{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Writing Custom Functions\n",
    "===="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Anatomy of a function\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The R function has the following structure\n",
    "\n",
    "```R\n",
    "name <- function(arg1, arg2, ...) {\n",
    "    body_of_function\n",
    "    return(value)\n",
    "    }\n",
    "```\n",
    "\n",
    "A function is created using the `function` keyword, followed by a series of arguments in parentheses. The main work done by the function is enclosed witin curly braces, and a `return` function is used to indicate the output of the function. Finally we can assign the funciton, just like any other R object, to a named variable for later use."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Our first custom function\n",
    "\n",
    "Let's write a function to calculate the mean of a vector of numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "my.mean <- function(xs) {\n",
    "    n <- length(xs)\n",
    "    return(sum(xs)/n)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "5.5"
      ],
      "text/latex": [
       "5.5"
      ],
      "text/markdown": [
       "5.5"
      ],
      "text/plain": [
       "[1] 5.5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my.mean(1:10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Work!\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a function `my.sd` that takes a vector of numbers and returns their standard deviation as calculated from the following formula:\n",
    "$$\n",
    "\\sqrt{\\frac{\\sum{(x - \\bar{x})^2}}{n-1}}\n",
    "$$\n",
    "where $x$ is some vector of numbers, $\\bar{x}$ is the mean of $x$ and $n$ is th number of elements in $x$. \n",
    "\n",
    "What is the standard deviation of `1:10`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.02765035409749"
      ],
      "text/latex": [
       "3.02765035409749"
      ],
      "text/markdown": [
       "3.02765035409749"
      ],
      "text/plain": [
       "[1] 3.02765"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my.sd <- function(xs) {\n",
    "    n <- length(xs)\n",
    "    xbar<-my.mean(xs)\n",
    "    xdiff<-xs-xbar\n",
    "    xdiffsquare<-xdiff^2\n",
    "    sumsquare<-sum(xdiffsquare)\n",
    "    sigmabar<-sqrt(sumsquare/(n-1))\n",
    "    return(sigmabar)\n",
    "}\n",
    "\n",
    "my.sd(1:10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Our second custom function\n",
    "\n",
    "Let's be more ambitious - let's write a function that will generate a 4 parameter logistic function commonly used for fitting dose-response curves\n",
    "\n",
    "$$\\frac{(A-D)}{1+\\left(\\frac{x}{C}\\right)^B} + D$$\n",
    "\n",
    "where $x$ is the input and $A$, $B$, $C$ and $D$ are the parameters that determine the shape of the curve:\n",
    "\n",
    "- A = minimum asymptote\n",
    "- B = Hill slope\n",
    "- C = inflection point\n",
    "- D = maximum asymptote"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "log4 <- function(x, a, b, c, d) {\n",
    "    return ((a-d)/(1 + ((x/c)^b)) + d)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x <- seq(0, 100, length.out = 51)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Arguments supplied by the user are matched by *position*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, log4(x, 0, 2, 50, 1), type=\"o\", col=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Default arguments\n",
    "----\n",
    "\n",
    "Perhaps we know that most of the time, the output will be normalized to fall between 0 and 1. In this case, we can set *default* arguments for $A$ and $D$ to simplify the function call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "log4 <- function(x, a=0, b, c, d=1) {\n",
    "    return ((a-d)/(1 + ((x/c)^b)) + d)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
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",
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       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, log4(x, b=2, c=50), type=\"o\", col=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note that we have to give *named* arguments otherwise R will assign the values to the wrong parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in log4(x, 2, 50): argument \"c\" is missing, with no default\n",
     "output_type": "error",
     "traceback": [
      "Error in log4(x, 2, 50): argument \"c\" is missing, with no default\n"
     ]
    }
   ],
   "source": [
    "plot(x, log4(x, 2, 50), type=\"l\", col=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### In many cases, it makes sense to move arguments with default to the end of the parameter list. While we're at it, we also use more meaningful parameter names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "log4 <- function(x, slope, inflection, min=0, max=1 ) {\n",
