#Generating normal distribution (Pseudo) random number

x<-rnorm(10)

x

x2<-rnorm(10,2,1)

x2

set.seed()

#Generating Poisson data

rpois(10,1)

rpois(10,2)

rpois(10,20)

ppois(2,2) #Cumulative distribution ##P r(x <= 2) 平均發生率為2

ppois(4,2) #Cumulative distribution ##P r(x <= 4) 平均發生率為4

#線性 y = B0+B1X+e

#e~N(0,2^2) 標準差為2正態分布

#assume x~N(0,1^2)  B0=o.5  B1=2

set.seed(20)

x <- rnorm(100)

e <- rnorm(100,0,2)

y <- 0.5 + 2 * x + e

summary(y)

plot(x,y)

# 若x為binary ex性別

set.seed(20)

x <- rbinom(100,1,0.5)   #得到1的機率為0.5

e <- rnorm(100,0,2)

y <- 0.5 + 2 * x + e

summary(y)

plot(x,y)

#廣義線性模組可能服從poisson分布 Y~Poisson(m)

#log mu = B0 + B1X       #log mu 服從線性

#B0 = 0.5  B1 =0.3       #y服從 平均值為mu 的 PD

set.seed(20)

x <- rnorm(100)

log.mu <- 0.5 + 0.3 * x

y <- rpois(100,exp(log.mu))

summary(y)

plot(x,y)

# sample(range vector, numbers)

# sample(range vector)  重新排列

# sample(range vector, replace = T)  重複性抽樣

#Profiler   profiling is better than guessing

#Premature optimization is the root of all evil

system.time()   #proc_time  (class)

#user time: time charged to the CPU(s) for this expression

#elapsed time: "wall clock" time 運行時間

#parallel processing via  parallel package

##elapsed time > user time

system.time(readlines("http://www.google.com"))

#elapsed time < user time

hilbert <- function(n){

  i <- 1:n

  1/outer(i -1, i, "+")

}

x <- hilbert(1000)

system.time(svd(x))    # svd 多線程線性代數