Dark (version 0.9.4)

H: This is a simple switch function.

Description

This function is used to transition from 'off' to 'on'.

Usage

H(x, k = 100, t)

Arguments

x

is the measured time.

k

is the transition constant, set arbitrarily high.

t

is the time at which the transition occurs.

Value

• For times before 't' the output is less than or equal to 0.5, after this time the the output is greater than 0.5. As 'k' grows larger the rate of transition from 0 to 1 increases.

Details

This helper function used in P5c and P7cenables the optim function to find parameters three times as quickly than if the transitions betwen the phases are modelled by a logical function e.g. a step function.

References

The logistic function: http://en.wikipedia.org/wiki/Logistic_function

The step function: http://en.wikipedia.org/wiki/Heaviside_step_function

Examples

x <- seq(0, 20, by=0.1)
k <- 10
t <- 10
op <- par(las=1, bty='n')
plot(x,H(x,k,t), 'l')
par(op)