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@heksamolako25
Created May 29, 2024 01:41
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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"id": "c901d4f2",
"metadata": {},
"outputs": [],
"source": [
"## Bilangan acak\n",
"Bilangan acak adalah sebuah bilangan yang dipilih seakan-akan secara kebetulan dari suatu distribusi tertentu sehingga seleksi suatu himpunan besar bilangan-bilangan ini mengha-silkan distribusi yang mendasarinya"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a7b9f321",
"metadata": {},
"outputs": [],
"source": [
"## Bilangan pseudo-acak (pseudo random\n",
"•Himpunan nilai atau elemen yang acak secara statistik, akan tetapi diturunkan dari sebuah titik awal yang diketahui dan umumnya diulang-ulang lagi dan lagi.\n",
"•Menyediakan nilai-nilai yang diperlukan bagi proses-proses yang membutuhkan keacakan, seperti menghasilkan sinyal uji.\n",
"•Disebut ‘pseudo’ acak karena algoritmanya dapat mengulangi pembangkitan kembali urutan bilangan-bilangan acak, dan sebenarnya tidaklah sepenuhnya ac"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d3b882bc",
"metadata": {},
"outputs": [],
"source": [
"## Algoritma\n",
"•Algoritme khusus tersedia untuk membangkitan bilangan pseudo-acak, yang memiliki sifat statistik terbandingkan, te-tapi nilainya tidak dapat diprediksi karena bergantung pada sejumlah nilai-nilai awal (seed).\n",
"•Sering suatu iterasi ri+1= f(ri)digunakan untuk menghitung deret bilanga pseudo-acak.\n",
"•Dengan bilangan bulat 32bit terdapat 2 32 bilangan berbeda, karenanya periode bilangan tidak dapat mecapai "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c8eb22ff",
"metadata": {},
"outputs": [],
"source": [
"## Metode Monte Carlo\n",
"•Permasalahan fisis seringkali melibatkan integral berdimensi tinggi, seperti misalnya pada integral lintasan (path integrals) dan rata-rata termodinamika (thermodynamics averages).\n",
"•Jenis integral ini tidak dapat dievaluasi dengan metode stan-dar: persegi, trapesium, Simpson atau Euler, Runge-Kutta"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "a6c13dde",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4 8 2 2 8 4 7 7 3 5 4 4 5 3 4 7 8 8 7 5 5 8 8 2 8 3 8 6 3 8 7 6 3 5 8 7 5 7 5 7 7 6 6 7 3 7 6 6 5 6 2 4 8 8 2 3 3 4 4 4 3 7 6 8 7 2 4 2 6 8 6 8 4 6 2 5 4 4 2 8 5 5 2 7 7 8 4 7 3 7 4 2 5 3 8 4 2 2 5 4 \n",
"\n",
"\n",
"100\n"
]
}
],
"source": [
"## Random numbers\n",
"import random as rnd\n",
"import matplotlib.pyplot as plt\n",
"N = 100\n",
"a = 2\n",
"b = 8\n",
"x = []\n",
"for i in range(N):\n",
" j = rnd.randint(a, b)\n",
" x.append(j)\n",
" print(j, end=' ')\n",
"print('\\n\\n')\n",
"\n",
