Lecture_NumPyBasics_3_6053Fall19.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "The core data type in Numpy is the ndarray, which enables fast and space-efficient \n",
    "multidimensional array processing.\n",
    "Note: This notebook is adapted from chapter 4 Python for Data Analysis by Wes McKinney \n",
    "and O'Reilly publishing. \n",
    "NumPy has many, many features that won't be covered here. \n",
    "The following snippets are just to illustrate basic data types and operations within numpy.\n",
    "\n",
    "Another good resource for learning more about ndarrays is here:\n",
    "http://docs.scipy.org/doc/numpy/reference/arrays.html\n",
    "'''\n",
    "\n",
    "#First, import NumPy\n",
    "#import numpy imports the numpy module under the np namespace, \n",
    "#so you would need to call objects within numpy using np.foo\n",
    "#good reference: http://docs.python-guide.org/en/latest/writing/structure/#modules\n",
    "#\"from numpy import *\" imports all objects from the numpy module into your current namespace, \n",
    "#so you would call objects within numpy using only foo. \n",
    "import numpy as np\n",
    "\n",
    "#It is easy to create Nx1 and NxM arrays from standard Python lists\n",
    "l1 = [0,1,2]\n",
    "l2 = [3,4,5]\n",
    "\n",
    "nd1 = np.array(l1)\n",
    "nd2 = np.array([l1,  l2])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The ndarray has dimension n=3 and m=1\n",
      "The ndarray has elements of type=int64\n",
      "The ndarray has dimension n=2 and m=3\n",
      "The ndarray has elements of type=int64\n"
     ]
    }
   ],
   "source": [
    "#Now, we can get ask for some basic info to describe the ndarray\n",
    "def desc_ndarray(nd):\n",
    "    try:\n",
    "        print(\"The ndarray has dimension n=%s and m=%s\" % (nd.shape[0],nd.shape[1]))\n",
    "    except:\n",
    "        print(\"The ndarray has dimension n=%s and m=1\" % nd.shape[0])\n",
    "    print(\"The ndarray has elements of type=%s\" % nd.dtype)\n",
    "\n",
    "desc_ndarray(nd1)\n",
    "\n",
    "desc_ndarray(nd2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([ 0.,  0.,  0.,  0.]),\n",
       " array([ 1.,  1.,  1.,  1.]),\n",
       " array([-1.11583341, -0.06828104,  0.33402334,  0.18742328])]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#There are short cuts for creating certain frequently used special ndarrays, i.e.,\n",
    "\n",
    "k=4\n",
    "\n",
    "#1. an ndarray of all zeros\n",
    "zero = np.zeros(k)\n",
    "\n",
    "#2. an ndarray of all ones\n",
    "one = np.ones(k)\n",
    "\n",
    "#3. an ndarray of random elements (this one is standard normal, but there are many distributions to choose from)\n",
    "rand = np.random.randn(k)\n",
    "\n",
    "[zero, one, rand]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.73730303])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "For indexing an array:\n",
    "1. If nx1 array, follow the same protocol as a regular Python list\n",
    "2. If nxm array use the following examples\n",
    "'''\n",
    "\n",
    "arr2d = np.random.randn(4,2)\n",
    "arr1d = np.random.randn(2,1)\n",
    "#A single index gets a full row\n",
    "arr1d[1]\n",
    "#2 indexes returns a value\n",
    "#[arr2d, arr2d[1],  arr2d[1,1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([ 0.40787826,  0.73260398,  0.4517492 , -0.53911959]),\n",
       " array([ 0.81575652,  1.46520796,  0.9034984 , -1.07823918]),\n",
       " array([ 0.81575652,  1.46520796,  0.9034984 , -1.07823918]),\n",
       " array([ 0.,  0.,  0., -0.])]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "Operations between Arrays and Scalars\n",
    "An important feature of ndarrays is they allow batch operations on data without writing \n",
    "any for loops.  This is called vectorization.\n",
    "Any arithmetic operations between equal-size arrays applies the operation elementwise. \n",
    "'''\n",
    "\n",
    "#examples\n",
    "\n",
    "k = 4\n",
    "rand = np.random.randn(k)\n",
