1673 lines
32 KiB
Plaintext
1673 lines
32 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## Uczenie maszynowe 2019/2020 – laboratoria\n",
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"### 2/3 marca 2020\n",
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"# 1. Python – listy składane, indeksowanie, biblioteka _NumPy_"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Listy składane (*List comprehension*)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Przypuśćmy, że mamy dane zdanie i chcemy utworzyć listę, która będzie zawierać długości kolejnych wyrazów tego zdania. Możemy to zrobić w następujący sposób:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[5, 4, 7, 3, 4, 1, 4, 3, 4, 1, 4, 7, 6, 4]\n"
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]
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}
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],
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"source": [
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"zdanie = 'tracz tarł tarcicę tak takt w takt jak takt w takt tarcicę tartak tarł'\n",
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"wyrazy = zdanie.split()\n",
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"dlugosci_wyrazow = []\n",
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"for wyraz in wyrazy:\n",
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" dlugosci_wyrazow.append(len(wyraz))\n",
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" \n",
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"print(dlugosci_wyrazow)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Możemy to też zrobić bardziej „pythonicznie”, przy użyciu list składanych:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[5, 4, 7, 3, 4, 1, 4, 3, 4, 1, 4, 7, 6, 4]\n"
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]
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}
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],
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"source": [
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"zdanie = 'tracz tarł tarcicę tak takt w takt jak takt w takt tarcicę tartak tarł'\n",
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"wyrazy = zdanie.split()\n",
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"dlugosci_wyrazow = [len(wyraz) for wyraz in wyrazy]\n",
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"\n",
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"print(dlugosci_wyrazow)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Jeżeli chcemy, żeby był sprawdzany dodatkowy warunek, np. chcemy pomijać wyraz „takt”, to wciąż możemy użyć list składanych:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[5, 4, 7, 3, 1, 3, 1, 7, 6, 4]\n"
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]
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}
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],
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"source": [
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"zdanie = 'tracz tarł tarcicę tak takt w takt jak takt w takt tarcicę tartak tarł'\n",
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"wyrazy = zdanie.split()\n",
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"dlugosci_wyrazow = [len(wyraz) for wyraz in wyrazy if wyraz != 'takt']\n",
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"print(dlugosci_wyrazow)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Indeksowanie"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Wszystkie listy i krotki w Pythonie, w tym łańcuchy (które trakowane są jak krotki znaków), są indeksowane od 0:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"a\n",
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"e\n"
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]
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}
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],
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"source": [
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"napis = 'abcde'\n",
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"print(napis[0]) # 'a'\n",
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"print(napis[4]) # 'e'"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Indeksy możemy liczyć również „od końca”:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"e\n",
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"d\n",
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"a\n"
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]
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}
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],
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"source": [
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"napis = 'abcde'\n",
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"print(napis[-1]) # 'e' („ostatni”)\n",
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"print(napis[-2]) # 'd' („drugi od końca”)\n",
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"print(napis[-5]) # 'a' („piąty od końca”)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Łańcuchy możemy też „kroić na plasterki” (_slicing_):"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"bcd\n",
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"b\n",
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"cd\n",
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"bcd\n",
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"de\n",
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"abc\n",
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"abcde\n"
