Matrix Indexing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Matrix Indexing\n",
    "*Matrix Indexing* is the way that we retrieve a subset of elements in a matrix or vector. The syntax mimics linear algebra matrix indexing you may already be familiar with.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##  Retrieving a Single Element\n",
    "First let's define a matrix $\\mathbf{A}$ that we can work with (in math notation, and MATLAB syntax.)\n",
    "\n",
    "$$\n",
    "\\mathbf{A} = \\begin{bmatrix} 1 & 2\\\\ 3 & 4\\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = [\n",
    "    1, 2;\n",
    "    3, 4\n",
    "];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get only the element in row 1, column 2, we would say the following in math notation:\n",
    "\n",
    "$$\n",
    "a_{1,2} = 2\n",
    "$$\n",
    "\n",
    "In MATLAB, this can be expressed with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  2\n"
     ]
    }
   ],
   "source": [
    "A(1, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Retrieving Rows or Columns\n",
    "If we want to get the elements of the first row, we would write the following, which can be read as \"Get row 1, columns 1 and 2\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "   1   2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A(1, [1, 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Equivalently, we can use a shorthand syntax to indicate we want to retrieve all of the columns in the row, which can be read as \"Get row one, *all* of the columns\". This will retrieve the first row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "   1   2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A(1, :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we could retrieve \"*all* of the rows, column 1\". This will retrieve the first column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "   1\n",
      "   3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A(:, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Assigning to Matrix Indicies\n",
    "You can mutate the value of an array at specific indicies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Boolean Masking\n",
    "Sometimes we want to use a matrix of true/false to say whether we want to retrieve a value from a matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Your Turn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the *trace* (the sum of the diagonal elements) of the following matrix:\n",
    "(Hint: we need a Boolean identity matrix to pick the elements of the diagonal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  4.3726\n",
      "ans =  5.6562\n",
      "ans =  5.6562\n",
      "ans =  5.6562\n"
     ]
    }
   ],
   "source": [
    "mat = rand(10);\n",
    "\n",
    "% Answer using indexing\n",
    "sum( mat(:)(1:10:100) ) % flatten array into column; skip every 10 elements\n",
    "\n",
    "% Tests using built-ins\n",
    "sum(mat( logical(eye(10)) )) %Logical masking\n",
    "sum(diag(mat))\n",
    "trace(mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "   10   10\n",
      "\n"
     ]
    }
   ],
   "source": [
    "size(mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "     1    11    21    31    41    51    61    71    81    91   101\n",
      "\n"
     ]
    }
   ],
   "source": [
    "1:10:101"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Octave",
   "language": "octave",
   "name": "octave"
  },
  "language_info": {
   "file_extension": ".m",
   "help_links": [
    {
     "text": "GNU Octave",
     "url": "https://www.gnu.org/software/octave/support.html"
    },
    {
     "text": "Octave Kernel",
     "url": "https://github.com/Calysto/octave_kernel"
    },
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "octave",
   "version": "4.2.2"
  },
  "rise": {
   "autolaunch": true,
   "scroll": true,
   "theme": "simple"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}