# dual-package: Automatic Differentiation with Dual Numbers In dual: Automatic Differentiation with Dual Numbers

 dual-package R Documentation

## Automatic Differentiation with Dual Numbers

### Description

Automatic differentiation is achieved by using dual numbers without providing hand-coded gradient functions. The output value of a mathematical function is returned with the values of its exact first derivative (or gradient). For more details see Baydin, Pearlmutter, Radul, and Siskind (2018) https://jmlr.org/papers/volume18/17-468/17-468.pdf.

### Details

 Package: dual Type: Package Version: 0.0.5 Date: 2023-10-02 License: GPL-3

For a complete list of exported functions, use `library(help = "dual")`.

### Author(s)

Luca Sartore drwolf85@gmail.com

Maintainer: Luca Sartore drwolf85@gmail.com

### References

Baydin, A. G., Pearlmutter, B. A., Radul, A. A., & Siskind, J. M. (2018). Automatic differentiation in machine learning: a survey. Journal of Marchine Learning Research, 18, 1-43.

Cheng, H. H. (1994). Programming with dual numbers and its applications in mechanisms design. Engineering with Computers, 10(4), 212-229.

### Examples

``````library(dual)

# Initilizing variables of the function
x <- dual(f = 1.5, grad = c(1, 0, 0))
y <- dual(f = 0.5, grad = c(0, 1, 0))
z <- dual(f = 1.0, grad = c(0, 0, 1))
# Computing the function and its gradient
exp(z - x) * sin(x)^y / x

# General use for computations with dual numbers
a <- dual(1.1, grad = c(1.2, 2.3, 3.4, 4.5, 5.6))
0.5 * a^2 - 0.1

# Johann Heinrich Lambert's W-function
lambertW <- function(x) {
w0 <- 1
w1 <- w0 - (w0*exp(w0)-x)/((w0+1)*exp(w0)-(w0+2)*(w0*exp(w0)-x)/(2*w0+2))
while(abs(w1-w0) > 1e-15) {
w0 <- w1
w1 <- w0 - (w0*exp(w0)-x)/((w0+1)*exp(w0)-(w0+2)*(w0*exp(w0)-x)/(2*w0+2))
}
return(w1)
}
lambertW(dual(1, 1))

``````

dual documentation built on Oct. 3, 2023, 9:07 a.m.