knitr::opts_chunk$set(collapse = TRUE, fig.asp = 0.7, fig.width = 7)
This vignette is identical to @rj, except for two changes:
We briefly review SI units, and discuss R packages that deal with measurement units, their compatibility and conversion. Built upon the UNIDATA udunits library, we introduce the package units that provides a class for maintaining unit metadata. When used in expression, it automatically converts units, and simplifies units of results when possible; in case of incompatible units, errors are raised. The class flexibly allows expansion beyond predefined units. Using units may eliminate a whole class of potential scientific programming mistakes. We discuss the potential and limitations of computing with explicit units.
Two quotes from @cobb -- Data are not just numbers,
they are numbers with a context and in data analysis,
context provides meaning -- illustrate that for a data analysis
to be meaningful, knowledge of the data's context is needed.
Pragmatic aspects of this context include who collected or generated
the data, how this was done, and for which purpose [@scheider];
semantic aspects concern what the data represents: which aspect
of the world do the data refer to, when and where were they measured,
and what a value of 1
means.
R does allow for keeping some context with data, for instance
data.frame
columns must have and list
elements may have names that can be used to describe context, using freetextmatrix
or array
objects may have dimnames
factor
or ordered
, levels
may indicate, using freetext, the categories of nominal or ordinal variablesPOSIXt
and Date
objects specify how numbers should be interpreted as time or date, with fixed units (second and day, respectively) and origin (Jan 1, 1970, 00:00 UTC)difftime
objects specify how time duration can be represented by numbers, with flexible units (secs, mins, hours, days, weeks); lubridate [@lubridate] extends some of this functionality.Furthermore, if spatial objects as defined in package sp [@sp] have a proper coordinate reference system set, they can be transformed to other datums, or converted to various flat (projected) representations of the Earth [@iliffe].
In many cases however, R drops contextual information. As an example, we
look at annual global land-ocean temperature index (from
http://climate.nasa.gov/vital-signs/global-temperature/
) since 1960:
temp_data = subset(read.table("647_Global_Temperature_Data_File.txt", header=TRUE)[1:2], Year >= 1960) temp_data$date = as.Date(paste0(temp_data$Year, "-01-01")) temp_data$time = as.POSIXct(temp_data$date) Sys.setenv(TZ="UTC") head(temp_data, 3) year_duration = diff(temp_data$date) mean(year_duration)
Here, the time difference units are reported for the difftime
object year_duration
, but if we would use it in a linear algebra operation
year_duration %*% rep(1, length(year_duration)) / length(year_duration)
the unit is dropped. Similarly, for linear regression coefficients we see
coef(lm(Annual_Mean ~ date, temp_data)) coef(lm(Annual_Mean ~ time, temp_data))
where the unit of change is in degrees Celsius but either per
day (date
) or per second (time
). For purely mathematical
manipulations, R often strips context from numbers when it is carried
in attributes, the linear algebra routines being a prime example.
Most variables are somehow attributed with information about
their units, which specify what the value 1
of this variable
represents. This may be counts of something, e.g. 1 apple
,
but it may also refer to some physical unit, such as distance
in meter. This article discusses how strong unit support can be
introduced in R.
The BIPM (Bureau International des Poids et Mesures) is "the intergovernmental organization through which Member States act together on matters related to measurement science and measurement standards. Its recommended practical system of units of measurement is the International System of Units (Système International d'Unités, with the international abbreviation SI) (https://www.bipm.org/en/measurement-units/)".
@si describe the SI units, where, briefly, SI units
kg
; as a base unit, kg can be part of coherent derived units); an example of a coherent derived unit is 1 watt = 1 joule per 1 second, base quantities, SI units and their symbols (from @si, p. 23):
| Base quantity | | SI base unit | | | -----------|--------|----------|------| | Name |Symbol|Name | Symbol | length | $l,x,r,$ etc.| meter | m | | mass | $m$ | kilogram | kg | | time, duration | $t$ | second | s | | electric current| $I, i$ | ampere | A | | thermodynamic temperature | $T$ | kelvin | K | | amount of substance | $n$ | mole | mol | | luminous intensity | $I_v$ | candela | cd |
Several R packages provide unit conversions.
