#--- Vectors --------------------------------
  X <- 11:21
  X <- X[-(3:5)]     #removes x[3:5]
  rep(0,10)          # ten 0's
  rep(1:5,3)         # 1:5,1:5,1:5
  rep(1:5,each=3)    # 111 222 333 
  seq(-1,1,.01)
  c(1,5,4)
  c(2,3, X)

  rev(X)             #flips vector
  t(X)               #transpose  !! teking t() on array doesn't do it!!!
  (X>15 & X<=19)     #logical
  sum(X>15 & X<=19)
  X[X>15 & X<=19]
  (1:length(X))[X>15 & X<=19]

  any(x > 0.8)       # True if any of x are < 0.8
  all(x < 0.8)       # True if all of x are < 0.8

  sort(X, index.return=T)
  unlist( sort(X, index.return=T)[2]  )      # index of sorted vec
  which( abs(x-5.2) == min(abs(x-5.2)) )     # index of entry closest to 5.2




#--- Call vector elements by name --------------------
  X <- c("A"=2, "B"=3)
  names(X)[1] <- "SS"
  X




#--- Set operations with Vector ----------------------------
  
  a <- c(1,3,4,5,7,8,9,29)
  b <- c(3,20,4,11,8)

  union(a,b)
  intersect(a,b)
  setdiff(a,b)

  setequal(a,b)         #- is set a equal to set b?

  is.element(a, b)      # takes each element of a, and askes if it is in b.



#--- Find index of a match in vector A. (not done)   ----------------------------

  X <- c(1,3,5,11,23,33,47)
  which(X==3)              #- find index of a that holds 3


  b <- c(3,11,33)
  which(X %in% b)          #- find index of b in X.  

  b <- c(3,9,33)
  which(X %in% b)          #- gives error since 9 is not in X









#--- Find match to a vector inside longer vector ----------------------------
  n.vmatch <- function(x,y){
    n <- length(x)
    m <- length(y)

    j <- numeric(0)
    for (i in 1:(n-m+1)) {
      if ( sum(x[i:(i+m-1)]==y) == m ) { j <- c(j,i) }
    }
    return(j)
  }

  n.vmatch(c(1,0,0,0,1,0,1,1), c(1,1,1))

  n.vmatch(c(1,0,0,0,1,1,1,1), c(1,1,1))










#--- Matrix ---------------------------------
  x <- matrix(1:6, 2, 3)           #2x3 matrix
  x <- matrix(1:6, 2, 3, byrow=T)         

  y <- 1:10
  dim(y) <- c(2,5)

  z1 <- 2:6
  z2 <- 3:7
  z  <- cbind(z1, z2)  #column bind 
  z  <- rbind(z1, z2)  #row bind

  y * .5
  y * 1:5  #funny multipication
  
  y; z; y * z      #elementwise multiplication

  y %*% t(z)          #matrix multiplication               


  

#--- Call matrix elements by their name ----------------
  x <- matrix(1:9, 3, 3, byrow=T)             
  rownames(x) <- c("up", "middle", "down")               
  colnames(x) <- c("left", "center", "right")  
  x
  x["up","right"]                         

  rownames(x)[1] <- "top"
  x      



#--- Row-wise Mean and Sum--------------------------
  x <- matrix(1:6, 2, 3, byrow=T)         

  rowMeans(x)  #row-wise mean
  rowSums(x)

  colMeans(x)  #column-wise mean
  colSums(x)

  apply(x, 1, mean)




#--- 3d array -------------------------------
  X <- array(0, c(10, 3, 3) )
  X[1,,]




#--- All possible combinations ----------------
  install.packages("gtools")
  library(gtools)


  permutations(2, 5, c(-1,1), repeats.allowed=TRUE)   #- all 2^5=32 possible seqences of (-1,1)

  permutations(4,2, 1:4, repeats.allowed=TRUE) #all coordinates of 4x4 matrix

  combinations(10, 5)           #- all choose(10, 5) = 252 possible group of 5 

  combinations(10, 2, 1:10)    #- All choose(10,2) = 45 possible pairs 

  combinations(10, 2, 1:10, repeats.allowed=TRUE)  #- above + (a,a)
  
  permutations(10, 2, 1:10, repeats.allowed=TRUE)  #- All 100 possible sequence





#--- Find rows in matrix that match with vector x (study later)-----------
  rowmatch <- function(A,B) {
    #-- Rows in A that match the rows in B
    f <- function(...) paste(..., sep=":")
   if(!is.matrix(B)) B <- matrix(B, 1, length(B))
    a <- do.call("f", as.data.frame(A))
    b <- do.call("f", as.data.frame(B))
    match(b, a)
  }

  A <- matrix(1:1000, 100, 10, byrow=TRUE)
  B <- matrix(21:40, 2, 10, byrow=TRUE)
  rowmatch(A, B )

  b <- 51:60
  rowmatch(A, b)



#--- Find index of n maximum elements of matrix ----

  MM <- matrix(runif(400, 0, 100), 20, 20)

  ixM <- sort(MM, decreasing=T, index.return=T)$ix

  A <- matrix(c(1:20), dim(MM)[1], dim(MM)[2], byrow=F)  #- matrix with row numbers
  B <- matrix(c(1:20), dim(MM)[1], dim(MM)[2], byrow=T)  #- matrix with col numbers


  cbind(MM[ixm], A[ixM], B[ixM])  #- element, and its row, and column

  cbind(A[ixM], B[ixM])[A[ixM] < B[ixM]]  #- only elements in upper triangle 




#--- Vectorize a function -----
  mu_hat <- function(t) { 

    sub1 <- function(t){  sum( t-(1:5) ) }
    sapply( t, sub1 ) 

  }