{ "metadata": { "kernelspec": { "name": "python", "display_name": "Python (Pyodide)", "language": "python" }, "language_info": { "codemirror_mode": { "name": "python", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8" }, "colab": { "provenance": [] } }, "nbformat_minor": 5, "nbformat": 4, "cells": [ { "id": "72472a7d", "cell_type": "markdown", "source": [ "# Uvod u Python\n", "\n", "Ova sveska je uvod u one mogućnosti Python-a koje će nam biti potrebne tokom kursa Uvod u numeričku matematiku. Cilj je da savladate tačno onaj skup alata koji se koristi u zadacima na vežbama i ispitu, bez upoznavanja sa svim funkcionalnostima programskog jezika Python.\n" ], "metadata": { "id": "72472a7d" } }, { "id": "05254259", "cell_type": "markdown", "source": [ "## 1. Osnove Python sintakse" ], "metadata": { "jp-MarkdownHeadingCollapsed": true, "id": "05254259" } }, { "id": "fdd3bbd2", "cell_type": "markdown", "source": [ "### 1.1 Promenljive, osnovni tipovi podataka i ispis\n", "\n", "Python je dinamički tipiziran jezik — tip promenljive se ne deklariše eksplicitno, već se određuje na osnovu vrednosti koja joj se dodeli. Osnovni tipovi koje ćemo koristiti su:\n", "\n", "- `int` — celi brojevi (npr. `5`, `-3`)\n", "- `float` — realni (decimalni) brojevi (npr. `3.14`, `1e-4`)\n", "- `bool` — logička vrednost (`True` / `False`)\n", "- `str` — tekstualni niz (string)\n", "\n", "Tip promenljive se proverava funkcijom `type()`. Ovo može biti korisno za pronalaženje i otklanjanje bagova.\n" ], "metadata": { "id": "fdd3bbd2" } }, { "id": "ba10d43c-823c-4cce-84ca-d5579aaa7029", "cell_type": "code", "source": [ "x = 5\n", "y = 3.14\n", "tol = 1e-4 # naučna notacija: 1e-4 = 0.0001\n", "naziv = \"Njutnova metoda\"\n", "tvrdjenje = False" ], "metadata": { "trusted": true, "id": "ba10d43c-823c-4cce-84ca-d5579aaa7029" }, "outputs": [], "execution_count": null }, { "id": "9e436329-3f21-432d-900e-f787939e0ccb", "cell_type": "markdown", "source": [ "#### Funkcija `print()`\n", "\n", "Da bismo videli vrednost neke promenljive ili rezultat proračuna, koristimo ugrađenu funkciju `print()`. Njoj prosleđujemo jednu ili više vrednosti (razdvojenih zarezom), a ona ih ispisuje u izlazu (ispod ćelije), razdvojene razmakom.\n" ], "metadata": { "id": "9e436329-3f21-432d-900e-f787939e0ccb" } }, { "id": "24b7e1cc", "cell_type": "code", "source": [ "print(\"Zdravo!\")\n", "print(x, type(x))\n", "print(y, type(y))\n", "print(tol, type(tol))\n", "print(naziv, type(naziv))\n", "print(tvrdjenje, type(tvrdjenje))" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "24b7e1cc", "outputId": "3378ed82-ef9c-479f-a593-db600f0a9ae2" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "Zdravo!\n,5 \n,3.14 \n,0.0001 \n,Njutnova metoda \n,False \n" } ], "execution_count": null }, { "id": "9d7bdf6d-135f-4f35-a9f6-8f360d1b1367", "cell_type": "markdown", "source": [ "#### f-stringovi\n", "\n", "Umesto da vrednosti nabrajamo kroz zarez, mnogo praktičniji način ispisa je preko **f-stringa** (formatted string literal). To je string ispred kog se piše slovo `f`, a unutar njega, u vitičastim zagradama `{}`, može stajati bilo koja promenljiva ili izraz čija se vrednost automatski ubacuje u tekst.\n", "\n", "Sintaksa: `f\"tekst {izraz} tekst\"`\n", "\n", "Kasnije ćemo videti kako se unutar `{}` dodatno kontroliše format ispisa.\n" ], "metadata": { "id": "9d7bdf6d-135f-4f35-a9f6-8f360d1b1367" } }, { "id": "a2529950-7bf6-470b-af5a-b162a5221fe0", "cell_type": "code", "source": [ "ime_metode = \"Njutnova metoda\"\n", "tol = 1e-4\n", "\n", "print(f\"Metoda: {ime_metode}\")\n", "print(f\"Tražena tačnost: {tol}\")" ], "metadata": { "trusted": true, "scrolled": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "a2529950-7bf6-470b-af5a-b162a5221fe0", "outputId": "67648726-60cf-44e9-c8b5-c7a734d43e71" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "Metoda: Njutnova metoda\n,Tražena tačnost: 0.0001\n" } ], "execution_count": null }, { "id": "ca156e23", "cell_type": "markdown", "source": [ "### 1.2 Aritmetički operatori\n", "\n", "| Operator | Značenje | Primer |\n", "|---|---|---|\n", "| `+` `-` `*` `/` | sabiranje, oduzimanje, množenje, deljenje | `7 / 2 = 3.5` |\n", "| `//` | celobrojno deljenje | `7 // 2 = 3` |\n", "| `%` | ostatak pri deljenju | `7 % 2 = 1` |\n", "| `**` | stepenovanje | `2 ** 3 = 8` |\n", "\n", "Deljenje `/` **uvek** vraća `float`, čak i kada su brojevi deljivi bez ostatka. Ukoliko je potrebno da krajnji rezultat bude tipa `int`, neophodno je izvršiti kastovanje `int(rezultat)`." ], "metadata": { "id": "ca156e23" } }, { "id": "4a60fb6f", "cell_type": "code", "source": [ "a = 7\n", "b = 2\n", "c = 6\n", "\n", "print(\"a / b =\", a / b)\n", "print(\"a // b =\", a // b)\n", "print(\"a % b =\", a % b)\n", "print(\"a ** b =\", a ** b)\n", "print(\"c / b =\", c / b)\n", "print(\"c / b =\", int(c / b))" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "4a60fb6f", "outputId": "b379a376-02b1-4ca7-f487-1fca20aaa653" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "a / b = 3.5\n,a // b = 3\n,a % b = 1\n,a ** b = 49\n,c / b = 3.0\n,c / b = 3\n" } ], "execution_count": null }, { "id": "c7ed5de3", "cell_type": "markdown", "source": [ "### 1.3 Operatori poređenja i logički operatori\n", "\n", "| Operator | Značenje |\n", "|---|---|\n", "| `==` | jednako |\n", "| `!=` | različito |\n", "| `<` `>` `<=` `>=` | manje, veće, manje ili jednako, veće ili jednako |\n", "| `and` | logičko I |\n", "| `or` | logičko ILI |\n", "| `not` | logička negacija |\n" ], "metadata": { "id": "c7ed5de3" } }, { "id": "392ab074", "cell_type": "code", "source": [ "a, b = 3, 5\n", "tol = 1e-4\n", "greska = 2.5e-5\n", "\n", "print(a < b)\n", "print(a == b)\n", "print(greska < tol)\n", "print(a < b and greska < tol)\n", "print(not (a == b))\n" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "392ab074", "outputId": "32dde58b-6a7e-41c4-8e00-fdd6a2b28d83" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "True\n,False\n,True\n,True\n,True\n" } ], "execution_count": null }, { "id": "6de3b58c", "cell_type": "markdown", "source": [ "### 1.4 Grananje: `if` / `elif` / `else`\n", "\n", "**Napomena o uvlačenju koda:** Python nema vitičaste zagrade `{}`. Blok koda koji pripada `if`, `for`, `while`, `def` itd. određen je isključivo uvlačenjem (indentacijom), po konvenciji 4 razmaka (tab).