Adding to the API Documentation

Documentation is an integral part of every collaborative software project. Good documentation not only encourages users of the package to try out different functionalities, but it also makes maintaining and expanding code significantly easier. Every code contribution to the package must come with appropriate documentation of the API. This guide details how to do this.


The main form of documentation are docstrings, multi-line comments beneath a class or function definition with a specific syntax, which detail its functionality. This package uses the NumPy docstring format. As a rule, all functions which are exposed to the user must have appropriate docstrings. Below is an example of a docstring for a probabilistic numerical method.

[ ]:
# %load -r 1-163 ../../../src/probnum/linalg/
"""Probabilistic numerical methods for solving linear systems.

This module provides routines to solve linear systems of equations in a
Bayesian framework. This means that a prior distribution over elements
of the linear system can be provided and is updated with information
collected by the solvers to return a posterior distribution.

import warnings
from typing import Callable, Dict, Optional, Tuple, Union

import numpy as np
import scipy.sparse

import probnum  # pylint: disable=unused-import
from probnum import linops, randvars, utils
from probnum.linalg.solvers.matrixbased import SymmetricMatrixBasedSolver
from probnum.typing import LinearOperatorArgType

# pylint: disable=too-many-branches

def problinsolve(
    A: Union[
    b: Union[np.ndarray, "randvars.RandomVariable[np.ndarray]"],
    A0: Optional[
    ] = None,
    Ainv0: Optional[
    ] = None,
    x0: Optional[Union[np.ndarray, "randvars.RandomVariable[np.ndarray]"]] = None,
    assume_A: str = "sympos",
    maxiter: Optional[int] = None,
    atol: float = 10 ** -6,
    rtol: float = 10 ** -6,
    callback: Optional[Callable] = None,
) -> Tuple[
    r"""Solve the linear system :math:`A x = b` in a Bayesian framework.

    Probabilistic linear solvers infer solutions to problems of the form

    .. math:: Ax=b,

    where :math:`A \in \mathbb{R}^{n \times n}` and :math:`b \in \mathbb{R}^{n}`.
    They return a probability measure which quantifies uncertainty in the output arising
    from finite computational resources or stochastic input. This solver can take prior
    information either on the linear operator :math:`A` or its inverse :math:`H=A^{
    -1}` in the form of a random variable ``A0`` or ``Ainv0`` and outputs a posterior
    belief about :math:`A` or :math:`H`. This code implements the method described in
    Wenger et al. [1]_ based on the work in Hennig et al. [2]_.

    A :
        *shape=(n, n)* -- A square linear operator (or matrix). Only matrix-vector
        products :math:`v \mapsto Av` are used internally.
    b :
        *shape=(n, ) or (n, nrhs)* -- Right-hand side vector, matrix or random
        variable in :math:`A x = b`.
    A0 :
        *shape=(n, n)* -- A square matrix, linear operator or random variable
        representing the prior belief about the linear operator :math:`A`.
    Ainv0 :
        representing the prior belief about the inverse :math:`H=A^{-1}`. This can be
        viewed as a preconditioner.
    x0 :
        *shape=(n, ) or (n, nrhs)* -- Prior belief for the solution of the linear
        system. Will be ignored if ``Ainv0`` is given.
    assume_A :
        Assumptions on the linear operator which can influence solver choice and
        behavior. The available options are (combinations of)

         generic matrix       ``gen``
         symmetric            ``sym``
         positive definite    ``pos``
         (additive) noise     ``noise``

    maxiter :
        Maximum number of iterations. Defaults to :math:`10n`, where :math:`n` is the
        dimension of :math:`A`.
    atol :
        Absolute convergence tolerance.
    rtol :
        Relative convergence tolerance.
    callback :
        User-supplied function called after each iteration of the linear solver. It is
        called as ``callback(xk, Ak, Ainvk, sk, yk, alphak, resid, **kwargs)`` and can
        be used to return quantities from the iteration. Note that depending on the
        function supplied, this can slow down the solver considerably.
    kwargs : optional
        Optional keyword arguments passed onto the solver iteration.

    x :
        Approximate solution :math:`x` to the linear system. Shape of the return matches
        the shape of ``b``.
    A :
        Posterior belief over the linear operator.
    Ainv :
        Posterior belief over the linear operator inverse :math:`H=A^{-1}`.
    info :
        Information on convergence of the solver.

