R: Sigmoid Function

sigmoid {pracma} | R Documentation

## 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

[Package pracma version 2.0.4 Index]