{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "70a97fda", "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "markdown", "id": "a075044c", "metadata": {}, "source": [ "# Tworzenie tablic w Numpy" ] }, { "cell_type": "markdown", "id": "c49f0c97", "metadata": {}, "source": [ "Podstawowym typem danych w numpy jest tablica (array). Poniżej pokażę jak możemy utworzyć tablicę oraz kilka użytecznych funkcji." ] }, { "cell_type": "code", "execution_count": 2, "id": "7b3251cd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 2 3 4 5]\n" ] } ], "source": [ "# tworzenie z listy \n", "tab = np.array( [1,2,3,4,5] )\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 3, "id": "2b585551", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 2 3 4 5]\n", "[1 2 3 4 5 6]\n" ] } ], "source": [ "# dodanie elementu na koncu (niewskazane)\n", "tab2 = np.append(tab, 6)\n", "print(tab) # nie zmienia sie \n", "print(tab2) # nowa tablica" ] }, { "cell_type": "code", "execution_count": 4, "id": "409992d2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n" ] } ], "source": [ "# tablica 10 zer\n", "tab = np.zeros(10)\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 5, "id": "6ad20d15", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n" ] } ], "source": [ "# tablica 10x10 zer\n", "tab = np.zeros(shape=(10,10))\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 6, "id": "0f84a837", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0 1 4 9 16 25 36 49 64 81]\n" ] } ], "source": [ "# tablica z istniejącej listy\n", "lista = [x**2 for x in range(10)]\n", "tab = np.array(lista)\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 7, "id": "33a04e1d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1. 0. 0. 0. 0.]\n", " [0. 1. 0. 0. 0.]\n", " [0. 0. 1. 0. 0.]\n", " [0. 0. 0. 1. 0.]\n", " [0. 0. 0. 0. 1.]]\n" ] } ], "source": [ "# macierz jednostkowa\n", "tab = np.eye(5)\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 8, "id": "5dc6c1f7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n" ] } ], "source": [ "# tablica samych jedynek\n", "tab = np.ones(10)\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 9, "id": "f43ecf44", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69\n", " 72 75 78 81 84 87 90 93 96 99]\n" ] } ], "source": [ "# tablica w stylu range: liczby całkowite od 0 do 100 co 3\n", "tab = np.arange(0, 100, 3)\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 10, "id": "b7ef9792", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-1. -0.77777778 -0.55555556 -0.33333333 -0.11111111 0.11111111\n", " 0.33333333 0.55555556 0.77777778 1. ]\n" ] } ], "source": [ "# tablica zawierająca N=10 równoodległych liczb rzeczywistych między -1 a 1\n", "tab = np.linspace(-1, 1, 10)\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 11, "id": "1ce354bf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.74956532 0.03347892 0.97571798 0.11167255 0.37396609 0.62097276\n", " 0.4060238 0.71551768 0.12457409 0.17107743 0.99945704 0.45472785\n", " 0.34283032 0.13786376 0.15515641 0.37338266 0.32479351 0.64910335\n", " 0.59414893 0.05779447 0.87401075 0.68359792 0.04838798 0.07924221\n", " 0.570686 0.19006888 0.33469417 0.01025991 0.45358835 0.22136124]\n" ] } ], "source": [ "# tablica 1D 1000 liczb z rozkładu jednostajnego\n", "from numpy.random import uniform\n", "tab = uniform(size=1000)\n", "# wypiszmy pierwsze 30 liczb\n", "print(tab[:30])" ] }, { "cell_type": "code", "execution_count": 