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]
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}
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],
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"source": [
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"napis = 'abcde'\n",
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"print(napis[1:4]) # 'bcd' („znaki od 1. włącznie do 4. wyłącznie”)\n",
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"print(napis[1:2]) # 'b' (to samo co `napis[1]`)\n",
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"print(napis[-3:-1]) # 'cd' (kroić można też stosując indeksowanie od końca)\n",
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"print(napis[1:-1]) # 'bcd' (możemy nawet mieszać te dwa sposoby indeksowania)\n",
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"print(napis[3:]) # 'cde' (jeżeli koniec przedziału nie jest podany, to kroimy do samego końca łańcucha)\n",
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"print(napis[:3]) # 'ab' (jeżeli początek przedziału nie jest podany, to kroimy od początku łańcucha)\n",
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"print(napis[:]) # 'abcde' (kopia całego napisu)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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|
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"source": [
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|
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"## Biblioteka _NumPy_"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Tablice"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Głównym obiektem w NumPy jest **jednorodna**, **wielowymiarowa** tablica. Przykładem takiej tablicy jest macierz `x`.\n",
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"\n",
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"Macierz $x =\n",
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" \\begin{pmatrix}\n",
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" 1 & 2 & 3 \\\\\n",
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" 4 & 5 & 6 \\\\\n",
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" 7 & 8 & 9\n",
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" \\end{pmatrix}$\n",
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"można zapisać jako:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[1 2 3]\n",
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" [4 5 6]\n",
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" [7 8 9]]\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"\n",
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"x = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
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"print(x)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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|
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"Najczęsciej używane metody tablic typu `array`:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(3, 3)"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"x.shape"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
|
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"data": {
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|
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"text/plain": [
|
|||
|
|
"array([12, 15, 18])"
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|
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]
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},
|
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|
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"execution_count": 9,
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"metadata": {},
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|
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"output_type": "execute_result"
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}
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],
|
|||
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"source": [
|
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|
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"x.sum(axis=0)"
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|
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]
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},
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{
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"cell_type": "code",
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|||
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"execution_count": 10,
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"metadata": {},
|
|||
|
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"outputs": [
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{
|
|||
|
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"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([2., 5., 8.])"
|
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|
|
]
|
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|
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},
|
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|
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"execution_count": 10,
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|||
|
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"metadata": {},
|
|||
|
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"output_type": "execute_result"
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|
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}
|
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|
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],
