Calculates expm(A) %*% v using plain series summation. The number of terms is determined adaptively when uniformization=TRUE.
The uniformization method essentially pushes the spectrum of the operator inside a zero centered disc, within which a uniform error bound is available.
If A is a generator matrix (i.e. expm(A) is a probability matrix) and if v is a probability vector, then the relative error of the result is bounded by tol.
expAv(A, v, transpose = FALSE, uniformization = TRUE, tol = 1e-08, ...)Vector (or matrix)
Sparse matrix (usually a generator)
Vector (or matrix)
Calculate expm(t(A)) %*% v ? (faster due to the way sparse matrices are stored)
Use uniformization method?
Accuracy if A is a generator matrix and v a probability vector.
Extra configuration parameters
Additional supported arguments via ... currently include:
Nmax Use no more than this number of terms even if the spcified accuracy cannot be met.
warn Give warning if number of terms is truncated by Nmax.
trace Trace the number of terms when it adaptively changes.
Grassmann, W. K. (1977). Transient solutions in Markovian queueing systems. Computers & Operations Research, 4(1), 47--53.
Sherlock, C. (2021). Direct statistical inference for finite Markov jump processes via the matrix exponential. Computational Statistics, 36(4), 2863--2887.