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math-ml-intro.ipynb
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| { | |
| "cells": [ | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "2 * 2", | |
| "execution_count": 1, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "4" | |
| }, | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "## Занятие про Python\nМы, наконец, запустили Jupyter Notebook." | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "(2 + 3) ** 5", | |
| "execution_count": 2, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "3125" | |
| }, | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "2 / 3", | |
| "execution_count": 3, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "0.6666666666666666" | |
| }, | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "5 // 3", | |
| "execution_count": 4, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "1" | |
| }, | |
| "execution_count": 4, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x = 10", | |
| "execution_count": 5, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x + 5", | |
| "execution_count": 6, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "15" | |
| }, | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "type(5)", | |
| "execution_count": 7, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "int" | |
| }, | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "type(1.)", | |
| "execution_count": 8, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "float" | |
| }, | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "y = 5", | |
| "execution_count": 9, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x + y", | |
| "execution_count": 10, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "15" | |
| }, | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "4 + 3\n5 + 10", | |
| "execution_count": 11, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "15" | |
| }, | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "print(x)\nprint(y)", | |
| "execution_count": 12, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "10\n5\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x = x + 1", | |
| "execution_count": 13, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x", | |
| "execution_count": 14, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "11" | |
| }, | |
| "execution_count": 14, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "for i in range(5):\n print(i)\n print(\"Next i, please\")\nprint(\"That's all\")", | |
| "execution_count": 18, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "0\nNext i, please\n1\nNext i, please\n2\nNext i, please\n3\nNext i, please\n4\nNext i, please\nThat's all\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "list(range(5))", | |
| "execution_count": 16, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[0, 1, 2, 3, 4]" | |
| }, | |
| "execution_count": 16, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "i", | |
| "execution_count": 17, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "4" | |
| }, | |
| "execution_count": 17, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list = [2, 10, 4, 3, 1, \"Hello\"]", | |
| "execution_count": 19, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list[0]", | |
| "execution_count": 20, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "2" | |
| }, | |
| "execution_count": 20, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false, | |
| "collapsed": true | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list[4] = 999", | |
| "execution_count": 23, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list", | |
| "execution_count": 24, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[2, 10, 4, 3, 999, 'Hello']" | |
| }, | |
| "execution_count": 24, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "for element in my_list:\n print(element)", | |
| "execution_count": 25, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "2\n10\n4\n3\n999\nHello\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "other_list = [4, 3, 5, 1]", | |
| "execution_count": 26, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list + other_list", | |
| "execution_count": 27, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[2, 10, 4, 3, 999, 'Hello', 4, 3, 5, 1]" | |
| }, | |
| "execution_count": 27, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list", | |
| "execution_count": 28, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[2, 10, 4, 3, 999, 'Hello']" | |
| }, | |
| "execution_count": 28, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list[2:5]", | |
| "execution_count": 29, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[4, 3, 999]" | |
| }, | |
| "execution_count": 29, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list[:4]", | |
| "execution_count": 30, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[2, 10, 4, 3]" | |
| }, | |
| "execution_count": 30, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list[4:]", | |
| "execution_count": 31, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[999, 'Hello']" | |
| }, | |
| "execution_count": 31, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list[-1]", | |
| "execution_count": 32, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "'Hello'" | |
| }, | |
| "execution_count": 32, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list[len(my_list)-1]", | |
| "execution_count": 33, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "'Hello'" | |
| }, | |
| "execution_count": 33, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_tuple = (2, 1, 5, 10)", | |
| "execution_count": 34, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_tuple[2] = 10", | |
| "execution_count": 35, | |
| "outputs": [ | |
| { | |
| "ename": "TypeError", | |
| "evalue": "'tuple' object does not support item assignment", | |
| "output_type": "error", | |
| "traceback": [ | |
