1 What Are If and If Else Statement in R

If, if else, and else if statements perform one of a set of possible tasks based on what condition is satisfied.

If, if else, and else if statements take the forms:

if(condition){
  task code chunk
}

if(condition){
  task code chunk
} else{
  alternative task code chunk
}

ifelse(condition, TRUE value, FALSE value)

The if else statement can be extended to multiple layers with else if:

if(condition){
  task code chunk
} else if(new condition){
  first alternative task code chunk
} else{
  second alternative task code chunk
}

This can continue with as many conditions and alternative statements as possible, provided they are well defined.

Basic examples:

You can use logical and relational operators to specify conditions.

a = 1
if(a < 3){
  print(a)
}

[1] 1

a = 3
if(a > 5){
  print("We have enough.")
} else{
  print("We need more.")
}

[1] "We need more."

a = 5
ifelse(a > 6, "Great!", "Retry!")

[1] "Retry!"

a = 12
if(a < 5){
  print("We need more.")
} else if(a < 10){
  print("We might need more.")
} else{
  print("We have enough.")
}

[1] "We have enough."

2 A Function to Return the Cube of Only Positive Numbers in R

The cube of a number \(y\) is \(y^3\).

The argument of interest is \(y>0\).

To create the function, use:

cubeY = function(y){
  if(y > 0){
    cube = y^3
  }
  return(cube)
}

For \(y=2\):

cubeY(2)

[1] 8

To allow for custom error statement when \(y<0\), update to:

cubeP = function(y){
  if(y > 0){
    cube = y^3
  } else {cube = "Error: this is a negative number."}
  return(cube)
}

You can then evaluate for the numbers \(y=4\) and \(y=-6\):

cubeP(4)

[1] 64

cubeP(-6)

[1] "Error: this is a negative number."

3 A Function to Find the Real Roots of a Quadratic Equation in R

A quadratic equation is of the form:

\[ax^2 + bx + c = 0\]

with \(a\ne0\), and \(a, \; b, \; c \;\) as integers.

The two roots or solutions are:

\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

• The discriminant is \(D = b^2 - 4ac\).

• For \(D > 0\), the equation has real and distinct roots.

• For \(D = 0\), the equation has real and equal roots.

• For \(D < 0\), the equation does not have real roots.

The arguments of interest are \(a\), \(b\) and \(c\).

To create the function to find the roots, use:

rootq = function(a, b, c){
  D = b^2 - 4*a*c
  if(D > 0){
    root1 = (-b - sqrt(b^2 - 4*a*c))/(2*a)
    root2 = (-b + sqrt(b^2 - 4*a*c))/(2*a)
    roots = c(root1, root2)
  } else if(D == 0){
    roots = paste("Equal roots:", -b/(2*a))
  } else {roots = "Real roots do not exist."}
  return(roots)
}

You can then derive the roots for \((a, b, c) = (1, 1, -6) , (1, 4, 4) \; \text{and} \; (1, 2, 8)\), that is \(x^2 + x - 6 = 0\), \(x^2 + 4x + 4 = 0\), and \(x^2 + 2x + 8 = 0\) respectively:

rootq(1, 1, -6)

[1] -3  2

rootq(1, 4, 4)

[1] "Equal roots: -2"

rootq(1, 2, 8)

[1] "Real roots do not exist."