simecol (version 0.5-5)

p.constrain: Transform data between unconstrained and box box-constrained scale

Description

These functions can be used to transform a vector of data or parameters between unconstrained [-Inf, Inf] and box-constrained representation (interval [lower, upper]).

Usage

p.constrain(p, lower = -Inf, upper = Inf, f = 1)
p.unconstrain(p, lower = -Inf, upper = Inf, f = 1)

Arguments

p

vector of data (e.g. model parameters),

lower, upper

vectors with lower resp. upper bounds used for transformation,

f

optional scaling factor.

Value

• vector with transformed (resp. back-transformed) values.

Details

These functions are employed by fitOdeModel link{ssqOdeModel} in order to be able to use the unconstrained optimizers of optim for constrained optimization. The transformation functions are $$p' = \tan(\pi/2 \cdot (2 p - upper - lower) / (upper - lower)) \cdot 1/f$$ and its inverse $$p = (upper + lower)/2 + (upper - lower) \cdot \arctan(f \cdot p')/\pi$$.

References

Reichert, T. (1998) AQUASIM 2.0 User Manual. Computer Program for the Identification and Simulation of Aquatic Systems. Swiss Federal Institute for Environmental Science and Technology (EAWAG), CH - 8600 Duebendorf Switzerland, http://www.aquasim.eawag.ch/e_aquasim_manual.html

See Also

fitOdeModel, link{ssqOdeModel}

Examples

xx <- seq(-100, 100, 2)
plot(xx, yy<-p.constrain(xx, -20, 45), type="l")
points(p.unconstrain(yy, -20, 45), yy, col="red")