Package: numericalunits
Package homepage at PyPI–Source code at github–
Written bySteve ByrnesThis package implements units and dimensional analysis in an unconventional
way that has the following unique advantages:Compatible with everything:Compatible with virtually any numerical
calculation routine, including numpy and scipy, and even including routines
not written in Python! That means, for example, if you have a decades-old
closed-source C routine for numerical integration, you can pass it a
quantity with units of velocity and an integration range with units of
time, and the final answer will magically have units of distance. This
extreme compatibility is possible because if the variablexrepresents
a quantity with dimensions (like “3.3 kg”),xis actually stored
internally as an ordinary floating-point number. The dimension is
encoded in the value as a multiplicative factor. When two numbers are
multiplied, their dimensions are automatically multiplied, and so on.Modular and non-intrusive:When you input data, you say what units
they are in. When you display results, you say what units you want to
display them in. These steps are very little trouble, and in fact help you
create nice, self-documenting code. Other than that, you have to do nothing
at all to pass dimensionful quantities into and out of any already-written
programs or routines.Powerful tool for debugging:Notallcalculation mistakes cause
violations of dimensional analysis, butmostdo–for example, if you
accidentally multiply two lengths instead of adding them, the result will
have the wrong dimension. If you use this package, it will alert you to
these sorts of mistakes.Zero storage overheadZero calculation overheadThese great features come with the disadvantage that the interface is lessslickthan other unit packages. If you have a quantity with units, you
cannot directly see what the units are. You are supposed to already know
what the units are, and then the package will tell you whether you made a
mistake. Even worse, you only get alerted to the mistake after running a
calculation all the way through twice.Therefore the package isnotsuggested for students exploring how units work.
Itissuggested for engineering and science professionals who want to make
their code more self-documenting and self-debugging.InstallationYou can install from PyPI:pip install numericalunitsAlternatively—since it’s a single module that requires no setup or
compilation—you can downloadnumericalunits.pyfromPyPIorgithuband use it directly.Usage and examplesTo assign a unit to a quantity,multiplyby the unit, e.g.my_length = 100 * mm. (In normal text you would write “100 mm”, but
unfortunately Python does not have “implied multiplication”.)To express a dimensionful quantity in a certain unit,divideby that unit,
e.g. when you seemy_length / cm, you pronounce it “my_length expressed
in cm”.Unit errors, like trying to add a length to a mass, will notimmediatelyannounce themselves as unit errors. Instead, you need to run the whole
calculation twice (in a new Python session each time). If you get the
same final answers both times, then congratulations, all your calculations
are almost guaranteed to pass dimensional analysis! If you get different
answers every time you run, then you made a unit error! It is up to you to
figure out where and what the error is.Example 1:What is 5 mL expressed in cubic nanometers?:from numericalunits import mL, nm
x = 5 * mL  # "Read: x is equal to 5 milliliters"
print(x / nm**3)   # "Read: x expressed in cubic nanometers is..." --> 5e21Example 2:An electron is in a 1e5 V/cm electric field. What is its
acceleration? (Express the answer in m/sÂ².)from numericalunits import V, cm, e, me, m, s
Efield = 1e5 * (V / cm)
force = e * Efield # (e is the elementary charge)
accel = force / me # (me is the electron mass)
print(accel / (m / s**2)) # Answer --> 1.7588e18Example 3:You measured a voltage as a function of the position of dial:
10 volts when the dial is at 1cm, 11 volts when the dial is at 2cm, etc.
