numpy/SciPy Numpy Extended Lectures Part 2 - Numerical operations on arrays.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "# Numerical operations with Numpy\n",
    "\n",
    "1.  **Elementwise operations**\n",
    "2.  **Basic reductions**\n",
    "3.  **Broadcasting**\n",
    "4.  **Array shape manipulation**\n",
    "5.  **Sorting data**\n",
    "6.  **Summary**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## Elementwise Operations\n",
    "\n",
    "### Basic Stuff\n",
    "\n",
    "\n",
    "#### With Scalars\n",
    "\n",
    "<img src=\"figures/dtype-hierarchy.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4, 5])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1,2,3,4])\n",
    "a+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  4,  8, 16])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2**a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### All arithmetics element-wise operation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.,  0.,  1.,  2.])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.ones(4) + 1\n",
    "a - b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.,  4.,  6.,  8.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   2,    3,    6,   13,   28,   59,  122,  249,  504, 1015])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "j = np.arange(10)\n",
    "2**(j + 1) - j"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### ... and lets see how fast is Numpy compared to Python's in-built operations "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.52 µs ± 219 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(10000)\n",
    "%timeit a + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "684 µs ± 5.29 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "p = range(10000)\n",
    "%timeit [i + 1 for i in p]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Clearly, Numpy is winning hands down! \n",
    "\n",
    "Another thing about multiplication * VS matrix multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.ones((4,4))\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c*c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  4.,  4.,  4.],\n",
       "       [ 4.,  4.,  4.,  4.],\n",
       "       [ 4.,  4.,  4.,  4.],\n",
       "       [ 4.,  4.,  4.,  4.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(c, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  4.,  4.,  4.],\n",
       "       [ 4.,  4.,  4.,  4.],\n",
       "       [ 4.,  4.,  4.,  4.],\n",
       "       [ 4.,  4.,  4.,  4.]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Or you can simply do\n",
    "c.dot(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## More operations\n",
    "\n",
    "### Comparisions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "a = np.array([1,2,3,4])\n",
    "b = np.array([5,2,6,4])\n",
    "c = np.array([1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False,  True], dtype=bool)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a == b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### array-wise comparisons "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array_equal(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array_equal(a, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Logical operations "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True, False], dtype=bool)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1,1,0,0], dtype=bool)\n",
    "b = np.array([1,0,1,0], dtype=bool)\n",
    "np.logical_or(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_and(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_not(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_xor(a,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Trancendentaal functions: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.84147098,  0.90929743,  0.14112001, -0.7568025 ])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(5)\n",
    "np.sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/tarrysingh/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in log\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([       -inf,  0.        ,  0.69314718,  1.09861229,  1.38629436])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.        ,   2.71828183,   7.3890561 ,  20.08553692,  54.59815003])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Shape mismatches: \n",
    "\n",
    "Throws a broacasting error. We'll get to that soon enough..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (5,) (2,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-48-0757768aa5bf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (5,) (2,) "
     ]
    }
   ],
   "source": [
    "a = np.arange(5)\n",
    "a + np.array([2,4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Transposition. what is it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  1.,  1.],\n",
       "       [ 0.,  0.,  1.,  1.],\n",
       "       [ 0.,  0.,  0.,  1.],\n",
       "       [ 0.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.triu(np.ones((4,4)), 1)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.],\n",
       "       [ 1.,  0.,  0.,  0.],\n",
       "       [ 1.,  1.,  0.,  0.],\n",
       "       [ 1.,  1.,  1.,  0.]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "##### See, what happened above? \n",
    "\n",
    "It flipped upside-down and then right-to-left"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "### Food for thought\n",
    "\n",
    "- Look at np.allclose versus np.isclose. What is the difference between the two according to you?\n",
    "- What is the difference between np.trui and np.tril?\n",
    "- Also play with Ranges: How is np.linspace different than np.logspace?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## Basic reductions\n",
    "\n",
    "### Calculating sums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([5,6,7,8])\n",
    "np.sum(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Adding by rows and by columns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 2],\n",
