Introduction to R Part 2: R Arithmetic

Now that we have R set up, this guide will illustrate R functionality by showing snippets of R code and the output they produce. Each code snippet will consist of 2 parts, an input block showing the actual code I'm running (possibly with some descriptive comments) followed by the output produced by the code. It is recommended that you keep RStudio open and play around with the commands yourself as you read along.

In this part, we will explore R's ability to perform basic computations. As we saw in part 1, typing an arbitrary mathematical expression into the console yields the result of the calculation, just as we'd expect when using a calculator. R accepts all the basic math symbols you'd expect:

In [1]:

# Use + for addition

4+5

Out[1]:

9

In [2]:

# Use - for subtraction

5-10

Out[2]:

-5

In [3]:

# Use * for multiplication

8*4

Out[3]:

32

In [4]:

# Use / for division

100/3

Out[4]:

33.3333333333333

In [5]:

# Use ^ for exponentiation

2^4

Out[5]:

16

Math expressions in R follow the normal order of operations so * and / are executed before + and -, and ^ is executed before multiplication and division.

In [6]:

# These operations are executed in reverse order of appearance.

2+3*5^2

Out[6]:

77

You can use parentheses in your math expressions to ensure that operations are carried out on the correct order. Operations within parentheses are carried out before operations that are external to the parentheses, just like you'd expect.

In [7]:

# Now the addition comes first and the exponentiation comes last.

((2+3) * 5 )^2

Out[7]:

625

If you're new to programming, you may not be familiar with the modulus operator, but it is another common math symbol that returns the remainder you'd get when dividing two numbers. Use two percentage signs to take the modulus.

In [8]:

# Use %% for modulus

100 %% 30

Out[8]:

10

Beyond symbolic operators, R contains a wide variety of named math functions. Here is brief summary of a few of the most common math functions you might want to access:

In [9]:

log(2.7182)  # log() takes the natural logarithm of its argument

Out[9]:

0.99996989653911

In [10]:

exp(10)  # exp() raises e to the power of its argument

Out[10]:

22026.4657948067

In [11]:

# If you ever need the constant e you can use:
exp(1)

Out[11]:

2.71828182845905

In [12]:

log10(100) # log10() takes the log base 10 of a number

Out[12]:

2

In [13]:

log2(64) # log2() takes the log base 2 of a number

Out[13]:

6

In [14]:

sqrt(64) # sqrt() returns the square root of its argument

Out[14]:

8

In [15]:

# round() rounds its argument to the nearest whole number:

round(233.234)

Out[15]:

233

In [16]:

# Add the "digits" argument to round to specified decimal place:

round(233.234, digits=1)

Out[16]:

233.2

In [17]:

# Entering -1 for digits rounds to the 10's place:

round(233.234, digits=-1)

Out[17]:

230

If a number is equal in distance between the two numbers it could round to, round() will prefer the even number. In other words, R does not always round up when it encounters a 5 in the decimal place you are rounding:

In [18]:

round(2.5) # Rounds down to the even digit 2
round(3.5) # Rounds up to the even digit 4

Out[18]:

2

Out[18]:

4

Use the floor() and ceiling() functions to round a number down to or up to the next whole number.

In [19]:

floor(2.8) # floor() always rounds down

Out[19]:

2

In [20]:

ceiling(2.2) # ceiling() always rounds up

Out[20]:

3

In [21]:

trunc(2.6) # trunc() rounds in the direction of zero
trunc(-2.6)

Out[21]:

2

Out[21]:

-2

In [22]:

abs(-10) # abs() returns the absolute value of the argument

Out[22]:

10

In [23]:

pi  # pi returns the constant pi

Out[23]:

3.14159265358979

Common trigonometric functions are also built-in. The trig functions assume your argument is expressed in terms of radians, not degrees.

In [24]:

cos(0) # Cosine

sin(pi/2) # Sine

tan(pi/4) # Tangent

Out[24]:

1

Out[24]:

1

Out[24]:

1

In [25]:

acos(1) # Inverse Cosine

asin(1) # Inverse Sine

atan(1) # Inverse Tangent

Out[25]:

0

Out[25]:

1.5707963267949

Out[25]:

0.785398163397448

Any time you need to perform a common mathematical operation in R, chances are there is a function for it built into R or available through an R package download (we'll discuss packages later.). When in doubt, try searching Google. Helpful blog posts and answers posted on programming sites like stackoverflow can often save you a lot time and help you learn better ways of doing things.

Next time: Introduction to R Part 3: Atomic Data Types