numpy-02.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6f216575",
   "metadata": {},
   "source": [
    "# numpy\n",
    "## part 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "106167f9",
   "metadata": {},
   "source": [
    "### آرایه‌های خاص"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f04346a",
   "metadata": {},
   "source": [
    "### arange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5b6c666a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.arange(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "087dcb16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "86a4b8a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 3., 5.])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(1,6,2,dtype=float)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af6b4ed2",
   "metadata": {},
   "source": [
    "### zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "251f5205",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((2,3),dtype=float)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b852c7d2",
   "metadata": {},
   "source": [
    "### ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b14be870",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1],\n",
       "       [1, 1, 1]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones((2,3),dtype=int)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3aa343c",
   "metadata": {},
   "source": [
    "### zeros_like ones_like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "947d6b1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[1,2,3],[4,5,6]])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c78a9665",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "80081c07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0],\n",
       "       [0, 0, 0]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros_like(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "90504c23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1],\n",
       "       [1, 1, 1]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones_like(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7056f0a1",
   "metadata": {},
   "source": [
    "### indentity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "70592db3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0.],\n",
       "       [0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.identity(4,dtype=float)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc57c330",
   "metadata": {},
   "source": [
    "### ریاضیات برداری"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "85c1d741",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1,2,3])\n",
    "b = np.array([5,2,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "575e32f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 4, 9])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c20cd70f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4,  0, -3])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a - b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5918e63a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5,  4, 18])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "79d2dc79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.2, 1. , 0.5])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a/b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "327447ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  5,   4, 216], dtype=int32)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b**a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "aa6ae60d",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[1,2],[3,4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "eb4fce41",
   "metadata": {},
   "outputs": [],
   "source": [
    "b= np.array([[2,0],[1,3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e42fa01f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  0],\n",
       "       [ 3, 12]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a*b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c46a685c",
   "metadata": {},
   "source": [
    "### sin cos exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ea9af396",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1,4,9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "cfd897b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3.])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "98f3c941",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97998ab7",
   "metadata": {},
   "source": [
    "$\\pi$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c17f7442",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cb85b18",
   "metadata": {},
   "source": [
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0a289270",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.718281828459045"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.e"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "145f182d",
   "metadata": {},
   "source": [
    "### عملیات مقایسه بین بردارها"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "39163887",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1,3,0])\n",
    "b = np.array([0,3,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "42942c2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a>b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "807dba92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a==b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "c3e0ec63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a>2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a387ad1f",
   "metadata": {},
   "source": [
    "### where"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f8bedbf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1,3,0],dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "1daa8bad",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\mojta\\AppData\\Local\\Temp\\ipykernel_6756\\261954055.py:1: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  1/a\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1.        , 0.33333333,        inf])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "52eb9aca",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\mojta\\AppData\\Local\\Temp\\ipykernel_6756\\3020106849.py:1: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  np.where(a!=0,1/a,a)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1.        , 0.33333333, 0.        ])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(a!=0,1/a,a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "ad10c4cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3, 2])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(a>0,3,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ec3de71",
   "metadata": {},
   "source": [
    "### ریاضیات ماتریسی و برداری"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba4d3638",
   "metadata": {},
   "source": [
    "### ضرب داخلی"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "8b69e145",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1,2,3])\n",
    "b = np.array([0,1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "27559590",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 3])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "477d7848",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "bfcc2aec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(b,a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "89d993a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[0,1],[2,3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "e8b42843",
   "metadata": {},
   "outputs": [],
   "source": [
    "b = np.array([2,3]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "ec257556",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = np.array([[1,1],[4,0]]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "b35c956e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6, 11])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(b,a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "6e4b9471",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2,)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "4a659260",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3, 13])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "3c2fc4f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.reshape(2,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "7ade1e8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.reshape(1,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "fe5762a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "cdc6e117",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.reshape(1,-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "feafe3fd",
   "metadata": {},
   "source": [
    "### matmul"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "5e4cb370",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6, 11]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matmul(b.reshape(1,-1),a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "01514fa9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 1)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.reshape(-1,1).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "4d925c3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3],\n",
       "       [13]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matmul(a,b.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a67cef3d",
   "metadata": {},
   "source": [
    "### ضرب خارجی"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "8cc61278",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1,4,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "db9a344f",
   "metadata": {},
   "outputs": [],
   "source": [
    "b = np.array([2,2,1]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "f604ac77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4, -1, -6])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cross(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "d492cab5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4,  1,  6])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cross(b,a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "876809e8",
   "metadata": {},
   "source": [
    "### linalg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "3598aefb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 2, 0],\n",
       "       [9, 3, 7],\n",
       "       [1, 2, 1]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[4,2,0],[9,3,7],[1,2,1]])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "2732c443",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-48.00000000000003"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.det(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "14055e75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.22916667,  0.04166667, -0.29166667],\n",
       "       [ 0.04166667, -0.08333333,  0.58333333],\n",
       "       [-0.3125    ,  0.125     ,  0.125     ]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.inv(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e404667b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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