R: Properly Compute the Logarithm of a Sum (of Exponentials)

lsum {DPQ} | R Documentation

## Properly Compute the Logarithm of a Sum (of Exponentials)

### Description

Properly compute log(x1 + .. + xn). for given log(x_1),..,log(x_n). Here, xi > 0 for all i.

If the inputs are denoted l_i = log(x_i) for i = 1,2,..,n, we compute `log(sum(exp(l[])))`, numerically stably.

Simple vector version of `copula:::lsum()` (CRAN package copula).

### Usage

    lsum(lx, l.off = max(lx))

### Arguments

`lx` | n-vector of values log(x_1),..,log(x_n).
`l.off` | the offset to substract and re-add; ideally in the order of the maximum of each column.

### Value

log(x_1 + .. + x_n) = log(sum(x)) = log(sum(exp(log(x)))) = = log(exp(log(x_max))*sum(exp(log(x)-log(x_max)))) = = log(x_max) + log(sum(exp(log(x)-log(x_max))))) = = lx.max + log(sum(exp(lx-lx.max)))

### Author(s)

Originally, via paired programming: Marius Hofert and Martin Maechler.

### See Also

`lssum()` which computes a sum in log scale with specified (typically alternating) signs.

### Examples

    ## The "naive" version :
    lsum0 <- function(lx) log(sum(exp(lx)))

    lx1 <- 10*(-80:70) # is easy
    lx2 <- 600:750     # lsum0() not ok [could work with rescaling]
    lx3 <- -(750:900)  # lsum0() = -Inf - not good enough
    m3 <- cbind(lx1,lx2,lx3)
    lx6 <- lx5 <- lx4 <- lx3
    lx4[149:151] <- -Inf ## = log(0)
    lx5[150] <- Inf
    lx6[1] <- NA_real_
    m6 <- cbind(m3,lx4,lx5,lx6)
    stopifnot(exprs = {
      all.equal(lsum(lx1), lsum0(lx1))
      all.equal((ls1 <- lsum(lx1)),  700.000045400960403, tol=8e-16)
      all.equal((ls2 <- lsum(lx2)),  750.458675145387133, tol=8e-16)
      all.equal((ls3 <- lsum(lx3)), -749.541324854612867, tol=8e-16)
      ## identical: matrix-version <==> vector versions
      identical(lsum(lx4), ls3)
      identical(lsum(lx4), lsum(head(lx4, -3))) # the last three were -Inf
      identical(lsum(lx5), Inf)
      identical(lsum(lx6), lx6[1])
      identical((lm3 <- apply(m3, 2, lsum)), c(lx1=ls1, lx2=ls2, lx3=ls3))
      identical(apply(m6, 2, lsum), c(lm3, lx4=ls3, lx5=Inf, lx6=lx6[1]))
    })

[Package DPQ version 0.4-4 Index]