# This is a simple switch function.

### Description

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

### Usage

1 |

### 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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