x + x is not 2x

A few days ago, Joel Courtheyn posted the following issue in the errors package repository on GitHub:

Experimenting with the new package I detected a difference in calculation of the error depending on the way a formula was written. Originally I tried to calculate the error for z1 <- (x^3 - 2y)/x^0.5 but this gave me a value which was different from the manual calculated error. When I transformed this formula to z <- x^2.5 - 2y*x^(-1/2), then I came to the right results.

As I wrote there, the TL;DR version is that both calculations are correct, but the first formula is an abuse of notation. What do I mean by that? Let us consider a shorter but more intuitive version of the issue: x + x vs. 2*x. In the first place, we define a quantity with a relative uncertainty of 5 %:

library(errors)
options(errors.notation = "plus-minus")
x <- 30
errors(x) <- x * 0.05
x
## 30 +/- 2

Now, let us see what happens:

x + x
## 60 +/- 2
2*x
## 60 +/- 3

First of all, we need to keep in mind that measurements with errors are not mathematical variables anymore: they are physical (in a broad sense) quantities. Imagine that we want to measure the width of a table, but we have a ruler that is only about half its width. So we manage to put a mark, by the means of some method (using a string, for instance), approximately at about half of the table. Then, we have two options: 1) to measure the first half and multiply it by two, or 2) to measure both halves and sum them.

Intuitively, 1), which corresponds to the 2*x case, has a larger uncertainty, because we are not measuring the second half of the table (and note that this is exactly what we obtained before!). But in 2), even if the result of the second measurement matches the first one, x + x is an abuse of notation: they are different measurements, so we should write x + y instead, and the derived uncertainty is smaller.

Therefore, we can scale a certain measurement, apply any function to it… but to sum, multiply, divide… a measurement by itself has no physical meaning. x+x = 2x is mathematically true, but x + x has no physical sense. We should say x + y (even ifx is the same value as y), and x + y != 2*x when it comes to propagation of the uncertainty. The errors package helps us in the arduous task of uncertainty propagation, but checking the physical correctness of the expressions of derived measurements cannot be automated, and it is still our responsibility.

Load a Python/pandas data frame from an HDF5 file into R

The title is self-descriptive, so I will not dwell on the issue at length before showing the code. Just a small note: to my knowledge, there is only one public snippet out there that addresses this particular problem. It uses the Bioc package rhdf5 and you can find it here. The main problem is that it only works when the HDF5 file contains a single data frame, which is not very useful. This gist overcomes this limitation and uses the CRAN package h5 instead:

errors 0.0.1

In physics, engineering and other disciplines, a single number, a bare quantity, is useless, meaningless. When you measure something, your results will be within the precision of your equipment, and then you need to propagate those errors up to whatever final indirect measure you are interested in. Finally, you need to express it properly. For instance, the elementary charge:

library(errors)
e <- set_errors(1.6021766208e-19, 0.0000000098e-19)
print(e, digits=2, notation="plus-minus")
## (1.6021766208 +/- 0.0000000098)e-19
print(e, digits=2, notation="parenthesis")
## 1.6021766208(98)e-19

Propagation of uncertainty (or propagation of error) is easy, but too labourious. Lately, for various reasons, I have been growing sick of this task, so I decided to write this small package. In a nutshell, the errors package, which is already on CRAN, provides support for painless automatic error propagation in numerical operations and pretty printing.

With errors, you can add errors to your numeric vectors:

x <- 1:10
errors(x) <- 0.1
x
## errors: 0.1 0.1 0.1 0.1 0.1 ...
##  [1]  1  2  3  4  5  6  7  8  9 10
errors(x)
##  [1] 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
errors(x) <- seq(0.1, 1, 0.1)
errors(x)
##  [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

The set_errors() method is a pipe-friendly version of the above:

(x <- set_errors(1:10, seq(0.1, 1, 0.1)))
## errors: 0.1 0.2 0.3 0.4 0.5 ...
##  [1]  1  2  3  4  5  6  7  8  9 10

Then, you simply work with your quantities without having to worry about errors anymore:

df <- as.data.frame(x)
(df$`3x` <- 3*x)
## errors: 0.3 0.6 0.9 1.2 1.5 ...
##  [1]  3  6  9 12 15 18 21 24 27 30
(df$`x^2` <- x^2)
## errors: 0.2 0.8 1.8 3.2 5 ...
##  [1]   1   4   9  16  25  36  49  64  81 100
(df$`sin(x)` <- sin(x))
## errors: 0.054030230586814 0.0832293673094285 0.296997748980134 0.261457448345445 0.141831092731613 ...
##  [1]  0.8414710  0.9092974  0.1411200 -0.7568025 -0.9589243 -0.2794155
##  [7]  0.6569866  0.9893582  0.4121185 -0.5440211
(df$`cumsum(x)` <- cumsum(x))
## errors: 0.1 0.223606797749979 0.374165738677394 0.547722557505166 0.741619848709566 ...
##  [1]  1  3  6 10 15 21 28 36 45 55

