{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sveiki! \n",
    "\n",
    "Šiandien pasimokysime modeliavimo pagrindų su python jupyter notebook aplinkoje.\n",
    "\n",
    "Kiekviename langelyje galime užrašyti ir įvyktdyti įvairias python komandas.\n",
    "\n",
    "    shift+enter = run cell and jump to the next (creating a new cell if there is no other new one)\n",
    "    ctrl+enter  = run cell-in place\n",
    "    alt+enter   = run cell and insert a new one below\n",
    "\n",
    "# Pirmas skyrius\n",
    "## Paprastos python komandos\n",
    "\n",
    "Pradėkime su paprasta spausdinimo funkcija."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sveikas pasaulį!\n"
     ]
    }
   ],
   "source": [
    "print(\"Sveikas pasaulį!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tekstą išskiriame kabutėmis. Galima naudoti viengubas '' ir dvigubas \"\" kabutes. Be kabučių simboliai yra interpretuojami kaip kintamųjų padavinimas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Šiandien yra vasario 17 d.\n",
      "Dabartiniai metai nera 2022\n"
     ]
    }
   ],
   "source": [
    "data = \"vasario 17 d.\"\n",
    "print(\"Šiandien yra\", data)\n",
    "print(\"Dabartiniai metai nera\",2022)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Su Python galima atlikti įvairius matematinius veiksmus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2+2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kelimas laipsniu, pavyzdžiui, $3^3$ yra rašomas taip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9543127065508336e+21"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3.0**45"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Didelius skaičius, pavyzdžiui, $6,3\\cdot 10^{23}$ taip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.3e+23"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "6.3e23"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sudėtingesnes funkcijas galime gauti, jei įkelsime **numpy** biblioteką."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 2.718281828459045 1.0 8.0 5\n"
     ]
    }
   ],
   "source": [
    "print(np.sin(np.pi/2), np.exp(1.0), np.log10(10), np.sqrt(64), np.abs(-5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Klausimas\n",
    "Kiek sekundžių trunka mikrometai?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31.536"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "365*24*60*60/1e6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Antras skyrius\n",
    "## numpy array\n",
    "Dažnai tenka manipuliuoti ne pavienius skaičius, bet duomenų masyvus: vektorius, matricas. Tam patogu naudoti nupmy array duomenų tipą."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ] (11,) 11\n"
     ]
    }
   ],
   "source": [
    "a=np.array([0.0, 0.1, 0.2,  0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0])\n",
    "print(a, a.shape, len(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python naudoja numeraciją prasidedančią nuo nulio. Galima naudoti ir neigiamus indeksus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 0.1 1.0 0.9\n"
     ]
    }
   ],
   "source": [
    "print(a[0], a[1], a[-1], a[-2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Galima manipuliuoti ir įvairiomis sekomis, pavyzdžiu a[1:5] (paskutinis indekas nera įskaičiuojamas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.  0.1 0.2 0.3 0.4]\n",
      "[0.5 0.6]\n"
     ]
    }
   ],
   "source": [
    "print(a[:5])\n",
    "print(a[5:7])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Įvairios kitos variacijos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.1 0.3 0.5 0.7]\n"
     ]
    }
   ],
   "source": [
    "print(a[1:8:2])\n",
    "#print(a[::-1])\n",
    "#print(a)\n",
    "#print(a>0.5)\n",
    "#print(a[a>0.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## automatinis generavimas ir veiksmai su numpy array\n",
    "Atliekant visokius skaičiavimus dažnai tenka naudoti vienodai įvairiais automatiškai sugeneruotus duomenų masyvus. Tam galima naudoti įvairias numpy komandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "n=15\n",
    "x0=0\n",
    "x1=10\n",
    "#print(np.linspace(x0,x1,n,endpoint=False ))\n",
    "#print(np.arange(2,n))\n",
    "print(np.zeros(n))\n",
    "print(np.ones(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "?np.linspace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "numpy array galima manipuliuoti kaip skaičius. Matematinės operacijos atliekamos su visais sekos nariais."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5]\n",
      "[1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "a=np.arange(1,6)\n",
    "b=np.ones(5)\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  4  9 16 25]\n",
      "[2. 2. 2. 2. 2.]\n",
      "[0. 1. 2. 3. 4.]\n"
     ]
    }
   ],
   "source": [
    "print(a**2)\n",
    "print(2*b)\n",
    "print(a-b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trečias skyrius\n",
    "## Grafikų braižymas\n",
    "Tam naudojama matplotlib biblioteka"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-38-9951e1c786fa>:2: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  y=1/x\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(0,1,100)\n",
    "y=1/x\n",
