Tugas APG uhuy

APG.r

vectorLength <- function(x) {
  if(!is.vector(x)) stop("x is not a vector")
  return(sqrt(sum(x^2)))
}

vectorAngelCos <- function(x, y){
  if(!is.vector(x) || !is.vector(y)) stop("x or y is not a vector")
  if(length(x) != length(y)) stop("x and y are not the same length")
  
  # cos value of vector angel of x and y is x'y/(L_x * L_y)
  cosValue = sum(x*y)/(vectorLength(x)*vectorLength(y))
  return(cosValue)
}

projection <- function(x, y){
  if(!is.vector(x) || !is.vector(y)) stop("x or y is not a vector")
  if(length(x) != length(y)) stop("x and y are not the same length")
  
  # projection vector of x on y is (x'y)*y/L_y^2
  vector = sum(x*y)*y/vectorLength(y)^2
  
  # projection lenght of x on y is L_x*cos(angel of x and y)
  length = vectorLength(x)*abs(vectorAngelCos(x, y))
  return(list("vector" = vector, "length" = length))
}

deviationVector <- function(x){
  if(!is.vector(x)) stop("x is not a vector")
  return(x-mean(x))
}

deviationMatrix <- function(x){
  if(!is.matrix(x)) stop("x is not a matrix")
  avg = apply(x, 2, mean)
  avgMatrix = matrix(rep(avg, nrow(x)), ncol = ncol(x), byrow = TRUE)
  return(x-avgMatrix)
}

covarianceMatrix <- function(x, method = "bias"){
  if(!is.matrix(x)) stop("x is not a matrix")
  d = deviationMatrix(data)
  biased <- switch (method,
    "bias" = 1/nrow(x),
    "unbias" = 1/(nrow(x)-1),
    1
  )
  return(crossprod(d)*biased)
}