12, "id": "46b5ee45", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([74., 63., 60., 68., 57., 63., 67., 54., 62., 71., 70., 72., 78.,\n", " 60., 81.]),\n", " array([4.20977951e-04, 6.70233823e-02, 1.33625787e-01, 2.00228191e-01,\n", " 2.66830595e-01, 3.33433000e-01, 4.00035404e-01, 4.66637809e-01,\n", " 5.33240213e-01, 5.99842617e-01, 6.66445022e-01, 7.33047426e-01,\n", " 7.99649830e-01, 8.66252235e-01, 9.32854639e-01, 9.99457044e-01]),\n", " )" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# sprawdzmy czy faktycznie rozkład jest jednostajny\n", "import matplotlib.pyplot as plt\n", "plt.hist(tab, 15)" ] }, { "cell_type": "code", "execution_count": 13, "id": "efb737dc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.66993795 0.99788546 -1.75696131 -0.36373961]\n", " [ 1.04493169 0.10122398 0.80691192 0.33439241]\n", " [ 1.43029884 -0.38870587 -0.08131077 0.23009756]]\n" ] } ], "source": [ "# tablica 2D (3x4) liczb losowych z rozkładu normalnego o sredniej 0 i odchyleniu 1\n", "from numpy.random import normal\n", "tab = normal(0, 1, size=(3,4))\n", "print(tab)" ] }, { "cell_type": "markdown", "id": "ccc44d19", "metadata": {}, "source": [ "# Rozmiary" ] }, { "cell_type": "markdown", "id": "2cdd8929", "metadata": {}, "source": [ "Każda tablica ma swój kształt \"shape\". Jeżeli chcemy operować na kilku tablicach to musimy pamiętać, \n", "żeby ich rozmiary były odpowiednie, np. do mnożenia macierzowego. Poniżej pokażę kilka użytecznych funkcji." ] }, { "cell_type": "code", "execution_count": 14, "id": "ba0e2b71", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15]\n" ] } ], "source": [ "tab = np.arange(16)\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 15, "id": "0c182f17", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(16,)\n" ] } ], "source": [ "# wypiszmy rozmiar tab\n", "print(tab.shape)" ] }, { "cell_type": "code", "execution_count": 16, "id": "f462d408", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(4, 4)\n", "[[ 0 1 2 3]\n", " [ 4 5 6 7]\n", " [ 8 9 10 11]\n", " [12 13 14 15]]\n" ] } ], "source": [ "# tab jest jendowymiarową tablicą, zróbmy z niej tablicę 4x4\n", "tab = tab.reshape(4,4) \n", "print(tab.shape)\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 17, "id": "bb155b4d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-1 0 1 2]\n", " [ 3 4 5 6]\n", " [ 7 8 9 10]\n", " [11 12 13 14]]\n" ] } ], "source": [ "# Stwórzmy drugą tablicę\n", "tab2 = np.arange(-1, 15).reshape(4,4)\n", "print(tab2)" ] }, { "cell_type": "code", "execution_count": 18, "id": "2dde6b97", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[[ 0 1 2 3]\n", " [ 4 5 6 7]\n", " [ 8 9 10 11]\n", " [12 13 14 15]]\n", "\n", " [[-1 0 1 2]\n", " [ 3 4 5 6]\n", " [ 7 8 9 10]\n", " [11 12 13 14]]]\n" ] } ], "source": [ "# Połączmy dwie tablice wzdluz osi 0\n", "stab = np.stack([tab, tab2], axis=0)\n", "print(stab)" ] }, { "cell_type": "code", "execution_count": 19, "id": "c03e2cc1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2, 4, 4)\n" ] } ], "source": [ "print(stab.shape)" ] }, { "cell_type": "code", "execution_count": 20, "id": "56453140", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[[ 0 1 2 3]\n", " [-1 0 1 2]]\n", "\n", " [[ 4 5 6 7]\n", " [ 3 4 5 6]]\n", "\n", " [[ 8 9 10 11]\n", " [ 7 8 9 10]]\n", "\n", " [[12 13 14 15]\n", " [11 12 13 14]]]\n" ] } ], "source": [ "# Połączmy dwie tablice wzdluz osi 1\n", "stab = np.stack([tab, tab2], axis=1)\n", "print(stab)" ] }, { "cell_type": "code", "execution_count": 21, "id": "8d65bbaa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(4, 