Fixed the line-too-long message for all modules under `probnum.lina…

…lg` subpackage. (#696)

* Fixed the `line-too-long` message for all modules under `probnum.linalg` subpackage.

* stopped ignoring the `line-too-long` issue for pylint checks by changing config in `tox.ini`.

* reduced lengths of all lines in `probnum.linalg` to under 88 in response to the failed pylint checks.

* Fixed minor formatting problems to fix `black` and `readthedocs` error messages.

* Fixed minor formatting problems in response to `black` error message.

* reformatted code using `black`

* disabled `line-too-long` check for `_probabilistic_linear_solver.py`

* Fixed formatting error in `_probabilistic_linear_solver.py`

* Added indentation in multi-line docstrings.

Co-authored-by: Qingxuan Wu <qingxuan.wu1@gmail.com>
Co-authored-by: Jonathan Wenger <jonathan.wenger@uni-tuebingen.de>

src/probnum/linalg/_bayescg.py

@@ -24,7 +24,8 @@ def bayescg(
     Parameters
     ----------
     A
-        *shape=(n, n)* -- A symmetric positive definite matrix (or linear operator). Only matrix-vector products :math:`Av` are used internally.
+        *shape=(n, n)* -- A symmetric positive definite matrix (or linear operator).
+        Only matrix-vector products :math:`Av` are used internally.
     b
         *shape=(n, )* -- Right-hand side vector.
     x0

src/probnum/linalg/solvers/_probabilistic_linear_solver.py

@@ -3,6 +3,8 @@
 Iterative probabilistic numerical methods solving linear systems :math:`Ax = b`.
 """
 
+# pylint: disable=line-too-long
+
 from __future__ import annotations
 
 from typing import Generator, Optional, Tuple
@@ -63,7 +65,8 @@ class ProbabilisticLinearSolver(
     See Also
     --------
     ~probnum.linalg.problinsolve : Solve linear systems in a Bayesian framework.
-    ~probnum.linalg.bayescg : Solve linear systems with prior information on the solution.
+    ~probnum.linalg.bayescg : Solve linear systems with prior information on the
+        solution.
 
     Examples
     --------
@@ -143,7 +146,8 @@ def solve_iterator(
         Parameters
         ----------
         prior
-            Prior belief about the quantities of interest :math:`(x, A, A^{-1}, b)` of the linear system.
+            Prior belief about the quantities of interest :math:`(x, A, A^{-1}, b)` of
+            the linear system.
         problem
             Linear system to be solved.
         rng
@@ -187,7 +191,8 @@ def solve(
         Parameters
         ----------
         prior
-            Prior belief about the quantities of interest :math:`(x, A, A^{-1}, b)` of the linear system.
+            Prior belief about the quantities of interest :math:`(x, A, A^{-1}, b)` of
+            the linear system.
         problem
             Linear system to be solved.
         rng
@@ -197,7 +202,9 @@ def solve(
         -------
         belief
             Posterior belief :math:`(\mathsf{x}, \mathsf{A}, \mathsf{H}, \mathsf{b})`
-            over the solution :math:`x`, the system matrix :math:`A`, its (pseudo-)inverse :math:`H=A^\dagger` and the right hand side :math:`b`.
+            over the solution :math:`x`, the system matrix :math:`A`, its
+            (pseudo-)inverse :math:`H=A^\dagger` and the right hand side
+            :math:`b`.
         solver_state
             Final state of the solver.
         """
@@ -247,7 +254,8 @@ class ProbabilisticKaczmarz(ProbabilisticLinearSolver):
 
     Probabilistic analogue of the (randomized) Kaczmarz method [1]_ [2]_, taking prior
     information about the solution and randomly choosing rows of the matrix :math:`A_i`
-    and entries :math:`b_i` of the right-hand-side to obtain information about the solution.
+    and entries :math:`b_i` of the right-hand-side to obtain information about
+    the solution.
 
