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{"sheet":"Úvod","index":0,"n_rows":141,"n_cols":6,"rows_kept":141,"cut":false,"hidden":false,"merged":[]}
["Numerické metody pro Excel",null,null,null,"Verze","V1.07"]
[]
["Moduly obsahují základní numerické metody pro výpočty v Excelu"]
["Spuštěním šablony Numer.xltm  se vytváří jednotlivé instance aplikace Numer1.xlsm, Numer2.xlsm,…"]
["V následujících listech je příklad použití"]
["Pokud už v konkrétní aplikaci nepotřebujete listy Úvod a příklady, můžete je smazat"]
["Některé metody existují ve dvou verzích: klasicky a přes class modul, který je obecnější"]
["U svých aplikací si přeprogramujte routiny F a FKT, FUN konkrétních tvarů rovnic"]
["Kvůli rutinám GAUSS je nastaveno Option Base 1  (indexy polí od 1)"]
[]
["Sub RKM(n, x, xe, Y(), delta, star, zz())"]
["Numerická integrace soustavy obyč. diferenciálních rovni metodou Runge-Kutta-Merson"]
["s automatickou regulací délky integračního kroku"]
["n - počet rovnic; x- počáteční x integrace; xe-koncové x pro vypočtený integrační krok"]
["delta -  požadovaná abs. Přesnost (např.: 0.00001); star - na počátku integrace nastavit na 1"]
["zz() - pole s parametry modelu"]
["Vyžaduje naprogramovat podprogram Sub FKT(n, x, Y(), F(), zz()) s konkrétním tvarem rovnic"]
["Více aplikací se řeší ve FKT přepínačem FKTPrep"]
[]
["Function Fmin(n, x() As Double, eps As Double) As Double"]
["Minimalizace funkce n-proměnných Rosenbrockovou metodou"]
["n -  počet proměnných; x() pole proměnných parametrů; eps -  požadovaná abs. Přesnost"]
["Vyžaduje naprogramovat fukci Function F(B() As Double) As Double s cílovou funkcí k minimalizaci"]
["Více aplikací se řeší ve F přepínačem FminPrep"]
[]
["Function Fmin1(n, x() As Double, eps As Double) As Double"]
["Minimalizace funkce n-proměnných metodou Nelder-Mead (simplex)"]
["n -  počet proměnných; x() pole proměnných parametrů; eps -  požadovaná abs. Přesnost"]
["Vyžaduje naprogramovat fukci Function F(B() As Double) As Double s cílovou funkcí k minimalizaci"]
[]
["Function GAUSS(A_, Optional n, Optional nCol)"]
["Řešení soustavy lineárních rovnic Gaussovou eliminací jako maticová funkce (Ctrl+Shift+Enter)"]
["A  rozšířená matice soustavy; n počet rovnic (nepovinné); nCol počet pravých stran (nepovinné)"]
["A se zadává jako rozmezí (range) na listu"]
[]
["Function GAUSST(A_, Optional n, Optional nRov)"]
["Řešení soustavy lineárních rovnic Gaussovou eliminací jako maticová funkce (Ctrl+Shift+Enter)"]
["Podprogram pro řešení přeurčené, obdélníkové soustavy lineárních rovnic"]
[" (více rovnic, než proměnných, řeší se ve smyslu nejmenších čtverců     AT.A.x = AT.b)"]
["A  rozšířená matice soustavy; n počet rovnic (nepovinné); nRov počet rovnic (řádků matice) (nepovinné)"]
[]
["Function Newton(n, nProm, nUnknown, XX, iPom, eps, alam, nIter,NewtPrep, form, _"]
["    Optional par1, Optional par2, Optional par3, Optional par4, Optional par5)"]
["Řešení soustavy nelineárních rovnic methodou Newton-Raphsonovou"]
["s výběrem neznamych z vektoru proměnných "]
["n - počet rovnic;  nProm - počet proměnných použitých v podprogramu FUN( )"]
["nUnknown - počet neznámých;  XX - vektor proměnných; "]
["iPom - vektor indexu proměnných uvažovaných jako neznámé; účinných je    "]
["           prvních nUnknown prvků, jejichž obsahy určují pořadové číslo neznámé"]
["eps - požadovaná relativni přesnost (doporučená  >=1.E-5)"]
["alam -        >0 a <2 ..maximální přípustná relativní korekce promenne (doporučeno 0.5)"]
["                    zachovává stejné znaménko proměnné !"]
["                    <0 .. v absolutní hodnotě stejný učinek. Umožňuje změnu znaménka proměnné !"]
["                    >2 .. zlomková část alam tvoří tlumicí konstantu pro klasické tlumeni abs.oprav kořenu"]
["nIter - maximalni přípustný počet iterací, na výstupu skutečný potřebný počet iterací"]
["NewtPrep - 0,1,2… přepínač aplikace pravých stran pro FUN()"]
["form - formát výstupu. Vektor výsledků: \"v\" vertikálně; \"h\" horizontálně"]
["par1, par2,...... uživatelské parametry soustavy rovnic (mohou být i poli (range))"]
["Vyžaduje naprogramovat fukci Sub FUN(x, f, Nequa, Optional par1, Optional par2, Optional par3, Optional par4, Optional par5)"]
["obsahující pravé strany rovnic  f(i)= ... proměnné jako  x(i,1)"]
["Více aplikací se řeší ve FUN přepínačem NewtPrep"]
[]
["Function RKMm(nRov, x_, xe, y_, delta, star_, FKTmPrepin, _"]
["       Optional Par1, Optional Par2, Optional Par3, Optional Par4, Optional Par5)"]
["Maticová funkce numerické integrace soustavy obyč. diferenciálních rovni metodou Runge-Kutta-Merson"]
["nRov  počet rovnic soustavy;     nOut  počet prvků pole pro výst.pomoc.prarmetry"]
["x_,xe   interval integrace v proměnné x;    y_()  vektor řešení"]
["delta -  abs.přesnost v jednotlivém kroku;     star =1 v počátečním intervalu, pak =0"]
["Star musí být v prvním použitém řádku větší než nula, pak je jedno! (lze přímo 1)"]
["FKTmPrep - 0,1,2...přepínač č. apliakce pravých stran"]
["Hodnoty par1 tvoří pole par1(1),par1(2).... a nelze je v těle RKMs ani FKTs měnit"]
["Vyžaduje naprogramovat podprogram Sub FKTm(n, x, y, f, Optional par1,...) s konkrétním tvarem rovnic"]
["Více aplikací se řeší ve FKT přepínačem FKTmPrep"]
[]
[]
["Function RKMs(nRov, x_, xe, y_, delta, star_,RKMsPrep, Optional ByVal nOut = 1, _"]
["    Optional par1, Optional par2, Optional par3, Optional par4, Optional par5)"]
["Maticová funkce numerické integrace soustavy obyč. diferenciálních rovni metodou Runge-Kutta-Merson"]
["po oblouku ds = Sqrt(dx2+dy2)"]
["nRov  počet rovnic soustavy;     nOut  počet prvků pole pro výst.pomoc.prarmetry"]
["x,xe   interval integrace v proměnné x;    y(2*nRov+3+nOut)  vektor řešení"]
["           v y(nRov+1) se přenáší hodnota proměnné x (duplicitně)"]
["           v y(nRov+2) se přenáší délka integračního oblouku s"]
["delta -  abs.přesnost v jednotlivém kroku;     star =1 v počátečním intervalu, pak =0"]
["Star musí být v prvním použitém řádku větší než nula, pak je jedno! (lze přímo 1)"]
["FKTsPrep - 0,1,2...přepínač č. apliakce pravých stran"]
["Hodnoty par1 tvoří pole par1(1),par1(2).... a nelze je v těle RKMs ani FKTs měnit"]
["Obdobně to platí i při použití par2: par2(1),par2(2)...."]