2, 4)\n" ] } ], "source": [ "print(stab.shape)" ] }, { "cell_type": "code", "execution_count": 22, "id": "0612b46d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0 1 2 3 -1 0 1 2 4 5 6 7 3 4 5 6 8 9 10 11 7 8 9 10\n", " 12 13 14 15 11 12 13 14]\n", "\n", "[ 0 1 2 3 -1 0 1 2 4 5 6 7 3 4 5 6 8 9 10 11 7 8 9 10\n", " 12 13 14 15 11 12 13 14]\n" ] } ], "source": [ "# spłaszczmy tablicę stab do 1D\n", "print(stab.reshape(-1))\n", "print()\n", "# inny sposób\n", "print(stab.flatten())" ] }, { "cell_type": "markdown", "id": "47d0f6f7", "metadata": {}, "source": [ "# Operacje na tablicach" ] }, { "cell_type": "markdown", "id": "cdec9ff4", "metadata": {}, "source": [ "Poniżej pokaże kilka podstawowych operacji na tablicach." ] }, { "cell_type": "code", "execution_count": 23, "id": "6f384d38", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-5\n", "-4\n", "-3\n", "-2\n", "-1\n", "0\n", "1\n", "2\n", "3\n", "4\n" ] } ], "source": [ "# iterowanie\n", "tab = np.arange(-5,5)\n", "for em in tab:\n", " print(em)" ] }, { "cell_type": "code", "execution_count": 24, "id": "0d023354", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1 2 3 4 5 6 7 8 9 10]\n", "[-10 -9 -8 -7 -6 -5 -4 -3 -2 -1]\n", "[-9 -7 -5 -3 -1 1 3 5 7 9]\n", "[11 11 11 11 11 11 11 11 11 11]\n" ] } ], "source": [ "# dodawanie i odejmowanie\n", "tab1 = np.arange(1,11)\n", "print(tab1)\n", "tab2 = np.arange(-10, 0)\n", "print(tab2)\n", "print(tab1+tab2)\n", "print(tab1-tab2)" ] }, { "cell_type": "code", "execution_count": 25, "id": "83e8aafc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[3. 0. 0.]\n", " [0. 3. 0.]\n", " [0. 0. 3.]]\n" ] } ], "source": [ "# mnożenie przez liczbę\n", "tab = np.eye(3)\n", "print(tab*3)" ] }, { "cell_type": "code", "execution_count": 26, "id": "f5f306e6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 2]\n", " [3 4 5]]\n", "\n", "[[0 3]\n", " [1 4]\n", " [2 5]]\n" ] } ], "source": [ "# transponowanie\n", "tab = np.arange(6).reshape(2,3)\n", "print(tab)\n", "print()\n", "print(tab.transpose())" ] }, { "cell_type": "code", "execution_count": 27, "id": "5e31a6e6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 0]\n", " [ 0 -1]]\n", "\n", "[[0 1]\n", " [1 0]]\n", "\n", "[[ 0 1]\n", " [-1 0]]\n" ] } ], "source": [ "# mnożenie macierzowe za pomocą operatora @\n", "A = np.array([[1,0],[0, -1]])\n", "B = np.array([[0,1],[1,0]])\n", "print(A)\n", "print()\n", "print(B)\n", "print()\n", "print(A @ B)" ] }, { "cell_type": "code", "execution_count": 28, "id": "a31b9997", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0 1]\n", " [-1 0]]\n" ] } ], "source": [ "# mnozenie macierzowe za pomocą metody .dot\n", "print(A.dot(B))" ] }, { "cell_type": "code", "execution_count": 29, "id": "91cd25c2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 0]\n", " [ 0 -4]]\n", "[[0 2]\n", " [3 0]]\n" ] } ], "source": [ "# mnożenie element po elemencie\n", "C = np.array([[1,2],[3,4]])\n", "print(A * C)\n", "print(B * C)" ] }, { "cell_type": "code", "execution_count": 275, "id": "234e1285", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-2.0000000000000004\n" ] } ], "source": [ "# liczenie wyznacznika\n", "M = [[1,2],[3,4]]\n", "print(np.linalg.det(M))" ] }, { "cell_type": "code", "execution_count": 274, "id": "7c051dee", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.25 0. ]\n", " [0. 