Log10Likelihood¶

The purpose of this class is to provide an interface for maximizing the likelihood. It computes, for a given set of observed open and shut intervals, the likelihood \(\frac{\ln(L(Q))}{ln 10}\), where \(L(Q)\) is declared in the likelihood equation.

class dcprogs.likelihood.Log10Likelihood(bursts, nopen, tau, tcritical=None, nmax=3, xtol=1e-10, rtol=1e-10, itermax=100, lower_bound=None, upper_bound=None)¶

Creates a functor for optimizing the likelihood.

This functor can as input a \(\mathcal{Q}\)-matrix and returns the resulting likelihood. The root finding process is performed by find_roots(). Most of the arguments to initialize this functor are parameters for that process.

nopen¶

Number of open states. Should be strictly positive.

tau¶

Maximum length of missed events. Should be positive.

tcritical¶

\(t_{\mathrm{crit}}\) for CHS vectors. If negative, None, or NaN, then the initial and final states are the equilibrium occupancies.

nmax¶

The exact missed-events likelihood will be computed for \(t < n_{\mathrm{max}} au\).

xtol¶

Tolerance criteria when computing roots via likelihood.brentq().

rtol¶

Tolerance criteria when computing roots via likelihood.brentq().

itermax¶

Maximum number of iterations when computing roots via likelihood.brentq().

lower_bound¶

Lower bound bracketing all roots. If None or NaN, then the lower bound will be computed during calls by find_lower_bound_for_root()

upper_bound¶

Upper bound bracketing all roots. If None or NaN, then the upper bound will be computed during calls by find_upper_bound_for_root()

__call__(self, _Q) → DCProgs::t_real¶

Computes the \(log_{10}\)-likelihood for the input Q-matrix

Parameters:	matrix – Can be either a square numpy array or a QMatrix object. In the first case, the number of open states is set to attribute nopen.

__delitem__(*args)¶

Deletes the nth burst.

__getitem__(*args)¶

Returns the nth burst.

__init__(bursts, nopen, tau, tcritical=None, nmax=3, xtol=1e-10, rtol=1e-10, itermax=100, lower_bound=None, upper_bound=None)¶

Initializes the missed-events likelihood.

Parameters:

bursts – A sequence of bursts. Each burst is a sequence of open and shut intervals. There should always be an odd number of intervals. And the first interval is open by default. nopen (integer) – Number of open states. Should be strictly positive. tau (float) – Maximum length of missed events. Should be positive. tcritical (float) – \(t_{\mathrm{crit}}\) for CHS vectors. If None, then the initial and final states are the equilibrium occupancies. nmax (integer) – The exact missed-events likelihood will be computed for \(t < n_{\matrm{max}} au\). xtol (float) – Tolerance criteria when computing roots via likelihood.brentq() rtol (float) – Tolerance criteria when computing roots via likelihood.brentq(). itermax (interger) – Maximum number of iterations when computing roots via likelihood.brentq(). 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().

__len__()¶

Number of bursts.

__setitem__(*args)¶

Sets the nth burst.

Parameters:	index – Index to the burst that should be changed. value – A list of time intervals with an odd number of components, in seconds.

__weakref__¶

list of weak references to the object (if defined)

insert(*args)¶

Inserts a burst at given index.

vector(self, _Q) → DCProgs::t_rvector¶

Computes the \(log_{10}\)-likelihood for each individual burst

The sum over the return of this function is the return of __call__(). This is merely a convenience function if one wants the likelihood associate with each burst

Parameters:	matrix – Can be either a square numpy array or a QMatrix object. In the first case, the number of open states is set to attribute nopen.
Returns:	A numpy array where each component contains the \(log_{10}\) likelihood of a single burst.