["Pokud uživatel definuje maticové pole širší (2*Nrov+3) buněk, zobrazí se mu kromě"]
["    integrovaných funkcí,x a oblouku i délka skutečného int. kroku a hodnoty derivací."]
["Deklaruje-li uživatel nOut>1 může použít nOut vnitřních prvků pole z_( ) do"]
["    kterých ve FKTs může ukládat hodnoty. Zobrazí se v buňkách 2*nRov+4 a následujících"]
["Vyžaduje naprogramovat podprogram Sub FKTs(n, x, y, f, Optional par1,...) s konkrétním tvarem rovnic"]
["Více aplikací se řeší ve FKT přepínačem FKTsPrep"]
[]
[]
["Function NonEQ(n, x, eps, alam, NewtPrep, Optional FminPrep,Optional par1, Optional par2, Optional par3)"]
["Maticové řešení soustavy nelineárních rovnic třemi metodami: methodou Newton-Raphsonovou"]
["Rosenbrock a Nelder-Mead"]
["Kvůli titulkům pro výsledky zvolte matici  (n+1)x6"]
["n- počet rovnic (stejné jako neznámých)"]
["x - rozmezí s počátečními odhady proměnných"]
["eps - požadovaná relativni přesnost (doporučená  >=1.E-5)"]
["alam -        >0 a <2 ..maximální přípustná relativní korekce promenne (doporučeno 0.5)"]
["                    zachovává stejné znaménko proměnné !"]
["                    <0 .. v absolutní hodnotě stejný učinek. Umožňuje změnu znaménka proměnné !"]
["                    >2 .. zlomková část alam tvoří tlumicí konstantu pro klasické tlumeni abs.oprav kořenu"]
["NewtPrep - 0,1,2… přepínač aplikace pravých stran pro FUN()"]
["FminPrep - 0,1,2… přepínač aplikace cílové funkce minimalizace f()"]
["                     pokud je FminPrep=0 nebo není zadán vytvoří se cílová fce minimalizace"]
["                     automaticky pomocí rutiny FUN z Newton"]
["par1, par2,...... uživatelské parametry soustavy rovnic (mohou být i poli (range))"]
[]
["Přidán list Regrese a funkce InsertCode(Modul as String,kod as String,Jednorazove as Boolean, sekvence as String,Optional bezHlasek as Integer, Optional radek as Integer)"]
["Modul        název modulu kam kod vkládáme"]
["kod              programový vkládaný kód zakončovaný vbCrLf  (i více řádků, na konci bez vbCrLf)"]
["Jednorazove   true jen jednoua konec; false opakovaně"]
["sekvence  textová sekvence, která se vyhledá ve stávajícím kodu a deginuje řádek k vložení a nahrazení (např. #regvz)"]
["bezHlasek 0-všechny hlášky; 1-jen hláška o vložení kodu; 2-žádné hlášky"]
["radek          0 nebo č. řádku, který s ekodem nahradí"]
[]
[]
["Function TranslateEQ(Code As String, yprom As String, konst As String, xprom As String) As String"]
["přeloží obecně zadaný regresná vztah ve tvaru y=f(x,a) nebo y=f(x,b) do konkrétních proměnných použitých v kódu"]
["Code      zadaný obecně definovaný vztah"]
["yprom   čím konkrétním se má nahradit identifikátor y   (např.\"regfun\")"]
["konst     čím konkrétním se má nahradit identifikátor hledaných konstant  a či b (např. \"par\")"]
["xprom   čím konkrétním se má nahradit identifikátor x   (např.\"xReg(i)\")"]
["Zavoláme-li na: Code=\"y = a1+a2*x+a3*x*x\""]
["Code = TranslateEQ(Code, \"regfun\", \"b\", \"xReg(i)\")      dostaneme v Code"]
["\"rgfun =  b(1)+b(2)*xReg(i)+b(3)*xReg(i)*xReg(i)\""]
["a to můžeme použít do kódu"]
[]
[]
["Function MatNas(A, B, Optional n as integer, Optional m as integer)"]
["násobení matic, vrací výsledek v matici C=A.B  "]
["A           první matice jako range"]
["B           druhá matice jako range"]
["n           počet řádků matice A (nepovinné, raději neuvádět)"]
["m          počet sloupců matice B (nepovinné, raději neuvádět)"]
["Výsledná matice má tolik řádků jako matice A a tolik sloupců jako matice B"]

{"sheet":"Integrace","index":1,"n_rows":58,"n_cols":9,"rows_kept":58,"cut":false,"hidden":false,"merged":[]}
["Integrace pomocí RKM",null,null,"klasicky"]
[null,null,null,null,"y1' = a*y1","y1(0) = 1"]
["a =",1,null,null,"y2' = -sin(x)","y2(0) = 1"]
[]
["x","y1","y1anal","y2","y2anal","D1","D2",null,"Public Sub Integrace()"]
[0,null,1,null,1,{"$f":"B6-C6","v":-1},{"$f":"D6-E6","v":-1},null,"' Klasická integrace bez class modulu"]
[0.1,1.1051709027777779,1.1051709180756477,0.99500416510450762,0.99500416527802582,{"$f":"B7-C7","v":-1.5297869859765001E-8},{"$f":"D7-E7","v":-1.7351819980859773E-10},null,"' Podprogramy RKM i FKT jsou součástí klasického modulu"]
[0.2,1.2214027243466483,1.2214027581601699,0.98006657714890288,0.98006657784124163,-3.381352153830619E-8,-6.9233874189222888E-10,null,"' zz()  parametry modelu"]
[0.30000000000000004,1.3498587515214227,1.3498588075760032,0.95533648757432799,0.95533648912560598,-5.605458053281609E-8,-1.5512779949489186E-9,null,"    Dim x As Double, xe As Double, dx As Double"]
[0.4,1.4918246150414147,1.4918246976412703,0.92106099126113139,0.9210609940028851,-8.2599855621978691E-8,-2.7417537129537095E-9,null,"    Dim Y(10), zz(10), a, ir As Integer"]
[0.5,1.648721156591431,1.6487212707001282,0.87758255763850179,0.87758256189037276,-1.1410869715788863E-7,-4.2518709664207677E-9,null,"    Set a = Worksheets(\"Integrace\")"]
[0.6,1.8221186490589738,1.8221188003905089,0.82533560884313717,0.82533561490967833,-1.5133153508095631E-7,-6.0665411583116224E-9,null,"    ir = 6"]
[0.7,2.0137525123487308,2.0137527074704766,0.76484217911685581,0.7648421872844885,-1.9512174587177356E-7,-8.1676326812996081E-9,null,"    Star = 1"]
[0.79999999999999993,2.2255406820434649,2.2255409284924674,0.69670669881301328,0.6967067093471655,-2.4644900253889546E-7,-1.0534152217189785E-8,null,"    eps = 0.00001"]
[0.89999999999999991,2.4596028047426475,2.4596031111569494,0.62160995512821038,0.6216099682706645,-3.0641430193156793E-7,-1.3142454124981384E-8,null,"    dx = 0.1"]
[0.99999999999999989,2.7182814521921861,2.7182818284590451,0.54030228990166251,0.54030230586813977,-3.7626685900349344E-7,-1.596647725143896E-8,null,"    zz(1) = a.Range(\"B3\")"]