|
|||
|
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"source": [
|
|||
|
|
"x.mean(axis=1)"
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|
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]
|
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|
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},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Do tworzenia sekwencji liczbowych jako obiekty typu `array` należy wykorzystać funkcję `arange`."
|
|||
|
|
]
|
|||
|
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},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 11,
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|||
|
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"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
|
|||
|
|
]
|
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|
|
},
|
|||
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|
"execution_count": 11,
|
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|
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"metadata": {},
|
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|
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"output_type": "execute_result"
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|
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}
|
|||
|
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],
|
|||
|
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"source": [
|
|||
|
|
"np.arange(10)"
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|||
|
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]
|
|||
|
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},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 12,
|
|||
|
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"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([5, 6, 7, 8, 9])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 12,
|
|||
|
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"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"np.arange(5, 10)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 13,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([5. , 5.5, 6. , 6.5, 7. , 7.5, 8. , 8.5, 9. , 9.5])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 13,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"np.arange(5, 10, 0.5)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Kształt tablicy można zmienić za pomocą metody `reshape`:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 14,
|
|||
|
|
"metadata": {
|
|||
|
|
"scrolled": true
|
|||
|
|
},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[ 1 2 3 4 5 6 7 8 9 10 11 12]\n",
|
|||
|
|
"[[ 1 2 3 4]\n",
|
|||
|
|
" [ 5 6 7 8]\n",
|
|||
|
|
" [ 9 10 11 12]]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.arange(1, 13)\n",
|
|||
|
|
"print(x)\n",
|
|||
|
|
"y = x.reshape(3, 4)\n",
|
|||
|
|
"print(y)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Funkcją podobną do `arange` jest `linspace`, która wypełnia wektor określoną liczbą elementów z przedziału o równych automatycznie obliczonych odstępach (w `arange` należy podać rozmiar kroku):"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 15,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[0. 1.25 2.5 3.75 5. ]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.linspace(0, 5, 5)\n",
|
|||
|
|
"print(x)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Dodatkowe informacje o funkcjach NumPy uzyskuje się za pomocą polecenia `help(nazwa_funkcji)`:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 16,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"Help on function shape in module numpy:\n",
|
|||
|
|
"\n",
|
|||
|
|
"shape(a)\n",
|
|||
|
|
" Return the shape of an array.\n",
|
|||
|
|
" \n",
|
|||
|
|
" Parameters\n",
|
|||
|
|
" ----------\n",
|
|||
|
|
" a : array_like\n",
|
|||
|
|
" Input array.\n",
|
|||
|
|
" \n",
|
|||
|
|
" Returns\n",
|
|||
|
|
" -------\n",
|
|||
|
|
" shape : tuple of ints\n",
|
|||
|
|
" The elements of the shape tuple give the lengths of the\n",
|
|||
|
|
" corresponding array dimensions.\n",
|
|||
|
|
" \n",
|
|||
|
|
" See Also\n",
|
|||
|
|
" --------\n",
|
|||
|
|
" alen\n",
|
|||
|
|
" ndarray.shape : Equivalent array method.\n",
|
|||
|
|
" \n",
|
|||
|
|
" Examples\n",
|
|||
|
|
" --------\n",
|
|||
|
|
" >>> np.shape(np.eye(3))\n",
|
|||
|
|
" (3, 3)\n",
|
|||
|
|
" >>> np.shape([[1, 2]])\n",
|
|||
|
|
" (1, 2)\n",
|
|||
|
|
" >>> np.shape([0])\n",
|
|||
|
|
" (1,)\n",
|
|||
|
|
" >>> np.shape(0)\n",
|
|||
|
|
" ()\n",
|
|||
|
|
" \n",
|
|||
|
|
" >>> a = np.array([(1, 2), (3, 4)], dtype=[('x', 'i4'), ('y', 'i4')])\n",
|
|||
|
|
" >>> np.shape(a)\n",
|
|||
|
|
" (2,)\n",
|
|||
|
|
" >>> a.shape\n",
|
|||
|
|
" (2,)\n",
|
|||
|
|
"\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"help(np.shape)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Tablice mogą składać się z danych różnych typów (ale tylko jednego typu danych równocześnie, stąd jednorodność)."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 17,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"int32\n",
|
|||
|
|
"[0.1 0.2 0.3]\n",
|
|||
|
|
"float64\n",
|
|||
|
|
"float64\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.array([1, 2, 3])\n",
|
|||
|
|
"print(x.dtype)\n",
|
|||
|
|
"x = np.array([0.1, 0.2, 0.3])\n",
|
|||
|
|
"print(x)\n",
|
|||
|
|
"print(x.dtype)\n",
|
|||
|
|
"x = np.array([1, 2, 3], dtype='float64')\n",
|
|||
|
|
"print(x.dtype)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Tworzenie tablic składających się z samych zer lub jedynek umożliwiają funkcje `zeros` oraz `ones`:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 18,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[[0. 0. 0. 0.]\n",
