# expokit_dgpadm_Qmat: EXPOKIT dgpadm matrix exponentiation on Q matrix In nmatzke/rexpokit: R Wrappers for EXPOKIT; Other Matrix Functions

## 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 nickmatzke.ncse@gmail.com and Drew Schmidt schmidt@math.utk.edu

`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)
{