MissedEventsG¶

class dcprogs.likelihood.MissedEventsG(*args, **kwargs)[source]¶

Computes missed-events likelihood.

Exact calculations take place for times smaller than \(n_{\mathrm{max}}\tau\). Asymptotic calculations take over for larger times.

af(self, t) → DCProgs::t_rmatrix[source]¶

Likelihood of an observed open time of length t

Parameters:	t – A scalar or something to a numpy array. In the latter case, the return is an array of matrices.

af_factor¶

Factor accounting for minimum shut time

It is the likelihood \(\mathcal{Q}_{AF}e^{-\mathcal{Q}_{FF}\tau}\) of a shut time of length \(\tau\).

fa(self, t) → DCProgs::t_rmatrix[source]¶

Likelihood of a shut time of length t

Parameters:	t – A scalar or something to a numpy array. In the latter case, the return is an array of matrices.

fa_factor¶

Factor accounting for minimum open time

It is the likelihood \(\mathcal{Q}_{FA}e^{-\mathcal{Q}_{AA}\tau}\) of an open time of length \(\tau\).

final_CHS_occupancies(*args)[source]¶

Computes final CHS occupancies.

final_occupancies¶

Equilibrium occupancies for final states.

Computes the right eigenvector of \({}^e\mathcal{G}_{FA}{}^e\mathcal{G}_{AF}\), where \({}^e\mathcal{G}_{FA}\) is the laplacian for \(s=0\) of the likelihood.

initial_CHS_occupancies(*args)[source]¶

Computes initial CHS occupancies.

initial_occupancies¶

Equilibrium occupancies for initial states.

Computes the left eigenvector of \({}^e\mathcal{G}_{AF}{}^e\mathcal{G}_{FA}\), where \({}^e\mathcal{G}_{AF}\) is the laplacian for \(s=0\) of the likelihood.

laplace_af(self, s) → DCProgs::t_rmatrix[source]¶

Exact missed-events G in Laplace space.

The exact expression is \(^{e}\mathcal{G}_{AF}(s) = {}^AR(s) e^{-s\tau}\mathcal{Q}_{AF}e^{\mathcal{Q}_{FF}\tau}\), with \({}^AR(s) = [sI - \mathcal{Q}_{AA} - \mathcal{Q}_{AF} \int_0^\tau e^{-st}e^{\mathcal{Q}_{FF}t}\partial t \mathcal{Q}_{FA}]^{-1}\).

Parameters:	s – The laplace scale. A real scalar or something convertible to a numpy array.
Returns:	A matrix if the input is scalar, an array of matrices otherwise, with the shape of the input.

laplace_fa(self, s) → DCProgs::t_rmatrix[source]¶

Exact missed-events G in Laplace space.

The exact expression is \(^{e}\mathcal{G}_{FA}(s) = {}^FR(s) e^{-s\tau}\mathcal{Q}_{FA}e^{\mathcal{Q}_{AA}\tau}\), with \({}^FR(s) = [sI - \mathcal{Q}_{FF} - \mathcal{Q}_{FA} \int_0^\tau e^{-st}e^{\mathcal{Q}_{AA}t}\partial t \mathcal{Q}_{AF}]^{-1}\).

Parameters:	s – The laplace scale. A real scalar or something convertible to a numpy array.
Returns:	A matrix if the input is scalar, an array of matrices otherwise, with the shape of the input.

nmax¶

Cut-off time of exact calculations in units of \(\\tau\).

nopen¶

Number of open-states.

nshut¶

Number of shut-states.

tau¶

Resolution or maximum length of the missed events.

tmax¶

Cut-off time of exact calculations \(t_{\mathrm{max}} = (n_{\mathrm{max}}-1)\\tau\).

For practical reasons, the minimum observation time has alreadybeen removed here.