| "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", | |
| "\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", | |
| "\u001b[1;32m<ipython-input-35-ba4bcf080663>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mmy_tuple\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", | |
| "\u001b[1;31mTypeError\u001b[0m: 'tuple' object does not support item assignment" | |
| ] | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "s = \"123\"", | |
| "execution_count": 36, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "s + 2", | |
| "execution_count": 38, | |
| "outputs": [ | |
| { | |
| "ename": "TypeError", | |
| "evalue": "must be str, not int", | |
| "output_type": "error", | |
| "traceback": [ | |
| "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", | |
| "\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", | |
| "\u001b[1;32m<ipython-input-38-1ffac3e9a4d8>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0ms\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", | |
| "\u001b[1;31mTypeError\u001b[0m: must be str, not int" | |
| ] | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "int(s)", | |
| "execution_count": 39, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "123" | |
| }, | |
| "execution_count": 39, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x", | |
| "execution_count": 40, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "11" | |
| }, | |
| "execution_count": 40, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x = 12\nif x > 10:\n print(\"x is large\")\nelse:\n print(\"x is small\")", | |
| "execution_count": 44, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "x is large\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x = -12\nif x > 10:\n print(\"x is large\")\nelif x > 0:\n print(\"x is small but positive\")\nelse:\n print(\"x is negative\")", | |
| "execution_count": 46, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "x is negative\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "sqrt(4)", | |
| "execution_count": 47, | |
| "outputs": [ | |
| { | |
| "ename": "NameError", | |
| "evalue": "name 'sqrt' is not defined", | |
| "output_type": "error", | |
| "traceback": [ | |
| "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", | |
| "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", | |
| "\u001b[1;32m<ipython-input-47-718d7f173e1d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0msqrt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", | |
| "\u001b[1;31mNameError\u001b[0m: name 'sqrt' is not defined" | |
| ] | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "import math", | |
| "execution_count": 48, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "math.sqrt(4)", | |
| "execution_count": 49, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "2.0" | |
| }, | |
| "execution_count": 49, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "math.sin(math.pi)", | |
| "execution_count": 50, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "1.2246467991473532e-16" | |
| }, | |
| "execution_count": 50, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "from math import sin, sqrt", | |
| "execution_count": 51, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "sin(5)", | |
| "execution_count": 52, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "-0.9589242746631385" | |
| }, | |
| "execution_count": 52, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "import math as mt", | |
| "execution_count": 53, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "mt.sqrt(100)", | |
| "execution_count": 54, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "10.0" | |
| }, | |
| "execution_count": 54, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "# from math import *\n# так лучше не делать", | |
| "execution_count": 55, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "import numpy as np", | |
| "execution_count": 56, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list", | |
| "execution_count": 57, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[2, 10, 4, 3, 999, 'Hello']" | |
| }, | |
| "execution_count": 57, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list.append(123)", | |
| "execution_count": 58, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "my_list", | |
| "execution_count": 59, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[2, 10, 4, 3, 999, 'Hello', 123]" | |
| }, | |
| "execution_count": 59, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers = [1., 2., 5.] * 1000", | |
| "execution_count": 60, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "$$\\{x^2\\mid x \\in \\mathbb N\\}$$" | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "%%timeit\nsquares = [x ** 2 for x in numbers]", | |
| "execution_count": 64, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "1000 loops, best of 3: 490 µs per loop\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false, | |
| "collapsed": true | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers_array = np.array(numbers)", | |
| "execution_count": 65, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x = np.array([1, 2, 3])\ny = np.array([2, 5, 10])", | |
| "execution_count": 66, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "y[2]", | |
| "execution_count": 70, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "10" | |
| }, | |
| "execution_count": 70, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x + y", | |
| "execution_count": 71, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([ 3, 7, 13])" | |
| }, | |
| "execution_count": 71, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x * 2", | |
| "execution_count": 72, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([2, 4, 6])" | |
| }, | |
| "execution_count": 72, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x * y", | |
