mclust (version 6.1)

logsumexp: Log sum of exponentials

Description

Efficient implementation (via Fortran) of the log-sum-exp function.

Usage

logsumexp(x, v = NULL)

Value

Returns a vector of values of length equal to the number of rows of x.

Arguments

x

a matrix of dimension $n\times k$ of numerical values. If a vector is provided, it is converted to a single-row matrix.

v

an optional vector of length $k$ of numerical values to be added to each row of x matrix. If not provided, a vector of zeros is used.

Author

Luca Scrucca

Details

Given the matrix x, for each row $x_{[i]}=[x_1,\dots ,x_k]$ (with $i=1,\dots ,n$), the log-sum-exp (LSE) function calculates $$\text{LSE}(x_{[i]})=\log \sum _{j=1}^k\exp (x_j+v_j)=m+\log \sum _{j=1}^k\exp (x_j+v_j-m)$$ where $m=max(x_1+v_1,\dots ,x_k+v_k)$.

See Also

softmax

Examples

x = matrix(rnorm(15), 5, 3)
v = log(c(0.5, 0.3, 0.2))
logsumexp(x, v)