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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang="" xml:lang="">
<head>
<title>units + errors = quantities</title>
<meta charset="utf-8" />
<meta name="author" content="Iñaki Úcar, postdoctoral fellow @ UC3M-Santander Big Data Institute (IBiDat) Edzer Pebesma, full professor @ Institute for Geoinformatics, University of Münster" />
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<textarea id="source">
class: center, middle, inverse, title-slide
# units + errors = quantities
## Quantity Calculus for R Vectors
### <strong>Iñaki Úcar</strong>, postdoctoral fellow @ UC3M-Santander Big Data Institute (IBiDat) <br>Edzer Pebesma, full professor @ Institute for Geoinformatics, University of Münster
### <br>November 15-16, 2019
---
# Quantity Calculus
.pull-left[
Two quotes from Cobb and Moore (1997):
> Data are not just numbers, they are numbers with a **context**.
>
> In data analysis, context provides meaning.
]
--
.pull-right[
Examples of context in R:
- Names of `data.frame` columns
- Dimensions of an array
- Levels of `factor`
- Time-related objects `POSIXt`, `Date`, `difftime`...
]
--
.pull-left[
<br>
From the International Vocabulary of Metrology (VIM):
> [A **quantity** is] a property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.
]
--
.pull-right[
<br>
`$$\LARGE \overbrace{10.45}^{\text{value}} \overbrace{\underbrace{\pm \quad 0.03}_{\text{uncertainty}} \quad \underbrace{\text{km}}_{\text{unit}}}^{\text{context}}$$`
]
---
# units
.footnote[
[1] Pebesma E, Mailund T, Hiebert J (2016). "Measurement Units in R." _R Journal_, 8(2), 486-494. doi: 10.32614/RJ-2016-061.
]
.pull-left[
The `units` package [1]:
- Support for measurement units in R vectors and arrays
- Automatic propagation, conversion, simplification
- Raising errors in case of unit incompatibility
- Compatible with the POSIXct, Date and difftime classes
- Uses Unidata's `UDUNITS-2` library and database
]
--
.pull-right[
```r
library(units)
x <- set_units(rnorm(3), m)
y <- set_units(rnorm(3), s)
sum(x)
```
```
## 1.169389 [m]
```
```r
x / y
```
```
## Units: [m/s]
## [1] 2.166281 -1.396840 -3.421720
```
```r
x + y
```
```
## Error: cannot convert s into m
```
]
--
.pull-left[
Specifics:
- S3 implementation
- Group Generics `Math`, `Ops`, `Summary` and more
- `?units_options` controls printing, parsing, autoconversion and simplification
- Installation of new units
]
---
# errors
.footnote[
[1] **Ucar I**, Pebesma E, Azcorra A (2018). "Measurement Errors in R." _R Journal_, 10(2), 549-557. doi: 10.32614/RJ-2018-075.
]
.pull-left[
The `errors` package [1]:
- Support for uncertainties in R vectors and arrays
- Automatic propagation (first-order TSM, as recommended by BIPM's GUM)
- Pretty printing (also following BIPM's GUM)
]
--
.pull-right[
```r
library(errors)
x <- set_errors(rnorm(3), 0.1)
y <- set_errors(rnorm(3), 0.1)
sum(x)
```
```
## 1.2(2)
```
```r
print(sum(x), notation="plus-minus", digits=2)
```
```
## 1.17 ± 0.17
```
```r
x / y
```
```
## Errors: 0.3770097 0.4249392 3.3591220
## [1] 2.166281 -1.396840 -3.421720
```
]
--
.pull-left[
Specifics:
- S3 implementation
- Correlations/covariances across objects
- Group Generics `Math`, `Ops`, `Summary` and more
- Options for printing control, by default
- `errors.notation = "parenthesis"`
- `errors.digits = 1`
]
---
# quantities
.footnote[
[1] R-Quantities organization on GitHub: https://github.com/r-quantities/
<br>[2] Announcement: https://www.r-consortium.org/announcement/2018/02/22/announcing-second-round-isc-funded-projects-2017
]
.pull-left[
The `quantities` framework [1]:
- Project funded by the R Consortium [2]
- Integrates `units` and `errors`
- Complete Quantity Calculus system for R
]
--
.pull-right[
```r
library(quantities)
x <- set_quantities(rnorm(3), m, 0.1)
y <- set_quantities(rnorm(3), s, 0.1)
sum(x)
```
```
## 1.2(2) [m]
```
```r
x / y
```
```
## Units: [m/s]
## Errors: 0.3770097 0.4249392 3.3591220
## [1] 2.166281 -1.396840 -3.421720
```
```r
x + y
```
```
## Error: cannot convert s into m
```
]
--
.pull-left[
Specifics:
- S3 implementation as a super-class
- Again, Group Generics and other stuff
- Support all conversions, resolve conflicts
- Data wrangling guide (see vignette)
- Parsers (see vignette)
]
---
# Example: a physics experiment
.pull-left[
## Surface tension in liquids
- Dispersion relation for capillary waves
`$$w^2 = \frac{\sigma}{\rho}|k|^3, \quad k = \frac{\pi}{n\lambda}\frac{c_n}{a}\sin\left(\frac{b}{a}\right)$$`
```r
str(df)