    "[rand, rand + rand, 2*rand, rand*np.zeros(4)]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([ 1.13096069, -0.49406484, -0.1066014 ]),\n",
       " array([ 0.08051299,  1.46072085, -0.56975871]),\n",
       " array([ 1.21147368,  0.96665601, -0.67636011])]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "Matrix operations\n",
    "It is easy to do matrix operations with Nd arrays. \n",
    "It is important to make sure matrix shapes are compatible, then standard addition, subtraction,\n",
    "multiplication and division work.\n",
    "'''\n",
    "\n",
    "k = 3\n",
    "r1 = np.random.randn(k)\n",
    "r2 = np.random.randn(k)\n",
    "\n",
    "#Matrix addition is the standard matrix operator\n",
    "[r1, r2 , r1 + r2]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 1.13096069, -0.49406484, -0.1066014 ],\n",
       "        [ 0.08051299,  1.46072085, -0.56975871]]),\n",
       " array([[ 1.13096069,  0.08051299],\n",
       "        [-0.49406484,  1.46072085],\n",
       "        [-0.1066014 , -0.56975871]])]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The Transpose can be taken with the attribute T\n",
    "arr2d = np.array([r1, r2])\n",
    "[arr2d, arr2d.T]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 1.13096069, -0.49406484, -0.1066014 ],\n",
       "        [ 0.08051299,  1.46072085, -0.56975871]]),\n",
       " array([[ 1.27907207,  0.24410006,  0.01136386],\n",
       "        [ 0.00648234,  2.1337054 ,  0.32462498]]),\n",
       " array([[ 1.53453599, -0.5698967 ],\n",
       "        [-0.5698967 ,  2.46481273]])]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "Matrix multiplication, like inner products can be done on arrays.\n",
    "Just remember that the standard multiplication operator does elementwise multiplication \n",
    "(provided they are the same shape).\n",
    "We need the dot method in order to do an inner product\n",
    "\n",
    "Numpy has a linalg library that can run most matrix operations on ndarrays:\n",
    "http://docs.scipy.org/doc/numpy/reference/routines.linalg.html\n",
    "\n",
    "One can also create a matrix object and use the methods in numpy.matrix to achieve the \n",
    "same thing:\n",
    "http://docs.scipy.org/doc/numpy/reference/generated/numpy.matrix.html\n",
    "'''\n",
    "\n",
    "[arr2d, arr2d * arr2d, arr2d.dot(arr2d.T)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "162 µs ± 3.01 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "One important feature of vectorization is that it allows elementwise processing that is \n",
    "much faster than writing a traditional loop.\n",
    "'''\n",
    "import math\n",
    "\n",
    "#show an example and profile i\n",
    "%timeit [math.sqrt(x) for x in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.35 µs ± 325 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit np.sqrt(np.arange(1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "The last thing we'll cover in this module is the numpy.random library. In general, it is \n",
    "advised to use numpy for random number generation as opposed to python's built in random module.\n",
    "\n",
    "Random number generation has many uses. One common use is generating fake (i.e. random) data to test modeling procedures\n",
    "or to do Monte Carlo Simulations\n",
    "'''\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Generate random pairs that have a multivariate normal distribution\n",
    "N = 1000 #Number of pairs of points\n",
    "mu = np.array([0,0]) #mean\n",
    "cov = 0.5\n",
    "sig = np.array([[1, cov],[cov, 1]]) #covariance matrix must be square, symmetric and non-negative definite"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#unpacking the x and y elements from the array transpose\n",
    "x, y = np.random.multivariate_normal(mu, sig, N).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "#Now let's plot and see what that looks like\n",
    "\n",
    "\n",
    "plt.plot(x, y,'x'); plt.axis('equal'); plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}