    "    return ((min-max)/(1 + ((x/inflection)^slope)) + max)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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",
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      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, log4(x, 2, 50), type=\"o\", col=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Work!\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 4 parameter logistic function always generates a symmetric curve. There is a 5 parameter logistic function that can generate asymmetrical curves:\n",
    "```\n",
    "A + (D/(1+(X/C)^B)^E)\n",
    "```\n",
    "where the new parameter $E$ controls the amount of asymmetry.\n",
    "\n",
    "Write a function that will generate the new 5PL curve, giving a default value for $E$ so that when the default is used, the 5PL and 4PL functions are the same. Use meaningful parameter names instead of A, B, C, D and E."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the 5 PL curve with the following values\n",
    "\n",
    "- min = 0\n",
    "- max = 1\n",
    "- slope = 3\n",
    "- inflection = 5\n",
    "- assymetry = 2\n",
    "\n",
    "for x between 0 and 10.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "plot without title"
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     },
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     "output_type": "display_data"
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   ],
   "source": [
    "log5 <- function(x, b, c,a=0, d=1,e=1) {\n",
    "    return ((d)/(1 + ((x/c)^b))^e + a)\n",
    "}\n",
    "\n",
    "x<-0:10\n",
    "plot(x, log5(x, 3, 5,e=2), type=\"o\", col=\"blue\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The EC50 for the 5PL is given by\n",
    "```\n",
    "C((2^(1/E) - 1)^(1/B))\n",
    "```\n",
    "    \n",
    "Write a function to calculate the EC50 given $B$, $C$ and $E$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Curve fitting\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we have some experimental data that we want to fit to a 4PL function. The data is read in from a text file to an R dataframe. We will have much more discusion of data frames in subsequent lectures. For now, treat them as a convenient structure for storing tabular data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df <- read.table(\"4PL_data.txt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `with` makes the columns of the data frame appear as regular vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with(df,\n",
    "    plot(x, y, type=\"p\", col=\"blue\")\n",
    "     )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lets estimate the slope and inflection by nonlinear least squares minimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Nonlinear regression model\n",
       "  model: y ~ log4(x, slope, inflection)\n",
       "   data: df\n",
       "     slope inflection \n",
       "     1.885     52.557 \n",
       " residual sum-of-squares: 1.564\n",
       "\n",
       "Number of iterations to convergence: 7 \n",
       "Achieved convergence tolerance: 3.273e-06"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "ename": "ERROR",
     "evalue": "Error in summary(fit): object 'fit' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in summary(fit): object 'fit' not found\n"
     ]
    }
   ],
   "source": [
    "with(df,(fit <- nls(y ~ log4(x, slope, inflection), start=list(slope=1, inflection=30), data=df)))\n",
    "summary(fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### When there are many statments following the `with`, use curly braces to group them together as a single exprssion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in predict(fit, x): object 'fit' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in predict(fit, x): object 'fit' not found\n"
     ]
    },
    {
     "data": {
      "application/pdf": 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      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with(df, \n",
    "     {\n",
    "         plot(x, y, 'p', col='blue')\n",
    "         lines(x, predict(fit, x), col=\"red\", lty=2)\n",
    "         lines(x, log4(x, 2,50), col=\"blue\")\n",
    "         legend(70, 0, lty=1:2, col=c(\"blue\", \"red\"), legend=c(\"True\", \"Fitted\"))\n",