```
```
## 'data.frame': 65 obs. of 3 variables:
## $ f : num 100 110 120 130 140 150 160 170 180 190 ...
## $ n : int 1 1 1 1 1 1 1 1 1 1 ...
## $ c_n: num 11 12 13 13 14 15 16 16 17 17 ...
```
]
--
.pull-right[
```r
library(quantities)
a <- set_quantities(3095, mm, 10)
b <- set_quantities(414+116-203, mm, 1+1+3)
l <- set_quantities(633, nm, 0)
df <- within(df, {
f <- set_quantities(f, Hz, 1)
c_n <- set_quantities(c_n, mm, 1)
* w2 <- set_units(2 * pi * f, rad/s)^2
* k3 <- set_units(
* pi/l/n * c_n/a * sin(set_units(b/a, rad)),
* rad/mm)^3
})
head(df[, c("w2", "k3")], 3)
```
```
## w2 k3
## 1 3.95(8)e5 [rad^2/s^2] 6(2) [rad^3/mm^3]
## 2 4.78(9)e5 [rad^2/s^2] 8(2) [rad^3/mm^3]
## 3 5.68(9)e5 [rad^2/s^2] 11(3) [rad^3/mm^3]
```
]
---
# Example: a physics experiment
.pull-left[
```r
library(ggplot2)
*library(ggforce)
ggplot(df) + aes(k3, w2) +
geom_errorbar(
* aes(ymin=errors_min(w2), ymax=errors_max(w2))) +
geom_errorbarh(
* aes(xmin=errors_min(k3), xmax=errors_max(k3))) +
geom_point() + geom_smooth(method="lm")
```
]
.pull-right[
<img src="img/figure-html/dispersion-relation-1.png" width="504" />
]
--
.pull-left[
.footnote[
[1] See https://www.r-spatial.org/r/2018/08/31/quantities-final.html#fitting-linear-models-with-quantities
]
Measure the surface tension:
```r
fit <- qlm(w2 ~ k3, df) # [1]
rho <- set_quantities(997, kg/m^3, 1)
sigma <- coef(fit)$k3 * rho
set_units(sigma, dyne/cm)
```
```
## 61.2(6) [dyne/cm]
```
]
---
# Summary
<br>
.font130[
- Transparent (almost) support for quantity calculus (i.e., computations with context) in R
- Assign units and/uncertainty metadata and go
- Automatic propagation, conversion, simplification and reporting
]
--
.font130[
- Published in the R Journal [1, 2], following BIPM's recommendations
]
.footnote[
[1] Pebesma E, Mailund T, Hiebert J (2016). "Measurement Units in R." _R Journal_, 8(2), 486-494. doi: 10.32614/RJ-2016-061.<br>
[2] **Ucar I**, Pebesma E, Azcorra A (2018). "Measurement Errors in R." _R Journal_, 10(2), 549-557. doi: 10.32614/RJ-2018-075.
]
--
.font130[
- `units` (reference) and `errors` (uncertainty) developed in separate packages
- Integrated within the `quantities` framework
]
---
class: center, middle, inverse, mline
# Thanks!
**https://github.com/r-quantities**
<br><br><br>
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