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The trapezoidal area under a curve given as points — sklearn.metrics.auc.

public static double Trapezoid(ReadOnlySpan<double> x, ReadOnlySpan<double> y)

Parameters — x is the x coordinates, monotonic in either direction, and y the y coordinates, one per x.

Returns — double, the area. A curve given right to left gives the same magnitude as the same curve given left to right, which is what the reference does too.

Exceptions — ArgumentException when the lengths disagree, when fewer than two points are given, or when x is neither increasing nor decreasing — a sequence that turns has no single area under it.

Example — integrating a ROC curve this package drew.

using Lodestar.Metrics;

int[] truth = [0, 0, 1, 1];
double[] scores = [0.1, 0.4, 0.35, 0.8];
RocCurve curve = RocCurve.Compute(truth, scores);

double area = Auc.Trapezoid([.. curve.FalsePositiveRate], [.. curve.TruePositiveRate]);  // => 0.75

Remarks — reaching for this over a precision-recall curve is the mistake AveragePrecision exists to avoid; see the type page.

Applies to — net10.0, netstandard2.0.

See also — RocCurve.Compute, RocAuc.Score, AveragePrecision.Score, the Python equivalence table.