Numerically Stable Log-Sum-Exp (Binary)

Computes log(exp(a) + exp(b)) in a numerically stable way, avoiding overflow and underflow.

Usage

logsumexp(a, b)

Arguments

a

Numeric vector of log-scale values.

b

Numeric vector of log-scale values (recycled to match length of a).

Value

Numeric vector of log(exp(a) + exp(b)).

Details

Uses the identity: $$\log(\exp(a) + \exp(b)) = \max(a,b) + \log(1 + \exp(-|a-b|))$$

This formulation ensures numerical stability even for extreme values (e.g., a = 1000 or a = -1000).

Special cases:

• If both inputs are -Inf, returns -Inf.

• If either input is Inf, returns Inf.

See also

logsumexp_vec for vector input

Examples

# Standard case
logsumexp(log(2), log(3))
#> [1] 1.609438

# Extreme values that would overflow with naive implementation
logsumexp(1000, 1000)
#> [1] 1000.693

# Edge cases with Inf
logsumexp(-Inf, -Inf)
#> [1] -Inf