrayLevel[0.85]}}, GridBoxFrame->{"Columns" -> False, "Rows" -> {{True}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{2}}, "Rows" -> {{0.62}}}], "Grid"]], "DisplayFormula", CellChangeTimes->{{3.57924620146875*^9, 3.579246284484375*^9}, 3.579320206390625*^9}, ShowStringCharacters->False], Cell[TextData[{ "Nap\[RHacek]\[IAcute]lad jeden z n\[AAcute]sleduj\[IAcute]c\[IAcute]ch \ vstup\[URing] zahrnuje nep\[RHacek]esn\[EAcute] \[CHacek]\[IAcute]slo ", StyleBox["4.0", "MR"], ", ", StyleBox["Mathematica", FontSlant->"Italic"], " vrac\[IAcute] p\[RHacek]ibli\[ZHacek]n\[YAcute] v\[YAcute]sledek." }], "MathCaption", CellChangeTimes->{{3.5792462958125*^9, 3.5792463449375*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"Cos", "[", FractionBox["\[Pi]", "4.0"], "]"}]], "Input", CellTags->"Working with Numbers"], Cell["\<\ Jestli\[ZHacek]e je vstup p\[RHacek]esn\[EAcute] \[CHacek]\[IAcute]slo, v\ \[YAcute]stup bude tak\[EAcute] p\[RHacek]esn\[EAcute] \[CHacek]\[IAcute]slo.\ \>", "MathCaption", CellChangeTimes->{{3.579320216484375*^9, 3.5793202406875*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"Cos", "[", FractionBox["\[Pi]", "4"], "]"}]], "Input", CellTags->"Working with Numbers"], Cell[TextData[{ Cell[BoxData[ RowBox[{"Cos", "[", "1", "]"}]]], "vyhodnot\[IAcute] jako p\[RHacek]esn\[YAcute] v\[YAcute]stup ", Cell[BoxData[ RowBox[{"Cos", "[", "1", "]"}]]], "." }], "MathCaption", CellChangeTimes->{{3.579320257765625*^9, 3.5793202669375*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"Cos", "[", "1", "]"}]], "Input", CellTags->"Working with Numbers"], Cell[TextData[{ "M\[URing]\[ZHacek]eme z\[IAcute]skat p\[RHacek]ibli\[ZHacek]nou aproximaci ", Cell[BoxData[ RowBox[{"Cos", "[", "1", "]"}]]], " bu\[DHacek] vlo\[ZHacek]en\[IAcute]m nep\[RHacek]esn\[EAcute]ho vstupu \ nebo aplikac\[IAcute] funkce ", Cell[BoxData[ ButtonBox["N", BaseStyle->"Link", ButtonData->"paclet:ref/N"]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.5793202786875*^9, 3.579320338890625*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"Cos", "[", "1.0", "]"}]], "Input", CellChangeTimes->{{3.579320360671875*^9, 3.579320368109375*^9}}], Cell[BoxData[ RowBox[{"N", "[", RowBox[{"Cos", "[", "1", "]"}], "]"}]], "Input", CellTags->"Working with Numbers"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Pr\[AAcute]ce s \[CHacek]\[IAcute]sly: ", "Color7", FontSlant->"Plain"], "\[CapitalCHacek]\[IAcute]sla s vysokou p\[RHacek]esnost\[IAcute]" }], "Subsection", CellChangeTimes->{{3.579320387953125*^9, 3.579320407703125*^9}}, CellTags->"Working with Numbers"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " um\[IAcute] tak\[EAcute] v\[YAcute]po\[CHacek]ty s vysokou \ p\[RHacek]esnost\[IAcute]." }], "Text", CellChangeTimes->{{3.579320667484375*^9, 3.579320677515625*^9}}, CellTags->"Working with Numbers"], Cell[TextData[{ "Druh\[YAcute] argument funkce ", Cell[BoxData[ ButtonBox["N", BaseStyle->"Link", ButtonData->"paclet:ref/N"]], "InlineFormula"], " p\[RHacek]esnost, pou\[ZHacek]itou pro p\[RHacek]ibli\[ZHacek]nou \ aproximaci." }], "MathCaption", CellChangeTimes->{{3.579320715125*^9, 3.579320755640625*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"N", "[", RowBox[{"\[Pi]", ",", "100"}], "]"}]], "Input", CellTags->"Working with Numbers"], Cell[TextData[{ "Jestli\[ZHacek]e druh\[YAcute] argument nen\[IAcute] uveden, funkce ", Cell[BoxData[ ButtonBox["N", BaseStyle->"Link", ButtonData->"paclet:ref/N"]], "InlineFormula"], " pou\[ZHacek]itje p\[RHacek]esnost danou hardware pou\[ZHacek]it\[EAcute]ho \ po\[CHacek]\[IAcute]ta\[CHacek]e." }], "MathCaption", CellChangeTimes->{{3.579320762515625*^9, 3.57932080225*^9}, { 3.579320838109375*^9, 3.579320842578125*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"N", "[", "\[Pi]", "]"}]], "Input", CellTags->"Working with Numbers"], Cell[TextData[{ "P\[RHacek]esnost po\[CHacek]\[IAcute]ta\[CHacek]e je obvykle ur\[CHacek]ena \ dan\[YAcute]m po\[CHacek]tem v\[EHacek]t\[SHacek]inou 16 desetinn\[YAcute]ch \ m\[IAcute]st. Obvykl\[AAcute] hodnota ", Cell[BoxData[ ButtonBox["$MachinePrecision", BaseStyle->"Link", ButtonData->"paclet:ref/$MachinePrecision"]], "InlineFormula"], " je ", Cell[BoxData[ FormBox[ RowBox[{"53", SubscriptBox["log", "10"], "2"}], TraditionalForm]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.57932081225*^9, 3.57932093878125*^9}}, CellTags->"Working with Numbers"], Cell[BoxData["$MachinePrecision"], "Input", CellTags->"Working with Numbers"], Cell["\<\ P\[RHacek]esnost hardware tak\[EAcute] ur\[CHacek]uje \[CHacek]\[IAcute]seln\ \[YAcute] rozsah, se kter\[YAcute]m po\[CHacek]\[IAcute]t\[AAcute]me.\ \>", "MathCaption", CellChangeTimes->{{3.57932095471875*^9, 3.579320979359375*^9}}, CellTags->"Working with Numbers"], Cell["$MinMachineNumber", "Input", CellChangeTimes->{3.579320988109375*^9}, CellTags->"Working with Numbers"], Cell["$MaxMachineNumber", "Input", CellTags->"Working with Numbers"], Cell["\<\ Hodnoty mimo uveden\[YAcute] rozsah jsou automaticky reprezetnov\[AAcute]ny v \ syst\[EAcute]mu, kter\[YAcute] pou\[ZHacek]\[IAcute]v\[AAcute] v\[YAcute]po\ \[CHacek]ty s vysokou p\[RHacek]esnost\[IAcute]. Pokud bychom po\[CHacek]\ \[IAcute]tali v r\[AAcute]mci p\[RHacek]esnosti po\[CAcute]\[IAcute]ta\ \[CHacek]e tj. s nep\[RHacek]esn\[YAcute]mi \ p\[RHacek]ibli\[ZHacek]n\[YAcute]mi hodnotami, dojde k \ p\[RHacek]ete\[CHacek]en\[IAcute] rozsahu.