0.5 ]]\n" ] } ], "source": [ "# odwracanie macierzy\n", "A = [[4,0],[0,2]]\n", "print(np.linalg.inv(A))" ] }, { "cell_type": "markdown", "id": "4cfb1b24", "metadata": {}, "source": [ "# Warunki logiczne i wybieranie danych" ] }, { "cell_type": "markdown", "id": "14278853", "metadata": {}, "source": [ "Poniżej pokażę jak można wybierać podzbiór danych z tablicy, na podstawie warunków logicznych." ] }, { "cell_type": "code", "execution_count": 30, "id": "4b6defe4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\n", " 24 25 26 27 28 29]\n" ] } ], "source": [ "tab = np.arange(0, 30)\n", "print(tab)" ] }, { "cell_type": "code", "execution_count": 31, "id": "ca5daf1d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ True False True False True False True False True False True False\n", " True False True False True False True False True False True False\n", " True False True False True False]\n" ] } ], "source": [ "# możemy używać operatorów \"na tablicach\" w wyniku dostajemy tablice wartości logicznych\n", "print(tab%2==0) " ] }, { "cell_type": "code", "execution_count": 32, "id": "e0882886", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28]\n" ] } ], "source": [ "# Używamy tablicy Prawda/Fałsz do stworzenia nowej tablicy z danych, dla których jest Prawda\n", "cond = tab%2==0\n", "print(tab[cond])" ] }, { "cell_type": "code", "execution_count": 33, "id": "87201274", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[False False False False False False False False False False False True\n", " False True False True False True False True False False False False\n", " False False False False False False]\n", "[11 13 15 17 19]\n" ] } ], "source": [ "# Możemy łączyć warunki stosując mnożenie element po elemencie\n", "cond1 = tab%2 == 1\n", "cond1.reshape(1, cond1.shape[0])\n", "cond2 = tab>10\n", "cond2.reshape(1, cond2.shape[0])\n", "cond3 = tab<20\n", "cond3.reshape(1, cond3.shape[0])\n", "cond = cond1 * cond2 * cond3\n", "print(cond)\n", "print(tab[cond])" ] }, { "cell_type": "code", "execution_count": 34, "id": "b3f6114a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(array([ 1, 2, 3, 7, 8, 9, 13, 14, 15, 19, 20, 21, 26, 27, 28]),)\n" ] } ], "source": [ "# inny sposób to użycie np.where\n", "print(np.where( np.sin(tab)>0 ) )" ] }, { "cell_type": "markdown", "id": "99b5d63a", "metadata": {}, "source": [ "# Zadanie 1 -- Estymacja liczby PI metodą Monte Carlo" ] }, { "cell_type": "markdown", "id": "851882f1", "metadata": {}, "source": [ "Symulacja Monte Carlo, nazywana również metodą Monte Carlo lub wielokrotną symulacją prawdopodobieństwa, jest metodą matematyczną stosowaną do określania możliwych skutków niepewnego zdarzenia. Metodę Monte Carlo wymyślili John von Neumann i Stanisław Ulam w czasie II wojny światowej w celu usprawnienia procesu podejmowania decyzji w niepewnych warunkach. Nazwa pochodzi od słynącego z kasyn osiedla Monako, ponieważ tak jak w grze w ruletkę podstawę modelowania stanowi tu element losowy." ] }, { "cell_type": "markdown", "id": "e566476a", "metadata": {}, "source": [ "Wykorzystamy metodę Monte Carlo do oszacowania liczby PI. Wyobraź sobie koło jednostkowe o środku w układzie współrzędnych. Na kole tym możemy opisać kwadrat o boku 2. Koło ma pole równe PI, natomiast kwadrat ma pole równe 4, zatem ich stosunek wynosi PI/4. Wyobraź sobie teraz, że wybierasz w sposób losowy punkt na kwadracie. Jeżeli punkt znajduje się wewnątrz koła to go zachowujesz, jeżeli poza kołem to odrzucasz. Następnie postępujesz w taki sam sposób z kolejnymi punktami. Przyjrzyj się poniższemu obrazkowi..." