Compute the area under the curve for two vectors.

Compute the area under the curve using linear or natural spline interpolation for two vectors where one corresponds to the x values and the other corresponds to the y values.

auc(
  x,
  y,
  from = min(x, na.rm = TRUE),
  to = max(x, na.rm = TRUE),
  type = c("linear", "spline"),
  absolutearea = FALSE,
  subdivisions = 100,
  ...
)

Arguments

x: a numeric vector of x values.
y: a numeric vector of y values of the same length as x.
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.
type: The type of interpolation. Defaults to "linear" for area under the curve for linear interpolation. The value "spline" results in the area under the natural cubic spline interpolation.
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.
subdivisions: an integer telling how many subdivisions should be used for integrate (for non-linear approximations)
...: 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.

Value

The value of the area under the curve.

Details

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, missing observations, ties for the time values, and integrating over part of the area or even outside the area.

Author

Claus Ekstrom claus@rprimer.dk

Examples


x <- 1:4
y <- c(0, 1, 1, 5)
auc(x, y)
#> [1] 4.5

# AUC from 0 to max(x) where we allow for extrapolation
auc(x, y, from=0, rule=2)
#> [1] 4.5

# Use value 0 to the left
auc(x, y, from=0, rule=2, yleft=0)
#> [1] 4.5

# Use 1/2 to the left
auc(x, y, from=0, rule=2, yleft=.5)
#> [1] 4.75

# Use 1/2 to the left with spline interpolation
auc(x, y, from=0, rule=2, yleft=.5)
#> [1] 4.75