Introduce MarkovSequence (#646)

* Renamed _markov_process module to _markov

* Extract reusable information from Markov processes

* Distinguish MarkovSequence and MarkovProcess through transition types.

* Import Markov sequence into toplevel namespace

* Markov* inputs are keyword-only

* Raise TypeError if MarkovProcess and MarkovSequence are mixed up.

* moved sample_at_input to interface

* delete redundant tests for auxiliary functions

* Improved error messages.

* Unified the functionality of MarkovProcess and MarkovSequence for now

* Updated output of problem zoo

* Fixed tests

* Update EKF/UKF test to MarkovSequence interface

* Correct else-return

* Corrected string concatenation

* Rudimentary docstring for MarkovSequence

* Updated benchmarks to MarkovSequence where necessary

* Use MarkovSequence in docs

* Added an accidentally-deleted line back in.

* Make codecov ignore an exception branch

Co-authored-by: Marvin Pförtner <marvin.pfoertner@icloud.com>

Co-authored-by: Marvin Pförtner <marvin.pfoertner@icloud.com>

benchmarks/filtsmooth.py

@@ -42,7 +42,7 @@ def setup(self, linearization_implementation):
             regression_problem.locations
         )
 
-        prior_process = randprocs.markov.MarkovProcess(
+        prior_process = randprocs.markov.MarkovSequence(
             transition=linearized_dynmod,
             initrv=prior_process.initrv,
             initarg=regression_problem.locations[0],
@@ -93,7 +93,7 @@ def setup(self, linearization_implementation):
             regression_problem.locations
         )
 
-        prior_process = randprocs.markov.MarkovProcess(
+        prior_process = randprocs.markov.MarkovSequence(
             transition=linearized_dynmod,
             initrv=prior_process.initrv,
             initarg=regression_problem.locations[0],
@@ -160,7 +160,7 @@ def setup(self, linearization_implementation, num_samples):
             regression_problem.locations
         )
 
-        prior_process = randprocs.markov.MarkovProcess(
+        prior_process = randprocs.markov.MarkovSequence(
             transition=linearized_dynmod,
             initrv=prior_process.initrv,
             initarg=regression_problem.locations[0],

docs/source/tutorials/filtsmooth/discrete_linear_gaussian_filtering_smoothing.ipynb

@@ -217,7 +217,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "prior_process = randprocs.markov.MarkovProcess(\n",
+    "prior_process = randprocs.markov.MarkovSequence(\n",
     "    transition=dynamics_model, initrv=initial_state_rv, initarg=0.0\n",
     ")"
    ]

docs/source/tutorials/filtsmooth/discrete_nonlinear_gaussian_filtering_smoothing.ipynb

@@ -325,7 +325,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "prior_process = randprocs.markov.MarkovProcess(\n",
+    "prior_process = randprocs.markov.MarkovSequence(\n",
     "    transition=linearised_dynamics_model, initrv=initial_state_rv, initarg=0.0\n",
     ")"
    ]

docs/source/tutorials/filtsmooth/particle_filtering.ipynb

@@ -205,7 +205,7 @@
    "outputs": [],
    "source": [
     "num_particles = 20\n",
-    "prior_process = randprocs.markov.MarkovProcess(\n",
+    "prior_process = randprocs.markov.MarkovSequence(\n",
     "    transition=dynamics_model, initrv=initial_state_rv, initarg=0.0\n",
     ")\n",
     "importance_distribution = filtsmooth.particle.LinearizationImportanceDistribution.from_ekf(\n",

src/probnum/filtsmooth/_kalman_filter_smoother.py

@@ -203,23 +203,24 @@ def smooth_rts(
 
 def _setup_prior_process(F, L, m0, C0, t0, prior_model):
     zero_shift_prior = np.zeros(F.shape[0])
+    initrv = randvars.Normal(m0, C0)
+    initarg = t0
     if prior_model == "discrete":
         prior = randprocs.markov.discrete.LTIGaussian(
             transition_matrix=F,
             noise=randvars.Normal(mean=zero_shift_prior, cov=L),
         )
-    elif prior_model == "continuous":
+        return randprocs.markov.MarkovSequence(
+            transition=prior, initrv=initrv, initarg=initarg
+        )
+    if prior_model == "continuous":
         prior = randprocs.markov.continuous.LTISDE(
             drift_matrix=F, force_vector=zero_shift_prior, dispersion_matrix=L
         )
-    else:
-        raise ValueError
-    initrv = randvars.Normal(m0, C0)
-    initarg = t0
-    prior_process = randprocs.markov.MarkovProcess(
-        transition=prior, initrv=initrv, initarg=initarg
-    )
-    return prior_process
+        return randprocs.markov.MarkovProcess(
+            transition=prior, initrv=initrv, initarg=initarg
+        )
+    raise ValueError
 
 
 def _setup_regression_problem(H, R, observations, locations):

src/probnum/problems/zoo/filtsmooth/_filtsmooth_problems.py

@@ -125,7 +125,7 @@ def car_tracking(
     # Set up regression problem
     time_grid = np.arange(*timespan, step=step)
 
