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Read and compare numerical data against reference data using exact, fuzzy or custom comparison operations. Simplify your regression testing pipeline.

Project description

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Project Status: Active – The project has reached a stable, usable state and is being actively developed. Test Pipelines. Coverage Report. API Documentation. Code style: black

fieldcompare is a Python package with command-line interface (CLI) that can be used to compare datasets for (fuzzy) equality. It was designed mainly to serve as a tool to realize regression tests for research software, and in particular research software that deals with numerical simulations. In regression tests, the output of a software is compared to reference data that was produced by the same software at an earlier time, in order to detect if changes to the code cause unexpected changes to the behavior of the software.

Simulations typically produce discrete field data defined on computational grids, and there exists a variety of standard and widely-used file formats. fieldcompare supports a number of VTK file formats out-of-the box, a variety of further formats can be used with the help of meshio. Besides mesh files, csv files are also supported, a format that is widely used in simulation frameworks to write out secondary data such as e.g. error norms and convergence rates.

Independent of the file type and format, fieldcompare reads all fields from those files and allows you to then check all entries of the fields for equality with custom absolute and relative tolerances. Programmatically, you can provide and use custom predicates (e.g. "smaller-than"), while the CLI is currently hardwired to (fuzzy) equality checks, which is the most common use case.

A common issue with regression testing of grid files is that the grid may be written with a different ordering of points or cells, while the actual field data on the grid may be the same. To this end, fieldcompare provides the option to make the fields read from a grid unique by sorting the grid by its point coordinates and cell connectivity. Moreover, one can choose to strip ghost points from the grid from that may occur, for instance, when merging the data from multiple grid partitions distributed over different processors.

GitHub Action

If you want to perform regression tests within your GitHub workflow, check out our fieldcompare action, which allows you to do so with minimal effort.

Getting started

Quick start

You can easily install fieldcompare through pip:

pip install fieldcompare[all]

Using the CLI, you can now compare data fields of tabular data (e.g. CSV) against reference data:

echo -e "0.0,0.0\n1.0,1.0\n2.0,2.0\n" > file1.csv
echo -e "0.0,0.0\n1.0,1.0\n2.0,2.001\n" > file2.csv
fieldcompare file file1.csv file1.csv
fieldcompare file file2.csv file1.csv
fieldcompare file file2.csv file1.csv --relative-tolerance 1e-2

In the same way, you can compare data fields in mesh files (e.g. data mapped on an unstructured grid VTK file format):

wget -O mesh1.vtu
wget -O mesh2.vtu
fieldcompare file mesh1.vtu mesh1.vtu
fieldcompare file mesh2.vtu mesh2.vtu

The default comparison scheme allows for small differences in the fields. Specifically, if the shape of the fields match, given a relative tolerance of $\rho$ and an absolute tolerance of $\epsilon$, two fields of floating-point values will be found equal if for each pair of scalar values $a$ and $b$ the following condition holds (for more details on fuzzy comparisons, see below):

\vert a - b \vert \leq max(\rho \cdot max(\vert a \vert, \vert b \vert), \epsilon)

If the field consist of strings or integers, all entries of the fields are compared for exact equality. Note that per default, $\epsilon = 0$, but it can be defined via the command line interface. Many more options are available and can be listed via:

fieldcompare file --help
fieldcompare dir --help

There is also a Python API to customize your comparisons with fieldcompare, see the examples below and/or the API Documentation.


As mentioned before, you can install fieldcompare simply via pip

pip install fieldcompare[all]

The suffix [all] instructs pip to also install all optional dependencies (for instance meshio). Omit this suffix if you want to install only the required dependencies.

For an installation from a local copy, navigate to the top folder of this repository and type

pip install .       # minimum installation
pip install .[all]  # full installation with all dependencies

To install the latest development version you can also install fieldcompare via pip directly from the git repository:

pip install "git+[all]

Command-line interface

The CLI exposes two subcommands, namely file and dir, where the former is used to compare two files for equality, and the latter can be used to compare all files with matching names in two given directories. That is, type


to compare two files, and


for comparing two directories. The latter command will scan both folders for files with matching names, and then run a file comparison on pairs of matching files. This can be useful if your simulation produces a number of files for which you have references stored in some reference folder, and you want to compare them all in a single command. For more info on the CLI options available, type in

fieldcompare file --help
fieldcompare dir --help

API and examples

The following code snippet reads the fields from two files (assuming their format is supported) and prints a message depending on if the success of their comparison:

from fieldcompare import FieldDataComparator
from import read_field_data

fields1 = read_field_data("FILENAME1")
fields2 = read_field_data("FILENAME2")
comparator = FieldDataComparator(fields1, fields2)

result = comparator()
if result:
    print("Comparison PASSED")
    print(f"Comparison failed, report: '{}'")

There are many more options you may use, and infos you can collect on performed comparisons. In the folder examples/api you can find examples with instructions on how to use the API of fieldcompare. For more details, have a look at the API Documentation.