\ \>", "MathCaption", CellChangeTimes->{{3.579321019921875*^9, 3.579321116015625*^9}, { 3.57932115828125*^9, 3.579321161109375*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"Exp", "[", "10000", "]"}]], "Input", CellChangeTimes->{{3.57932112640625*^9, 3.579321133484375*^9}}], Cell[BoxData[ RowBox[{"Exp", "[", "10000.", "]"}]], "Input", CellChangeTimes->{{3.579321143765625*^9, 3.57932115371875*^9}}, CellTags->"Working with Numbers"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Pr\[AAcute]ce s \[CHacek]\[IAcute]sly:", "Color7", FontSlant->"Plain"], StyleBox[" V\[YAcute]po\[CHacek]ty s vysokou p\[RHacek]esnost\[IAcute]", "Color7"] }], "Subsection", CellChangeTimes->{{3.5793211771875*^9, 3.579321199703125*^9}}, CellTags->"Working with Numbers"], Cell[TextData[{ "P\[RHacek]i pr\[AAcute]ci s \[CHacek]\[IAcute]sly ", StyleBox["Mathematica", FontSlant->"Italic"], " vrac\[IAcute] v\[YAcute]sledek, jeho\[ZHacek] p\[RHacek]esnost je d\ \[AAcute]na p\[RHacek]esnost\[IAcute] vstupu." }], "Text", CellChangeTimes->{{3.579321210953125*^9, 3.579321246359375*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"Vstupy s vysokou p\[RHacek]esnost\[IAcute]\"\>", "\<\"\ \[LongRightArrow]\"\>", RowBox[{ "V\[YAcute]stupy", " ", "s", " ", "vysokou", " ", "p\[RHacek]esnost\[IAcute]"}]}, {"\<\"P\[RHacek]ibli\[ZHacek]n\[EAcute] vstupy\"\>", "\<\"\ \[LongRightArrow]\"\>", RowBox[{"P\[RHacek]ibli\[ZHacek]n\[EAcute]", " ", "v\[YAcute]stupy"}]} }, AutoDelete->False, BaseStyle->{"SR"}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Center}}}, GridBoxBackground->{"Columns" -> {{ RGBColor[1, 1, 0.85]}}}, GridBoxDividers->{ "ColumnsIndexed" -> {1 -> GrayLevel[0.5]}, "RowsIndexed" -> {2 -> GrayLevel[0.85]}}, GridBoxFrame->{"Columns" -> False, "Rows" -> {{True}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{2}}, "Rows" -> {{0.62}}}], "Grid"]], "DisplayFormula", CellChangeTimes->{{3.57924620146875*^9, 3.579246284484375*^9}, 3.579320206390625*^9, {3.579321320640625*^9, 3.579321424671875*^9}, 3.57933140225*^9}, ShowStringCharacters->False], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad vysoce p\[RHacek]esn\[AAcute] hodnota argumentu \ funkce ", Cell[BoxData[ ButtonBox["Cos", BaseStyle->"Link", ButtonData->"paclet:ref/Cos"]], "InlineFormula"], " vede k vysoce p\[RHacek]esn\[EAcute] funk\[CHacek]n\[IAcute] hodnot\ \[EHacek]." }], "MathCaption", CellChangeTimes->{{3.5793214401875*^9, 3.579321496359375*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"Cos", "[", "1.0471975511965977461542144610931676280657", "]"}]], "Input", CellTags->"Working with Numbers"], Cell[TextData[{ "Funkce ", Cell[BoxData[ ButtonBox["N", BaseStyle->"Link", ButtonData->"paclet:ref/N"]], "InlineFormula"], " nezv\[YAcute]\[SHacek]\[IAcute] p\[RHacek]esnost v\[YAcute]stupu, jestli\ \[ZHacek]e vlo\[ZHacek]\[IAcute]me hodnotu s malou p\[RHacek]esnost\[IAcute]." }], "MathCaption", CellChangeTimes->{{3.57932150928125*^9, 3.57932157953125*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"N", "[", RowBox[{ RowBox[{"Cos", "[", "1.04712", "]"}], ",", "1000"}], "]"}]], "Input", CellTags->"Working with Numbers"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Pr\[AAcute]ce s \[CHacek]\[IAcute]sly: \ \[CapitalCHacek]\[IAcute]seln\[EAcute] v\[YAcute]po\[CHacek]ty s vysokou p\ \[RHacek]esnost\[IAcute]", "Color7", FontSlant->"Plain"]], "Subsection", CellChangeTimes->{{3.579321597375*^9, 3.579321619171875*^9}}, CellTags->"Working with Numbers"], Cell["\<\ Ve v\[EHacek]t\[SHacek]in\[EHacek] numerick\[YAcute]ch aplikac\[IAcute] jsou \ chyby, vypl\[YAcute]vaj\[IAcute]c\[IAcute] z v\[YAcute]po\[CHacek]t\[URing] s \ nep\[RHacek]esn\[YAcute]mi \[CHacek]\[IAcute]sly pouze jednou z p\[RHacek]\ \[IAcute]\[CHacek]in numerick\[YAcute]ch chyb. P\[RHacek]i v\[YAcute]po\ \[CHacek]tu \[CHacek]\[IAcute]seln\[EAcute]ho integr\[AAcute]lu se mohou \ vyskytnout i chyby s ohledem na interpolaci \[CHacek]i \[SHacek]patn\[EHacek] \ ur\[CHacek]en\[YAcute] rozsah. Pokud chceme z\[IAcute]skat vysoce \ p\[RHacek]esn\[YAcute] v\[YAcute]sledek, je t\[RHacek]eba uva\[ZHacek]ovat v\ \[SHacek]echny tyto zdroje chyb.\ \>", "Text", CellChangeTimes->{{3.579321637203125*^9, 3.57932169896875*^9}, { 3.5793217438125*^9, 3.579321856328125*^9}}, CellTags->"Working with Numbers"], Cell[TextData[{ "Funkce ", Cell[BoxData[ ButtonBox["NIntegrate", BaseStyle->"Link", ButtonData->"paclet:ref/NIntegrate"]], "InlineFormula"], " poskytuje n\[EHacek]kolik nastaviteln\[YAcute]ch parametr\[URing], pomoc\ \[IAcute] kter\[YAcute]ch m\[URing]\[ZHacek]eme specifikovat toleranci v p\ \[RHacek]\[IAcute]pad\[EHacek] numerick\[YAcute]ch chyb." }], "MathCaption", CellChangeTimes->{{3.579321860296875*^9, 3.579321947421875*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"Options", "[", "NIntegrate", "]"}]], "Input", CellTags->"Working with Numbers"], Cell["\<\ N\[AAcute]sleduj\[IAcute]c\[IAcute] p\[RHacek]\[IAcute]kaz ukazuje \ v\[YAcute]po\[CHacek]et integr\[AAcute]l\[URing] s vysokou p\[RHacek]esnost\ \[IAcute] vzhledem k p\[RHacek]esn\[EAcute] \[CHacek]\[IAcute]seln\[EAcute] \ hodnot\[EHacek] na vstupu jako argumentu funkce Sin.