\n" ], "metadata": { "id": "6de3b58c" } }, { "id": "c8a1d2a3", "cell_type": "code", "source": [ "x = -3.2\n", "\n", "if x > 0:\n", " print(\"x je pozitivan\")\n", "elif x < 0:\n", " print(\"x je negativan\")\n", "else:\n", " print(\"x je nula\")\n" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "c8a1d2a3", "outputId": "fd1fe098-cdac-4a62-feab-29589baea241" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "x je negativan\n" } ], "execution_count": null }, { "id": "bc96234b", "cell_type": "markdown", "source": [ "### 1.5 `while` petlja\n", "\n", "`while` petlja se izvršava **dok god** je zadati uslov tačan. Skok u sledeću iteraciju se postiže komandom `continue`, a iz petlje se može izaći i komandom `break`.\n" ], "metadata": { "id": "bc96234b" } }, { "id": "a7d8867d", "cell_type": "code", "source": [ "x0 = 0.3\n", "iterMax = 100\n", "iteracija = 0\n", "tol = 1e-3\n", "\n", "while iteracija < iterMax:\n", " x1 = x0**0.5\n", " iteracija += 1\n", " if abs(x1 - x0) < tol:\n", " break\n", " x0 = x1\n", "\n", "print(f\"Rešenje: {x1:.6f}\")\n", "print(f\"Broj iteracija: {iteracija}\")" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "a7d8867d", "outputId": "f906a2c3-71bc-462a-d40f-7e91119182ed" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "Rešenje: 0.999412\n,Broj iteracija: 11\n" } ], "execution_count": null }, { "id": "96aa82e4", "cell_type": "markdown", "source": [ "### 1.6 `for` petlja i `range`\n", "\n", "`for` petlja se koristi kada unapred znamo koliko puta treba da se nešto ponovi, npr. prolazak kroz sve vrste matrice, sabiranje članova niza, konstrukcija tablice.\n", "\n", "- `range(n)` generiše `0, 1, 2, ..., n-1`\n", "- `range(a, b)` generiše `a, a+1, ..., b-1`\n", "- `range(a, b, k)` generiše `a, a+k, ..., a+tk`, gde je `a+tk` najveći broj manji od b" ], "metadata": { "id": "96aa82e4" } }, { "id": "9baf3899", "cell_type": "code", "source": [ "n = 5\n", "\n", "for i in range(n):\n", " print(f\"i = {i}, kvadrat = {i**2}\")" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "9baf3899", "outputId": "d3e6d436-f2bb-4ffc-86e8-a111103f213a" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "i = 0, kvadrat = 0\n,i = 1, kvadrat = 1\n,i = 2, kvadrat = 4\n,i = 3, kvadrat = 9\n,i = 4, kvadrat = 16\n" } ], "execution_count": null }, { "id": "cd6bc734", "cell_type": "markdown", "source": [ "### 1.7 Liste i list comprehension\n", "\n", "Lista (`list`) je uređena, promenljiva kolekcija vrednosti. Liste ćemo najčešće koristiti da opišemo niz vrednosti (npr. niz tolerancija koje testiramo, niz čvorova) — mada za same numeričke proračune ćemo uglavnom koristiti NumPy nizove (sledeća sekcija).\n", "\n", "- Indeksiranje: `lista[0]` je prvi element, `lista[-1]` je poslednji.\n", "- Slajsovanje: `lista[1:4]` (elementi od indeksa 1 do 3).\n", "- `len(lista)` — dužina liste.\n", "- `lista.append(x)` — dodavanje elementa na kraj liste\n" ], "metadata": { "id": "cd6bc734" } }, { "id": "c572837c", "cell_type": "code", "source": [ "tolerancije = [1e-4, 1e-6, 1e-8, 1e-10, 1e-12]\n", "\n", "print(tolerancije[0]) # prvi element\n", "print(tolerancije[-1]) # poslednji element\n", "print(tolerancije[1:4]) # slajsovanje\n", "print(len(tolerancije)) # duzina liste" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "c572837c", "outputId": "111bf920-30fd-48d5-e377-b5a7a0d0f203" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "0.0001\n,1e-12\n,[1e-06, 1e-08, 1e-10]\n,5\n" } ], "execution_count": null }, { "id": "4001e379", "cell_type": "code", "source": [ "tolerancije = []\n", "for k in range(4, 13, 2):\n", " tolerancije.append(10 ** (-k))" ], "metadata": { "trusted": true, "id": "4001e379" }, "outputs": [], "execution_count": null }, { "id": "2a4b93dc", "cell_type": "code", "source": [ "# kompaktniji zapis iste ideje korišćenjem sa list comprehension:\n", "tolerancije = [10 ** (-k) for k in range(4, 11, 2)]\n", "print(tolerancije)\n", "\n", "# list comprehension sa uslovom:\n", "pozitivni = [x for x in [-2, -1, 0, 1, 2, 3] if x > 0]\n", "print(pozitivni)" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "2a4b93dc", "outputId": "1c4db966-f1b4-4c35-d6dd-928c735eb501" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "[0.0001, 1e-06, 1e-08, 1e-10]\n,[1, 2, 3]\n" } ], "execution_count": null }, { "id": "4db4b6fd-610b-4b33-84c3-c28040fedc06", "cell_type": "markdown", "source": [ "Ukoliko su nam istovremeno potrebni i indeksi i vrednosti liste, koristimo `enumerate`." ], "metadata": { "id": "4db4b6fd-610b-4b33-84c3-c28040fedc06" } }, { "id": "08ab097d", "cell_type": "code", "source": [ "niz = [1.5, 1.8, 2.3, 3.4]\n", "for i, vrednost in enumerate(niz):\n", " print(f\"X[{i}] = {vrednost}\")" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "08ab097d", "outputId": "d0c305ee-619e-4813-8973-6a9a20fb086c" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "X[0] = 1.5\n,X[1] = 1.8\n,X[2] = 2.3\n,X[3] = 3.4\n" } ], "execution_count": null }, { "id": "29a5ac80", "cell_type": "markdown", "source": [ "### 1.8 Torke (tuple) i višestruko dodeljivanje\n", "\n", "Torka (`tuple`) je slična listi, ali je **nepromenljiva** (immutable) — jednom kreirana, ne može se menjati. Torke se prirodno javljaju kada funkcija vraća više vrednosti odjednom (npr. broj iteracija i rešenje), što ćemo koristiti u sledećoj sekciji o funkcijama.