# labsimplex: Generates a simplex object In labsimplex: Simplex Optimization Algorithms for Laboratory and Manufacturing Processes

## Description

The simplex (a list with class `smplx`) contains the coordinates of the n+1 vertices that define a simplex in an n-dimensional space. By default, the function produces a regular simplex centered at the origin. The coordinates of the regular simplex are transformed into the real variables space by using the information of the start or centroid and step-size. The only non-optional parameter is `n` that relates the simplex dimensionality. Once the simplex is generated, the experiments under the conditions indicated for each variable at each vertex must be carried and the response obtained. Those responses are assigned to the `smplx` object at the moment of generating the new vertex (see `generateVertex`).

## Usage

 ```1 2``` ```labsimplex(n, start = NULL, centroid = NULL, stepsize = NULL, usrdef = NULL, var.name = NULL) ```

## Arguments

 `n` dimensionality of the simplex (i.e. number of variables) `start` numeric vector of size `n` with coordinates of the first vertex `centroid` numeric vector of size `n` with coordinates of the centroid `stepsize` numeric vector of size `n` with the step-sizes for each coordinate `usrdef` `(n+1)xn` matrix containig in (n+1) rows the n coordinates for each vertex `var.name` vector containing the names for the variables

## Details

The regular simplex coordinates are generated following the general algorithm for the cartesian coordinates of a regular n-dimensional simplex. This algorithm considers that all vertices must be equally distanced from simplex centroid and all angles subtended between any two vertexes and the centroid of a simplex are equal to arccos(-1/n).
If the vertexes coordinates are manually given (in `usr.def` parameter), the function checks if the faces produced belong to different hyperplanes. This avoids the generation of a degenerated simplex.

## Value

An object of class `smplx` with the information of the new simplex.

## Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Jesús Ágreda, jagreda@unal.edu.co

## References

Nelder, J. A., and R. Mead. 1965. “A Simplex Method for Function Minimization.” The Computer Journal 7 (4): 308–13.

Spendley, W., G. R. Hext, and F. R0. Himsworth. 1962. “Sequential Application of Simplex Designs in Optimization and Evolutionary Operation.” Technometrics 4 (4): 441–61.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ``` simplex <- labsimplex(n = 3) simplex <- labsimplex(n = 3, centroid = c(350, 7, 0.4), stepsize = c(35, 2, 0.3), var.name = c('temperature', 'pH', 'concentration')) simplex <- labsimplex(n = 3, usrdef = rbind(c(390, 8, 0.2), c(330, 8, 0.2), c(330, 6, 0.6), c(330, 6, 0.1))) ## Not run: ## User defined coordinates may define a degenerated simplex: simplex <- labsimplex(n = 3, usrdef = rbind(c(390, 8, 0.3), c(340, 8, 0.3), c(355, 8, 0.3), c(340, 5, 0.1))) ## End(Not run) ```

labsimplex documentation built on July 1, 2020, 9:08 p.m.