Overview

Date-time data can be frustrating to work with in R. R commands for date-times are generally unintuitive and change depending on the type of date-time object being used. Moreover, the methods we use with date-times must be robust to time zones, leap days, daylight savings times, and other time related quirks, and R lacks these capabilities in some situations. Lubridate makes it easier to do the things R does with date-times and possible to do the things R does not.

Resources

Lubridate tutorial

Let’s explore some of the functions within the lubridate package.

But first, installation!

# The easiest way to get lubridate is to install the whole tidyverse:
install.packages("tidyverse")

# Alternatively, install just lubridate:
install.packages("lubridate")

# Or the the development version from GitHub:
# install.packages("devtools")
devtools::install_github("tidyverse/lubridate")

Some of these functions can be done usng strptime and strftime in base R but we will be focusing on lubridate.

Load package

library(lubridate)

Quick note:

POSI….what? There are two internal implementations of date/time: POSIXct, which stores seconds since UNIX epoch (+some other data), and POSIXlt, which stores a list of day, month, year, hour, minute, second, etc.

Lubridate features

Reference points

today = today()
today
[1] "2018-09-12"
now = now()
now
[1] "2018-09-12 18:49:39 SAST"

Parsing dates and times

To create POSIXlt objects from strings, lubridate has a number of aptly named functions: - ymd(), ymd_hms, dmy(), dmy_hms, mdy(), …

# When is Women's day?
ymd("20180809")
[1] "2018-08-09"
mdy("08-09-2018")
[1] "2018-08-09"
dmy("09/08/2018")
[1] "2018-08-09"
# You try

# Parse as date
___("17 Sep 2018")

____("March 6, 1957")

# Parse as date and time (with no seconds!)
_____("July 15, 2012 12:56")

# Parse as date-time (with seconds)
______('2011-04-06 08:00:10')

# Parse all as dates
x <- c("2009-01-01", "2009-01-02", "2009-01-03")
___(x)

# Format to display date as "2018-01-01"
___(180101, 180102)

# Format to display "2010-02-01"
___(010210)

# Format to display "2010-01-02"
___(010210)

You see that these functions contain the formatting of the string in their name. In addition, they are robust in which separators are used (e.g. : or -). Note that you can set the tz input argument to set the timezone.

Extracting information from date-times

womensday<-ymd_hms("2018-08-09-12-30-30", tz="GMT")
womensday
[1] "2018-08-09 12:30:30 GMT"
# Extract only the date
date(womensday)
[1] "2018-08-09"
# Is it a leap year?
leap_year(womensday)
[1] FALSE

GET components of date-times

Getting useful information using functions such as year(), month(), mday(), hour(), minute() and second():

year(womensday)
[1] 2018
month(womensday)
[1] 8
week(womensday)
[1] 32
wday(womensday)
[1] 5
wday(womensday, label=TRUE)
[1] Thu
Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
yday(womensday)
[1] 221
hour(womensday)
[1] 12
# You try
# Save your birthday as a date-time object (make up a time if you don't know!)
bday <- _______()

# What number week in the year were you born?
_____(bday)

# What number day in the year were you born
____(bday)

# Were you born in a leap year?
____(bday)

# What day of the week were you born? Print out the full, unabbreviated weekday
____(bday)

SET components of date-time

Lubridate can be used to not only extract but also change prts of date-time objects

month(womensday) <- 12
womensday
[1] "2018-12-09 12:30:30 GMT"
second(womensday) <-99
womensday
[1] "2018-12-09 12:31:39 GMT"
# Use update to change multiple values
youthday <- update(womensday, year = 1976, day = 16, month = 6, hour = 8)
# You try
# Change your birth date to your birthday this year

bday_2018 <- ____
bday_2018

Arithmetic with dates

Some important time spans

intervals

  • The time information between two points in time.
  • Intervals are specific time spans (because they are tied to specific dates).
  • Can be created by subtracting two instants, or using the new_interval function.
# Create an interval in time
my_int <- interval(womensday, now)
my_int
[1] 2018-12-09 12:31:39 GMT--2018-09-12 16:49:39 GMT
# Access the start of an interval
start <- int_start(my_int)
start
[1] "2018-12-09 12:31:39 GMT"
# Access the end point of an interval
end <- int_end(my_int)
end
[1] "2018-09-12 16:49:39 GMT"
# Flip an interval
tni_ym <- int_flip(my_int)
tni_ym
[1] 2018-09-12 16:49:39 GMT--2018-12-09 12:31:39 GMT

