LogStatFunctions.jl

Numerically stable logarithms of the mean, variance, and standard deviation of exponentials — a small companion to LogExpFunctions.jl.

Given an array A, these compute log-of-a-statistic-of-exp.(A) without ever forming exp.(A) (which would overflow for large entries):

function	computes
`logmeanexp(A; dims=:)`	`log.(mean(exp.(A); dims))`
`logvarexp(A; dims=:, corrected=true)`	`log.(var(exp.(A); dims, corrected))`
`logstdexp(A; dims=:, corrected=true)`	`log.(std(exp.(A); dims, corrected))`

using LogStatFunctions

A = 1000 .* randn(10^4)      # exp.(A) would overflow Float64
logmeanexp(A)                # finite and accurate
logstdexp(A; corrected=false)

logvarexp and logstdexp also accept logmean to reuse a precomputed logmeanexp(A; dims).

Each function has an in-place variant (logmeanexp!, logvarexp!, logstdexp!) that writes the result into a preallocated output array, reducing over the singleton dimensions of out:

A = randn(10, 5)
out = zeros(1, 5)
logmeanexp!(out, A)          # same as logmeanexp(A; dims=1)

All three functions have ChainRules derivative rules for real arrays (loaded automatically when ChainRulesCore is in the environment), so they can be differentiated with ChainRules-based AD packages such as Zygote. Complex arrays are not covered by these rules.

Reference

LogStatFunctions.logmeanexp — Function

logmeanexp(A; dims=:)

Computes log.(mean(exp.(A); dims)), in a numerically stable way.

source

LogStatFunctions.logvarexp — Function

logvarexp(A; dims=:, corrected=true, logmean=logmeanexp(A; dims))

Computes log.(var(exp.(A); dims)), in a numerically stable way.

source

LogStatFunctions.logstdexp — Function

logstdexp(A; dims=:, corrected=true, logmean=logmeanexp(A; dims))

Computes log.(std(exp.(A); dims)), in a numerically stable way.

source

LogStatFunctions.logmeanexp! — Function

logmeanexp!(out, A)

In-place version of logmeanexp: computes log.(mean(exp.(A); dims)) over the singleton dimensions of out, and writes the result to out.

source

LogStatFunctions.logvarexp! — Function

logvarexp!(out, A; corrected=true, logmean=logmeanexp!(similar(out), A))

In-place version of logvarexp: computes log.(var(exp.(A); dims, corrected)) over the singleton dimensions of out, and writes the result to out.

source

LogStatFunctions.logstdexp! — Function

logstdexp!(out, A; corrected=true, logmean=logmeanexp!(similar(out), A))

In-place version of logstdexp: computes log.(std(exp.(A); dims, corrected)) over the singleton dimensions of out, and writes the result to out.

source