    "     }\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Work!\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the same data to the 5 PL and estimate the slope, inflection and asymmetry parameters. You may assume that min and max are 0 and 1 respectively and do not have to be estimated. Plot the curve and fitted values as in the example above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the estimated ED50? You can use `fit$m$getPars()` to find the values of all fitted parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Program Logic\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A program is just a list of commands that fit together logically. There are some basic principles and concepts that are common to every programming language and environment. We will briefly introduce these in the context of R."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H3> Flow Control "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H4> If Else"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes, a we want to execute a command only under certain conditions. For example, suppose we are calculating an admission price to a theater, where children under age 6 are admitted free and children age 6-11 are half-price:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "admission_price<-function(full_price = 12,age=18){\n",
    "      if (age < 6)\n",
    "         price_result<-0.0\n",
    "      else\n",
    "     {\n",
    "      if (age < 12)\n",
    "         price_result<-full_price/2\n",
    "      else\n",
    "         price_result<-full_price\n",
    "     }\n",
    "     return(price_result)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "50"
      ],
      "text/latex": [
       "50"
      ],
      "text/markdown": [
       "50"
      ],
      "text/plain": [
       "[1] 50"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "admission_price(full_price=100,age=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R has a nice shortcut for the if-else construct called 'ifelse':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "admission_price_mod<-function(full_price = 12,age=18){\n",
    "     ifelse (age < 6,price_result<-0,ifelse (age<12,price_result<-full_price/2,price_result<-full_price)) \n",
    "     return(price_result)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in eval(expr, envir, enclos): could not find function \"admission_price_mod\"\n",
     "output_type": "error",
     "traceback": [
      "Error in eval(expr, envir, enclos): could not find function \"admission_price_mod\"\n"
     ]
    }
   ],
   "source": [
    "admission_price_mod(full_price=100,age=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
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      "text/latex": [
       "\\begin{enumerate*}\n",
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       "\\item 1\n",
       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. 0\n",
       "2. 0\n",
       "3. 0\n",
       "4. 0\n",
       "5. 1\n",
       "6. 1\n",
       "7. 1\n",
       "8. 1\n",
       "9. 1\n",
       "10. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 0 0 0 0 1 1 1 1 1 1"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x <- 1:10\n",
    "ifelse(x < 5, 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H4> Loops"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loops are used when a bit of code must be repeated many times. There are different types of loops, depending upon the 'termination condition' (what makes the loop stop?)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H5>For Loops"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For loops are used when we know how many times a loop must be iterated. The number of times could be variable - say 'n' times, but the important point is that at the time the loop is entered, the program knows how many iterations are necessary. For loops therefore have a counter and a termination condition that depends upon the value of the counter. One last element is an incrementor. Suppose we want a randomization scheme that assigns every third patient to a treatment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<table>\n",
       "<thead><tr><th scope=col>patient</th><th scope=col>treatment</th></tr></thead>\n",
       "<tbody>\n",
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       "\t<tr><td>99</td><td> 1</td></tr>\n",
       "\t<tr><td>100</td><td>  0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{ll}\n",
       " patient & treatment\\\\\n",
       "\\hline\n",
       "\t 1 & 0\\\\\n",
       "\t 2 & 0\\\\\n",
       "\t 3 & 1\\\\\n",
       "\t 4 & 0\\\\\n",
       "\t 5 & 0\\\\\n",
       "\t 6 & 1\\\\\n",
       "\t 7 & 0\\\\\n",
       "\t 8 & 0\\\\\n",
       "\t 9 & 1\\\\\n",
       "\t 10 &  0\\\\\n",
       "\t 11 &  0\\\\\n",
       "\t 12 &  1\\\\\n",
       "\t 13 &  0\\\\\n",
       "\t 14 &  0\\\\\n",
       "\t 15 &  1\\\\\n",
       "\t 16 &  0\\\\\n",
       "\t 17 &  0\\\\\n",
       "\t 18 &  1\\\\\n",