\ \>", "MathCaption", CellChangeTimes->{{3.579321952609375*^9, 3.5793219848125*^9}, { 3.579322113671875*^9, 3.579322163078125*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{"Sin", "[", RowBox[{ FractionBox["7", "10"], "x"}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"WorkingPrecision", "\[Rule]", "36"}], ",", RowBox[{"PrecisionGoal", "\[Rule]", "30"}]}], "]"}]], "Input", CellTags->"Working with Numbers"], Cell[TextData[{ "Funkce ", Cell[BoxData[ ButtonBox["NIntegrate", BaseStyle->"Link", ButtonData->"paclet:ref/NIntegrate"]], "InlineFormula"], " generuje varovnou zpr\[AAcute]vu, pokud je hodnota na vstupu \ zad\[AAcute]na s malou p\[RHacek]esnost\[IAcute]. A\[CHacek]koliv je v\ \[YAcute]sledek uveden s vysokou p\[RHacek]esnost\[IAcute], \ posledn\[IAcute]ch n\[EHacek]kolik \[CHacek]\[IAcute]slic m\[URing]\[ZHacek]e \ b\[YAcute]t ur\[CHacek]eno \[SHacek]patn\[EHacek]." }], "MathCaption", CellChangeTimes->{{3.579322000484375*^9, 3.5793220953125*^9}}, CellTags->"Working with Numbers"], Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{"Sin", "[", RowBox[{"0.7", "x"}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"WorkingPrecision", "\[Rule]", "36"}], ",", RowBox[{"PrecisionGoal", "\[Rule]", "30"}]}], "]"}]], "Input", CellTags->"Working with Numbers"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Velk\[AAcute] pole", "Section", CellChangeTimes->{{3.5793221870625*^9, 3.579322193015625*^9}}, CellTags->"Large Arrays"], Cell["Obsah", "OverviewSubsection", CellChangeTimes->{{3.57932219653125*^9, 3.5793221969375*^9}}, CellTags->"Large Arrays"], Cell[CellGroupData[{ Cell["\<\ \[UAcute]vod do pr\[AAcute]ce s velk\[YAcute]mi poli dat\ \>", "Item", CellChangeTimes->{{3.579322200734375*^9, 3.579322223953125*^9}}, CellTags->"Large Arrays"], Cell["\<\ vytvo\[RHacek]en\[IAcute] a prohl\[IAcute]\[ZHacek]en\[IAcute] \[RHacek]\ \[IAcute]dk\[YAcute]ch pol\[IAcute]\ \>", "Item", CellChangeTimes->{{3.57932223065625*^9, 3.579322243*^9}}, CellTags->"Large Arrays"], Cell["v\[YAcute]po\[CHacek]ty s \[RHacek]\[IAcute]dk\[YAcute]mi poli", "Item", CellChangeTimes->{{3.579322245671875*^9, 3.57932225478125*^9}}, CellTags->"Large Arrays"], Cell["\[UAcute]vod do komprimovan\[YAcute]ch pol\[IAcute]", "Item", CellChangeTimes->{{3.5793222580625*^9, 3.579322268609375*^9}}, CellTags->"Large Arrays"], Cell["pr\[AAcute]ce s komprimov\[AAcute]n\[YAcute]mi poli", "Item", CellChangeTimes->{{3.579322279609375*^9, 3.57932228896875*^9}}, CellTags->"Large Arrays"] }, Open ]], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Velk\[AAcute] pole", "Color7", FontSlant->"Plain"]], "Subsection", CellChangeTimes->{{3.579322292296875*^9, 3.57932229690625*^9}}, CellTags->"Large Arrays"], Cell["\<\ Pokud pracujete s velk\[YAcute]m objemem dat, je velmi d\[URing]le\[ZHacek]it\ \[EAcute], aby v\[YAcute]po\[CHacek]ty byly co nejv\[IAcute]ce efektivn\ \[IAcute] s ohledem na \[CHacek]as i pam\[EHacek]\[THacek]ov\[EAcute] n\ \[AAcute]roky.\ \>", "Text", CellChangeTimes->{{3.579322303*^9, 3.5793223516875*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Pokud nap\[RHacek]\[IAcute]klad chceme reperezentovat matici ", Cell[BoxData[ FormBox[ RowBox[{"100000", "\[Cross]", "100000"}], TraditionalForm]]], ", pot\[RHacek]ebujeme velmi velk\[EAcute] mno\[ZHacek]stv\[IAcute] pameti." }], "MathCaption", CellChangeTimes->{{3.57932236115625*^9, 3.5793224015*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{ RowBox[{"N", "[", RowBox[{ SuperscriptBox["10", "5"], " ", SuperscriptBox["10", "5"], " ", "16"}], "]"}], " ", "Byte"}]], "Input", CellTags->"Large Arrays"], Cell["To je 160 gigabyte!", "Text", CellChangeTimes->{{3.579322403875*^9, 3.57932241309375*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Jednodu\[SHacek]e \[RHacek]e\[CHacek]eno, pokud v", StyleBox["Mathematica", FontSlant->"Italic"], " pracujeme s velk\[YAcute]mi datov\[YAcute]mi poli, pou\[ZHacek]ijeme \ efektivn\[IAcute] zp\[URing]sob reprezentace takov\[YAcute]ch dat a rychle \ algoritmy, kter\[EAcute] s nimi pracuj\[IAcute]. V t\[EAcute]to \[CHacek]\ \[AAcute]sti si stru\[CHacek]n\[EHacek] p\[RHacek]edstav\[IAcute]me dv\ \[EHacek] z t\[EHacek]chto technologi\[IAcute]\[LongDash]\[RHacek]\[IAcute]dk\ \[AAcute] a komprimovan\[AAcute] pole." }], "Text", CellChangeTimes->{{3.5793224363125*^9, 3.57932271309375*^9}}, CellTags->"Large Arrays"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Velk\[EAcute] pole: ", "Color7", FontSlant->"Plain"], "Vytvo\[RHacek]en\[IAcute] \[RHacek]\[IAcute]dk\[YAcute]ch pol\[IAcute]" }], "Subsection", CellChangeTimes->{{3.57932288334375*^9, 3.57932289578125*^9}}, CellTags->"Large Arrays"], Cell["\<\ Mnoho aplikac\[IAcute] zahrnuje pr\[AAcute]ci s velmi velk\[YAcute]mi \ maticemi, kter\[EAcute] obsahuj\[IAcute] v\[EHacek]t\[SHacek]inou 0. Takov\ \[YAcute]m objekt\[URing]m \[RHacek]\[IAcute]k\[AAcute]me \ \[RHacek]\[IAcute]dk\[AAcute] pole a byly vyvinuty velice efektivn\[IAcute] a \ rychl\[EAcute] algoritmy pro jejich reprezentaci a pr\[AAcute]ci s nimi.