Finally, you probably need to report your data in a consistent way. No problem: just print your table.

df
##         x     3x     x^2  sin(x) cumsum(x)
## 1  1.0(1) 3.0(3)  1.0(2) 0.84(5)    1.0(1)
## 2  2.0(2) 6.0(6)  4.0(8) 0.91(8)    3.0(2)
## 3  3.0(3) 9.0(9)    9(2)  0.1(3)    6.0(4)
## 4  4.0(4)  12(1)   16(3) -0.8(3)   10.0(5)
## 5  5.0(5)  15(2)   25(5) -1.0(1)   15.0(7)
## 6  6.0(6)  18(2)   36(7) -0.3(6)  21.0(10)
## 7  7.0(7)  21(2)  49(10)  0.7(5)     28(1)
## 8  8.0(8)  24(2)  60(10)  1.0(1)     36(1)
## 9  9.0(9)  27(3)  80(20)  0.4(8)     45(2)
## 10  10(1)  30(3) 100(20) -0.5(8)     55(2)

By default, errors uses parenthesis notation (which is more compact) and a single significant digit for errors. If you prefer the plus-minus notation or you need more significant digits, just pass the notation and digits arguments to the print() method, as in the first example, or set them as global options with options(errors.notation="plus-minus", errors.digits=2).

The inner workings of this package have been inspired by Edzer Pebesma and his excellent units package. As a next step, I envision numeric vectors with errors and units for R. Thus, I publicly invite Edzer to collaborate with me in making our packages work together.

Poor man’s parallel con Bash

GNU Parallel es «una herramienta para ejecutar tareas en paralelo usando uno o varias computadoras». Es realmente compleja y versátil, pero muchas veces su uso se reduce a paralelizar un bucle. Algo así, para ejecutar 10 tasks utilizando 4 cores:

task() {
echo "running $1..."
sleep $(($1%4))
echo "$1 stopped"
}
export -f task
for i in {1..10}; do
sem -j4 task $i
done
sem --wait

Pero si no está disponible o da problemas, y no importa que la salida pueda intercalarse, se puede hacer lo mismo solo con Bash:

task() {
echo "running $1..."
sleep $(($1%4))
echo "$1 stopped"
}
pmsem() { ((_i=_i%$1)); ((_i++==0)) && wait -n && ((_i--)); }
for i in {1..10}; do
pmsem 4; task $i &
done
wait

simmer 3.6.1

A new patch release of simmer, the Discrete-Event Simulator for R, is on CRAN. Three months have passed since the last release. The last year was a period of intense development (one release per month). Now, the package has reached some level of maturity, so we intend to extend the release cycle.

In this maintenance release, the replacement operators for trajectories ([<-, [[<-) now work as expected. Also, we have removed previously deprecated plotting capabilities, which are covered and extended by the simmer.plot package.

Last but not least, we have extended the from_to() convenience function with a parameter every, which enables the generation of arrivals in cycles. For instance, let us suppose we want to simulate different patient arrival rates in the morning, evening and night:

library(simmer)
library(simmer.plot)
## Loading required package: ggplot2
set.seed(1234)
# units are hours
# visit time between 10 and 20 minutes
patient <- trajectory() %>%
seize("doctor", 1) %>%
timeout(function() runif(1, 10/60, 20/60)) %>%
release("doctor", 1)
morning <- from_to(start_time = 8,
stop_time = 16,
dist = function() rexp(1, 60/15),
arrive = FALSE, 
every = 24)
evening <- from_to(start_time = 16,
stop_time = 24,
dist = function() rexp(1, 60/30),
arrive = FALSE, 
every = 24)
night   <- from_to(start_time = 0,
stop_time = 8,
dist = function() rexp(1, 60/60),
arrive = FALSE, 
every = 24)
env <- simmer() %>%
add_resource("doctor", 1) %>%
add_generator("morning", patient, morning) %>%
add_generator("evening", patient, evening) %>%
add_generator("night",   patient, night) %>%
run(24 * 5) # simulate 5 days
breaks <- c(0, cumsum(rep(8, 3 * 5)))
env %>%
get_mon_arrivals() %>%
dplyr::mutate(generator = factor(gsub("\\d", "", name))) %>%
ggplot(aes(start_time, fill=generator)) + xlab("time") +
stat_bin(breaks = breaks) +
scale_x_continuous(breaks = breaks)

plot(env, what="resources", metric="usage", "doctor", steps=TRUE) +
scale_x_continuous(breaks = breaks)

Minor changes and fixes:

  • Recycle logical indexes when subsetting (2526e75).
  • Implement replacement operators, [<- and [[<- (#88).
  • Provide rep() S3 method for trajectories (7fa515e).
  • Remove plotting functions (bb9656b), deprecated since v3.6.0. The new simmer.plot package (on CRAN) already covers these features among others.
  • Don’t evaluate vignette chunks if Suggests are not installed (e40e5b6).
  • Rewrite DESCRIPTION (3f26516).
  • Add an every parameter to the from_to() convenience function (9d68887).