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# 原先 R 裡面的"lm()"是用來擬合線性模型。
# "lm()"詳細說明 : https://stat.ethz.ch/R-manual/R-devel/library/stats/html/lm.html
> lm <- function(x) { x * x } # 重新定義"lm()"
> lm
function(x) { x * x }
# 使用"search()"顯示 R 搜尋列表的內容(依照順序排列)。
> search()
[1] ".GlobalEnv" "tools:rstudio"
[3] "package:stats" "package:graphics"
[5] "package:grDevices" "package:utils"
[7] "package:datasets" "package:methods"
[9] "Autoloads" "package:base"
# 這裡有一個自由變數: z (未在函數中定義)
f <- function(x, y) {
x^2 + y / z
}
# 在函數內定義另外一個函數
> make.power <- function(n) { # "make.power()"的參數"n"
+ pow <- function(x) { # "pow()"的參數是"x"
+ x^n
+ }
+ pow # 回傳"pow()"的值
>
> cube <- make.power(3)
> square <- make.power(2)
> cube(3)
[1] 27
> square(3)
[1] 9
# 使用"ls()"查看環境
> ls(environment(cube))
[1] "n" "pow"
> get("n", environment(cube))
[1] 3
> ls(environment(square))
> get("n", environment(square))
[1] 2
# "詞法作用域 (Lexical Scoping)"
> y <- 10 # "y"
> f <- function(x) { # "f()"
+ y <- 2
+ y^2 + g(x) # 這裡"y"的值為"2"
> g <- function(x) { # "g()"
+ x*y # 這裡"y"的值為"10"
> f(3)
[1] 34
# "詞法作用域"VS"動態作用域"的結果看起來相同
> # 情況1:還沒有定義"y"
> g <- function(x) { # "x"是形式參數
+ a <- 3
+ x+a+y # "y"是自由變數
> g(2)
Error in g(2) : object "y" not found
> # 情況2:已經定義"y"了
> y <- 3
[1] 8
# 對數概似函數
> make.NegLogLik <- function(data, fixed=c(FALSE,FALSE)) {
+ params <- fixed
+ function(p) {
+ params[!fixed] <- p
+ mu <- params[1]
+ sigma <- params[2]
+ a <- -0.5*length(data)*log(2*pi*sigma^2)
+ b <- -0.5*sum((data-mu)^2) / (sigma^2)
+ -(a + b)
> set.seed(1); normals <- rnorm(100, 1, 2)
> nLL <- make.NegLogLik(normals)
> nLL
function(p) {
params[!fixed] <- p
mu <- params[1]
sigma <- params[2]
a <- -0.5*length(data)*log(2*pi*sigma^2)
b <- -0.5*sum((data-mu)^2) / (sigma^2)
-(a + b)
}
<environment: 0x08d25c7c>
> ls(environment(nLL))
[1] "data" "fixed" "params"
> optim(c(mu = 0, sigma = 1), nLL)$par
mu sigma
1.218239 1.787343
> nLL <- make.NegLogLik(normals, c(FALSE, 2))
> optimize(nLL, c(-1, 3))$minimum
[1] 1.217775
> nLL <- make.NegLogLik(normals, c(1, FALSE))
> optimize(nLL, c(1e-6, 10))$minimum
[1] 1.800596
> x <- seq(1.7, 1.9, len = 100)
> y <- sapply(x, nLL)
> plot(x, exp(-(y - min(y))), type = "l")
> x <- seq(0.5, 1.5, len = 100)
整理自 R Programming (Week 2) -- Scoping Rules
Control Structures - Introduction[0:54](已完成)Control Structures - If-else[1:58](已完成)Control Structures - For loops[4:25](已完成)Control Structures - While loops[3:22](已完成)Control Structures - Repeat, Next, Break[4:57](已完成)Your First R Function[10:29](僅觀看)Functions(part1)[9:17](已完成)Functions(part2)[7:13](已完成)（一）Scoping Rules - Symbol Binding
# 原先 R 裡面的"lm()"是用來擬合線性模型。# "lm()"詳細說明 : https://stat.ethz.ch/R-manual/R-devel/library/stats/html/lm.html> lm <- function(x) { x * x } # 重新定義"lm()"> lmfunction(x) { x * x }# 使用"search()"顯示 R 搜尋列表的內容(依照順序排列)。> search() [1] ".GlobalEnv" "tools:rstudio" [3] "package:stats" "package:graphics" [5] "package:grDevices" "package:utils" [7] "package:datasets" "package:methods" [9] "Autoloads" "package:base"# 這裡有一個自由變數: z (未在函數中定義)f <- function(x, y) { x^2 + y / z}（二）Scoping Rules - R Scoping Rules
# 在函數內定義另外一個函數> make.power <- function(n) { # "make.power()"的參數"n"+ pow <- function(x) { # "pow()"的參數是"x"+ x^n+ }+ pow # 回傳"pow()"的值+ }>>> cube <- make.power(3)> square <- make.power(2)> cube(3)[1] 27> square(3)[1] 9# 使用"ls()"查看環境> ls(environment(cube))[1] "n" "pow"> get("n", environment(cube))[1] 3>>> ls(environment(square))[1] "n" "pow"> get("n", environment(square))[1] 2# "詞法作用域 (Lexical Scoping)"> y <- 10 # "y"> f <- function(x) { # "f()"+ y <- 2+ y^2 + g(x) # 這裡"y"的值為"2"+ }> g <- function(x) { # "g()"+ x*y # 這裡"y"的值為"10"+ }>> f(3)[1] 34# "詞法作用域"VS"動態作用域"的結果看起來相同> # 情況1:還沒有定義"y"> g <- function(x) { # "x"是形式參數+ a <- 3+ x+a+y # "y"是自由變數+ }> g(2)Error in g(2) : object "y" not found>> # 情況2:已經定義"y"了> y <- 3> g(2)[1] 8（三）Scoping Rules - Optimization Example (OPTIONAL)
# 對數概似函數> make.NegLogLik <- function(data, fixed=c(FALSE,FALSE)) {+ params <- fixed+ function(p) {+ params[!fixed] <- p+ mu <- params[1]+ sigma <- params[2]+ a <- -0.5*length(data)*log(2*pi*sigma^2)+ b <- -0.5*sum((data-mu)^2) / (sigma^2)+ -(a + b)+ }+ }>>> set.seed(1); normals <- rnorm(100, 1, 2)> nLL <- make.NegLogLik(normals)> nLLfunction(p) { params[!fixed] <- p mu <- params[1] sigma <- params[2] a <- -0.5*length(data)*log(2*pi*sigma^2) b <- -0.5*sum((data-mu)^2) / (sigma^2) -(a + b) }<environment: 0x08d25c7c>>> ls(environment(nLL))[1] "data" "fixed" "params">>> optim(c(mu = 0, sigma = 1), nLL)$par mu sigma1.218239 1.787343>> nLL <- make.NegLogLik(normals, c(FALSE, 2))> optimize(nLL, c(-1, 3))$minimum[1] 1.217775>> nLL <- make.NegLogLik(normals, c(1, FALSE))> optimize(nLL, c(1e-6, 10))$minimum[1] 1.800596>>> nLL <- make.NegLogLik(normals, c(1, FALSE))> x <- seq(1.7, 1.9, len = 100)> y <- sapply(x, nLL)> plot(x, exp(-(y - min(y))), type = "l")>>> nLL <- make.NegLogLik(normals, c(FALSE, 2))> x <- seq(0.5, 1.5, len = 100)> y <- sapply(x, nLL)> plot(x, exp(-(y - min(y))), type = "l")>