"print(len(x))"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "5d6e464e",
"metadata": {},
"outputs": [
{
"data": {
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H2NR7FABp27pUBesrvF1JmS0X5eWXX8aBAweQn59fLqXx19/bwm7dugUrKytUqVLluddTmCJ2SQFA9erVMWnSJHTr1s3gD2ZhHTp0wMOHD402rG+//Vb//dIqqok7d+4MGxsbXLlyRf8fduGv4nz00UdwdHTUH5QsTAihP6224BfirwdMAeCf//xnqZ/PX7355psAgDVr1hiMp6am4sKFCyW+XqY2WODPXWQFfwAqip+fH06fPm0wtnv3bjx8+LDY+6lUKgghjF7Pb775Bnl5eQZjpflPrOD1Kvx6/vDDD3j06FGZtr+i1lPe27k5dO3aVX+ar6nfl4LtRaVSwcbGxuAg9OPHj7F69eoKz1hw1lvh7ep5Trbo0qULnjx5YnCGlSlS927Ur18f1atXx9q1aw3OGnv06BF++OEH/ZlT5U0xMwwA+Oyzz0pc5v3338eXX36JiIgIpKeno3Hjxjhw4ADmzJmDsLAwdOzYsdTrbdy4MQBgwYIFiIiIgFqtRv369eHn54eZM2di6tSpuHr1Kt566y1UqVIFv/32G44cOQJHR8diT+/z9/fH+vXr0adPHzRr1kz/xj3g2ZvFli9fDiEE3n77bQQEBKB27dqYMmUKhBBwc3PDTz/9hKSkpFI/n7+qX78+PvjgAyxcuBBWVlbo0qWL/iwpHx8ffPTRR8Xev3PnzqhRowa6deuGgIAA5Ofn4+TJk/j888/h5ORU4W9qGzRoEKKjozF9+nQEBQXh/PnzWLRokcnTlP/KxcUF7du3x7x581C1alX4+flh7969WLZsmdGbMwve+bx06VI4OzvDzs4O/v7+JnfBdOrUCZ07d8bkyZORnZ2NNm3a6M+Sat68OQYNGlQuz7sitvMC2dnZ+P77743GX375ZQQFBT1PbMycORNJSUlo3bo1xo4di/r16+PJkydIT0/H9u3bsWTJEtSoUQPh4eGYP38++vfvjw8++ACZmZn4+9//blTwFaFatWro2LEj4uLiUKVKFfj6+mLXrl3YuHFjmR+zX79+WLFiBUaOHImLFy8iJCQE+fn5OHz4MBo0aIC+ffsCePa3Jjk5GT/99BO8vLzg7OyM+vXrGz2elZUV4uPjMWDAAHTt2hUjRoyAVqvFvHnz8Mcff0j6W1kmkg+Pm9lfz5IqTuGzpIQQIjMzU4wcOVJ4eXkJGxsb4evrK6KiosSTJ08MlgMgIiMjjR6z8Bk2QggRFRUlvL29hZWVldEZFJs3bxYhISHCxcVFaDQa4evrK3r16iV++eUXSc/1ypUrYtSoUaJOnTpCo9EIe3t78corr4gJEyYYnJl1/vx50alTJ+Hs7CyqVKkievfuLa5fv250plDBWRG///670bpMneGSl5cn5s6dK+rVqyfUarWoWrWqGDhwoLhx40aJ2Tds2CD69+8v6tatK5ycnIRarRY1a9YUgwYNEufPnzdYtqizpObNm2ewXMEZIf/+978Nxk1tE1qtVnz88cfCx8dH2Nvbi6CgIHHy5ElJZ0n997//Fe+++66oUqWKcHZ2Fm+99ZY4e/asyZ9/QkKC8Pf3F9bW1gZnyhQ+S0qIZ2cHTZ48Wfj6+gq1Wi28vLzEhx9+KO7fv2+wnK+vrwgPDzd6TQu/TkWRup2X9iwpmDiDCIA+U1FnSUl9Lr///rsYO3as8Pf3F2q1Wri5uYnXXntNTJ06VTx8+FC/3PLly0X9+vWFRqMRtWrVEnFxcWLZsmVGZywWte6iRERECEdHx2KXuX37tujVq5dwc3MTrq6uYuDAgeLo0aMmz5Iy9VimXqPHjx+L6dOni7p16wpbW1vh7u4u3nzzTXHw4EH9MidPnhRt2rQRDg4OBq95UWdubd68WbzxxhvCzs5OODo6ig4dOoj//Oc/JrMU/ntQ8PtU+OzP4qiEKPQuGCIiIhMUcwyDiIjkxcIgIiJJWBhERCSJrIURFxeHFi1awNnZGR4eHujZsycuXrxY5PIjRoyASqUy+vwoIiKqeLIWxt69exEZGYlDhw4hKSkJubm5CA0NNflBeZs3b8bhw4cr/Lx+IiIyTdb3YezYscPg9ooVK+Dh4YFjx44ZfFLnzZs3MXr0aOzcudPo84WIiMg8LOqNewXvdv7rZwjl5+dj0KBBmDRpEho2bFjiY2i1WoO39Ofn5+PevXtwd3dX9GUliYgKCCHw4MGDcv18KikspjCEEJgwYQLatm1rcE3huXPnwsbGBmPHjpX0OHFxcc918RQiIqW4ceOGWa9+aDGFMXr0aJw+fRoHDhzQjx07dgwLFizA8ePHJc8OoqKiMGHCBP3trKws/afCSr3+t06nw549exASElLqiwGZk1JyAsrJqpScgHKyKiUnoJys9+7dQ7169ST/TSsvFlEYY8aMwZYtW7Bv3z6Dtty/fz/u3Llj8Bn7eXl5mDhxIhISEpCenm70WBqNxuTnzRRc5lEKnU4HBwcHuLu7W/RGo5ScgHKyKiUnoJysSskJKCsrUL6f0iuFrIUhhMCYMWOwadMmJCcnw9/f3+D7gwYNMvoQtc6dO2PQoEEYMmSIOaMSEVV6shZGZGQk1q5dix9//BHOzs7IyMgAALi6usLe3h7u7u5GnwiqVqtRrVo1k5/gSEREFUfW92EsXrwYWVlZCA4OhpeXl/5rw4YNcsYiIiITZN8lVVqmjlsQEVHF42dJERGRJCwMIiKShIVBRESSsDCIiEgSFgYREUnCwiAiIklYGEREJAkLg4iIJGFhEBGRJCwMIiKShIVBRPQ/Z29myx3BolnE9TCIiOTkN2XbX27ZICxMtigWjTMMIqrUDMuCisMZBhFVSt0WHsCZm1lG4wsCc2VIowycYRBRpeM3ZZvJsrg8K1SGNMrBGQYRVRpfJF3Cgl2XjcbTPwsH8Oya3lQ0FgYRVQpFHasoKAsqGQuDiF5oBy7fxcBlh43G0+LCoFKpZEikXCwMInphcVZRvlgYRPTCuZ31GIFxu43Gz8SEwtlOLUOiFwMLg4heKJxVVBwWBhG9EJ7m5qPetJ+Nxn8e1w4NvFxkSPTiYWEQkeJxVmEeLAwiUjRTZfH33k3R67UaMqR5sbEwiEiROKswP340CBEpjqmyeKd5dZZFBeMMg4gUg7MKeck6w4iLi0OLFi3g7OwMDw8P9OzZExcvXjRYRgiBmJgYeHt7w97eHsHBwTh37pxMiYlILqbKwk5txbIwI1kLY+/evYiMjMShQ4eQlJSE3NxchIaG4tGjR/pl4uPjMX/+fCxatAipqamoVq0aOnXqhAcPHsiYnIjMxW/KNpNlkf5ZOP5vVhcZElVesu6S2rFjh8HtFStWwMPDA8eOHUP79u0hhEBCQgKmTp2Kd955BwCwatUqeHp6Yu3atRgxYoQcsYnITLgLyrJY1DGMrKxnn0/v5uYGAEhLS0NGRgZCQ//8jHqNRoOgoCAcPHjQZGFotVpotVr97ezsZ9fo1el0kj+6uGA5S/+oY6XkBJSTVSk5AeVkLUvOtxcfwtlbxtfXLrheRUU9Z6W9puamEkIIWdZciBACPXr0wP3797F//34AwMGDB9GmTRvcvHkT3t7e+mU/+OADXLt2DTt37jR6nJiYGMTGxhqNr127Fg4ODhX3BIioXIxLMf1/LK+E96ecnBz0798fWVlZcHEx37vYLWaGMXr0aJw+fRoHDhww+l7hjyAWQhT5scRRUVGYMGGC/nZ2djZ8fHwQGhoq+YXV6XRISkpCp06doFZb7geVKSUnoJysSskJKCer1Jz/2P0rFu65ajRuzqvgKeU1zczMlGW9FlEYY8aMwZYtW7Bv3z7UqPHnuzOrVasGAMjIyICXl5d+/M6dO/D09DT5WBqNBhqNxmhcrVaXegMoy33koJScgHKyKiUnoJysxeW0tGMVlv6aypVN1rOkhBAYPXo0Nm7ciN27d8Pf39/g+/7+/qhWrRqSkpL0Y0+fPsXevXvRunVrc8clonJ24PJdk2WRFhfGA9sWSNYZRmRkJNauXYsff/wRzs7OyMjIAAC4urrC3t4eKpUK48ePx5w5c1C3bl3UrVsXc+bMgYODA/r37y9ndCJ6TpY2q6CSyVoYixcvBgAEBwcbjK9YsQKDBw8GAHz88cd4/PgxRo0ahfv37+ONN95AYmIinJ2dzZyWiMoDL26kXLIWhpQTtFQqFWJiYhATE1PxgYioQnFWoWwWcdCbiF5suflA3ehEo3Fe3EhZWBhEVKGeFYXxnxrOKpSHhUFEFYYXN3qxsDCIqNzxWMWLiRdQIqJyZaosbFTCrO/YporBGQYRlYuiZhWXZ4Vi+/btZk5DFYEzDCJ6btwFVTlwhkFEZcaiqFw4wyCiMmFZVD6cYRBRqbAoKi/OMIhIMpZF5cYZBhGV6J2v/oPj1/8wGmdRVC4sDCIqFmcVVICFQUQmrU5JR/SP54zG0+LCirxEMr3YWBhEZISzCjKFhUFEehczHqBzwj6j8WPTOsLdSSNDIrIkLAwiAsBZBZWMhUFUyT3R5SEgeofR+OphLdGu7ssyJCJLxcIgqsQ4q6DS4Bv3iCopU2UxtI0/y4KKxBkGUSXDWQWVFWcYRJWIqbJwsLVmWZAknGEQVQKcVVB54AyD6AXHsqDywhkG0QuKRUHljTMMohcQy4IqAmcYRC8QFgVVJM4wiF4QLAuqaLIWxr59+9CtWzd4e3tDpVJh8+bNRstcuHAB3bt3h6urK5ydndGqVStcv37d/GGJLFSvfx42WRbpn4WzLKhcyVoYjx49QtOmTbFo0SKT379y5Qratm2LgIAAJCcn49SpU4iOjoadnZ2ZkxJZpnEpNjj13yyjcRYFVQRZj2F06dIFXbp0KfL7U6dORVhYGOLj4/VjtWrVMkc0Iou26mA6ZmzhxY3IvCz2oHd+fj62bduGjz/+GJ07d8aJEyfg7++PqKgo9OzZs8j7abVaaLVa/e3s7GwAgE6ng06nk7TuguWkLi8XpeQElJNVCTnrRieaHL88KxS5ublmTlMyJbymBZSSVa58KiGEkGXNhahUKmzatElfBhkZGfDy8oKDgwM+/fRThISEYMeOHfjkk0+wZ88eBAUFmXycmJgYxMbGGo2vXbsWDg4OFfkUiCrUrUfA3NPG/+PNfj0XTmoZApFscnJy0L9/f2RlZcHFxcVs67XYwrh16xaqV6+Ofv36Ye3atfrlunfvDkdHR6xbt87k45iaYfj4+ODu3buSX1idToekpCR06tQJarXl/iYqJSegnKyWmrOoWcWCwFyLy1qYpb6mpigla2ZmJry8vMxeGBa7S6pq1aqwsbHBK6+8YjDeoEEDHDhwoMj7aTQaaDTGl5JUq9Wl3gDKch85KCUnoJyslpLz8dM8NJhufHGj9R+0wms+Lti+fbvFZC2JUnIClp9VrmwWWxi2trZo0aIFLl68aDB+6dIl+Pr6ypSKyHxKel+Fpe9npxePrIXx8OFD/Prrr/rbaWlpOHnyJNzc3FCzZk1MmjQJffr0Qfv27fXHMH766SckJyfLF5rIDEyVxeiQOvhb5/oypCF6RtbCOHr0KEJCQvS3J0yYAACIiIjAypUr8fbbb2PJkiWIi4vD2LFjUb9+ffzwww9o27atXJGJKhTfrU2WTNbCCA4ORknH3IcOHYqhQ4eaKRGRfEyVRTUXOxz6pIMMaYiMWewxDKLKgrMKUgp++CCRjFgWpCScYRDJgEVBSsQZBpGZsSxIqTjDIDITFgUpHWcYRGbAsqAXAWcYRBXovSUpOJJ+z2icRUFKxMIgqiCcVdCLhoVBVM6+TUnH9B95cSN68bAwiMoRZxX0ImNhEJWDC7ez0WXBfqPxE9GdUMXRVoZEROWPhUH0nDiroMqChUFURkVd3GjDB63wRi13GRIRVSwWBlEZcFZBlRELg6iUeHEjqqxYGEQScVZBlR0/GoRIAlNl4eVqx7KgSoUzDKJicFZB9CfOMIiKwLIgMsQZBlEh41JsMC4l0WicRUGVHWcYRH9RN9q4KACWBRHAGQYRAO5+IpKCMwyq9FgWRNJwhkGVVvg/9uPcrWyj8QWBuQgLC5MhEZFl4wyDKiW/KdtMlsXlWaEypCFSBs4wqFL5Zv9VfLrtgtF4wcWNdDqdDKmIlIGFQZUGj1UQPR9Zd0nt27cP3bp1g7e3N1QqFTZv3qz/nk6nw+TJk9G4cWM4OjrC29sb77//Pm7duiVfYFKkszezTJbFyemdWBZEpSBrYTx69AhNmzbFokWLjL6Xk5OD48ePIzo6GsePH8fGjRtx6dIldO/eXYakpFR+U7ah68IDRuPpn4XjJQdeCY+oNEq9S2rw4MEYOnQo2rdv/9wr79KlC7p06WLye66urkhKSjIYW7hwIVq2bInr16+jZs2az71+enHlPM3FK9N3Go3z4kZEZVfqwnjw4AFCQ0Ph4+ODIUOGICIiAtWrV6+IbEaysrKgUqnw0ksvFbmMVquFVqvV387OfnYmjE6nk3xAs2A5Sz8AqpScgHmzFvVu7YIzoIrLwNe0/CklJ6CcrHLlUwkhRGnvlJmZiTVr1mDlypU4e/YsOnbsiGHDhqFHjx5Qq9VlC6JSYdOmTejZs6fJ7z958gRt27ZFQEAA1qxZU+TjxMTEIDY21mh87dq1cHBwKFM2Uo5xKcb/A3Xwzkd333wZ0hBVjJycHPTv3x9ZWVlwcXEx23rLVBh/deLECSxfvhzffPMNnJycMHDgQIwaNQp169YtXZBiCkOn06F37964fv06kpOTi32BTM0wfHx8cPfuXckvrE6nQ1JSEjp16lTmAjQHpeQEKj5rSbMKqfialj+l5ASUkzUzMxNeXl5mL4znOq329u3bSExMRGJiIqytrREWFoZz587hlVdeQXx8PD766KPnDqjT6fDee+8hLS0Nu3fvLvHF0Wg00Gg0RuNqtbrUG0BZ7iMHpeQEKiarqTOg3BxtcTy6U5kfs7K/phVBKTkBy88qV7ZSF4ZOp8OWLVuwYsUKJCYmokmTJvjoo48wYMAAODs7AwDWr1+PDz/88LkLo6AsLl++jD179sDdnQcr6U98XwWReZW6MLy8vJCfn49+/frhyJEjaNasmdEynTt3LvbAdIGHDx/i119/1d9OS0vDyZMn4ebmBm9vb/Tq1QvHjx/H1q1bkZeXh4yMDACAm5sbbG15SmRlxrIgMr9SF8YXX3yB3r17w87OrshlqlSpgrS0tBIf6+jRowgJCdHfnjBhAgAgIiICMTEx2LJlCwAYldKePXsQHBxc2uj0AmBREMmn1IUxaNCgclt5cHAwijvm/pzH4+kFw7Igkhc/S4osHouCyDLw483JorEsiCwHZxhkkd5K2If/y3hgNM6iIJIPC4MsDmcVRJaJhUEWY+m+K5iz/f+MxgsubkRE8mJhkEXgrILI8rEwSFZn/puFbouMr1dxanooXB0s96MZiCojFgbJhrMKImVhYZDZFXVxo3+NCERLfzcZEhGRFCwMMquiPoacswoiy8c37pHZmLq4UWRIbZYFkUJwhkEVjscqiF4MnGFQhTJVFu6OtiwLIgXiDIMqRFGzisuzQi36SmZEVDTOMKjcFVUWCwJzzZyEiMoTZxhUboo7VqHT6bB9+3YzJyKi8sQZBpULHtgmevFxhkHPhUVBVHlwhkFlxrIgqlw4w6BSG7ziCJIv/m40zqIgerGxMKhUOKsgqrxYGCTJuiPXEbXxjNE4L25EVHmwMKhEnFUQEcDCoGJczHiAzgn7jMbPxITC2Y7v1iaqbFgYZBJnFURUGAuDDDx+mocG03cYjW8Z3QZNarxk/kBEZDFYGKTHWQURFYeFQQBMl8W08AYY3q6WDGmIyBJZ9Du9c3NzMW3aNPj7+8Pe3h61atXCzJkzkZ+fL3e0F4bflG0myyL9s3CWBREZsOgZxty5c7FkyRKsWrUKDRs2xNGjRzFkyBC4urpi3LhxcsdTPFNF0cznJWyObCNDGiKydBZdGCkpKejRowfCw5/tQ/fz88O6detw9OhRmZMpG49VEFFZWHRhtG3bFkuWLMGlS5dQr149nDp1CgcOHEBCQkKR99