Lubridate also provides two helper functions for general time spans:

durations

  • Which measure the exact amount of time between two points.
  • Did you know seconds are the only time unit with a consistent length?! Durations are always measured in seconds.
  • Helper functions for creating durations are named after the units of time (plural) but begin with a “d” (for duration).
  • For example dhours, dseconds
# Create durations
d <- ddays(14)
d
[1] "1209600s (~2 weeks)"
w <- dweeks(104)
w
[1] "62899200s (~1.99 years)"
# Create duration from numeric
as.duration(100)
[1] "100s (~1.67 minutes)"
# Create duration from a time interval
my_int_d <- as.duration(my_int)
my_int_d
[1] "7587719.47534204s (~12.55 weeks)"

periods

  • Which accurately track clock times despite leap years, leap seconds, and day light savings time
  • Helper functions for creating periods are named after the units of time (plural)
  • For example, you use functions like years, months. Note that these are not the same as the function year and month.
# Create periods
p <- months(3) + days(12)
p
[1] "3m 12d 0H 0M 0S"
# Create a period from a time interval
my_int_p <- as.period(my_int)
my_int_p
[1] "-2m -26d -19H -41M -59.4753420352936S"

Why two classes?

minutes(2) # period
[1] "2M 0S"
## 2 minutes
dminutes(2) # duration
[1] "120s (~2 minutes)"
## 120s (~2 minutes)
my_int_d == my_int_p
[1] FALSE

Comparing the “timeline” and the “number line”

leap_year(2011)
[1] FALSE
## FALSE
ymd(20110101) + dyears(1)
[1] "2012-01-01"
## "2012-01-01 UTC"
ymd(20110101) + years(1)
[1] "2012-01-01"
## "2012-01-01 UTC"
 
leap_year(2012)
[1] TRUE
## TRUE
ymd(20120101) + dyears(1)
[1] "2012-12-31"
## "2012-12-31 UTC"
ymd(20120101) + years(1)
[1] "2013-01-01"
## "2013-01-01 UTC"
# Is my date within an interval?
a = ymd(20170101)
a
[1] "2017-01-01"
a %within% my_int
[1] FALSE
b = a + years(1) + months(7) + days(10)
b
[1] "2018-08-11"
b %within% my_int
[1] FALSE
# You try

# How many seconds in 6 months?


# Create a period of 2 seconds and 34 milliseconds


# Add four hours onto now and save as bedtime


# What interval in time has passed since your birthday and now?


# How old are you in seconds at this point in time?


# Create an interval of time from beginning of this year to now


# Has your birthday this year occured within this interval?


# How long until you turn 100 years old?!
---
title: "R-Ladies Cape Town: What's in a date?"
author: "Megan Beckett"
date: "16 August 2018"
output:
  html_notebook:
    fig_height: 4.5
    fig_width: 7
    toc: yes
---
# Overview
Date-time data can be frustrating to work with in R. R commands for date-times are generally unintuitive and change depending on the type of date-time object being used. Moreover, the methods we use with date-times must be robust to time zones, leap days, daylight savings times, and other time related quirks, and R lacks these capabilities in some situations. Lubridate makes it easier to do the things R does with date-times and possible to do the things R does not.

# Resources
- Make sure you check out the very handy R-Studio cheatsheet: https://rawgit.com/rstudio/cheatsheets/master/lubridate.pdf
- The chapter in R for Data Science on dates and times: http://r4ds.had.co.nz/dates-and-times.html

# Lubridate tutorial
Let's explore some of the functions within the lubridate package.

## But first, installation!
```{r message=FALSE,warning=FALSE}
# The easiest way to get lubridate is to install the whole tidyverse:
install.packages("tidyverse")

# Alternatively, install just lubridate:
install.packages("lubridate")

# Or the the development version from GitHub:
# install.packages("devtools")
devtools::install_github("tidyverse/lubridate")
```

Some of these functions can be done usng strptime and strftime in base R but we will be focusing on lubridate.

## Load package
```{r message=FALSE,warning=FALSE}
library(lubridate)

```
### Quick note:
POSI....what?
There are two internal implementations of date/time: POSIXct, which stores seconds since UNIX epoch (+some other data), and POSIXlt, which stores a list of day, month, year, hour, minute, second, etc.

## Lubridate features
### Reference points
```{r}
today = today()
today
now = now()
now
```

### Parsing dates and times
To create POSIXlt objects from strings, lubridate has a number of aptly named functions:
- ymd(), ymd_hms, dmy(), dmy_hms, mdy(), …

```{r}
# When is Women's day?

ymd("20180809")
mdy("08-09-2018")
dmy("09/08/2018")
```

```{r message=FALSE,warning=FALSE}
# You try

# Parse as date
___("17 Sep 2018")

____("March 6, 1957")

# Parse as date and time (with no seconds!)
_____("July 15, 2012 12:56")

# Parse as date-time (with seconds)
______('2011-04-06 08:00:10')

# Parse all as dates
x <- c("2009-01-01", "2009-01-02", "2009-01-03")
___(x)

# Format to display date as "2018-01-01"
___(180101, 180102)

# Format to display "2010-02-01"
___(010210)

# Format to display "2010-01-02"
___(010210)

```
You see that these functions contain the formatting of the string in their name. In addition, they are robust in which separators are used (e.g. : or  -). Note that you can set the tz input argument to set the timezone.

