R/XinyuJiangToolsRfunctions.R

In Xinyu-Jiang/XinyuJiangTools: Tools for STAT 3701

#' Calculate Mean, Variane, SD
#'
#' Computes the mean, variance and sd of a vector
#'
#' @param x vector
#'
#' @return list
#' @export
#' @examples
#' func1(rnorm(10))
func1 <- function(x){
  a = sum(x)/length(x)
  b = sum((x-a)^2)/length(x)
  c = sqrt(b)
  return(list(mean=a,var=b,sd=c))
}

#' Calculate Mean, Variane, SD (again)
#'
#' Computes the mean, variance and sd of a vector, but with user checks
#'
#' @param x vector
#'
#' @return list
#' @export
#' @examples
#' func2(rnorm(10))
func2 <- function(x){
  stopifnot(is.numeric(x))
  stopifnot(length(x)!=0)
  stopifnot(is.finite(x))
  stopifnot(!is.na(x))
  stopifnot(!is.nan(x))
  
  a = sum(x)/length(x)
  b = sum((x-a)^2)/length(x)
  c = sqrt(b)
  return(list(mean=a,var=b,sd=c))
}

#' MLE of gamma distribution
#'
#' Computes the liklihood of a gamma distribution
#'
#' @param x vector
#'
#' @return scalar
#' @export
#' @examples
#' func3(rnorm(10))
func3 <- function(x){
  alpha <- pi
  log <- function(alpha)
    sum(dgamma(x, shape = alpha, log = TRUE))
  interval <- mean(x) + c(-1,1) * 3 * sd(x)
  interval <- pmax(mean(x) / 1e3, interval)
  
  oout<- optimize(log, maximum = TRUE, interval)
  return (oout$maximum)
}

#' Weighted mean, var, sd
#'
#' Computes the weighted mean, var, sd
#'
#' @param d data.frame
#'
#' @return list
#' @export
#' @examples
#' data(d)
#' func4(d)
func4 <- function(d){
  
  a = sum(d$x * d$p)
  b = sum(((d$x - a)^2) * d$p)
  c = sqrt(b)
  return(list(mean=a,var=b,sd=c))
  
}

#' Weighted mean, var, sd with user checkes
#'
#' Computes the weighted mean, var, sd with user checks
#'
#' @param d data.frame
#'
#' @return list
#' @export
#' @examples
#' d <- read.table(url("http://www.stat.umn.edu/geyer/3701/data/q1p4.txt"),header = TRUE)
#' func5(d)
func5 <- function(d){
  
  stopifnot(is.numeric(d$x))
  stopifnot(is.numeric(d$p))
  
  stopifnot(length(d$x)!=0)
  stopifnot(length(d$p)!=0)
  
  stopifnot(is.finite(d$x))
  stopifnot(is.finite(d$p))
  
  stopifnot(!is.na(d$x))
  stopifnot(!is.na(d$p))
  
  stopifnot(!is.nan(d$x))
  stopifnot(!is.nan(d$p))
  
  stopifnot(all.equal(sum(d$p),1))
  
  a = sum(d$x * d$p)
  b = sum(((d$x - a)^2) * d$p)
  c = sqrt(b)
  return(list(mean=a,var=b,sd=c))
  
}

#' Highlevel check function
#'
#' Checks and throws error if not numeric, finit, zero lenth, NA, NAN
#'
#' @param x object
#'
#' @return object
#' @export
#' @examples
#' func6(NA)

func6 <- function(x){
  
  tryCatch(stopifnot(is.numeric(x)), error=function(e){print("not numeric")})
  tryCatch(stopifnot(is.finite(x)), error=function(e){print("not finite")})
  tryCatch(stopifnot(length(x)!=0), error=function(e){print("has 0 length")})
  tryCatch(stopifnot(!is.nan(x)), error=function(e){print("NA or NAN")})
  tryCatch(stopifnot(!is.na(x)), error=function(e){print("NA or NAN")})
  
}

#' MLE 
#'
#' Computes the liklihood of a given distribution for data x
#'
#' @param x vector
#' @param func function, e.g., `function(theta, x) dgamma(x, shape = theta, log = TRUE)`
#' @param interval vector, i.e., interval for optimize function
#'
#' @return scalar
#' @export
#' @examples
#' x1=rgamma(100,3)
#' func1 = function(theta, x) dgamma(x, shape = theta, log = TRUE)
#' result7_gamma <- func7(x1,func1,c(0,3))
#' result7_gamma
#' 
func7 <- function(x, func, interval){
  
  f7 <- function(theta, x)
  {sum(func(theta, x))}
  
  oout<- optimize(f7, maximum = TRUE, interval, x=x)
  return(oout$maximum)
} 

#' Quiz 2 - 1
#' 
#'calculates $x^T A^{-1} x$ 
#'
#' @param a matrix
#' @param x vector
#'
#' @return object
#' @export
 
func8 <- function(a, x){
  stopifnot(is.numeric(x))
  stopifnot(is.numeric(a))
  stopifnot(is.matrix(a))
  stopifnot(nrow(a) == length(x))

  s <- solve(a,x)
  sum(x * s)
}


#' Quiz 2 - 2
#' 
#'calculates $x^T A^{-1} x$ but it is a binary operator rather than an apparent function call,
#'
#' @param a matrix
#' @param x vector
#'
#' @return object
#' @export

"%func9%" <- function(a, x){
  stopifnot(is.numeric(x))
  stopifnot(is.numeric(a))
  stopifnot(is.matrix(a))
  stopifnot(nrow(a) == length(x))
  
  s <- solve(a,x)
  sum(x * s)
}


#' Quiz 2 - 3
#' 
#'a function that takes a numeric matrix and standardizes its columns
#'
#' @param a matrix
#'
#' @return matrix
#' @export

func10 <- function(a){
  stopifnot(is.matrix(a))
  stopifnot(!is.na(a))
  stopifnot(!is.nan(a))
  stopifnot(is.finite(a))
  stopifnot(is.numeric(a))
  
  for(i in 1:ncol(a)){
    b <- a[,i]
    a[,i] <- (b - mean(b)) / sd(b)
  }
  return (a)
}


#' HW 2 - 1
#' 
#'a function that takes a numeric matrix and standardizes its columns. but do it without loops.
#'
#' @param a matrix
#'
#' @return object
#' @export

func11 <- function(a){
  stopifnot(is.matrix(a))
  stopifnot(!is.na(a))
  stopifnot(!is.nan(a))
  stopifnot(is.finite(a))
  stopifnot(is.numeric(a))
  
  x <- function(a) {
    (a - mean(a)) / sd(a)
  }
  
  apply(a, 2, x)
}



#' HW 2 - 2
#' 
#'a function just like the function array in the R base package,
#'
#' @param X matrix
#' @param MARGIN margin of object to work
#' @param FUN function 
#' @param ... probability
#' 
#' @return array
#' @export

func12 <- function(X, MARGIN, FUN, ...)
{
  
  stopifnot(length(dim(X))==2)
  
  if(length(dim(X))!=2)
  {
    stop("matrix is not 2d")
  } 
  if(!(MARGIN %in% c(1,2)))
  {
    stop("margin is not in 1 or 2")
  }
  R = dim(X)[1]
  C = dim(X)[2]
  f = match.fun(FUN)
  
  if (MARGIN == 1)
  {
    result = list()
    for(i in 1:R)
    {
      result[[i]] = f(X[i,],...)
    }
  }else if(MARGIN == 2)
  {
    result = list()
    for(j in 1:C)
    {
      result[[j]] = f(X[,j],...)
    }
  }
  return(simplify2array(result))
}