Source code for stonesoup.models.transition.categorical

# -*- coding: utf-8 -*-

from datetime import timedelta

import numpy as np
from scipy.stats import multinomial

from .base import Property
from ...models.transition import TransitionModel
from ...types.array import Matrix, StateVector

[docs]class MarkovianTransitionModel(TransitionModel): r"""The transition model for categorical states This is a time invariant, transition model of a Markov process. A state space vector takes the form :math:`\alpha_t^i = P(\phi_t^i)`, representing a categorical distribution over a discrete, finite set of possible categories :math:`\Phi = \{\phi^m|m\in \mathbf{N}, m\le M\}` (for some finite :math:`M`). Models the transition from one category to another. Intended to be used in conjunction with the :class:`~.CategoricalState` type. """ transition_matrix: Matrix = Property( doc=r"Stochastic matrix :math:`F_t^{ij} = F^{ij} = P(\phi_t^i|\phi_{t-1}^j)` determining " r"the conditional probability that an object is category :math:`\phi^i` at 'time' " r":math:`t` given that it was category :math:`\phi^j` at 'time' :math:`t-1`. " r"Columns are normalised.") def __init__(self, *args, **kwargs): super().__init__(*args, **kwargs) # Normalise matrix columns self.transition_matrix = self.transition_matrix / np.sum(self.transition_matrix, axis=0)
[docs] def function(self, state, time_interval: timedelta = None, noise: bool = False, **kwargs): r"""Applies the linear transformation: .. math:: F^{ij}\alpha_{t-1}^j = P(\phi_t^i|\phi_{t-1}^j)P(\phi_t^j) The resultant vector is normalised. Though this model is time-invariant, a check is made to see whether the time-interval given is 0. In this instance, no transformation is applied. Parameters ---------- state: :class:`~.CategoricalState` The state to be transitioned. time_interval: datetime.timedelta Duration to transition state for. noise: bool Indicates whether transitioned vector is sampled from and the resultant category returned instead. This is a discrete category instead of a distribution over the state space. It is represented by an M-tuples, with all components equal to 0, except at an index corresponding to the relevant category. For example :math:`e^k` indicates that the category is :math:`\phi^k`. If `False`, the resultant distribution is returned. Returns ------- state_vector: :class:`stonesoup.types.array.StateVector` of shape (:py:attr:`~ndim_state, 1`). The resultant state vector of the transition. """ if time_interval is None or time_interval.total_seconds() == 0: return state.state_vector new_vector = self.transition_matrix @ state.state_vector new_vector = new_vector / np.sum(new_vector) # normalise if noise: rv = multinomial(n=1, p=new_vector.flatten()) return StateVector(rv.rvs(size=1, random_state=None)) else: return StateVector(new_vector)
@property def ndim_state(self): return self.transition_matrix.shape[1]
[docs] def rvs(self): raise NotImplementedError
[docs] def pdf(self): raise NotImplementedError