# Functions.r -- basic tutorial on functional programming in R
# CSE 446
# Author: Daryl Hansen

# Say we have a function that does something. For simplicity, it adds two numbers
# (in reality we'd use the + operator if that's all we wanted)
plus <- function(a, b) {
  return(a+b)
}

plus(5,3)

# We can change the arguments by wrapping it in another function, like so:
add.seven <- function(a) {
  return(plus(a,7))
}

multiply.and.add <- function(a, b, n) {
  return(plus(n*a, n*b))
}

add.seven(13)

multiply.and.add(7, 8, 2)

# We can also pass in functions as arguments to other functions
fun.max <- function(v, w, fun) {
  first <- max(v)
  second <- max(w)
  return(fun(first, second))
}

x <- c(1,3,5,7)
y <- c(-1, 0, 1, 2)

fun.max(x, y, plus)

# Once again reducing the number of arguments
add.max.y <- function(v) {
  return(fun.max(v, y, plus))
}

add.max.y(x)

# Notice how the behavior of max.and.half.y changes when we change y
# (despite y not being one of its arguments)
y <- c(1,2,4)
add.max.y(x)

# We can then use this to manipulate rows of a matrix:
X <- matrix(c(0,0,0,1,0,1,0,2,5), 3, 3)

# 'apply' takes a matrix, a dimension, and a function
#   if dim=1, it applies the function to each row of the matrix
#   if dim=2, it applies it to each column
apply(X, 1, add.max.y)
apply(X, 2, add.max.y)



# 'apply' is much faster than using a loop:
bigX = matrix(1:500000, 50000, 10)

# Compare the runtime of this line (~1 second on my machine)
mean(apply(bigX, 1, add.max.y))

# with this equivalent loop: (~7 seconds on my machine)
z = c()
for (i in 1:50000) {
  z[i] = add.max.y(bigX[i,])
}
mean(z)