|
|||
|
|
" [0. 0. 0. 0.]\n",
|
|||
|
|
" [0. 0. 0. 0.]]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.zeros([3,4])\n",
|
|||
|
|
"print(x)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 19,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[[1. 1. 1. 1.]\n",
|
|||
|
|
" [1. 1. 1. 1.]\n",
|
|||
|
|
" [1. 1. 1. 1.]]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.ones([3,4])\n",
|
|||
|
|
"print(x)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Podstawowe operacje arytmetyczne"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Operatory arytmetyczne na tablicach w NumPy działają **element po elemencie**."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 20,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[2. 3. 4.]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"import numpy as np\n",
|
|||
|
|
"\n",
|
|||
|
|
"a = np.array([3, 4, 5])\n",
|
|||
|
|
"b = np.ones(3)\n",
|
|||
|
|
"print(a - b)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Za mnożenie macierzy odpowiada funkcja `dot` (nie operator `*`):"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 21,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[[1 2]\n",
|
|||
|
|
" [3 4]]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a = np.array([[1, 2], [3, 4]])\n",
|
|||
|
|
"print(a)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 22,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[[1 2]\n",
|
|||
|
|
" [3 4]]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"b = np.array([[1, 2], [3, 4]])\n",
|
|||
|
|
"print(b)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 23,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([[ 1, 4],\n",
|
|||
|
|
" [ 9, 16]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 23,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a * b"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 24,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([[ 7, 10],\n",
|
|||
|
|
" [15, 22]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 24,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"np.dot(a,b)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Przykłady innych operacji dodawania i mnożenia:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 25,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([[5., 5.],\n",
|
|||
|
|
" [5., 5.]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 25,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a = np.zeros((2, 2), dtype='float')\n",
|
|||
|
|
"a += 5\n",
|
|||
|
|
"a"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 26,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([[25., 25.],\n",
|
|||
|
|
" [25., 25.]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 26,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a *= 5\n",
|
|||
|
|
"a"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 27,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([[50., 50.],\n",
|
|||
|
|
" [50., 50.]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 27,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a + a"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Sklejanie tablic:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 28,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([1, 2, 3, 4, 5, 6, 7, 8, 9])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 28,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a = np.array([1, 2, 3])\n",
|
|||
|
|
"b = np.array([4, 5, 6])\n",
|
|||
|
|
"c = np.array([7, 8, 9])\n",
|
|||
|
|
"np.hstack([a, b, c])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 29,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([[1, 2, 3],\n",
|
|||
|
|
" [4, 5, 6],\n",
|
|||
|
|
" [7, 8, 9]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 29,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"np.vstack([a, b, c])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Typowe funkcje matematyczne:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 30,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([3.14159265, 4.44288294, 5.44139809, 6.28318531])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 30,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.arange(1, 5)\n",
|
|||
|
|
"np.sqrt(x) * np.pi"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 31,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"16"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 31,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"2**4"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 32,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"16"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 32,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"np.power(2, 4)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 33,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"1.0"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 33,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"np.log(np.e)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 34,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"4"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 34,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.arange(5)\n",
|
|||
|
|
"x.max() - x.min()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Indeksy i zakresy"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Tablice jednowymiarowe zachowują sie podobnie do zwykłych list pythonowych."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 35,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([2, 3])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 35,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a = np.arange(10)\n",