| "execution_count": 73, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([ 2, 10, 30])" | |
| }, | |
| "execution_count": 73, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "np.sin(x)", | |
| "execution_count": 74, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([ 0.84147098, 0.90929743, 0.14112001])" | |
| }, | |
| "execution_count": 74, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "np.exp(x)", | |
| "execution_count": 75, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([ 2.71828183, 7.3890561 , 20.08553692])" | |
| }, | |
| "execution_count": 75, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false, | |
| "collapsed": true | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers_array = np.array(numbers)", | |
| "execution_count": 77, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "%%timeit\nsquares_array = numbers_array ** 2", | |
| "execution_count": 80, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "The slowest run took 9.99 times longer than the fastest. This could mean that an intermediate result is being cached.\n100000 loops, best of 3: 2.89 µs per loop\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers_array[0] = \"Hello\"", | |
| "execution_count": 82, | |
| "outputs": [ | |
| { | |
| "ename": "ValueError", | |
| "evalue": "could not convert string to float: 'Hello'", | |
| "output_type": "error", | |
| "traceback": [ | |
| "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", | |
| "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", | |
| "\u001b[1;32m<ipython-input-82-6cb524a95af9>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mnumbers_array\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m\"Hello\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", | |
| "\u001b[1;31mValueError\u001b[0m: could not convert string to float: 'Hello'" | |
| ] | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers_array.dtype", | |
| "execution_count": 83, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "dtype('float64')" | |
| }, | |
| "execution_count": 83, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "string_array = np.array([\"one\", \"two\", \"three\"])", | |
| "execution_count": 84, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "string_array", | |
| "execution_count": 85, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array(['one', 'two', 'three'], \n dtype='<U5')" | |
| }, | |
| "execution_count": 85, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "string_array[0] = \"This is a test\"", | |
| "execution_count": 86, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "string_array", | |
| "execution_count": 87, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array(['This ', 'two', 'three'], \n dtype='<U5')" | |
| }, | |
| "execution_count": 87, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "string_array[2] = 123567", | |
| "execution_count": 90, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "string_array", | |
| "execution_count": 91, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array(['This ', 'two', '12356'], \n dtype='<U5')" | |
| }, | |
| "execution_count": 91, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "objects = np.array([1, 2, '123', 'some string'], \n dtype='object')", | |
| "execution_count": 92, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "objects", | |
| "execution_count": 93, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([1, 2, '123', 'some string'], dtype=object)" | |
| }, | |
| "execution_count": 93, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "table = [[2, 5, 10], [1, 2, 5]]", | |
| "execution_count": 94, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "table[0][0]", | |
| "execution_count": 96, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "2" | |
| }, | |
| "execution_count": 96, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "[row[0] for row in table]", | |
| "execution_count": 97, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[2, 1]" | |
| }, | |
| "execution_count": 97, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d = np.array(table)", | |
| "execution_count": 98, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d", | |
| "execution_count": 99, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 2, 5, 10],\n [ 1, 2, 5]])" | |
| }, | |
| "execution_count": 99, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d[0, 1]", | |
| "execution_count": 100, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "5" | |
| }, | |
| "execution_count": 100, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d[0]", | |
| "execution_count": 101, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([ 2, 5, 10])" | |
| }, | |
| "execution_count": 101, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d[:,1]", | |
| "execution_count": 102, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([5, 2])" | |
| }, | |
| "execution_count": 102, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "v = np.array([4, 2, 1])", | |
| "execution_count": 104, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d", | |
| "execution_count": 105, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 2, 5, 10],\n [ 1, 2, 5]])" | |
| }, | |
| "execution_count": 105, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d @ v", | |
| "execution_count": 107, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([28, 13])" | |
| }, | |
| "execution_count": 107, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d.dot(v)", | |
| "execution_count": 108, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([28, 13])" | |
| }, | |
| "execution_count": 108, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "u = np.array([2, 1, 4])", | |
| "execution_count": 109, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "u @ v", | |
| "execution_count": 110, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "14" | |
| }, | |