       "       [6, 6]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[2,2,], [6,6]])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8, 8])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum(axis=0) #column-wise addition, first dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8, 8)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# more complex way to doing it, but you get the idea\n",
    "x[:, 0].sum(), x[:, 1].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4, 12])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Le's do row-wise\n",
    "x.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 12)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0, :].sum(), x[1, :].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.59277357,  0.05258387],\n",
       "        [ 0.63162507,  0.47989509]],\n",
       "\n",
       "       [[ 0.48050849,  0.32805422],\n",
       "        [ 0.08282492,  0.86972591]]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In higher dimensions\n",
    "x = np.random.rand(2,2,2)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1115201595752902"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum(axis=2)[0, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1115201595752902"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# inspecting it more in detail\n",
    "x[0, 1, :].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "### Other forms of reductions\n",
    "\n",
    "#### Extrema"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([2,5,6])\n",
    "x.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.argmin() # Index of mimimum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.argmax() # index of maximum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Logic Functions for Truth Value Testing\n",
    "\n",
    "**Numpy.all**\n",
    "\n",
    "`all(a[, axis, out, keepdims])`\tTest whether all array elements along a given axis evaluate to True.\n",
    "\n",
    "Try help(numpy.all) for more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all([True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all([[True, True], [False, True]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True], dtype=bool)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all([[True, True], [False, True]], axis=0) #axis=1 should give you the opposite result as you'll see"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all([-5, 4, 7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all([1.0, np.nan])\n",
    "# We'll get to np.nan - Not a number i.e; later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4507411280, 4507411280, array([ True], dtype=bool))"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([False])\n",
    "d = np.all([-1, 4, 5], out=c, keepdims=True)\n",
    "id(d), id(d), c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Try the above operation with keepdims\n",
    "\n",
    "What did you encounter? And why?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "**Numpy.any**\n",
    "\n",
    "`any(a[, axis, out, keepdims])`\tTest whether any array element along a given axis evaluates to True."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any([True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any([[True, False], [True, True]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True], dtype=bool)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any([[True, False], [True, True]], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any([-1, 0, 7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any(np.nan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4506119824, 4506119824, array([ True], dtype=bool))"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([False])\n",
    "d = np.any([-1, 4, 5], out=c, keepdims=True)\n",
    "id(d), id(d), c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d is c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4506119824, 4506119824)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "id(d), id(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True], dtype=bool)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "# Can we try array comparisons?\n",
    "\n",
    "a = np.zeros((200,200))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any(a != 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all( a == a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([3,4,5,6])\n",
    "b = np.array([4,5,6,7])\n",
    "c = np.array([6,7,3,2])\n",
    "((a <= b) & (b <= c)).all() # np.all(((a <= b) & (b <= c)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a <= b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True, False, False], dtype=bool)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b <= c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### If we would have done `np.any()`...\n",
    "\n",
    "What would then the answer be then?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((a <= b) & (b <= c)).any()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "### Finite and Infinite\n",
    "\n",
    "Test element-wise for finiteness and infinity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isfinite(1) # 1 is finite"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isfinite(np.exp(100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/tarrysingh/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: overflow encountered in exp\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isfinite(np.exp(1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/tarrysingh/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: overflow encountered in exp\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Above is a limitation of my computer...\n",
    "\n",
    "The answer should actually be true...\n",
    "\n",