|
|||
|
|
"a[2:4]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 36,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([0, 2, 4, 6, 8])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 36,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a[:10:2]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 37,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 37,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a[::-1]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Tablice wielowymiarowe mają po jednym indeksie na wymiar:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 38,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([[ 0, 1, 2, 3],\n",
|
|||
|
|
" [ 4, 5, 6, 7],\n",
|
|||
|
|
" [ 8, 9, 10, 11]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 38,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.arange(12).reshape(3, 4)\n",
|
|||
|
|
"x"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 39,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"11"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 39,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x[2, 3]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 40,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([1, 5, 9])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 40,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x[:, 1]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 41,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([4, 5, 6, 7])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 41,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x[1, :]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 42,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([[ 4, 5, 6, 7],\n",
|
|||
|
|
" [ 8, 9, 10, 11]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 42,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x[1:3, :]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Warunki"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Warunki pozwalają na selekcję elementów tablicy."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 43,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([2, 2, 2, 3, 3, 3])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 43,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a = np.array([1, 1, 1, 2, 2, 2, 3, 3, 3])\n",
|
|||
|
|
"a[a > 1]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 44,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([3, 3, 3])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 44,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a[a == 3]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 45,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"(array([0, 1, 2, 3, 4, 5], dtype=int64),)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 45,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"np.where(a < 3)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 46,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([0, 1, 2, 3, 4, 5], dtype=int64)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 46,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"np.where(a < 3)[0]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 47,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"(array([], dtype=int64),)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 47,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"np.where(a > 9)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Pętle i wypisywanie"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 48,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"ename": "SyntaxError",
|
|||
|
|
"evalue": "Missing parentheses in call to 'print'. Did you mean print(row)? (<ipython-input-48-5346ec1a1aa1>, line 2)",
|
|||
|
|
"output_type": "error",
|
|||
|
|
"traceback": [
|
|||
|
|
"\u001b[1;36m File \u001b[1;32m\"<ipython-input-48-5346ec1a1aa1>\"\u001b[1;36m, line \u001b[1;32m2\u001b[0m\n\u001b[1;33m print row\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m Missing parentheses in call to 'print'. Did you mean print(row)?\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"for row in x:\n",
|
|||
|
|
" print row"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"for element in x.flat:\n",
|
|||
|
|
" print element, "
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Liczby losowe"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"np.random.randint(0, 10, 5)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"np.random.normal(0, 1, 5) "
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"np.random.uniform(0, 2, 5)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Macierze"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"NumPy jest pakietem wykorzystywanym do obliczeń w dziedzinie algebry liniowej, co jeszcze szczególnie przydatne w uczeniu maszynowym. \n",
|
|||
|
|
"\n",
|
|||
|
|
"Wektor o wymiarach $1 \\times N$ \n",
|
|||
|
|
"$$\n",
|
|||
|
|
" x =\n",
|
|||
|
|
" \\begin{pmatrix}\n",
|
|||
|
|
" x_{1} \\\\\n",
|
|||
|
|
" x_{2} \\\\\n",
|
|||
|
|
" \\vdots \\\\\n",
|
|||
|
|
" x_{N}\n",
|
|||
|
|
" \\end{pmatrix} \n",
|
|||
|
|
"$$\n",
|
|||
|
|
"\n",
|
|||
|
|
"i jego transpozycję $x^\\top = (x_{1}, x_{2},\\ldots,x_{N})$ można wyrazić w Pythonie w następujący sposób:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"import numpy as np\n",
|
|||
|
|
"\n",
|
|||
|
|
"x = np.array([[1, 2, 3]]).T\n",
|
|||
|
|
"x.shape"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"xt = x.T\n",
|
|||
|
|
"xt.shape"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"**Macierz kolumnowa** w NumPy.\n",
|
|||
|
|