[1.0999999999999999,3.0041655665233269,3.0041660239464325,0.45359610244757254,0.45359612142557748,-4.5742310561536215E-7,-1.8978004945324756E-8,null,"'   počáteční podmínky"]
[1.2,3.3201163712484996,3.3201169227365472,0.36235773232972668,0.36235775447667362,-5.5148804767313209E-7,-2.2146946943024659E-8,null,"      a.Cells(ir, 1) = x"]
[1.3,3.6692960073399843,3.6692966676192444,0.26749880318294716,0.26749882862458735,-6.6027926015621574E-7,-2.5441640183476721E-8,null,"      a.Cells(ir, 2) = Y(1)"]
[1.4000000000000001,4.0551991809908259,4.0551999668446754,0.16996711407107559,0.16996714290024081,-7.8585384954976689E-7,-2.8829165221733177E-8,null,"      a.Cells(ir, 3) = Exp(x)"]
[1.5000000000000002,4.4816881397993367,4.4816890703380654,7.0737169392027691E-2,7.0737201667702684E-2,-9.3053872873838372E-7,-3.2275674993753611E-8,null,"      a.Cells(ir, 4) = Y(2)"]
[1.6000000000000003,4.9530313274304927,4.9530324243951167,-2.9199558048022184E-2,-2.9199522301289037E-2,-1.0969646240255315E-6,-3.5746733146463372E-8,null,"      a.Cells(ir, 5) = Cos(x)"]
[1.7000000000000004,5.4739461036229731,5.4739473917272017,-0.12884453350318309,-0.12884449429552508,-1.2881042286139177E-6,-3.9207658009132729E-8,null,"      ir = ir + 1"]
[1.8000000000000005,6.0496459570979004,6.0496474644129492,-0.22720213731695668,-0.22720209469308753,-1.5073150487765474E-6,-4.2623869156432903E-8,null,"    Y(1) = 1: Y(2) = 1"]
[1.9000000000000006,6.6858926838918205,6.685894442279273,-0.32328961282473689,-0.32328956686350396,-1.7583874525328724E-6,-4.5961232930658014E-8,null,"     Do             ' integrace v termočlánkových bodech"]
[2.0000000000000004,7.3890540533320621,7.3890560989306531,-0.4161468857335463,-0.4161468365471428,{"$f":"B26-C26","v":-2.0455985909606511E-6},{"$f":"D26-E26","v":-4.9186403505707688E-8},null,"      xe = x + dx"]
[null,null,null,null,null,null,null,null,"      RKM 2, x, xe, Y(), eps, Star, zz()    ' vlastní integrace"]
[null,null,null,null,null,null,null,null,"'      Debug.Print \"*x,y1,y2: \", x, Y(1); Exp(x), Y(2); Cos(x)"]
[null,null,null,null,null,null,null,null,"'      x = x + dx   ' Nedávat! dělá se automaticky"]
[null,null,null,null,null,null,null,null,"      ' zapiš výsledky do listu"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 1) = x"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 2) = Y(1)"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 3) = Exp(x * zz(1))"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 4) = Y(2)"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 5) = Cos(x)"]
[null,null,null,null,null,null,null,null,"      ir = ir + 1"]
[null,null,null,null,null,null,null,null,"     Loop While x <= 2"]
[null,null,null,null,null,null,null,null,"End Sub"]
[]
[null,null,null,null,null,null,null,null,"Public Sub FKT(ByVal nn, x, Y(), F(), zz())"]
[null,null,null,null,null,null,null,null,"' Procedura pravých stran pro integraci - model reaktoru"]
[null,null,null,null,null,null,null,null,"    Dim pom, pp, Cp, Tw, Tw1, q, q1, w, s, it As Integer, i As Integer"]
[null,null,null,null,null,null,null,null,"    Select Case FKTPrep"]
[null,null,null,null,null,null,null,null,"     Case 0:"]
[null,null,null,null,null,null,null,null,"' úvodní příklad"]
[null,null,null,null,null,null,null,null,"        F(1) = Y(1) * zz(1)"]
[null,null,null,null,null,null,null,null,"        F(2) = -Sin(x)"]
[null,null,null,null,null,null,null,null,"     Case 1:"]
[null,null,null,null,null,null,null,null,"' Strato skok"]
[null,null,null,null,null,null,null,null,"        ro = zz(2) * Exp(-zz(2) * 9.81 * Y(1) / zz(1))"]
[null,null,null,null,null,null,null,null,"        F(1) = -Y(2)"]
[null,null,null,null,null,null,null,null,"        F(2) = 9.81 - zz(5) * ro * Y(2) * Y(2) * zz(4) / zz(3) / 2"]
[null,null,null,null,null,null,null,null,"        zz(9) = ro"]
[null,null,null,null,null,null,null,null,"     Case 2:"]
[null,null,null,null,null,null,null,null,"    ' aplikace...."]
[null,null,null,null,null,null,null,null,"     Case 3:"]
[null,null,null,null,null,null,null,null,"    End Select"]
[null,null,null,null,null,null,null,null,"End Sub"]

{"sheet":"IntegraceClass","index":2,"n_rows":47,"n_cols":9,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["Integrace pomocí RKM",null,null,null,"přes class modul"]
[null,null,null,null,null,"y1' = a*y1","y1(0) = 1"]
["a =",2,null,null,null,"y2' = cos(x)","y2(0) = 1"]
[]
["x","y1","y1anal","y2","y2anal","D1","D2",null,"Public myNum As New Numer"]
[0,null,1,null,0,{"$f":"B6-C6","v":-1},{"$f":"D6-E6","v":0},null,"Public Sub IntegraceC()"]
[0.1,0.81873111111111108,0.81873075307798182,9.9833420114298174E-2,9.9833416646828155E-2,{"$f":"B7-C7","v":3.5803312925519748E-7},{"$f":"D7-E7","v":3.4674700194470276E-9},null,"' Integrace přes class modul"]
[0.2,0.67032063230123451,0.67032004603563933,0.19866933769535544,0.19866933079506122,5.8626559518160093E-7,6.9002942248985732E-9,null,"' Podprogramy RKM i FKT jsou součástí class modulu"]
[0.30000000000000004,0.54881235608469225,0.54881163609402639,0.29552021692551256,0.2955202066613396,7.1999066586503346E-7,1.0264172956020445E-8,null,"' zz()  parametry modelu"]
[0.4,0.44932975008872689,0.44932896411722156,0.38941835583414597,0.38941834230865052,7.8597150532377924E-7,1.3525495445865232E-8,null,"    Dim x As Double, xe As Double, dx As Double"]
[0.5,0.36788024554542126,0.36787944117144233,0.47942555525587871,0.47942553860420301,8.0437397892429985E-7,1.6651675704970614E-8,null,"    Dim Y(10), zz(10)"]
[0.6,0.30119500219123119,0.30119421191220214,0.56464249300651326,0.56464247339503537,7.9027902905037806E-7,1.9611477886094519E-8,null,"    Set a = Worksheets(\"IntegraceClass\")"]
[0.7,0.24659771880514025,0.24659696394160649,0.64421770961301972,0.64421768723769102,7.5486353376397197E-7,2.2375328700974251E-8,null,"    ir = 6"]