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "6859bd40", "metadata": {}, "source": [ "![image.png](attachment:image.png)" ] }, { "cell_type": "markdown", "id": "28868086", "metadata": {}, "source": [ "Prawdopodobieństwo można interpretować geometrycznie. Jeżeli szansa na wylosowanie jakiegoś punktu w kwadracie wynosi P=1, to szansa wylosowania punktu wewnątrz koła wynosi P', gdzie P' < P. Ile wynosi P'? Tyle co stosunek pola koła do pola kwadratu, czyli PI/4. Zatem możemy przeprowadzić następujący eksperyment:\n", "\n", "1) Losujemy N punktów w kwadracie\n", "\n", "2) Liczymy ile z nich znajduje się wewnątrz koła: M\n", "\n", "3) Estymujemy PI = 4* M/N\n", "\n", "**Napisz program, który dokona estymacji liczby PI metodą Monte Carlo. Wykorzystaj do tego bibliotekę numpy. Nie używaj żadnych pętli. Korzystając z matplotlib narysuj obrazek podobny do przedstawionego powyżej. Przetestuj dla różnych wartości N i zaobserwuj poprawę dokładności.**" ] }, { "cell_type": "markdown", "id": "d44da37d", "metadata": {}, "source": [ "### Rozwiązanie" ] }, { "cell_type": "code", "execution_count": 35, "id": "7f0d7e1a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PI=3.1504\n" ] } ], "source": [ "N = 10000\n", "points = uniform(-1, 1, size=(2,N))\n", "incircle = lambda v: np.sqrt(v[0]**2+v[1]**2) <= 1\n", "\n", "cond = incircle(points)\n", "\n", "ok_points = np.array([points[0][cond], points[1][cond]])\n", "nook_points = np.array([points[0][~cond], points[1][~cond]])\n", "\n", "print(f\"PI={4*ok_points.shape[1]/N}\")" ] }, { "cell_type": "code", "execution_count": 36, "id": "1e93d3df", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-1.0, 1.0)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(4,4))\n", "plt.scatter(*nook_points, marker='.', color='gray')\n", "plt.scatter(*ok_points, marker='.', color='blue')\n", "plt.xlim(-1,1)\n", "plt.ylim(-1,1)" ] }, { "cell_type": "markdown", "id": "897aac91", "metadata": {}, "source": [ "# Zadanie 2 -- regresja liniowa" ] }, { "cell_type": "markdown", "id": "c3b293f7", "metadata": {}, "source": [ "W fizyce i innych naukach zdarza się, że dane układają się wzdłuż prostej, jednakże z uwagi na niepewności pomiarowe nie da się narysować jednej prostej przechodzącej przez wszystkie punkty. Powstaje zatem problem: jaka prosta najlepiej opisuje obserwowany zbiór danych? Okazuje się, że ten problem jest na tyle prosty, iż posiada rozwiązanie analityczne zwane *regresją liniową*.\n", "\n", "Generalnie, termin \"regresja\" oznacza problem opisania współzależności pomiędzy zmiennymi za pomocą funkcji matematycznej. W rozważanym przypadku funkcja jest liniowa, stąd regresja liniowa.\n", "\n", "Niech X będzie wektorem **kolumnowym** zawierającym dwie **kolumny**: pierwsza to kolumna samych jedynek, druga zawiera współrzędne punktów pomiarowych na osi OX (jest ich N). Niech C będzie wektorem **kolumnowym**: C = [c0, c1].T\n", "\n", "Wtedy \n", "\n", "Y = X * C (mnożenie macierzowe) \n", "\n", "reprezentuje równanie:\n", "\n", "y_i = x_i * c1 + c0 \n", "\n", "dla każdego i ze zbioru przykładów.\n", "\n", "W przedstawionym problemie znamy X i Y, ale nie znamy C. Okazuje się, że istnieje prosty wzór analityczny wyznaczający optymalne wartości parametrów C:\n", "\n", "C = (X' * X)^-1 * X' * Y\n", "\n", "gdzie * oznacza mnożenie macierzowe, X' to transponowany wektor X, a A^-1 oznacza macierz odwrotną do A." ] }, { "cell_type": "markdown", "id": "b9bf9f6e", "metadata": {}, "source": [ "**Korzystając z numpy i powyższego wzoru zilustruj przykład działania regresji liniowej.