qspec.simulate.ct_markov_analytic  (  t ,  n ,  rates ,  r = 1.0  )[source]

Computes the analytic solution of the evolution of a linear continuous-time markov chain. CAUTION! Computation of analytic solution problematic (Multiplication of very small numbers with very large numbers).

Parameters:

tarray_like

The time at which the probability is returned (us).

narray_like

The number of the state for which the probability is returned. The first state corresponds to 'n' = 0.

ratesarray_like

The rate(s) at which the markov chain is transferring population from state i to state i + 1. If 'rates' is a scalar, this rate is assumed for all 0 ≤ i ≤ 'n'. If 'rates' is an Iterable, it must have length max('n') + 1 and individual rates 'rates[i]' are assumed for the states 0 ≤ i ≤ 'n'.

rarray_like

The ratio of the population which is transferred from state i to state i + 1. Then 1 - r is the ratio of the population that is lost during the transition from state i to state i + 1.

Returns:

outNone

The probability for the markov chain to be in state 'n' after the time 't' for P(t=0, n=0) = 1. The normalization condition is sum_n(P(n, t0)) = 1 for every single point in time t0. If 't' and 'n' are Iterables, a 2-d array is returned with shape (t.size, n.size), containing all probabilities P(t, n).