sigmoid | R Documentation |
Sigmoid function (aka sigmoidal curve or logistic function).
sigmoid(x, a = 1, b = 0)
logit(x, a = 1, b = 0)
x |
numeric vector. |
a , b |
parameters. |
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))
The parameters must be scalars; if they are vectors, only the first component will be taken.
Numeric/complex scalar or vector.
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
# logit is the inverse of the sigmoid function
x <- c(-0.75, -0.25, 0.25, 0.75)
y <- sigmoid(x)
logit(y) #=> -0.75 -0.25 0.25 0.75
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