From 73482884f167e69f07f9e4b4ff9f747abba5205e Mon Sep 17 00:00:00 2001 From: aleksacirkovic99 Date: Sun, 31 Mar 2024 16:10:44 +0200 Subject: [PATCH 1/2] DomacaNaloga1_AleksaCirkovic --- DomNal/Manifest.toml | 1142 +++++++++++++++++++++++++++ DomNal/Project.toml | 11 + DomNal/README.md | 16 + DomNal/demo.html | 725 +++++++++++++++++ DomNal/demo.jl | 38 + DomNal/demo.log | 202 +++++ DomNal/demo.pdf | Bin 0 -> 64900 bytes DomNal/demo.tex | 174 ++++ DomNal/interpolacijska_krivulja.png | Bin 0 -> 15539 bytes DomNal/jl_tTLIBa/demo_0_1.png | Bin 0 -> 15539 bytes DomNal/src/Domaca01.jl | 88 +++ DomNal/test/runtests.jl | 29 + 12 files changed, 2425 insertions(+) create mode 100644 DomNal/Manifest.toml create mode 100644 DomNal/Project.toml create mode 100644 DomNal/README.md create mode 100644 DomNal/demo.html create mode 100644 DomNal/demo.jl create mode 100644 DomNal/demo.log create mode 100644 DomNal/demo.pdf create mode 100644 DomNal/demo.tex create mode 100644 DomNal/interpolacijska_krivulja.png create mode 100644 DomNal/jl_tTLIBa/demo_0_1.png create mode 100644 DomNal/src/Domaca01.jl create mode 100644 DomNal/test/runtests.jl diff --git a/DomNal/Manifest.toml b/DomNal/Manifest.toml new file mode 100644 index 0000000..5646979 --- /dev/null +++ b/DomNal/Manifest.toml @@ -0,0 +1,1142 @@ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.2" +manifest_format = "2.0" +project_hash = "7ce631423f44f2a21536b91efe661df9c7ef1f6c" + +[[deps.ArgTools]] +uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" +version = "1.1.1" + +[[deps.Artifacts]] +uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" + +[[deps.Base64]] +uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" + +[[deps.BitFlags]] +git-tree-sha1 = "2dc09997850d68179b69dafb58ae806167a32b1b" +uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35" +version = "0.1.8" + +[[deps.Bzip2_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = 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"1.4.1+1" diff --git a/DomNal/Project.toml b/DomNal/Project.toml new file mode 100644 index 0000000..71d9026 --- /dev/null +++ b/DomNal/Project.toml @@ -0,0 +1,11 @@ +name = "Domaca01" +uuid = "f153e40a-130e-47db-a76c-f06db57af828" +authors = ["aleksacirkovic99 "] +version = "0.1.0" + +[deps] +IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" +Weave = "44d3d7a6-8a23-5bf8-98c5-b353f8df5ec9" diff --git a/DomNal/README.md b/DomNal/README.md new file mode 100644 index 0000000..d18ebfb --- /dev/null +++ b/DomNal/README.md @@ -0,0 +1,16 @@ +Naravni zlepek + +Aleksa Ćirković + +Opis naloge: + - Naloga je, da se poveže niz točk na grafu na gladek način. Obstaja več točk, vsaka s svojo X in Y vrednostjo, in je potrebno narisati gladko krivuljo, ki gre skozi vse te točke. + +Navodila kako uporabiti kodo: + - Kloniraj ali prenesi ta repozitorij na svoj računalnik. + - Odpri terminal ali ukazno vrstico in se pomakni do mape projekta. + - Začni Julia v interaktivnem načinu z ukazom julia. + - Za izvedbo interpolacije in vizualizacijo rezultatov vključi skripto demo.jl z ukazom include("path/to/demo.jl"), kjer je path/to/demo.jl pot do datoteke demo.jl znotraj projekta. + +Navodila, kako pognati teste: + - V terminalu znotraj mape projekta zaženi Julia. + - Uporabi ukaz include("path/to/tests/runtests.jl"), da zaženeš testne skripte, kjer path/to/tests/runtests.jl predstavlja pot do datoteke runtests.jl. \ No newline at end of file diff --git a/DomNal/demo.html b/DomNal/demo.html new file mode 100644 index 0000000..c99d272 --- /dev/null +++ b/DomNal/demo.html @@ -0,0 +1,725 @@ + + + + + + + + + + + + + + + + + + + + + +
+
+
+
+ + + +
+ + +
+#Aleksa Ćirković
+
+#Naloga je, da se poveže niz točk na grafu na gladek način. Obstaja več točk, vsaka s svojo X in Y vrednostjo, in je potrebno narisati gladko krivuljo, ki gre skozi vse te točke.
+
+#Začne se s seznamom točk, ki jih je potrebno povezati. Vsaka točka ima X in Y vrednost.
+
+#Za povezovanje teh točk z gladko krivuljo uporablja se "Naravni interpolacijski kubični zlepek". To pomeni, da med vsakim parom točk narišete mini-krivulje, ki se lepo prilegajo skupaj in ustvarijo eno gladko krivuljo.
+
+#Na koncu se nariše ta krivulja na grafu. Za boljšo preglednost tudi so označene originalne točke in uporabljene različne barve za prikaz različnih delov krivulje.
+
+#Struktura Zlepek je osnova. Hrani vse potrebne informacije o interpolacijskih točkah (x in y vrednosti) ter koeficiente (a, b, c, d), ki so potrebni za izračun kubičnih zlepkov.
+
+#Funkcija interpoliraj izračuna koeficiente za kubični zlepek na podlagi danih točk. Uporablja matriko A in vektor v za rešitev sistema enačb, ki določajo koeficiente zlepka. Ti koeficienti so ključni za risanje gladke krivulje skozi vse dane točke.
+
+#Funkcija vrednost omogoča izračun vrednosti interpolirane krivulje pri kateri koli danem x. To je uporabno za preverjanje, kako dobro krivulja ustreza podatkom ali za napovedovanje vrednosti na novih točkah.
+
+#Funkcija plotDN prikaže graf, ki vizualno predstavi kako krivulja poteka skozi dane točke. Uporablja se za preverjanje pravilnosti interpolacije in za predstavitev rezultatov. Funkcija menja barve med segmenti krivulje, da olajša vizualno analizo.