     Parameters
     ----------
@@ -257,9 +265,12 @@ class ProbabilisticKaczmarz(ProbabilisticLinearSolver):
     References
     ----------
     .. [1] Kaczmarz, Stefan, Angenäherte Auflösung von Systemen linearer Gleichungen,
-        *Bulletin International de l'Académie Polonaise des Sciences et des Lettres. Classe des Sciences Mathématiques et Naturelles. Série A, Sciences Mathématiques*, 1937
+        *Bulletin International de l'Académie Polonaise des Sciences et des
+        Lettres. Classe des Sciences Mathématiques et Naturelles. Série A,
+        Sciences Mathématiques*, 1937
     .. [2] Strohmer, Thomas; Vershynin, Roman, A randomized Kaczmarz algorithm for
-        linear systems with exponential convergence, *Journal of Fourier Analysis and Applications*, 2009
+        linear systems with exponential convergence, *Journal of Fourier Analysis and
+        Applications*, 2009
     """
 
     def __init__(
@@ -278,8 +289,9 @@ def __init__(
 class MatrixBasedPLS(ProbabilisticLinearSolver):
     r"""Matrix-based probabilistic linear solver.
 
-    Probabilistic linear solver updating beliefs over the system matrix and its
-    inverse. The solver makes use of prior information and iteratively infers the matrix and its inverse by matrix-vector multiplication.
+    Probabilistic linear solver updating beliefs over the system matrix and its inverse.
+    The solver makes use of prior information and iteratively infers the matrix and
+    its inverse by matrix-vector multiplication.
 
     This code implements the method described in Wenger et al. [1]_.
 
@@ -313,7 +325,9 @@ def __init__(
 class SymMatrixBasedPLS(ProbabilisticLinearSolver):
     r"""Symmetric matrix-based probabilistic linear solver.
 
-    Probabilistic linear solver updating beliefs over the symmetric system matrix and its inverse. The solver makes use of prior information and iteratively infers the matrix and its inverse by matrix-vector multiplication.
+    Probabilistic linear solver updating beliefs over the symmetric system matrix and
+    its inverse. The solver makes use of prior information and iteratively infers the
+    matrix and its inverse by matrix-vector multiplication.
 
     This code implements the method described in Wenger et al. [1]_.
 
@@ -339,6 +353,8 @@ def __init__(
         super().__init__(
             policy=policy,
             information_op=information_ops.MatVecInformationOp(),
-            belief_update=belief_updates.matrix_based.SymmetricMatrixBasedLinearBeliefUpdate(),
+            belief_update=(
+                belief_updates.matrix_based.SymmetricMatrixBasedLinearBeliefUpdate()
+            ),
             stopping_criterion=stopping_criterion,
         )

src/probnum/linalg/solvers/_state.py

@@ -16,10 +16,13 @@
 class LinearSolverState:
     """State of a probabilistic linear solver.
 
-    The solver state separates the state of a probabilistic linear solver from the algorithm itself, making the solver stateless.
-    The state contains the problem to be solved, the current belief over the quantities of interest and any miscellaneous quantities
-    computed during an iteration of a probabilistic linear solver. The solver state is passed between the different components of the
-    solver and may be used internally to cache quantities which are used more than once.
+    The solver state separates the state of a probabilistic linear solver from the
+    algorithm itself, making the solver stateless.
+    The state contains the problem to be solved, the current belief over the quantities
+    of interest and any miscellaneous quantities computed during an iteration of
+    a probabilistic linear solver.
+    The solver state is passed between the different components of the solver and
+    may be used internally to cache quantities which are used more than once.
 
     Parameters
     ----------

src/probnum/linalg/solvers/belief_updates/_linear_solver_belief_update.py

@@ -12,7 +12,8 @@
 class LinearSolverBeliefUpdate(abc.ABC):
     r"""Belief update for the quantities of interest of a linear system.
 
-    Given a solver state containing information about the linear system collected in the current step, update the belief about the quantities of interest.
+    Given a solver state containing information about the linear system collected
+    in the current step, update the belief about the quantities of interest.
     """
 
     @abc.abstractmethod

src/probnum/linalg/solvers/belief_updates/matrix_based/_matrix_based_linear_belief_update.py

@@ -10,9 +10,14 @@
 
 
 class MatrixBasedLinearBeliefUpdate(LinearSolverBeliefUpdate):
-    r"""Gaussian belief update in a matrix-based inference framework assuming linear information.
+    r"""Gaussian belief update in a matrix-based inference framework assuming
+    linear information.
 
