OOMpy a/k/a order-of-magnitude python

OOMpy is a python package for working with physical units and quantities. Unlike astropy it works in gaussian units, supports a multitude of physical dimensions, constants, and conversion between them (including vague conversions between incompatible units).

Installation

pip install oompy

Usage

Importing the main objects:

# import units and constants
from oompy import Units as u
from oompy import Constants as c

Simple manipulations and unit conversions

Several common usage examples:

# example #1
m_m87 = 6.5e9 * u.Msun
rg_m87 = c.G * m_m87 / c.c**2
rg_m87 >> 'au'
#       ^
#       |
# basic conversion
#
# Output: 64.16104122314108 au

# example #2
psr_bfield = 1e12 * u.G    # magnetic field in Gauss
gold_density = 19.3 * u.g / u.cm**3
((psr_bfield / c.c)**2).cgs
#                        ^
#                        |
#                 convert to cgs
#
# Output: 1112.6500560536185 g cm^-3
#
# equivalently:
((psr_bfield / c.c)**2).cgs >> "CGS"
#
# Output: 1112.6500560536185 g cm^-3
#
(psr_bfield / c.c)**2 / gold_density >> ""
#
# Output: 57.650261971690085

# example #3
gamma_factor = 1000
b_field = u.MG        # = Mega Gauss 
omega_B = (c.q_e * b_field / (c.m_e * c.c))
sync_omega = gamma_factor**2 * omega_B

c.hbar * sync_omega >> 'keV'
#                       ^
#                       |
#             understands prefixes for the powers of 10
#               (works from 1e-24 "y*" to 1e24 "Y*")
#
# Output: 11.576759893742388 keV

# example #4
# compare physical quantities in arbitrary units
(c.R_sun >> 'ly') == c.R_sun # True
c.M_sun < (c.m_e >> "lb") # False
c.R_sun >= (c.m_e >> "lb") # Error: incompatible units

# example #5
# formatting
print (f"rest-mass energy of an electron is {c.m_e * c.c**2 >> 'MeV':.2f}")
#
# Output: rest-mass energy of an electron is 0.51 MeV

# example #6
# get the reduced physical type of the quantity (i.e., dimension in base units)
# can be utilized for further parsing, integration to other APIs, etc.
~(c.hbar * sync_omega)
#
# Output: {<Type.MASS: 3>: Fraction(1, 1), <Type.LENGTH: 1>: Fraction(2, 1), <Type.TIME: 2>: Fraction(-2, 1)}

To see all units and/or constants:

u.all
c.all

Create your own quantities:

from oompy import Quantity
# example #7
my_speed = Quantity('25 m sec^-1')
#                      ^
#                      |
#                 as a string
rabbit_speed = Quantity(55, 'mi hr^-1')
#                         ^
#                         |
#                     as a tuple
elephant_speed = Quantity('km hr^-1')
(elephant_speed * my_speed / rabbit_speed) >> 'ly Gyr^-1'
#                                                  ^
#                                                  |
#                                           converts lightyear per Gigayear :)
#
# Output: 0.9421232705492877 ly Gyr^-1
#
# more concise way:
rabbit_speed2 = 55 * u.mi / u.hr

Vague conversions

This technique enables a comparison between incompatible units under certain assumptions. For instance, one might assume that we consider a photon, and thus its energy, wavelength and frequency are connected via c and h.

from oompy import Assumptions as assume, Quantity

# uses h
freq = 5 * u.GHz
freq >> assume.Light >> "cm"
#
# Output: 5.995849160000001 cm

# uses h-bar as freq has a dimension of radians per second
freq = 2 * c.pi * u.rad / u.sec
freq >> assume.Light >> "eV"
#
# Output: 4.1356667496413186e-15 eV

# temperature to/from energy
10000 * u.K >> assume.Thermal >> "eV"
#
# Output: 0.8617339407568576 eV

# compute co-moving distance for a redshift
Quantity(5, "") >> assume.Redshift >> "Gly"
#
# Output: 25.878013331255335 Gly
#
# compute redshift for a co-moving distance
5 * u.Gpc >> assume.Redshift >> ""
#
# Output: 1.8018944589315433

To list all the available assumptions:

list(assume)

Matplotlib and numpy support

One can combine dimensional quantities into arrays or lists and plot them using matplotlib:

import numpy as np
import matplotlib.pyplot as plt

# call this function to enable matplotlib support
from oompy import matplotlib_support
matplotlib_support()

ms = np.logspace(0, 2, 2) * u.Msun
rs = [10 * u.cm, 2.5 * u.ft]
#            ^           ^
#       can have different units

plt.plot(rs, ms)

For developers

Testing the code is done in three steps using black to check the formatting, mypy to check the types and typehints, and pytest to run the tests. First install all the dependencies:

pip install -r requirements.txt

Then run the tests one-by-one:

black oompy --check --diff
mypy oompy
pytest

Build the new version of the package using:

python -m build --sdist --outdir dist .

The same tests are also run automatically on every commit using GitHub Actions.

To do

• add more units & constants
  • (added in v1.3.5) knots
  • (added in v1.4.1) Rsun
  • (added in v1.4.1) fathom
  • (added in v1.4.1) nautical miles
  • (added in v2.0.0) Amps, Coulombs, Teslas (for conversion only)
• (added in v1.1.0) comparison of quantities (==, !=, >, <, >=, <=)
• (added in v1.1.0) conversion with an rshift (>>) operator
• (added in v1.1.0) base unit extraction (with ~)
• (added in v1.2.0) add a possibility to perform vague conversions (e.g. Kelvin to eV, Hz to erg) etc.
• (added in v1.3.0) unit tests
• add support for Ki, Mi, Gi (2e10, 2e20, 2e30)
• (added in v1.3.5) distance to redshift vague conversion
• (added in v1.4.0) work with numpy arrays
  • (added in v1.4.1) additional tests for numpy arrays
  • (added in v2.0.0) numpy array multiplication works both ways
• (added in v2.0.0) matplotlib support
• (added in v2.0.0) add formatting and TeX support
• add a way to work with scaling relations
• (added in v1.4.1) add __format__ for Quantity objects