ExampleSurfaces {labsimplex}

Multivariate functions that define hypothetical response surfaces.

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

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, [e-mail]

Jesús Ágreda, [e-mail]

See Also

cntr, prspctv and exampleOptimization

Examples

  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)