\n" ], "metadata": { "id": "29a5ac80" } }, { "id": "3a5f696e", "cell_type": "code", "source": [ "# Visestruko dodeljivanje u jednoj liniji\n", "a, b = 3, 5\n", "print(\"a =\", a, \", b =\", b)\n", "\n", "# Zamena vrednosti dve promenljive bez pomocne promenljive\n", "a, b = b, a\n", "print(\"Posle zamene: a =\", a, \", b =\", b)\n", "\n", "# Raspakivanje torke, npr. granica intervala\n", "interval = (0, 2)\n", "leva_granica, desna_granica = interval\n", "print(f\"Interval: [{leva_granica}, {desna_granica}]\")\n" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "3a5f696e", "outputId": "1ac6adad-6574-49fc-c3d8-44bbc40c2a2a" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "a = 3 , b = 5\n,Posle zamene: a = 5 , b = 3\n,Interval: [0, 2]\n" } ], "execution_count": null }, { "id": "8e348d24", "cell_type": "markdown", "source": [ "### 1.9 Biblioteka `math`\n", "\n", "Modul `math` je deo standardne biblioteke Python-a i sadrži osnovne matematičke konstante i funkcije. Kasnije ćemo uvesti i biblioteku `numpy`, koja ima svoje verzije istih funkcija (`np.sin`, `np.exp`, ...).Razlika je u tome što `numpy` funkcije rade i nad **nizovima** vrednosti odjednom, dok `math` funkcije rade samo nad pojedinačnim brojevima.\n", "\n", "Da bismo koristili modul, prvo ga uvozimo naredbom `import math`, a zatim njegovim funkcijama i konstantama pristupamo sa: `math.ime_funkcije(...)`.\n" ], "metadata": { "id": "8e348d24" } }, { "id": "b5ac7dff", "cell_type": "code", "source": [ "import math\n", "\n", "print(\"pi =\", math.pi)\n", "print(\"e =\", math.e)\n", "\n", "print(\"sqrt(2) =\", math.sqrt(2))\n", "print(\"exp(1) =\", math.exp(1))\n", "print(\"log(e) =\", math.log(math.e)) # prirodni logaritam\n", "print(\"log10(100) =\", math.log10(100))\n", "\n", "print(\"sin(pi / 2) =\", math.sin(math.pi / 2))\n", "print(\"cos(0) =\", math.cos(0))\n", "\n", "print(\"factorial(5) =\", math.factorial(5)) # 5! - koristi se npr. kod Njutnovih polinoma sa konacnim razlikama\n", "\n", "print(\"floor(3.7) =\", math.floor(3.7))\n", "print(\"ceil(3.2) =\", math.ceil(3.2))\n" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "b5ac7dff", "outputId": "5f17de84-6f0e-4316-9381-855fe3339fbf" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "pi = 3.141592653589793\n,e = 2.718281828459045\n,sqrt(2) = 1.4142135623730951\n,exp(1) = 2.718281828459045\n,log(e) = 1.0\n,log10(100) = 2.0\n,sin(pi / 2) = 1.0\n,cos(0) = 1.0\n,factorial(5) = 120\n,floor(3.7) = 3\n,ceil(3.2) = 4\n" } ], "execution_count": null }, { "id": "36f15a85", "cell_type": "markdown", "source": [ "### 1.10 Formatiranje ispisa unutar f-stringova\n", "\n", "U 1.1 smo uveli osnovnu sintaksu f-stringova: `f\"tekst {izraz} tekst\"`. Unutar vitičastih zagrada `{}`, iza vrednosti se može staviti dvotačka `:` i **format** koji određuje kako se ta vrednost ispisuje (broj decimala, naučna notacija, poravnanje).\n", "\n", "Najčešći formati koje ćete koristiti:\n", "\n", "| Format | Značenje | Primer |\n", "|---|---|---|\n", "| `{x:.4f}` | fiksni broj decimala (float) | `3.1416` |\n", "| `{x:.2e}` | naučna notacija | `1.23e-04` |\n" ], "metadata": { "id": "36f15a85" } }, { "id": "da218999", "cell_type": "code", "source": [ "import math\n", "\n", "x = math.pi\n", "n_iter = 7\n", "\n", "print(f\"x = {x:.4f}\")\n", "print(f\"x (naučna notacija) = {x:.4e}\")\n" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "da218999", "outputId": "23f2d105-e3a5-4a17-85bc-4f5dc84f4ce1" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "x = 3.1416\n,x (naučna notacija) = 3.1416e+00\n" } ], "execution_count": null }, { "id": "e6da7f5d-b323-4eb9-b054-6d253a48678c", "cell_type": "markdown", "source": [ "## 2. Funkcije" ], "metadata": { "jp-MarkdownHeadingCollapsed": true, "id": "e6da7f5d-b323-4eb9-b054-6d253a48678c" } }, { "id": "dd796839-553f-4b67-91d8-31ef9866067b", "cell_type": "markdown", "source": [ "Funkcije su takođe jedan od osnovnih objekata u Python-u i koriste se kako bi se objedinili nizovi naredbi. Svaka funkcija može, a i ne mora imati ulazne podatke i povratne rezultate (naglasak na množinu)." ], "metadata": { "id": "dd796839-553f-4b67-91d8-31ef9866067b" } }, { "id": "ed5d1843-9319-4a96-b42d-8a51e6470bb0", "cell_type": "markdown", "source": [ "### 2.1 Osnovna sintaksa: `def` i `return`\n", "\n", "Funkcija se definiše ključnom rečju `def`, praćenom imenom funkcije i listom ulaznih podataka (parametara) u zagradama. Telo funkcije je uvučeno, a `return` određuje šta funkcija vraća kao rezultat. Ako funkcija nema `return`, ona vraća `None`.\n" ], "metadata": { "id": "ed5d1843-9319-4a96-b42d-8a51e6470bb0" } }, { "id": "15d0d95b-b831-45a0-a861-1d32f23a860a", "cell_type": "code", "source": [ "def kvadrat(x):\n", " return x ** 2\n", "\n", "def zbir_kvadrata(a, b):\n", " rezultat = a ** 2 + b ** 2\n", " return rezultat\n", "\n", "print(kvadrat(3))\n", "print(zbir_kvadrata(3, 4))\n" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "15d0d95b-b831-45a0-a861-1d32f23a860a", "outputId": "61962b5d-ef92-4530-d7b4-f58c0f89592f" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "9\n,25\n" } ], "execution_count": null }, { "id": "ff0a78e9-4f2e-4cf5-977e-ccc115a9ed4f", "cell_type": "markdown", "source": [ "### 2.2 Podrazumevani (default) argumenti\n", "\n", "Parametru funkcije možemo dodeliti podrazumevanu vrednost koja se koristi ako pri pozivu funkcije taj argument izostavimo. Parametri sa podrazumevanom vrednošću moraju biti navedeni posle parametara bez podrazumevane vrednosti.