def __init__(self, matrix: Sequence[Sequence[float]],
safe: bool = False,
tol: float = 1e-3):
"""
Constructor of a continuous time Markov chain.
Parameters
----------
matrix : 2-D array_like
An infinitesimal matrix (chain generator).
safe : bool, optional
Flag indicating the matrix is safe to use. If `False` (default),
no validation or attempts to fix will be performed.
tol : float, optional
Tolerance used when fixing broken infinitesimal generator matrix.
If `safe = True` is set, this field is ignored. Default: 1e-3.
"""
need_copy = False
if not isinstance(matrix, np.ndarray):
matrix = np.asarray(matrix)
else:
need_copy = True
if not safe and not is_infinitesimal(matrix):
matrix = fix_infinitesimal(matrix, tol=tol)[0]
need_copy = False
self._matrix = matrix if not need_copy else matrix.copy()
self._order = order_of(matrix)
def __init__(self, matrix: Union[Sequence[Sequence[float]], np.ndarray],
safe: bool = False, tol: float = 1e-3):
"""
Discrete time Markov chain constructor.
Parameters
----------
matrix : 2-D array_like
Transition matrix. If `safe = False` it is checked to be stochastic
and, if check fails, attempt to fix it with `fix_stochastic()`
call is made. When fixing, use tolerance `tol`.
safe : bool, optional
Flag indicating whether there is no need to validate matrix.
Default: `False`.
tol : float, optional
Tolerance used when fixing broken transition matrix.
If `safe = True` is set, this field is ignored. Default: 1e-3.
"""
if not isinstance(matrix, np.ndarray):
matrix = np.asarray(matrix)
else:
matrix = matrix.copy() # copy to avoid side-effects
if not is_square(matrix):
raise MatrixShapeError('(N, N)', matrix.shape, 'transition matrix')
if not safe and not is_stochastic(matrix):
matrix = fix_stochastic(matrix, tol=tol)[0]
self._matrix = matrix
self._order = order_of(matrix)
def __init__(self, matrix, check=True, tol=1e-8, dtype=None):
if check:
if not is_infinitesimal(matrix, tol, tol):
raise ValueError("not infinitesimal matrix")
self._matrix = np.asarray(matrix, dtype=dtype)
self._order = order_of(self._matrix)
self.__cache__ = {}
def test_order_of_numpy_lists(self):
self.assertEqual(qumo.order_of(self.l1), 1)
self.assertEqual(qumo.order_of(self.l2), 2)
self.assertEqual(qumo.order_of(self.l11), 1)
self.assertEqual(qumo.order_of(self.l12), 2)
self.assertEqual(qumo.order_of(self.l21), 2)
self.assertEqual(qumo.order_of(self.l22), 2)
with self.assertRaises(ValueError):
qumo.order_of(self.l23)
def test_order_of_ndarray(self):
self.assertEqual(qumo.order_of(self.m1), 1)
self.assertEqual(qumo.order_of(self.m2), 2)
self.assertEqual(qumo.order_of(self.m11), 1)
self.assertEqual(qumo.order_of(self.m12), 2)
self.assertEqual(qumo.order_of(self.m21), 2)
self.assertEqual(qumo.order_of(self.m22), 2)
with self.assertRaises(ValueError):
qumo.order_of(self.m23)
def f(x, subgenerator, pmf0):
pmf0 = np.asarray(pmf0)
ones = np.ones(shape=(order_of(subgenerator)))
s = np.asarray(subgenerator)
if 0 <= x < np.inf:
return pmf0.dot(linalg.expm(x * s)).dot(-s).dot(ones)
else:
return 0.0
def order(self):
return order_of(self.D0)
def __init__(self,
d0: Union[np.ndarray, Sequence[Sequence[float]]],
d1: Union[np.ndarray, Sequence[Sequence[float]]],
safe: bool = False,
tol: float = 1e-3,
factory: RandomsFactory = None):
"""
Create MAP process with the given D0 and D1 matrices.
If `safe = False` is set (this is default), we validate matrices
D0 and D1. These matrices must comply three requirements:
1) Sum `D0 + D1` must be an infinitesimal matrix
2) All elements of D1 must be non-negative
3) All elements of D0 except the main diagonal must be non-negative
To avoid problems with "1e-12 is not zero", constructor accepts
parameters `tol` (tolerance). If matrices D0 and D1 fail the check,
it tries to fix them using `fix_markovian_arrival()` call with this
tolerance.
Sometimes it is useful to avoid matrices validation (e.g., when MAP
matrices are obtained as a result of another computation). To disable
validation, set `safe = True`.
Parameters
----------
d0 : array_like
Matrix D0, it must be subinfinitesimal
d1 : array_like
Matrix D1, all its elements must be non-negative
safe : bool, optional
Flag indicating whether not to validate or try to fix matrices D0
and D1 if they don't satisfy requirements. By default, `False`.
tol : float, optional
If `safe = False` and matrices D0 and D1 violate requirements,
try to fix errors those are less then `tol`. If `safe = True`
this parameter is ignored. Default: 1e-3.
"""
super().__init__(factory)
need_copy = [False, False]
matrices = [d0, d1]
for i in range(2):
if not isinstance(matrices[i], np.ndarray):
matrices[i] = np.asarray(matrices[i])
else:
need_copy[i] = True
if not safe and not check_markovian_arrival(matrices):
matrices, _ = fix_markovian_arrival(matrices, tol=tol)
# Since matrices are re-built, no need to copy them:
for i in range(2):
need_copy[i] = False
# Copy matrices if needed:
for i in range(2):
if need_copy[i]:
matrices[i] = matrices[i].copy()
# Extract matrices:
self._matrices = tuple(matrices)
self._generator = sum(self._matrices)
self._order = order_of(self._matrices[0])
self._inv_d0 = np.linalg.inv(self._matrices[0])
# Since we will use Mmap for data generation, we need to generate
# special matrices for transitions probabilities and rates.
# 1) We need to store rates (we will use them when choosing random
# time we spend in the state):
self._rates = -self._matrices[0].diagonal()
# 2) Then, we need to store cumulative transition probabilities P.
# We store them in a stochastic matrix of shape N x (K*N):
# P[I, J] is a probability, that:
# - new state will be J (mod N), and
# - if J < N, then no packet is generated, or
# - if J >= N, then packet of type J // N is generated.
# self._trans_pmf = np.hstack((
# self._matrices[0] + np.diag(self._rates),
# self._matrices[1]
# )) / self._rates[:, None]
# Build embedded DTMC and CTMC:
self._ctmc = ContinuousTimeMarkovChain(self._generator, safe=True)
self._dtmc = DiscreteTimeMarkovChain(-self._inv_d0.dot(self.d1),
safe=True)
self._states = [
Exponential(rate, factory=factory) for rate in self._rates
]