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Vectorized Log-Sum-Exp

Source: R/00_constants.R
logsumexp_vec.Rd

Computes log(sum(exp(x))) for a numeric vector in a numerically stable way.

Usage

logsumexp_vec(x)

Arguments

x

Numeric vector of log-scale values.

Value

Scalar value equal to log(sum(exp(x))).

Details

Subtracts the maximum before exponentiating to prevent overflow: $$\log\sum_i \exp(x_i) = \max_i x_i + \log\sum_i \exp(x_i - \max_i x_i)$$

Special cases:

  • If all entries are -Inf, returns -Inf.

  • If any entry is Inf, returns Inf.

  • Empty vector throws an error.

See also

logsumexp for binary operation

Examples

# Sum of equal values
logsumexp_vec(c(0, 0, 0, 0))
#> [1] 1.386294

# Extreme values
logsumexp_vec(c(1000, 1000, 1000))
#> [1] 1001.099

# All -Inf
logsumexp_vec(c(-Inf, -Inf))
#> [1] -Inf