function birth_death_chain¶
- deeptime.data.birth_death_chain(q, p, sparse=False)¶
Generates a birth and death chain simulator from annihilation and creation probabilities q and p.
A general birth and death chain on a d-dimensional state space has the transition matrix
\[p_{ij} = \begin{cases} q_i &\text{, if } j=i-1 \text{ and } i>0,\\ r_i &\text{, if } j=i,\\ p_i &\text{, if } j=i+1 \text{ and } i < d-1 \end{cases}\]The annihilation probability of state \(i=1\) must not be zero, same for the creation probability of the last state \(i=n\). The sum of the probabilities must be bounded component-wise, i.e., \(q_i + p_i \leq 1\;\forall i=1,\ldots ,n\).
(Source code, png, hires.png, pdf)
- Parameters:
q (array_like) – Annihilation probabilities for transition from i to i-1.
p (array_like) – Creation probabilities for transition from i to i+1.
sparse (bool, optional, default=False) – Whether to use sparse matrices.
- Returns:
chain – The chain.
- Return type:
