Slicing & Indexing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Arrays Slicing & indexing\n",
    "\n",
    "It is very important to first understand how basic indexing and slicing works in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "raw_mimetype": "text/markdown"
   },
   "source": [
    "Consider the below string \"Python\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO4AAABYCAIAAAB9H1wdAAAAA3NCSVQICAjb4U/gAAAAGXRFWHRT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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='./Files/String.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first row of numbers gives the position of the indices 0...6 in the string; \n",
    "\n",
    "The second row gives the corresponding negative indices. The slice from i to j consists of all characters between the edges labeled i and j, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "s = \"Python\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now as we access please refer to the above index table. That way you will understand things easily"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'y'"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[1] # Look at the first row of the index table. This will return 'y'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'n'"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[-1] # Look at the second row. This will return 'n'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Python Slicing mechanism\n",
    "**Syntax  : L[start:end:stride]**\n",
    "\n",
    "Ever since Python 1.4, the slicing syntax has supported an optional third `step` or `stride` argument. For example, these are all legal Python syntax: L[1:10:2], L[:-1:1], L[::-1]. This was added to Python at the request of the developers of Numerical Python, which uses the third argument extensively.\n",
    "\n",
    "Let us have a look at a few examples :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Py'"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[0:2]  # characters from position 0 (included) to 2 (excluded)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, what happens if we take strides of 1 from the back.( Take the hint!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'nohtyP'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's play with a list of numbers now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = range(10)\n",
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L[0:10] #start = 0, end = 10(excluded), stride = 1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L[::] # No slicing indices provided? Return everything!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Now, comes the fun part!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 2, 4, 6, 8]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L[::2] #you can now easily extract the elements of a list that have even indexes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 7, 5, 3, 1]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L[::-2] #Take strides of 2 but from the back"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# NUMPY ARRAY Slicing\n",
    "Arrays in numpy are similar to Python Lists, except that they should always have elements of the same type i.e. `float` or `int`. Now, we will learn about array slicing and indexing. \n",
    "\n",
    "**CAUTION** : This will need thorough understanding of basic list slicing in Python(explained above). Make sure you have understood that well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "A = np.array([1, 2, 3, 5, 6, 7], float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  3.,  5.,  6.,  7.])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Arrays can also be multidimensional. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "b = np.array([[1, 2, 3,], [4, 5, 6]], float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  2.,  3.],\n",
       "       [ 4.,  5.,  6.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  2.,  3.],\n",
       "       [ 4.,  5.,  6.]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[:2] # Get me everything from 0th row until 2nd Row(1st Axis). This is same as b[:2,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  5.,  6.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[1:2] # Dealing in the first Axis i.e. Rows. Get me everything that starts from 2nd row until the 2nd Row "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Unlike lists, different axes are accessed using commas inside\n",
    "bracket notation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  5.,  6.]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[1:,] # First Axis - Get me the first row. 2nd Axis: get me everything in the column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  5.,  6.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[1:] # Same as above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.,  6.])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[:,2] # Get me everything of the first Axis, but from 3rd Column(2nd Axis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  5.,  6.]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[-1:] # Get me the last row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  2.,  3.]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[:-1] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  5.,  6.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[-1:,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.,  6.]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[-1:, -2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  5.,  6.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[-1:,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6.,  4.]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[-1:, ::-2] # Everything in the last row(-1) and pick elements from the last column at strides of 2"
   ]
  }
 ],
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