+
+using Domaca01
+using Plots
+
+# Nabor točk, za interpolacijo
+x_tocke = [1.0, 2.0, 3.0, 4.0, 5.0]
+y_tocke = [1.0, 4.0, 9.0, 16.0, 25.0]
+
+# Funkcija interpoliraj za izračun koeficientov
+zlepek = Domaca01.interpoliraj(x_tocke, y_tocke)
+
+# Risanje grafa z uporabo funkcije plotDN
+Domaca01.plotDN(zlepek)
+
+# Prikaz vrednost krivulje na določeni točki
+# Na primer, izračunati vrednost krivulje pri x = 2.5
+vrednost_pri_2_5 = Domaca01.vrednost(zlepek, 2.5)
+println("Vrednost krivulje pri x = 2.5 je: $vrednost_pri_2_5")
+
+# Shranevanje grafa za poročilo
+savefig("interpolacijska_krivulja.png")
+
+ + +
+Vrednost krivulje pri x = 2.5 je: 6.232142857142857
+"C:\\Users\\Aki\\Files\\1MAG\\NM\\nummat-2324\\DomNal\\interpolacijska_kriv
+ulja.png"
+
+ + + + +
+
+

+ Published from demo.jl + using Weave.jl v0.10.12 on 2024-03-31. +

+
+
+
+
+ + + diff --git a/DomNal/demo.jl b/DomNal/demo.jl new file mode 100644 index 0000000..f7f3fec --- /dev/null +++ b/DomNal/demo.jl @@ -0,0 +1,38 @@ +#Aleksa Ćirković + +#Naloga je, da se poveže niz točk na grafu na gladek način. Obstaja več točk, vsaka s svojo X in Y vrednostjo, in je potrebno narisati gladko krivuljo, ki gre skozi vse te točke. + +#Začne se s seznamom točk, ki jih je potrebno povezati. Vsaka točka ima X in Y vrednost. + +#Za povezovanje teh točk z gladko krivuljo uporablja se "Naravni interpolacijski kubični zlepek". To pomeni, da med vsakim parom točk narišete mini-krivulje, ki se lepo prilegajo skupaj in ustvarijo eno gladko krivuljo. + +#Na koncu se nariše ta krivulja na grafu. Za boljšo preglednost tudi so označene originalne točke in uporabljene različne barve za prikaz različnih delov krivulje. + +#Struktura Zlepek je osnova. Hrani vse potrebne informacije o interpolacijskih točkah (x in y vrednosti) ter koeficiente (a, b, c, d), ki so potrebni za izračun kubičnih zlepkov. + +#Funkcija interpoliraj izračuna koeficiente za kubični zlepek na podlagi danih točk. Uporablja matriko A in vektor v za rešitev sistema enačb, ki določajo koeficiente zlepka. Ti koeficienti so ključni za risanje gladke krivulje skozi vse dane točke. + +#Funkcija vrednost omogoča izračun vrednosti interpolirane krivulje pri kateri koli danem x. To je uporabno za preverjanje, kako dobro krivulja ustreza podatkom ali za napovedovanje vrednosti na novih točkah. + +#Funkcija plotDN prikaže graf, ki vizualno predstavi kako krivulja poteka skozi dane točke. Uporablja se za preverjanje pravilnosti interpolacije in za predstavitev rezultatov. Funkcija menja barve med segmenti krivulje, da olajša vizualno analizo. + +using Domaca01 +using Plots + +# Nabor točk, za interpolacijo +x_tocke = [1.0, 2.0, 3.0, 4.0, 5.0] +y_tocke = [1.0, 4.0, 9.0, 16.0, 25.0] + +# Funkcija interpoliraj za izračun koeficientov +zlepek = Domaca01.interpoliraj(x_tocke, y_tocke) + +# Risanje grafa z uporabo funkcije plotDN +Domaca01.plotDN(zlepek) + +# Prikaz vrednost krivulje na določeni točki +# Na primer, izračunati vrednost krivulje pri x = 2.5 +vrednost_pri_2_5 = Domaca01.vrednost(zlepek, 2.5) +println("Vrednost krivulje pri x = 2.5 je: $vrednost_pri_2_5") + +# Shranevanje grafa za poročilo +savefig("interpolacijska_krivulja.png") diff --git a/DomNal/demo.log b/DomNal/demo.log new file mode 100644 index 0000000..7225acf --- /dev/null +++ b/DomNal/demo.log @@ -0,0 +1,202 @@ +This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2024.3.4) 31 MAR 2024 03:19 +entering extended mode + \write18 enabled. + %&-line parsing enabled. +**demo.tex +(./demo.tex +LaTeX2e <2023-11-01> patch level 1 +L3 programming layer <2024-02-20> +(c:/Users/Aki/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/article.cls +Document Class: article 2023/05/17 v1.4n Standard LaTeX document class +(c:/Users/Aki/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/size12.clo +File: size12.clo 2023/05/17 v1.4n Standard LaTeX file (size option) +) +\c@part=\count184 +\c@section=\count185 +\c@subsection=\count186 +\c@subsubsection=\count187 +\c@paragraph=\count188 +\c@subparagraph=\count189 +\c@figure=\count190 +\c@table=\count191 +\abovecaptionskip=\skip48 +\belowcaptionskip=\skip49 +\bibindent=\dimen140 +) (c:/Users/Aki/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/geometry/geometry.sty +Package: geometry 2020/01/02 v5.9 Page Geometry + (c:/Users/Aki/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/keyval.sty +Package: keyval 2022/05/29 v1.15 key=value parser (DPC) +\KV@toks@=\toks17 +) (c:/Users/Aki/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/iftex/ifvtex.sty +Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. 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colorlinks=TRUE, + linkcolor=black, + citecolor=blue, + urlcolor=blue + } + + + + +\usepackage{upquote} +\usepackage{listings} +\usepackage{xcolor} +\lstset{ + basicstyle=\ttfamily\footnotesize, + upquote=true, + breaklines=true, + breakindent=0pt, + keepspaces=true, + showspaces=false, + columns=fullflexible, + showtabs=false, + showstringspaces=false, + escapeinside={(*@}{@*)}, + extendedchars=true, +} +\newcommand{\HLJLt}[1]{#1} +\newcommand{\HLJLw}[1]{#1} +\newcommand{\HLJLe}[1]{#1} +\newcommand{\HLJLeB}[1]{#1} +\newcommand{\HLJLo}[1]{#1} +\newcommand{\HLJLk}[1]{\textcolor[RGB]{148,91,176}{\textbf{#1}}} +\newcommand{\HLJLkc}[1]{\textcolor[RGB]{59,151,46}{\textit{#1}}} +\newcommand{\HLJLkd}[1]{\textcolor[RGB]{214,102,97}{\textit{#1}}} +\newcommand{\HLJLkn}[1]{\textcolor[RGB]{148,91,176}{\textbf{#1}}} +\newcommand{\HLJLkp}[1]{\textcolor[RGB]{148,91,176}{\textbf{#1}}} +\newcommand{\HLJLkr}[1]{\textcolor[RGB]{148,91,176}{\textbf{#1}}} 