calc_prob_forward_onebranch_sparse: Sparse matrix exponentiation forward on a branch, with...
In BioGeoBEARS: BioGeography with Bayesian (and Likelihood) Evolutionary Analysis in R Scripts

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Take input probabilities, and get the probabilities at the end of a branch using matrix exponentiation.

  calc_prob_forward_onebranch_sparse(relprobs_branch_bottom,
    branch_length, tmpQmat_in_REXPOKIT_coo_fmt,
    coo_n = coo_n, anorm = anorm, check_for_0_rows = TRUE,
    TRANSPOSE_because_forward = TRUE)

`relprobs_branch_bottom`	The relative probability of each state at the base of the branch (should sum to 1).
`branch_length`	The length of the branch.
`tmpQmat_in_REXPOKIT_coo_fmt`	A Q transition matrix in sparse (COO) format. See `mat2coo`.
`coo_n`	If a COO matrix is input, `coo_n` specified the order (# rows, equals # columns) of the matrix.
`anorm`	`dgexpv` requires an initial guess at the norm of the matrix. Using the R function `norm` might get slow with large matrices. If so, the user can input a guess manually (`Lagrange` seems to just use 1 or 0, if I recall correctly).
`check_for_0_rows`	If TRUE or a numeric value, the input Qmat is checked for all-zero 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 off-diagonal cells in the row (and the diagonal value is normalized), which should fix the problem.
`TRANSPOSE_because_forward`	For non-time-reversible models, the forward calculation is different than the backward one. Fortunately this just means switching the rows and columns of a transition matrix.

The calc_loglike_sp function calculates most transition probabilities internally via rexpokit. These are then stored and can be used again when an uppass is being done for ancestral state estimates. However, if there is a root branch below the lowest fork, the uppass needs to calculate the forward probabilities.

actual_probs_after_forward_exponentiation The probabilities of each state at the top of the branch.

Go BEARS!

Nicholas J. Matzke matzke@berkeley.edu

http://phylo.wikidot.com/matzke-2013-international-biogeography-society-poster http://www.bioinf.org/molsys/data/idiots.pdf

Matzke_2012_IBS

FosterIdiots

expokit_dgpadm_Qmat2, expokit_dgpadm_Qmat, rexpokit

# 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.
require("rexpokit")

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)
tmpQmat_in_REXPOKIT_coo_fmt = mat2coo(Qmat)

relprobs_branch_bottom = c(0.25, 0.25, 0.25, 0.25)

# Make a series of t values
branch_length = 0.1

calc_prob_forward_onebranch_sparse(relprobs_branch_bottom, branch_length,
tmpQmat_in_REXPOKIT_coo_fmt, coo_n=4, anorm=1, check_for_0_rows=TRUE,
TRANSPOSE_because_forward=TRUE)
calc_prob_forward_onebranch_sparse(relprobs_branch_bottom, branch_length=0.5,
tmpQmat_in_REXPOKIT_coo_fmt, coo_n=4, anorm=1, check_for_0_rows=TRUE,
TRANSPOSE_because_forward=TRUE)
calc_prob_forward_onebranch_sparse(relprobs_branch_bottom, branch_length=1,
tmpQmat_in_REXPOKIT_coo_fmt, coo_n=4, anorm=1, check_for_0_rows=TRUE,
TRANSPOSE_because_forward=TRUE)
calc_prob_forward_onebranch_sparse(relprobs_branch_bottom, branch_length=2,
tmpQmat_in_REXPOKIT_coo_fmt, coo_n=4, anorm=1, check_for_0_rows=TRUE,
TRANSPOSE_because_forward=TRUE)
calc_prob_forward_onebranch_sparse(relprobs_branch_bottom, branch_length=10,
tmpQmat_in_REXPOKIT_coo_fmt, coo_n=4, anorm=1, check_for_0_rows=TRUE,
TRANSPOSE_because_forward=TRUE)
calc_prob_forward_onebranch_sparse(relprobs_branch_bottom, branch_length=20,
tmpQmat_in_REXPOKIT_coo_fmt, coo_n=4, anorm=1, check_for_0_rows=TRUE,
TRANSPOSE_because_forward=TRUE)