For instance, measurements [@measurements] provides
a collection of tools to make working with physical measurements
easier. It converts between metric and imperial units, or calculates
a dimension's unknown value from other dimensions' measurements. It
does this by the conv_unit
function:
library(measurements) conv_unit(2.54, "cm", "inch") conv_unit(c("101 44.32","3 19.453"), "deg_dec_min", "deg_min_sec") conv_unit(10, "cm_per_sec", "km_per_day")
but uses for instance kph
instead of km_per_hour
, and then
m3_per_hr
for flow -- unit names seem to come from convention rather
than systematic composition. Object
conv_unit_options
contains all 173 supported units, categorized by
the physical dimension they describe:
names(conv_unit_options) conv_unit_options$volume
Function conv_dim
allows for the conversion of units in products or ratios,
e.g.
conv_dim(x = 100, x_unit = "m", trans = 3, trans_unit = "ft_per_sec", y_unit = "min")
computes how many minutes it takes to travel 100 meters at 3 feet per second.
Package NISTunits [@NISTunits] provides fundamental
physical constants (Quantity, Value, Uncertainty, Unit) for SI and
non-SI units, plus unit conversions, based on the data from NIST
(National Institute of Standards and Technology). The package
provides a single function for every
unit conversion; all but 5 from its 896 functions are of the form
NISTxxxTOyyy
where xxx
and yyy
refer to two
different units. For instance, converting from W m$^{-2}$ to W inch$^{-2}$
is done by
library(NISTunits) NISTwattPerSqrMeterTOwattPerSqrInch(1:5)
Both measurements and NISTunits are written entirely in R.
Udunits, developed by UCAR/UNIDATA, advertises itself on its web page as: "The udunits package supports units of physical quantities. Its C library provides for arithmetic manipulation of units and for conversion of numeric values between compatible units. The package contains an extensive unit database, which is in XML format and user-extendable."
Unlike the measurements and NISTunits, the underlying udunits2 C library parses units as expressions, and bases its logic upon the convertibility of expressions, rather than the comparison of fixed strings:
m100_a = paste(rep("m", 100), collapse = "*") dm100_b = "dm^100" units::ud_are_convertible(m100_a, dm100_b)
This has the advantage that through complex computations, intermediate objects can have units that are arbitrarily complex, and that can potentially be simplified later on. It also means that the package practically supports an unlimited amount of derived units.
Another set of encodings for measurement units is the Unified Code for Units of Measure (UCUM, @ucum). A dedicated web site\footnote{\url{http://coastwatch.pfeg.noaa.gov/erddap/convert/units.html}} describes the details of the differences between udunits and UCUM, and provides a conversion service between the two encoding sets.
The UCUM website refers to some Java implementations, but some of the links seem to be dead. UCUM is the preferred encoding for standards from the Open Geospatial Consortium. udunits on the other hand is the units standard of choice by the climate science community, and is adopted by the CF (Climate and Forecast) conventions, which mostly uses NetCDF. NetCDF [@netcdf] is a binary data format that is widely used for atmospheric and climate model predictions.
The udunits library is a C library that has strong support from UNIDATA, and we decided to build our developments on this, rather than on Java implementations of UCUM with a less clear provenance.
The units package builds units
objects from scratch,
e.g. where
library(units) x = set_units(1:5, m/s) str(x)
represents speed values in m/s
. The units m
and s
are resolved
from the udunits2 C library (but could be user-defined units).
Units can be used in arbitrary R expressions like
set_units(1:3, m/s^2)
Several manipulations with units
objects will now be illustrated.
Manipulations that do not involve unit conversion are for instance addition:
x = set_units(1:3, m/s) x + 2 * x
Explicit unit conversion is done by assigning new units:
(x = set_units(x, cm/s)) as.numeric(x)
similar to the behaviour of difftime
objects, this modifies
the numeric values without modifying their meaning (what the numbers
refer to).
When mixing units in sums, comparisons or concatenation, units are automatically converted to those of the first argument:
y = set_units(1:3, km/h) x + y y + x x == y c(y, x)
where c(y, x)
concatenates y
and x
after converting x
to the
units of y
. Derived units are created where appropriate:
x * y
x^3
and meaningful error messages appear when units are not compatible:
e = try(z <- x + x * y) attr(e, "condition")[[1]]
The full set of methods and method groups for units
objects is shown by
methods(class = "units")
where the method groups
Ops
include operations that require compatible units, converting when necessary (+
, -
, ==
, !=
, <
, >
, <=
, >=
), and operations that create new units (*
, /
, ^
and **
),Math
include abs
, sign
, floor
, ceiling
, trunc
, round
, signif
, log
, cumsum
, cummax
, cummin
, andSummary
include sum
, min
, max
and range
, and all convert to the unit of the first argument.When possible, new units are simplified:
a = set_units(1:10, m/s) b = set_units(1:10, h) a * b ustr1 = paste(rep("m", 101), collapse = "*") ustr2 = "dm^100" as_units(ustr1) / as_units(ustr2)
Units are printed as simple R expressions, e.g.
