Units of Measurement for R Vectors: an Introduction

knitr::opts_chunk$set(collapse = TRUE, fig.asp = 0.7, fig.width = 7)
units:::units_options(negative_power = FALSE)

R has little support for physical measurement units. The exception is formed by time differences: time differences objects of class difftime have a units attribute that can be modified:

t1 = Sys.time() 
t2 = t1 + 3600 
d = t2 - t1
units(d) = "secs"

We see here that the units method is used to retrieve and modify the unit of time differences.

The units package generalizes this idea to other physical units, building upon the udunits2 C library. The udunits2 library provides the following operations:

The units R package uses the udunits2 C library to extend R with functionality for manipulating numeric vectors that have physical measurement units associated with them, in a similar way as difftime objects behave.

Setting units, unit conversion

We can set units to numerical values by set_units:

(a <- set_units(runif(10),  m/s))

the result, e.g.

set_units(10, m/s)

literally means "10 times 1 m divided by 1 s". In writing, the "1" values are omitted, and the multiplication is implicit.

Unit conversion

When conversion is meaningful, such as hours to seconds or meters to kilometers, conversion can be done explicitly by setting the units of a vector

b = a
units(b) <- make_units(km/h)

Basic manipulations

Arithmetic operations

Arithmetic operations verify units, and create new ones

a + a
a * a
a ^ 2
a ** -2

and convert to the units of the first argument if necessary:

a + b # m/s + km/h -> m/s

Currently, powers are only supported for integer powers, so using a ** 2.5 would result in an error.

Unit simplification

There are some basic simplification of units:

t <- make_units(s)
a * t

which also work when units need to be converted before they can be simplified:

t <- make_units(min)
a * t

Simplification to unit-less values gives the "1" as unit:

m <- make_units(m)
a * t / m

Allowed operations that require convertible units are +, -, ==, !=, <, >, <=, >=. Operations that lead to new units are *, /, and the power operations ** and ^.

Mathematical functions

Mathematical operations allowed are: abs, sign, floor, ceiling, trunc, round, signif, log, cumsum, cummax, cummin.

signif(a ** 2 / 3, 3)
log(a) # base defaults to exp(1)
log(a, base = 10)
log(a, base = 2)

Summary functions

Summary functions sum, min, max, and range are allowed:

make_units(min(m/s, km/h)) # converts to first unit:


Following difftime, printing behaves differently for length-one vectors:



The usual subsetting rules work:




concatenation converts to the units of the first argument, if necessary:

c(a,b) # m/s, km/h -> m/s
c(b,a) # km/h, m/s -> km/h

Conversion to/from difftime

From difftime to units:

t1 = Sys.time() 
t2 = t1 + 3600 
d = t2 - t1
(du = as_units(d))

vice versa:

(dt = as_difftime(du))

units in matrix objects

set_units(matrix(1:4,2,2), m/s)
set_units(matrix(1:4,2,2), m/s * m/s)


set_units(matrix(1:4,2,2), m/s) %*% set_units(4:3, m/s)

strips units.

units objects in data.frames

units in data.frame objects are printed, but do not appear in summary:.

d <- data.frame(x = runif(4), 
                    y = set_units(runif(4), s), 
                    z = set_units(1:4, m/s))
d$yz = with(d, y * z)
d[1, "yz"]


Units are often written in the form m2 s-1, for square meter per second. This can be defined as unit, and also parsed by as_units:

(x = 1:10 * as_units("m2 s-1"))

udunits understands such string, and can convert them

y = 1:10 * make_units(m^2/s)
x + y

Printing units in this form is done by



Base scatter plots and histograms support automatic unit placement in axis labels. In the following example we first convert to SI units. (Unit in needs a bit special treatment, because in is a reserved word in R.)

mar = par("mar") + c(0, .3, 0, 0)
displacement = mtcars$disp * as_units("in")^3
units(displacement) = make_units(cm^3)
weight = mtcars$wt * 1000 * make_units(lb)
units(weight) = make_units(kg)
par(mar = mar)
plot(weight, displacement)

We can change grouping symbols from [ ] into ( ):

units_options(group = c("(", ")") )  # parenthesis instead of square brackets
par(mar = mar)
plot(weight, displacement)

We can also remove grouping symbols, increase space between variable name and unit by:

units_options(sep = c("~~~", "~"), group = c("", ""))  # no brackets; extra space
par(mar = mar)
plot(weight, displacement)

More complex units can be plotted either with negative powers, or as divisions, by modifying one of units's global options using units_options:

gallon = as_units("gallon")
consumption = mtcars$mpg * make_units(mi/gallon)
units(consumption) = make_units(km/l)
par(mar = mar)
plot(displacement, consumption) # division in consumption
units_options(negative_power = TRUE) # division becomes ^-1
plot(displacement, consumption) # division in consumption

As usual, units modify automatically in expressions:

units_options(negative_power = TRUE) # division becomes ^-1
par(mar = mar)
plot(displacement, consumption)
plot(1/displacement, 1/consumption)
units_options(negative_power = FALSE) # division becomes /

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units documentation built on May 29, 2024, 10:24 a.m.