\ \>", "Text", CellChangeTimes->{{3.579322926609375*^9, 3.579323062953125*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " automaticky rozezn\[AAcute] pole jako \[RHacek]\[IAcute]dk\[EAcute] a \ automaticky pou\[ZHacek]ije vhodn\[EAcute] algoritmy." }], "MathCaption", CellChangeTimes->{{3.579323080171875*^9, 3.57932311184375*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"mat1", "=", RowBox[{"ExampleData", "[", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"MatrixPlot", "[", "mat1", "]"}]}], "Input"], Cell[TextData[{ "\[CapitalRHacek]\[IAcute]dk\[EAcute] pole je mo\[ZHacek]n\[EAcute] vytvo\ \[RHacek]it pomoc\[IAcute] funkce ", Cell[BoxData[ ButtonBox["SparseArray", BaseStyle->"Link", ButtonData->"paclet:ref/SparseArray"]], "InlineFormula"], ". N\[AAcute]sleduj\[IAcute]c\[IAcute] nap\[RHacek]\[IAcute]klad vytvo\ \[RHacek]\[IAcute] ", Cell[BoxData[ FormBox[ RowBox[{"4", "\[Cross]", "4"}], TraditionalForm]]], " \[RHacek]\[IAcute]dk\[EAcute] pole s 1 na diagon\[AAcute]le." }], "MathCaption", CellChangeTimes->{{3.5793232069375*^9, 3.579323266171875*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"mat2", "=", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{ RowBox[{"Band", "[", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "]"}], "\[Rule]", "1"}], ",", RowBox[{"{", RowBox[{"4", ",", "4"}], "}"}]}], "]"}]}]], "Input", CellTags->"Large Arrays"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " reprezentuje takov\[YAcute] objekt intern\[EHacek] jako speci\[AAcute]ln\ \[IAcute] datov\[YAcute] typ ", Cell[BoxData[ ButtonBox["SparseArray", BaseStyle->"Link", ButtonData->"paclet:ref/SparseArray"]], "InlineFormula"], " objekt. Konverzi tohoto objektu do form\[AAcute]tu b\[EHacek]\[ZHacek]n\ \[EAcute] natice lze prov\[EAcute]st pomoc\[IAcute] funkce ", Cell[BoxData[ ButtonBox["Normal", BaseStyle->"Link", ButtonData->"paclet:ref/Normal"]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.5793232880625*^9, 3.579323380703125*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"Normal", "[", "mat2", "]"}]], "Input", CellTags->"Large Arrays"], Cell[TextData[{ "Nebo ji jednodu\[SHacek]e zobrazit jako klasickou matici pomoc\[IAcute] ", Cell[BoxData[ ButtonBox["MatrixForm", BaseStyle->"Link", ButtonData->"paclet:ref/MatrixForm"]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.57932338825*^9, 3.579323413890625*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"MatrixForm", "[", "mat2", "]"}]], "Input", CellTags->"Large Arrays"], Cell[TextData[{ "Jestli\[ZHacek]e chceme pou\[ZHacek]\[IAcute]t explicitn\[IAcute] substitu\ \[CHacek]n\[IAcute] pr\[AAcute]vidla, sv\[AAcute]zan\[AAcute] s objektem ", Cell[BoxData[ ButtonBox["SparseArray", BaseStyle->"Link", ButtonData->"paclet:ref/SparseArray"]], "InlineFormula"], ", pou\[ZHacek]ijeme ", Cell[BoxData[ ButtonBox["ArrayRules", BaseStyle->"Link", ButtonData->"paclet:ref/ArrayRules"]], "InlineFormula"], "." }], "MathCaption", CellChangeTimes->{{3.57932342734375*^9, 3.579323481703125*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"ArrayRules", "[", "mat2", "]"}]], "Input", CellTags->"Large Arrays"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Velk\[AAcute] pole: ", "Color7", FontSlant->"Plain"], "Vizualizace \[RHacek]\[IAcute]dk\[YAcute]ch pol\[IAcute]" }], "Subsection", CellChangeTimes->{{3.579323492765625*^9, 3.5793235091875*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Pou\[ZHacek]ijte ", Cell[BoxData[ ButtonBox["ArrayPlot", BaseStyle->"Link", ButtonData->"paclet:ref/ArrayPlot"]], "InlineFormula"], " (nebo ", Cell[BoxData[ ButtonBox["MatrixPlot", BaseStyle->"Link", ButtonData->"paclet:ref/MatrixPlot"]], "InlineFormula"], ") ke zobrazen\[IAcute] \[RHacek]\[IAcute]dk\[YAcute]ch (i jin\[YAcute]ch) \ pol\[IAcute]." }], "Text", CellChangeTimes->{{3.5793235125*^9, 3.579323545984375*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"ArrayPlot", "[", "mat2", "]"}]], "Input", CellTags->"Large Arrays"], Cell[TextData[{ "Je mo\[ZHacek]n\[EAcute] specifikovat barvy, pou\[ZHacek]it\[EAcute] pro ka\ \[ZHacek]d\[YAcute] prvek matice nastaven\[IAcute]m ", Cell[BoxData[ ButtonBox["ColorRules", BaseStyle->"Link", ButtonData->"paclet:ref/ColorRules"]], "InlineFormula"], " volby." }], "MathCaption", CellChangeTimes->{{3.57932356184375*^9, 3.5793236031875*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"ArrayPlot", "[", RowBox[{"mat2", ",", RowBox[{"ColorRules", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"0", "\[Rule]", "Red"}], ",", RowBox[{"1", "\[Rule]", "Blue"}]}], "}"}]}]}], "]"}]], "Input", CellTags->"Large Arrays"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Velk\[AAcute] pole: ", "Color7", FontSlant->"Plain"], "Pr\[AAcute]ce s \[RHacek]\[IAcute]dk\[YAcute]mi poli" }], "Subsection", CellChangeTimes->{{3.5793236141875*^9, 3.579323627765625*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " pracuje se speci\[AAcute]ln\[IAcute]m algoritmy p\[RHacek]i manipulaci s \ \[RHacek]\[IAcute]dk\[YAcute]mi poli. Nav\[IAcute]c jsou \[RHacek]\[IAcute]dk\ \[AAcute] pole ulo\[ZHacek]ena v pam\[EHacek]ti velice efektivn\[IAcute]m zp\ \[URing]sobem, kter\[YAcute] umo\[ZHacek]\[NHacek]uje pracovat s \[RHacek]\ \[IAcute]dk\[YAcute]mi objekty, kter\[EAcute] jsou rozsahem v\[EHacek]t\ \[SHacek]\[IAcute] ne\[ZHacek] odpov\[IAcute]daj\[IAcute]c\[IAcute] \ b\[EHacek]\[ZHacek]n\[EAcute] objekty." }], "Text", CellChangeTimes->{{3.57932374609375*^9, 3.579323835859375*^9}, { 3.5793238875*^9, 3.57932391825*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad zde je ", Cell[BoxData[ FormBox[ RowBox[{"100000", "\[Cross]", "100000"}], TraditionalForm]]], " \[RHacek]\[IAcute]dk\[EAcute] pole s n\[AAcute]hodn\[YAcute]mi \[CHacek]\ \[IAcute]sly na diagon\[AAcute]le a dv\[EHacek] nad ni a pod n\[IAcute], \ ostatn\[IAcute] prvky jsou 0." }], "MathCaption", CellChangeTimes->{{3.579323927515625*^9, 3.57932405671875*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"mat", "=", RowBox[{"SparseArray", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"i_", ",", "j_"}], "}"}], "/;", RowBox[{ RowBox[{"Abs", "[", RowBox[{"i", "-", "j"}], "]"}], "\[LessEqual]", "2"}]}], "\[RuleDelayed]", RowBox[{"RandomReal", "[", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ SuperscriptBox["10", "5"], ",", SuperscriptBox["10", "5"]}], "}"}]}], "]"}]}]], "Input", CellTags->"Large Arrays"], Cell["\<\ Velikost takto ulo\[ZHacek]en\[EAcute]ho objektu je z\[RHacek]ejm\[EHacek] p\ \[RHacek]ekvapuj\[IAcute]c\[IAcute].