Area Under the Curve

Description

Calculate the area under the curve with a naive algorithm and with a more elaborated spline approach. The curve must be given by vectors of xy-coordinates.

Usage

AUC(x, y, method = c("trapezoid", "step", "spline"), na.rm = FALSE)

Arguments

Details

If method is set to "trapezoid" then the curve is formed by connecting all points by a direct line (composite trapezoid rule). If "step" is chosen then a stepwise connection of two points is used. For calculating the area under a spline interpolation the splinefun function is used in combination with integrate.
The AUC function will handle unsorted x values (by sorting x) and ties for the x values (by ignoring duplicates).

Value

Numeric value of the area under the curve.

Author(s)

Andri Signorell <andri@signorell.net>, spline part by Claus Ekstrom <claus@rprimer.dk>

See Also

integrate, splinefun

Examples

AUC(x=c(1,3), y=c(1,1))

AUC(x=c(1,2,3), y=c(1,2,4), method="trapezoid")
AUC(x=c(1,2,3), y=c(1,2,4), method="step")

plot(x=c(1,2,2.5), y=c(1,2,4), type="l", col="blue", ylim=c(0,4))
lines(x=c(1,2,2.5), y=c(1,2,4), type="s", col="red")

x <- seq(0, pi, length.out=200)
AUC(x=x, y=sin(x)) 
AUC(x=x, y=sin(x), method="spline")