Ubrzavanje.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pi_approx(n):\n",
    "    x = np.linspace(0, 1, n + 1)[1:]\n",
    "    s = (1 - x**2) ** .5\n",
    "    return (1/2 + s.sum()) / n * 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 136 ms, sys: 32 ms, total: 168 ms\n",
      "Wall time: 167 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.1415926535526095"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time pi_approx(10 ** 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def py_approx(n):\n",
    "    t = sum((1 - (i/n)**2) ** .5 for i in range(1, n+1))\n",
    "    return (t + 1/2) / n * 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.08 s, sys: 0 ns, total: 3.08 s\n",
      "Wall time: 3.08 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.141592653552712"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time py_approx(10 ** 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}