# ExampleSurfaces: Multivariate functions that define hypothetical response... In labsimplex: Simplex Optimization Algorithms for Laboratory and Manufacturing Processes

## Description

The functions in this section simulate the yield of hypothetical chemical reactions as a function of temperature, pH, and concentration (the latter only for `exampleSurfaceR3()`). Those functions are useful to illustrate most concepts of the simplex optimization algorithms implemented in the `labsimplex` package, as shown in the vignentte of the package. This vignette can be visualized by running `vignette('labsimplex')`.

## Usage

 ```1 2 3 4 5``` ```exampleSurfaceR2(x1, x2, noise = 0) exampleSurfaceR2.2pks(x1, x2, noise = 0) exampleSurfaceR3(x1, x2, x3, noise = 0) ```

## Arguments

 `x1` temperature in Kelvin. Numeric between 278 and 365. `x2` pH. Numeric between 0 and 14. `noise` absolute noise included in the response surface result. Default to zero. `x3` concentration in arbitrary units. Numeric between 0 and 1. Only used in `exampleSurfaceR3()`.

## Details

Parameters `x1`, `x2`, and `x3` may be supplied as vectors in which case all must have the same length.
Boundary values are proposed consistently with real-life limitations in aqueous media. If such boundaries are violated in the variables input, a negative result without physical meaning is returned. This negative value represents an infinitely bad response that will force the simplex to move in another direction.

## Value

`exampleSurfaceR2(x1, x2, noise = 0)` defines a response surface with one maximum at pH 10 and 300 K.

`exampleSurfaceR2.2pks(x1, x2, noise = 0)` defines a response surface with global and local maxima at pH 10 and 300 K and pH 4.5 and 340 K, respectively.

`exampleSurfaceR3(x1, x2, x3, noise = 0)` defines a response surface with one maximum at pH 10, 300 K and a concentration of 0.5.

## Author(s)

Cristhian Paredes, craparedesca@unal.edu.co

Jesús Ágreda, jagreda@unal.edu.co

`cntr`, `prspctv` and `exampleOptimization`
 ``` 1 2 3 4 5 6 7 8 9 10``` ``` exampleSurfaceR2(x1 = 320, x2 = 4.5) exampleSurfaceR2(x1 = c(310, 320), x2 = c(4.5, 5.8)) exampleSurfaceR2(x1 = c(310, 320), x2 = c(4.5, 5.8), noise = 5) exampleSurfaceR2.2pks(x1 = 320, x2 = 4.5) exampleSurfaceR2.2pks(x1 = c(310, 320), x2 = c(4.5, 5.8)) exampleSurfaceR2.2pks(x1 = c(310, 320), x2 = c(4.5, 5.8), noise = 5) exampleSurfaceR3(x1 = 320, x2 = 4.5, x3 = 0.3) exampleSurfaceR3(x1 = c(310, 320), x2 = c(4.5, 5.8), x3 = c(0.3, 0.5)) exampleSurfaceR3(x1 = c(310, 320), x2 = c(4.5, 5.8), x3 = c(0.3, 0.5), noise = 5) ```