format_multiple_errors

A small library intended to make it easy to format numbers like

$$1.623(11)({}^{3}_{4})\times 10^{-7}$$

or

$$(6.829 \pm 0.013 {}^{+0.104}_{-0.096})\times10^{5}$$

Installation

To install the bare library, open a terminal and run:

pip install format-multiple-errors

If you will be formatting tables, additional dependencies are required. To install these, instead run

pip install format-multiple-errors[tables]

Usage as a library

Formatting numbers

The format_multiple_errors package provides a function to format numbers, also named format_multiple_errors.

from format_multiple_errors import format_multiple_errors

This function takes a central value, and zero or more uncertainties. It returns a string containing all numbers formatted to the same absolute precision.

Uncertainties may be single numbers:

>>> format_multiple_errors(1, 0.1, 0.2)
'1.00 ± 0.10 ± 0.20'

or they may also be tuples of two numbers, representing the upper and lower error respectively:

>>> format_multiple_errors(1, 0.1, (0.2, 0.3))
'1.00 ± 0.10 (+0.20 / -0.30)'

A number of keyword arguments control the formatting. The abbreviate option uses the compact form of expressing errors:

>>> format_multiple_errors(1.001, 0.010, (0.020, 0.034), abbreviate=True)
'1.001(10)(+20 / -34)'

The latex option uses LaTeX macros rather than Unicode characters, and generally formats the result for inclusion in a LaTeX document:

>>> format_multiple_errors(1.001, 0.010, (0.020, 0.034), latex=True)
'1.001 \\pm 0.010 {}^{+0.020}_{-0.034}'

Numbers are formatted by default with leading or trailing zeroes. To use exponential notation instead, use the exponential parameter:

>>> format_multiple_errors(0.00123, 0.00045, (0.00067, 0.00089), exponential=True)
'(1.23 ± 0.45 (+0.67 / -0.89))e-3'

By default the precision is controlled by setting the number of significant digits presented for the smallest uncertainty. Setting length_control="central" instead controls the significant digits of the central value:

>>> format_multiple_errors(1.0, 0.1, (0.2, 0.3), length_control="central")
'1.0 ± 0.1 (+0.2 / -0.3)'

The number of significant figures presented can be controlled with the significant_figures parameter:

>>> format_multiple_errors(1.001, 0.001, (0.002, 0.0034), significant_figures=1)
'1.001 ± 0.001 (+0.002 / -0.003)'

These options may be combined:

>>> format_multiple_errors(123.45, 3.14, (2.82, 12.91), length_control="central", significant_figures=5, latex=True, abbreviate=True, exponential=True)
'1.2345(314)({}^{282}_{1291}) \\times 10^{2}'

Other options for length_control are:

• "largest": controls the significant digits of the largest uncertainty
• "decimal_places": instead sets the absolute number of decimal places, which must be non-negative.

Formatting DataFrames

The library provides two functions for working with Pandas DataFrames.

The format_column_errors function accepts and returns columns. For example, it can take pd.Series objects:

>>> import pandas as pd
>>> from format_multiple_errors import format_column_errors
>>> df = pd.DataFrame([{"a": 3.14, "b": 0.59, "c": 0.26}, {"a": 2.17, "b": 0.82, "c":   0.81}])
>>> format_column_errors(df["a"], (df["b"], df["c"]), abbreviate=True)
0    3.14(+59/-26)
1    2.17(+82/-81)
dtype: object

It can also take a pd.DataFrame and specifications of the column names to use:

>>> format_column_errors("a", ("b", "c"), df=df, abbreviate=True)
0    3.14(+59/-26)
1    2.17(+82/-81)
dtype: object

Interaction with pyerrors and uncertainties

If the central value passed to format_multiple_errors already has an uncertainty, due to being an instance of pyerrors.Obs or uncertainties.UFloat, then this is prepended to the list of errors. For example,

>>> from uncertainties import ufloat
>>> result = ufloat(1.01, 0.1)
>>> systematic = (0.2, 0.34)
>>> format_multiple_errors(result, systematic)
'1.01 ± 0.10 (+0.20 / -0.34)'

Instances of pyerrors.Obs must already have an uncertainty computed (must have had the .gamma_method() method called on them) before being passed to format_multiple_errors, otherwise an error is raised.

Command-line interface

A command-line interface is also provided. To format a single number, use the format_multiple_errors format command:

$ format_multiple_errors --abbreviate format 3.141 0.059 0.026,0.053
3.141(59)(+26/-53)

To format a CSV as a LaTeX table, use the format_multiple_errors table command:

$ format_multiple_errors --latex --abbreviate table input.csv \
> a b c_value,c_error d_value,d_upper-d_lower,d_systematic \
> --headings '$a$' '$b$' '$c$' '$d$' --output_file output.tex
$ cat output.tex
\begin{tabular}{rrll}
\toprule
$a$ & $b$ & $c$ & $d$ \\
\midrule
3 & 1 & $4.16(26)$ & $3.59({}^{79}_{24})(46)$ \\
2 & 7 & $1.83(18)$ & $8.459({}^{45}_{235})(360)$ \\
\bottomrule
\end{tabular}

Formatting options are specified before the subcommand (format or table). Options specific to the command are specified afterwards.

Development

To be able to run the test suite, create a virtual environment using the tooling of your choice, and then install the developer dependencies:

pip install -r requirements_dev.txt

The test suite can then be run by calling

pytest

Before committing, you should ensure that the repository's pre-commit hooks are installed:

pre-commit install

Then some basic code quality checks will be run by Git before it accepts your commit.