Jupyter_environment.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discovering the environment\n",
    "\n",
    "The partical lab is based on the following tools :\n",
    " - **python** : a general purpose language\n",
    "   - modern language / very clean / not limited\n",
    "   - gentle learning curve - easy for beginners\n",
    " - python **standard library**\n",
    "   - HUGE\n",
    " - **jupyter notebook** an interactive layer over the python language\n",
    "   - a nice GUI of this stuff, also includes **R** and other languages\n",
    "   - many added convenient utilities added\n",
    "   - check the `%magic` commands\n",
    " - **numpy** a library making numeric vectors first class python objects\n",
    " - **scipy** a library holding *most* standards mathematical and statistical methods\n",
    "   - other library available.\n",
    " - **matplotlib** a library for scientific plots\n",
    "\n",
    "there are also libraries that we will not use, but can be very usefull for data-scientists:\n",
    "   - **pandas** is a very comprehensie data-analysis environment for python - *similar to R*\n",
    "   - **SymPy** is a symbolic environment *similar to Mapple*\n",
    "   - **scikit-learn** a machine-earning envirnment for python\n",
    "\n",
    "---\n",
    "\n",
    "### getting documentation\n",
    "This is a very important part - you'll find yourself spending more time reading doc than writting code !\n",
    "\n",
    "Do not hesitate to go through the different help systems - available from here,\n",
    "( *look at the Help menu of this page, you will recognize the list * )\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Notebook\n",
    "it is organized in cells, each cell can either contain formatted text ( *this cell!* ), or a python program.\n",
    "\n",
    "When executed, the result is displayed below the program cell"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### commands\n",
    "- shell type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'/Users/mad/Documents/ mad/cours/FT/Fourier_Transform'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pwd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- python command"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "there is a slight difficult with python version 2 and 3 co-existing.\n",
    "In practice, there is very little differences, unless you dig deep into the environment.\n",
    "At our level, the following command insures that both versions will behave in an equivalent manner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division    # this insures python 2 / python 3 compatibility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this course will last 1.5 hours\n"
     ]
    }
   ],
   "source": [
    "print( 'this course will last', 1 + 0.5, 'hours')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- python programs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 1\n",
      "2 : 2\n",
      "3 : 3\n",
      "4 : 5\n",
      "5 : 8\n",
      "6 : 13\n",
      "7 : 21\n",
      "8 : 34\n",
      "9 : 55\n",
      "10 : 89\n"
     ]
    }
   ],
   "source": [
    "def fibonacci(n):\n",
    "    \"the simplest (and inefficient) definition of the fibonacci series\"\n",
    "    if n == 0 or n == 1:\n",
    "        f = 1\n",
    "    else:\n",
    "        f = fibonacci(n-1) + fibonacci(n-2)\n",
    "    return f\n",
    "\n",
    "for i in range(10):\n",
    "    print (i+1, ':', fibonacci(i+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## the python language\n",
    "python is a simple program, one of its strength lies in all the libraries available - in particular scientific ones (see above)\n",
    "\n",
    "Some libraries are directly a part of the standard language (web interface, cryptography, data-base, etc. *you name it* )\n",
    "Other are developped independently, with the standard scientific stack : **numpy, scipy, sympy, matplotlib, pandas** (look at the help menu) or other more specific to a particular domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# numpy provides a fast computation of large numerical arrays\n",
    "import numpy as np     # (here we just give numpy the (standard) nick name np for a lighter source code)\n",
    "\n",
    "# matplotlib is the graphic library\n",
    "# matplotlib.pylab is an easy to use utility, a bit reminiscent to matlab graphics\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "# %matplotlib is a \"magic\" command to insert directly the graphics in the web page\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with these tools we can easily build and display complex functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "length of vectors, x: 1000 y: 1000\n",
      "433th value: 4.324324324324325 -0.3783976870885793\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(0,10,1000)                 # 1000 points equi-distant from 0.0 to 10.0\n",
    "y = np.cos(x)                              # takes the cos() values of all points in x\n",
    "print('length of vectors, x:',len(x), 'y:',len(y))\n",
    "print('433th value:', x[432], y[432])      # !!! array indices are from 0 to 999 !!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d576898>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# and plot it - like in Excel !\n",
    "plt.plot(x,y)                   # whole curve\n",
    "plt.plot(x[432],y[432], 'ro')   # a set of points   - r is for red   o is for round points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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
}