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+\newcommand{\HLJLnil}[1]{\textcolor[RGB]{59,151,46}{#1}} +\newcommand{\HLJLnoB}[1]{\textcolor[RGB]{59,151,46}{#1}} +\newcommand{\HLJLoB}[1]{\textcolor[RGB]{102,102,102}{\textbf{#1}}} +\newcommand{\HLJLow}[1]{\textcolor[RGB]{102,102,102}{\textbf{#1}}} +\newcommand{\HLJLp}[1]{#1} +\newcommand{\HLJLc}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLch}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcm}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcp}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcpB}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcs}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcsB}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLg}[1]{#1} +\newcommand{\HLJLgd}[1]{#1} +\newcommand{\HLJLge}[1]{#1} +\newcommand{\HLJLgeB}[1]{#1} +\newcommand{\HLJLgh}[1]{#1} +\newcommand{\HLJLgi}[1]{#1} +\newcommand{\HLJLgo}[1]{#1} +\newcommand{\HLJLgp}[1]{#1} +\newcommand{\HLJLgs}[1]{#1} +\newcommand{\HLJLgsB}[1]{#1} +\newcommand{\HLJLgt}[1]{#1} + + +\begin{document} + + + +\begin{lstlisting} +(*@\HLJLcs{{\#}Aleksa}@*) (*@\HLJLcs{Ćirković}@*) + +(*@\HLJLcs{{\#}Naloga}@*) (*@\HLJLcs{je,}@*) (*@\HLJLcs{da}@*) (*@\HLJLcs{se}@*) (*@\HLJLcs{poveže}@*) (*@\HLJLcs{niz}@*) (*@\HLJLcs{točk}@*) (*@\HLJLcs{na}@*) (*@\HLJLcs{grafu}@*) (*@\HLJLcs{na}@*) (*@\HLJLcs{gladek}@*) (*@\HLJLcs{način.}@*) (*@\HLJLcs{Obstaja}@*) (*@\HLJLcs{več}@*) (*@\HLJLcs{točk,}@*) (*@\HLJLcs{vsaka}@*) (*@\HLJLcs{s}@*) (*@\HLJLcs{svojo}@*) (*@\HLJLcs{X}@*) (*@\HLJLcs{in}@*) (*@\HLJLcs{Y}@*) (*@\HLJLcs{vrednostjo,}@*) (*@\HLJLcs{in}@*) (*@\HLJLcs{je}@*) (*@\HLJLcs{potrebno}@*) (*@\HLJLcs{narisati}@*) (*@\HLJLcs{gladko}@*) (*@\HLJLcs{krivuljo,}@*) (*@\HLJLcs{ki}@*) (*@\HLJLcs{gre}@*) (*@\HLJLcs{skozi}@*) (*@\HLJLcs{vse}@*) (*@\HLJLcs{te}@*) (*@\HLJLcs{točke.}@*) + +(*@\HLJLcs{{\#}Začne}@*) (*@\HLJLcs{se}@*) (*@\HLJLcs{s}@*) (*@\HLJLcs{seznamom}@*) (*@\HLJLcs{točk,}@*) (*@\HLJLcs{ki}@*) (*@\HLJLcs{jih}@*) (*@\HLJLcs{je}@*) (*@\HLJLcs{potrebno}@*) (*@\HLJLcs{povezati.}@*) (*@\HLJLcs{Vsaka}@*) (*@\HLJLcs{točka}@*) (*@\HLJLcs{ima}@*) (*@\HLJLcs{X}@*) (*@\HLJLcs{in}@*) (*@\HLJLcs{Y}@*) (*@\HLJLcs{vrednost.}@*) + +(*@\HLJLcs{{\#}Za}@*) (*@\HLJLcs{povezovanje}@*) (*@\HLJLcs{teh}@*) (*@\HLJLcs{točk}@*) (*@\HLJLcs{z}@*) (*@\HLJLcs{gladko}@*) (*@\HLJLcs{krivuljo}@*) (*@\HLJLcs{uporablja}@*) (*@\HLJLcs{se}@*) (*@\HLJLcs{"{}Naravni}@*) (*@\HLJLcs{interpolacijski}@*) (*@\HLJLcs{kubični}@*) (*@\HLJLcs{zlepek"{}.}@*) (*@\HLJLcs{To}@*) (*@\HLJLcs{pomeni,}@*) (*@\HLJLcs{da}@*) (*@\HLJLcs{med}@*) (*@\HLJLcs{vsakim}@*) (*@\HLJLcs{parom}@*) (*@\HLJLcs{točk}@*) (*@\HLJLcs{narišete}@*) (*@\HLJLcs{mini-krivulje,}@*) (*@\HLJLcs{ki}@*) (*@\HLJLcs{se}@*) (*@\HLJLcs{lepo}@*) (*@\HLJLcs{prilegajo}@*) (*@\HLJLcs{skupaj}@*) (*@\HLJLcs{in}@*) (*@\HLJLcs{ustvarijo}@*) (*@\HLJLcs{eno}@*) (*@\HLJLcs{gladko}@*) (*@\HLJLcs{krivuljo.}@*) + +(*@\HLJLcs{{\#}Na}@*) (*@\HLJLcs{koncu}@*) (*@\HLJLcs{se}@*) (*@\HLJLcs{nariše}@*) (*@\HLJLcs{ta}@*) (*@\HLJLcs{krivulja}@*) (*@\HLJLcs{na}@*) (*@\HLJLcs{grafu.}@*) (*@\HLJLcs{Za}@*) (*@\HLJLcs{boljšo}@*) (*@\HLJLcs{preglednost}@*) (*@\HLJLcs{tudi}@*) (*@\HLJLcs{so}@*) (*@\HLJLcs{označene}@*) (*@\HLJLcs{originalne}@*) (*@\HLJLcs{točke}@*) (*@\HLJLcs{in}@*) (*@\HLJLcs{uporabljene}@*) (*@\HLJLcs{različne}@*) (*@\HLJLcs{barve}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{prikaz}@*) (*@\HLJLcs{različnih}@*) (*@\HLJLcs{delov}@*) (*@\HLJLcs{krivulje.}@*) + +(*@\HLJLcs{{\#}Struktura}@*) (*@\HLJLcs{Zlepek}@*) (*@\HLJLcs{je}@*) (*@\HLJLcs{osnova.}@*) (*@\HLJLcs{Hrani}@*) (*@\HLJLcs{vse}@*) (*@\HLJLcs{potrebne}@*) (*@\HLJLcs{informacije}@*) (*@\HLJLcs{o}@*) (*@\HLJLcs{interpolacijskih}@*) (*@\HLJLcs{točkah}@*) (*@\HLJLcs{(x}@*) (*@\HLJLcs{in}@*) (*@\HLJLcs{y}@*) (*@\HLJLcs{vrednosti)}@*) (*@\HLJLcs{ter}@*) (*@\HLJLcs{koeficiente}@*) (*@\HLJLcs{(a,}@*) (*@\HLJLcs{b,}@*) (*@\HLJLcs{c,}@*) (*@\HLJLcs{d),}@*) (*@\HLJLcs{ki}@*) (*@\HLJLcs{so}@*) (*@\HLJLcs{potrebni}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{izračun}@*) (*@\HLJLcs{kubičnih}@*) (*@\HLJLcs{zlepkov.}@*) + +(*@\HLJLcs{{\#}Funkcija}@*) (*@\HLJLcs{interpoliraj}@*) (*@\HLJLcs{izračuna}@*) (*@\HLJLcs{koeficiente}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{kubični}@*) (*@\HLJLcs{zlepek}@*) (*@\HLJLcs{na}@*) (*@\HLJLcs{podlagi}@*) (*@\HLJLcs{danih}@*) (*@\HLJLcs{točk.}@*) (*@\HLJLcs{Uporablja}@*) (*@\HLJLcs{matriko}@*) (*@\HLJLcs{A}@*) (*@\HLJLcs{in}@*) (*@\HLJLcs{vektor}@*) (*@\HLJLcs{v}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{rešitev}@*) (*@\HLJLcs{sistema}@*) (*@\HLJLcs{enačb,}@*) (*@\HLJLcs{ki}@*) (*@\HLJLcs{določajo}@*) (*@\HLJLcs{koeficiente}@*) (*@\HLJLcs{zlepka.}@*) (*@\HLJLcs{Ti}@*) (*@\HLJLcs{koeficienti}@*) (*@\HLJLcs{so}@*) (*@\HLJLcs{ključni}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{risanje}@*) (*@\HLJLcs{gladke}@*) (*@\HLJLcs{krivulje}@*) (*@\HLJLcs{skozi}@*) (*@\HLJLcs{vse}@*) (*@\HLJLcs{dane}@*) (*@\HLJLcs{točke.}@*) + +(*@\HLJLcs{{\#}Funkcija}@*) (*@\HLJLcs{vrednost}@*) (*@\HLJLcs{omogoča}@*) (*@\HLJLcs{izračun}@*) (*@\HLJLcs{vrednosti}@*) (*@\HLJLcs{interpolirane}@*) (*@\HLJLcs{krivulje}@*) (*@\HLJLcs{pri}@*) (*@\HLJLcs{kateri}@*) (*@\HLJLcs{koli}@*) (*@\HLJLcs{danem}@*) (*@\HLJLcs{x.