\n" ], "metadata": { "id": "ff0a78e9-4f2e-4cf5-977e-ccc115a9ed4f" } }, { "id": "75fd3ea0-f0c9-46c0-9893-66704419e62a", "cell_type": "code", "source": [ "def stepenuj(x, n=2):\n", " return x ** n\n", "\n", "print(stepenuj(5)) # koristi podrazumevano n=2\n", "print(stepenuj(5, 3)) # eksplicitno prosledjeno n=3" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "75fd3ea0-f0c9-46c0-9893-66704419e62a", "outputId": "593198ee-8108-47f2-fa6c-da9b8ad8d489" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "25\n,125\n" } ], "execution_count": null }, { "id": "5095e0fe-e980-43e9-ac6a-81ed8b9b723d", "cell_type": "markdown", "source": [ "### 2.3 Više povratnih vrednosti\n", "\n", "Python funkcija može vratiti više vrednosti odjednom. Jednostavno ih navedemo razdvojene zarezom iza `return`. Python ih tada \"upakuje\" u torku (tuple), a mi ih pri pozivu odmah raspakujemo u odgovarajući broj promenljivih.\n" ], "metadata": { "id": "5095e0fe-e980-43e9-ac6a-81ed8b9b723d" } }, { "id": "3e68ab4d-8aa3-468c-9504-636797db94bb", "cell_type": "code", "source": [ "def podeli_sa_ostatkom(a, b):\n", " kolicnik = a // b\n", " ostatak = a % b\n", " return kolicnik, ostatak\n", "k, o = podeli_sa_ostatkom(17, 5)\n", "print(f\"količnik = {k}, ostatak = {o}\")" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/" }, "id": "3e68ab4d-8aa3-468c-9504-636797db94bb", "outputId": "577d0892-ed83-4ece-e2f0-47fc6b91f290" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "količnik = 3, ostatak = 2\n" } ], "execution_count": null }, { "id": "8631f9cf-4ff6-4746-b323-d108af21fe29", "cell_type": "markdown", "source": [ "### 2.4 Prekid izvršavanja: `raise ValueError` i `sys.exit`\n", "\n", "Ponekad ulazni podaci ne zadovoljavaju uslove pod kojima metoda ima smisla (npr. deljenje nulom, matrica koja nije kvadratna, funkcija koja ne menja znak na zadatom intervalu). U tim slučajevima izvršavanje treba prekinuti uz jasnu poruku o grešci, umesto da program nastavi sa pogrešnim rezultatom.\n", "\n", "- `raise ValueError(\"poruka\")` — podiže **izuzetak** (exception); ovo je uobičajen način da funkcija signalizira da su joj prosleđeni neispravni argumenti." ], "metadata": { "id": "8631f9cf-4ff6-4746-b323-d108af21fe29" } }, { "id": "4913c451-4c6d-40ee-807b-ab62e563dd71", "cell_type": "code", "source": [ "def koren(a, b, c):\n", "\n", " D = b ** 2 - 4 * a * c\n", " if D < 0:\n", " raise ValueError(\"Jednačina nema realnih rešenja (D < 0).\")\n", " x1 = (-b + math.sqrt(D)) / (2 * a)\n", " x2 = (-b - math.sqrt(D)) / (2 * a)\n", " return x1, x2\n", "\n", "print(koren(1, -3, 2)) # ima realna resenja\n", "print(koren(1, -1, 3)) # nema realna rešenja" ], "metadata": { "trusted": true, "colab": { "base_uri": "https://localhost:8080/", "height": 315 }, "id": "4913c451-4c6d-40ee-807b-ab62e563dd71", "outputId": "2c476ae9-e566-47d7-9a55-2de8c1574b55" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "(2.0, 1.0)\n" }, { "output_type": "error", "ename": "ValueError", "evalue": "Jednačina nema realnih rešenja (D < 0).", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m/tmp/ipykernel_1396/1138346578.py\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkoren\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# ima realna resenja\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkoren\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# nema realna rešenja\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m/tmp/ipykernel_1396/1138346578.py\u001b[0m in \u001b[0;36mkoren\u001b[0;34m(a, b, c)\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mD\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m4\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mD\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Jednačina nema realnih rešenja (D < 0).\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mx1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mb\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mD\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0mx2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mb\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mD\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mValueError\u001b[0m: Jednačina nema realnih rešenja (D < 0)." ] } ], "execution_count": null }, { "id": "01deea71-7278-4ad7-81fa-a14aa0eedea2", "cell_type": "markdown", "source": [ "### 2.5 `lambda` funkcije\n", "\n", "`lambda` je način da se kratka, bezimena (anonimna) funkcija definiše u jednoj liniji, bez `def` i `return`. Sintaksa je:\n", "\n", "```python\n", "lambda argumenti: izraz\n", "```\n", "\n", "Rezultat izraza se automatski vraća. `lambda` funkcije se najčešće koristi da se definiše funkcija $f(x)$ čiju nulu, ekstremum ili integral tražimo, bez potrebe da se za nju piše čitav `def` blok.\n" ], "metadata": { "id": "01deea71-7278-4ad7-81fa-a14aa0eedea2" } }, { "id": "70b272ff-1e09-4aa0-ad53-3b51467c09ba", "cell_type": "code", "source": [ "f = lambda x: x ** 2 - 2\n", "g = lambda x, y: x + y\n", "\n", "print(f(3))\n", "print(g(2, 5))" ], "metadata": { "trusted": true, "id": "70b272ff-1e09-4aa0-ad53-3b51467c09ba" }, "outputs": [], "execution_count": null }, { "id": "6a638735", "cell_type": "markdown", "source": [ "## 3. NumPy" ], "metadata": { "id": "6a638735", "jp-MarkdownHeadingCollapsed": true } }, { "id": "7f8733ab", "cell_type": "markdown", "source": [ "**NumPy** je biblioteka za rad sa **nizovima** (vektorima) i **matricama**, i predstavlja osnovni alat za sve numeričke proračune. Standardno se uvozi pod skraćenim imenom `np`.\n", "\n", "Ključna razlika u odnosu na obične Python liste (odeljak 1.7): NumPy nizovi omogućavaju **vektorizovane** operacije, matematičku operaciju primenjujemo odjednom na ceo niz, bez pisanja `for` petlje.\n" ], "metadata": { "id": "7f8733ab" } }, { "id": "3c25a678", "cell_type": "code", "source": [ "import numpy as np" ], "metadata": { "id": "3c25a678", "trusted": true }, "outputs": [], "execution_count": null }, { "id": "11cf0068", "cell_type": "markdown", "source": [ "### 3.1 Kreiranje nizova\n", "\n", "| Funkcija | Šta pravi |\n", "|---|---|\n", "| `np.array([...])