# expAv: Matrix exponential of sparse matrix multiplied by a vector. In RTMB: 'R' Bindings for 'TMB'

 expAv R Documentation

## Matrix exponential of sparse matrix multiplied by a vector.

### Description

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`.

### Usage

``````expAv(A, v, transpose = FALSE, uniformization = TRUE, tol = 1e-08, ...)
``````

### Arguments

 `A` Sparse matrix (usually a generator) `v` Vector (or matrix) `transpose` Calculate `expm(t(A)) %*% v` ? (faster due to the way sparse matrices are stored) `uniformization` Use uniformization method? `tol` Accuracy if A is a generator matrix and v a probability vector. `...` Extra configuration parameters

### Details

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.

### Value

Vector (or matrix)

### References

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.

RTMB documentation built on May 29, 2024, 8:45 a.m.