-    prior_process = randprocs.markov.MarkovProcess(
+    prior_process = randprocs.markov.MarkovSequence(
         transition=discrete_dynamics_model, initrv=initrv, initarg=time_grid[0]
     )
 
@@ -377,7 +377,7 @@ def dh(t, x):
 
     if initarg is None:
         initarg = time_grid[0]
-    prior_process = randprocs.markov.MarkovProcess(
+    prior_process = randprocs.markov.MarkovSequence(
         transition=dynamics_model, initrv=initrv, initarg=initarg
     )
 

src/probnum/randprocs/markov/__init__.py

@@ -6,15 +6,17 @@
 """
 
 from . import continuous, discrete, integrator, utils
-from ._markov_process import MarkovProcess
+from ._markov import MarkovProcess, MarkovSequence
 from ._transition import Transition
 
 # Public classes and functions. Order is reflected in documentation.
 __all__ = [
     "MarkovProcess",
+    "MarkovSequence",
     "Transition",
 ]
 
 # Set correct module paths. Corrects links and module paths in documentation.
 MarkovProcess.__module__ = "probnum.randprocs.markov"
+MarkovSequence.__module__ = "probnum.randprocs.markov"
 Transition.__module__ = "probnum.randprocs.markov"

src/probnum/randprocs/markov/_markov_process.py → src/probnum/randprocs/markov/_markov.py

@@ -7,48 +7,24 @@
 
 from probnum import _function, randvars, utils
 from probnum.randprocs import _random_process, kernels
-from probnum.randprocs.markov import _transition
+from probnum.randprocs.markov import _transition, continuous, discrete
 from probnum.typing import ShapeLike
 
 InputType = Union[np.floating, np.ndarray]
 OutputType = Union[np.floating, np.ndarray]
 
 
-class MarkovProcess(_random_process.RandomProcess):
-    r"""Random processes with the Markov property.
-
-    A Markov process is a random process with the additional property that
-    conditioned on the present state of the system its future and past states are
-    independent. This is known as the Markov property or as the process being
-    memoryless. A Markov process can be fully defined via an initial state and a
-    state transition.
-
-    Parameters
-    ----------
-    initarg
-        Initial starting input of the process.
-    initrv
-        Random variable describing the initial state.
-    transition
-        State transition of the system.
-
-    See Also
-    --------
-    RandomProcess : Random processes.
-    GaussianProcess : Gaussian processes.
-    """
-
+class _MarkovBase(_random_process.RandomProcess):
     def __init__(
         self,
-        initarg: np.ndarray,
+        *,
         initrv: randvars.RandomVariable,
         transition: _transition.Transition,
+        input_shape: ShapeLike = (),
     ):
-        self.initarg = initarg
         self.initrv = initrv
         self.transition = transition
 
-        input_shape = np.asarray(initarg).shape
         output_shape = initrv.shape
 
         super().__init__(
@@ -60,7 +36,7 @@ def __init__(
                 input_shape=input_shape,
                 output_shape=output_shape,
             ),
-            cov=MarkovProcess.Kernel(
+            cov=_MarkovBase.Kernel(
                 self.__call__,
                 input_shape=input_shape,
                 output_shape=2 * output_shape,
@@ -124,3 +100,68 @@ def _evaluate(self, x0: np.ndarray, x1: Optional[np.ndarray]) -> np.ndarray:
                 return self._markov_proc_call(args=x0).cov
 