[0.79999999999999993,0.20189722431479784,0.20189651799465544,0.71735611581513536,0.71735609089952268,7.0632014240179508E-7,2.4915612684139887E-8,null,"    Star = 1"]
[0.89999999999999991,0.16529953879350368,0.16529888822158656,0.78332693683443133,0.7833269096274833,6.5057191711570539E-7,2.7206948027824751E-8,null,"    eps = 0.00001"]
[0.99999999999999989,0.13533587506255948,0.13533528323661273,0.84147101403433699,0.84147098480789639,5.9182594674966893E-7,2.9226440600993442E-8,null,"    dx = 0.1"]
[1.0999999999999999,0.11080369136316384,0.11080315836233391,0.89120739101534741,0.89120736006143531,5.3300082993035236E-7,3.0953912100173397E-8,null,"    zz(1) = a.Range(\"B3\")"]
[1.2,9.0718429344975746E-2,9.0717953289412512E-2,0.93203911833932873,0.93203908596722629,4.760555632338237E-7,3.2372102443112283E-8,null,"'   počáteční podmínky"]
[1.3,7.4274000455866809E-2,7.4273578214333877E-2,0.96355821888403437,0.96355818541719296,4.222415329324658E-7,3.3466841409257597E-8,null,"      a.Cells(ir, 1) = x"]
[1.4000000000000001,6.0810434919899001E-2,6.0810062625217952E-2,0.985449764215651,0.98544972998846025,3.7229468104887919E-7,3.4227190748303826E-8,null,"      a.Cells(ir, 2) = Y(1)"]
[1.5000000000000002,4.978739494911881E-2,4.9787068367863924E-2,0.99749502124960787,0.99749498660405445,3.2658125488638223E-7,3.4645553426138065E-8,null,"      a.Cells(ir, 3) = Exp(x)"]
[1.6000000000000003,4.0762489186019754E-2,4.076220397836619E-2,0.99957363775925423,0.99957360304150511,2.8520765356365718E-7,3.4717749120005692E-8,null,"      a.Cells(ir, 4) = Y(2)"]
[1.7000000000000004,3.3373518062924601E-2,3.3373269960326052E-2,0.99166484489552509,0.99166481045246857,2.4810259854901595E-7,3.4443056518007609E-8,null,"      a.Cells(ir, 5) = Sin(x)"]
[1.8000000000000005,2.7323937525344989E-2,2.7323722447292535E-2,0.97384766470241535,0.97384763087819504,2.1507805245471467E-7,3.3824220313505293E-8,null,"      ir = ir + 1"]
[1.9000000000000006,2.2370957730056283E-2,2.237077185616557E-2,0.94630012055483792,0.94630008768741425,1.8587389071303417E-7,3.2867423671589791E-8,null,"    Y(1) = 1: Y(2) = 0"]
[2.0000000000000004,1.8315799078948685E-2,1.8315638888734165E-2,0.90929745840790799,0.90929742682568149,{"$f":"B26-C26","v":1.6019021452026716E-7},{"$f":"D26-E26","v":3.1582226500681543E-8},null,"     Do             ' integrace v termočlánkových bodech"]
[null,null,null,null,null,null,null,null,"      xe = x + dx"]
[null,null,null,null,null,null,null,null,"      myNum.RKM 2, x, xe, Y(), eps, Star, zz()    ' vlastní integrace"]
[null,null,null,null,null,null,null,null,"'      Debug.Print \"x,y1,y2: \", x, Y(1); Exp(-x), Y(2); Sin(x)"]
[null,null,null,null,null,null,null,null,"'      x = x + dx   ' Nedávat! dělá se automaticky"]
[null,null,null,null,null,null,null,null,"      ' zapiš výsledky do listu"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 1) = x"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 2) = Y(1)"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 3) = Exp(-x * zz(1))"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 4) = Y(2)"]
[null,null,null,null,null,null,null,null,"      a.Cells(ir, 5) = Sin(x)"]
[null,null,null,null,null,null,null,null,"      ir = ir + 1"]
[null,null,null,null,null,null,null,null,"     Loop While x <= 2"]
[null,null,null,null,null,null,null,null,"End Sub"]
[]
[null,null,null,null,null,null,null,null,"Public Sub FKT(ByVal nn, x, Y(), F(), zz())"]
[null,null,null,null,null,null,null,null,"' Procedura pravých stran pro integraci - model reaktoru"]
[null,null,null,null,null,null,null,null,"    Dim pom, pp, Cp, Tw, Tw1, q, q1, w, s, it As Integer, i As Integer"]
[null,null,null,null,null,null,null,null,"    Static Alfaout"]
[null,null,null,null,null,null,null,null,"    F(1) = -Y(1) * zz(1)"]
[null,null,null,null,null,null,null,null,"    F(2) = Cos(x)"]
[null,null,null,null,null,null,null,null,"End Sub"]

{"sheet":"Minimalizace","index":3,"n_rows":39,"n_cols":17,"rows_kept":39,"cut":false,"hidden":false,"merged":[]}
["Minimalizace funkce",null,null,null,null,null,null,null,null,"Pokusy:"]
[null,null,"Řešení",null,null,null,null,null,null,"x","y","z","MSE",null,null,null,"Public Sub Minimalizace()"]
["x1(0)=",0.4,0,null,null,null,null,null,1,0,0.5,0,2.5,null,null,null,"' Spuštění minimalizace"]
["x2(0)=",-0.7,-1,null,null,null,null,null,2,0.5,0.8,-0.5,4.49,null,null,null,"    Dim i As Integer, FF As Double, eps As Double, A, c"]
["x2(0)=",0.25,0.5,"počet rovnic",3,"od ř.",1,null,3,0.3,0.1,0.8,1.3900000000000003,null,null,null,"    Set A = Worksheets(\"Minimalizace\")"]
[null,null,null,null,null,null,null,null,4,1,-0.7,0.3,{"$f":"MSE(J6,K6,L6)","v":1.58},null,null,null,"    c = A.Range(\"B5\")"]
["Metoda","f","x","y","z","iter",null,null,5,-0.38,0.25,0.1,0.21690000000000001,null,null,null,"    B(1) = A.Range(\"B3\")"]
["Rosenbrock",5.0640676228127128E-11,6.8837908005772451E-6,-0.99999979649766779,0.50000165859239443,321,null,null,6,0.04,-0.1,0.3,0.1016,null,null,null,"    B(2) = A.Range(\"B4\")"]
["Nelder-Mead",7.6480490410759295E-8,2.8347961076179955E-5,-1.0000460542430587,0.49993111526363193,67,null,null,7,0.15,0.4,0.55000000000000004,0.4850000000000001,null,null,null,"    eps = 0.00001"]
[null,null,null,null,null,null,null,null,8,0.28000000000000003,-0.6,0.27,0.51129999999999998,null,null,null,"    FminPrep = 0    ' nastavení přepínače úlohy aplikace"]
[null,null,null,null,null,null,null,null,9,0.15,0.4,-0.25,0.24500000000000002,null,null,null,"    FF = Fmin(2, B(), eps)"]
[null,null,null,null,null,null,null,null,10,-0.39,0.8,-0.1,0.80210000000000015,null,null,null,"    ' zapiš výsledky"]
