Style Guide

This style guide summarizes code conventions used in ProbNum. This is intended as a reference for developers.

ProbNum uses *Black*‘s formatting ruleset, which can be viewed as a strict subset of PEP 8, and we recommend *Black* for automated code formatting.

With respect to code style, the Google Python Style Guide should be applied with some notable additions and exceptions (i.e. docstrings, …). We summarize and expand on this style guide below.



Use absolute imports over relative imports.

  • import x for importing packages and modules.

  • from x import y where x is the package prefix and y is the module name with no prefix.

  • from x import y as z if two modules named y are to be imported or if y is an inconveniently long name.

  • import y as z only when z is a standard abbreviation (e.g. np for numpy).

Use __all__ = [...] in files to fix the order in which the methods are visible in the documentation. This also avoids importing unnecessary functions via import statements from ... import *. Many classes and functions are “pulled up” to a higher-level namespace via __init__. py files. Import from there wherever there is no chance for confusion and/or circular imports. This makes imports more readable. When changing the namespace of classes make sure to to correct module paths in the documentation by adding SuperClass.__module__ = "probnum.module" to the corresponding __init.py__.


If imports are shortened, the following conventions should be used. Full import paths are always acceptable.

  • import probnum as pn

  • from probnum import randvars, linalg, diffeq, statespace

An exception from these rules are type-related modules, which include typing and probnum.type. Types are always imported directly.

  • from typing import Optional, Callable

  • from probnum.type import FloatArgType

Please do not abbreviate import paths unnecessarily. We do not use the following imports:

  • import probnum.random_variables as pnrv or import probnum.filtsmooth as pnfs (correct would be from probnum import randvars, filtsmooth)

  • from probnum import random_variables as rvs or import probnum.random_variables as rvs (the randvars name is sufficiently short and does not need to be abbreviated)

While all of these rules obey the Google Python Style Guide, we use one import convention that deviates from this guide. If two objects (functions, classes) share the same namespace (i.e. RandomVariable and Normal are both imported via probnum.randvars, but their implementation is in different files, randvars/ and randvars/ and one object needs to be imported into the module of the other object, use relative imports. For instance, in randvars/ the import reads

  • from ._randomvariables import RandomVariable

which helps with making the code in Normal more compact and readable.

Type Standardization

Many types representing numeric values, shapes, dtypes, random states, etc. have different possible representations. For example a shape could be specified in the following ways: n, (n,), (n, 1), [n], [n, 1].

For this reason most types should be standardized internally to a core set of types defined in probnum.type, e.g. for numeric types np.generic, np.ndarray. Methods for input argument standardization can be found in probnum.utils.argutils.


The package itself is written “ProbNum” except when referred to as a package import, then probnum should be used.

Classes, Functions, Methods and Variables

  • joined_lower for functions, methods, attributes, variables

  • joined_lower or ALL_CAPS for constants

  • StudlyCaps for classes

  • camelCase only to conform to pre-existing conventions, e.g. in unittest

Probabilistic Numerical Methods

Function names and signatures of PN methods attempt to replicate numpy or scipy naming conventions. For example

  • probsolve_ivp(...) (scipy: solve_ivp(...))

  • problinsolve(...) (scipy: linalg.solve(...))

Methods with “Bayesian” in the name come with the prefix bayes, e.g. bayesquad; Bayesian quadrature, BayesFilter; Bayesian filter, BayesSmoother; Bayesian smoother.

Printable Representations

The way an object is represented in the console or printed is defined by the following functions:

  • repr(obj) is defined by obj.__repr__() and should return a developer-friendly representation of obj. If possible, this should be code that can recreate obj.

  • str(obj) is defined by obj.__str__() and should return a user-friendly representation of obj. If no .__str__() method is implemented, Python will fall back to the .__repr__() method.

As an example consider numpy‘s array representation

array([[1, 0],
       [0, 1]])

versus its output of str.

[[1 0]
 [0 1]]

Notational Conventions

Stick to the first few letters for abbreviations if they are sufficiently descriptive:

  • cov: covariance

  • fun: function

  • mat: matrix

  • vec: vector

  • arr: array; wherever applicable, specify vec or mat

Further conventions are

  • unit2unit: convert between types or units, e.g. mat2arr: convert matrix to array or s2ms: convert seconds to milliseconds. Can also be used for simple adapter methods, along the lines of filt2odefilt.

  • proj: projection (if required: projmat, projvec, projlinop, …)

  • precon: preconditioner

  • driftmat: drift-matrix, forcevec: force-vector, dispmat dispersion-matrix, dynamicsmat dynamics-matrix, diffmat diffusion-matrix, plus the respective driftmatfun, driftfun, dispmatfun, etc.

  • inv*: for inverse of a matrix; e.g. invprecond, invcovmat, …

  • optional arguments via **kwargs, e.g.: fun(t, x, **kwargs)

  • msg: message, e.g. for issuing raising and warnings (errmsg, warnmsg)

  • rv: random variable; if concatenated with e.g. init, abbreviate to initrv (initial random variable)

  • data: data (don’t abbreviate that one)

  • functions/methods that do something from time t0 to time t1 with step size h use the signature (start, stop, step, **kwargs) or any corresponding subset of that. This is in line with np.arange for instance. Use it like (start=t0, stop=t1, step=h, **kwargs).

  • jacob: Jacobian, if necessary use jacobfun. Hessians are hess, respectively hessfun.

  • param(s): parameter(s). If abbreviations are necessary (e.g. in inline-function definition, use par(s)).

  • Indices via idx (either idx1, idx2, … or idx, jdx, kdx) and not via i, j, k. The former is more readable (and follows PEP8); the latter may collide with the built-in imaginary constant j=sqrt(-1).

  • A function maps from its domain to its range. The range of a random variable is the domain of its distribution.

  • Whenever a time-grid is searched for the nearest neighbour of a location (e.g. used in continuous-time evaluation of a Gauss-Markov posterior), consider using np.searchsorted(..., side="left") (which is the default configuration). This is how it is done everywhere in statespace, filtsmooth, and diffeq.

Errors and Warnings

  • Stick to the built-in python exceptions (TypeError, NotImplementedError, …)

  • If dunder method is not implemented for a type, return NotImplemented

  • Warnings via warnings.warn(). See or

  • Recall the difference between TypeError and ValueError

    • TypeError Passing arguments of the wrong type (e.g. passing a list when an int is expected) should result in a TypeError. Example: float(['5 ']) since a list cannot be converted to float.

    • ValueError: Raised when a built-in operation or function receives an argument that has the right type but an inappropriate value. Example: The float function can take a string, i.e. float('5'), but float('string') fails since 'string' is a non-convertible string.

Package Structure

Modules and Folders

  • low (shortened lower caps) for modules/folders in the namespace, e.g. probnum.linalg.linops

  • lower for modules/folders not in the namespace, e.g. probnum/linalg/linearsolvers. Rule of thumb: the more low-level the module is, the longer (more descriptive) the file name can be, because the chances that access is provided through higher-level namespaces are rather high.

Interfaces to PN methods should be in a separate module, while their implementation (in classes) is in the same folder in other files.


All documentation is written in American English. Every publicly visible class or function must have a docstring. Do not use extensive documentation as a clutch for spaghetti code – divide and conquer instead!