Test functions are used whenever one needs to evaluate an algorithm. For example, an optimization algorithm should be tested on many different functions to make sure that it works and is robust. Thus many optimization test functions are very tricky, such as those with many local minima meant to make the global minimum harder to find.
Each of the test functions is called like any other function. The first argument,
be a vector representing one point or a matrix that has points in its rows. This can cause
problems if you are using a 1-dimensional function and pass in a vector of values.
Instead you should pass them in as a matrix with a single column, or vectorize the function.
The code below shows how the
branin function can be used, taking in either a vector or a matrix.
set.seed(0) library(TestFunctions) branin(runif(2)) branin(matrix(runif(20), ncol=2))
A contour of the banana function is shown below.
The functions are all designed to be run by default in the $[0,1]^D$ unit cube.
If you want to run the function on the original input values, you can set
Independent Gaussian noise can be added to most functions by passing the standard deviation of the noise as the
noise parameter. The plots below show the original function, then what data from the function with noise looks like.
tf1 <- function(xx) powsin(x=matrix(xx,ncol=1), noise=0) curve(tf1, main="Function without noise") x1 <- runif(1e2) y1 <- powsin(x=matrix(x1,ncol=1), noise=.1) plot(x1,y1, col=2, pch=19, cex=.3, main="Data with noise") curve(tf1,add=T)
RFF_get will return a random wave function with any given number of dimensions. The function is created by combining many different one dimensional waves passing through the input area with various directions, magnitude, and offset. The default is composed of sine waves, but this can be changed to block or v waves.
Below is an example of a one dimensional wave.
tf <- RFF_get(D=1) curve(tf)
Below is an example of a random wave in two dimensions.
There are some functions that modify other functions.
add_linear_terms adds linear terms to a function.
add_noise adds random noise to a function.
add_null_dims adds extra dimensions that do not affect the function output.
add_zoom lets you zoom in on part of a function. Below are two examples of zooming in on the banana function.
ContourFunctions::cf(banana) ContourFunctions::cf(add_zoom(banana, c(0,.5), c(1,1))) ContourFunctions::cf(add_zoom(banana, c(.2,.5), c(.8,1)))
Many of the functions, along with code implementing the function, can be found at https://www.sfu.ca/~ssurjano/. The code was not taken from this site, but some of my implementations were checked against theirs for consistency.
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