pca <- function(X) {
  
  #   Run principal component analysis on the dataset X
  #
  #   U,d,V <- pca(X) computes eigenvectors of the covariance matrix of X
  #   Returns the eigenvectors in U and the eigenvalues in d as a vector
  #
  
  # Useful values
  m <- dim(X)[1]
  
  # ========================= YOUR CODE HERE =======================
  # Instructions: You should first compute the covariance matrix. Then, you
  #               should use the 'svd' function to compute the eigenvectors
  #               and eigenvalues of the covariance matrix.
  #
  # Note: When computing the covariance matrix, remember to divide by m (the
  #       number of examples).
  #
  

  
  # ================================================================
  return(list(D = diag(svd_out$d), U = svd_out$u ))
}