** W tym celu:\n", "\n", "1) wygeneruj dane na przedziale [-1,1] dla prostej y=0.5*x+0.1 przyjmując N=30\n", "\n", "2) dodaj do nich szum z rozkładu Gaussa o średniej 0.0 i odchyleniu 0.1\n", "\n", "3) znajdź optymalne wartości parametrów c0 i c1\n", "\n", "4) narysuj na wykresie dane z rozrzutem statystycznym, *prawdziwą* prostą oraz prostą ze znalezionymi parametrami (patrz wykres poniżej, znalezione parametry mogą się różnić)\n", "\n", "5) przetestuj co się stanie, gdy zmienisz odchylenie standardowe i liczbę generowanych punktów" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "266dbd8d", "metadata": {}, "source": [ "![image.png](attachment:image.png)" ] }, { "cell_type": "code", "execution_count": 224, "id": "fc21974d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.1]\n", " [0.5]]\n", "[[ 1. -1. ]\n", " [ 1. -0.93103448]\n", " [ 1. -0.86206897]\n", " [ 1. -0.79310345]\n", " [ 1. -0.72413793]]\n" ] } ], "source": [ "# prawdziwe parametry\n", "c0 = 0.1\n", "c1 = 0.5\n", "# tworzymy wektor\n", "N = 30\n", "C = np.array([c0,c1]).reshape(1,2).T\n", "print(C)\n", "# generujemy liczby na przedziale [-1,1]\n", "X = np.linspace(-1, 1, N)\n", "# dodajemy jedynki\n", "X = np.stack([np.ones(N), X], axis=0).T\n", "print(X[:5])\n", "# liczymy Y\n", "Y = X @ C\n", "# dodajemy szum\n", "Y = Y + np.random.normal(loc=0.0, scale=0.1, size=Y.shape)" ] }, { "cell_type": "code", "execution_count": 225, "id": "25c4311b", "metadata": {}, "outputs": [], "source": [ "# regresja liniowa\n", "XX = X.T @ X\n", "inv = np.linalg.inv(XX)\n", "C_reg = inv @ X.T @ Y" ] }, { "cell_type": "code", "execution_count": 226, "id": "944c6771", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.09346216]\n", " [0.46508306]]\n" ] } ], "source": [ "# znalezione parametry\n", "print(C_reg)" ] }, { "cell_type": "code", "execution_count": 227, "id": "233e1e66", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 227, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(X[:,1], X @ C, label=f\"y={c1}x+{c0}\")\n", "plt.plot(X[:,1], X@C_reg, label=\"y={:1.2f}x + {:1.2f}\".format(C_reg[1,0], C_reg[0,0]) )\n", "plt.scatter(X[:,1], Y.T[0], label='data', color='green', alpha=0.5)\n", "plt.xlim(-1, 1)\n", "plt.ylim(-1, 1)\n", "plt.grid()\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "ab32530c", "metadata": {}, "source": [ "# Zadanie 3 -- regresja liniowa za pomocą sklearn" ] }, { "cell_type": "markdown", "id": "fff16f6d", "metadata": {}, "source": [ "Regresji liniowej można używać również dla większej liczby wymiarów, tzn. dla funkcji f(x1, x2, ..., xn) o ile zależy ona liniowo od wszystkich zmiennych (inaczej wynik nie będzie za dobry -- źle wybrany model teoretyczny). Poniższy przykład pokazuje użycie bilbioteki sklearn do funkcji dwóch zeminnych x1 i x2. Zapoznaj się z przykładem i użyj implementacji w sklearn do danych wygenerowanych w poprzednim zadaniu. Sprawdź, że dopasowane parametry są takie same w obu przypadkach." ] }, { "cell_type": "code", "execution_count": 234, "id": "70ffcbf5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "parametry [1. 2.]\n", "parametr wolny 3.0000000000000018\n", "y(3,5)=15.999999999999998\n" ] } ], "source": [ "from sklearn.linear_model import LinearRegression\n", "x = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])\n", "# y = 1 * x_0 + 2 * x_1 + 3\n", "y = np.dot(x, np.array([1, 2])) + 3\n", "reg = LinearRegression().fit(x, y)\n", "\n", "print('parametry {}'.format(reg.coef_))\n", "print('parametr wolny {}'.format(reg.intercept_))\n", "print('y(3,5)={}'.format(*reg.predict(np.array([[3, 5]]))))" ] }, { "cell_type": "markdown", "id": "708333f5", "metadata": {}, "source": [ "### Rozwiązanie" ] }, { "cell_type": "code", "execution_count": 235, "id": "cece9b02", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "parametry [[0. 