       "\t 19 &  0\\\\\n",
       "\t 20 &  0\\\\\n",
       "\t 21 &  1\\\\\n",
       "\t 22 &  0\\\\\n",
       "\t 23 &  0\\\\\n",
       "\t 24 &  1\\\\\n",
       "\t 25 &  0\\\\\n",
       "\t 26 &  0\\\\\n",
       "\t 27 &  1\\\\\n",
       "\t 28 &  0\\\\\n",
       "\t 29 &  0\\\\\n",
       "\t 30 &  1\\\\\n",
       "\t 31 &  0\\\\\n",
       "\t 32 &  0\\\\\n",
       "\t 33 &  1\\\\\n",
       "\t 34 &  0\\\\\n",
       "\t 35 &  0\\\\\n",
       "\t 36 &  1\\\\\n",
       "\t 37 &  0\\\\\n",
       "\t 38 &  0\\\\\n",
       "\t 39 &  1\\\\\n",
       "\t 40 &  0\\\\\n",
       "\t 41 &  0\\\\\n",
       "\t 42 &  1\\\\\n",
       "\t 43 &  0\\\\\n",
       "\t 44 &  0\\\\\n",
       "\t 45 &  1\\\\\n",
       "\t 46 &  0\\\\\n",
       "\t 47 &  0\\\\\n",
       "\t 48 &  1\\\\\n",
       "\t 49 &  0\\\\\n",
       "\t 50 &  0\\\\\n",
       "\t 51 &  1\\\\\n",
       "\t 52 &  0\\\\\n",
       "\t 53 &  0\\\\\n",
       "\t 54 &  1\\\\\n",
       "\t 55 &  0\\\\\n",
       "\t 56 &  0\\\\\n",
       "\t 57 &  1\\\\\n",
       "\t 58 &  0\\\\\n",
       "\t 59 &  0\\\\\n",
       "\t 60 &  1\\\\\n",
       "\t 61 &  0\\\\\n",
       "\t 62 &  0\\\\\n",
       "\t 63 &  1\\\\\n",
       "\t 64 &  0\\\\\n",
       "\t 65 &  0\\\\\n",
       "\t 66 &  1\\\\\n",
       "\t 67 &  0\\\\\n",
       "\t 68 &  0\\\\\n",
       "\t 69 &  1\\\\\n",
       "\t 70 &  0\\\\\n",
       "\t 71 &  0\\\\\n",
       "\t 72 &  1\\\\\n",
       "\t 73 &  0\\\\\n",
       "\t 74 &  0\\\\\n",
       "\t 75 &  1\\\\\n",
       "\t 76 &  0\\\\\n",
       "\t 77 &  0\\\\\n",
       "\t 78 &  1\\\\\n",
       "\t 79 &  0\\\\\n",
       "\t 80 &  0\\\\\n",
       "\t 81 &  1\\\\\n",
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       "\t 83 &  0\\\\\n",
       "\t 84 &  1\\\\\n",
       "\t 85 &  0\\\\\n",
       "\t 86 &  0\\\\\n",
       "\t 87 &  1\\\\\n",
       "\t 88 &  0\\\\\n",
       "\t 89 &  0\\\\\n",
       "\t 90 &  1\\\\\n",
       "\t 91 &  0\\\\\n",
       "\t 92 &  0\\\\\n",
       "\t 93 &  1\\\\\n",
       "\t 94 &  0\\\\\n",
       "\t 95 &  0\\\\\n",
       "\t 96 &  1\\\\\n",
       "\t 97 &  0\\\\\n",
       "\t 98 &  0\\\\\n",
       "\t 99 &  1\\\\\n",
       "\t 100 &   0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "4. 4\n",
       "5. 5\n",
       "6. 6\n",
       "7. 7\n",
       "8. 8\n",
       "9. 9\n",
       "10. 10\n",
       "11. 11\n",
       "12. 12\n",
       "13. 13\n",
       "14. 14\n",
       "15. 15\n",
       "16. 16\n",
       "17. 17\n",
       "18. 18\n",
       "19. 19\n",
       "20. 20\n",
       "21. 21\n",
       "22. 22\n",
       "23. 23\n",
       "24. 24\n",
       "25. 25\n",
       "26. 26\n",
       "27. 27\n",
       "28. 28\n",
       "29. 29\n",
       "30. 30\n",
       "31. 31\n",
       "32. 32\n",
       "33. 33\n",
       "34. 34\n",
       "35. 35\n",
       "36. 36\n",
       "37. 37\n",
       "38. 38\n",
       "39. 39\n",
       "40. 40\n",
       "41. 41\n",
       "42. 42\n",
       "43. 43\n",
       "44. 44\n",
       "45. 45\n",
       "46. 46\n",
       "47. 47\n",
       "48. 48\n",
       "49. 49\n",
       "50. 50\n",
       "51. 51\n",
       "52. 52\n",
       "53. 53\n",
       "54. 54\n",
       "55. 55\n",
       "56. 56\n",
       "57. 57\n",
       "58. 58\n",
       "59. 59\n",
       "60. 60\n",
       "61. 61\n",
       "62. 62\n",
       "63. 63\n",
       "64. 64\n",
       "65. 65\n",
       "66. 66\n",
       "67. 67\n",
       "68. 68\n",
       "69. 69\n",
       "70. 70\n",
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       "99. 99\n",
       "100. 100\n",
       "101. 0\n",
       "102. 0\n",
       "103. 1\n",
       "104. 0\n",
       "105. 0\n",
       "106. 1\n",
       "107. 0\n",
       "108. 0\n",
       "109. 1\n",
       "110. 0\n",
       "111. 0\n",
       "112. 1\n",
       "113. 0\n",
       "114. 0\n",
       "115. 1\n",
       "116. 0\n",
       "117. 0\n",
       "118. 1\n",
       "119. 0\n",
       "120. 0\n",
       "121. 1\n",
       "122. 0\n",
       "123. 0\n",
       "124. 1\n",
       "125. 0\n",
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       "127. 1\n",
       "128. 0\n",
       "129. 0\n",
       "130. 1\n",
       "131. 0\n",
       "132. 0\n",
       "133. 1\n",
       "134. 0\n",
       "135. 0\n",
       "136. 1\n",
       "137. 0\n",
       "138. 0\n",
       "139. 1\n",
       "140. 0\n",
       "141. 0\n",
       "142. 1\n",
       "143. 0\n",
       "144. 0\n",
       "145. 1\n",
       "146. 0\n",
       "147. 0\n",
       "148. 1\n",
       "149. 0\n",
       "150. 0\n",
       "151. 1\n",
       "152. 0\n",
       "153. 0\n",
       "154. 1\n",
       "155. 0\n",
       "156. 0\n",
       "157. 1\n",
       "158. 0\n",
