Calculate Area Under Curve (AUC) using trapezoidal rule

Computes the area under a curve using the trapezoidal rule of numerical integration.

Usage

trap_roc(x, y)

Arguments

x

Numeric vector (arma::vec) of x-coordinates (should be sorted in increasing order)

y

Numeric vector (arma::vec) of y-coordinates corresponding to x-coordinates

Value

A numerical value representing the computed area under the curve as a double precision value.

Details

The trapezoidal rule approximates the area under the curve by dividing it into trapezoids. For each pair of adjacent points (x[i], y[i]) and (x[i+1], y[i+1]), it calculates the area of the trapezoid formed. The total AUC is the sum of all these individual trapezoid areas.

Special cases: - Returns 0 if there are fewer than 2 points (no area can be calculated) - Handles both increasing and decreasing x values (though typically x should be increasing for ROC curves)

See also

integrate for R's built-in integration functions

Examples

# R code example:
x <- c(0, 0.5, 1, 1.5, 2)
y <- c(0, 0.7, 0.9, 0.95, 1)
trap_roc(x, y)
#> [1] 1.525