set_units(1, m^5/s^4)
Another way to print units commonly seen in Climate and Forecast Conventions\footnote{CF, \url{http://cfconventions.org/Data/cf-standard-names/34/build/cf-standard-name-table.html}} is m2 s-1
for m$^2$/s. These are not R expressions, but they can be parsed by as_units
, and created by deparse_unit
:
as_units("m2 s-1") deparse_unit(set_units(1, m^2*s^-1))
The plot
and hist
methods add units to default axis labels, an
example is shown in the following figures. For ggplot2 plots
[@ggplot2], automatic unit placement in default axis label is also provided; demo(ggplot2)
gives an example.
library(units) units_options(negative_power = TRUE) # initialize variables with units: mtcars$consumption = set_units(mtcars$mpg, mi/gallon) # "in" is also a reserved R keyword, and so needs back-quotes: mtcars$displacement = set_units(mtcars$disp, `in`^3) # convert to SI: mtcars$consumption = set_units(mtcars$consumption, km/l) mtcars$displacement = set_units(mtcars$displacement, cm^3) par(mar = par("mar") + c(0, .3, 0, 0)) with(mtcars, plot(1/displacement, 1/consumption))
library(ggplot2) ggplot(mtcars) + geom_point(aes(x = 1/displacement, y = 1/consumption))
Automatic conversion between units
and difftime
is provided:
(dt = diff(Sys.time() + c(0, 1, 1+60, 1+60+3600))) # class difftime (dt.u = as_units(dt)) identical(as_difftime(dt.u), dt)
as well as to and from POSIXct
or Date
:
(t1 <- as_units(as.POSIXct("2017-08-20 17:03:00"))) (t2 <- as_units(as.POSIXct("2017-08-20 17:03:00"), "hours since 2017-08-20")) (d1 <- as_units(as.Date("2017-08-20"))) as.POSIXct(t1) as.Date(d1)
Objects of class units
can be used as columns in data.frame
objects, as well as in tbl_df
[@tibble]. They can also be matrix
or array
, with the constraint that a single unit holds for all
elements.
The units R package provides a new class, units
,
for numeric data with associated measurement units. Operations
on objects of this class retain the unit metadata and provide
automated dimensional analysis: dimensions are taken into consideration
in computations and comparisons. Combining different units that are
compatible triggers automatic unit conversion, derived units
are automatically generated and simplified where possible, and
meaningful error messages are given when a user tries to add objects
with incompatible units. This verifies that computations are not
only syntactically and numerically allowed, but also semantically,
and in the case of physical units, physically allowed, which may
support code verification and provenance tracking. Using this
package may eliminate a whole class of potential scientific
programming mistakes.
Where the R packages measurements and NISTunits provide conversion between a fixed number of units, with the help of the udunits2 C library and unit database, R package units handles arbitrarily complex derived units. By treating units as expressions it can derive, convert and simplify units. In addition, beyond the SI units packaged, units handles user-defined units.
Data in units
vectors can be stored as columns in
data.frame
or tbl_df
objects, and can be
converted to and from difftime
. When units
objects have associated time and location information,
they could be stored in spatial or spatio-temporal objects
provided by sp or
spacetime
[@spacetime] as these store attribute data in
data.frame
slots, but for instance not in zoo
[@zoo] or xts
[@xts] objects, as these latter
two set the class attribute of a vector or matrix.
Despite all standardization efforts, units may still be ambiguous,
or subject to interpretation. For instance for the duration of one
year NISTunits gives
us an answer that depends on whether we want a common, leap,
Gregorian, Julian, tropical or siderial year (@lang, see
also demo(year)
). This illustrates that those who apply
unit conversion should be aware of possible pitfalls. Support for
calendars in udunits seems not as well developed as in R.
Future work includes extending packages that read external data from formats, databases or interfaces with support for measurement unit information into R, preserving the measurement unit information. Examples would be interfaces to HDF5 (e.g., h5, @h5), RNetCDF [@RNetCDF] or sos4R [@sos4R]. It would be nice to see units of measurements propagate into units of regression coefficient estimates.
We acknowledge three anonymous reviewers and the handling editor for
their constructive comments, and Thomas Lin Pedersen for implementing
the ggplot extensions in package ggforce
(ported to the units
package
since v0.8-0) that automatically add units to default ggplot axis labels.
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