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
class(d)
## [1] "difftime"
units(d)
## [1] "hours"
d
## Time difference of 1 hours
units(d) = "secs"
d
## Time difference of 3600 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 R package, which in turn is build upon the udunits2 C library. The udunits2
library provides the following operations:
m/s
is a valid physical unitm/s
and km/h
are convertibleThe units
R package uses R package udunits2
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.
We can set units to numerical values by set_units
:
library(units)
(a <- set_units(runif(10), m/s))
## Units: [m/s]
## [1] 0.832006439 0.359083909 0.603057928 0.576472604 0.613411909 0.830128625
## [7] 0.642478956 0.800919445 0.464359833 0.006960209
the result, e.g.
set_units(10, m/s)
## 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.
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)
b
## Units: [km/h]
## [1] 2.99522318 1.29270207 2.17100854 2.07530137 2.20828287 2.98846305
## [7] 2.31292424 2.88331000 1.67169540 0.02505675
Arithmetic operations verify units, and create new ones
a + a
## Units: [m/s]
## [1] 1.66401288 0.71816782 1.20611586 1.15294521 1.22682382 1.66025725
## [7] 1.28495791 1.60183889 0.92871967 0.01392042
a * a
## Units: [m^2/s^2]
## [1] 6.922347e-01 1.289413e-01 3.636789e-01 3.323207e-01 3.762742e-01
## [6] 6.891135e-01 4.127792e-01 6.414720e-01 2.156301e-01 4.844451e-05
a ^ 2
## Units: [m^2/s^2]
## [1] 6.922347e-01 1.289413e-01 3.636789e-01 3.323207e-01 3.762742e-01
## [6] 6.891135e-01 4.127792e-01 6.414720e-01 2.156301e-01 4.844451e-05
a ** -2
## Units: [s^2/m^2]
## [1] 1.444597 7.755470 2.749679 3.009142 2.657637
## [6] 1.451140 2.422603 1.558915 4.637572 20642.175610
and convert to the units of the first argument if necessary:
a + b # m/s + km/h -> m/s
## Units: [m/s]
## [1] 1.66401288 0.71816782 1.20611586 1.15294521 1.22682382 1.66025725
## [7] 1.28495791 1.60183889 0.92871967 0.01392042
Currently, powers are only supported for integer powers, so using a ** 2.5
would result in an error.
There are some basic simplification of units:
t <- make_units(s)
a * t
## Units: [m]
## [1] 0.832006439 0.359083909 0.603057928 0.576472604 0.613411909 0.830128625
## [7] 0.642478956 0.800919445 0.464359833 0.006960209
which also work when units need to be converted before they can be simplified:
t <- make_units(min)
a * t
## Units: [m]
## [1] 49.9203864 21.5450345 36.1834757 34.5883562 36.8047145 49.8077175
## [7] 38.5487374 48.0551667 27.8615900 0.4176125
Simplification to unit-less values gives the “1” as unit:
m <- make_units(m)
a * t / m
## Units: [1]
## [1] 49.9203864 21.5450345 36.1834757 34.5883562 36.8047145 49.8077175
## [7] 38.5487374 48.0551667 27.8615900 0.4176125
Allowed operations that require convertible units are +
, -
, ==
, !=
, <
, >
, <=
, >=
. Operations that lead to new units are *
, /
, and the power operations **
and ^
.
Mathematical operations allowed are: abs
, sign
, floor
, ceiling
, trunc
, round
, signif
, log
, cumsum
, cummax
, cummin
.
signif(a ** 2 / 3, 3)
## Units: [m^2/s^2]
## [1] 2.31e-01 4.30e-02 1.21e-01 1.11e-01 1.25e-01 2.30e-01 1.38e-01 2.14e-01
## [9] 7.19e-02 1.61e-05
cumsum(a)
## Units: [m/s]
## [1] 0.8320064 1.1910903 1.7941483 2.3706209 2.9840328 3.8141614 4.4566404
## [8] 5.2575598 5.7219196 5.7288799
log(a) # base defaults to exp(1)
## Units: [(ln(re 1 m.s-1))]
## [1] -0.1839151 -1.0241992 -0.5057420 -0.5508275 -0.4887186 -0.1861746
## [7] -0.4424212 -0.2219949 -0.7670955 -4.9675458
log(a, base = 10)
## Units: [(lg(re 1 m.s-1))]
## [1] -0.07987331 -0.44480406 -0.21964097 -0.23922133 -0.21224780 -0.08085461
## [7] -0.19214109 -0.09641116 -0.33314535 -2.15737773
log(a, base = 2)
## Units: [(lb(re 1 m.s-1))]
## [1] -0.2653334 -1.4776071 -0.7296315 -0.7946760 -0.7050719 -0.2685932
## [7] -0.6382789 -0.3202709 -1.1066849 -7.1666537
Summary functions sum