### Extracting information from date-times

```{r}
womensday<-ymd_hms("2018-08-09-12-30-30", tz="GMT")
womensday

# Extract only the date
date(womensday)

# Is it a leap year?
leap_year(womensday)
```

### GET components of date-times
Getting useful information using functions such as year(), month(), mday(), hour(), minute() and second():

```{r}
year(womensday)
month(womensday)
week(womensday)
wday(womensday)
wday(womensday, label=TRUE)
yday(womensday)
hour(womensday)

```
```{r message=FALSE,warning=FALSE}
# You try
# Save your birthday as a date-time object (make up a time if you don't know!)
bday <- _______()

# What number week in the year were you born?
_____(bday)

# What number day in the year were you born
____(bday)

# Were you born in a leap year?
____(bday)

# What day of the week were you born? Print out the full, unabbreviated weekday
____(bday)


```

### SET components of date-time
Lubridate can be used to not only extract but also change prts of date-time objects

```{r}
month(womensday) <- 12
womensday

second(womensday) <-99
womensday

# Use update to change multiple values
youthday <- update(womensday, year = 1976, day = 16, month = 6, hour = 8)

```

```{r}
# You try
# Change your birth date to your birthday this year

bday_2018 <- ____
bday_2018

```

### Arithmetic with dates
#### Some important time spans

**intervals**

- The time information between two points in time. 
- Intervals are specific time spans (because they are tied to specific dates).
- Can be created by subtracting two instants, or using the `new_interval` function.

```{r}
# Create an interval in time
my_int <- interval(womensday, now)
my_int

# Access the start of an interval
start <- int_start(my_int)
start

# Access the end point of an interval
end <- int_end(my_int)
end

# Flip an interval
tni_ym <- int_flip(my_int)
tni_ym
```


Lubridate also provides two helper functions for *general* time spans:

**durations** 

- Which measure the exact amount of time between two points.
- Did you know seconds are the only time unit with a consistent length?! Durations are always measured in seconds.
- Helper functions for creating durations are named after the units of time (plural) but begin with a “d” (for duration).
- For example `dhours`, `dseconds`

```{r}
# Create durations
d <- ddays(14)
d
w <- dweeks(104)
w

# Create duration from numeric
as.duration(100)

# Create duration from a time interval
my_int_d <- as.duration(my_int)
my_int_d

```

**periods**

- Which accurately track clock times despite leap years, leap seconds, and day light savings time
- Helper functions for creating periods are named after the units of time (plural)
- For example, you use functions like `years`, `months`. Note that these are not the same as the function `year` and `month`.

```{r}
# Create periods
p <- months(3) + days(12)
p

# Create a period from a time interval
my_int_p <- as.period(my_int)
my_int_p

```

**Why two classes?**

```{r}
minutes(2) # period
## 2 minutes
dminutes(2) # duration
## 120s (~2 minutes)

my_int_d == my_int_p

```

*Comparing the "timeline" and the "number line"*

- The durations class will always supply mathematically precise results. 
- A duration year will always equal 365 days. 
- Periods fluctuate the same way the timeline does to give intuitive results. This makes them useful for modelling clock times.
- (from https://www.r-statistics.com/2012/03/do-more-with-dates-and-times-in-r-with-lubridate-1-1-0/)


```{r}
leap_year(2011)
## FALSE
ymd(20110101) + dyears(1)
## "2012-01-01 UTC"
ymd(20110101) + years(1)
## "2012-01-01 UTC"
 
leap_year(2012)
## TRUE
ymd(20120101) + dyears(1)
## "2012-12-31 UTC"
ymd(20120101) + years(1)
## "2013-01-01 UTC"
```

```{r}
# Is my date within an interval?

a = ymd(20170101)
a

a %within% my_int

b = a + years(1) + months(7) + days(10)
b

b %within% my_int
```

```{r}
# You try

# How many seconds in 6 months?


# Create a period of 2 seconds and 34 milliseconds


# Add four hours onto now and save as bedtime


# What interval in time has passed since your birthday and now?


# How old are you in seconds at this point in time?


# Create an interval of time from beginning of this year to now


# Has your birthday this year occured within this interval?


# How long until you turn 100 years old?!



```


