32 Math Functions with R.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math Functions with R\n",
    "\n",
    "We've talked a bit about some of the built-in math functions and features in R, but let's have one more look at a few of them:\n",
    "\n",
    "- __abs()__: computes the absolute value.\n",
    "- __sum()__: returns the sum of all the values present in the input.\n",
    "- __mean()__: computes the arithmetic mean.\n",
    "- __round()__: rounds values (additional arguments to nearest)\n",
    "- __sqrt(x)__:\tsquare root\n",
    "- __ceiling(x)__:\tceiling(3.475) is 4\n",
    "- __floor(x)__:\tfloor(3.475) is 3\n",
    "- __trunc(x)__:\ttrunc(5.99) is 5\n",
    "- __round(x, digits=n)__:\tround(3.475, digits=2) is 3.48\n",
    "- __signif(x, digits=n)__:\tsignif(3.475, digits=2) is 3.5\n",
    "- __cos(x), sin(x), tan(x)__:\talso acos(x), cosh(x), acosh(x), etc.\n",
    "- __log(x)__:\tnatural logarithm\n",
    "- __log10(x)__:\tcommon logarithm\n",
    "- __exp(x)__:\te^x\n",
    "\n",
    "Here's a quick example of each:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1</li><li>0</li><li>2</li><li>3</li><li>4</li><li>5</li><li>6</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 5\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 0\n",
       "3. 2\n",
       "4. 3\n",
       "5. 4\n",
       "6. 5\n",
       "7. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 0 2 3 4 5 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v <- c(-1,0,2,3,-4,5,6)\n",
    "abs(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "11"
      ],
      "text/latex": [
       "11"
      ],
      "text/markdown": [
       "11"
      ],
      "text/plain": [
       "[1] 11"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.57142857142857"
      ],
      "text/latex": [
       "1.57142857142857"
      ],
      "text/markdown": [
       "1.57142857142857"
      ],
      "text/plain": [
       "[1] 1.571429"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.571"
      ],
      "text/latex": [
       "1.571"
      ],
      "text/markdown": [
       "1.571"
      ],
      "text/plain": [
       "[1] 1.571"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "round(mean(v),3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1</li><li>0</li><li>1.4142135623731</li><li>1.73205080756888</li><li>2</li><li>2.23606797749979</li><li>2.44948974278318</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 0\n",
       "\\item 1.4142135623731\n",
       "\\item 1.73205080756888\n",
       "\\item 2\n",
       "\\item 2.23606797749979\n",
       "\\item 2.44948974278318\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 0\n",
       "3. 1.4142135623731\n",
       "4. 1.73205080756888\n",
       "5. 2\n",
       "6. 2.23606797749979\n",
       "7. 2.44948974278318\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1.000000 0.000000 1.414214 1.732051 2.000000 2.236068 2.449490"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sqrt(abs(v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1</li><li>0</li><li>2</li><li>2</li><li>2</li><li>3</li><li>3</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 0\n",
       "3. 2\n",
       "4. 2\n",
       "5. 2\n",
       "6. 3\n",
       "7. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 0 2 2 2 3 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ceiling(sqrt(abs(v)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1</li><li>0</li><li>1</li><li>1</li><li>2</li><li>2</li><li>2</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 0\n",
       "3. 1\n",
       "4. 1\n",
       "5. 2\n",
       "6. 2\n",
       "7. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 0 1 1 2 2 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "floor(sqrt(abs(v)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1</li><li>0</li><li>1</li><li>1</li><li>2</li><li>2</li><li>2</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 0\n",
       "3. 1\n",
       "4. 1\n",
       "5. 2\n",
       "6. 2\n",
       "7. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 0 1 1 2 2 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trunc(sqrt(abs(v)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "x <- seq(0,10, by = 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jrO5q6Z2vlgH+OqGlLJZ9UfV5dH0tFN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\nkCCAkCCAkCCAkCCAkCCAkCCAkCDAf3B67qi7CtzVAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(sin(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KRz8zjrNm9+X/H8IQAHFn9C9qP/3d9t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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(cos(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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URwtDD714eP300EJ+2cm7F7s0oSE8Gl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\nQoIAIUGAkCBASBDwD2ZV8XNOqS9RAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(tan(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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O+foCghQYCQIGCoITlHoqjhhmTVjoIG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\nkCDgP0zdDX8NsH7YAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(log(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2rv20XuJ8mGv+XdZUfXWoa0/FpAWDfz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\nQoIAIUGAkCBASBAgJAj4DxTy8dnLf2nPAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(log10(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(exp(x))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}