expokit_dgpadm_Qmat {rexpokit}

EXPOKIT dgpadm matrix exponentiation on Q matrix

Description

This function exponentiates a matrix via the EXPOKIT padm function (designed for small dense matrices) and wrapper function wrapalldgpadm_ around dmexpv.

Usage

  expokit_dgpadm_Qmat(Qmat = NULL, t = 2.1,
    transpose_needed = TRUE)

Arguments

Qmat

an input Q transition matrix

t

one or more time values to exponentiate by

transpose_needed

If TRUE (default), matrix will be transposed (apparently EXPOKIT needs the input matrix to be transposed compared to normal)

Details

From EXPOKIT:

* Computes exp(t*H), the matrix exponential of a general matrix in
* full, using the irreducible rational Pade approximation to the
* exponential function exp(x) = r(x) = (+/-)( I + 2*(q(x)/p(x)) ),
* combined with scaling-and-squaring.

If Qmat is NULL (default), a default matrix is input.

Value

tmpoutmat the output matrix. wrapalldmexpv_ produces additional output relating to accuracy of the output matrix etc.; these can be obtained by a direct call of wrapalldmexpv_.

Author(s)

Nicholas J. Matzke [e-mail] and Drew Schmidt [e-mail]

See Also

mat2coo

Examples

# 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 dgpadm (good for small dense matrices)
for (t in tvals)
	{
	Pmat = expokit_dgpadm_Qmat(Qmat=Qmat, t=t, transpose_needed=TRUE)
	cat("\n\nTime=", t, "\n", sep="")
	print(Pmat)
	}