, min
, max
, and range
are allowed:
sum(a)
## 5.72888 [m/s]
min(a)
## 0.006960209 [m/s]
max(a)
## 0.8320064 [m/s]
range(a)
## Units: [m/s]
## [1] 0.006960209 0.832006439
make_units(min(m/s, km/h)) # converts to first unit:
## 0.2777778 [m/s]
Following difftime
, printing behaves differently for length-one vectors:
a
## Units: [m/s]
## [1] 0.832006439 0.359083909 0.603057928 0.576472604 0.613411909 0.830128625
## [7] 0.642478956 0.800919445 0.464359833 0.006960209
a[1]
## 0.8320064 [m/s]
The usual subsetting rules work:
a[2:5]
## Units: [m/s]
## [1] 0.3590839 0.6030579 0.5764726 0.6134119
a[-(1:9)]
## 0.006960209 [m/s]
c(a,a)
## Units: [m/s]
## [1] 0.832006439 0.359083909 0.603057928 0.576472604 0.613411909 0.830128625
## [7] 0.642478956 0.800919445 0.464359833 0.006960209 0.832006439 0.359083909
## [13] 0.603057928 0.576472604 0.613411909 0.830128625 0.642478956 0.800919445
## [19] 0.464359833 0.006960209
concatenation converts to the units of the first argument, if necessary:
c(a,b) # m/s, km/h -> m/s
## Units: [m/s]
## [1] 0.832006439 0.359083909 0.603057928 0.576472604 0.613411909 0.830128625
## [7] 0.642478956 0.800919445 0.464359833 0.006960209 0.832006439 0.359083909
## [13] 0.603057928 0.576472604 0.613411909 0.830128625 0.642478956 0.800919445
## [19] 0.464359833 0.006960209
c(b,a) # km/h, m/s -> km/h
## Units: [km/h]
## [1] 2.99522318 1.29270207 2.17100854 2.07530137 2.20828287 2.98846305
## [7] 2.31292424 2.88331000 1.67169540 0.02505675 2.99522318 1.29270207
## [13] 2.17100854 2.07530137 2.20828287 2.98846305 2.31292424 2.88331000
## [19] 1.67169540 0.02505675
difftime
From difftime
to units
:
t1 = Sys.time()
t2 = t1 + 3600
d = t2 - t1
(du = as_units(d))
## 1 [h]
vice versa:
(dt = as_difftime(du))
## Time difference of 1 hours
class(dt)
## [1] "difftime"
matrix
objectsset_units(matrix(1:4,2,2), m/s)
## Units: [m/s]
## [,1] [,2]
## [1,] 1 3
## [2,] 2 4
set_units(matrix(1:4,2,2), m/s * m/s)
## Units: [m^2/s^2]
## [,1] [,2]
## [1,] 1 3
## [2,] 2 4
but
set_units(matrix(1:4,2,2), m/s) %*% set_units(4:3, m/s)
## [,1]
## [1,] 13
## [2,] 20
strips units.
data.frame
sunits in data.frame
objects are printed, but do not appear in summary
:.
set.seed(131)
d <- data.frame(x = runif(4),
y = set_units(runif(4), s),
z = set_units(1:4, m/s))
d
## x y z
## 1 0.2064370 0.8463468 [s] 1 [m/s]
## 2 0.1249422 0.5292048 [s] 2 [m/s]
## 3 0.2932732 0.5186254 [s] 3 [m/s]
## 4 0.3757797 0.2378545 [s] 4 [m/s]
summary(d)
## x y z
## Min. :0.1249 Min. :0.2379 Min. :1.00
## 1st Qu.:0.1861 1st Qu.:0.4484 1st Qu.:1.75
## Median :0.2499 Median :0.5239 Median :2.50
## Mean :0.2501 Mean :0.5330 Mean :2.50
## 3rd Qu.:0.3139 3rd Qu.:0.6085 3rd Qu.:3.25
## Max. :0.3758 Max. :0.8463 Max. :4.00
d$yz = with(d, y * z)
d
## x y z yz
## 1 0.2064370 0.8463468 [s] 1 [m/s] 0.8463468 [m]
## 2 0.1249422 0.5292048 [s] 2 [m/s] 1.0584095 [m]
## 3 0.2932732 0.5186254 [s] 3 [m/s] 1.5558761 [m]
## 4 0.3757797 0.2378545 [s] 4 [m/s] 0.9514180 [m]
d[1, "yz"]
## 0.8463468 [m]
Units are often written in the form m2 s-1
, for square meter per second. This can be defined as unit, and also parsed by as_units
:
(x = 1:10 * as_units("m2 s-1"))
## Units: [m^2/s]
## [1] 1 2 3 4 5 6 7 8 9 10
udunits understands such string, and can convert them
y = 1:10 * make_units(m^2/s)
x + y
## Units: [m^2/s]
## [1] 2 4 6 8 10 12 14 16 18 20
Printing units in this form is done by
deparse_unit(x)
## [1] "m2 s-1"
Base scatter plots and histograms support automatic unit placement in axis labels. In the following example we first convert to SI units. (Unit in
needs a bit special treatment, because in
is a reserved word in R.)
mar = par("mar") + c(0, .3, 0, 0)
displacement = mtcars$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)