MissedEventsG¶

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

Computes missed-events likelihood.

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

__init__(*args, **kwargs)¶

Initializes the missed-events likelihood.

Exact calculations take place for times smaller than nmax * tau. Asymptotic calculations take over for larger times.

There are three possible ways to instantiate this object:

>>> MissedEvents(determinant_af, roots_af, determinant_fa, roots_fa[, nmax=2])
>>> MissedEvents(matrix, nopen, tau, **kwargs)
>>> MissedEvents(qmatrix, tau, **kwargs)

The parameters between brackets are optional. The last two versions will try and calculate the roots of the determinant equations automatically. A number of parameters can be given to control this process.

Parameters:

determinant_af – A DeterminantEq instance, specifically for the af block. roots_af – The roots of the af determinant equation. The should come in the format [(root, multiplicity), (root, multiplicity), ...]. determinant_fa – A DeterminantEq instance, specifically for the fa block. It should the transpose of determinant_af. It is required so it need not be recomputed, since it most likely already exists. roots_fa – The roots of the fa determinant equation. The should come in the format [(root, multiplicity), (root, multiplicity), ...]. matrix – An object convertible to a square matrix. nopen (integer) – Number of open states. qmatrix – A QMatrix instance. nmax (int) – The exact missed event likelihood will be computed for times $t \in [0, n_{\mathrm{max}} au$. Defaults to 3. xtol (float) – Tolerance criteria when computing roots using brentq(). Defaults to 1e-12. rtol (float) – Tolerance criteria when computing roots using brentq(). Defaults to 1e-12. itermax (float) – Maximum number of iterations when computing roots using brentq(). Defaults to 100. lower_bound (float) – Lower bound for all roots. Defaults to None, in which the case the lower bound is computed from find_lower_bound_for_roots(). upper_bound (float) – Upper bound for all roots. Defaults to None, in which the case the upper bound is computed from find_upper_bound_for_roots().

__weakref__¶

list of weak references to the object (if defined)

af(self, t) → DCProgs::t_rmatrix¶

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¶

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)¶

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)¶

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¶

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¶

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.