}@*) (*@\HLJLcs{To}@*) (*@\HLJLcs{je}@*) (*@\HLJLcs{uporabno}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{preverjanje,}@*) (*@\HLJLcs{kako}@*) (*@\HLJLcs{dobro}@*) (*@\HLJLcs{krivulja}@*) (*@\HLJLcs{ustreza}@*) (*@\HLJLcs{podatkom}@*) (*@\HLJLcs{ali}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{napovedovanje}@*) (*@\HLJLcs{vrednosti}@*) (*@\HLJLcs{na}@*) (*@\HLJLcs{novih}@*) (*@\HLJLcs{točkah.}@*) + +(*@\HLJLcs{{\#}Funkcija}@*) (*@\HLJLcs{plotDN}@*) (*@\HLJLcs{prikaže}@*) (*@\HLJLcs{graf,}@*) (*@\HLJLcs{ki}@*) (*@\HLJLcs{vizualno}@*) (*@\HLJLcs{predstavi}@*) (*@\HLJLcs{kako}@*) (*@\HLJLcs{krivulja}@*) (*@\HLJLcs{poteka}@*) (*@\HLJLcs{skozi}@*) (*@\HLJLcs{dane}@*) (*@\HLJLcs{točke.}@*) (*@\HLJLcs{Uporablja}@*) (*@\HLJLcs{se}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{preverjanje}@*) (*@\HLJLcs{pravilnosti}@*) (*@\HLJLcs{interpolacije}@*) (*@\HLJLcs{in}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{predstavitev}@*) (*@\HLJLcs{rezultatov.}@*) (*@\HLJLcs{Funkcija}@*) (*@\HLJLcs{menja}@*) (*@\HLJLcs{barve}@*) (*@\HLJLcs{med}@*) (*@\HLJLcs{segmenti}@*) (*@\HLJLcs{krivulje,}@*) (*@\HLJLcs{da}@*) (*@\HLJLcs{olajša}@*) (*@\HLJLcs{vizualno}@*) (*@\HLJLcs{analizo.}@*) + +(*@\HLJLk{using}@*) (*@\HLJLn{Domaca01}@*) +(*@\HLJLk{using}@*) (*@\HLJLn{Plots}@*) + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Nabor}@*) (*@\HLJLcs{točk,}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{interpolacijo}@*) +(*@\HLJLn{x{\_}tocke}@*) (*@\HLJLoB{=}@*) (*@\HLJLp{[}@*)(*@\HLJLnfB{1.0}@*)(*@\HLJLp{,}@*) (*@\HLJLnfB{2.0}@*)(*@\HLJLp{,}@*) (*@\HLJLnfB{3.0}@*)(*@\HLJLp{,}@*) (*@\HLJLnfB{4.0}@*)(*@\HLJLp{,}@*) (*@\HLJLnfB{5.0}@*)(*@\HLJLp{]}@*) +(*@\HLJLn{y{\_}tocke}@*) (*@\HLJLoB{=}@*) (*@\HLJLp{[}@*)(*@\HLJLnfB{1.0}@*)(*@\HLJLp{,}@*) (*@\HLJLnfB{4.0}@*)(*@\HLJLp{,}@*) (*@\HLJLnfB{9.0}@*)(*@\HLJLp{,}@*) (*@\HLJLnfB{16.0}@*)(*@\HLJLp{,}@*) (*@\HLJLnfB{25.0}@*)(*@\HLJLp{]}@*) + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Funkcija}@*) (*@\HLJLcs{interpoliraj}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{izračun}@*) (*@\HLJLcs{koeficientov}@*) +(*@\HLJLn{zlepek}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{Domaca01}@*)(*@\HLJLoB{.}@*)(*@\HLJLnf{interpoliraj}@*)(*@\HLJLp{(}@*)(*@\HLJLn{x{\_}tocke}@*)(*@\HLJLp{,}@*) (*@\HLJLn{y{\_}tocke}@*)(*@\HLJLp{)}@*) + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Risanje}@*) (*@\HLJLcs{grafa}@*) (*@\HLJLcs{z}@*) (*@\HLJLcs{uporabo}@*) (*@\HLJLcs{funkcije}@*) (*@\HLJLcs{plotDN}@*) +(*@\HLJLn{Domaca01}@*)(*@\HLJLoB{.}@*)(*@\HLJLnf{plotDN}@*)(*@\HLJLp{(}@*)(*@\HLJLn{zlepek}@*)(*@\HLJLp{)}@*) + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Prikaz}@*) (*@\HLJLcs{vrednost}@*) (*@\HLJLcs{krivulje}@*) (*@\HLJLcs{na}@*) (*@\HLJLcs{določeni}@*) (*@\HLJLcs{točki}@*) +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Na}@*) (*@\HLJLcs{primer,}@*) (*@\HLJLcs{izračunati}@*) (*@\HLJLcs{vrednost}@*) (*@\HLJLcs{krivulje}@*) (*@\HLJLcs{pri}@*) (*@\HLJLcs{x}@*) (*@\HLJLcs{=}@*) (*@\HLJLcs{2.5}@*) +(*@\HLJLn{vrednost{\_}pri{\_}2{\_}5}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{Domaca01}@*)(*@\HLJLoB{.}@*)(*@\HLJLnf{vrednost}@*)(*@\HLJLp{(}@*)(*@\HLJLn{zlepek}@*)(*@\HLJLp{,}@*) (*@\HLJLnfB{2.5}@*)(*@\HLJLp{)}@*) +(*@\HLJLnf{println}@*)(*@\HLJLp{(}@*)(*@\HLJLs{"{}Vrednost}@*) (*@\HLJLs{krivulje}@*) (*@\HLJLs{pri}@*) (*@\HLJLs{x}@*) (*@\HLJLs{=}@*) (*@\HLJLs{2.5}@*) (*@\HLJLs{je:}@*) (*@\HLJLsi{{\$}vrednost{\_}pri{\_}2{\_}5}@*)(*@\HLJLs{"{}}@*)(*@\HLJLp{)}@*) + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Shranevanje}@*) (*@\HLJLcs{grafa}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{poročilo}@*) +(*@\HLJLnf{savefig}@*)(*@\HLJLp{(}@*)(*@\HLJLs{"{}interpolacijska{\_}krivulja.png"{}}@*)(*@\HLJLp{)}@*) +\end{lstlisting} + +\begin{lstlisting} +Vrednost krivulje pri x = 2.5 je: 6.232142857142857 +(*@{"{}}@*)C:(*@{{\textbackslash}}@*)(*@{{\textbackslash}}@*)Users(*@{{\textbackslash}}@*)(*@{{\textbackslash}}@*)Aki(*@{{\textbackslash}}@*)(*@{{\textbackslash}}@*)Files(*@{{\textbackslash}}@*)(*@{{\textbackslash}}@*)1MAG(*@{{\textbackslash}}@*)(*@{{\textbackslash}}@*)NM(*@{{\textbackslash}}@*)(*@{{\textbackslash}}@*)nummat-2324(*@{{\textbackslash}}@*)(*@{{\textbackslash}}@*)DomNal(*@{{\textbackslash}}@*)(*@{{\textbackslash}}@*)interpolacijska(*@{{\_}}@*)kriv +ulja.png(*@{"{}}@*) +\end{lstlisting} + +\includegraphics[width=\linewidth]{jl_sCze9i/demo_0_1.pdf} + + +\end{document} diff --git a/DomNal/interpolacijska_krivulja.png b/DomNal/interpolacijska_krivulja.png new file mode 100644 index 0000000000000000000000000000000000000000..faf5e4f84bfa50e1325fb122fa4116d1ecfa6e34 GIT binary patch literal 15539 zcmb7rcR1C3{P#h2K=R?Ua(_Xk=x!gAIoSx+NOP&pdifF`T{hyyHTkJ6^`9`%q^X)N>jTrWI?VLt$Boav- z8y_!bb#m~j_WT!yPqe#3pDQ{||54YY^6!;#I%DpJ{kZzIKBq9Ujj2j22M1ZF*~VyA 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zlG=G|oe02c;U2@v(vrA@#8wFU+y37qUs$@XpFianua4hG#{g$6^J1$JWG1jKt*y%c tO$A&o`WpG{Rgic7-}|!v|Np<^``B7wfOk5l8EzpX?kK2X^5l(Q{x4xWnkE1M literal 0 HcmV?d00001 diff --git a/DomNal/src/Domaca01.jl b/DomNal/src/Domaca01.jl new file mode 100644 index 0000000..ed6af26 --- /dev/null +++ b/DomNal/src/Domaca01.jl @@ -0,0 +1,88 @@ +module Domaca01 + +export Zlepek, interpoliraj, vrednost, plotDN + +using LinearAlgebra +using Plots + +struct Zlepek + x::Vector{Float64} + y::Vector{Float64} + a::Vector{Float64} + b::Vector{Float64} + c::Vector{Float64} + d::Vector{Float64} +end + + +function interpoliraj(x::Vector{Float64}, y::Vector{Float64})::Zlepek + n = length(x) - 1 + h = diff(x) + + + A = zeros(n + 1, n + 1) + A[1, 1], A[end, end] = 1, 1 + v = zeros(n + 1) + for i = 2:n + A[i, i] = 2 * (h[i - 1] + h[i]) + A[i, i - 1] = h[i - 1] + A[i, i + 1] = h[i] + v[i] = 3 * (y[i + 1] - y[i]) / h[i] - 3 * (y[i] - y[i - 1]) / h[i - 1] + end + + c = A \ v + + + b = zeros(n) + d = zeros(n) + for i = 1:n + b[i] = (y[i + 1] - y[i]) / h[i] - h[i] * (2c[i] + c[i + 1]) / 3 + d[i] = (c[i + 1] - c[i]) / (3 * h[i]) + end + + a = y[1:end-1] + + Zlepek(x, y, a, b, c[1:end-1], d) +end + + +function vrednost(z::Zlepek, x::Float64)::Float64 + for i = 1:length(z.x)-1 + if x >= z.x[i] && x <= z.x[i+1] + dx = x - z.x[i] + return z.a[i] + z.b[i]*dx + z.c[i]*dx^2 + z.d[i]*dx^3 + end + end + error("Value out of interpolation range.") +end + + +function plotDN(z::Zlepek) + + if length(z.x) < 2 + error("Not enough points to plot.") + end + + + first_xs = collect(range(z.x[1], stop=z.x[2], length=100)) + first_ys = [vrednost(z, xi) for xi in first_xs] + p = Plots.plot(first_xs, first_ys, label="Spline", linewidth=2, color="red") + + + for i in 2:length(z.x)-1 + segment_xs = collect(range(z.x[i], stop=z.x[i+1], length=100)) + segment_ys = [vrednost(z, xi) for xi in segment_xs] + segment_color = (i-1) % 2 == 0 ? "blue" : "red" + Plots.plot!(p, segment_xs, segment_ys, label="", linewidth=2, color=segment_color) + end + + + Plots.scatter!(p, z.x, z.y, label="Data Points", color="red", marker=:circle, markersize=6) + + display(p) +end + + +end + + diff --git a/DomNal/test/runtests.jl b/DomNal/test/runtests.jl new file mode 100644 index 0000000..f372b8a --- /dev/null +++ b/DomNal/test/runtests.jl @@ -0,0 +1,29 @@ +using Test +using Domaca01 + + +include("../src/Domaca01.jl") + + +@testset "Interpolation Accuracy" begin + x_points = [1.0, 2.0, 3.0, 4.0] + y_points = x_points .^ 2 + spline = interpoliraj(x_points, y_points) + + for (x, expected_y) in zip(x_points, y_points) + @test vrednost(spline, x) ≈ expected_y atol=1e-6 + end +end + +@testset "Boundary Conditions" begin + + x_points = [0.0, 0.5, 1.0, 1.5, 2.0] + y_points = [0.0, 0.25, 1.0, 2.25, 4.0] + spline = interpoliraj(x_points, y_points) + + + plotDN(spline) + println("Manually verify boundary conditions in the plot.") +end + + From aeb707f80f1675e64d217e44332b580afffb77f5 Mon Sep 17 00:00:00 2001 From: aleksacirkovic99 Date: Sat, 18 May 2024 16:09:07 +0200 Subject: [PATCH 2/2] Domaca Naloga 2 --- DomNal2/Manifest.toml | 1106 ++++++++++++++++++++++++++++++++++++++ DomNal2/Project.toml | 10 + DomNal2/README.md | 19 + DomNal2/demo.aux | 5 + DomNal2/demo.jl | 25 + DomNal2/demo.log | 591 ++++++++++++++++++++ DomNal2/demo.out | 0 DomNal2/demo.pdf | Bin 0 -> 18203 bytes DomNal2/demo.tex | 157 ++++++ DomNal2/src/DomNal2.jl | 24 + DomNal2/test/runtests.jl | 45 ++ Manifest.toml | 75 ++- Project.toml | 2 + 13 files changed, 2053 insertions(+), 6 deletions(-) create mode 100644 DomNal2/Manifest.toml create mode 100644 DomNal2/Project.toml create mode 100644 DomNal2/README.md create mode 100644 DomNal2/demo.aux create mode 100644 DomNal2/demo.jl create mode 100644 DomNal2/demo.log create mode 100644 DomNal2/demo.out create mode 100644 DomNal2/demo.pdf create mode 100644 DomNal2/demo.tex create mode 100644 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"4fea590b89e6ec504593146bf8b988b2c00922b2" +uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" +version = "2021.5.5+0" + +[[deps.x265_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" +uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" +version = "3.5.0+0" + +[[deps.xkbcommon_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] +git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37" +uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" +version = "1.4.1+1" diff --git a/DomNal2/Project.toml b/DomNal2/Project.toml new file mode 100644 index 0000000..6662fe0 --- /dev/null +++ b/DomNal2/Project.toml @@ -0,0 +1,10 @@ +name = "DomNal2" +uuid = "9eae297a-06a1-4eb6-a561-50e2c4012a07" +authors = ["aleksacirkovic99 "] +version = "0.1.0" + +[deps] +ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" +Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" diff --git a/DomNal2/README.md b/DomNal2/README.md new file mode 100644 index 0000000..0f83ccb --- /dev/null +++ b/DomNal2/README.md @@ -0,0 +1,19 @@ +Avtor: +Aleksa Ćirković + +Opis naloge: +Ta projekt vključuje implementacijo numerične metode za izračun integralov s pomočjo Gauss-Legendreove kvadrature z dvema točkama. Cilj naloge je razviti in testirati funkcijo, ki omogoča aproksimacijo integrala poljubne funkcije na določenem intervalu. Projekt prav tako vključuje oceno napake integracije. + +Kako uporabiti kodo: + - Namestitev: Za zagon kode potrebujete programsko okolje Julia. Kodo prenesite na svoj računalnik. + - Uvoz modula: V vašem Julia okolju uvozite modul z ukazom include("pot/do/DomNal2.jl"), kjer je "pot/do/" dejanska lokacija datoteke na vašem sistemu. + - Uporaba funkcije: Po uvozu modula lahko funkcijo gauss_legendre_2 uporabite za izračun integrala funkcije na želenem intervalu, npr., gauss_legendre_2(f, 0, 1), kjer je f funkcija, ki jo želite integrirati. + +Navodila za poganjanje testov: +Prepričajte se, da imate vse potrebne odvisnosti: Pred zagonom testov namestite vse potrebne pakete v Julia z Pkg.add("ImePaketa"). Jaz sem uporabil paket ForwardDiff, tako da ga morate namestiti. +Zagon testov: Teste poženete z vključitvijo datoteke runtests.jl znotraj vašega Julia okolja, na primer z include("pot/do/runtests.jl"). +Kako ustvariti poročilo +Če želite ustvariti poročilo o izvedbi in rezultatih testov: + +Zagon testov z beleženjem