\ \>", "MathCaption", CellChangeTimes->{{3.57932408228125*^9, 3.579324111359375*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{ RowBox[{"N", "[", RowBox[{"ByteCount", "[", "mat", "]"}], "]"}], "Byte"}]], "Input", CellTags->"Large Arrays"], Cell["\<\ B\[EHacek]\[ZHacek]n\[EAcute] pole takov\[EAcute] velikosti vy\[ZHacek]aduje \ \[RHacek]\[AAcute]dov\[EHacek] p\[EHacek]tkr\[AAcute]t v\[IAcute]ce pam\ \[EHacek]ti, tak\[ZHacek]e pr\[AAcute]ce s takov\[YAcute]mi objekty zat\ \[IAcute]m p\[RHacek]esahuje b\[EAcute]\[ZHacek]n\[EAcute] mo\[ZHacek]nosti \ pou\[ZHacek]\[IAcute]van\[YAcute]ch po\[CHacek]\[IAcute]ta\[CHacek]\[URing]. \ \>", "MathCaption", CellChangeTimes->{{3.579324184375*^9, 3.5793242785*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{ RowBox[{"N", "[", RowBox[{ SuperscriptBox["10", "5"], " ", SuperscriptBox["10", "5"], " ", "16"}], "]"}], " ", "Byte"}]], "Input", CellTags->"Large Arrays"], Cell[TextData[{ "N\[AAcute]sleduj\[IAcute]c\[IAcute] tabulka ukazuje rozd\[IAcute] v \ rychlosti proveden\[IAcute] operac\[IAcute] na \ \[RHacek]\[IAcute]dk\[YAcute]mi a klasick\[YAcute]mi objekty. Pro \ v\[YAcute]po\[CHacek]ty byla pou\[ZHacek]ita matice ", Cell[BoxData[ FormBox[ RowBox[{"2000", "\[Cross]", "2000"}], TraditionalForm]]], "." }], "MathCaption", CellChangeTimes->{{3.57932431365625*^9, 3.579324381015625*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ TagBox[GridBox[{ { StyleBox[ RowBox[{ StyleBox["n", StripOnInput->False, FontWeight->"Bold"], "=", " ", "2000"}], StripOnInput->False, FontWeight->"Bold"], StyleBox["\[RHacek]\[IAcute]dk\[AAcute]", StripOnInput->False, FontWeight->"Bold"], StyleBox["klasick\[AAcute]", StripOnInput->False, FontWeight->"Bold"]}, { StyleBox["Transpose", "MR", StripOnInput->False], RowBox[{"0.`", " ", "vte\[RHacek]in"}], RowBox[{"0.03125`4.515449934959718", " ", "vte\[RHacek]in"}]}, { StyleBox["LinearSolve", "MR", StripOnInput->False], RowBox[{"0.015625`4.214419939295737", " ", "vte\[RHacek]in"}], RowBox[{"0.875`5.962607966301938", " ", "vte\[RHacek]in"}]}, { StyleBox["Dot", "MR", StripOnInput->False], RowBox[{"0.03125`4.515449934959718", " ", "vte\[RHacek]in"}], RowBox[{"1.171875`6.089481202687438", " ", "vte\[RHacek]in"}]} }, AutoDelete->False, GridBoxAlignment->{ "Columns" -> {Right, Left, Left}, "Rows" -> {{Baseline}}}, GridBoxBackground->{"Columns" -> {{ GrayLevel[0.85]}}}, GridBoxDividers->{"Columns" -> {1, 0}, "Rows" -> {1, 0}}, GridBoxFrame->{"ColumnsIndexed" -> {{{1, -1}, {1, -1}} -> True}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxItemStyle->{"Columns" -> {{FontFamily -> "Times"}}}, GridBoxSpacings->{"Columns" -> {{1.1}}, "Rows" -> {{0.5}}}], "Grid"]], "Text", CellChangeTimes->{{3.57932450578125*^9, 3.5793246064375*^9}, { 3.579324640484375*^9, 3.579324647921875*^9}}], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Velk\[AAcute] pole: ", "Color7", FontSlant->"Plain"], "Komprimovan\[AAcute] pole" }], "Subsection", CellChangeTimes->{{3.579324940875*^9, 3.579324951140625*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Jestli\[ZHacek]e vytvo\[RHacek]\[IAcute]te ", StyleBox["Mathematica ", FontSlant->"Italic"], "seznam, je vnit\[RHacek]n\[EHacek] reprezentovan\[YAcute] jako \ v\[YAcute]raz s hlavi\[CHacek]kou ", Cell[BoxData[ ButtonBox["List", BaseStyle->"Link", ButtonData->"paclet:ref/List"]], "InlineFormula"], " i p\[RHacek]esto, \[ZHacek]e jeho ", Cell[BoxData[ ButtonBox["OutputForm", BaseStyle->"Link", ButtonData->"paclet:ref/OutputForm"]], "InlineFormula"], " je obvykl\[YAcute] seznam se slo\[ZHacek]en\[YAcute]mi z\[AAcute]vorkami." }], "Text", CellChangeTimes->{{3.579324958234375*^9, 3.5793250650625*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"lis", "=", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "5"}], "}"}]}]], "Input", CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"FullForm", "[", "lis", "]"}]], "Input", CellTags->"Large Arrays"], Cell[TextData[{ "Ka\[ZHacek]d\[EAcute] cel\[EAcute] \[CHacek]\[IAcute]slo v seznamu je samo \ o sob\[EHacek] tak\[EAcute] v\[YAcute]raz. Ve vnit\[RHacek]n\[IAcute]m ", StyleBox["Mathematica", FontSlant->"Italic"], " C k\[OAcute]du jsou data ulo\[ZHacek]ena spolu s informac\[IAcute] o typu \ v\[YAcute]razu (v tomto p\[RHacek]\[IAcute]pad\[EHacek] samotn\[YAcute] \ seznam a cel\[AAcute] \[CHacek]\[IAcute]sla jako prvky tohoto seznamu)." }], "Text", CellChangeTimes->{{3.579325091796875*^9, 3.57932522625*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "P\[RHacek]i pou\[ZHacek]it\[IAcute] vestav\[EHacek]n\[EAcute] funkce ", Cell[BoxData[ ButtonBox["Range", BaseStyle->"Link", ButtonData->"paclet:ref/Range"]], "InlineFormula"], " se vytvo\[RHacek]\[IAcute] stejn\[YAcute] seznam jako v\[YAcute]sledek, \ kter\[YAcute] vypad\[AAcute] stejn\[EHacek] (shodn\[AAcute] ", Cell[BoxData[ ButtonBox["OutputForm", BaseStyle->"Link", ButtonData->"paclet:ref/OutputForm"]], "InlineFormula"], "), ale ve vnit\[RHacek]n\[IAcute] reprezentaci je ulo\[ZHacek]ena v odli\ \[SHacek]n\[EAcute] datov\[EAcute] struktu\[RHacek]e." }], "MathCaption", CellChangeTimes->{{3.579325243640625*^9, 3.5793253399375*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"packedlist", "=", RowBox[{"Range", "[", "5", "]"}]}]], "Input", CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"packedlist", "===", "lis"}]], "Input", CellTags->"Large Arrays"], Cell[TextData[{ "Abychom vid\[EHacek]li, \[ZHacek]e oba seznamy jsou ulo\[ZHacek]eny rozd\ \[IAcute]ln\[EHacek] pou\[ZHacek]ijeme predik\[AAcute]tovou funkci ", StyleBox["PackedArrayQ,", "MR"], " kter\[AAcute] je k dispozici v bal\[IAcute]ku ", StyleBox["Developer`", "MR"], "." }], "MathCaption", CellChangeTimes->{{3.579325375046875*^9, 3.5793254344375*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"Developer`PackedArrayQ", "[", "lis", "]"}]], "Input", CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"Developer`PackedArrayQ", "[", "packedlist", "]"}]], "Input", CellTags->"Large Arrays"], Cell["\<\ Komprimovan\[AAcute] pole jsou v podstat\[EHacek] efektivn\[IAcute] datov\ \[EAcute] struktury pro reprezentaci a v\[YAcute]po\[CHacek]ty s \ velk\[YAcute]mi objemy dat. Hlavn\[IAcute] v\[YAcute]hody jejich \ pou\[ZHacek]it\[IAcute] je men\[SHacek]\[IAcute] pam\[EHacek]\[THacek]ov\ \[AAcute] n\[AAcute]ro\[CHacek]nost a rychlost \ v\[YAcute]po\[CHacek]t\[URing]. Toto ukazuje n\[EHacek]kolik p\[RHacek]\ \[IAcute]klad\[URing].\ \>", "Text", CellChangeTimes->{{3.579325463890625*^9, 3.57932560515625*^9}}, CellTags->"Large Arrays"], Cell["\<\ N\[AAcute]sleduj\[IAcute]c\[IAcute] vrac\[IAcute] mno\[ZHacek]stv\[IAcute] \ pam\[EHacek]ti v bytech, kter\[AAcute] je pot\[RHacek]eba k ulo\[ZHacek]en\ \[IAcute] 1000 re\[AAcute]ln\[YAcute]ch \[CAcute]\[IAcute]sel.\ \>", "MathCaption", CellChangeTimes->{{3.579325665671875*^9, 3.579325709984375*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"ByteCount", "[", RowBox[{"pvec", "=", RowBox[{"N", "[", RowBox[{"Range", "[", "1000", "]"}], "]"}]}], "]"}]], "Input", CellTags->"Large Arrays"], Cell["\<\ Pokud vlo\[ZHacek]\[IAcute]me do libovoln\[EAcute]ho prvku pole hodnotu jin\ \[EAcute]ho typu (v tomto p\[RHacek]\[IAcute]pad\[EHacek] cel\[EAcute] \ \[CHacek]\[IAcute]slo), pole p\[RHacek]est\[AAcute]v\[AAcute] b\[YAcute]t \ komprimovan\[EAcute]. \ \>", "MathCaption", CellChangeTimes->{{3.579325744578125*^9, 3.579325777328125*^9}, { 3.57932583365625*^9, 3.5793258683125*^9}}, CellTags->"Large Arrays"], Cell[BoxData[{ RowBox[{ RowBox[{"qvec", "=", "pvec"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"qvec", "[", RowBox[{"[", "1", "]"}], "]"}], "=", "1"}], ";"}], "\[IndentingNewLine]", RowBox[{"ByteCount", "[", "qvec", "]"}]}], "Input", CellTags->"Large Arrays"], Cell["\<\ \[CapitalUAcute]spora pam\[EHacek]ti je v tomto p\[RHacek]\[IAcute]pad\ \[EHacek] n\[EHacek]kolikan\[AAcute]sobn\[AAcute]. \ \>", "MathCaption", CellChangeTimes->{{3.57932588871875*^9, 3.5793259255625*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{ FractionBox[ RowBox[{"ByteCount", "[", "qvec", "]"}], RowBox[{"ByteCount", "[", "pvec", "]"}]], "//", "N"}]], "Input", CellTags->"Large Arrays"], Cell["\<\ Patrn\[AAcute] je i \[CHacek]asov\[AAcute] \[UAcute]spora, pokud pracujeme s \ komprimovan\[YAcute]mi poli. Tato \[UAcute]spora roste se zvy\[SHacek]uj\ \[IAcute]c\[IAcute]m se objemem dat.\ \>", "MathCaption", CellChangeTimes->{{3.579325942984375*^9, 3.579325980609375*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", RowBox[{"Do", "[", RowBox[{ RowBox[{"pvec", "+", "pvec"}], ",", RowBox[{"{", "1000", "}"}]}], "]"}], "]"}]], "Input", CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", RowBox[{"Do", "[", RowBox[{ RowBox[{"qvec", "+", "qvec"}], ",", RowBox[{"{", "1000", "}"}]}], "]"}], "]"}]], "Input", CellTags->"Large Arrays"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Velk\[AAcute] pole: ", "Color7", FontSlant->"Plain"], "Pou\[ZHacek]it\[IAcute] komprimovan\[YAcute]ch pol\[IAcute]" }], "Subsection", CellChangeTimes->{{3.57932603734375*^9, 3.579326051375*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Danou efektivitu p\[RHacek]i ukl\[AAcute]d\[AAcute]n\[IAcute] \ velk\[YAcute]ch pol\[IAcute] i v rychlosti p\[RHacek]i pr\[AAcute]ci s nimi \ je t\[RHacek]eba vyu\[ZHacek]\[IAcute]vat kdykoliv je to \ mo\[ZHacek]n\[EAcute]. V n\[AAcute]sleduj\[IAcute]c\[IAcute]m je prezentov\ \[AAcute]no n\[EHacek]kolik rozd\[IAcute]ln\[YAcute]ch situac\[IAcute], ve \ kter\[YAcute]ch jsou komprimovan\[AAcute] pole v ", StyleBox["Mathematica ", FontSlant->"Italic"], "pou\[ZHacek]ita." }], "Text", CellChangeTimes->{{3.579326086328125*^9, 3.57932620421875*^9}}, CellTags->"Large Arrays"], Cell["", "OverviewSubsection", CellChangeTimes->{3.57932622765625*^9}, CellTags->"Large Arrays"], Cell[TextData[{ "N\[AAcute]sleduje uk\[AAcute]zka seznamu vestav\[EHacek]n\[YAcute]ch funkc\ \[IAcute], kter\[EAcute] maj\[IAcute] atribut ", Cell[BoxData[ ButtonBox["Listable", BaseStyle->"Link", ButtonData->"paclet:ref/Listable"]], "InlineFormula"], " (cel\[YAcute] seznam je mo\[ZHacek]n\[EAcute] z\[IAcute]skat odstran\ \[EHacek]n\[IAcute]m ", StyleBox["//Short", "MR"], ")." }], "Text", CellChangeTimes->{{3.57932623678125*^9, 3.579326305609375*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{ RowBox[{"Select", "[", RowBox[{ RowBox[{"Names", "[", "\"\\"", "]"}], ",", " ", RowBox[{ RowBox[{"MemberQ", "[", RowBox[{ RowBox[{"Attributes", "[", "#", "]"}], ",", " ", "Listable"}], "]"}], "&"}]}], "]"}], "//", "Short"}]], "Input", CellTags->"Large Arrays"], Cell["\<\ V\[EHacek]t\[SHacek]ina t\[EHacek]chto fukc\[IAcute] v seznamu generuje na v\ \[YAcute]stupu komprimovan\[EAcute] pole a akceptuje komprimovan\[AAcute] \ pole jako vstup.