    "...**but** if we do `np.isinf()'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/tarrysingh/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: overflow encountered in exp\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isinf(np.exp(1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isfinite(np.inf) # Kind of obvious as infinity is definitely NOT finite"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/tarrysingh/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in log\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n",
      "/Users/tarrysingh/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in log\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([False,  True, False], dtype=bool)"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isfinite([np.log(-1.), 1., np.log(0)]) # Trying same but in a different way..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### How about `np.NINF` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on float object:\n",
      "\n",
      "class float(object)\n",
      " |  float(x) -> floating point number\n",
      " |  \n",
      " |  Convert a string or number to a floating point number, if possible.\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __abs__(self, /)\n",
      " |      abs(self)\n",
      " |  \n",
      " |  __add__(self, value, /)\n",
      " |      Return self+value.\n",
      " |  \n",
      " |  __bool__(self, /)\n",
      " |      self != 0\n",
      " |  \n",
      " |  __divmod__(self, value, /)\n",
      " |      Return divmod(self, value).\n",
      " |  \n",
      " |  __eq__(self, value, /)\n",
      " |      Return self==value.\n",
      " |  \n",
      " |  __float__(self, /)\n",
      " |      float(self)\n",
      " |  \n",
      " |  __floordiv__(self, value, /)\n",
      " |      Return self//value.\n",
      " |  \n",
      " |  __format__(...)\n",
      " |      float.__format__(format_spec) -> string\n",
      " |      \n",
      " |      Formats the float according to format_spec.\n",
      " |  \n",
      " |  __ge__(self, value, /)\n",
      " |      Return self>=value.\n",
      " |  \n",
      " |  __getattribute__(self, name, /)\n",
      " |      Return getattr(self, name).\n",
      " |  \n",
      " |  __getformat__(...) from builtins.type\n",
      " |      float.__getformat__(typestr) -> string\n",
      " |      \n",
      " |      You probably don't want to use this function.  It exists mainly to be\n",
      " |      used in Python's test suite.\n",
      " |      \n",
      " |      typestr must be 'double' or 'float'.  This function returns whichever of\n",
      " |      'unknown', 'IEEE, big-endian' or 'IEEE, little-endian' best describes the\n",
      " |      format of floating point numbers used by the C type named by typestr.\n",
      " |  \n",
      " |  __getnewargs__(...)\n",
      " |  \n",
      " |  __gt__(self, value, /)\n",
      " |      Return self>value.\n",
      " |  \n",
      " |  __hash__(self, /)\n",
      " |      Return hash(self).\n",
      " |  \n",
      " |  __int__(self, /)\n",
      " |      int(self)\n",
      " |  \n",
      " |  __le__(self, value, /)\n",
      " |      Return self<=value.\n",
      " |  \n",
      " |  __lt__(self, value, /)\n",
      " |      Return self<value.\n",
      " |  \n",
      " |  __mod__(self, value, /)\n",
      " |      Return self%value.\n",
      " |  \n",
      " |  __mul__(self, value, /)\n",
      " |      Return self*value.\n",
      " |  \n",
      " |  __ne__(self, value, /)\n",
      " |      Return self!=value.\n",
      " |  \n",
      " |  __neg__(self, /)\n",
      " |      -self\n",
      " |  \n",
      " |  __new__(*args, **kwargs) from builtins.type\n",
      " |      Create and return a new object.  See help(type) for accurate signature.\n",
      " |  \n",
      " |  __pos__(self, /)\n",
      " |      +self\n",
      " |  \n",
      " |  __pow__(self, value, mod=None, /)\n",
      " |      Return pow(self, value, mod).\n",
      " |  \n",
      " |  __radd__(self, value, /)\n",
      " |      Return value+self.\n",
      " |  \n",
      " |  __rdivmod__(self, value, /)\n",
      " |      Return divmod(value, self).\n",
      " |  \n",
      " |  __repr__(self, /)\n",
      " |      Return repr(self).\n",
      " |  \n",
      " |  __rfloordiv__(self, value, /)\n",
      " |      Return value//self.\n",
      " |  \n",
      " |  __rmod__(self, value, /)\n",
      " |      Return value%self.\n",
      " |  \n",
      " |  __rmul__(self, value, /)\n",
      " |      Return value*self.\n",
      " |  \n",
      " |  __round__(...)\n",
      " |      Return the Integral closest to x, rounding half toward even.\n",
      " |      When an argument is passed, work like built-in round(x, ndigits).\n",
      " |  \n",
      " |  __rpow__(self, value, mod=None, /)\n",
      " |      Return pow(value, self, mod).\n",
      " |  \n",
      " |  __rsub__(self, value, /)\n",
      " |      Return value-self.\n",
      " |  \n",
      " |  __rtruediv__(self, value, /)\n",
      " |      Return value/self.\n",
      " |  \n",
      " |  __setformat__(...) from builtins.type\n",
      " |      float.__setformat__(typestr, fmt) -> None\n",
      " |      \n",
      " |      You probably don't want to use this function.  It exists mainly to be\n",
      " |      used in Python's test suite.\n",
      " |      \n",
      " |      typestr must be 'double' or 'float'.  fmt must be one of 'unknown',\n",
      " |      'IEEE, big-endian' or 'IEEE, little-endian', and in addition can only be\n",
      " |      one of the latter two if it appears to match the underlying C reality.\n",
      " |      \n",
      " |      Override the automatic determination of C-level floating point type.\n",
      " |      This affects how floats are converted to and from binary strings.\n",
      " |  \n",
      " |  __str__(self, /)\n",
      " |      Return str(self).\n",
      " |  \n",
      " |  __sub__(self, value, /)\n",
      " |      Return self-value.\n",
      " |  \n",
      " |  __truediv__(self, value, /)\n",
      " |      Return self/value.\n",
      " |  \n",
      " |  __trunc__(...)\n",