FqtdBqtfrb2dnZAACdTgedTidpvQXLSV1eLmXJWTc60eT45VmhFfp8X+TXVC5KyaqUnIByssqVTyWEELKsWQIhBD755BPMnTsX1tbWyMvLw+zZsxEVFVXkfWJiYhAbG2s0vnbtWjg4OFRkXIs2LsX0/wa8Ch6R8uTk5KB///7IysqCi4uL2dZr0YWxfv16TJo0CfPmzUPDhg1x8uRJjB8/HvPnz0dERITJ+5iaYfj4+ODu3buSX1idToekpCR06tTJoq8/LTVncbMKc3nRXlNLoJSsSskJKCdrZmYmvLy8zF4YFr1LatKkSZgyZQr69u0LAGjcuDGuXbuGuLi4IgtDo9FAo9EYjavV6lJvAGW5jxyKymmJxyqU/ppaIqVkVUpOwPKzypXNok+rzcnJgZWVYURra2ueViuBJZYFESmbRc8wunXrhtmzZ6NmzZpo2LAhTpw4gfnz52Po0KFyR7NYA745hP/8mmk0zqIgoudl0YWxcOFCREdHY9SoUbhz5w68vb0xYsQITJ8+Xe5oFomzCiKqSBZdGM7OzkhISCj2NFoC1qXewPQtF4zGWRREVJ4sujCoZM9Ol2VZEFHFY2Eo1J3sJ2g5Z5fR+NnYznDS8MdKROWPf1kUiMcqiEgOLAwFeZqbj3rTfjYa3zSyFZr7ucuQiIgqExaGQhQ1q1gQmItG1c33Tk8iqrws+o179IypstjwQSuzfrQHERFnGBaspGMVlv6JmkT0YmFhWChTZRHbvSEiWvuZPwwREVgYFodnQBGRpeIxDAtiqiy6NfVmWRCRReAMwwK8NisJmY+eGo2zKIjIkrAwZGZqVuFiZ4PTMZ1lSENEVDQWhkw+2nASm07cNBrnrIKILBULQwY8sE1ESsTCMKM1h65h2uazRuMsCiJSAhaGmXBWQURKx8KoYMeu3ce7iw8ajbMoiEhpWBgViLMKInqRsDAqQFEXN7r46VvQ2FjLkIiI6PmxMMoZZxVE9KJiYZQTbW4e6k/bYTR++JMO8HSxkyEREVH5YmGUA84qiKgyYGE8J1Nl8f3IQLzu5yZDGiKiisPCKCPOKoiosmFhlIGpsvi0ZyMMbOUrQxoiIvNgYZQCZxVEVJnxAkoSmSqLHs14cSMiqjwUVRhxcXFQqVQYP3682db52qwkk2WR/lk4FvRtbrYcRERyU8wuqdTUVCxduhRNmjQx2zrrRicajVVxUOPE9FCzZSAishSKmGE8fPgQAwYMwNdff40qVapU+Pr+9v0ZjEsx7tL0z8JZFkRUaSlihhEZGYnw8HB07NgRn376abHLarVaaLVa/e3s7GwAgE6ng06nK3Fd7684ipSr94zGL88KlXR/cyrIY2m5TFFKVqXkBJSTVSk5AeVklSufSgghZFmzROvXr8fs2bORmpoKOzs7BAcHo1mzZkhISDC5fExMDGJjY43G165dCwcHhxLXV3hmsSAwt0y5iYgqSk5ODvr374+srCy4uLiYbb0WXRg3btzA66+/jsTERDRt2hQASiwMUzMMHx8f3L17V/ILWzc6EV4OArv+9ibUavVzP4+KotPpkJSUhE6dOll0TkA5WZWSE1BOVqXkBJSTNTMzE15eXmYvDIveJXXs2DHcuXMHr732mn4sLy8P+/btw6JFi6DVamFtbfhx4RqNBhqNxuix1Gq15A3g8qxQbN++vVT3kZNScgLKyaqUnIBysiolJ2D5WeXKZtGF0aFDB5w5c8ZgbMiQIQgICMDkyZONyoKIiCqORReGs7MzGjVqZDDm6OgId3d3o3EiIqpYijitloiI5GfRMwxTkpOT5Y5ARFQpcYZBRESSsDCIiEgSFgYREUnCwiAiIklYGEREJAkLg4iIJGFhEBGRJCwMIiKShIVBRESSsDCIiEgSFgYREUnCwiAiIklYGEREJAkLg4iIJGFhEBGRJCwMIiKShIVBRESSsDCIiEgSFgYREUnCwiAiIklYGEREJAkLg4iIJGFhEBGRJCwMIiKShIVBRESSsDCIiEgSFgYREUnCwiAiIkkUURhfffUV/P39YWdnh9deew379++XOxIRUaVj8YWxYcMGjB8/HlOnTsWJEyfQrl07dOnSBdevX5c7GhFRpWLxhTF//nwMGzYMw4cPR4MGDZCQkAAfHx8sXrxY7mhERJWKjdwBivP06VMcO3YMU6ZMMRgPDQ3FwYMHTd5Hq9VCq9Xqb2dlZQEA7t27B51OJ2m9Op0OOTk5yMzMhFqtLmP6iqeUnIBysiolJ6CcrErJCSgn67179wAAQgizrteiC+Pu3bvIy8uDp6enwbinpycyMjJM3icuLg6xsbFG4/7+/hWSkYhILpmZmXB1dTXb+iy6MAqoVCqD20IIo7ECUVFRmDBhgv52fn4+7t27B3d39yLvU1h2djZ8fHxw48YNuLi4lD14BVNKTkA5WZWSE1BOVqXkBJSTNSsrCzVr1oSbm5tZ12vRhVG1alVYW1sbzSbu3LljNOsooNFooNFoDMZeeumlMq3fxcXFojeaAkrJCSgnq1JyAsrJqpScgHKyWlmZ9zC0RR/0trW1xWuvvYakpCSD8aSkJLRu3VqmVERElZNFzzAAYMKECRg0aBBef/11BAYGYunSpbh+/TpGjhwpdzQiokrF4gujT58+yMzMxMyZM3H79m00atQI27dvh6+vb4WtU6PRYMaMGUa7tiyNUnICysmqlJyAcrIqJSegnKxy5VQJc5+XRUREimTRxzCIiMhysDCIiEgSFgYREUnCwiAiIklYGP8TFxeHFi1awNnZGR4eHujZsycuXrwodyyTFi9ejCZNmujfXBQYGIiff/5Z7lgliouLg0qlwvjx4+WOYiQmJgYqlcrgq1q1anLHMunmzZsYOHAg3N3d4eDggGbNmuHYsWNyxzLi5+dn9JqqVCpERkbKHc1Abm4upk2bBn9/f9jb26NWrVqYOXMm8vPz5Y5m5MGDBxg/fjx8fX1hb2+P1q1bIzU11Wzrt/jTas1l7969iIyMRIsWLZCbm4upU6ciNDQU58+fh6Ojo9zxDNSoUQOfffYZ6tSpAwBYtWoVevTogRMnTqBhw4YypzMtNTUVS5cuRZMmTeSOUqSGDRvil19+0d+2traWMY1p9+/fR5s2bRASEoKff/4ZHh4euHLlSpk/zaAipaamIi8vT3/77Nmz6NSpE3r37i1jKmNz587FkiVLsGrVKjRs2BBHjx7FkCFD4OrqinHjxskdz8Dw4cNx9uxZrF69Gt7e3lizZg06duyI8+fPo3r16hUfQJBJd+7cEQDE3r175Y4iSZUqVcQ333wjdwyTHjx4IOrWrSuSkpJEUFCQGDdunNyRjMyYMUM0bdpU7hglmjx5smjbtq3cMcpk3Lhxonbt2iI/P1/uKAbCw8PF0KFDDcbeeecdMXDgQJkSmZaTkyOsra3F1q1bDcabNm0qpk6dapYM3CVVhIKPRTf3h3uVVl5eHtavX49Hjx4hMDBQ7jgmRUZGIjw8HB07dpQ7SrEuX74Mb29v+Pv7o2/fvrh69arckYxs2bIFr7/+Onr37g0PDw80b94cX3/9tdyxSvT06VOsWbMGQ4cOlfwhoObStm1b7Nq1C5cuXQIAnDp1CgcOHEBYWJjMyQzl5uYiLy8PdnZ2BuP29vY4cOCAeUKYpZYUJj8/X3Tr1s2i/5M7ffq0cHR0FNbW1sLV1VVs27ZN7kgmrVu3TjRq1Eg8fvxYCCEsdoaxfft28f3334vTp0/rZ0Kenp7i7t27ckczoNFohEajEVFRUeL48eNiyZIlws7OTqxatUruaMXasGGDsLa2Fjdv3pQ7ipH8/HwxZcoUoVKphI2NjVCpVGLOnDlyxzIpMDBQBAUFiZs3b4rc3FyxevVqoVKpRL169cyyfhaGCaNGjRK+vr7ixo0bckcpklarFZcvXxapqaliypQpomrVquLcuXNyxzJw/fp14eHhIU6ePKkfs9TCKOzhw4fC09NTfP7553JHMaBWq0VgYKDB2JgxY0SrVq1kSiRNaGio6Nq1q9wxTFq3bp2oUaOGWLdunTh9+rT49ttvhZubm1i5cqXc0Yz8+uuvon379gKAsLa2Fi1atBADBgwQDRo0MMv6WRiFjB49WtSoUUNcvXpV7iil0qFDB/HBBx/IHcPApk2b9Bt2wRcAoVKphLW1tcjNzZU7YrE6duwoRo4cKXcMAzVr1hTDhg0zGPvqq6+Et7e3TIlKlp6eLqysrMTmzZvljmJSjRo1xKJFiwzGZs2aJerXry9TopI9fPhQ3Lp1SwghxHvvvSfCwsLMsl6eJfU/QgiMGTMGmzZtQnJysuKu0CeEMLg0rSXo0KEDzpw5YzA2ZMgQBAQEYPLkyRZ5FlIBrVaLCxcuoF27dnJHMdCmTRuj070vXbpUoR/G+bxWrFgBDw8PhIeHyx3FpJycHKPrSlhbW1vkabUFHB0d4ejoiPv372Pnzp2Ij483z4rNUksK8OGHHwpXV1eRnJwsbt++rf/KycmRO5qRqKgosW/fPpGWliZOnz4tPvnkE2FlZSUSExPljlYiS90lNXHiRJGcnCyuXr0qDh06JLp27SqcnZ1Fenq63NEMHDlyRNjY2IjZs2eLy5cvi++++044ODiINWvWyB3NpLy8PFGzZk0xefJkuaMUKSIiQlSvXl1s3bpVpKWliY0bN4qqVauKjz/+WO5oRnbs2CF+/vlncfXqVZGYmCiaNm0qWrZsKZ4+fWqW9bMw/geAya8VK1bIHc3I0KFDha+vr7C1tRUvv/yy6NChgyLKQgjLLYw+ffoILy8voVarhbe3t3jnnXcs7phQgZ9++kk0atRIaDQaERAQIJYuXSp3pCLt3LlTABAXL16UO0qRsrOzxbhx40TNmjWFnZ2dqFWrlpg6darQarVyRzOyYcMGUatWLWFrayuqVasmIiMjxR9//GG29fPjzYmISBK+D4OIiCRhYRARkSQsDCIikoSFQUREkrAwiIhIEhYGERFJwsIgIiJJWBhERCQJC4OIiCRhYRARkSQsDCIikoSFQfQcfv/9d1SrVg1z5szRjx0+fBi2trZITEyUMRlR+eOHDxI9p+3bt6Nnz544ePAgAgIC0Lx5c4SHhyMhIUHuaETlioVBVA4iIyPxyy+/oEWLFjh16hRSU1NhZ2cndyyicsXCICoHjx8/RqNGjXDjxg0cPXoUTZo0kTsSUbnjMQyicnD16lXcunUL+fn5uHbtmtxxiCoEZxhEz+np06do2bIlmjVrhoCAAMyfPx9nzpyBp6en3NGIyhULg+g5TZo0Cd9//z1OnToFJycnhISEwNnZGVu3bpU7GlG54i4poueQnJyMhIQErF69Gi4uLrCyssLq1atx4MABLF68WO54ROWKMwwiIpKEMwwiIpKEhUFERJKwMIiISBIWBhERScLCICIiSVgYREQkCQuDiIgkYWEQEZEkLAwiIpKEhUFERJKwMIiISJL/BypK8r33kMTRAAAAAElFTkSuQmCC",