` | niz od liste (ili liste listi — matrica) |\n", "| `np.zeros(n)` / `np.zeros((m, n))` | niz/matrica nula |\n", "| `np.eye(n)` | jedinična matrica $n\\times n$ |\n", "| `np.diag(d)` | dijagonalna matrica sa elementima iz `d` na dijagonali |\n", "| `np.linspace(a, b, n)` | `n` ravnomerno raspoređenih tačaka na $[a, b]$ (uključujući oba kraja) |\n", "| `np.logspace(a, b, n)` | `n` tačaka ravnomerno raspoređenih u **logaritamskoj** skali, od $10^a$ do $10^b$ |\n", "| `np.arange(a, b, korak)` | tačke od `a` do `b` (isključivo) sa zadatim korakom |\n" ], "metadata": { "id": "11cf0068" } }, { "id": "514ac970", "cell_type": "code", "source": [ "v = np.array([1, 2, 3, 4])\n", "A = np.array([[1, 2], [3, 4]])\n", "\n", "nule = np.zeros(5)\n", "nule_matrica = np.zeros((2, 3))\n", "I = np.eye(3)\n", "D = np.diag([1,3,5])\n", "\n", "x_lin = np.linspace(0, 1, 5)\n", "x_log = np.logspace(-4, 0, 5)\n", "x_ar = np.arange(0, 10, 2.5)\n", "\n", "print(\"v =\", v)\n", "print(\"A =\\n\", A)\n", "print(\"nule =\", nule)\n", "print(\"nule_matrica =\\n\", nule_matrica)\n", "print(\"I =\\n\", I)\n", "print(\"D =\\n\", D)\n", "print(\"x_lin =\", x_lin)\n", "print(\"x_log =\", x_log)\n", "print(\"x_ar =\", x_ar)\n" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.192280Z", "iopub.status.busy": "2026-09-08T15:33:33.192072Z", "iopub.status.idle": "2026-09-08T15:33:33.201330Z", "shell.execute_reply": "2026-09-08T15:33:33.200470Z" }, "id": "514ac970" }, "outputs": [], "execution_count": null }, { "id": "3c9dd3b9", "cell_type": "markdown", "source": [ "### 3.2 Osnovne osobine niza\n", "\n", "- `len(niz)` — dužina prve dimenzije\n", "- `.shape` — dimenzije niza (torka); za matricu `(broj_vrsta, broj_kolona)`\n", "- `.dtype` — tip elemenata niza (npr. `int64`, `float64`)\n" ], "metadata": { "id": "3c9dd3b9" } }, { "id": "f0d7f53a", "cell_type": "code", "source": [ "A = np.array([[1, 2, 3], [4, 5, 6]])\n", "\n", "print(\"len:\", len(A)) # broj vrsta\n", "print(\"shape:\", A.shape)\n", "print(\"dtype:\", A.dtype)\n", "\n", "v = np.array([1.0, 2.0, 3.0])\n", "# v = np.array([[1.0, 2.0, 3.0]])\n", "print(\"shape vektora:\", v.shape)\n" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.203590Z", "iopub.status.busy": "2026-09-08T15:33:33.202995Z", "iopub.status.idle": "2026-09-08T15:33:33.208300Z", "shell.execute_reply": "2026-09-08T15:33:33.207528Z" }, "id": "f0d7f53a" }, "outputs": [], "execution_count": null }, { "id": "7e6d48a2", "cell_type": "markdown", "source": [ "### 3.3 Indeksiranje i slajsovanje\n", "\n", "Indeksiranje se ponaša slično kao kod lista, uz proširenje na više dimenzija. Za matricu `A`, prvi indeks je **vrsta**, drugi je **kolona**. Znak `:` znači \"sve\" po toj dimenziji.\n", "\n", "| Izraz | Značenje |\n", "|---|---|\n", "| `A[i, j]` | element u vrsti `i`, koloni `j` |\n", "| `A[i, :]` | cela `i`-ta vrsta |\n", "| `A[:, j]` | cela `j`-ta kolona |\n", "| `A[1:-1]` | svi elementi osim prvog i poslednjeg |\n", "| `A[i:]` | od indeksa `i` do kraja |\n", "| `A[:n-i]` | od početka do indeksa `n-i` (isključivo) |\n", "| `np.diag(A)` | elementi sa dijagonale |\n", "\n", "Izvučene vrste i kolone matrice automatski se pretvaraju u jednodimenzioni niz. Umesto indeksa, takođe se mogu proslediti i liste (nizovi) indeksa ili niz istinitosnih vrednosti (bool-ova)." ], "metadata": { "id": "7e6d48a2" } }, { "id": "3d6244ad", "cell_type": "code", "source": [ "A = np.array([[1, 2, 3],\n", " [4, 5, 6],\n", " [7, 8, 9]])\n", "\n", "print(\"A[0, 0] =\", A[0, 0])\n", "print(\"A[1, :] =\", A[1, :])\n", "print(\"A[:, 2] =\", A[:, 2])\n", "print(\"A[-1, -1] =\", A[-1, -1])\n", "print(\"A[1, [0,2]] =\", A[1, [0,2]])\n", "print(\"np.diag(A) =\",np.diag(A))\n", "\n", "v = np.array([10, 20, 30, 40, 50])\n", "print(\"v[1:-1] =\", v[1:-1])\n", "print(\"v[2:] =\", v[2:])\n", "print(\"v[:3] =\", v[:3])\n", "print(\"v[[True, False, True, True, False]] =\",v[[True, False, True, True, False]])\n", "\n", "print(\"shape od A[1, :]\", np.shape(A[1, :]))" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.210009Z", "iopub.status.busy": "2026-09-08T15:33:33.209846Z", "iopub.status.idle": "2026-09-08T15:33:33.215476Z", "shell.execute_reply": "2026-09-08T15:33:33.214697Z" }, "id": "3d6244ad" }, "outputs": [], "execution_count": null }, { "id": "d1396d2f", "cell_type": "markdown", "source": [ "### 3.4 Vektorizovane operacije\n", "\n", "Aritmetički operatori (`+ - * / **`) nad NumPy nizovima rade **element po element**, pa nema potrebe za `for` petljom. Kada su dimenzije nizova \"kompatibilne\" (jedan je npr. skalar, ili im se dimenzije poklapaju), NumPy automatski \"razvlači\" manji niz da odgovara većem.\n" ], "metadata": { "id": "d1396d2f" } }, { "id": "b955f90d", "cell_type": "code", "source": [ "x = np.array([1, 2, 3, 4])\n", "y = np.array([10, 20, 30, 40])\n", "\n", "print(\"x + y =\", x + y)\n", "print(\"x * y =\", x * y)\n", "print(\"x ** 2 =\", x ** 2)\n", "print(\"2 * x =\", 2 * x)\n", "print(\"x / 2 =\", x / 2)\n" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.229135Z", "iopub.status.busy": "2026-09-08T15:33:33.228502Z", "iopub.status.idle": "2026-09-08T15:33:33.234277Z", "shell.execute_reply": "2026-09-08T15:33:33.233248Z" }, "id": "b955f90d" }, "outputs": [], "execution_count": null }, { "id": "fe38c9b6", "cell_type": "code", "source": [ "x_novo = np.array([1.001, 2.0002, 3.1])\n", "x_staro = np.array([1.0, 2.0, 3.0])\n", "a=np.array([3,4,5])\n", "tol = 1e-2\n", "\n", "razlika = np.abs(x_novo - x_staro)\n", "print(\"razlika:\", razlika)\n", "print(\"Koje koordinate su ispod tolerancije:\", razlika < tol)\n", "print(\"Da li SVE koordinate zadovoljavaju uslov:\", np.all(razlika < tol))\n", "print(\"Da li neka koordinata zadovoljava uslov:\", np.any(razlika < tol))\n", "print(\"Elementi koji zadovoljavaju uslov:\", x_novo[razlika < tol])" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.236194Z", "iopub.status.busy": "2026-09-08T15:33:33.235550Z", "iopub.status.idle": "2026-09-08T15:33:33.241457Z", "shell.execute_reply": "2026-09-08T15:33:33.240651Z" }, "id": "fe38c9b6" }, "outputs": [], "execution_count": null }, { "id": "7c01f83e", "cell_type": "markdown", "source": [ "### 3.5 Matrično množenje: `@` vs. `*`\n", "\n", "Ovo je jedna od **najčešćih grešaka** na koju treba obratiti pažnju. Simbol `*` između dva NumPy niza množi **element po element**, dok je za **pravo matrično množenje** (u smislu linearne algebre) potreban operator `@` ili funkcija `np.dot`.