\ \>", "Text", CellChangeTimes->{{3.579326356359375*^9, 3.579326416296875*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Nav\[IAcute]c mnoh vestav\[EHacek]n\[YAcute]ch funkc\[IAcute], \ kter\[EAcute] realizuj\[IAcute] struktur\[AAcute]ln\[IAcute] operace jako ", Cell[BoxData[ ButtonBox["Part", BaseStyle->"Link", ButtonData->"paclet:ref/Part"]], "InlineFormula"], ", ", Cell[BoxData[ ButtonBox["Join", BaseStyle->"Link", ButtonData->"paclet:ref/Join"]], "InlineFormula"], ", ", Cell[BoxData[ ButtonBox["Transpose", BaseStyle->"Link", ButtonData->"paclet:ref/Transpose"]], "InlineFormula"], ", pou\[ZHacek]\[IAcute]vaj\[IAcute] komprimovan\[AAcute] pole. " }], "MathCaption", CellChangeTimes->{{3.579326444796875*^9, 3.579326545578125*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{ RowBox[{"mat", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"RandomReal", "[", "]"}], ",", RowBox[{"{", "500", "}"}], ",", RowBox[{"{", "500", "}"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.393844785014451*^9, 3.393844786529744*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"Developer`PackedArrayQ", "[", "mat", "]"}]], "Input", CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", RowBox[{ RowBox[{"newmat", "=", RowBox[{"Transpose", "[", "mat", "]"}]}], ";"}], "]"}]], "Input", CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"Developer`PackedArrayQ", "[", "newmat", "]"}]], "Input", CellTags->"Large Arrays"], Cell["U\[ZHacek]it\[IAcute] komprimovan\[YAcute]ch pol\[IAcute]", \ "MoreExamplesSection", CellChangeTimes->{{3.579326577328125*^9, 3.57932658440625*^9}}], Cell["\<\ N\[AAcute]sleduje p\[RHacek]\[IAcute]klad, kter\[YAcute] ukazuje jak pou\ \[ZHacek]it\[IAcute] komprimovan\[YAcute]ch pol\[IAcute] m\[URing]\[ZHacek]e \ v\[YAcute]razn\[EHacek] zrychlit v\[YAcute]po\[CHacek]ty. Vytvo\[RHacek]\ \[IAcute]me jednoduchou funkci na v\[YAcute]po\[CHacek]et n\[AAcute]hodn\ \[EAcute] proch\[AAcute]zky ve dvoudimenzion\[AAcute]ln\[IAcute]m prostoru.\ \>", "Text", CellChangeTimes->{{3.5793271834375*^9, 3.5793272626875*^9}}], Cell[TextData[{ "Definujeme z\[AAcute]kladn\[IAcute] sm\[EHacek]ry proch\[AAcute]zky. ", StyleBox["NSEW", "MR"], " nen\[IAcute] komprimovan\[EAcute] pole." }], "MathCaption", CellChangeTimes->{{3.579327281578125*^9, 3.57932728346875*^9}, { 3.57932740365625*^9, 3.579327438671875*^9}, 3.5793275390625*^9}], Cell[BoxData[{ RowBox[{ RowBox[{"NSEW", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Developer`PackedArrayQ", "[", "NSEW", "]"}]}], "Input"], Cell["\<\ Definice funkce n\[AAcute]hodn\[EAcute] proch\[AAcute]zky.\ \>", "MathCaption", CellChangeTimes->{{3.57932745390625*^9, 3.579327470140625*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"walk2D", "[", "t_", "]"}], ":=", RowBox[{"Accumulate", "[", RowBox[{"RandomChoice", "[", RowBox[{"NSEW", ",", "t"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{3.49244785715458*^9}], Cell[TextData[{ "Ur\[CHacek]\[IAcute]me jak dlouho trv\[AAcute] v\[YAcute]po\[CHacek]et ", Cell[BoxData[ FormBox["10000000", TraditionalForm]], "None"], "-krokov\[EAcute] proch\[AAcute]zky." }], "MathCaption", CellChangeTimes->{{3.57932748128125*^9, 3.579327505640625*^9}}], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", RowBox[{ RowBox[{"walk2D", "[", SuperscriptBox["10", "7"], "]"}], ";"}], "]"}]], "Input"], Cell["\<\ Nyn\[IAcute] vytvo\[RHacek]\[IAcute]me komprimovanou verzi.\ \>", "MathCaption", CellChangeTimes->{{3.579327525671875*^9, 3.57932755234375*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"NSEWpacked", "=", "\[IndentingNewLine]", RowBox[{"Developer`ToPackedArray", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Developer`PackedArrayQ", "[", "NSEWpacked", "]"}]}], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"walk2Dpacked", "[", "t_", "]"}], ":=", RowBox[{"Accumulate", "[", RowBox[{"RandomChoice", "[", RowBox[{"NSEWpacked", ",", "t"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.492447907229608*^9, 3.4924479161363792`*^9}}], Cell["\<\ Je vid\[EHacek]t \[RHacek]\[AAcute]dov\[EAcute] zrychlen\[IAcute] \ v\[YAcute]po\[CHacek]tu.