      " |      Return the Integral closest to x between 0 and x.\n",
      " |  \n",
      " |  as_integer_ratio(...)\n",
      " |      float.as_integer_ratio() -> (int, int)\n",
      " |      \n",
      " |      Return a pair of integers, whose ratio is exactly equal to the original\n",
      " |      float and with a positive denominator.\n",
      " |      Raise OverflowError on infinities and a ValueError on NaNs.\n",
      " |      \n",
      " |      >>> (10.0).as_integer_ratio()\n",
      " |      (10, 1)\n",
      " |      >>> (0.0).as_integer_ratio()\n",
      " |      (0, 1)\n",
      " |      >>> (-.25).as_integer_ratio()\n",
      " |      (-1, 4)\n",
      " |  \n",
      " |  conjugate(...)\n",
      " |      Return self, the complex conjugate of any float.\n",
      " |  \n",
      " |  fromhex(...) from builtins.type\n",
      " |      float.fromhex(string) -> float\n",
      " |      \n",
      " |      Create a floating-point number from a hexadecimal string.\n",
      " |      >>> float.fromhex('0x1.ffffp10')\n",
      " |      2047.984375\n",
      " |      >>> float.fromhex('-0x1p-1074')\n",
      " |      -5e-324\n",
      " |  \n",
      " |  hex(...)\n",
      " |      float.hex() -> string\n",
      " |      \n",
      " |      Return a hexadecimal representation of a floating-point number.\n",
      " |      >>> (-0.1).hex()\n",
      " |      '-0x1.999999999999ap-4'\n",
      " |      >>> 3.14159.hex()\n",
      " |      '0x1.921f9f01b866ep+1'\n",
      " |  \n",
      " |  is_integer(...)\n",
      " |      Return True if the float is an integer.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors defined here:\n",
      " |  \n",
      " |  imag\n",
      " |      the imaginary part of a complex number\n",
      " |  \n",
      " |  real\n",
      " |      the real part of a complex number\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(np.NINF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isfinite(np.NINF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isfinite(np.nan) # Remember, NaN = Not is number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 0])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([-np.inf, 0., np.inf])\n",
    "y = np.array([2,2,2])\n",
    "np.isfinite(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-inf,   0.,  inf])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 0])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## Statistics - A quick brush up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "a = np.array([5,6,7,8])\n",
    "b = np.array([[1,2,3], [4,5,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.5"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Doing a simple pythonic mean\n",
    "a.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.5"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(a) # Numpy gives the same value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.5"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(a) # OK, same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's do for b\n",
    "np.median(b) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.,  5.])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For last axis\n",
    "np.median(b, axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.5,  3.5,  4.5])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for second last axis\n",
    "np.median(b, axis=-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Standard deviation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1180339887498949"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.707825127659933"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1180339887498949"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0615528128088303"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([[4,5], [8,9]])\n",
    "np.std(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 5],\n",
       "       [8, 9]])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.,  2.])"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(c, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.5,  0.5])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(c, axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.5,  0.5])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(c, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### But standard can also be inaccurate... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "c = np.zeros((2, 256*256), dtype=np.float16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "c[0, :] = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "c[1, :] = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "##### What happened up there???\n",
    "\n",
    "Now doing same with float32..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4500123"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(c, dtype=np.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "##### How about `np.float64`? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45001220703125"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(c, dtype=np.float64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "##### `np.float128`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45001220703125"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(c, dtype=np.float128) # as you can see the accuracy doesnt change as you increasing floating point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "### Working with some data\n",
    "\n",
    "Let's look at the population of hares, lynxes and carrots in Northern Canada for a period of 20 years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# year\thare\tlynx\tcarrot\r\n",
      "1900\t30e3\t4e3\t48300\r\n",
      "1901\t47.2e3\t6.1e3\t48200\r\n",
      "1902\t70.2e3\t9.8e3\t41500\r\n",
      "1903\t77.4e3\t35.2e3\t38200\r\n",
      "1904\t36.3e3\t59.4e3\t40600\r\n",
      "1905\t20.6e3\t41.7e3\t39800\r\n",
      "1906\t18.1e3\t19e3\t38600\r\n",
      "1907\t21.4e3\t13e3\t42300\r\n",
      "1908\t22e3\t8.3e3\t44500\r\n",