0.46508306]]\n", "parametr wolny [0.09346216]\n" ] } ], "source": [ "# najpierw poprzedni przykład\n", "reg = LinearRegression(fit_intercept=True).fit(X, Y)\n", "print('parametry {}'.format(reg.coef_))\n", "print('parametr wolny {}'.format(reg.intercept_))" ] }, { "cell_type": "markdown", "id": "df75bbf6", "metadata": {}, "source": [ "# Zadanie 4 -- Support Vector Machine (SVM)" ] }, { "cell_type": "markdown", "id": "f8702fd6", "metadata": {}, "source": [ "Regresja liniowa sprawdza się dobrze tylko dla danych opisywanych funkjcją liniową. Co jeżeli dane charakteryzują się większą złożonością? Wtedy trzeba użyć innych metod regresji, zaliczanych do tzw. *metod uczenia maszynowego*. Jedną z takich metod jest Maszyna Wektorów Nośnych. Tłumaczenie metod uczenia maszynowego wykracza poza ramy tego przedmiotu, ale chcę wam przekazać dobrą wiadomość: sklearn posiada wspólny interfejs dla wielu różnych metod. Dlatego już teraz jesteście w stanie użyć SVM do rozwiązania problemów, pomimo iż zapewne nie wiecie co to jest ani jak działa. Generalnie, powinniście wiedzieć jakich narzędzi użycwacie, ale tym razem po prsotu zaufajcie mi, że to narzędzie jest właściwe." ] }, { "cell_type": "markdown", "id": "80972f7f", "metadata": {}, "source": [ "Poniższa komórka importuje SVM" ] }, { "cell_type": "code", "execution_count": null, "id": "71101815", "metadata": {}, "outputs": [], "source": [ "from sklearn.svm import SVR" ] }, { "cell_type": "markdown", "id": "e0ce6431", "metadata": {}, "source": [ "Wykonaj następujące kroki:\n", "\n", "1) Wygeneruj 30 iksów na przedziale [0, 2PI]\n", "\n", "2) Dla każdego z nich policz wartość sin(X)\n", "\n", "3) Niech Y = sin(X) + szum, gdzie szum jest z rozkładu normalnego o średniej 0 i odchyleniu 0.3\n", "\n", "4) Dopasuj SVM do danych. W tym celu musisz powtórzyć kroki z poprzedniego zadania:\n", "\n", " a) Stwórz obiekt, tym razem typu SVM a nie LinearRegression\n", " \n", " b) Dofituj dane\n", " \n", " c) Wykorzystaj metodę .fit() dla 50 *nowych* iksów na tym samym przedziale\n", "\n", "5) Narysuj na wykresie zaszumione dane, oryginalnego sinusa i funkcję dopasowaną za pomocą SVM. Powinieneś dostać coś takiego jak ponizej." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "6b64c245", "metadata": {}, "source": [ "![image.png](attachment:image.png)" ] }, { "cell_type": "markdown", "id": "dd65a424", "metadata": {}, "source": [ "### Rozwiązanie" ] }, { "cell_type": "code", "execution_count": 273, "id": "8439e0c2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 273, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X = np.linspace(0.0, 6.28, 30)\n", "Y = np.sin(X) + np.random.normal(0, 0.3, size=X.shape)\n", "\n", "plt.plot(X, np.sin(X), color='blue', label='sin(x)')\n", "plt.scatter(X,Y, color='green', label='data')\n", "\n", "model = SVR().fit(X.reshape(X.shape[0], 1), Y)\n", "x = np.linspace(0.0, 6.28, 50)\n", "x = x.reshape(x.shape[0],1)\n", "y = model.predict(x)\n", "plt.plot(x,y, color='red', label='SVM')\n", "plt.legend()\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "code", "execution_count": null, "id": "f5a42725", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.6" } }, "nbformat": 4, "nbformat_minor": 5 }