-    Updates the belief over the quantities of interest of a linear system :math:`Ax=b` given matrix-variate Gaussian beliefs with Kronecker covariance structure and linear observations :math:`y=As`. The belief update computes :math:`p(M \mid y) = \mathcal{N}(M; M_{i+1}, V \otimes W_{i+1})`, [1]_ [2]_ such that
+    Updates the belief over the quantities of interest of a linear system :math:`Ax=b`
+    given matrix-variate Gaussian beliefs with Kronecker covariance structure and
+    linear observations :math:`y=As`.
+    The belief update computes :math:`p(M \mid y) = \mathcal{N}(M; M_{i+1},
+    V \otimes W_{i+1})`, [1]_ [2]_ such that
 
     .. math ::
         \begin{align}
@@ -60,7 +65,9 @@ def _matrix_based_update(
         """Matrix-based inference update for linear information."""
         if not isinstance(matrix.cov, linops.Kronecker):
             raise ValueError(
-                f"Covariance must have Kronecker structure, but is '{type(matrix.cov).__name__}'."
+                f"""Covariance must have Kronecker structure, but is
+                '{type(matrix.cov).__name__}'.
+                """
             )
 
         pred = matrix.mean @ action

src/probnum/linalg/solvers/belief_updates/matrix_based/_symmetric_matrix_based_linear_belief_update.py

@@ -10,13 +10,19 @@
 
 
 class SymmetricMatrixBasedLinearBeliefUpdate(LinearSolverBeliefUpdate):
-    r"""Symmetric Gaussian belief update in a matrix-based inference framework assuming linear information.
+    r"""Symmetric Gaussian belief update in a matrix-based inference framework assuming
+    linear information.
 
-    Updates the belief over the quantities of interest of a linear system :math:`Ax=b` given symmetric matrix-variate Gaussian beliefs with symmetric Kronecker covariance structure and linear observations. The belief update computes :math:`p(M \mid y) = \mathcal{N}(M; M_{i+1}, W_{i+1} \otimes_s W_{i+1})`, [1]_ [2]_ such that
+    Updates the belief over the quantities of interest of a linear system :math:`Ax=b`
+    given symmetric matrix-variate Gaussian beliefs with symmetric Kronecker covariance
+    structure and linear observations.
+    The belief update computes :math:`p(M \mid y) = \mathcal{N}(M; M_{i+1}, W_{i+1}
+    \otimes_s W_{i+1})`, [1]_ [2]_ such that
 
     .. math ::
         \begin{align}
-            M_{i+1} &= M_i + (y - M_i s) u^\top + u (y - M_i s)^\top - u s^\top(y - M_i s)u^\top,\\
+            M_{i+1} &= M_i + (y - M_i s) u^\top + u (y - M_i s)^\top
+            - u s^\top(y - M_i s)u^\top,\\
             W_{i+1} &= W_i - W_i s (s^\top W_i s)^\dagger s^\top W_i.
         \end{align}
 
@@ -61,7 +67,9 @@ def _symmetric_matrix_based_update(
         """Symmetric matrix-based inference update for linear information."""
         if not isinstance(matrix.cov, linops.SymmetricKronecker):
             raise ValueError(
-                f"Covariance must have symmetric Kronecker structure, but is '{type(matrix.cov).__name__}'."
+                f"""Covariance must have symmetric Kronecker structure, but
+                is'{type(matrix.cov).__name__}'.
+                """
             )
 
         pred = matrix.mean @ action

src/probnum/linalg/solvers/belief_updates/solution_based/_projected_residual_belief_update.py

@@ -13,12 +13,18 @@
 class ProjectedResidualBeliefUpdate(LinearSolverBeliefUpdate):
     r"""Gaussian belief update given projected residual information.
 
-    Updates the belief over the quantities of interest of a linear system :math:`Ax=b` given a Gaussian belief over the solution :math:`x` and information of the form :math:`s\^top r_i = s^\top (b - Ax_i) = s^\top A (x - x_i)`. The belief update computes the posterior belief about the solution, given by :math:`p(x \mid y) = \mathcal{N}(x; x_{i+1}, \Sigma_{i+1})`, such that
+    Updates the belief over the quantities of interest of a linear system :math:`Ax=b`
+    given a Gaussian belief over the solution :math:`x` and information of the form
+    :math:`s\^top r_i = s^\top (b - Ax_i) = s^\top A (x - x_i)`.
+    The belief update computes the posterior belief about the solution, given by
+    :math:`p(x \mid y) = \mathcal{N}(x; x_{i+1}, \Sigma_{i+1})`, such that
 
