- Original code was written by Thomas Mailund (https://github.com/mailund)
- In late 2022 Thomas and I (Konrad Krämer) extanded
dfdr - In 2022 maintanance was passed to Konrad Krämer
The dfdr package implements a simple version of automatic differentiation. It takes functions that consist of a single expression and construct the derivative with respect to a specific variable.
To install dfdr you can use devtools.
install.packages("devtools")
devtools::install_github("mailund/dfdr")and then load the library with
library(dfdr)To compute the derivative of a function, you use the function d. It takes two arguments, the function to compute the derivative of and the variable to compute the derivative with respect to.
f <- function(x) x^2 + sin(x)
df <- d(f, "x")
df## function (x)
## 2 * x + cos(x)
We can plot a function together with selected tangents to see how it works:
plot_tangent <- function(f, var, at, L = 1, df = NULL) {
if (is.null(df)) {
x <- substitute(var)
df <- d(f, x)
}
a <- df(at)
w <- L / sqrt(1 + a^2)
v <- a * w
x <- c(at - w, at + w)
y <- c(f(at) - v, f(at) + v)
lines(x, y, lty = "dashed", col = "darkred")
points(at, f(at), pch = 20)
}
x <- seq(-1.5, 0.9, length.out = 100)
plot(x, f(x), type = "l", asp = 1)
plot_tangent(f, x, -1)
plot_tangent(f, x, -0.2)
plot_tangent(f, x, 0.1)
plot_tangent(f, x, 0.7)
plot(x, sin(x), type = "l", asp = 1)
plot_tangent(sin, x, -2)
plot_tangent(sin, x, -1)
plot_tangent(sin, x, 0.5)
plot_tangent(sin, x, 2.5)
plot(x, exp(x), type = "l")
plot_tangent(exp, x, -2, L = 1)
plot_tangent(exp, x, 0.0, L = 1)
plot_tangent(exp, x, 1.5, L = 3)
plot_tangent(exp, x, 2.5, L = 4)
The body of the deriatives are simplified to a certain extend, but in a depth-first approach with no rewriting of expressions, so thehy sometimes can be more complex than you would normally see them.
Currently, it just handles arithmetic expressions and a few builtin functions, but I will implement handling of functions in the expressions as well, soon.