vws (version 0.3.0)

log_sum_exp: Log-Sum-Exp

Description

Compute arithmetic on the log-scale in a more stable way than directly taking logarithm and exponentiating.

Usage

log_sum_exp(x)
log_add2_exp(x, y)
log_sub2_exp(x, y)

Value

log_add2_exp and log_sub2_exp return a vector of pointwise results whose \(i\)th element is the result based on x[i] and y[i]. log_sum_exp returns a single scalar.

Arguments

x

A numeric vector.

y

A numeric vector; it should have the same length as x.

Details

The function log_sum_exp computes log(sum(exp(x))) using the method in StackExchange post https://stats.stackexchange.com/a/381937.

The functions log_add2_exp and log_sub2_exp compute log(exp(x) + exp(y)) and log(exp(x) - exp(y)), respectively. The function log_sub2_exp expects that each element of x is larger than or equal to its corresponding element in y. Otherwise, NaN will be returned with a warning.

Examples

pi = 1:6 / sum(1:6)
x = log(2*pi)
log(sum(exp(x)))
log_sum_exp(x)

# Result should be 0
x = c(-Inf -Inf, 0)
log_sum_exp(x)

# Result should be -Inf
x = c(-Inf -Inf, -Inf)
log_sum_exp(x)

# Result should be Inf
x = c(-Inf -Inf, Inf)
log_sum_exp(x)

# Result should be 5 on the original scale
out = log_add2_exp(log(3), log(2))
exp(out)

# Result should be 7 on the original scale
out = log_sub2_exp(log(12), log(5))
exp(out)