## R as a calculator
5^2 + 100

## assign a variable a value
a = 5
# do calculations with a
a*5

## vectors 
b = numeric(3)

b = c(1,1,1)
b = rep(1,3)

b = c(1, 2, 3)
b = 1:3 

d = 4:6
b*d

# compute the mean of b
(1 + 2 + 3)/3
# or 
sum(b)/3
# or
mean(b)

## getting help about the function
?mean

## get certain elements in a vector
b
b[1]
b[2:3]

## assign a new value
b[1] = 20
b

## matrices
m = matrix(1:6, nrow=2, ncol=3, byrow=T)
m

# sum the entries in each column
colSums(m)

# get the first row and second column entry
m[1,2]

# matrix multiplication
m2 = matrix(c(2,3,2,1,4,2), nrow=3, ncol=2, byrow=T)

m%*%m2

# does there a determinant function exist?
m = matrix(1:4, 2,2)
??determinant
det(m)

# inverse of a matrix
m = matrix(c(0.2, 0.7, 0.1, 0.7), 2,2, byrow=T)
solve(m)

# identity matrix of dimension 3
diag(3)
solve(diag(2) - m)


## random numbers
sample(1:5, 5, prob=c(0.1, 0.2, 0.5, 0.1, 0.1), replace=TRUE)


## sample from known distributions
a = rnorm(1000)
mean(a)
var(a)

hist(a, freq=F)

## if-statement
w = 3
if(w > 2){
    print("hei")
} else {
    print("bye")
}

## for-loop
for(i in 1:10){
    cat("hei", i, "\n")
}

n = 10 
a = numeric(n)
for(i in 1:n){
    a[i] <- i + 5
}

## writing a function
# my.mat : matrix you would like to multiply n-times with it self
# n.times : number of times you would do matrix multiplication
my.matrixMultiply = function(my.mat, n.times){

    res.matrix = my.mat
    for(i in 1:n.times){
      res.matrix = res.matrix %*% my.mat
    }
    return(res.matrix)
}
m = matrix(1:4, 2,2)
my.matrixMultiply(m,2)
m%*%m%*%m
my.matrixMultiply(m,3)



my.func2 = function(x){
    return(x^2)
}

curve(my.func2(x), from=-5, to=5)
curve(dnorm(x, mean=3, sd=1), from=-2, to=7)

x = seq(from=-5, to=5, by=0.01)
y = my.func2(x)

plot(x,y, type="l")

## comparisons 
a = c(1,3,5)
b = c(3,3,3)
d = c(0,3,1)

a > b
a == b

# elementwise comparison
(a > b) & (a > d)
# The longer form with two & evaluates left to right examining 
# only the first element of each vector.  Evaluation proceeds 
# only until the result is determined. 
(a > b) && (a > d)

# elementwise comparison
(a >= b) | (a > d)
# longer form
(a >= b) || (a > d)

## some mathematical functions

# modulo
10%%5
10%%6

# factorial
factorial(3)

# binomial coefficient
choose(n=5, k=2)