# Simple arithmetic functions

#1. element by element
 x <- 3:12
 abs(x)
 log(x)
 log10(x)
 sqrt(x)  
 exp(x)
 sin(x)

#2. operate on entire vector:
 # returns a scalar value
 sum(x)
 prod(x)  #multiply each term

 #return vector of same length
 cumsum(x)       #x[1], x[1]+x[2], x[1]+x[2]+x[3]
 cumprod(x)      #x[1], x[1]*x[2], x[1]*x[2]*x[3]

#3. conversion to integers, rounding,..
 x <- 103.652
 round(x)
 round(x,1)
 round(x,2)
 trunc(x)     #nearest integer in direction of 0
 trunc(-0.8)
 floor(x)     #nearest integer in direction of negative infinity
 floor(-0.8)
 ceiling(x)   #nearest integer in direction of positive infinity
 ceiling(-0.8) 

#4. max, min related
 x <- c(3,5,5,9)
 y <- c(5,3,5,11)

 max(x)
 min(x)
 range(x)   #useful for setting limits on graph axes
 pmax(x,y)  #per position [i] return maximum of x[i] and y[i]
 pmin(x,y)
 
#5. ordering
 x <- c(12,5,6,6,-1)
 sort(x)
 rev(x)
 order(x)       #returns position of smallest, next smallest, ...
 rev(order(x))  #returns position of largest, next largest,...
 rank(x)        #rank of x[1], then rank of x[2]; useful for ranksum statistics

#6. simple statistics 
 x <- c(8,12,5,4,19,2,1)
 y <- rnorm(length(x),mean=3+2*x,sd=1)
 mean(x)
 var(x)
 median(x)
 quantile(x,probs=c(0.25,0.75))
 summary(x)     #a generic function used on lots of classes of data