rezultatov: Teste poženite tako, da rezultate izpišete v datoteko ali jih zapišete v obliki, ki jo lahko kasneje obdelate. +Analiza rezultatov: Rezultate analizirajte ročno ali z orodji za avtomatizirano analizo, da ustvarite končno poročilo. \ No newline at end of file diff --git a/DomNal2/demo.aux b/DomNal2/demo.aux new file mode 100644 index 0000000..b1ab02f --- /dev/null +++ b/DomNal2/demo.aux @@ -0,0 +1,5 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand*\HyPL@Entry[1]{} +\HyPL@Entry{0<>} +\gdef \@abspage@last{1} diff --git a/DomNal2/demo.jl b/DomNal2/demo.jl new file mode 100644 index 0000000..4c321e0 --- /dev/null +++ b/DomNal2/demo.jl @@ -0,0 +1,25 @@ + +include("../DomNal2/src/DomNal2.jl") +using .DomNal2 + +# Poročilo +# Poročilo za projekt Gauss-Legendre Quadrature +# Avtor: Aleksa Cirkovic + +# Opis naloge +# Naloga obravnava numerično integracijo z uporabo dvo-točkovne Gauss-Legendreove kvadrature. Metoda se temelji na aproksimaciji integrala funkcije preko dveh točk znotraj integracijskega intervala, ki minimizirata napako. + +# Opis rešitve +# Implementirana funkcija gauss_legendre_2 izračuna integral dane funkcije na intervalu [a, b], kjer funkcija sprejme kot argumente funkcijo "f", spodnjo mejo "a" in zgornjo mejo "b". Za izračun napake se uporabi funkcija gauss_legendre_error_estimate, ki izračuna oceno napake kvadrature. + + +# Primer funkcije +f(x) = x^4 + sin(x) + +# Izračun integrala +result = DomNal2.gauss_legendre_2(f, 0, 2) +error_estimate = DomNal2.gauss_legendre_error_estimate(f, 0, 2) + +println("Rezultat integracije ∫ from 0 to 2 of x^4 + sin(x) dx: ", result) +println("Ocena napake: ", error_estimate) + diff --git a/DomNal2/demo.log b/DomNal2/demo.log new file mode 100644 index 0000000..d472f14 --- /dev/null +++ b/DomNal2/demo.log @@ -0,0 +1,591 @@ +This is XeTeX, Version 3.141592653-2.6-0.999996 (MiKTeX 24.3) (preloaded format=xelatex 2024.5.18) 18 MAY 2024 16:04 +entering extended mode + \write18 enabled. + %&-line parsing enabled. +**./demo.tex +(demo.tex +LaTeX2e <2023-11-01> patch level 1 +L3 programming layer <2024-03-14> +(C:\Users\Aki\AppData\Local\Programs\MiKTeX\tex/latex/base\article.cls +Document Class: article 2023/05/17 v1.4n Standard LaTeX document class +(C:\Users\Aki\AppData\Local\Programs\MiKTeX\tex/latex/base\size12.clo +File: size12.clo 2023/05/17 v1.4n Standard LaTeX file (size option) +) +\c@part=\count184 +\c@section=\count185 +\c@subsection=\count186 +\c@subsubsection=\count187 +\c@paragraph=\count188 +\c@subparagraph=\count189 +\c@figure=\count190 +\c@table=\count191 +\abovecaptionskip=\skip48 +\belowcaptionskip=\skip49 +\bibindent=\dimen140 +) +(C:\Users\Aki\AppData\Local\Programs\MiKTeX\tex/latex/geometry\geometry.sty +Package: geometry 2020/01/02 v5.9 Page Geometry + +(C:\Users\Aki\AppData\Local\Programs\MiKTeX\tex/latex/graphics\keyval.sty +Package: keyval 2022/05/29 v1.15 key=value parser (DPC) +\KV@toks@=\toks17 +) +(C:\Users\Aki\AppData\Local\Programs\MiKTeX\tex/generic/iftex\ifvtex.sty +Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. 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defs for Latin Modern +) +LaTeX Font Info: Trying to load font information for OMS+lmsy on input line +146. + +(C:\Users\Aki\AppData\Local\Programs\MiKTeX\tex/latex/lm\omslmsy.fd +File: omslmsy.fd 2015/05/01 v1.6.1 Font defs for Latin Modern +) +LaTeX Font Info: Trying to load font information for OMX+lmex on input line +146. + +(C:\Users\Aki\AppData\Local\Programs\MiKTeX\tex/latex/lm\omxlmex.fd +File: omxlmex.fd 2015/05/01 v1.6.1 Font defs for Latin Modern +) +LaTeX Font Info: External font `lmex10' loaded for size +(Font) <10> on input line 146. +LaTeX Font Info: External font `lmex10' loaded for size +(Font) <7> on input line 146. +LaTeX Font Info: External font `lmex10' loaded for size +(Font) <5> on input line 146. +LaTeX Font Info: Trying to load font information for U+msa on input line 146 +. + +(C:\Users\Aki\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\umsa.fd +File: umsa.fd 2013/01/14 v3.01 AMS symbols A +) 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+\newcommand{\HLJLch}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcm}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcp}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcpB}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcs}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLcsB}[1]{\textcolor[RGB]{153,153,119}{\textit{#1}}} +\newcommand{\HLJLg}[1]{#1} +\newcommand{\HLJLgd}[1]{#1} +\newcommand{\HLJLge}[1]{#1} +\newcommand{\HLJLgeB}[1]{#1} +\newcommand{\HLJLgh}[1]{#1} +\newcommand{\HLJLgi}[1]{#1} +\newcommand{\HLJLgo}[1]{#1} +\newcommand{\HLJLgp}[1]{#1} +\newcommand{\HLJLgs}[1]{#1} +\newcommand{\HLJLgsB}[1]{#1} +\newcommand{\HLJLgt}[1]{#1} + + +\begin{document} + + + +\begin{lstlisting} +(*@\HLJLnf{include}@*)(*@\HLJLp{(}@*)(*@\HLJLs{"{}../DomNal2/src/DomNal2.jl"{}}@*)(*@\HLJLp{)}@*) +(*@\HLJLk{using}@*) (*@\HLJLoB{.}@*)(*@\HLJLn{DomNal2}@*) + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Poročilo}@*) +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Poročilo}@*) (*@\HLJLcs{za}@*) (*@\HLJLcs{projekt}@*) (*@\HLJLcs{Gauss-Legendre}@*) (*@\HLJLcs{Quadrature}@*) +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Avtor:}@*) (*@\HLJLcs{Aleksa}@*) (*@\HLJLcs{Cirkovic}@*) + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Opis}@*) (*@\HLJLcs{naloge}@*) +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Naloga}@*) (*@\HLJLcs{obravnava}@*) (*@\HLJLcs{numerično}@*) (*@\HLJLcs{integracijo}@*) (*@\HLJLcs{z}@*) (*@\HLJLcs{uporabo}@*) (*@\HLJLcs{dvo-točkovne}@*) (*@\HLJLcs{Gauss-Legendreove}@*) (*@\HLJLcs{kvadrature.