"$$X =\n",
|
|||
|
|
" \\begin{pmatrix}\n",
|
|||
|
|
" 3 \\\\\n",
|
|||
|
|
" 4 \\\\\n",
|
|||
|
|
" 5 \\\\\n",
|
|||
|
|
" 6 \n",
|
|||
|
|
" \\end{pmatrix}$$"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.array([[3,4,5,6]]).T\n",
|
|||
|
|
"x"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"**Macierz wierszowa** w NumPy.\n",
|
|||
|
|
"$$ X =\n",
|
|||
|
|
" \\begin{pmatrix}\n",
|
|||
|
|
" 3 & 4 & 5 & 6\n",
|
|||
|
|
" \\end{pmatrix}$$"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.array([[3,4,5,6]])\n",
|
|||
|
|
"x"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Oprócz obiektów typu `array` istnieje wyspecjalizowany obiekt `matrix`, dla którego operacje `*` (mnożenie) oraz `**-1` (odwracanie) są określone w sposób właściwy dla macierzy (w przeciwieństwie do operacji elementowych dla obiektów `array`)."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.array([1,2,3,4,5,6,7,8,9]).reshape(3,3)\n",
|
|||
|
|
"x"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"X = np.matrix(x)\n",
|
|||
|
|
"X"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"**Wyznacznik macierzy**"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"a = np.array([[3,-9],[2,5]])\n",
|
|||
|
|
"np.linalg.det(a)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"**Macierz odwrotna**"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"A = np.array([[-4,-2],[5,5]])\n",
|
|||
|
|
"A"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"invA = np.linalg.inv(A)\n",
|
|||
|
|
"invA"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"np.round(np.dot(A, invA))"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"(ponieważ $AA^{-1} = A^{-1}A = I$)."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"**Wartości i wektory własne**"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"a = np.diag((1, 2, 3))\n",
|
|||
|
|
"a"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"w, v = np.linalg.eig(a)\n",
|
|||
|
|
"print(w) # wartości własne\n",
|
|||
|
|
"print(v) # wektory własne"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"# Zadania"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Zadanie 1.1 (1 pkt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"Dla danej listy `input_list` zawierającej liczby utwórz nową listę `output_list`, która będzie zawierała kwadraty liczb dodatnich z `input_list`. Użyj _list comprehension_!"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"# Przykładowe dane\n",
|
|||
|
|
"\n",
|
|||
|
|
"input_list = [34.6, -203.4, 44.9, 68.3, -12.2, 44.6, 12.7]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Zadanie 1.2 (1 pkt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"Za pomocą jednowierszowego polecenia utwórz następującą macierz jako obiekt typu `array`:\n",
|
|||
|
|
"$$A = \\begin{pmatrix}\n",
|
|||
|
|
"1 & 2 & \\cdots & 10 \\\\\n",
|
|||
|
|
"11 & 12 & \\cdots & 20 \\\\\n",
|
|||
|
|
"\\vdots & \\ddots & \\ddots & \\vdots \\\\\n",
|
|||
|
|
"41 & 42 & \\cdots & 50 \n",
|
|||
|
|
"\\end{pmatrix}$$"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Zadanie 1.3 (1 pkt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"Dla macierzy $A$ z zadania 1.2:\n",
|
|||
|
|
" * określ liczbę elementów, kolumn i wierszy,\n",
|
|||
|
|
" * stwórz wektory średnich po wierszach oraz po kolumnach,\n",
|
|||
|
|
" * wypisz jej trzecią kolumnę,\n",
|
|||
|
|
" * wypisz jej czwarty wiersz.\n",
|
|||
|
|
" \n",
|
|||
|
|
"Użyj odpowiednich metod obiektu `array`."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Zadanie 1.4 (1 pkt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"Utwórz macierze\n",
|
|||
|
|
"$$ A = \\begin{pmatrix}\n",
|
|||
|
|
"0 & 4 & -2 \\\\\n",
|
|||
|
|
"-4 & -3 & 0\n",
|
|||
|
|
"\\end{pmatrix} $$\n",
|
|||
|
|
"$$ B = \\begin{pmatrix}\n",
|
|||
|
|
"0 & 1 \\\\\n",
|
|||
|
|
"1 & -1 \\\\\n",
|
|||
|
|
"2 & 3\n",
|
|||
|
|
"\\end{pmatrix} $$\n",
|
|||
|
|
"oraz wektor\n",
|
|||
|
|
"$$ x = \\begin{pmatrix}\n",
|
|||
|
|
"2 \\\\\n",
|
|||
|
|
"1 \\\\\n",
|
|||
|
|
"0\n",
|
|||
|
|
"\\end{pmatrix} $$\n",
|
|||
|
|
"\n",
|
|||
|
|
"Oblicz:\n",
|
|||
|
|
" * iloczyn macierzy $A$ z wektorem $x$ \n",
|
|||
|
|
" * iloczyn macierzy $A \\cdot B$\n",
|
|||
|
|
" * wyznacznik $\\det(A \\cdot B)$\n",
|
|||
|
|
" * wynik działania $(A \\cdot B)^\\top - B^\\top \\cdot A^\\top$"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Zadanie 1.5 (1 pkt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"Czym różni się operacja `A**-1` dla obiektów typu `array` i `matrix`? Pokaż na przykładzie."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Zadanie 1.6 (1 pkt)\n",
|
|||
|
|
"\n",
|
|||
|
|
"Dla macierzy $X = \\left[\n",
|
|||
|
|
" \\begin{array}{rrr}\n",
|
|||
|
|
" 1 & 2 & 3\\\\\n",
|
|||
|
|
" 1 & 3 & 6 \\\\\n",
|
|||
|
|
" \\end{array}\n",
|
|||
|
|
" \\right]$ oraz wektora $y = \\left[\n",
|
|||
|
|
" \\begin{array}{r}\n",
|
|||
|
|
" 5 \\\\\n",
|
|||
|
|
" 6 \\\\\n",
|
|||
|
|
" \\end{array}\n",
|
|||
|
|
" \\right]$ oblicz wynikowy wektor: \n",
|
|||
|
|
"$$ \\theta = (X^\\top \\, X)^{-1} \\, X^\\top \\, y^\\top \\, . $$\n",
|
|||
|
|
"Wykonaj te same obliczenia raz na obiektach typu `array`, a raz na obiektach typu `matrix`.\n",
|
|||
|
|
"W przypadku obiektów typu `matrix` zastosuj możliwie krótki zapis. "
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"metadata": {
|
|||
|
|
"celltoolbar": "Slideshow",
|
|||
|
|
"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": "3.8.3"
|
|||
|
|
},
|
|||
|
|
"livereveal": {
|
|||
|
|
"start_slideshow_at": "selected",
|
|||
|
|
"theme": "amu"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
"nbformat": 4,
|
|||
|
|
"nbformat_minor": 4
|
|||
|
|
}
|