ELynx.MarkovProcess.RateMatrix

Some helper functions that come handy when working with rate matrices of continuous-time discrete-state Markov processes.

• Changelog

To be imported qualified.

Documentation

type RateMatrix = Matrix R

A rate matrix is just a real matrix.

type ExchangeabilityMatrix = Matrix R

A matrix of exchangeabilities, we have q = e * pi, where q is a rate matrix, e is the exchangeability matrix and pi is the diagonal matrix containing the stationary frequency distribution.

type StationaryDistribution = Vector R

Stationary distribution of a rate matrix.

isValid :: StationaryDistribution -> Bool

True if distribution sums to 1.0.

normalizeSD :: StationaryDistribution -> StationaryDistribution

Normalize a stationary distribution so that the elements sum to 1.0.

totalRate :: RateMatrix -> Double

Get average number of substitutions per unit time.

totalRateWith :: StationaryDistribution -> RateMatrix -> Double

Get average number of substitutions per unit time.

normalize :: RateMatrix -> RateMatrix

Normalizes a Markov process generator such that one event happens per unit time. Calculates stationary distribution from rate matrix.

normalizeWith :: StationaryDistribution -> RateMatrix -> RateMatrix

Normalizes a Markov process generator such that one event happens per unit time. Faster, but stationary distribution has to be given.

setDiagonal :: RateMatrix -> RateMatrix

Set the diagonal entries of a matrix such that the rows sum to 0.

toExchangeabilityMatrix :: RateMatrix -> StationaryDistribution -> ExchangeabilityMatrix

Extract the exchangeability matrix from a rate matrix.

fromExchangeabilityMatrix :: ExchangeabilityMatrix -> StationaryDistribution -> RateMatrix

Convert exchangeability matrix to rate matrix.

getStationaryDistribution :: RateMatrix -> StationaryDistribution

Get stationary distribution from RateMatrix. Involves eigendecomposition. If the given matrix does not satisfy the required properties of transition rate matrices and no eigenvector with an eigenvalue nearly equal to 0 is found, an error is thrown. Is there an easier way to calculate the stationary distribution or a better way to handle errors (of course I could use the Maybe monad, but then the error report is just delayed to the calling function)?

exchFromListLower :: (RealFrac a, Container Vector a) => Int -> [a] -> Matrix a

Build exchangeability matrix from list denoting lower triangular matrix, and excluding diagonal. This is how the exchangeabilities are specified in PAML.

exchFromListUpper :: (RealFrac a, Container Vector a) => Int -> [a] -> Matrix a

Build exchangeability matrix from list denoting upper triangular matrix, and excluding diagonal.