This is a simple switch function.

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Description

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

Usage

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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.

Details

This helper function used in P5c and P7c enables 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.

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.

Note

H is a logistic function that maps inputs to a values between zero and one

Author(s)

Jeremiah MF Kelly

Faculty of Life Sciences, The University of Manchester, M13 9PL, UK

References

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

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

See Also

P5c, P7c

Examples

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