8. Functions
## 8.1 Functions for Confidence Intervals and Tests
## 8.1.1 The t-test and associated confidence interval
## 8.1.2 Chi-Square tests for two-way tables

## 8.2 Matching and Ordering
match(<vec1>, <vec2>)  ## For each element of <vec1>, returns the 
                       ## position of the first occurrence in <vec2>
order(<vector>)        ## Returns the vector of subscripts giving
                       ## the order in which elements must be taken
                       ## so that <vector> will be sorted.
rank(<vector>)         ## Returns the ranks of the successive elements.
x <- rep(1:5,rep(3,5))
x
two4 <- x %in% c(2,4)
two4
# Now pick out the 2s and the 4s
x[two4]

## 8.3 String Functions
substring(<vector of text strings>, <first position>, <last position>)
nchar(<vector of text strings>)       
            ## Returns vector of number of characters in each element.
## *8.3.1 Operations with Vectors of Text Strings - A Further Example
car.brandnames <- sapply(strsplit(as.character(Cars93$Make), " ", fixed=TRUE),
+                          function(x)x[1])
car.brandnames[1:5]

## 8.4 Application of a Function to the Columns of an Array or Data Frame 
apply(<array>, <dimension>, <function>)
lapply(<list>, <function>) 
             ## N. B. A dataframe is a list.  Output is a list.
sapply(<list>, <function>)              
             ## As lapply(), but simplify (e.g. to a vector
             ## or matrix), if possible.
## 8.4.1 apply()
apply(airquality,2,mean)   # All elements must be numeric!
apply(airquality,2,mean,na.rm=TRUE)
## 8.4.2 sapply()
sapply(airquality, function(x)sum(is.na(x)))
sapply(moths,is.factor)		# Determine which columns are factors
# How many levels does each factor have?
sapply(moths, function(x)if(!is.factor(x))return(0) else length(levels(x)))

## *8.5 aggregate() and tapply()
str(cabbages)
attach(cabbages)
aggregate(HeadWt, by=list(Cult=Cult, Date=Date), FUN=mean)

*8.6 Merging Data Frames
Cars93.summary
new.Cars93 <- merge(x=Cars93,y=Cars93.summary[,4,drop=F],
 			by.x="Type",by.y="row.names") 
## 8.7 Dates
# Electricity Billing Dates
dd <- as.Date(c("2003/08/24","2003/11/23","2004/02/22","2004/05/23"))
diff(dd)
as.Date("1/1/1960", format="%d/%m/%Y")
as.Date("1:12:1960",format="%d:%m:%Y")
as.Date("1960-12-1")-as.Date("1960-1-1")
as.Date("31/12/1960","%d/%m/%Y")
as.integer(as.Date("1/1/1970","%d/%m/%Y")
as.integer(as.Date("1/1/2000","%d/%m/%Y"))
dec1 <- as.Date("2004-12-1")
format(dec1, format="%b %d %Y")
format(dec1, format="%a %b %d %Y")

## 8.8. Writing Functions and other Code
fahrenheit2celsius <- function(fahrenheit=32:40)(fahrenheit-32)*5/9
# Now invoke the function
fahrenheit2celsius(c(40,50,60))
mean.and.sd <- function(x=1:10){
+ av <- mean(x)
+ sd <- sqrt(var(x))
+ c(mean=av, SD=sd)
+ }
>
# Now invoke the function
mean.and.sd()
mean.and.sd(hills$climb)
## 8.8.1 Syntax and Semantics
## 8.8.2 A Function that gives Data Frame Details
faclev <- function(x)if(!is.factor(x))return(0) else 
   			    length(levels(x))
sapply(moths, faclev) 
sapply(moths, function(x)if(!is.factor(x))return(0) 
else length(levels(x)))
check.df <- function(df=moths) 
          sapply(df, function(x)if(!is.factor(x))return(0) else 
                                                 length(levels(x)))
## 8.8.3 Compare Working Directory Data Sets with a Reference Set
dsetnames <- objects()
additions <- function(objnames = dsetnames)
{
      newnames <- objects(pos=1)
      existing <- as.logical(match(newnames, objnames, nomatch = 0))
      newnames[!existing]
}
additions(dsetnames)
## 8.8.4 Issues for the Writing and Use of Functions
## 8.8.5 Functions as aids to Data Management
attributes(elasticband)$title <- 
  "Extent of stretch of band, and Resulting Distance"
## 8.8.6 Graphs
## 8.8.7 A Simulation Example
guesses <- runif(100)
correct.answers <- 1*(guesses < .2)
correct.answers
## 8.8.8 Poisson Random Numbers
## 8.9 Exercises
## ex4. 
plot.one <- function(){
xyrange <- range(milk)   # Calculates the range of all values in the data frame
par(pin=c(6.75, 6.75))      # Set plotting area = 6.75 in. by 6.75 in.
plot(four, one, data=milk, xlim=xyrange, ylim=xyrange, pch=16)
abline(0,1)                  # Line where four = one
}