hypercube | simple hypercube/tesseract animation

I am having trouble navigating the source code to see how the design variables in the initial population for the SimpleGA and DifferentialEvolution Drivers are set. Is there some sort of Latin Hypercube sampling of the design variable ranges? Do the initial values I set in my problem instance get used like they would for the other drivers (Scipy and pyOptSparse)?

Many thanks, Garrett

I try to use workflowsets package or approach in which I get an error. Here are the R codes (Sorry, the codes are quite long):

I'm attempting to design an algorithm that, given n, m, and vertices (where n = the dimension of a hypercube, m = the dimension of the faces we're trying to generate, and vertices is an ordered list of vertices in an n-dimensional hypercube), returns an array of arrays of vertices representing m-faces in an n-dimensional hypercube.

That may have been a confusing way to word it, so here are a few examples:

Say we wanted to get an array of edges (1-faces) in a cube (3-dimensional hypercube). If we assume vertices is an ordered array of binary representations of vertices in a cube (i.e. [[0, 0, 0], [0, 0, 1], [0, 1, 0], ..., [1, 1, 1]]), we would have:

I have an equation with three parameters namely a, b, and c. I am minimizing the parameters of this equation by comparing it to a measured behaviour. For this purpose, I am trying to generate a Latin Hypercube Sampling of three-dimensional parameter space (namely for a, b, and c) and want to use different samples as an initial guess for the minimization. Also, I want to generate these samples within bounds ((1e-15,1e-05), (1,5), (0,1)) for each parameter respectively.

I have the following code for the generation of scaled parameter space:

Currently I am doing some experiments with hyperparameter tuning for XGBoost regression on time series, using a latin hypercube sampling strategy. When running the code below, all the models fail during the tune_grid operation. The cause seems to be the recipe object. I used step_dummy() to transform the value column of my univariate time series In the .notes object appears the Error message: preprocessor 1/1: Error: unused argument (values)

I found some other post where this issue popped up, but none of the solutions helped in my case.

For a project, I need to be able to sample random points uniformly from linear subspaces (ie. lines and hyperplanes) within a certain radius. Since these are linear subspaces, they must go through the origin. This should work for any dimension n from which we draw our subspaces for in Rn.

I want my range of values to be from -0.5 to 0.5 (ie, all the points should fall within a hypercube whose center is at the origin and length is 1). I have tried to do the following to generate random subspaces and then points from those subspaces but I don't think it's exactly correct (I think I'm missing some form of normalization for the points):

I have been trying to write a function for the Hilbert curve map and inverse map. Fortunately there was another SE post on it, and the accepted answer was highly upvoted, and featured code based on a paper in a peer-reviewed academic journal.

Unfortunately, I played around with the code above and looked at the paper, and I'm not sure how to get this to work. What appears to be broken is that my code drawing the second half of a 2-bit 2-dimensional Hilbert Curve backwards. If you draw out the 2-d coordinates in the last column, you'll see the second half of the curve (position 8 and on) backwards.

I don't think I'm allowed to post the original C code, but the C++ version below is only lightly edited. A few things that are different in my code.

1. C code is less strict on types, so I had to use std::bitset

2. In addition to the bug mentioned by @PaulChernoch in the aforementioned SE post, the next for loop segfaults, too.

3. The paper represents one-dimensional coordinates weirdly. They call it the number's "Transpose." I wrote a function that produces a "Transpose" from a regular integer.

Another thing about this algorithm: it doesn't produce a map between unit intervals and unit hypercubes. Rather, it stretches the problem out and maps between intervals and cubes with unit spacing.

I am trying to subsample a data.frame in a way that the sample would have observations that capture as much variation as possible among a set of columns of the original data.frame.

An example with the mtcars dataset: I'd like to find 3 cars that are the most different from each other by mpg, vs and carb. Looking at the data visually, it would probably be Toyota Corolla (high mpg, vs 1, low carb), Cadillac Fleetwood (low mpg, vs 0, medium carb) and either Maserati Bora (low-med mpg, vs 0, high carb) or Ferrari Dino (medium mpg, vs 0, med-high carb):

I need to create a custom Monte Carlo integration function to adapt to custom multi-dimensional distribution objects using NumPy. I need it to integrate over the same values in each dimension. It works correctly for a single dimension, but underestimates in multiple dimensions, which gets worse with higher dimensions. I am using this paper (equation 5) as a guide. Is my equation of Volume * Mean Density incorrect? Is my sampling method incorrect? I'm really at a loss for what the error is.