Functions to compute the logarithm of the mean (and cumulative means) of vectors of logarithms
Given a vector of numeric values of real values
represented in log form,
the logarithm of the mean of the (exponentiated) values.
logCumMeanExpLogs computes the logarithm of the
A vector of (log) values
Given a vector of values of log values v, one could
log(mean(exp(v))) in R. However,
exponentiating and summing will cause a loss of
precision, and possibly an overflow. These functions use
log(e^a + e^b) = a + log[ 1 + e^(b-a) ]
and the method of computing log(1+e^x) that avoids overflow (see the references). The code is written in C for very fast computations.
logMeanExpLogs returns a single value;
logCumMeanExpLogs returns a vector of values of
the same length as v.
Richard D. Morey (firstname.lastname@example.org)
For details of the approximation of log(1+e^x) used to prevent loss of precision, see http://www.codeproject.com/Articles/25294/Avoiding-Overflow-Underflow-and-Loss-of-Precision.
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# Sample 100 values y = log(rexp(100,1)) # These will give the same value, # since e^y is "small" logMeanExpLogs(y) log(mean(exp(y))) # We can make e^x overflow by multiplying # e^y by e^1000 largeVals = y + 1000 # This will return 1000 + log(mean(exp(y))) logMeanExpLogs(largeVals) # This will overflow log(mean(exp(largeVals)))
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