    "plt.plot(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grafikus galima papildyti ir pagražinti įvairiomis papildomis funkcijomis. Gražus duomenų apipavidalinimas yra labai svarbus mokslo sklaidoje!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "font = {'family' : 'sans',\n",
    "        'weight' : 'bold',\n",
    "        'size'   : 14}\n",
    "matplotlib.rc('font', **font)\n",
    "\n",
    "\n",
    "x=np.linspace(-1,1,100)\n",
    "y=np.sin(2*np.pi*x)\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "\n",
    "plt.plot(x,y, \"r-.\", lw=\"3\", label=\"$y=\\sin(2\\pi x)$\")\n",
    "plt.plot(x,y*0, 'k')\n",
    "plt.plot(x,np.cos(2*np.pi*x), \"b--\", lw=\"3\", label=\"$y=\\cos(2\\pi x)$\")\n",
    "plt.fill_between(x,np.cos(2*np.pi*x),y)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.xlim([-1,1.0])\n",
    "plt.ylim([-1.2,1.2])\n",
    "#ax=plt.gca()\n",
    "#ax.set_aspect('equal')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Užduotis\n",
    "Nubrėžkite spindulio $r=3$ apskritimą. \n",
    "\n",
    "Jei apskritimas atrodo kaip elipsė, išbandykite šias komandas\n",
    "\n",
    "ax=plt.gca()\n",
    "\n",
    "ax.set_aspect('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(-3,3,100)\n",
    "# x^2+y^2=r^2\n",
    "# y = sqrt(r^2-x^2)\n",
    "y=np.sqrt(3**2-x**2)\n",
    "plt.plot(x,y,\"b\")\n",
    "plt.plot(x,-y,\"b\")\n",
    "ax=plt.gca()\n",
    "ax.set_aspect('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ketvirtas skyrius\n",
    "## **for** ir **if** komandos bei fukcijos\n",
    "\n",
    "Programavime dažnai naudojami ciklai bei loginės operacijos\n",
    "\n",
    "Skirtingus blokus python atskiria atitraukimu nuo krašto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12 yra lyginis skačius\n"
     ]
    }
   ],
   "source": [
    "x=12\n",
    "# \"x % 2\" yra modulio komanda, tai yra X % 2 nuoda dalybos is 2 liekaną\n",
    "if x % 2 == 0:\n",
    "    print(x,\"yra lyginis skačius\")\n",
    "elif x % 2 == 1:\n",
    "    print(x,\"yra nelyginis skačius\")\n",
    "else:\n",
    "    print(x,\"nėra sveikasis skačius\")\n",
    "    \n",
    "x=7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Patogu sukurti funkciją, kuri atspausdintų atsakymą"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def arlyginis(x):\n",
    "    if x % 2 == 0:\n",
    "        print(x, \"yra lyginis skačius\")\n",
    "    elif x % 2 == 1:\n",
    "        print(x, \"yra nelyginis skačius\")\n",
    "    else:\n",
    "        print(x, \"nėra sveikasis skačius\")\n",
    "    \n",
    "    return x % 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13 yra nelyginis skačius\n",
      "liekana yra  1\n"
     ]
    }
   ],
   "source": [
    "print(\"liekana yra \", arlyginis(13))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for ciklo metu yra įvykdoma tos pačios komandos pakartotinai"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 yra lyginis skačius\n",
      "1 yra nelyginis skačius\n",
      "2 yra lyginis skačius\n",
      "3 yra nelyginis skačius\n",
      "4 yra lyginis skačius\n",
      "5 yra nelyginis skačius\n",
      "6 yra lyginis skačius\n",
      "7 yra nelyginis skačius\n",
      "8 yra lyginis skačius\n",
      "9 yra nelyginis skačius\n",
      "10 yra lyginis skačius\n",
      "11 yra nelyginis skačius\n",
      "12 yra lyginis skačius\n",
      "13 yra nelyginis skačius\n",
      "14 yra lyginis skačius\n"
     ]
    }
   ],
   "source": [
    "for x in np.arange(15):\n",
    "    liekana=arlyginis(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "be numpy array galima naudoti ir python list duomenų tipą."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32\n",
      "1 N\n",
      "2 e\n",
      "3 b\n",
      "4 e\n",
      "5 p\n",
      "6 r\n",
      "7 i\n",
      "8 s\n",
      "9 i\n",
      "10 k\n",
      "11 i\n",
      "12 š\n",
      "13 k\n",
      "14 i\n",
      "15 a\n",
      "16 k\n",
      "17 o\n",
      "18 p\n",
      "19 u\n",
      "20 s\n",
      "21 t\n",
      "22 e\n",
      "23 l\n",
      "24 i\n",
      "25 a\n",
      "26 u\n",
      "27 d\n",
      "28 a\n",
      "29 v\n",
      "30 o\n",
      "31 m\n",
      "32 e\n"
     ]
    }
   ],
   "source": [
    "žodis=\"Nebeprisikiškiakopusteliaudavome\"\n",
    "print(len(žodis))\n",
    "i=1\n",
    "for raidė in žodis:\n",
    "    print(i,raidė)\n",
    "    i = i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Žiema\n",
      "žiema\n",
      "bėk\n",
      "iš\n",
      "kiemo\n"
     ]
    }
   ],
   "source": [
    "sakinys=[\"Žiema\", \"žiema\", \"bėk\", \"iš\", \"kiemo\"]\n",
    "for žodis in sakinys:\n",
    "    print(žodis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Užduotis\n",
    "Suskaičiuokite sveikųjų skaičių nuo vieno iki šimto kvadratų sumą.\n",
    "\n",
    "Pabandykite panauditi for ciklą.\n",
    "\n",
    "Python for ciklai nėra greiti. Tą patį atsakymą galima gauti daug greičiau naudojant numpy array\n",
    "\n",
    "np.sum(np.arange(1,101)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "338350\n"
     ]
    }
   ],
   "source": [
    "sum=0\n",
    "for x in np.arange(101):\n",
    "    sum = sum + x**2\n",
    "print(sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "338350"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.arange(1,101)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}