     .. math ::
         \begin{align}
-            x_{i+1} &= x_i + \Sigma_i A^\top s (s^\top A \Sigma_i A^\top s + \lambda)^\dagger s^\top r_i,\\
-            \Sigma_{i+1} &= \Sigma_i - \Sigma_i A^\top s (s^\top A \Sigma_i A s + \lambda)^\dagger s^\top A \Sigma_i,
+            x_{i+1} &= x_i + \Sigma_i A^\top s (s^\top A \Sigma_i A^\top s +
+            \lambda)^\dagger s^\top r_i,\\
+            \Sigma_{i+1} &= \Sigma_i - \Sigma_i A^\top s (s^\top A \Sigma_i A s +
+            \lambda)^\dagger s^\top A \Sigma_i,
         \end{align}
 
     where :math:`\lambda` is the noise variance.

src/probnum/linalg/solvers/beliefs/_linear_system_belief.py

@@ -1,7 +1,7 @@
 """Linear system belief.
 
-Class defining a belief about the quantities of interest of a linear system such as its
-solution or the matrix inverse and any associated hyperparameters.
+Class defining a belief about the quantities of interest of a linear system such
+as its solution or the matrix inverse and any associated hyperparameters.
 """
 
 from functools import cached_property
@@ -16,13 +16,13 @@ class LinearSystemBelief:
     r"""Belief about quantities of interest of a linear system.
 
     Random variables :math:`(\mathsf{x}, \mathsf{A}, \mathsf{H}, \mathsf{b})`
-    modelling the solution :math:`x`, the system matrix :math:`A`, its (pseudo-)inverse
-    :math:`H=A^{\dagger}` and the right hand side :math:`b` of a linear system :math:`Ax=b`,
-    as well as any associated hyperparameters.
+    modelling the solution :math:`x`, the system matrix :math:`A`, its
+    (pseudo-)inverse :math:`H=A^{\dagger}` and the right hand side :math:`b` of
+    a linear system :math:`Ax=b`, as well as any associated hyperparameters.
 
-    For instantiation either a belief about the solution or the inverse and right hand side
-    must be provided. Note that if both are specified, their consistency is not checked and
-    depending on the algorithm either may be used.
+    For instantiation either a belief about the solution or the inverse and right
+    hand side must be provided. Note that if both are specified, their consistency
+    is not checked and depending on the algorithm either may be used.
 
     Parameters
     ----------
@@ -56,14 +56,17 @@ def __init__(
         def dim_mismatch_error(**kwargs):
             argnames = list(kwargs.keys())
             return ValueError(
-                f"Dimension mismatch. The shapes of {argnames[0]} : {kwargs[argnames[0]].shape} "
+                f"Dimension mismatch. The shapes of {argnames[0]} :\
+                {kwargs[argnames[0]].shape} "
                 f"and {argnames[1]} : {kwargs[argnames[1]].shape} must match."
             )
 
         if x is not None:
             if x.ndim > 2 or x.ndim < 1:
                 raise ValueError(
-                    f"Belief over solution must have either one or two dimensions, but has {x.ndim}."
+                    f"""Belief over solution must have either one or two dimensions,
+                     but has {x.ndim}.
+                    """
                 )
             if A is not None:
                 if A.shape[1] != x.shape[0]:
@@ -79,7 +82,9 @@ def dim_mismatch_error(**kwargs):
         if Ainv is not None:
             if Ainv.ndim != 2:
                 raise ValueError(
-                    f"Belief over the inverse system matrix may have at most two dimensions, but has {Ainv.ndim}."
+                    f"""Belief over the inverse system matrix may have at most two
+                     dimensions, but has {Ainv.ndim}.
+                     """
                 )
             if A is not None:
                 if A.shape != Ainv.shape:
@@ -88,7 +93,9 @@ def dim_mismatch_error(**kwargs):
         if A is not None:
             if A.ndim != 2:
                 raise ValueError(
-                    f"Belief over the system matrix may have at most two dimensions, but has {A.ndim}."
+                    f"""Belief over the system matrix may have at most two dimensions
+                    , but has {A.ndim}.
+                    """
                 )
             if b is not None:
                 if A.shape[0] != b.shape[0]:
@@ -97,24 +104,34 @@ def dim_mismatch_error(**kwargs):
         if b is not None:
             if b.ndim > 2 or b.ndim < 1:
                 raise ValueError(
-                    f"Belief over right-hand-side may have either one or two dimensions but has {b.ndim}."
+                    f"""Belief over right-hand-side may have either one or two
+                    dimensions but has {b.ndim}.
+                     """
                 )
 
