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, from = min(x, na.rm = TRUE), to = max(x, na.rm = TRUE), 
    method = c("trapezoid", "step", "spline", "linear"), 
    absolutearea = FALSE, subdivisions = 100, na.rm = FALSE, ...)

Value

Numeric value of the area under the curve.

Arguments

x, y: the xy-points of the curve
method: The type of interpolation. Can be "trapezoid" (default), "step", "linear" or "spline". The value "spline" results in the area under the natural cubic spline interpolation.
from: The value from where to start calculating the area under the curve. Defaults to the smallest x value.
to: The value from where to end the calculation of the area under the curve. Defaults to the greatest x value.
absolutearea: A logical value that determines if negative areas should be added to the total area under the curve. By default the auc function subtracts areas that have negative y values. Set absolutearea=TRUE to _add_ the absolute value of the negative areas to the total area. Ignored if method is not spline.
subdivisions: an integer telling how many subdivisions should be used for integrate (for non-linear approximations). Ignored if method is not 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.
...: additional arguments passed on to approx (for linear approximations). In particular rule can be set to determine how values outside the range of x is handled.

Author

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

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 linear interpolation the AUC() function computes the area under the curve using the composite trapezoid rule. For area under a spline interpolation, AUC() uses the splinefun function in combination with the integrate to calculate a numerical integral.

The AUC() function can handle unsorted time values (by sorting x), missing observations, ties for the x values (by ignoring duplicates), and integrating over part of the area or even outside the area.

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")

Run the code above in your browser using DataLab