}@*) (*@\HLJLcs{Metoda}@*) (*@\HLJLcs{se}@*) (*@\HLJLcs{temelji}@*) (*@\HLJLcs{na}@*) (*@\HLJLcs{aproksimaciji}@*) (*@\HLJLcs{integrala}@*) (*@\HLJLcs{funkcije}@*) (*@\HLJLcs{preko}@*) (*@\HLJLcs{dveh}@*) (*@\HLJLcs{točk}@*) (*@\HLJLcs{znotraj}@*) (*@\HLJLcs{integracijskega}@*) (*@\HLJLcs{intervala,}@*) (*@\HLJLcs{ki}@*) (*@\HLJLcs{minimizirata}@*) (*@\HLJLcs{napako.}@*) + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Opis}@*) (*@\HLJLcs{rešitve}@*) +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Implementirana}@*) (*@\HLJLcs{funkcija}@*) (*@\HLJLcs{gauss{\_}legendre{\_}2}@*) (*@\HLJLcs{izračuna}@*) (*@\HLJLcs{integral}@*) (*@\HLJLcs{dane}@*) (*@\HLJLcs{funkcije}@*) (*@\HLJLcs{na}@*) (*@\HLJLcs{intervalu}@*) (*@\HLJLcs{[a,}@*) (*@\HLJLcs{b],}@*) (*@\HLJLcs{kjer}@*) (*@\HLJLcs{funkcija}@*) (*@\HLJLcs{sprejme}@*) (*@\HLJLcs{kot}@*) (*@\HLJLcs{argumente}@*) (*@\HLJLcs{funkcijo}@*) (*@\HLJLcs{"{}f"{},}@*) (*@\HLJLcs{spodnjo}@*) (*@\HLJLcs{mejo}@*) (*@\HLJLcs{"{}a"{}}@*) (*@\HLJLcs{in}@*) (*@\HLJLcs{zgornjo}@*) (*@\HLJLcs{mejo}@*) (*@\HLJLcs{"{}b"{}.}@*) (*@\HLJLcs{Za}@*) (*@\HLJLcs{izračun}@*) (*@\HLJLcs{napake}@*) (*@\HLJLcs{se}@*) (*@\HLJLcs{uporabi}@*) (*@\HLJLcs{funkcija}@*) (*@\HLJLcs{gauss{\_}legendre{\_}error{\_}estimate,}@*) (*@\HLJLcs{ki}@*) (*@\HLJLcs{izračuna}@*) (*@\HLJLcs{oceno}@*) (*@\HLJLcs{napake}@*) (*@\HLJLcs{kvadrature.}@*) + + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Primer}@*) (*@\HLJLcs{funkcije}@*) +(*@\HLJLnf{f}@*)(*@\HLJLp{(}@*)(*@\HLJLn{x}@*)(*@\HLJLp{)}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{x}@*)(*@\HLJLoB{{\textasciicircum}}@*)(*@\HLJLni{4}@*) (*@\HLJLoB{+}@*) (*@\HLJLnf{sin}@*)(*@\HLJLp{(}@*)(*@\HLJLn{x}@*)(*@\HLJLp{)}@*) + +(*@\HLJLcs{{\#}}@*) (*@\HLJLcs{Izračun}@*) (*@\HLJLcs{integrala}@*) +(*@\HLJLn{result}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{DomNal2}@*)(*@\HLJLoB{.}@*)(*@\HLJLnf{gauss{\_}legendre{\_}2}@*)(*@\HLJLp{(}@*)(*@\HLJLn{f}@*)(*@\HLJLp{,}@*) (*@\HLJLni{0}@*)(*@\HLJLp{,}@*) (*@\HLJLni{2}@*)(*@\HLJLp{)}@*) +(*@\HLJLn{error{\_}estimate}@*) (*@\HLJLoB{=}@*) (*@\HLJLn{DomNal2}@*)(*@\HLJLoB{.}@*)(*@\HLJLnf{gauss{\_}legendre{\_}error{\_}estimate}@*)(*@\HLJLp{(}@*)(*@\HLJLn{f}@*)(*@\HLJLp{,}@*) (*@\HLJLni{0}@*)(*@\HLJLp{,}@*) (*@\HLJLni{2}@*)(*@\HLJLp{)}@*) + +(*@\HLJLnf{println}@*)(*@\HLJLp{(}@*)(*@\HLJLs{"{}Rezultat}@*) (*@\HLJLs{integracije}@*) (*@\HLJLs{\ensuremath{\int}}@*) (*@\HLJLs{from}@*) (*@\HLJLs{0}@*) (*@\HLJLs{to}@*) (*@\HLJLs{2}@*) (*@\HLJLs{of}@*) (*@\HLJLs{x{\textasciicircum}4}@*) (*@\HLJLs{+}@*) (*@\HLJLs{sin(x)}@*) (*@\HLJLs{dx:}@*) (*@\HLJLs{"{}}@*)(*@\HLJLp{,}@*) (*@\HLJLn{result}@*)(*@\HLJLp{)}@*) +(*@\HLJLnf{println}@*)(*@\HLJLp{(}@*)(*@\HLJLs{"{}Ocena}@*) (*@\HLJLs{napake:}@*) (*@\HLJLs{"{}}@*)(*@\HLJLp{,}@*) (*@\HLJLn{error{\_}estimate}@*)(*@\HLJLp{)}@*) +\end{lstlisting} + +\begin{lstlisting} +Rezultat integracije (*@\ensuremath{\int}@*) from 0 to 2 of x(*@{{\textasciicircum}}@*)4 + sin(x) dx: 7.632379203887603 +Ocena napake: 0.2777777744388643 +\end{lstlisting} + + + +\end{document} diff --git a/DomNal2/src/DomNal2.jl b/DomNal2/src/DomNal2.jl new file mode 100644 index 0000000..dbc570f --- /dev/null +++ b/DomNal2/src/DomNal2.jl @@ -0,0 +1,24 @@ +module DomNal2 + +using ForwardDiff + +export gauss_legendre_2, gauss_legendre_error_estimate + +# Function to calculate the Gauss-Legendre quadrature with two points +function gauss_legendre_2(f, a, b) + x1 = (b - a) / 2 * (-1 / sqrt(3)) + (b + a) / 2 + x2 = (b - a) / 2 * (1 / sqrt(3)) + (b + a) / 2 + return (b - a) / 2 * (f(x1) + f(x2)) +end + +# Function to estimate the error of the Gauss-Legendre quadrature +function gauss_legendre_error_estimate(f, a, b) + + f_fourth = x -> ForwardDiff.derivative(t -> ForwardDiff.derivative(s -> ForwardDiff.derivative(u -> ForwardDiff.derivative(f, u), s), t), x) + + f_max = maximum([f_fourth(x) for x in range(a, b, length=1000)]) + + return (b - a)^5 / 2880 * f_max +end + +end diff --git a/DomNal2/test/runtests.jl b/DomNal2/test/runtests.jl new file mode 100644 index 0000000..bd6769e --- /dev/null +++ b/DomNal2/test/runtests.jl @@ -0,0 +1,45 @@ +using Test +include("../src/DomNal2.jl") +using .DomNal2 + +@testset "Gauss-Legendre Quadrature Tests" begin + let + # Define the function f locally within the let block + f(x) = 3x^2 - 2x + 1 + a, b = 0, 1 + exact_integral = (b^3 - a^3) - (b^2 - a^2) + (b - a) + @test isapprox(gauss_legendre_2(f, a, b), exact_integral, atol=1e-4) + end + + let + # Another local definition of f + f(x) = x^4 + estimated_error = gauss_legendre_error_estimate(f, 0, 1) + actual_error = abs(gauss_legendre_2(f, 0, 1) - (1/5)) + @test estimated_error >= actual_error + end + + let + j(x) = x < 0.5 ? 