"text/plain": [
"<Figure size 400x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Linear function\n",
"def f(x):\n",
" y = 3*(x-2) +4\n",
" return y\n",
"\n",
"y = [f(i) for i in x]\n",
"\n",
"plt.figure(figsize=(4, 3))\n",
"plt.plot(x, y)\n",
"plt.xticks(range(a, b + 2))\n",
"plt.yticks(range(0, 26,4))\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.title(\"Monte Carlo Simulation of Linear Function\")\n",
"plt.grid()\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "4b45404b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Quadratic function\n",
"import numpy as np\n",
"\n",
"def quadratic(x, a, b, c):\n",
" return a * x**2 + b * x + c\n",
"\n",
"a = 2 # Coefficient of x^2\n",
"b = 3 # Coefficient of x\n",
"c = 1 # Constant term\n",
"\n",
"x_min = -5\n",
"x_max = 5\n",
"num_samples = 10000 # Number of random samples\n",
"\n",
"x_values = np.random.uniform(low=x_min, high=x_max, size=num_samples)\n",
"y_values = quadratic(x_values, a, b, c)\n",
"\n",
"theoretical_x = np.linspace(x_min, x_max, 100) # 100 points for smooth curve\n",
"theoretical_y = quadratic(theoretical_x, a, b, c)\n",
"\n",
"plt.scatter(x_values, y_values, alpha=0.5, label=\"Simulated Points\")\n",
"plt.plot(theoretical_x, theoretical_y, label=\"Theoretical Curve\")\n",
"plt.xlabel(\"X-Values\")\n",
"plt.ylabel(\"Y-Values\")\n",
"plt.title(\"Monte Carlo Simulation of a Quadratic Function\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "eb69ba61",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral: 2.533045268367675e-05\n",
"Analytical solution (optional): 0.25\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Cubic function\n",
"def cubic_function(x):\n",
" return x**3\n",
"\n",
"a = 0\n",
"b = 1\n",
"iterations = 10000\n",
"\n",
"x_samples = np.random.uniform(a, b, iterations)\n",
"y_samples = cubic_function(x_samples)\n",
"area_rectangle = (b - a) * (b - a)\n",
"\n",
"estimated_integral = (area_rectangle * np.mean(y_samples)) / iterations\n",
"analytical_solution = (b**4 - a**4) / 4\n",
"\n",
"print(\"Estimated integral:\", estimated_integral)\n",
"print(\"Analytical solution (optional):\", analytical_solution)\n",
"\n",
"plt.plot(np.linspace(a, b, 100), cubic_function(np.linspace(a, b, 100)), label=\"Cubic Function\")\n",
"plt.scatter(x_samples, y_samples, alpha=0.3, label=\"Random Samples\")\n",
"plt.xlabel(\"X\")\n",
"plt.ylabel(\"Y\")\n",
"plt.title(\"Monte Carlo Integration of Cubic Function\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "057b7542",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral of sin^2(x) from 0 to 3.141592653589793 using 10000 samples: 1.5789858455233527\n",
