scipyspeciallogsumexp

scipy.special.logsumexp is a function in the SciPy library that computes the logarithm of a sum of exponentials in a numerically stable way. It evaluates log(sum(exp(a))) for input array a, with optional reduction along a specified axis. The implementation avoids overflow and underflow that can occur when exponentiating large or very small values, making it reliable for large ranges of input magnitudes.

The function accepts the input array a, an optional weight array b of the same broadcastable shape, and an axis argument to specify the reduction axis. If provided, b allows computing log(sum(b * exp(a))). A return_sign flag is available to handle cases where the weighted sum can be negative; when true, the function returns both the log of the absolute value and the sign of the sum to support cancellation scenarios.

Numerical method: logsumexp uses the log-sum-exp trick. It computes with a shifted maximum along the reduction axis to prevent overflow: m = max(a, axis); result = m + log(sum(exp(a - m) * (b if provided else 1), axis)). This yields accurate results across a wide range of magnitudes and preserves shape, returning an array or scalar depending on axis.

Usage and relation: logsumexp is widely used in probabilistic models, statistics, and machine learning for computing log-probabilities and in softmax computations. It is part of SciPy’s special module and is documented as scipy.special.logsumexp. For numerical stability, using logsumexp is generally preferred over manually applying log and exp to large ranges of numbers.