             raise NotImplementedError
+
+
+class MarkovProcess(_MarkovBase):
+    r"""Random processes with the Markov property.
+
+    A Markov process is a random process with the additional property that
+    conditioned on the present state of the system its future and past states are
+    independent. This is known as the Markov property or as the process being
+    memoryless. A Markov process can be fully defined via an initial state and a
+    state transition.
+
+    Parameters
+    ----------
+    initarg
+        Initial starting input of the process.
+    initrv
+        Random variable describing the initial state.
+    transition
+        State transition of the system.
+
+    See Also
+    --------
+    RandomProcess : Random processes.
+    GaussianProcess : Gaussian processes.
+    """
+
+    def __init__(
+        self,
+        *,
+        initarg: np.ndarray,
+        initrv: randvars.RandomVariable,
+        transition: continuous.SDE,
+    ):
+        if not isinstance(transition, continuous.SDE):  # pragma: no cover
+            msg = "The transition is not continuous. Did you mean 'MarkovSequence'?"
+            raise TypeError(msg)
+
+        super().__init__(
+            initrv=initrv,
+            transition=transition,
+            input_shape=np.asarray(initarg).shape,
+        )
+        self.initarg = initarg
+
+
+class MarkovSequence(_MarkovBase):
+    """Discrete-time Markov processes."""
+
+    def __init__(
+        self,
+        *,
+        initarg: np.ndarray,
+        initrv: randvars.RandomVariable,
+        transition: continuous.SDE,
+    ):
+        if not isinstance(transition, discrete.NonlinearGaussian):  # pragma: no cover
+            msg = "The transition is not discrete. Did you mean 'MarkovProcess'?"
+            raise TypeError(msg)
+
+        super().__init__(
+            initrv=initrv,
+            transition=transition,
+            input_shape=np.asarray(initarg).shape,
+        )
+        self.initarg = initarg

src/probnum/randprocs/markov/integrator/_ioup.py

@@ -4,11 +4,11 @@
 import numpy as np
 
 from probnum import randvars
-from probnum.randprocs.markov import _markov_process, continuous
+from probnum.randprocs.markov import _markov, continuous
 from probnum.randprocs.markov.integrator import _integrator, _preconditioner
 
 
-class IntegratedOrnsteinUhlenbeckProcess(_markov_process.MarkovProcess):
+class IntegratedOrnsteinUhlenbeckProcess(_markov.MarkovProcess):
     r"""Integrated Ornstein-Uhlenbeck process.
 
     Convenience access to :math:`\nu` times integrated (:math:`d` dimensional)

src/probnum/randprocs/markov/integrator/_iwp.py

@@ -7,11 +7,11 @@
 import scipy.special
 
 from probnum import config, linops, randvars
-from probnum.randprocs.markov import _markov_process, continuous, discrete
+from probnum.randprocs.markov import _markov, continuous, discrete
 from probnum.randprocs.markov.integrator import _integrator, _preconditioner
 
 
-class IntegratedWienerProcess(_markov_process.MarkovProcess):
+class IntegratedWienerProcess(_markov.MarkovProcess):
     r"""Integrated Wiener process.
 
     Convenience access to :math:`\nu` times integrated (:math:`d` dimensional)

src/probnum/randprocs/markov/integrator/_matern.py

@@ -5,11 +5,11 @@
 import scipy.special
 
 from probnum import randvars
-from probnum.randprocs.markov import _markov_process, continuous
+from probnum.randprocs.markov import _markov, continuous
 from probnum.randprocs.markov.integrator import _integrator, _preconditioner
 
 
-class MaternProcess(_markov_process.MarkovProcess):
+class MaternProcess(_markov.MarkovProcess):
     r"""Matern process.
 
     Convenience access to (:math:`d` dimensional) Matern(:math:`\nu`) processes.

src/probnum/randprocs/markov/utils/_generate_measurements.py

@@ -2,12 +2,12 @@
 
 import numpy as np
 
-from probnum.randprocs.markov import _markov_process, _transition
+from probnum.randprocs.markov import _markov, _transition
 
 
 def generate_artificial_measurements(
     rng: np.random.Generator,
-    prior_process: _markov_process.MarkovProcess,
+    prior_process: _markov.MarkovProcess,
     measmod: _transition.Transition,
     times: np.ndarray,
 ):

tests/test_filtsmooth/test_gaussian/test_approx/_linearization_test_interface.py

@@ -84,7 +84,7 @@ def test_filtsmooth_pendulum(self, rng):
         )
 
         initrv = prior_process.initrv
-        prior_process = randprocs.markov.MarkovProcess(
+        prior_process = randprocs.markov.MarkovSequence(
             transition=ekf_dyna, initrv=initrv, initarg=regression_problem.locations[0]
         )
         method = filtsmooth.gaussian.Kalman(prior_process)