\ \>", "MathCaption", CellChangeTimes->{{3.5793275784375*^9, 3.579327596375*^9}}], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", RowBox[{ RowBox[{"walk2Dpacked", "[", SuperscriptBox["10", "7"], "]"}], ";"}], "]"}]], "Input"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Velk\[AAcute] pole: ", "Color7", FontSlant->"Plain"], "Vestav\[EHacek]n\[EAcute] funkce, kter\[EAcute] vrac\[IAcute] komprimovan\ \[AAcute] pole" }], "Subsection", CellChangeTimes->{{3.579327615203125*^9, 3.57932764040625*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Funkce jako je nap\[RHacek]. ", Cell[BoxData[ ButtonBox["Fourier", BaseStyle->"Link", ButtonData->"paclet:ref/Fourier"]], "InlineFormula"], " prov\[AAcute]d\[IAcute] v\[YAcute]po\[CHacek]ty v p\[RHacek]esnosti \ hardware a v\[ZHacek]dy pou\[ZHacek]\[IAcute]vaj\[IAcute] pole. V takov\ \[YAcute]ch p\[RHacek]\[IAcute]padech tyto funkce vrac\[IAcute] sv\[EAcute] v\ \[YAcute]stupy jako komprimovan\[AAcute] pole. " }], "Text", CellChangeTimes->{{3.579327649375*^9, 3.579327736578125*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"Developer`PackedArrayQ", "[", RowBox[{"Fourier", "[", RowBox[{"N", "[", RowBox[{"Range", "[", "1000", "]"}], "]"}], "]"}], "]"}]], "Input", CellTags->"Large Arrays"], Cell[TextData[{ "A\[THacek] je vstupn\[IAcute] parametr komprimovan\[EAcute] pole \[CHacek]i \ nikoliv, pokud funkce ", Cell[BoxData[ ButtonBox["Fourier", BaseStyle->"Link", ButtonData->"paclet:ref/Fourier"]], "InlineFormula"], " prov\[AAcute]d\[IAcute] sv\[EAcute] v\[YAcute]po\[CHacek]ty s \ p\[RHacek]esnost\[IAcute] harware, vnit\[RHacek]n\[EHacek] pou\[ZHacek]\ \[IAcute]v\[AAcute] pole a proto je p\[RHacek]irozen\[EAcute], \[ZHacek]e v\ \[YAcute]stupy vrac\[IAcute] jako komprimovan\[AAcute] pole." }], "Text", CellChangeTimes->{{3.579327759078125*^9, 3.579327861546875*^9}}, CellTags->"Large Arrays"], Cell[" ", "Spacer"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Velk\[AAcute] pole: Tipy na pr\[AAcute]ci s \ komprimovan\[YAcute]mi poli", "Color7", FontSlant->"Plain"]], "Subsection", CellChangeTimes->{{3.579327869*^9, 3.579327891890625*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Snad nejd\[URing]le\[ZHacek]it\[EHacek]j\[SHacek]\[IAcute] v\[EHacek]c\ \[IAcute] je ujistit se, \[ZHacek]e prov\[AAcute]d\[IAcute]te operace na \ seznamu prvk\[URing] v\[SHacek]echny najednou nebo ve skupin\[AAcute]ch. \ Funkcion\[AAcute]ln\[IAcute] styl programov\[AAcute]n\[IAcute] a mnoho \ konstrukt\[URing] ", StyleBox["Mathematica, ", FontSlant->"Italic"], "zalo\[ZHacek]en\[YAcute]ch na pr\[AAcute]ci se seznamy \ umo\[ZHacek]\[NHacek]uje prov\[AAcute]d\[EHacek]t v\[SHacek]echny tyto \ operace mnohem jednodu\[SHacek]eji. " }], "Item", CellChangeTimes->{{3.5793314503125*^9, 3.579331587140625*^9}}, CellTags->"Large Arrays"], Cell["\<\ N\[AAcute]sleduj\[IAcute]c\[IAcute]ch n\[EHacek]kolik p\[RHacek]\[IAcute]klad\ \[URing] pou\[ZHacek]\[IAcute]v\[AAcute] n\[EHacek]kter\[EAcute] \ u\[ZHacek]ite\[CHacek]n\[EAcute] n\[AAcute]stroje pomohou sestavit \ k\[OAcute]d, kter\[YAcute] vyu\[ZHacek]\[IAcute]v\[AAcute] v\[YAcute]hody \ komprimovan\[YAcute]ch pol\[IAcute].\ \>", "Text", CellChangeTimes->{{3.57933162109375*^9, 3.579331692015625*^9}, { 3.579332051671875*^9, 3.5793320526875*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"Developer`PackedArrayForm", "[", RowBox[{"Range", "[", "10000", "]"}], "]"}]], "Input", CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"SetSystemOptions", "[", RowBox[{"PackedArrayOptions", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", "\[Rule]", "True"}], "}"}]}], "]"}]], "Input", CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", RowBox[{"Apply", "[", RowBox[{"Plus", ",", " ", RowBox[{"N", "[", RowBox[{"Range", "[", "10000", "]"}], "]"}]}], "]"}], "]"}]], "Input", CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"AbsoluteTiming", "[", RowBox[{"Total", "[", RowBox[{"N", "[", RowBox[{"Range", "[", "10000", "]"}], "]"}], "]"}], "]"}]], "Input", CellTags->"Large Arrays"], Cell["\<\ Mnoho vestav\[EHacek]n\[YAcute]ch funkc\[IAcute] m\[AAcute] omezen\[IAcute], \ za kter\[YAcute]ch je mo\[ZHacek]n\[EAcute] pou\[ZHacek]\[IAcute]t \ technologii komprimovan\[YAcute]ch pol\[IAcute].\ \>", "Text", CellChangeTimes->{{3.5793318068125*^9, 3.579331864671875*^9}, { 3.579331954109375*^9, 3.57933195471875*^9}}, CellTags->"Large Arrays"], Cell[TextData[{ "Nap\[RHacek]\[IAcute]klad pro mal\[AAcute] pole, funkce ", Cell[BoxData[ ButtonBox["Table", BaseStyle->"Link", ButtonData->"paclet:ref/Table"]], "InlineFormula"], " sv\[EAcute] v\[YAcute]stupy nevrac\[IAcute] ve form\[AAcute]tu komprimovan\ \[EAcute]ho pole." }], "MathCaption", CellChangeTimes->{{3.579332208140625*^9, 3.579332265671875*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"Developer`PackedArrayQ", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Sin", "[", RowBox[{"i", " ", RowBox[{"Pi", "/", "10."}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", " ", "100"}], "}"}]}], "]"}], "]"}]], "Input", CellTags->"Large Arrays"], Cell["\<\ Ale pro v\[EHacek]t\[SHacek]\[IAcute] pole ji\[ZHacek] v\[YAcute]sledek \ komprimuje\ \>", "MathCaption", CellChangeTimes->{{3.579332307484375*^9, 3.579332322984375*^9}}, CellTags->"Large Arrays"], Cell[BoxData[ RowBox[{"Developer`PackedArrayQ", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Sin", "[", RowBox[{"i", " ", RowBox[{"Pi", "/", "10."}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "500"}], "}"}]}], "]"}], "]"}]], "Input", CellTags->"Large Arrays"], Cell[TextData[{ "Zde je uk\[AAcute]zka seznamu n\[EHacek]kolika nastaven\[IAcute] syst\ \[EAcute]mu, kter\[EAcute] ur\[CHacek]uj\[IAcute] meze pro pr\[AAcute]ci \ vestav\[EHacek]n\[YAcute]ch funkc\[IAcute]. 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