      "1909\t25.4e3\t9.1e3\t42100\r\n",
      "1910\t27.1e3\t7.4e3\t46000\r\n",
      "1911\t40.3e3\t8e3\t46800\r\n",
      "1912\t57e3\t12.3e3\t43800\r\n",
      "1913\t76.6e3\t19.5e3\t40900\r\n",
      "1914\t52.3e3\t45.7e3\t39400\r\n",
      "1915\t19.5e3\t51.1e3\t39000\r\n",
      "1916\t11.2e3\t29.7e3\t36700\r\n",
      "1917\t7.6e3\t15.8e3\t41800\r\n",
      "1918\t14.6e3\t9.7e3\t43300\r\n",
      "1919\t16.2e3\t10.1e3\t41300\r\n",
      "1920\t24.7e3\t8.6e3\t47300\r\n"
     ]
    }
   ],
   "source": [
    "# Let's view the data\n",
    "!cat data/populations.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "# load the data\n",
    "data = np.loadtxt('data/populations.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1900.,  30000.,   4000.,  48300.],\n",
       "       [  1901.,  47200.,   6100.,  48200.],\n",
       "       [  1902.,  70200.,   9800.,  41500.],\n",
       "       [  1903.,  77400.,  35200.,  38200.],\n",
       "       [  1904.,  36300.,  59400.,  40600.],\n",
       "       [  1905.,  20600.,  41700.,  39800.],\n",
       "       [  1906.,  18100.,  19000.,  38600.],\n",
       "       [  1907.,  21400.,  13000.,  42300.],\n",
       "       [  1908.,  22000.,   8300.,  44500.],\n",
       "       [  1909.,  25400.,   9100.,  42100.],\n",
       "       [  1910.,  27100.,   7400.,  46000.],\n",
       "       [  1911.,  40300.,   8000.,  46800.],\n",
       "       [  1912.,  57000.,  12300.,  43800.],\n",
       "       [  1913.,  76600.,  19500.,  40900.],\n",
       "       [  1914.,  52300.,  45700.,  39400.],\n",
       "       [  1915.,  19500.,  51100.,  39000.],\n",
       "       [  1916.,  11200.,  29700.,  36700.],\n",
       "       [  1917.,   7600.,  15800.,  41800.],\n",
       "       [  1918.,  14600.,   9700.,  43300.],\n",
       "       [  1919.,  16200.,  10100.,  41300.],\n",
       "       [  1920.,  24700.,   8600.,  47300.]])"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "year, hares, lynxes, carrots = data.T # What did I just do and why?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10e43a588>"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVoAAAEJCAYAAADVS+8vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e3abcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.axes([0.2, 0.1, 0.5, 0.8])\n",
    "plt.plot(year, hares, year, lynxes, year, carrots)\n",
    "plt.legend(('Hare', 'Lynx', 'Carrot'), loc=(1.05, 0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### So what was mean (median) population over time?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 34080.95238095,  20166.66666667,  42400.        ])"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pop = data[:, 1:]\n",
    "pop.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 20897.90645809,  16254.59153691,   3322.50622558])"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pop.std(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Which animal had the highest population each year? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 2, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(pop, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Diffusion using a random walk algorithm\n",
    "\n",
    "<img src=\"figures/random_walk.png\">\n",
    "\n",
    "Let us consider a simple 1D random walk process: at each time step a walker jumps right or left with equal probability.\n",
    "\n",
    "\n",
    "We are interested in finding the typical distance from the origin of a random walker after t left or right jumps? We are going to simulate many “walkers” to find this law, and we are going to do so using array computing tricks: we are going to create a 2D array with the “stories” (each walker has a story) in one direction, and the time in the other:\n",
    "<img src=\"figures/random_walk_schema.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Step 1 : Let's initialize number of stories and max duration where we follow the walkers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_stories = 1000 # number of walkers\n",
    "t_max = 200 # duration of time in which we follow the walkers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Step 2: Let's randomly choose all steps 1 or -1 of the walk "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/tarrysingh/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:2: DeprecationWarning: This function is deprecated. Please call randint(0, 1 + 1) instead\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "t = np.arange(t_max)\n",
    "steps = 2 * np.random.random_integers(0, 1, (n_stories, t_max)) - 1\n",
    "# use instead np.random.randint(0, 1 + 1) logic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Step 3:  Lets verify if all steps are 1 or -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1,  1])"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Step 4: OK, we build the walks by summing steps along the time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [],
   "source": [
    "positions = np.cumsum(steps, axis=1) # this is axis = 1, dimension of time\n",
    "square_dist = np.square(positions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Step 5: Lets get the mean in the axis of the stories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mean_square_dist = np.mean(square_dist, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Step 6: Finally lets plot the results "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10f299e10>"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfsAAAF5CAYAAACY84MBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTqiAc27GoJQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ecce240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(t, np.sqrt(mean_square_dist), 'g.', t, np.sqrt(t), 'r-')\n",
    "plt.xlabel(r\"$t$\")\n",
    "plt.ylabel(r\"$\\sqrt{\\langle (\\delta x)^2 \\rangle}$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_code_all_hidden": false,
  "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}