AUC: 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

x, y

the xy-points of the curve

method

can be "trapezoid" (default), "step" or "spline".

na.rm

logical, indicating whether NA values should be stripped before the computation proceeds. In this case only the complete.cases of x and y will be used. na.rm defaults to FALSE.

Value

Numeric value of the area under the curve.

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).

Examples

Run this code

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")

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