# STAT_540_R_Lec_03.R

# Defining your own functions

# see if something is a function
is.function(mean)

# make your own function

logistic <- function(x) exp(x) / (1 + exp(x))

logistic(2)
exp(2) / (1 + exp(2))

plot(logistic)
plot(logistic, xlim = c(-5,5))


logistic2 <- function(x,a,b) exp(a + b*x)/(1 + exp(a + b*x))

logistic2(2,1,-2)
logistic2(x = 2, b = 1,a =-2) # naming the arguments

logistic2(2)

# set a = 0 and b = 1 as defaults
logistic3 <- function(x,a=0,b=1) exp(a + b*x)/(1 + exp(a + b*x))

logistic3(1/2,3,4)
logistic3(1/2,a = 3,b = 4)


# to plot nice pictures of the function...

x <- seq(-5,5,length=100)

plot(logistic3(x)~x, type = "l")
lines(logistic3(x,a=3,b=-1)~x, col="red")
lines(logistic3(x,a=-1,b=2)~x, col="blue")

# functions which execute more than one line of code!!!!

logistic4 <- function(x,a,b){ # curly braces
  
    y <- a + x*b
    ey <- exp(y)
    val <- ey / (1 + ey) # this is value I want to return
    
    return(val)
  
}

logistic3(1,2,3)
logistic4(1,2,3)

# I want my function to return a list with the value of the function
# as well as the values of a and b I used

logistic5 <- function(x,a,b){ # curly braces
  
  y <- a + x*b
  ey <- exp(y)
  val <- ey / (1 + ey) # this is value I want to return
  
  output <- list(val = val, a = a, b = b)
  
  return(output)
  
}

obj <- logistic5(0,-1,1)
obj$val
obj$a
obj$b


# this is a BAD way to define a function -- we SHOULD include 
# a and b as arguments in the function, since they are used 
# in the function
a <- 3
b <- -1

logistic6 <- function(x){ # curly braces
  
  y <- a + x*b
  ey <- exp(y)
  val <- ey / (1 + ey) # this is value I want to return
  
  return(val)
  
}

logistic6(1)

# Rule of thumb: Every value you use in the function should be 
# put in as one of the arguments.


## Conditional programming

my_birthday <- "01/15"
today <- format(Sys.Date(),"%m/%d")

if(today == my_birthday){
  
  wish1 <- c("Happy birthday!")
  wish2 <- c("So glad you were born!")
  wishes <- c(wish1, wish2)
  wish <- sample(wishes,1)
  
  say <- paste("It is your birthday.", wish)
  print(say)

} else {
  
  print("Sorry, it is not your birthday.")
  
}

## else if, to introduce more possibilities

bfun <- function(my_birthday){
  
  my_birthday_month <- substr(my_birthday,start = 1,stop =2)  # use substr() to extract part of a character string
  today <- format(Sys.Date(),"%m/%d")
  today_month <- format(Sys.Date(),"%m")
  
  if(today == my_birthday){
    
    wish1 <- c("Happy birthday!")
    wish2 <- c("So glad you were born!")
    wishes <- c(wish1, wish2)
    wish <- sample(wishes,1)
    
    say <- paste("It is your birthday.", wish)
    print(say)
    
  } else if(today_month == my_birthday_month){
    
    print("It is not your birthday, but it's your birthday month!")
    
  } else {
    
    print("Sorry, it is not your birthday.")
    
  }

}

bfun("08/04")
bfun("08/28")
bfun("01/15")

# a piecewise-defined function

trifun <- function(x){
  
  if(x < -1){
    
    val <- 0
    
  } else if( (x >= -1) & (x < 0)) {
    
    val <- 1 + x
    
  } else if( (x >= 0) & (x < 1) ){
    
    val <- 1 - x
    
  } else if(x >= 1){
    
    val <- 0
    
  }
  
  return(val)
  
}

# let's say I want to plot a picture of my function

trifun(.5)

x <- seq(-2,2,by=.1)
trifun(x) # problem here because if() can only take a single logical value -- not a vector

# USEFUL FUNCTION: sapply()

fx <- sapply(x,FUN = trifun) # evaluates trifun() at each entry in x

plot(fx ~ x,type = "l")


# take advantage of how logicals can be used as numeric values
trifun2 <- function(x) (1 + x) * ((x >= -1) & (x < 0)) + (1-x) * ((x >= 0) & (x < 1))

# handier, because I can give this new function a vector input
plot(trifun2(x) ~x,type = "l")


# ifelse()

x <- 1.5

if( x > 1){
  
  val <- 50
  
} else {
  
  val <- 100
}

val

ifelse(x > 1,50,-100)

x <- .5
ifelse(x > 1,50,-100)