"Analytical solution: 0.0\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Sine squared function\n",
"\n",
"def f(x):\n",
" return np.sin(x)**2\n",
"\n",
"a = 0\n",
"b = np.pi\n",
"N = 10000\n",
"\n",
"x = np.random.uniform(a, b, size=N)\n",
"y = f(x)\n",
"\n",
"integral_estimate = (b - a) * np.mean(y)\n",
"print(\"Estimated integral of sin^2(x) from\", a, \"to\", b, \"using\", N, \"samples:\", integral_estimate)\n",
"analytical_integral = (1 - np.cos(2*b)) / 2 - (1 - np.cos(2*a)) / 2\n",
"print(\"Analytical solution:\", analytical_integral)\n",
"\n",
"x_axis = np.linspace(a, b, 1000)\n",
"plt.plot(x_axis, f(x_axis), label=\"sin^2(x)\")\n",
"plt.axhline(y=integral_estimate, color='r', linestyle='--', label=\"Estimated Integral Area\")\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"f(x)\")\n",
"plt.title(\"Monte Carlo Integration of sin^2(x)\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3eef87db",
"metadata": {},
"outputs": [],
"source": [
"## Fast Fourier Transform\n",
"Is a powerful algorithm used to analyze signals in the frequency domain. It efficiently calculates the Discrete Fourier Transform (DFT) of a signal, which decomposes the signal into its constituent frequencies and their amplitudes. \n",
"In Python, the scipy.fftpack library provides functions for performing FFT calculations."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a62888e7",
"metadata": {},
"outputs": [],
"source": [
"## Importance\n",
"-Used in various applications like\n",
"-Signal processing (filtering noise, analyzing audio/images)\n",
"-Data compression (removing redundant information)\n",
"-Solving differential equations"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "0e0b1a10",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.fftpack import fft, fftshift\n",
"\n",
"t = np.linspace(0, 1, 1000) # Time samples\n",
"f = 2 # Frequency of the signal\n",
"y = np.sin(2*np.pi*f*t) # Generate the sine wave\n",
"\n",
"fft_data = fft(y)\n",
"fft_abs = np.abs(fft_data)\n",
"freqs = np.fft.fftfreq(len(y)) * f # Calculate frequencies\n",
"fft_shifted = fftshift(fft_abs)\n",
"freqs_shifted = fftshift(freqs)\n",
"\n",
"plt.subplot(2, 1, 1)\n",
"plt.plot(t, y)\n",
"plt.xlabel(\"Time (s)\")\n",
"plt.ylabel(\"Signal\")\n",
"plt.title(\"Original Signal\")\n",
"\n",
"plt.subplot(2, 1, 2)\n",
"plt.plot(freqs_shifted, fft_shifted)\n",
"plt.xlabel(\"Frequency (Hz)\")\n",
"plt.ylabel(\"Magnitude\")\n",
"plt.title(\"Magnitude of the FFT\")\n",
"plt.xlim(-f, f) # Set frequency axis limits\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d416eeb4",
"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": "3.11.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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