| "execution_count": 110, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "u.T", | |
| "execution_count": 112, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([2, 1, 4])" | |
| }, | |
| "execution_count": 112, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d", | |
| "execution_count": 113, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 2, 5, 10],\n [ 1, 2, 5]])" | |
| }, | |
| "execution_count": 113, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d.T", | |
| "execution_count": 114, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 2, 1],\n [ 5, 2],\n [10, 5]])" | |
| }, | |
| "execution_count": 114, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d", | |
| "execution_count": 115, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 2, 5, 10],\n [ 1, 2, 5]])" | |
| }, | |
| "execution_count": 115, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "new_matrix = np.array([[4, 3], [1, 2], [3, 5]])", | |
| "execution_count": 116, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "array_2d @ new_matrix", | |
| "execution_count": 117, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[43, 66],\n [21, 32]])" | |
| }, | |
| "execution_count": 117, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "new_matrix @ array_2d", | |
| "execution_count": 118, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[11, 26, 55],\n [ 4, 9, 20],\n [11, 25, 55]])" | |
| }, | |
| "execution_count": 118, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "u", | |
| "execution_count": 119, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([2, 1, 4])" | |
| }, | |
| "execution_count": 119, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "v", | |
| "execution_count": 120, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([4, 2, 1])" | |
| }, | |
| "execution_count": 120, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "sum(u * v)", | |
| "execution_count": 123, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "14" | |
| }, | |
| "execution_count": 123, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "u @ v", | |
| "execution_count": 122, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "14" | |
| }, | |
| "execution_count": 122, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "u = np.array([1, 2, 1, 2, 14, 5, 3, 4, 16])", | |
| "execution_count": 124, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "np.mean(u)", | |
| "execution_count": 126, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "5.333333333333333" | |
| }, | |
| "execution_count": 126, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "u - np.mean(u)", | |
| "execution_count": 127, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([ -4.33333333, -3.33333333, -4.33333333, -3.33333333,\n 8.66666667, -0.33333333, -2.33333333, -1.33333333, 10.66666667])" | |
| }, | |
| "execution_count": 127, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "X = np.array([[1, 2], [15, 4], [6, 3], [4, 6]])", | |
| "execution_count": 128, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "X", | |
| "execution_count": 129, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 1, 2],\n [15, 4],\n [ 6, 3],\n [ 4, 6]])" | |
| }, | |
| "execution_count": 129, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "X - np.mean(X, axis=0)", | |
| "execution_count": 133, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[-5.5 , -1.75],\n [ 8.5 , 0.25],\n [-0.5 , -0.75],\n [-2.5 , 2.25]])" | |
| }, | |
| "execution_count": 133, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false, | |
| "collapsed": true | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers = np.array([1, 2, 4, 6])", | |
| "execution_count": 141, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers", | |
| "execution_count": 142, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([1, 2, 4, 6])" | |
| }, | |
| "execution_count": 142, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers.reshape(2, 2)", | |
| "execution_count": 143, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[1, 2],\n [4, 6]])" | |
| }, | |
| "execution_count": 143, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers.reshape(2, -1)", | |
| "execution_count": 144, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[1, 2],\n [4, 6]])" | |
| }, | |
| "execution_count": 144, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers.reshape(1, -1)", | |
| "execution_count": 145, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[1, 2, 4, 6]])" | |
| }, | |
| "execution_count": 145, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "numbers.reshape(-1, 1)", | |
| "execution_count": 146, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[1],\n [2],\n [4],\n [6]])" | |
| }, | |
| "execution_count": 146, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "q = np.arange(12)", | |
| "execution_count": 147, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "q", | |
| "execution_count": 148, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])" | |
| }, | |
| "execution_count": 148, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "q.reshape(3, 4)", | |
| "execution_count": 149, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])" | |
| }, | |
| "execution_count": 149, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "q.reshape(2, 6)", | |
| "execution_count": 150, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 0, 1, 2, 3, 4, 5],\n [ 6, 7, 8, 9, 10, 11]])" | |
| }, | |
| "execution_count": 150, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "q.reshape(2, -1)", | |
| "execution_count": 151, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 0, 1, 2, 3, 4, 5],\n [ 6, 7, 8, 9, 10, 11]])" | |
| }, | |
| "execution_count": 151, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "import matplotlib.pyplot as plt\n%matplotlib inline", | |
| "execution_count": 152, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "plt.plot([1, 2, 3, 5], [4, 2, 8, 0], '-.*');", | |