["Příklad:","f = [(b1-2)2+(b2-5)2]",null,null,null,null,null,null,11,0.3,0.2,0.34,0.24560000000000004,null,null,null,"    A.Cells(8, 2) = FF"]
["Odhady:",1,2,null,null,null,null,null,12,-0.15,-0.17,-0.47,0.27229999999999999,null,null,null,"    A.Cells(8, 3) = B(1)"]
["Metoda","f","b1","b2","iter",null,null,null,13,0.24,0.36,0.3,0.2772,null,null,null,"    A.Cells(8, 4) = B(2)"]
["Rosenbrock",4.066976665512523E-11,1.9999997064188781,5.0000063705240585,80,null,null,null,14,-0.05,0.24,-0.14000000000000001,7.9700000000000007E-2,null,null,null,"    A.Cells(8, 5) = nIter"]
["Nelder-Mead",4.4502593943802308E-6,2.0009526896696754,5.0001964388379481,26,null,null,null,15,0.67,0.2,0.2,0.52890000000000015,null,null,null,"    B(1) = A.Range(\"B3\")"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    B(2) = A.Range(\"B4\")"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    FF = Fmin1(2, B(), eps)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    ' zapiš výsledky"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    A.Cells(9, 2) = FF"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    A.Cells(9, 3) = B(1)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    A.Cells(9, 4) = B(2)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    A.Cells(9, 5) = nIter"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"End Sub"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Function F(B() As Double) As Double"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"' Minimalizovaná funkce"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    Dim s As Double, YV As Double, i As Integer, j As Integer, xexp As Double"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    Select Case FminPrep"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     Case 0:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     ' úvodní příklad"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"        F = (B(1) - 2) ^ 2 + (B(2) - 5) ^ 2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     Case 1:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     ' aplikace...."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     Case 2:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     ' aplikace...."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    End Select"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"End Function"]

{"sheet":"Gauss","index":4,"n_rows":36,"n_cols":22,"rows_kept":36,"cut":false,"hidden":false,"merged":[]}
["Použití funkce GAUSS a maticové násobení z šablony NUMER.XLTM"]
[]
[]
[]
[]
["volání :"]
[]
["Public Function GAUSS(A, N, NCOL)"]
[]
["A) volání s jednou pravou stranou"]
[]
["A(i,j)",null,"b(i)","řešení",null,null,null,null,"A(i,j)",null,"b(i)","řešení"]
[1,3,5,{"$f":"GAUSS(A13:C14,C15,C16)","v":0.5},null,null,null,null,2,3,5,{"$f":"GAUSS(I13:K14)","v":4}]
[-1,1,1,1.5,null,null,null,null,1,1,3,-1]
["počet rovnic             :",null,2]
["počet pravých stran :",null,1]
[]
["B) volání s více pravými stranami (a bez volitelných parametrů)",null,null,null,null,null,null,null,"Public Function MatNas(A, B)"]
[null,null,null,null,"inverzní matice"]
["A(i,j)",null,"b(i)",null,"řešení",null,null,null,null,"A",null,null,null,"B",null,null,"C"]
[1,1,1,0,{"$f":"GAUSS(A21:D22)","v":0.5},-0.5,null,null,1,3,null,2,1,3,null,{"$f":"MatNas(I21:J23,L21:N22)","v":5},1,0]
[-1,1,0,1,0.5,0.5,null,null,2,-1,null,1,0,-1,null,3,2,7]
["počet rovnic             :",null,2,null,null,null,null,null,4,2,null,null,null,null,null,10,4,10]
["počet pravých stran :",null,2]
[]
["C) volání GAUSST pro přeurčenou soustavu (a bez volitelných parametrů)",null,null,null,null,null,null,null,1,2,4,null,2,1,null,{"$f":"MatNas(I26:K27,M26:N28)","v":16},-3]
["Public Function GAUSST(A, N, Nrov)",null,null,null,null," N - počet neznámých",null,null,3,-1,2,null,1,0,null,11,1]
[null,null,null,null,null," Nrov - počet rovnic  >= N",null,null,null,null,null,null,3,-1]
["A(i,j)",null,null,"b(i)","řešení"," N, Nrov  Optional"]
[1,2,1,3,{"$f":"GAUSST(A30:D34)","v":0.55525425891660829},null,null,null,null,null,null,null,null,null,null,"Inverzní matice"]
[2,5,-4,2,0.44975435462259927,null,null,null,1,2,1,1,0,0,null,{"$f":"GAUSS(I31:N33)","v":0.33333333333333337},0,-0.33333333333333331,null,{"$f":"MatNas(I31:K33,P31:R33)","v":1},0,0]
[-2,2,1,6,1.1642314808907035,null,null,null,2,5,-4,0,1,0,null,0.15384615384615383,7.6923076923076913E-2,0.15384615384615383,null,0,1,0]
[2,-5,3,7,null,null,null,null,-2,2,1,0,0,1,null,0.35897435897435898,-0.15384615384615385,2.564102564102564E-2,null,0,0,0.99999999999999989]
[3,2,3,4]
["počet neznámých",null,3]
["počet rovnic",null,5]

{"sheet":"Newton","index":5,"n_rows":64,"n_cols":16,"rows_kept":64,"cut":false,"hidden":false,"merged":[]}
["Použití funkce Newton z šablony NUMER.XLTM"]
[]
["funkce je vektorová - vkládá se Ctrl+Shift+Enter"]
[]
[]
["volání  :"]
["Public Function Newton(N; Nprom; NUnknown;  X; IPOM;  Eps; Alam; Niter; NewtPrep; Format; par1; par2;...)"]
[]
[]
[]
[]
[]
[]
["1) \"vertikální\" volání :"]
[null,null,null,null,"NewtPrep",null,null,null,"NewtPrep"]
["x0(i)","ipom(i)","řešení x(i)","residua f(i)",0,null,null,null,1]
[1,1,{"$f":"Newton(7,5,5,A17:A21,B17:B21,0.0000005,0.5,500,0,\"v\",A22,B22:B23)","v":2.0095621103114052},5.7005741055489167E-3,8.6644914177729708E-4,null,{"$f":"Newton(3,3,3,A17:A21,B17:B21,0.0000005,0.5,500,$I$16,\"v\",G21)","v":0.85486064124635353},7.5612021532833751E-8,5.7219837223445396E-15]
[1,2,1.9721421544424012,4.2301325109406207E-7,0,null,0.7247207984215327,5.2226667435206764E-11,0]
[1,3,1.9952185444639194,-2.3077190782274215E-2,"Iter =  9",null,1.3206032895746385,2.1916191361714965E-9,"Iter =  6"]
[1,4,1.9325119802583646,2.4373259943644143E-7,"O.K.",null,0,0,0]
[1,5,2.0105174699845909,1.652247377137428E-6,"",null,0.1]
