Lab2-1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "38447fea-a05f-4f5e-987e-f2ae3579cd95",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d1b3e9ce-174d-42d4-a88f-9e760d198aa4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vector: [ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15]\n",
      "Two dimensional array: [[ 1  2  3  4  5]\n",
      " [ 6  7  8  9 10]\n",
      " [11 12 13 14 15]]\n"
     ]
    }
   ],
   "source": [
    "array2=np.array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15])\n",
    "print(\"Vector:\",array2)\n",
    "a=array2.reshape(3,5)\n",
    "print(\"Two dimensional array:\",a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c4848299-33be-4db8-b197-8a0489246428",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape: (3, 5)\n",
      "dimension: 2\n",
      "data type: int32\n",
      "size: 15\n",
      "type: <class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "print(\"shape:\",a.shape)\n",
    "print(\"dimension:\",a.ndim)\n",
    "print(\"data type:\",a.dtype.name)\n",
    "print(\"size:\",a.size)\n",
    "print(\"type:\",type(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e55ff1f7-8cb0-4e5f-8911-4c0613fe6602",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5 7 9]\n",
      "[-3 -3 -3]\n",
      "[1 4 9]\n"
     ]
    }
   ],
   "source": [
    "x=np.array([1,2,3])\n",
    "y=np.array([4,5,6])\n",
    "print(x+y)\n",
    "print(x-y)\n",
    "print(x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "52130d21-6ba7-4d20-96d2-12a67304b33b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "[5 2 3] [5 2 3] [5 2 3]\n"
     ]
    }
   ],
   "source": [
    "a=np.array([1,2,3])\n",
    "d=a.copy()\n",
    "print(d)\n",
    "b=a\n",
    "c=a\n",
    "b[0]=5\n",
    "print(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "44ad6dca-6119-40d9-82a8-f360a22c72ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "[1 2 3 4]\n"
     ]
    }
   ],
   "source": [
    "a=np.array([1,2,3,4,5,6,7])\n",
    "print(a[0])\n",
    "print(a[0:4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e02bb7b5-ac6b-488f-a814-2a6434e42f4d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7 6 5 4 3 2 1]\n"
     ]
    }
   ],
   "source": [
    "reverse_array=a[::-1]\n",
    "print(reverse_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5d7bacc3-038d-4e79-bfee-aa81e53d604b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3  4  5]\n",
      " [ 6  7  8  9 10]]\n",
      "7\n",
      "[2 7]\n",
      "[ 6  7  8  9 10]\n",
      "[7 8 9]\n",
      "[ 6  7  8  9 10]\n",
      "[ 5 10]\n"
     ]
    }
   ],
   "source": [
    "b=np.array([[1,2,3,4,5],[6,7,8,9,10]])\n",
    "print(b)\n",
    "print(b[1,1])\n",
    "print(b[:,1])\n",
    "print(b[1,:])\n",
    "print(b[1,1:4])\n",
    "print(b[-1,:])\n",
    "print(b[:,-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "794a8a95-eb0b-44ae-984e-a559b6dd48c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Matplotlib is building the font cache; this may take a moment.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "data = np.random.randn(1000)\n",
    "\n",
    "plt.hist(data,bins=30)\n",
    "plt.title(\"histogram\")\n",
    "plt.xlabel(\"Values\")\n",
    "plt.ylabel(\"Frequencies\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "34c9aecb-2395-4b69-b88d-b62475d164f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sizes=[30,25,15,10,5,5]\n",
    "plt.pie(sizes)\n",
    "plt.title(\"Pie Chart\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d19cfbc7-24eb-4448-b816-4135a10f473f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}