       "159. 0\n",
       "160. 1\n",
       "161. 0\n",
       "162. 0\n",
       "163. 1\n",
       "164. 0\n",
       "165. 0\n",
       "166. 1\n",
       "167. 0\n",
       "168. 0\n",
       "169. 1\n",
       "170. 0\n",
       "171. 0\n",
       "172. 1\n",
       "173. 0\n",
       "174. 0\n",
       "175. 1\n",
       "176. 0\n",
       "177. 0\n",
       "178. 1\n",
       "179. 0\n",
       "180. 0\n",
       "181. 1\n",
       "182. 0\n",
       "183. 0\n",
       "184. 1\n",
       "185. 0\n",
       "186. 0\n",
       "187. 1\n",
       "188. 0\n",
       "189. 0\n",
       "190. 1\n",
       "191. 0\n",
       "192. 0\n",
       "193. 1\n",
       "194. 0\n",
       "195. 0\n",
       "196. 1\n",
       "197. 0\n",
       "198. 0\n",
       "199. 1\n",
       "200. 0\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "       patient treatment\n",
       "  [1,]       1         0\n",
       "  [2,]       2         0\n",
       "  [3,]       3         1\n",
       "  [4,]       4         0\n",
       "  [5,]       5         0\n",
       "  [6,]       6         1\n",
       "  [7,]       7         0\n",
       "  [8,]       8         0\n",
       "  [9,]       9         1\n",
       " [10,]      10         0\n",
       " [11,]      11         0\n",
       " [12,]      12         1\n",
       " [13,]      13         0\n",
       " [14,]      14         0\n",
       " [15,]      15         1\n",
       " [16,]      16         0\n",
       " [17,]      17         0\n",
       " [18,]      18         1\n",
       " [19,]      19         0\n",
       " [20,]      20         0\n",
       " [21,]      21         1\n",
       " [22,]      22         0\n",
       " [23,]      23         0\n",
       " [24,]      24         1\n",
       " [25,]      25         0\n",
       " [26,]      26         0\n",
       " [27,]      27         1\n",
       " [28,]      28         0\n",
       " [29,]      29         0\n",
       " [30,]      30         1\n",
       " [31,]      31         0\n",
       " [32,]      32         0\n",
       " [33,]      33         1\n",
       " [34,]      34         0\n",
       " [35,]      35         0\n",
       " [36,]      36         1\n",
       " [37,]      37         0\n",
       " [38,]      38         0\n",
       " [39,]      39         1\n",
       " [40,]      40         0\n",
       " [41,]      41         0\n",
       " [42,]      42         1\n",
       " [43,]      43         0\n",
       " [44,]      44         0\n",
       " [45,]      45         1\n",
       " [46,]      46         0\n",
       " [47,]      47         0\n",
       " [48,]      48         1\n",
       " [49,]      49         0\n",
       " [50,]      50         0\n",
       " [51,]      51         1\n",
       " [52,]      52         0\n",
       " [53,]      53         0\n",
       " [54,]      54         1\n",
       " [55,]      55         0\n",
       " [56,]      56         0\n",
       " [57,]      57         1\n",
       " [58,]      58         0\n",
       " [59,]      59         0\n",
       " [60,]      60         1\n",
       " [61,]      61         0\n",
       " [62,]      62         0\n",
       " [63,]      63         1\n",
       " [64,]      64         0\n",
       " [65,]      65         0\n",
       " [66,]      66         1\n",
       " [67,]      67         0\n",
       " [68,]      68         0\n",
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       " [99,]      99         1\n",
       "[100,]     100         0"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patient<-1:100\n",
    "treatment<-rep(0,100)\n",
    "patient_assignment<-cbind(patient,treatment)\n",
    "for (counter in seq(3,100,3)){\n",
    "    patient_assignment[counter,2]<-1\n",
    "    }\n",
    "patient_assignment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H4> While loop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A while loop is used when the termination condition can happen at any time, depending upon some action within the loop. Suppose we want to simulate a coin toss, but stop when we have 10 heads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nheads<-0\n",
    "while (nheads<10){\n",
    "       toss<-rbinom(1,1,0.5)\n",
    "       if (nheads == 0)\n",
    "           experiment<-toss\n",
    "       else\n",
    "           experiment<-c(toss,experiment)\n",
    "       nheads<-nheads+toss\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
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   "source": [
    "experiment\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H2> Work!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write loops for the following:\n",
    "\n",
    "* Compute the mean of the vector v<-c(1,4,2,4,6,8,1,0) using a `for` loop\n",