\n" ], "metadata": { "id": "7c01f83e" } }, { "id": "6a7dfa5e", "cell_type": "code", "source": [ "A = np.array([[1, 2],\n", " [3, 4]])\n", "B = np.array([[5, 6],\n", " [7, 8]])\n", "\n", "print(\"A * B (element po element) =\\n\", A * B)\n", "print(\"A @ B (matricno mnozenje) =\\n\", A @ B)\n", "print(\"np.dot(A, B) (isto sto i @) =\\n\", np.dot(A, B))\n", "\n", "x = np.array([1, 2])\n", "print(\"A @ x (matrica puta vektor kolone) =\", A @ x)\n", "print(\"x @ A (vektor vrste puta matrica) =\", x @ A)\n", "# Rezultat je u oba slučaja niz dimenzije 1, a ne vektor kolone/vrste" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.242991Z", "iopub.status.busy": "2026-09-08T15:33:33.242841Z", "iopub.status.idle": "2026-09-08T15:33:33.247935Z", "shell.execute_reply": "2026-09-08T15:33:33.247126Z" }, "id": "6a7dfa5e" }, "outputs": [], "execution_count": null }, { "id": "e0c9d283", "cell_type": "markdown", "source": [ "### 3.6 Kopiranje nizova — `.copy()`\n", "\n", "Ako se NumPy nizu dodeli druga promenljiva sa `B = A`, **ne pravi se kopija**, već `B` samo postaje drugo ime za isti niz u memoriji. Odnosno, izmena `B` menja i `A`! Ovo je česta greška na koju treba obratiti pažnju, naročito u iterativnim metodama gde se čuva \"prethodna\" i \"nova\" aproksimacija. Da bismo napravili **nezavisnu** kopiju, koristimo `.copy()`.\n" ], "metadata": { "id": "e0c9d283" } }, { "id": "09f0976b", "cell_type": "code", "source": [ "A = np.array([1.0, 2.0, 3.0])\n", "B = A\n", "B[0] = 100.0\n", "print(\"A =\", A)\n", "\n", "A = np.array([1.0, 2.0, 3.0])\n", "C = A.copy()\n", "C[0] = 100.0\n", "print(\"A =\", A)\n", "print(\"C =\", C)\n" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.249512Z", "iopub.status.busy": "2026-09-08T15:33:33.249246Z", "iopub.status.idle": "2026-09-08T15:33:33.254429Z", "shell.execute_reply": "2026-09-08T15:33:33.253666Z" }, "id": "09f0976b" }, "outputs": [], "execution_count": null }, { "id": "406d463d", "cell_type": "markdown", "source": [ "### 3.7 Agregatne i vektorizovane matematičke funkcije\n", "\n", "NumPy nudi vektorizovane verzije matematičkih funkcija iz `math` biblioteke, koje rade nad **celim nizom odjednom**, kao i funkcije koje niz svode na jedan broj (agregatne funkcije).\n", "\n", "**Matematičke (element po element):** `np.sin`, `np.cos`, `np.exp`, `np.log`, `np.sqrt`, `np.abs`\n", "\n", "**Agregatne (svode niz na broj):** `np.sum`, `np.prod`, `np.max`, `np.min`, `np.mean`\n" ], "metadata": { "id": "406d463d" } }, { "id": "64ce2e39", "cell_type": "code", "source": [ "x = np.array([0, np.pi/6, np.pi/4, np.pi/2])\n", "\n", "print(\"np.sin(x) =\", np.sin(x))\n", "print(\"np.sqrt(np.array([1, 4, 9, 16])) =\", np.sqrt(np.array([1, 4, 9, 16])),\"\\n\")\n", "\n", "v = np.array([1, 2, 3, 4, 5])\n", "print(\"v =\",v)\n", "print(\"np.sum(v) =\", np.sum(v))\n", "print(\"np.prod(v) =\", np.prod(v))\n", "print(\"np.max(v) =\", np.max(v))\n", "print(\"np.min(v) =\", np.min(v),\"\\n\")\n", "\n", "A = np.array([[1,2,3],[6,5,4],[7,8,9]])\n", "print(\"A =\\n\",A)\n", "print(\"np.sum(A) =\", np.sum(A))\n", "print(\"np.sum(A) =\", np.max(A))\n", "print(\"np.sum(A) =\", np.sum(A,0)) # ukoliko želimo da se ograničimo na agregiranje po vrstama/kolonama\n", "print(\"np.max(A) =\", np.max(A,1))" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.256405Z", "iopub.status.busy": "2026-09-08T15:33:33.255863Z", "iopub.status.idle": "2026-09-08T15:33:33.263265Z", "shell.execute_reply": "2026-09-08T15:33:33.262293Z" }, "id": "64ce2e39" }, "outputs": [], "execution_count": null }, { "id": "0e9e1770", "cell_type": "markdown", "source": [ "### 3.8 Linearna algebra — `np.linalg`\n", "\n", "Podmodul `np.linalg` sadrži funkcije za standardne operacije linearne algebre.\n", "\n", "| Funkcija | Šta radi |\n", "|---|---|\n", "| `np.linalg.solve(A, b)` | rešava sistem $Ax = b$ |\n", "| `np.linalg.inv(A)` | inverzna matrica $A^{-1}$ |\n", "| `np.linalg.det(A)` | determinanta matrice |\n", "| `np.linalg.norm(x)` | euklidska norma vektora (ili matrice); parametrom `ord` biramo tip norme (npr. `ord=np.inf`) |\n" ], "metadata": { "id": "0e9e1770" } }, { "id": "e82fe258", "cell_type": "code", "source": [ "A = np.array([[2.0, 1.0],\n", " [1.0, 3.0]])\n", "b = np.array([3.0, 5.0])\n", "\n", "x = np.linalg.solve(A, b)\n", "print(\"rešenje x =\", x)\n", "print(\"provera A @ x =\", A @ x)\n", "\n", "print(\"det(A) =\", np.linalg.det(A))\n", "print(\"A^-1 =\\n\", np.linalg.inv(A))\n", "\n", "print(\"norma(x) =\", np.linalg.norm(x))\n", "print(\"norma(x, ord=inf) =\", np.linalg.norm(x, ord=np.inf))\n" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.273462Z", "iopub.status.busy": "2026-09-08T15:33:33.273177Z", "iopub.status.idle": "2026-09-08T15:33:33.281936Z", "shell.execute_reply": "2026-09-08T15:33:33.280970Z" }, "id": "e82fe258" }, "outputs": [], "execution_count": null }, { "id": "9ee7d6cf", "cell_type": "markdown", "source": [ "### 3.9 Rad sa polinomima\n", "\n", "U NumPy-u se polinom predstavlja kao niz koeficijenata, **počevši od najvišeg stepena**. Na primer, $p(x) = 2x^2 - 3x + 1$ se predstavlja kao `np.array([2, -3, 1])`.