[0,0,0,-4.4640326814281671E-5,""]
[null,0,0,1.7360698906320415E-2,""]
[]
[]
[]
[]
[]
[]
[]
[]
["2) \"horizontální \" volání :",null,null,null,"par2(1-2)",1,0.5]
[]
["par1","x(1)","x(2)","x(3)","x(4)","x(5)","f(1)","f(2)","f(3)","f(4)","f(5)","f(6)","f(7)","sumres","ID","iter"]
[0,{"$f":"Newton(7,5,5,$A$17:$A$21,$B$17:$B$21,0.0000005,0.05,500,0,\"h\",A35,$F$32:$G$32)","v":2.0505411550135495},1.7497232366517141,1.9842059065498296,1.5421771398627593,2.0793110144975118,-6.1351828394154317E-2,-8.9097001982452184E-5,0.28447029821509329,-3.8403144743792694E-5,-7.5971602445790154E-4,2.7769859483962267E-2,-0.21607085679845639,0.13214576424878302,0,"Iter =  36"]
[1,{"$f":"Newton(7,5,5,$A$17:$A$21,$B$17:$B$21,0.0000005,0.05,500,0,\"h\",A36,$F$32:$G$32)","v":1.787883083716167},1.764984340293233,2.0813079840601021,2.7876943336748168,2.0677845825941139,4.2818245391765597E-2,-7.6564015660096629E-4,0.13417540806950257,-1.8217088298033701E-4,-7.7639364224637575E-3,0.27890149887794691,-0.10370767564666483,0.10843866843329832,0,"Iter =  38"]
[2,{"$f":"Newton(7,5,5,$A$17:$A$21,$B$17:$B$21,0.0000005,0.05,500,0,\"h\",A37,$F$32:$G$32)","v":1.4962967188626135},1.8282690174704375,2.1298143827678424,3.1898678693312537,2.0414862523385606,0.19698727111730241,-1.5191753260879182E-3,-4.5619880899106846E-2,-3.1589306043589005E-4,-1.5743061351731313E-2,0.54418953347594712,8.0834002382799142E-3,0.33734299988249289,0,"Iter =  41"]
[3,{"$f":"Newton(7,5,5,$A$17:$A$21,$B$17:$B$21,0.0000005,0.05,500,0,\"h\",A38,$F$32:$G$32)","v":1.1917198512473774},1.8787450503768177,2.1554413743572516,3.3495237872264587,2.0165319296785182,0.45438262859114076,-2.4020859441975517E-3,-0.27409372401855325,-4.7568203701642275E-4,-2.4728169426424529E-2,0.82381207843114079,8.4186424734069121E-2,0.96796211604376026,0,"Iter =  43"]
[]
["3) zkrácené formy volání :"]
[]
["par(1)","x(1)","x(2)","x(3)","x(4)","x(5)"]
[1,{"$f":"Newton(7,5,5,$A$17:$A$21,$B$17:$B$21,0.0005,0.5,500,0,\"h\",A43,$F$32:$G$32)","v":1.7878948632691083},1.7649497561714862,2.0813049548642493,2.7876721877237194,2.0677957054292322,"f(1)","f(2)","f(3)","f(4)","f(5)","f(6)","f(7)"]
[1,{"$f":"Newton(7,5,5,$A$17:$A$21,$B$17:$B$21,0.0000005,0.05,500,0,\"h\",A44,$F$32:$G$32)","v":1.787883083716167},1.764984340293233,2.0813079840601021,2.7876943336748168,2.0677845825941139,4.2818245391765597E-2,-7.6564015660096629E-4,0.13417540806950257,-1.8217088298033701E-4,-7.7639364224637575E-3,0.27890149887794691,-0.10370767564666483]
[]
["NewtPrep",2]
[null,"x(1)","x(2)","f(1)","f(2)","sumres","ID","iter"]
[null,{"$f":"Newton(2,2,2,A17:A21,B17:B21,0.0000005,0.5,500,2,\"h\")","v":0.99999999984338861},2.0000000004698335,1.722722409169819E-9,0,2.9677724990558653E-18,0,"Iter =  6"]
[]
["Petr:"]
["IPOM","Odhady","Řešení","Reziduum","Sumres","xodhad",{"$f":"NonEQ(3,F52:F54,0.0005,0.5,4,0)","v":"xNewton"},"rezid","","xRosen","xNelder","rezid"]
[1,0.4,{"$f":"Newton(3,3,3,$B$52:$B$54,$A$52:$A$54,0.0005,0.5,500,4,\"v\")","v":9.2291530005891464E-9},-1.9958872776726366E-8,1.1950698075526466E-15,0.4,-2.0146667858536208E-6,4.3569044243518817E-6,5.6947848484941303E-11,-1.8365771859507093E-7,-9.6700954788962674E-5,3.0010073019613179E-12]
[2,-0.7,-0.99999999462186062,-1.9958872776726366E-8,0,-0.5,-1.0000011740144579,4.3569044239077925E-6,"Rit=339",-1.000000344238938,-0.99998364645703275,3.7969685390505022E-7]
[3,1,0.50000000431579117,-1.9958872776726366E-8,"Iter =  14",0.7,0.49999905788963239,4.3569044243518817E-6,"Iter =  13",0.49999997894243819,0.49984181401534389,"NMit = 57"]
[]
["IPOM","Odhady","Řešení","Reziduum","Sumres"]
[1,0.8,{"$f":"Newton(3,3,3,$B$57:$B$59,$A$52:$A$54,0.0005,0.5,500,4,\"v\")","v":1.6964351375785627E-6},-3.6686890576564934E-6,4.0377838218339272E-11]
[2,-2,-0.99999901142988357,-3.6686890592108057E-6,0]
[3,-0.2,0.50000079329700675,-3.6686890578785381E-6,"Iter =  19"]
[]
["IPOM","Odhady","Řešení","Reziduum","Sumres"]
[1,1,1,1,1]
[2,1,1,1,1]
[3,1,1,1,1]

{"sheet":"RKMm","index":6,"n_rows":31,"n_cols":8,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["Použití RKMm - řešení počátečního problému ODE maticová fce"]
[]
[]
[]
["volání  :"]
["Public Function RKMm(nEqua,  x0,  XE,  y0,  delta,  start, FKTmPrep,  par1, ..., par5)"]
[]
[]
[]
[]
[]
[]
[]
[]
["start",1,"FKTmPrep:",0]
["delta",1E-8]
["par",2]
[]
["x","y1","y2","krok","exp(x)","exp(par*x)","dy1 %","dy2 %"]
[0,1,1,"-",{"$f":"EXP(A20)","v":1},{"$f":"EXP(2*A20)","v":1},{"$f":"(B20-E20)/E20*100","v":0},0]
[4.5,{"$f":"RKMm(2, A20, A21,B20:C20,$B$16, $B$15, $D$15, $B$17)","v":90.017131135679705},8103.0834532145209,2.0041649376763004E-3,{"$f":"EXP(A21*$B$17)","v":8103.0839275753842},{"$f":"EXP($B$17*A21)","v":8103.0839275753842},-98.889100348210079,-5.8540781210707054E-6]
[0,{"$f":"RKMm(2, A21, A22,B21:C21,$B$16, $B$15, $D$15, $B$17)","v":0.99999999971255804},0.99999999081205648,-2.5741771781990358E-2,{"$f":"EXP(A22*$B$17)","v":1},{"$f":"EXP($B$17*A22)","v":1},-2.8744195912366877E-8,-9.1879435171193791E-7]
[1,{"$f":"RKMm(2, A22, A23,B22:C22,$B$16, $B$15, $D$15, $B$17)","v":2.7182818236905844},7.3890556846149318,5.8950354425982843E-3,7.3890560989306504,7.3890560989306504,-63.212055947389864,-5.6071535129095747E-6]
[1.5,{"$f":"RKMm(2, A23, A24,B23:C23,$B$16, $B$15, $D$15, $B$17)","v":4.4816890615908713},20.085535670064363,1.5693143277790256E-2,20.085536923187668,20.085536923187668,-77.686984028706732,-6.2389335643398964E-6]
[2,{"$f":"RKMm(2, A24, A25,B24:C24,$B$16, $B$15, $D$15, $B$17)","v":7.3890560838577564},54.598146472882497,1.0756029848799864E-2,54.598150033144236,54.598150033144236,-86.4664717039457,-6.5208468356419748E-6]
[3,{"$f":"RKMm(2, A25, A26,B25:C25,$B$16, $B$15, $D$15, $B$17)","v":20.085536881061966},403.42876644465599,5.2142542675230885E-3,403.42879349273511,403.42879349273511,-95.021293173655536,-6.7045484990085718E-6]
