#Assignment: the "<-" operator

a<-1

a


#Typed vectors

x<-c(1,2,3)

y<-5:7

z<-seq(0,50,1)

u<-rep(11,5)


#Vector manipulation

x+3

y/2

z*2

x+y

u^2

y%%5 #this gives the integer remainder after dividing by 5


#Question: Find the first 23 multiples of the number 7 and 
#assign this to a variable called mul7
#----------------------------------------------------------

#----------------------------------------------------------


#Isolating parts of vectors

#remember we had y<-5:7 from before

y[1]
y[2]
y[3]
y[1:2]
y[c(1,3)]
y[c(FALSE,TRUE,TRUE)]


#Question: Find the 18th multiple of 7
#--------------------------------------

#--------------------------------------


#Logic operations

#remember we had a<-1

a==1
a==2
a!=3
a>=1
a<0


#Question: Test whether a is strictly less than -1
#-------------------------------------------------

#-------------------------------------------------

b<-2

a==1 & b==2
a==1 | b==1


#Question: Find out which multiples of 7 are also multiples of 4
#---------------------------------------------------------------

#---------------------------------------------------------------



#Conditional and loop statements:

#remember we had a<-1

if(a==2) {
  q<-2
} else {
  q<-1
} 

q

v<-rep(0,10)


for(i in 1:10) {
  v[i]<-i
}

v	

# Question: Using a "for" loop, construct a vector of perfect squares x^2 for x from 1 to 10
#-----------------------------------------------------------------------------------------

#-----------------------------------------------------------------------------------------


#Writing simple functions:

MySum.f<-function(a,b) {
  return(a+b)
}

MySum.f(2,3)

MySum.f(x,y)

MyQuadForm.f<-function(a,b,c) {
  sol<-rep(0,2)
  sol[1]<-((-b+sqrt(b^2-4*a*c))/(2*a))
  sol[2]<-((-b-sqrt(b^2-4*a*c))/(2*a))
  return(sol)
}

MyQuadForm.f(1,1,-1)


# Question: Write a function to give the nth number in the Fibonacci sequence:
# 1 1 2 3 5 8 13 21 ...
#---------------------------------------------------------------------------------

#---------------------------------------------------------------------------------


#Tools for stochasticity:

#Take a random sample from a vector without replacement
sample(x,size=3,replace=FALSE)

#Take a random sample from a vector with replacement
sample(y,size=10,replace=TRUE)

#Question: Write a function that takes a bitstring (a vector
#of 0's and 1's) and returns a new bitstring with a specified
#number of random mutations
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#----------------------------------------------------------

#Random uniformly distributed number:
runif(n=1, min=0, max=1)

#Random normally distributed number:
rnorm(n=1, mean=10, sd=2)

#Random Poisson distributed number:
rpois(n=1, lambda=4)

#Random binomially distributed number:
rbinom(n=1, size=20, prob=0.5)

#Question: Give the random number of offspring (out of 100) 
#with a recessive phenotype resulting from a cross 
#between two heterozygotes
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#----------------------------------------------------------