# for loops

x <- c(3,4,8,5,1,4,9,4)

sum(x)

n <- length(x)
val <- 0
for(i in 1:n){ # val gets added to in each step of the loop
  
  val <- val + x[i]
  
}
val
sum(x)


# another way:

val <- 0
# don't need curly braces if there is only one line
for(xvalue in x) val <- val + xvalue 
val

# we can put a for loop inside a function :)
my_sum <- function(x){
  
  n <- length(x)
  val <- 0
  for(i in 1:n){ # val gets added to in each step of the loop
    
    val <- val + x[i]
    
  }
  
  return(val)
  
}

my_sum(x)

# counting characters in a string with a for loop

ch <- "stRawberry"
n <- nchar(ch) # get number of characters
nr <- 0 # initialize the count at 0
for(i in 1:n){
  
  # if(substr(ch,i,i) == "r"){
  #   
  #   nr <- nr + 1
  #   
  # }
  
  nr <- nr + any(substr(ch,i,i) == c("r","R"))
  
}
nr

# 

N <- 100
val <- 0
for(i in 1:N){
  
  val <- val + (-1)^(i+1) / (2*i - 1)
  
}
val
pi/4

# what if I want to keep track of the approximation as I go along??


N <- 100
val <- numeric(N) # make an empty vector (or a vector of 0s)
val[1] <- 1
for(i in 2:N){
  
  val[i] <- val[i-1] + (-1)^(i+1)/(2*i-1)
  
}

plot(val,type = "l")
abline(h=pi/4,lty=3)

val
pi/4


# double for loop!

x

my_sort <- function(x){
  
  n <- length(x)
  for(i in 1:(n-1))
    for(j in (i+1):n){
      
      if(x[i] > x[j]){
        
        tmp <- x[j]
        x[j] <- x[i]
        x[i] <- tmp
        
      }
    }
  
 return(x) 
  
}

x <- c(3,7,89,4,6,1,3,7,8,0)
my_sort(x)
sort(x)

# super cool 3d plot

myfun <- function(x,y) x*sin(x)*(1-y^2)

gs <- 50 # grid size
x <- seq(0,pi,length=gs)
y <- seq(-1,1,length=gs)

fxy <- matrix(0,gs,gs) # make an empty matrix
for(i in 1:gs){
  
  for(j in 1:gs){
    
    fxy[i,j] <- myfun(x[i],y[j])
    
  }
  
}


# use the persp()
par(mar=c(1,1,1,1))
persp(x = x, y = y, z = fxy, 
      box = F,
      theta = 30,
      phi = 30)


# in this situation, we can use the 
# function outer() to avoid the double for loop


# use the outer() function to evalute myfun() at
# every combination of x and y and return a matrix
fxy2 <- outer(x,y,FUN = myfun)

persp(x,y,fxy2)