0 : 1 # Step function + a, b = 0, 1 + # The exact integral is known analytically + exact_integral = 0.5 + @test isapprox(gauss_legendre_2(j, a, b), exact_integral, atol=1e-2) + end + + let + g(x) = exp(-x^2) # Gaussian function + a, b = -1, 1 + known_integral = 1.493648 # Approximate value from more accurate numerical methods + @test isapprox(gauss_legendre_2(g, a, b), known_integral, atol=0.1) + end + + + let + k(x) = sin(1000 * x) # Highly oscillatory function + a, b = 0, 1 + @test isapprox(gauss_legendre_2(k, a, b), 0, atol=1.0) # Realistically, we can only expect a rough approximation. + end + +end + diff --git a/Manifest.toml b/Manifest.toml index e6e6cb7..69fdf4b 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -2,7 +2,7 @@ julia_version = "1.10.2" manifest_format = "2.0" -project_hash = "9bdd3397d207b5330eb045cfa0ef3c9454c9a2df" +project_hash = "1ea9b7d1768381bc2f47ce2bbf0e8355b02c019a" [[deps.ANSIColoredPrinters]] git-tree-sha1 = "574baf8110975760d391c710b6341da1afa48d8c" @@ -76,19 +76,23 @@ deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statist git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249" uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4" version = "0.10.0" +weakdeps = ["SpecialFunctions"] [deps.ColorVectorSpace.extensions] SpecialFunctionsExt = "SpecialFunctions" - [deps.ColorVectorSpace.weakdeps] - SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" - [[deps.Colors]] deps = ["ColorTypes", "FixedPointNumbers", "Reexport"] git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a" uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" version = "0.12.10" +[[deps.CommonSubexpressions]] +deps = ["MacroTools", "Test"] +git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7" +uuid = "bbf7d656-a473-5ed7-a52c-81e309532950" +version = "0.3.0" + [[deps.Compat]] deps = ["TOML", "UUIDs"] git-tree-sha1 = "75bd5b6fc5089df449b5d35fa501c846c9b6549b" @@ -158,6 +162,18 @@ git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae" uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" version = "1.9.1" +[[deps.DiffResults]] +deps = ["StaticArraysCore"] +git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621" +uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5" +version = "1.1.0" + +[[deps.DiffRules]] +deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"] +git-tree-sha1 = "23163d55f885173722d1e4cf0f6110cdbaf7e272" +uuid = "b552c78f-8df3-52c6-915a-8e097449b14b" +version = "1.15.1" + [[deps.Distributed]] deps = ["Random", "Serialization", "Sockets"] uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b" @@ -174,6 +190,12 @@ git-tree-sha1 = "2613dbec8f4748273bbe30ba71fd5cb369966bac" uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4" version = "1.2.1" +[[deps.DomNal2]] +deps = ["ForwardDiff", "Plots", "QuadGK", "Test"] +path = "DomNal2" +uuid = "9eae297a-06a1-4eb6-a561-50e2c4012a07" +version = "0.1.0" + [[deps.Downloads]] deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" @@ -230,6 +252,18 @@ git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8" uuid = "59287772-0a20-5a39-b81b-1366585eb4c0" version = "0.4.2" +[[deps.ForwardDiff]] +deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"] +git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad" +uuid = "f6369f11-7733-5829-9624-2563aa707210" +version = "0.10.36" + + [deps.ForwardDiff.extensions] + ForwardDiffStaticArraysExt = "StaticArrays" + + [deps.ForwardDiff.weakdeps] + StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" + [[deps.FreeType2_jll]] deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"] git-tree-sha1 = "d8db6a5a2fe1381c1ea4ef2cab7c69c2de7f9ea0" @@ -616,6 +650,12 @@ git-tree-sha1 = "60e3045590bd104a16fefb12836c00c0ef8c7f8c" uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" version = "3.0.13+0" +[[deps.OpenSpecFun_jll]] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1" +uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e" +version = "0.5.5+0" + [[deps.Opus_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720" @@ -712,6 +752,12 @@ git-tree-sha1 = "37b7bb7aabf9a085e0044307e1717436117f2b3b" uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56" version = "6.5.3+1" +[[deps.QuadGK]] +deps = ["DataStructures", "LinearAlgebra"] +git-tree-sha1 = "9b23c31e76e333e6fb4c1595ae6afa74966a729e" +uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" +version = "2.9.4" + [[deps.REPL]] deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" @@ -805,6 +851,23 @@ deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"] uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" version = "1.10.0" +[[deps.SpecialFunctions]] +deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"] +git-tree-sha1 = "2f5d4697f21388cbe1ff299430dd169ef97d7e14" +uuid = "276daf66-3868-5448-9aa4-cd146d93841b" +version = "2.4.0" + + [deps.SpecialFunctions.extensions] + SpecialFunctionsChainRulesCoreExt = "ChainRulesCore" + + [deps.SpecialFunctions.weakdeps] + ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" + +[[deps.StaticArraysCore]] +git-tree-sha1 = "36b3d696ce6366023a0ea192b4cd442268995a0d" +uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c" +version = "1.4.2" + [[deps.Statistics]] deps = ["LinearAlgebra", "SparseArrays"] uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" @@ -918,13 +981,13 @@ uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d" version = "0.2.0" [[deps.Vaje02]] -deps = ["IJulia", "Plots", "Test"] +deps = ["IJulia", "Test"] path = "Vaje02" uuid = "d6267224-3601-4518-956b-40f0190f698e" version = "0.1.0" [[deps.Vaje03]] -deps = ["SparseArrays"] +deps = ["SparseArrays", "Test"] path = "Vaje03" uuid = "6f966dfe-e158-425e-8be4-67cb0561743b" version = "0.1.0" diff --git a/Project.toml b/Project.toml index b348437..599c147 100644 --- a/Project.toml +++ b/Project.toml @@ -2,6 +2,8 @@ BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" Coverage = "a2441757-f6aa-5fb2-8edb-039e3f45d037" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" +DomNal2 = "9eae297a-06a1-4eb6-a561-50e2c4012a07" +ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"