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sigmoid

Sigmoid Function


Description

Sigmoid function (aka sigmoidal curve or logistic function).

Usage

sigmoid(x, a = 1, b = 0)
logit(x, a = 1, b = 0)

Arguments

x

numeric vector.

a, b

parameters.

Details

The sigmoidal function with parameters a,b is the function

y = 1/(1 + e^{-a (x-b)})

The sigmoid function is also the solution of the ordinary differentialequation

y' = y (1-y)

with y(0) = 1/2 and has an indefinite integral \ln(1 + e^x).

The logit function is the inverse of the sigmoid function and is (therefore) omly defined between 0 and 1. Its definition is

y = b + 1/a log(x/(1-x))

Value

Numeric/complex scalar or vector.

Examples

x <- seq(-6, 6, length.out = 101)
y1 <- sigmoid(x)
y2 <- sigmoid(x, a = 2)
## Not run: 
plot(x, y1, type = "l", col = "darkblue", 
        xlab = "", ylab = "", main = "Sigmoid Function(s)")
lines(x, y2, col = "darkgreen")
grid()
## End(Not run)

# The slope in 0 (in x = b) is a/4
# sigmf with slope 1 and range [-1, 1].
sigmf <- function(x) 2 * sigmoid(x, a = 2) - 1

pracma

Practical Numerical Math Functions

v2.3.3
GPL (>= 3)
Authors
Hans W. Borchers [aut, cre]
Initial release
2021-01-22

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