Compute AUC (Area Under ROC)

Metrics & Evaluation

Easy

Compute the area under a ROC curve with the trapezoidal rule. For consecutive points $(x_i,y_i)=(\operatorname{FPR}_i,\operatorname{TPR}_i)$ :

\operatorname{AUC} = \sum_{i=1}^{M-1}(x_{i+1}-x_i)\frac{y_i+y_{i+1}}{2}

Here, $M$ is the number of curve points. Return the summed area as a Python float.

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Examples

Input: fpr = [0, 0, 1], tpr = [0, 1, 1]

Output: 1.0

Explanation: The curve rises vertically to a true-positive rate of one before spanning the full false-positive range.

Input: fpr = [0, 1], tpr = [0, 1]

Output: 0.5

Hint 1

Use np.diff(fpr) for trapezoid widths.

Hint 2

Use 0.5 * (tpr[:-1] + tpr[1:]) for their heights.

Requirements

Compute each interval width from consecutive FPR values
Multiply by the average of the neighboring TPR values
Sum all trapezoid areas
Return a Python float

Constraints

fpr and tpr have the same length of at least two
fpr is nondecreasing
Both arrays contain values between 0 and 1
Use NumPy only

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