[4,{"$f":"RKMm(2, A26, A27,B26:C26,$B$16, $B$15, $D$15, $B$17)","v":54.598149918008289},2980.957786087647,2.9565069161714419E-3,2980.9579870417283,2980.9579870417283,-98.16843611498895,-6.7412584188919052E-6]
[5,{"$f":"RKMm(2, A27, A28,B27:C27,$B$16, $B$15, $D$15, $B$17)","v":148.41315878926261},22026.464308323575,5.0456129365974434E-3,22026.465794806718,22026.465794806718,-99.326205301513895,-6.7486230276171159E-6]
[6,{"$f":"RKMm(2, A28, A29,B28:C28,$B$16, $B$15, $D$15, $B$17)","v":403.42879264087071},162754.78043288784,3.2604961664084442E-3,162754.79141900392,162754.79141900392,-99.752124782856782,-6.750103009998702E-6]
[0,{"$f":"RKMm(2, A29, A30,B29:C29,$B$16, $B$15, $D$15, $B$17)","v":0.99999999943549478},0.99999998195594564,-2.0396009879205403E-2,1,{"$f":"EXP(2*A30)","v":1},-5.6450522034623418E-8,-1.8044054361787687E-6]
[-8,{"$f":"RKMm(2, A30, A31,B30:C30,$B$16, $B$15, $D$15, $B$17)","v":3.3546982743429206E-4},1.126030105580958E-7,-7.9328778946488931E-2,1.1253517471925912E-7,{"$f":"EXP($B$17*A31)","v":1.1253517471925912E-7},298002.19628768234,6.0279676115410408E-2]

{"sheet":"RKMs","index":7,"n_rows":30,"n_cols":12,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
["Použití RKMs - integrace ODE po oblouku"]
[]
[]
[]
["volání  :"]
["Public Function RKMs(Nrov,  x0,  XE,  y0,  DELTA,  START, FKTsPrep, Nout, par1, ..., par5)"]
[]
[]
[]
[]
[]
[]
[]
[]
["start",1,"FKTsPrep:",0]
["delta",5.0000000000000002E-5]
["par",1,2.0099999999999998]
[]
["x","y1 ","y2 ","y3 = x","oblouk s","int. krok v s","dy1 ","dy2 ","out1","out2","exp(p1*x)","exp(p2*x)"]
[0,1,1,0,0,{"$f":"EXP(2*A20)","v":1},null,null,null,null,{"$f":"EXP($B$17*$A20)","v":1},{"$f":"EXP($C$17*$A20)","v":1}]
[0.1,{"$f":"RKMs(2,A20,A21,B20:E20,$B$16,1,$D$15,1,$B$17:$C$17)","v":1.1051691882749011},1.2226209019905976,9.9998493260068017E-2,0.26580419876386763,0.37229033737942424,0.38452478647856914,0.8550341187597138,0.34793295954883385,1.2395589052382829,{"$f":"EXP($B$17*$A21)","v":1.1051709180756477},{"$f":"EXP($C$17*$A21)","v":1.2226247718233272}]
[0.2,{"$f":"RKMs(2,A21,A22,B21:E21,$B$16,1,$D$15,1,$B$17:$C$17)","v":1.2213970396755125},1.4947971727731402,0.19999693424946316,0.57825206848052302,0.40599186813051841,0.3598718417978683,0.8852569167542349,0.29463952351949579,1.2451287585521031,{"$f":"EXP($B$17*$A22)","v":1.2214027581601699},{"$f":"EXP($C$17*$A22)","v":1.4948113326760426}]
[0.3,{"$f":"RKMs(2,A22,A23,B22:E22,$B$16,0,$D$15,1,$B$17:$C$17)","v":1.3498520684063329},1.827574535352035,0.29999987070172401,0.94876663084284596,0.40599186813051841,0.33417759197283864,0.90941540043917435,0.2475660850506208,1.243592992412013,1.3498588075760032,1.82759336453197]
[0.4,{"$f":"RKMs(2,A23,A24,B23:E23,$B$16,0,$D$15,1,$B$17:$C$17)","v":1.4918167218748331},2.2344357128207037,0.39999985068341432,1.3911848970057084,0.40599186813051841,0.30841797873526761,0.92851331767144241,0.20673985900068534,1.2369312964067101,1.4918246976412703,2.2344609202967267]
[0.5,{"$f":"RKMs(2,A24,A25,B24:E24,$B$16,0,$D$15,1,$B$17:$C$17)","v":1.6487116780385456},2.7318732771422769,0.4999996787133959,1.9223240802535053,0.6115223537828447,0.28329362841750994,0.94351476353839137,0.17182727106933654,1.2268083919559012,1.6487212707001282,2.7319072728259268]
[0.6,{"$f":"RKMs(2,A25,A26,B25:E25,$B$16,0,$D$15,1,$B$17:$C$17)","v":1.8221074508544972},3.3400519862524809,0.59999983037667814,2.5626377915514733,0.6115223537828447,0.25926811811425993,0.95526620829714259,0.14229024638073526,1.2145343264114026,1.8221188003905089,3.3400975060812859]
[0.7,{"$f":"RKMs(2,A26,A27,B26:E26,$B$16,0,$D$15,1,$B$17:$C$17)","v":2.0137392252619288},4.083625179983585,0.69999973818996819,3.3370306535818122,0.86036622768678228,0.23661947609027567,0.96447103448923055,0.11750254110459527,1.2010905105795062,2.0137527074704766,4.0836859512402963]
[0.8,{"$f":"RKMs(2,A27,A28,B27:E27,$B$16,0,$D$15,1,$B$17:$C$17)","v":2.2255250372333566},4.9927347663666319,0.79999981738018477,4.2758604784452503,0.86036622768678228,0.21549009526085797,0.97169368735818906,9.6826632662260562E-2,1.187183782619047,2.2255409284924679,{"$f":"EXP($C$17*$A28)","v":4.9928156043332947}]
[0.9,{"$f":"RKMs(2,A28,A29,B28:E28,$B$16,0,$D$15,1,$B$17:$C$17)","v":2.4595842110703066},6.104232762538615,0.89999963637231017,5.4161622849715094,1.2240433581322614,0.19592815490026436,0.97737740561777031,7.9659055387660285E-2,1.1733055605180347,2.4596031111569499,{"$f":"EXP($C$17*$A29)","v":6.104340039003942}]
[1,{"$f":"RKMs(2,A29,A30,B29:E29,$B$16,0,$D$15,1,$B$17:$C$17)","v":2.7182596728633071},7.4631758599473299,0.99999980915098907,6.8031470854421325,1.2240433581322614,0.17791942244650605,0.98186583984887332,6.5453431187128916E-2,1.1597852622953795,2.7182818284590451,{"$f":"EXP($C$17*$A30)","v":7.4633173473191929}]

{"sheet":"Regrese","index":8,"n_rows":23,"n_cols":34,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["Nelineární regrese s vložením rovnice do kódu",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Bez vah"]
["Regresní rovnice:",null,"y = a1 +a2*x +b3*x*x",null,null,null,null,null,null,null,null,null,null,null,"regfun=b(1)+b(2)*xReg(i)+b(3)*xReg(i)*xReg(i)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Zadané váhy"]
["(např. parabola: regfun=b(1)+b(2)*xReg(i)+b(3)*xReg(i)*xReg(i)  nebo y = a1 +a2*x +b3*x*x )",null,null,null,null,null,null,null,null,null,null,null,null,null,"regfun=b(1)+b(2)*xReg(i)+b(3)*exp(xReg(i))",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Váhy 1/Abs(y)"]
["Odhady parametrů:",null,0,0.5,0.04,null,null,null,null,null,null,null,null,null,"y = a1 +a2*x +b3*x*x",null,null,"y = a1 +a2*Exp(-a3*x)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Váhy 1/(Abs(y))n "]
