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### R BASICS WORKSHOP                                                        ###
### PRESENTATION 5: OPERATORS                                                ###
###                                                                          ###
### Center for Conservation and Sustainable Development                      ###
### Missouri Botanical Garden                                                ###
### Website: rbasicsworkshop.weebly.com                                      ###
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### A. TYPES AND HELP WITH OPERATORS #####################################################

# Main types of operators:
# 1. Arithmetic
# 2. Comparison
# 3. Logical
# 4. Other

# Help:
?* # This does not work
help ("*") # This works



### B. ARITHMETIC OPERATORS ####################################################

# A pair of vectors and matrices that we will use for examples:
p <- seq(from = 1, to = 10, b = 1)
z <- seq(9, 18, 1)

p
z

P <- matrix(seq(1, 25, 1), ncol = 5)
Z <- matrix(seq(26, 50, 1), ncol = 5)

P
Z

# Arithmetic operations are the most common:
# + Sum
# - Subtraction
# * Multiplication
# / Division
# ^ Power
# %% Module - calculates the remainder in a division
# %/% Integer division - calculates the integer portion of a division


## IMPORTANT: It is critical to understand how operators work on different
## situations. This also applies to other types of operators!


## Case 1. Two scalars (single numbers): the simplest case ##
10 + 3

10 - 3

10 * 3

10 / 3

10 ^ 3

10 %% 3

10 %/% 3


## Case 2. A vector or matrix and a scalar ##
p
P

p - 3
P - 3

# The operation occurs between each element in the matrix and the scalar. The
# result is the same size as the vector or matrix.

p ^ 3
P ^ 3

p %% 3
P %% 3


## Case 3. Two vectors or matrices of the same size ##
z
Z

p * z
P / Z

# In this case, the operation is between the two corresponding elements
# of each vector or matrix. The result is the same size as the original objects.


## Case 4. Two vectors or matrices of different sizes ##
length(p)

p - c(1,2)

p - rep(c(1,2), time = 5)

p - c(1,2,3)

## IMPORTANT: in the first case, the length of the small object (2) is a
## multiple of the length of the large (10). The operation is done "recycling"
## or repeating elements of the smaller object. In the second case, the length
## of the smaller object (3) is not a multiple of the
## large one (10). This generates a warning message.


## Case 5. Operations with NA

# In any situation where there are NAs, operations return NA
p - NA

p - c(1, NA)



### B. COMPARATIVE OPERATORS ###################################################

# > Greater than
# < Less than
# >= Greater than or equal to
# <= Less than or equal to
# == equal than (not a single "=", but both together!)
# != Not equal to


## IMPORTANT: Comparisons between objects follow the same rues as those for
## arithmetic operators.

## These operators return logical values: TRUE or FALSE

p < 5
z > 8

p <= z
Z >= P

p == c(33, 37)

Z != c(NA, 37)



# Although not operators, functions *is.na* and *!is.na* are useful in this context
x <- c(3, NA, 34, 23, 19, NA)

is.na(x)

!is.na(x)


p < c(5, NA)

is.na(p < c(5, NA))

!is.na(p < c(5, NA))



### C. LOGICAL OPERATORS #######################################################

# &: Means 'and'
# |: Means 'or'

5 > 3 # This is TRUE

5 < 3 # This is FALSE


2 > 4 # This is FALSE

2 < 4 # This is TRUE


## & ##

# is 5 less than three AND 2 greater than 4?
5<3 & 2>4 # This is FALSE because NONE of comparisons are TRUE

# is 5 more than 3 AND 2 greater than 4?
5>3 & 2>4 # This is also FALSE because NOT ALL comparisons are TRUE

# is 5 more than 3 AND 2 less than 4?
5> 3 & 2<4 # Now both comparisons are TRUE, so all together is also TRUE


## | ##

# is 5 less than 3 OR 2 greater than 4?
5<3 | 2>4 # This is FALSE because NONE of comparisons are TRUE

# is 5 greater than 3 OR 2 greater than 4?
5>3 | 2>4 # This is TRUE because AT LEAST ONE comparisons is TRUE

# is 5 greater than 3 OR 2 less than 4?
5>3 | 2<4 # This is also TRUE because AT LEAST ONE comparisons are TRUE


## IMPORTANT: When *&* or *|* used with vectors or matrices, comparisons are
## made element by element. For example:

p > 5
z < 18


p>5 & z<18 # is TRUE only for items where p>5 AND z<18 are TRUE

p>5 | z<18 # is TRUE for items where p>5 OR z<18 are TRUE


## IMPORTANT: *&&* AND *||* also exist but make the comparison only for the
## first element of vectors

p> 5 && z <18

p> 5 || z <18