def add_MC_uncertainty(self, Markov_states, transition_matrix):
"""Add a Markov chain process.
Parameters
----------
Markov_states: list of matrix-like
Markov state spaces in each stage. The shape of matrix-like must be
(p,q) where q is the dimension index of the Markov chain and p is the
index of the Markov states
transition_matrix: list of matrix-like
Markov chain transition matrices in each stage. The shape of
must be compatible with the Markov states
start: start period (inclusive) of the Markov chain process
end: end period (exclusive) of the Markov chain process
The dimension of all entries in Markov states and transition matrices
must be in the form of: Markov_states: [1], [p_{1}], ... , [p_{T-1}]
transition_matrix: [[1]], [1,p_{1}], [p_{1},p_{2}], [p_{T-2},p_{T-1}]
where p_1,...p_{T-1} are integers.
Examples
--------
>>> add_MC_uncertainty(
... Markov_states=[[[0]],[[4],[6]],[[4],[6]]],
... transition_matrix=[
... [[1]],
... [[0.5,0.5]],
... [[0.3,0.7],[0.7,0.3]]
... ]
... )
Three dimensional Markov chain
>>> add_MC_uncertainty(
... Markov_states=[[[0]],[[4,6,5],[6,3,4]],[[4,6,5],[6,3,4]]],
... transition_matrix=[
... [[1]],
... [[0.5,0.5]],
... [[0.3,0.7],[0.7,0.3]]
... ]
... )
"""
if hasattr(self, "Markovian_uncertainty") or hasattr(
self, "Markov_states"):
raise ValueError("Markovian uncertainty has already added!")
info = check_Markov_states_and_transition_matrix(
Markov_states, transition_matrix, self.T)
self.dim_Markov_states, self.n_Markov_states = info
self.Markov_states = Markov_states
self.transition_matrix = [
numpy.array(item) for item in transition_matrix
]
self._type = 'Markov chain'
def add_MC_uncertainty(
self,
Markov_states,
transition_matrix
):
"""Add a Markov chain process.
Parameters
----------
Markov_states: list of array-like
Markov state spaces in each stage.
transition_matrix: list of matrix-like
Markov chain transition matrices in each stage.
start: start period (inclusive) of the Markov chain process
end: end period (exclusive) of the Markov chain process
The dimension of all entries in Markov states and transition matrices
must be in the form of:
Markov_states: [1], [p_{1}], ... , [p_{T-1}]
transition_matrix: [[1]], [1,p_{1}], [p_{1},p_{2}], [p_{T-2},p_{T-1}]
where p_1,...p_{T-1} are integers.
Examples
--------
Suppose there are three stages.
add_MC_uncertainty(
Markov_states=[
[0.2],
[0.3,0.5],
[0.4,0.6]
],
transition_matrix=[
[[1]],
[[0.2,0.8]],
[[0.6,0.4],[0.3,0.7]]
]
)
"""
if hasattr(self, "Markovian_uncertainty") or hasattr(self,"Markov_states"):
raise ValueError("Markovian uncertainty has already added!")
info = check_Markov_states_and_transition_matrix(
Markov_states, transition_matrix, self.T
)
self.dim_Markov_states,self.n_Markov_states = info
self.Markov_states = Markov_states
self.transition_matrix = transition_matrix
self._type = 'Markov chain'
def discretize(self,
n_samples=None,
random_state=None,
replace=True,
n_Markov_states=None,
method='SA',
n_sample_paths=None,
Markov_states=None,
transition_matrix=None,
int_flag=0):
"""Discretize Markovian continuous uncertainty by k-means or (robust)
stochasitic approximation.
Parameters
----------
n_samples: int, optional, default=None
number of i.i.d. samples to generate for stage-wise independent
randomness.
random_state: None | int | instance of RandomState, optional, default=None
If int, random_state is the seed used by the
random number generator;
If RandomState instance, random_state is the
random number generator;
If None, the random number generator is the
RandomState instance used by numpy.random.
replace: bool, optional, default=True
Indicates generating i.i.d. samples with/without replacement for
stage-wise independent randomness.
n_Markov_states: list | int, optional, default=None
If list, it specifies different dimensions of Markov state space
over time. Length of the list should equal length of the Markovian
uncertainty.
If int, it specifies dimensions of Markov state space.
Note: If the uncertainties are int, trained Markov states will be
rounded to integers, and duplicates will be removed. In such cases,
there is no guaranttee that the number of Markov states is n_Markov_states.
method: binary, optional, default=0
'input': the approximating Markov chain is given by user input (
through specifying Markov_states and transition_matrix)
'SAA': use k-means to train Markov chain.
'SA': use stochastic approximation to train Markov chain.
'RSA': use robust stochastic approximation to train Markov chain.
n_sample_paths: int, optional, default=None
number of sample paths to train the Markov chain.
Markov_states/transition_matrix: matrix-like, optional, default=None
The user input of approximating Markov chain.
"""
if n_samples is not None:
if isinstance(n_samples, (numbers.Integral, numpy.integer)):
if n_samples < 1:
raise ValueError("n_samples should be bigger than zero!")
n_samples = ([1] + [n_samples] * (self.T - 1))
elif isinstance(n_samples, (abc.Sequence, numpy.ndarray)):
if len(n_samples) != self.T:
raise ValueError(
"n_samples list should be of length {} rather than {}!"
.format(self.T, len(n_samples)))
if n_samples[0] != 1:
raise ValueError(
"The first stage model should be deterministic!")
else:
raise ValueError("Invalid input of n_samples!")
# discretize stage-wise independent continuous distribution
random_state = check_random_state(random_state)
for t in range(1, self.T):
self.models[t]._discretize(n_samples[t], random_state, replace)
if n_Markov_states is None and method != 'input': return
if method == 'input' and (Markov_states is None
or transition_matrix is None):
return
if n_Markov_states is not None:
if isinstance(n_Markov_states, (numbers.Integral, numpy.integer)):
if n_Markov_states < 1:
raise ValueError(
"n_Markov_states should be bigger than zero!")
n_Markov_states = ([1] + [n_Markov_states] * (self.T - 1))
elif isinstance(n_Markov_states, (abc.Sequence, numpy.ndarray)):
if len(n_Markov_states) != self.T:
raise ValueError(
"n_Markov_states list should be of length {} rather than {}!"
.format(self.T, len(n_Markov_states)))
if n_Markov_states[0] != 1:
raise ValueError(
"The first stage model should be deterministic!")
else:
raise ValueError("Invalid input of n_Markov_states!")
from msppy.discretize import Markovian
if method in ['RSA', 'SA', 'SAA']:
markovian = Markovian(
f=self.Markovian_uncertainty,
n_Markov_states=n_Markov_states,
n_sample_paths=n_sample_paths,
int_flag=int_flag,
)
if method in ['RSA', 'SA', 'SAA']:
self.Markov_states, self.transition_matrix = getattr(
markovian, method)()
elif method == 'input':
dim_Markov_states, n_Markov_states = (
check_Markov_states_and_transition_matrix(
Markov_states=Markov_states,
transition_matrix=transition_matrix,
T=self.T,
))
if dim_Markov_states != self.dim_Markov_states:
raise ValueError(
"The dimension of the given sample path " +
"generator is not the same as the given Markov chain " +
"approximation!")
self.Markov_states = Markov_states
self.transition_matrix = [
numpy.array(item) for item in transition_matrix
]
self._flag_discrete = 1
self.n_Markov_states = n_Markov_states
if method in ['RSA', 'SA', 'SAA']:
return markovian
