sigmoid: Sigmoid function and gradient
In tkmckenzie/ikde: Iterative Kernel Density Estimation

Description Usage Arguments Details Value Examples

Sigmoid function and gradient

1	sigmoid(x, lower.limit = 0, upper.limit = 1)

`x`	Point to evaluate sigmoid function and gradient
`lower.limit`	Lower limit of the sigmoid function; defaults to 0
`upper.limit`	Upper limit of the sigmoid function; defaults to 1

Evaluates the sigmoid function ((upper.bound - lower.bound) / (1 + exp(-x)) + lower.bound) and its gradient ((upper.bound - lower.bound) * exp(-x) / (1 + exp(-x))^2).

Returns a list with two elements, each with the same number of elements as x

`value`	Value of the sigmoid function at x
`gradient`	Value of the gradient of the sigmoid function at x

x <- seq(-5, 5, length.out = 100)
sigmoid.result <- sigmoid(x)

plot(sigmoid.result$value ~ x, type = "l")
plot(sigmoid.result$gradient ~ x, type = "l")