\n", "\n", "| Funkcija | Šta radi |\n", "|---|---|\n", "| `np.polyval(p, x)` | vrednost polinoma `p` u tački (ili nizu tačaka) `x` |\n", "| `np.polyder(p)` | izvod polinoma (niz koeficijenata izvoda) |\n", "| `np.roots(p)` | nule (koreni) polinoma |\n", "| `np.convolve(p, q)` | množenje dva polinoma `p` i `q` (konvolucija koeficijenata) |\n" ], "metadata": { "id": "9ee7d6cf" } }, { "id": "00b33578", "cell_type": "code", "source": [ "p = np.array([1, -3, 2])\n", "\n", "print(\"p(0) =\", np.polyval(p, 0))\n", "print(\"p([0, 1, 2, 5]) =\", np.polyval(p, np.array([0, 1, 2, 5])))\n", "\n", "p_izvod = np.polyder(p)\n", "print(\"p'(x) koeficijenti:\", p_izvod)\n", "\n", "koreni = np.roots(p)\n", "print(\"koreni polinoma p:\", koreni)\n" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.289469Z", "iopub.status.busy": "2026-09-08T15:33:33.288729Z", "iopub.status.idle": "2026-09-08T15:33:33.296213Z", "shell.execute_reply": "2026-09-08T15:33:33.295340Z" }, "id": "00b33578" }, "outputs": [], "execution_count": null }, { "id": "59937d8d", "cell_type": "code", "source": [ "p = np.array([1, -1])\n", "q = np.array([1, -2])\n", "\n", "r = np.convolve(p, q) # r(x) = (x-1)(x-2) = x^2 - 3x + 2\n", "print(\"r =\", r)\n", "print(\"provera preko roots:\", np.roots(r))" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.298323Z", "iopub.status.busy": "2026-09-08T15:33:33.297647Z", "iopub.status.idle": "2026-09-08T15:33:33.303359Z", "shell.execute_reply": "2026-09-08T15:33:33.302476Z" }, "id": "59937d8d", "outputId": "448cbd11-ca20-45ff-9fba-aa0654309db5", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "r = [ 1 -3 2]\n,provera preko roots: [2. 1.]\n" } ], "execution_count": null }, { "id": "78583ffc", "cell_type": "markdown", "source": [ "### 3.10 Ostale korisne funkcije\n", "\n", "- `np.argsort(x)` — vraća indekse koji bi niz `x` sortirali (korisno npr. da se urede čvorovi interpolacije)\n", "- `np.allclose(a, b)` — proverava da li su dva niza **približno jednaka** (do na malu toleranciju) — bolje od `a == b` kada radimo sa `float` brojevima\n", "- `np.isreal(z)` — proverava da li je (kompleksan) broj realan; u kombinaciji sa `.real` izdvajamo realan deo. Koristi se npr. kod filtriranja realnih korena polinoma dobijenih preko `np.roots`\n" ], "metadata": { "id": "78583ffc" } }, { "id": "baf85d92", "cell_type": "code", "source": [ "x = np.array([3.0, 1.0, 4.0, 1.5, 2.0])\n", "indeksi = np.argsort(x)\n", "print(\"indeksi za sortiranje:\", indeksi)\n", "print(\"sortiran niz:\", x[indeksi])\n", "\n", "print(np.allclose(0.1 + 0.2, 0.3))\n", "print(0.1 + 0.2 == 0.3)" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.322988Z", "iopub.status.busy": "2026-09-08T15:33:33.322200Z", "iopub.status.idle": "2026-09-08T15:33:33.328267Z", "shell.execute_reply": "2026-09-08T15:33:33.327438Z" }, "id": "baf85d92", "outputId": "abde11a6-86db-4a2f-dfe3-c97e12394188", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "indeksi za sortiranje: [1 3 4 0 2]\n,sortiran niz: [1. 1.5 2. 3. 4. ]\n,True\n,False\n" } ], "execution_count": null }, { "id": "aa1d5b43", "cell_type": "code", "source": [ "p = np.array([1, -1, 1, -1]) # p(x) = x^2 + 1 -> koreni su 1, i, -i\n", "koreni = np.roots(p)\n", "print(\"svi koreni:\", koreni)\n", "\n", "realni = koreni[np.isreal(koreni)].real\n", "print(\"samo realni koreni:\", realni)" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.330584Z", "iopub.status.busy": "2026-09-08T15:33:33.329999Z", "iopub.status.idle": "2026-09-08T15:33:33.335206Z", "shell.execute_reply": "2026-09-08T15:33:33.334216Z" }, "id": "aa1d5b43", "outputId": "b11a1d83-64c1-42e3-e4d4-84d1a8b81413", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "svi koreni: [1.+0.j 0.+1.j 0.-1.j]\n,samo realni koreni: [1.]\n" } ], "execution_count": null }, { "id": "c6a888d9", "cell_type": "markdown", "source": [ "### 3.11 Kontrola ispisa NumPy nizova\n", "\n", "Podrazumevano, NumPy ispisuje nizove sa ograničenim brojem decimala. Preko `np.set_printoptions` možemo trajno promeniti format ispisa za sve nizove u nastavku sveske (npr. broj decimala, potiskivanje naučne notacije).\n" ], "metadata": { "id": "c6a888d9" } }, { "id": "d6d62bf3", "cell_type": "code", "source": [ "np.set_printoptions()\n", "x = np.array([1/3, 2/7, np.pi])\n", "print(\"podrazumevano:\", x)\n", "\n", "np.set_printoptions(precision=4, suppress=True) # 3 decimale, bez naucne notacije\n", "print(\"posle set_printoptions:\", x)\n", "\n", "np.set_printoptions()" ], "metadata": { "execution": { "iopub.execute_input": "2026-09-08T15:33:33.336936Z", "iopub.status.busy": "2026-09-08T15:33:33.336605Z", "iopub.status.idle": "2026-09-08T15:33:33.342050Z", "shell.execute_reply": "2026-09-08T15:33:33.341064Z" }, "id": "d6d62bf3", "outputId": "dfec0915-9195-4589-aa0a-f741b878a64a", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": "podrazumevano: [0.3333 0.2857 3.1416]\n,posle set_printoptions: [0.3333 0.2857 3.1416]\n" } ], "execution_count": null }, { "id": "f683acc1-de72-4c92-9fec-a3d719c473de", "cell_type": "markdown", "source": [ "## 4. Matplotlib" ], "metadata": { "id": "f683acc1-de72-4c92-9fec-a3d719c473de" } }, { "id": "a1b979f4-eeb2-48e8-a99a-921e7c28ad56", "cell_type": "markdown", "source": [ "**Matplotlib** je biblioteka za crtanje grafika. U ovom kursu će nam biti potrebna prvenstveno za:\n", "- crtanje grafika funkcije i njene aproksimacije (npr. interpolacionog polinoma preko originalne funkcije),\n", "- vizuelizaciju konvergencije numeričke metode (greška u zavisnosti od broja iteracija ili broja čvorova).\n", "\n", "Podmodul koji koristimo zove se `pyplot`, standardno se uvozi pod skraćenim imenom `plt`.\n" ], "metadata": { "id": "a1b979f4-eeb2-48e8-a99a-921e7c28ad56" } }, { "id": "6d2c30d2-b95c-44db-9a1f-01e706383c86", "cell_type": "code", "source": [ "import matplotlib.pyplot as plt\n" ], "metadata": { "trusted": true, "id": "6d2c30d2-b95c-44db-9a1f-01e706383c86" }, "outputs": [], "execution_count": null }, { "id": "ed749dd2-f3e6-4aa9-9fc1-6d91e9768208", "cell_type": "markdown", "source": [ "### 4.1 Osnovni grafik: `plt.plot`\n", "\n", "Funkcija `plt.plot(x, y)` crta liniju kroz tačke zadate nizovima `x` i `y` (najčešće NumPy nizovima, iz odeljka 3). Grafik se prikazuje pozivom `plt.show()` na kraju.\n", "\n", "Za crtanje grafika funkcije na nekom intervalu, neophodno je koristiti velik broj gusto raspoređenih tačaka. Ovo se postiže pozivanjem funkcije `np.linspace`.\n" ], "metadata": { "id": "ed749dd2-f3e6-4aa9-9fc1-6d91e9768208" } }, { "id": "90265421-ee53-479c-94ba-7dcb8e9b21cb", "cell_type": "code", "source": [ "x = np.linspace(-2, 2, 200) # 200 gusto rasporedjenih tacaka\n", "y = x ** 2\n", "\n", "plt.plot(x, y)\n", "plt.show()\n" ], "metadata": { "trusted": true, "id": "90265421-ee53-479c-94ba-7dcb8e9b21cb", "outputId": "65365b83-78c4-4ad3-d2e0-ff642b284d4e" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
