kexpmv-package: Matrix exponentiation using Krylov subspace routines

In kexpmv: Matrix Exponential using Krylov Subspace Routines

Description

Matrix Exponential using Krylov subspace routines

Details

This package utilises some of the matrix exponential routines included in EXPOKIT (http://www.maths.uq.edu.au/expokit/), which is software designed to calculate matrix exponentials for both small dense and large sparse matrices. The use of Krylov subspace methods implemented within these routines should result in more efficient computations.

The EXPOKIT software was developed by Roger B. Sidje. Nicholas J. Matzke went on to adapt this software for the R package Rexpokit, which enables users to make use of EXPOKIT, a FORTRAN library, within an R environment. Kexpmv uses the foundations of Rexpokit with the aim of making computing matrix exponentials more efficient, especially for large sparse matrices which can often be computationally complex.

Permission to distribute the EXPOKIT source under GPL was obtained from Roger B. Sidje.

EXPOKIT includes functions for exponentiating both small dense matrices and large sparse matrices. Fast and efficient matrix exponentiation is needed for different application areas, i.e. Markov models. This package allows the user to calculate both the matrix exponential in isolation as well as the matrix exponential with the product of a vector, which is essential for multi-state Markov models. Both expokit_dgexpv and expokit_dmexpv functions can compute both of these calculations with the use of the vector arguement.

When the matrix has large dimensions and is sparse in nature, this means the matrix has a high volume of elements equal to zero. Similiar to EXPOKIT this package transforms the matrix into Compressed Row Storage (CRS) format before the matrix exponentiation is performed. See functions mat2crs and crs2mat for more details.

Acknowledgements/sources

1. Nicholas Matzke [e-mail] helped greatly with the initial setup of the package. See his Rexpokit for another R implementation of EXPOKIT routines.

2. EXPOKIT, original FORTRAN package, by Roger B. Sidje [e-mail], Department of Mathematics, University of Queensland, Brisbane, QLD-4072, Australia, (c) 1996-2013 All Rights Reserved. Sidje has given permission to include EXPOKIT code in this R package under the usual GPL license for CRAN R packages. For the full EXPOKIT copyright and license, see expokit_copyright.txt under inst/notes.

3. The development of this package was helped by advice and discussions with my PhD supervisors Adele Marshall and Karen Cairns.

Examples

library(kexpmv)

# Construct a square (nxn) matrix
mat=matrix(c(-0.071207, 0.065573, 0.005634, 0, -0.041206, 0.041206, 0, 0, 0), 
nrow=3, byrow=TRUE) 
 
# Define value for t 
t = 15
 
# Exponentiate this matrix using DGPADM for t = 15 
OutputMat = expokit_dgpadm( mat = mat, t = t, transpose_needed = TRUE)
print(OutputMat)

# Construct column (nx1) vector
v = matrix(0,3,1)
v[1] = 1
 	
# Exponentiate the matrix using DMEXPV for t = 15 with the product of vector v.
OutputMat = expokit_dmexpv( mat = mat, t = t, vector = v, transpose_needed = TRUE,
transform_to_crs = TRUE)

# Print corresponding (nx1) results vector
print(OutputMat$output_probs)

# Print message to determine whether the mxstep value needs increased. If NULL
# then mxstep value is valid.
print(OutputMat$message)

# Exponentiate the matrix using DGEXPV for t = 15.
OutputMat = expokit_dgexpv( mat = mat, t = t, vector = NULL, transpose_needed = TRUE,
transform_to_crs = TRUE)
print(OutputMat$output_mat)
print(OutputMat$message)

# Functions DMEXPV and DGEXPV are very similiar, with the only difference being DMEXPV
# carries out an additional check for Markov chains.

kexpmv documentation built on May 1, 2019, 7:56 p.m.