expokit_dmexpv_Qmat  R Documentation 
This function converts a matrix to COO format and
exponentiates it via the EXPOKIT dmexpv function
(designed for sparse matrices) and wrapper functions
wrapalldmexpv_
around dmexpv.
expokit_dmexpv_Qmat(Qmat = NULL, t = 2.1,
inputprobs_for_fast = NULL, transpose_needed = TRUE,
transform_to_coo_TF = TRUE, coo_n = NULL, anorm = NULL,
check_for_0_rows = TRUE)
Qmat 
an input Q transition matrix 
t 
one or more time values to exponentiate by 
inputprobs_for_fast 
If NULL (default), the full
probability matrix (Pmat) is returned. However, the full
speed of EXPOKIT on sparse matrices will be exploited if
inputprobs_for_fast=c(starting probabilities). In this
case these starting probabilities are input to

transpose_needed 
If TRUE (default), matrix will be transposed (apparently EXPOKIT needs the input matrix to be transposed compared to normal) 
transform_to_coo_TF 
Should the matrix be tranposed
to COO? COO format is required for EXPOKIT's
sparsematrix functions (like dmexpv and unlike the
padmrelated functions. Default TRUE; if FALSE, user must
put a COOformated matrix in 
coo_n 
If a COO matrix is input, 
anorm 

check_for_0_rows 
If TRUE or a numeric value, the
input Qmat is checked for allzero rows, since these will
crash the FORTRAN wrapalldmexpv function. A small nonzero
value set to check_for_0_rows or the default
(0.0000000000001) is input to offdiagonal cells in the
row (and the diagonal value is normalized), which should
fix the problem. R function 
From EXPOKIT:
* The method used is based on
Krylov subspace projection
* techniques and the
matrix under consideration interacts only
* via
the external routine 'matvec' performing the
matrixvector
* product (matrixfree
method).
*
* This is a customised
version for Markov Chains. This means that a
*
check is done within this code to ensure that the
resulting vector
* w is a probability vector,
i.e., w must have all its components
* in
[0,1], with sum equal to 1. This check is done at some
expense
* and the user may try DGEXPV which is
cheaper since it ignores
* probability
constraints.
COO (coordinated list) format is a compressed format that
is
required for EXPOKIT's sparsematrix functions
(like dmexpv and
unlike EXPOKIT's padmrelated
functions.
COO (coordinated list) format is described here:
https://en.wikipedia.org/wiki/Sparse_matrix#Coordinate_list_.28COO.29
If Qmat
is NULL (default), a default matrix is
input.
tmpoutmat
the output matrix. wrapalldmexpv_
produces additional output relating to accuracy of the
output matrix etc.; these can be by a direct call of
dmexpv.
Nicholas J. Matzke nickmatzke.ncse@gmail.com and Drew Schmidt schmidt@math.utk.edu
mat2coo
expokit_wrapalldmexpv_tvals
# Example:
# Make a square instantaneous rate matrix (Q matrix)
# This matrix is taken from Peter Foster's (2001) "The Idiot's Guide
# to the Zen of Likelihood in a Nutshell in Seven Days for Dummies,
# Unleashed" at:
# \url{http://www.bioinf.org/molsys/data/idiots.pdf}
#
# The Q matrix includes the stationary base freqencies, which Pmat
# converges to as t becomes large.
Qmat = matrix(c(1.218, 0.504, 0.336, 0.378, 0.126, 0.882, 0.252, 0.504, 0.168,
0.504, 1.05, 0.378, 0.126, 0.672, 0.252, 1.05), nrow=4, byrow=TRUE)
# Make a series of t values
tvals = c(0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 1, 2, 5, 14)
# Exponentiate each with EXPOKIT's dmexpv (should be fast for large sparse matrices)
for (t in tvals)
{
Pmat = expokit_dmexpv_Qmat(Qmat=Qmat, t=t, transpose_needed=TRUE)
cat("\n\nTime=", t, "\n", sep="")
print(Pmat)
}
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