R: Matematika Dasar
Contoh operasi matematika
2 ^ 2 2 * 2 2 / 2 2 + 2 2 - 2 4 * 3 ^ 3
vector -4 s/d 3
-4:3
abs remainder
absolute
abs(-4:3)
remainder
(-4:3) %% 2 (-4:3) %/% 3
sign
sign(-4:3)
round
round(7/18,2)
7/118
options(digits=2) 7/118
floor(0.39) ceiling(0.39)
Trigonometry
sin(pi/2) tan(pi/4) cos(pi)
summary functions
sum(1:3) prod(c(3,5,7)) min(c(1,6,-14,-154,0)) max(c(1,6,-14,-154,0)) range(c(1,6,-14,-154,0))
any(c(1,6,-14,-154,0)<0) which(c(1,6,-14,-154,0)<0) all(c(1,6,-14,-154,0)<0) # all checks if criteria is met by each element
Complex
# Plot of Characteristic Function of a U(-1,1) Random Variable a <- -1; b <- 1 t <- seq(-20,20,.1) chu <- (exp(1i*t*b)-exp(1i*t*a))/(1i*t*(b-a)) plot(t,chu,"l",ylab=(expression(varphi(t))),main="Characteristic Function of Uniform Distribution [-1, 1]")
# Plot of Characteristic Function of a N(0,1) Variable mu <- 0; sigma <- 1 t <- seq(-5,5,0.1) chsnv <- exp(1i*t*mu-.5*(sigma^2)*(t^2)) plot(t,chsnv,"l",ylab=(expression(varphi(t))),main="Characteristic Function of Standard Normal Distribution")
# Plot of Characteristic Function of Poisson Random Variable lambda <- 6 t <- seq(0,20,.1) chpois <- exp(lambda*(exp(1i*t)-1)) plot(t,chpois,"l") # Warning omitted and left as exercise # for the reader to interpret
Spesial
factorial(3) factorial(3000) # any guess? lfactorial(3000) #lfactorial helps out sum(log(3000:2))
stirling <- function(n) {sqrt(2*pi)*n^{n+.5}*exp(-n)}
stirling(100)
factorial(100)/stirling(100)
choose(10,4) choose(10,10) # just verifying choose(100,10) # how about large n?
prod(10:(10-4+1)) # permutations of 10 p 4 prod(100:(100-10+1)) #permutations of 100 p 10