unit02_simp_lin_reg/demo1_intro_vectors.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Getting Started with Numpy Vectors\n",
    "\n",
    "The `numpy` package has a number of powerful and fast tools for manipulating vectors.  In this demo, we will illustrate some of the features of the package that will be used throughout the class.  A more complete summary of `python` and `numpy` can be found at:\n",
    "\n",
    "http://cs231n.github.io/python-numpy-tutorial/\n",
    "\n",
    "For this tutorial, we start by importing the package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating vectors\n",
    "We can create vectors a number of ways.  We can manually create a vector by specifying the elements from a list.  Note that, unlike MATLAB, there is no difference between a row and column vector.  Also, you have to call the `print` command to print the object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 4]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1,2,4])\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also set through a range of numbers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1 = [0 1 2 3 4 5 6 7 8 9]\n",
      "x2 = [2 3 4 5 6]\n"
     ]
    }
   ],
   "source": [
    "x1 = np.arange(10)   # numbers from 0 to 9 (note 10 is NOT included)\n",
    "x2 = np.arange(2,7)  # numbers from 2 to 6\n",
    "print(\"x1 = \"+str(x1))\n",
    "print(\"x2 = \"+str(x2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use a third `step` argument.  The step does not need to be positive or integer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10 15 20 25 30 35 40 45]\n",
      "[  0.    2.5   5.    7.5  10. ]\n"
     ]
    }
   ],
   "source": [
    "x1 = np.arange(10,50,5)   # Increments of 5.  Note this ends on 45, not 50\n",
    "print(x1)\n",
    "\n",
    "# Increments of 2.5.  To ensure it includes the value 10, we make the endpoint slightly >10.\n",
    "step = 2.5\n",
    "x2 = np.arange(0,10+step/2,step)\n",
    "print(x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most operations can be vectorized meaning that the operation is applied to each component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = [2 3 4 5]\n",
      "y = [ 4  9 16 25]\n"
     ]
    }
   ],
   "source": [
    "x = np.array(range(2,6))\n",
    "y = x**2\n",
    "print(\"x = \" + str(x))\n",
    "print(\"y = \" + str(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**  Write code to create the following vectors.  Use the `range` function along with basic mathematical operations.  For the case of `z2` you may consider using the `np.abs()` function.\n",
    "\n",
    "    z1 = [2,4,6,8,10,...,20]  \n",
    "    z2 = [50,40,30,...,10,0,10,20,...,50]\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the examples in the labs, we will load the vectors from data files.  We will show how to do this later using the `pandas` package."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting vectors\n",
    "The `matplotlib` package has excellent routines for plotting data and uses a very similar interface as MATLAB.  To load the package use the following commands.  The second line `%matplotlib inline` is only used when running python in `jupyter notebook.`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple illustration to plot $\\sin(2\\pi(3)t)$ vs. $t$ for $t \\in [0,2]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1d4377bf2b0>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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ddZh4ftQOJjz3XPv75s2byytQCtQ1N5L6DNG10AnRtdDjE9S1snFJZB5gMJFZ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\nFEVRouX/B0BISejd0GZBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4376d3748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = 3\n",
    "t = np.linspace(0,2,100)  # Similar to the MATLAB linspace command\n",
    "y = np.sin(2*np.pi*f*t)\n",
    "\n",
    "plt.plot(t,y)\n",
    "plt.grid()\n",
    "plt.xlabel('t', fontsize=16)\n",
    "plt.ylabel('sin(2pi ft)', fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also stack plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1d4377b9668>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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J8DOC0IIMH8i8bmokCA8fPlz0mGJFdSlnbOmb/MyVPiqQa/nJ158quGYEci0T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\n+aJbQgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4376dc6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ysq = y**2\n",
    "plt.plot(t,y)\n",
    "plt.plot(t,ysq)\n",
    "plt.grid()\n",
    "plt.xlabel('t')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise** Create a plot of $y = e^{-2x}$ vs. $x$ for $x \\in [-1,3]$.  Use 200 points in the values of $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indexing and Slicing Vectors\n",
    "\n",
    "You can access individual elements by `x[i]`.  Unlike MATLAB, the indexing starts at 0!  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Element 0 is 2\n",
      "Element 3 is 8\n"
     ]
    }
   ],
   "source": [
    "x = np.array([2,4,6,8,10])\n",
    "print(\"Element 0 is \"+str(x[0]))\n",
    "print(\"Element 3 is \"+str(x[3])) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to MATLAB, you can obtain *slices* from `numpy` vectors, meaning subsets of components.  Use the `:` operator as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=      [ 0.058  0.073  0.522  0.379  0.157  0.319  0.802  0.72   0.484  0.448]\n",
      "x[2:5]= [ 0.522  0.379  0.157]\n",
      "x[:4]=  [ 0.058  0.073  0.522  0.379]\n",
      "x[7:]=  [ 0.72   0.484  0.448]\n",
      "xlast=  0.448\n"
     ]
    }
   ],
   "source": [
    "x = np.random.rand(10)  # 10 random elements from 0 to 1\n",
    "x1 = x[2:5]             # Elements 2,3,4  (Note 5 is NOT included)\n",
    "x2 = x[:4]              # Elements 0,1,2,3  (Starts at 0, element 4 NOT included)\n",
    "x3 = x[7:]              # Elements 7,8,9 (Element 7 IS included.  Ends at 9 NOT 10)\n",
    "xlast = x[-1]           # The last element\n",
    "\n",
    "print(\"x=      \"+np.array_str(x,precision=3))\n",
    "print(\"x[2:5]= \"+np.array_str(x1,precision=3))\n",
    "print(\"x[:4]=  \"+np.array_str(x2,precision=3))\n",
    "print(\"x[7:]=  \"+np.array_str(x3,precision=3))\n",
    "print(\"xlast=  {0:5.3f}\".format(xlast))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Exercise **  Suppose we construct a vector `x` by:\n",
    "\n",
    "    x = np.array(range(1,5))**2\n",
    "    \n",
    "What are the vectors created by the following slicing operations:\n",
    "\n",
    "    x1 = x[:3]\n",
    "    x2 = x[3:]\n",
    "    x3 = x[1:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
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}