["Počet parametrů:",null,3,null,"Počet bodů:",null,{"$f":"COUNT(B9:B50)","v":15},null,null,null,null,null,"Kontrolovat počet koeficinetů?",null,null,"ano",null,"Váhy dat:"]
["Hodnota cílové funkce:",null,null,77.008395214005745,null,null,"Znovu s dosaženými koef.?",null,null,"ne",null,"i opakovaně",null,null,"nvah ",0.2]
["váhy","x","y","yvypR","yparab ","yvypNM","Výsledky",null,"f","iter","b(1)","b(2)","b(3)"]
[null,1,0,4.2605397513397083,{"$f":"$C$5+$D$5*B9+$E$5*B9*B9","v":0.54},2.3140638591195222,"Rosenbrock"]
[null,2,9,8.6141625044298475,{"$f":"$C$5+$D$5*B10+$E$5*B10*B10","v":1.1599999999999999},7.291767355740058,"Nelder-Mead",null,null,null,null,null,null,null,null,null,null,{"$f":"D10-D9","v":4.3536227530901392},null,{"$f":"F10-F9","v":4.9777034966205358}]
[null,3,13,14.001752037839228,1.8599999999999999,13.219021036874528,null,null,null,null,null,null,null,null,null,null,null,{"$f":"D11-D10","v":5.3875895334093808},null,{"$f":"F11-F10","v":5.92725368113447}]
[null,4,23,20.423308351567847,2.64,20.095824902522935,null,null,null,null,null,null,null,null,null,null,null,6.4215563137286189,null,6.876803865648407]
[null,5,29,27.878831445615706,3.5,27.922178952685279,null,null,null,null,null,null,null,null,null,null,null,7.4555230940478587,null,7.8263540501623439]
[null,6,34,36.368321319982805,4.4399999999999995,36.698083187361547,null,null,null,null,null,null,null,null,null,null,null,8.4894898743670986,null,8.7759042346762683]
[null,7,48,45.891777974669139,5.46,46.423537606551761,null,null,null,null,null,null,null,null,null,null,null,9.5234566546863348,null,9.7254544191902141]
[null,8,54,56.449201409674721,6.5600000000000005,57.098542210255914,null,null,null,null,null,null,null,null,null,null,null,10.557423435005582,null,10.675004603704153]
[null,9,70,68.040591624999536,7.74,68.723096998473991,null,null,null,null,null,null,null,null,null,null,null,11.591390215324815,null,11.624554788218077]
[null,10,74,80.665948620643604,9,81.297201971206022,null,null,null,null,null,null,null,null,null,null,null,12.625356995644069,null,12.57410497273203]
[null,11,105,94.325272396606891,10.34,94.820857128451962,null,null,null,null,null,null,null,null,null,null,null,13.659323775963287,null,13.52365515724594]
[null,12,109,109.01856295288944,11.76,109.29406247021184,null,null,null,null,null,null,null,null,null,null,null,14.693290556282548,null,14.473205341759879]
[null,13,120,124.74582028949122,13.26,124.71681799648566,null,null,null,null,null,null,null,null,null,null,null,15.727257336601781,null,15.422755526273818]
[null,14,143,141.50704440641223,14.84,141.08912370727342,null,null,null,null,null,null,null,null,null,null,null,16.761224116921014,null,16.372305710787757]
[null,15,158.41,159.30223530365248,16.5,158.41097960257511,null,null,null,null,null,null,null,null,null,null,null,17.795190897240246,null,17.321855895301695]

{"sheet":"Strato","index":9,"n_rows":298,"n_cols":15,"rows_kept":298,"cut":false,"hidden":false,"merged":[]}
["Pád parašutisty ve stratosféře"]
["Skok z (m)",39000]
["p0 (Pa)",101325,null,"m (kg)",85,null,"cx",0.56000000000000005,null,"hustota s výškou",null,"r(h) =r0*exp[-r0*g*h/p0]"]
["r0 (kg/m3)",1.206,null,"S (m2)",{"$f":"1.8*0.45","v":0.81},null,"Dt (s)",1,null,"brzdící síla",null,"cx*1/2*r(h)*v2*S",null,"cx - koef. odporu;   S příčný povrch tělesa; v rychlost"]
[{"$f":"INDIRECT(\"A\"&COUNT(A7:A9999)+6)","v":291},"Max:",{"$f":"MAX(C7:C9999)","v":313.97017968614284},{"$f":"MAX(D7:D9999)","v":1130.2926468701141}]
["Čas (s)","Výška (m)","Rychlost (m/s)","v (km/h)","r(h) (kg/m3)",null,null,null,null,"dif.rov.pro  rychlost",null,"dv/dt = g -cx*1/2*r(h)*v2*S/m",null,null,"v(0) = 0"]
[0,39000,0,{"$f":"C7*3600/1000","v":0},{"$f":"B4*EXP(-B4*9.81*B7/B3)","v":1.2696996730372482E-2}]
[1,38995.095271731916,9.8089129886564059,{"$f":"C8*3600/1000","v":35.312086759163059},1.2704270174067146E-2]
[2,38980.384349558844,19.611298426468881,{"$f":"C9*3600/1000","v":70.600674335287977},1.2726110664082758E-2]
[3,38955.877035104029,29.400601307830421,105.84216470818951,1.2762578722478397E-2]
[4,38921.58971013777,39.170211789616843,141.01276244262064,1.281377535158078E-2]
[5,38877.545405050667,48.913437951012021,176.08837662364328,1.2879842227144403E-2]
[6,38823.773894460413,58.623478780421358,211.04452360951689,1.296096196592756E-2]
[7,38760.311819679104,68.293397484884906,245.85623094558568,1.3057358461342958E-2]
[8,38687.202837663724,77.916095234857778,280.49794284548801,1.3169297280949385E-2]
[9,38604.497795949086,87.484285478934083,314.94342772416269,1.329708611788788E-2]
[10,38512.25493291537,96.990468989235666,349.16568836124839,1.3441075286583587E-2]
[11,38410.540102566585,106.42690982878483,383.13687538362541,1.3601658251138552E-2]
[12,38299.427022787946,115.78561246717669,416.82820488183609,1.3779272172793637E-2]
[13,38178.997545804508,125.05830031012411,450.20988111644681,1.3974398460625028E-2]
[14,38049.341949276597,134.23639595170829,483.25102542614985,1.4187563307256082E-2]
[15,37910.559246135381,143.31100350502274,515.91961261808183,1.441933818881116E-2]
[16,37762.757510881864,152.27289341673682,548.1824163002525,1.4670340305623024E-2]
[17,37606.054219640886,161.11249022307368,580.00496480306526,1.4941232937351844E-2]
[18,37440.576600777968,169.81986375764916,611.3515095275369,1.5232725683213381E-2]
[19,37266.461992350007,178.38472437405557,642.18500774660004,1.5545574554994536E-2]
[20,37083.85820207261,186.79642279610698,672.46712206598511,1.588058188751942E-2,null,null,"Skok z (m)","vmax (m/s)","vmax (km/h)","tletu (s)"]
[21,36892.923864850789,195.04395525396188,702.15823891426271,1.6238596028303538E-2,null,null,100,39.260700279173555,141.3385210050248,5]
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