         if x is not None and not isinstance(x, randvars.RandomVariable):
             raise TypeError(
-                f"The belief about the solution 'x' must be a RandomVariable, but is {type(x)}."
+                f"""The belief about the solution 'x' must be a RandomVariable, but
+                 is {type(x)}.
+                """
             )
         if A is not None and not isinstance(A, randvars.RandomVariable):
             raise TypeError(
-                f"The belief about the matrix 'A' must be a RandomVariable, but is {type(A)}."
+                f"""The belief about the matrix 'A' must be a RandomVariable, but
+                 is {type(A)}.
+                """
             )
         if Ainv is not None and not isinstance(Ainv, randvars.RandomVariable):
             raise TypeError(
-                f"The belief about the inverse matrix 'Ainv' must be a RandomVariable, but is {type(Ainv)}."
+                f"""The belief about the inverse matrix 'Ainv' must be a RandomVariable,
+                 but is {type(Ainv)}.
+                """
             )
         if b is not None and not isinstance(b, randvars.RandomVariable):
             raise TypeError(
-                f"The belief about the right-hand-side 'b' must be a RandomVariable, but is {type(b)}."
+                f"""The belief about the right-hand-side 'b' must be a RandomVariable,
+                 but is {type(b)}.
+                """
             )
 
         self._x = x

src/probnum/linalg/solvers/information_ops/__init__.py

@@ -4,7 +4,8 @@
 by observing the numerical problem to be solved given an action. When solving
 linear systems, the information operator takes an action vector and observes
 the tuple :math:`(A, b)`, returning an observation vector. For example, one might
-observe the right hand side :math:`y = b^\top s = (Ax)^\top s` with the action :math:`s`.
+observe the right hand side :math:`y = b^\top s = (Ax)^\top s` with the action
+:math:`s`.
 """
 
 from ._linear_solver_information_op import LinearSolverInformationOp

src/probnum/linalg/solvers/information_ops/_linear_solver_information_op.py

@@ -9,12 +9,14 @@
 class LinearSolverInformationOp(abc.ABC):
     r"""Information operator of a (probabilistic) linear solver.
 
-    For a given action, the information operator collects information about the linear system to be solved.
+    For a given action, the information operator collects information about the
+    linear system to be solved.
 
     See Also
     --------
     MatVecInformationOp: Collect information via matrix-vector multiplication.
-    ProjectedResidualInformationOp: Collect information via a projection of the current residual.
+    ProjectedResidualInformationOp: Collect information via a projection of the
+        current residual.
     """
 
     @abc.abstractmethod

src/probnum/linalg/solvers/information_ops/_projected_residual.py

@@ -9,13 +9,17 @@
 class ProjectedResidualInformationOp(LinearSolverInformationOp):
     r"""Projected residual information operator.
 
-    Obtain information about a linear system by projecting the residual :math:`b-Ax_{i-1}` onto a given action :math:`s_i` resulting in :math:`s_i \mapsto s_i^\top r_{i-1} = s_i^\top (b - A x_{i-1}) = s_i^\top A (x - x_{i-1})`.
+    Obtain information about a linear system by projecting the residual
+    :math:`b-Ax_{i-1}` onto a given action :math:`s_i` resulting in :math:`s_i
+    \mapsto s_i^\top r_{i-1} = s_i^\top (b - A x_{i-1}) = s_i^\top
+    A (x - x_{i-1})`.
     """
 
     def __call__(
         self, solver_state: "probnum.linalg.solvers.LinearSolverState"
     ) -> np.ndarray:
-        r"""Projected residual :math:`s_i^\top r_{i-1} = s_i^\top (b - A x_{i-1})` of the linear system.
+        r"""Projected residual :math:`s_i^\top r_{i-1} = s_i^\top (b - A x_{i-1})`
+        of the linear system.
 
         Parameters
         ----------