    "* Flip a coin until you get a head\n",
    "\n",
    "\n",
    "What is wrong with the following code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.25"
      ],
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       "3.25"
      ],
      "text/markdown": [
       "3.25"
      ],
      "text/plain": [
       "[1] 3.25"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v<-c(1,4,2,4,6,8,1,0)\n",
    "s<-0\n",
    "for (i in 1:length(v))\n",
    "    s<-s+v[i]\n",
    "s/length(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# n<-1\n",
    "# while (n>0)\n",
    "#    print(n-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<H2> Vectorization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have learned to write loops, it is time to tell you to avoid them at all costs! This is not always possible, and sometimes it is a whole lot easier to write a loop than to figure out how to get R to do what you want using so-called 'vectorized' operations, but it is a whole lot faster. This doesn't really matter when you have a small amount of data to process. But when sample sizes get large, using loops can slow you down to the point of futility.\n",
    "\n",
    "What is vectorization? Simply put, it means feeding a whole vector to an R function, rather than doing operations on each element. For example, you just wrote a `for` loop to compute the mean of a vector. You can do that - but it would be much better to just use the R base function `mean`. Compare the following: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   user  system elapsed \n",
       "  0.472   0.004   0.476 "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v<-rnorm(1000000)\n",
    "sum<-0\n",
    "system.time(for (i in 1:length(v))\n",
    "    sum<-sum+v[i])\n",
    "    \n",
    "mean_v<-sum/length(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   user  system elapsed \n",
       "  0.002   0.000   0.002 "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system.time(mean_v<-mean(v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<H3>Simple Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1] 0.686323807 0.229189741 0.943499958 0.008288366 0.512752363 0.104759536\n",
      " [7] 0.430474185 0.548812798 0.956030584 0.626014339\n",
      " [1] 0.6021211 0.0143703 0.2431529 0.3023300 0.6619266 0.8759128 0.9916874\n",
      " [8] 0.6461957 0.2210742 0.1097788\n",
      " [1] 1.2884449 0.2435600 1.1866529 0.3106184 1.1746789 0.9806723 1.4221616\n",
      " [8] 1.1950085 1.1771048 0.7357931\n"
     ]
    }
   ],
   "source": [
    "v1<-runif(10)\n",
    "v2<-runif(10)\n",
    "print(v1)\n",
    "print(v2)\n",
    "print(v1+v2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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   "source": [
    "v1*v2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
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    "collapsed": false
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   "outputs": [
    {
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       "\\begin{tabular}{l}\n",
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       "2.14124191630535"
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       "         [,1]\n",
       "[1,] 2.141242"
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    "v1%*%v2"
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  {
   "cell_type": "code",
   "execution_count": 29,
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    "collapsed": false
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    {
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     "execution_count": 29,
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   "source": [
    "v1^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
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       " [7] 0.55279149 0.80794152 0.06505588 0.61354327"
      ]
     },
     "execution_count": 30,
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   ],
   "source": [
    "sqrt(v1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Work!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a program to simulate 10,000 coin tosses and count the number of heads."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "5059"
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       "5059"
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       "5059"
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      "text/plain": [
       "[1] 5059"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v<-rbinom(10000,1,prob=.5)\n",
    "#print(v)\n",
    "sum(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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