| "execution_count": 167, | |
| "outputs": [ | |
| { | |
| "data": { | |
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| |
| "text/plain": "<matplotlib.figure.Figure at 0x8cddb38>" | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x = np.linspace(-np.pi, np.pi, 10 )", | |
| "execution_count": 172, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "plt.figure(figsize=(6, 6))\nplt.plot(np.cos(x), np.sin(x))", | |
| "execution_count": 173, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[<matplotlib.lines.Line2D at 0xa1589b0>]" | |
| }, | |
| "execution_count": 173, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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9NydlJHfl04iIhL1AHEFMAwqcc5udc3XAs8Dso7aZDTzpmn0C9DGz9DbuGzDr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\nItIiBYSIiLRIASEiIi1SQIiISIv+P+0dieZpusXfAAAAAElFTkSuQmCC\n", | |
| "text/plain": "<matplotlib.figure.Figure at 0xa0fc6d8>" | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "x = np.linspace(-np.pi, np.pi, 200)\nplt.figure(figsize=(6, 6))\nplt.plot(x, np.sin(x**2))", | |
| "execution_count": 175, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[<matplotlib.lines.Line2D at 0xa29f6a0>]" | |
| }, | |
| "execution_count": 175, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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hBltbW2VY9nzS+SKKJVENANVDs8dh2OBzoVjCeDyj+8CzRMjrwM7OJuznOEMV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\nfwGiyayCNQSVZQAAAABJRU5ErkJggg==\n", | |
| "text/plain": "<matplotlib.figure.Figure at 0xa223080>" | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "points = np.array([[0, 0], [2, 0], [2, 2], [1, 3], [0, 2], \n [0, 0]])\n", | |
| "execution_count": 182, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "A @ points.T", | |
| "execution_count": 184, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[ 0. , 4. , 4. , 2. , 0. , 0. ],\n [ 0. , 0. , -1. , -1.5, -1. , 0. ]])" | |
| }, | |
| "execution_count": 184, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "A = np.array([[1, 1], [0, -0.5]])\nplt.figure(figsize=(4, 4))\nplt.xlim(-5, 5)\nplt.ylim(-5, 5)\nnew_points = A @ points.T\n\nplt.plot(points[:, 0], points[:, 1], '-o')\nplt.plot(new_points[0], new_points[1], '-o')", | |
| "execution_count": 189, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "[<matplotlib.lines.Line2D at 0xa34bdd8>]" | |
| }, | |
| "execution_count": 189, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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| |
| "text/plain": "<matplotlib.figure.Figure at 0xa3a2fd0>" | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false, | |
| "collapsed": true | |
| }, | |
| "cell_type": "code", | |
| "source": "A = np.array([[1, 4], [3, 2]])", | |
| "execution_count": 191, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false, | |
| "collapsed": true | |
| }, | |
| "cell_type": "code", | |
| "source": "eigvals, eigvects = np.linalg.eig(A)", | |
| "execution_count": 193, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "eigvals", | |
| "execution_count": 195, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([-2., 5.])" | |
| }, | |
| "execution_count": 195, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "eigvects", | |
| "execution_count": 196, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[-0.8 , -0.70710678],\n [ 0.6 , -0.70710678]])" | |
| }, | |
| "execution_count": 196, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "np.diag(eigvals)", | |
| "execution_count": 197, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "array([[-2., 0.],\n [ 0., 5.]])" | |
| }, | |
| "execution_count": 197, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false, | |
| "collapsed": true | |
| }, | |
| "cell_type": "code", | |
| "source": "A = np.random.uniform(size=(100, 100))\neigvals, eigvects = np.linalg.eig(A)", | |
| "execution_count": 200, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false, | |
| "collapsed": true | |
| }, | |
| "cell_type": "code", | |
| "source": "A_rec = eigvects @ np.diag(eigvals) @ np.linalg.inv(eigvects)", | |
| "execution_count": 202, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "np.all(np.isclose(A, A_rec))", | |
| "execution_count": 212, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "True" | |
| }, | |
| "execution_count": 212, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true, | |
| "collapsed": true | |
| }, | |
| "cell_type": "code", | |
| "source": "import numpy as np\nimport matplotlib.pyplot as plt\n%matplotlib inline", | |
| "execution_count": 1, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "n = 30 # размер выборки\np = 0.3\nnumber_of_samples = 10000\nsamples = ((np.random.uniform(size=(number_of_samples, n))) < p) * 1\nplt.xlim(0, 1)\nplt.hist(samples.mean(axis=1), bins=20);", | |
| "execution_count": 8, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": "<matplotlib.figure.Figure at 0x1042a8ba8>", | |
| "image/png": 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| |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "collapsed": true, | |
| "trusted": false | |
| }, | |
| "cell_type": "code", | |
| "source": "", | |
| "execution_count": null, | |
| "outputs": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "name": "python3", | |
| "display_name": "Python 3", | |
| "language": "python" | |
| }, | |
| "language_info": { | |
| "name": "python", | |
| "version": "3.6.1", | |
| "mimetype": "text/x-python", | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "pygments_lexer": "ipython3", | |
| "nbconvert_exporter": "python", | |
| "file_extension": ".py" | |
| }, | |
| "gist": { | |
| "id": "", | |
| "data": { | |
| "description": "math-ml-intro.ipynb", | |
| "public": false | |
| } | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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