", "image/png": 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" }, "metadata": {} } ], "execution_count": null }, { "id": "1e0632d0-a26b-468b-8b4a-fea379ad54b6", "cell_type": "markdown", "source": [ "### 4.2 Više grafika na istoj slici, više slika, legenda\n", "\n", "Više poziva `plt.plot(...)` pre `plt.show()` iscrtava sve grafike na **istoj** slici. Za razlikovanje grafika na slici korsino je napraviti legendu, što se postiže argumentom `label` i pozivanjem `plt.legend()` pre crtanja.\n", "\n", "Kako bi se grafici razdvojili na više slika, neophodno je pozvati `plt.figure()`, pre crtanja sledećeg grafika.\n" ], "metadata": { "id": "1e0632d0-a26b-468b-8b4a-fea379ad54b6" } }, { "id": "1089e59a-9ac3-4763-82b7-6d0b6ad00f9b", "cell_type": "code", "source": [ "x = np.linspace(0, 2 * np.pi, 200)\n", "\n", "plt.plot(x, np.sin(x), label=\"sin(x)\")\n", "plt.plot(x, np.cos(x), label=\"cos(x)\")\n", "plt.legend()\n", "plt.figure()\n", "plt.plot(x,np.exp(x))\n", "plt.show()" ], "metadata": { "trusted": true, "scrolled": true, "id": "1089e59a-9ac3-4763-82b7-6d0b6ad00f9b", "outputId": "ff81e69c-b572-4920-8f9c-1666dd033b1f" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
", "image/png": 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" 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" }, "metadata": {} } ], "execution_count": null }, { "id": "54505439-6ea3-40f6-b09c-af121e3ff6d8", "cell_type": "markdown", "source": [ "### 4.3 Tačke na grafiku: `plt.scatter`\n", "\n", "Dok `plt.plot` povezuje tačke linijom, `plt.scatter(x, y)` iscrtava **samo tačke** (bez povezivanja). Koristi se npr. da se na grafiku istaknu čvorovi interpolacije preko krive funkcije ili interpolacionog polinoma.\n" ], "metadata": { "id": "54505439-6ea3-40f6-b09c-af121e3ff6d8" } }, { "id": "bdfa643c-aaf4-455e-8edb-1c68c834b8bc", "cell_type": "code", "source": [ "f = lambda x: np.sin(x)\n", "\n", "x = np.linspace(0, 2 * np.pi, 200)\n", "cvorovi = np.linspace(0, 2 * np.pi, 6)\n", "\n", "plt.plot(x, f(x), label=\"f(x) = sin(x)\")\n", "plt.scatter(cvorovi, f(cvorovi), label=\"čvorovi interpolacije\")\n", "plt.legend()\n", "plt.show()" ], "metadata": { "trusted": true, "id": "bdfa643c-aaf4-455e-8edb-1c68c834b8bc", "outputId": "f441b9e4-6259-4a03-9787-5f970e62825f" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
", "image/png": 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" }, "metadata": {} } ], "execution_count": null }, { "id": "df00645e-bd29-49e6-ada9-6cb8049687c8", "cell_type": "markdown", "source": [ "### 4.4 Logaritamske ose: `plt.semilogy`, `plt.semilogx`\n", "\n", "Kada analiziramo **konvergenciju** numeričke metode, greška često opada eksponencijalno brzo sa brojem iteracija. Na običnom (linearnom) grafiku bi to izgledalo kao linija zalepljena za nulu. Zato se greška obično crta na logaritamskoj y-osi:\n", "\n", "- `plt.semilogy(x, y)` — logaritamska skala na y-osi\n", "- `plt.semilogx(x, y)` — logaritamska skala na x-osi\n", "- (postoji i `plt.loglog` — logaritamska skala na obe ose)\n", "\n", "Na ovakvom grafiku, geometrijski (eksponencijalno) opadajuća greška izgleda kao prava linija.\n" ], "metadata": { "id": "df00645e-bd29-49e6-ada9-6cb8049687c8" } }, { "id": "cb8345e2-84dd-4196-a223-92d963467108", "cell_type": "code", "source": [ "n_iter = np.arange(1, 15)\n", "greska = 0.5 ** n_iter\n", "\n", "plt.plot(n_iter, greska)\n", "plt.show()\n", "\n", "plt.figure()\n", "plt.semilogy(n_iter, greska)\n", "plt.show()" ], "metadata": { "trusted": true, "scrolled": true, "id": "cb8345e2-84dd-4196-a223-92d963467108", "outputId": "7951b690-c2c0-4fef-c745-b095c5a1aae2" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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" 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" }, "metadata": {} } ], "execution_count": null }, { "id": "746d0fac-f890-4d49-bb86-429f45b4d4dc", "cell_type": "markdown", "source": [ "### 4.5 Dodatna podešavanja grafika\n", "\n", "- `plt.axhline(y)` — crta horizontalnu pravu\n", "- `plt.avhline(x)` — crta vertikalnu pravu \n", "- `plt.xlim(a, b)` / `plt.ylim(a, b)` — ograničava opseg prikaza na osama\n", "- `plt.grid(True)` —\n", "- `plt.xlabel(\"...\")` — dodaje opis x ose\n", "- `plt.ylabel(\"...\")` — dodaje opis y ose\n", "- `plt.title(\"...\")` — dodaje naslov grafiku" ], "metadata": { "id": "746d0fac-f890-4d49-bb86-429f45b4d4dc" } }, { "id": "5fbbf08c-d670-42ec-9371-7f9503669a92", "cell_type": "code", "source": [ "x = np.linspace(-3, 3, 200)\n", "y = x ** 3 - 3 * x\n", "\n", "plt.plot(x, y)\n", "plt.axhline(y=0)\n", "plt.axvline(x=0)\n", "plt.ylim(-5, 5)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"f(x)\")\n", "plt.title(\"f(x) = x^3 - 3x\")\n", "plt.grid(True)\n", "plt.show()" ], "metadata": { "trusted": true, "id": "5fbbf08c-d670-42ec-9371-7f9503669a92", "outputId": "74158ccc-885e-4165-eb96-74cc961ef257" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
", "image/png": 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" }, "metadata": {} } ], "execution_count": null } ] }