Contribution Guidelines

Contributions are highly welcome! For bug reports, please file an issue. If you want to contribute with features, improvements or bug fixes please fork this project and open a merge request into the main branch of this repository.

Development and test suite

The test suite is automated through tox. To run all tests and linters run


This runs tox with several different environments. To only test under a specfific environment use the tox option -e. For example, to test under Python 3.9

tox -e py39

All developer dependencies are listed in requirements.txt and can be installed by

pip install -r requirements.txt

fieldcompare uses the auto-formatting tool black, the linter flake8, and we check type hints with the static type checker mypy. When running tox, all these checks are performed.

The main developer branch is main and release versions are tagged and deployed to PyPI in an automated CI/CD pipeline. Deployment is triggered whenever the package version in pyproject.toml is increased and the change is merged to main.


fieldcompare is licensed under the terms and conditions of the GNU General Public License (GPL) version 3 or - at your option - any later version. The GPL can be read online or in the LICENSE.txt file in this repository. See LICENSE.txt for full copying permissions.

The fuzzy details

Fuzziness is crucial when comparing fields of floating-point values, which are unlikely to be bit-wise identical to a reference solution when computed on different machines and/or after slight modifications to the code. The equation for fuzzy equality as was shown above is implemented in the FuzzyEquality predicate of fieldcompare, which is the default predicate for fields that contain floating-point values.

Per default, the FuzzyEquality predicate uses an absolute tolerance of $\epsilon = 0$, which means that each pair of scalars is tested by a relative criterion. The default relative tolerance depends on the data type and is chosen as ulp(1.0), where ulp refers to the unit of least precision. These are rather strict default values that were selected to minimize the chances of false positives when using fieldcompare without any tolerance settings. Generally, the tolerances should be carefully chosen for the context at hand.

A common issue, in particular in numerical simulations, is that the values in a field may span over several orders of magnitude, which possibly has a negative impact on the precision one can expect from the smaller values. For such scenarios, a suitable choice for the absolute tolerance $\epsilon$ comes into play, which can help to avoid false negatives from comparing the small values in a field, as $\epsilon$ defines a lower bound for the allowed difference between field values. This is illustrated in the plots below, which visualize the pairs of values $(a, b)$ that evaluate fuzzy-equal for different tolerances.

Custom $\epsilon$ Default $\epsilon$

In the figures, $b_{min}$ and $b_{max}$ show the minimum and maximum values that are fuzzy-equal to a given value $a$. As can be seen, while for $\epsilon = 0$ the allowed difference between values goes down to zero as $a \rightarrow 0$, a constant residual difference is allowed for small values of $a$ in the case of $\epsilon > 0$. A suitable choice for $\epsilon$ depends on the fields to be compared, and when comparing a large number of fields, it can be cumbersome to define $\epsilon$ for all of them. We found that a useful heuristic is to define $\epsilon$ as a fraction of the maximum absolute value of both fields as an estimate for the precision that can be expected from the smaller values. Using the fieldcompare API, this can be achieved with the ScaledTolerance class, which is accepted by all interfaces receiving tolerances. An example of this is shown below, where we use the predicate_selector argument of FieldDataComparator to pass in a customized FuzzyEquality:

from fieldcompare import FieldDataComparator
from import read_field_data
from fieldcompare.predicates import FuzzyEquality, ScaledTolerance

assert FieldDataComparator(
    predicate_selector=lambda _, __: FuzzyEquality(

With the above code, the absolute tolerance is computed for a pair of fields $f_1$ and $f_2$ via $\epsilon = max(mag(f_1), mag(f_2)) \cdot 10^{-12}$, where mag estimates the magnitude as the maximum absolute scalar value in a field. In the CLI, this functionality is exposed via the following syntax:

fieldcompare file test_mesh.vtu \
                  test_mesh_permutated.vtu \
                  -atol 1e-12*max

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