        If size mismatches detected or input matrices are not square.
        If the matrix ``A`` is singular.
        If an ill-conditioned input ``A`` is detected.

    For a specific class of priors the posterior mean of :math:`x_k=Hb` coincides with
    the iterates of the conjugate gradient method. The matrix-based view taken here
    recovers the solution-based inference of :func:`bayescg` [3]_.

    .. [1] Wenger, J. and Hennig, P., Probabilistic Linear Solvers for Machine Learning,
       *Advances in Neural Information Processing Systems (NeurIPS)*, 2020
    .. [2] Hennig, P., Probabilistic Interpretation of Linear Solvers, *SIAM Journal on
       Optimization*, 2015, 25, 234-260
    .. [3] Bartels, S. et al., Probabilistic Linear Solvers: A Unifying View,
       *Statistics and Computing*, 2019

    See Also
    bayescg : Solve linear systems with prior information on the solution.

    >>> import numpy as np
    >>> np.random.seed(1)
    >>> n = 20
    >>> A = np.random.rand(n, n)
    >>> A = 0.5 * (A + A.T) + 5 * np.eye(n)
    >>> b = np.random.rand(n)
    >>> x, A, Ainv, info = problinsolve(A=A, b=b)
    >>> print(info["iter"])

General Rules

  • Cover Parameters, Returns, Raises and Examples, if applicable, in every publicly visible docstring—in that order.

  • Examples are tested via doctest. Ensure doctest does not fail by running the test suite.

  • Include appropriate References, in particular for probabilistic numerical methods.

  • Do not use docstrings as a clutch for spaghetti code!


  • Parameter types are automatically documented via type hints in the function signature.

  • Always provide shape hints for objects with a .shape attribute in the following form:

arr :
    *(shape=(m, ) or (m, n))* -- Parameter array of an example function.
  • Hyperparameters should have default values and explanations on how to choose them.

  • For callables provide the expected signature as part of the docstring: foobar(x, y, z, \*\*kwargs). Backslashes remove semantic meaning from special characters.


  • Stick to the imperative style of writing in the docstring header (i.e.: first line).

  • Yes: “Compute the value”.

  • No: “This function computes the value / Let’s compute the value”.

The rest of the explanation talks about the function, e. g. “This function computes the value by computing another value”. - Use full sentences inside docstrings when describing something. - Yes: “This value is irrelevant, because it is not being passed on” - No: “Value irrelevant, not passed on”. - When in doubt, more explanation rather than less. A little text inside an example can be helpful, too. - A little maths can go a long way, but too much usually adds confusion.

Interface Documentation

Which functions and classes actually show up in the documentation is determined by an __all__ statement in the corresponding file inside a module. The order of this list is also reflected in the documentation. For example, linalg has the following

[ ]:
# %load ../../../src/probnum/linalg/
"""Linear Algebra.

This package implements probabilistic numerical methods for the solution
of problems arising in linear algebra, such as the solution of linear
systems :math:`Ax=b`.
from probnum.linalg._problinsolve import bayescg, problinsolve

# Public classes and functions. Order is reflected in documentation.
__all__ = [

# Set correct module paths. Corrects links and module paths in documentation.
problinsolve.__module__ = "probnum.linalg"
bayescg.__module__ = "probnum.linalg"

If you are documenting a subclass, which has a different path in the file structure than the import path due to __all__ statements, you can correct the links to superclasses in the documentation via the .__module__ attribute.


ProbNum uses Sphinx to parse docstrings in the codebase automatically and to create its API documentation. You can configure Sphinx itself or its extensions in the ./docs/ file.

from IPython.display import Image

display(Image(filename="../assets/img/developer_guides/sphinx_logo.png", embed=True))

ProbNum makes use of a number of Sphinx plugins to improve the API documentation, for example to parse this Jupyter notebook. The full list of used packages can be found in ./docs/sphinx-requirements.txt and ./docs/notebook-requirements.txt.

Building and Viewing the Documentation

In order to build the documentation locally and view the HTML version of the API documentation, simply run:

tox -e docs



cd docs
make clean
make html