etc. Interpolate from this data to get the expected voltage when the dial is
at 41mm, and express the answer in mV.from numericalunits import cm, V, mm, mV
from numpy import array
from scipy.interpolate import interp1d
voltage_data = array([[1 * cm, 10 * V],
                      [2 * cm, 11 * V],
                      [3 * cm, 13 * V],
                      [4 * cm, 16 * V],
                      [5 * cm, 18 * V]])
f = interp1d(voltage_data[:,0], voltage_data[:,1])
print(f(41 * mm) / mV) # Answer --> 16200Example 4:A unit mistake … what is 1 cm expressed in atmospheres?from numericalunits import cm, atm
print((1 * cm) / atm) # --> a randomly-varying number
# The answer randomly varies every time you run this (in a new Python
# session), indicating that you are violating dimensional analysis.How it worksA complete set of independent base units (meters, kilograms, seconds,
coulombs, kelvins) are defined as randomly-chosen positive floating-point
numbers. All other units and constants are defined in terms of those. In a
dimensionally-correct calculation, the units all cancel out, so the final
answer is deterministic, not random. In a dimensionally-incorrect
calculations, there will be random factors causing a randomly-varying final
answer.Included units and constantsIncludes a variety of common units, both SI and non-SI, everything from
frequency to magnetic flux. Also includes common physical constants like
Planck’s constant and the speed of light. Browse the source code to see a
complete list. It is very easy to add in any extra units and constants that
were left out.NotesNotes on implementation and useWhat does it mean to “run the calculation again in a new Python
session?”You know that you’ve started a new Python session if all
the variable definitions have been forgotten. Three examples: In Spyder, each “Console”
tab is its own session. In Jupyter, make a new Python session by selecting
“Restart kernel”. From the command line, each time you typepython blah.py, you are opening a new Python session.For little, self-contained calculations (a few lines that are all within a
single module), it is possible to check the units without opening a new Python
session: Run the functionnumericalunits.reset_units()at the beginning of
the calculation before any variables are defined; then check for
dimensional errors by re-running the whole calculation (including thereset_units()part). Note that if you are usingfrom-style imports,
likefrom numericalunits import cm, you need to put themafterreset_units()in the code.While debugging a program, it may be annoying to have intermediate values
in the calculation that randomly vary every time you run the program. In
this case, you can usereset_units('SI')instead of the normalreset_units(). This puts all dimensionful variables in standard (MKS)
SI units: All times are in seconds, all lengths are in meters, all forces
are in newtons, etc. Alternatively,reset_units(123)uses123as
the seed for the random-number generator. Obviously, in these modes, you
willnotget any indication of dimensional-analysis errors. As above,
if you are going to use any version ofreset_units(), make sure you do
it before any dimensionful variable is defined in any module.There are very rare, strange cases where the final answer does not seem to
randomly vary even though there was a dimensional-analysis violation: For
example, the expression(1 +1e-50* cm / atm)fails dimensional
analysis, so if you calculate it the answer is randomly-varying. But, it is
only randomly varying around the 50th decimal point, so the variation is
hidden from view. You would not notice it as an error.Since units are normal Pythonfloat-type numbers, they follow the normal
casting rules. For example,2 * cmis a pythonfloat, not anint.
This is usually what you would want and expect.You can give a dimension to complex numbers in the same way as real
numbers–for example(2.1e3 + 3.9e4j) * ohm.Requires Python 3. (For Python 2 compatibility, install numericalunits
version 1.23 or earlier.)If you find bugs, please tell me byemailorgithub issue board.If you get overflows or underflows, you can edit the unit initializations.
For example, the package sets the meter to a random numerical value between 0.1
and 10. Therefore, if you’re doing molecular simulation, most lengths you
use will be tiny numbers. You should probably set the meter instead to be
between, say, a random numerical value between 1e8 and 1e10.Some numerical routines use a defaultabsolutetolerance, rather than
relative tolerance, to decide convergence. This can cause the calculation
result to randomly vary even though there is no dimensional analysis error.
When this happens, you should set the absolute tolerance to a value with the
appropriate units. Alternatively, you can scale the data before running the
algorithm and scale it back afterwards. Maybe this sounds like a hassle, but
it’s actually a benefit: If your final result is very sensitive to some
numerical tolerance setting, then you really want to be aware of that.Notes on unit definitionsFor electromagnetism, all units are intended for use in SI formulas. If
you plug them into cgs-gaussian electromagnetism formulas, or cgs-esu
electromagnetism formulas, etc., you will get nonsense results.The package does not keep track of “radians” as an independent unit
assigned a random number. The reason is that the “radians” factor does not
always neatly cancel out of formulas.The package does not keep track of “moles” as an independent unit assigned
a random number; insteadmolis just a pure number (~6e23), like you
would say “dozen”=12. That means: (1) gram/mol is exactly the same as amu,
and Boltzmann constant is exactly the same as the ideal gas constant, and so
on. (2) You should rarely need to use Avogadro’s numberNA– it is just a
synonym ofmol(NA = mol ~ 6e23). Here are a few examples using moles:from numericalunits import um, uM, kcal, mol, fmol, J

# There are eight copies of a protein inside a yeast nucleus of volume
# 3 cubic microns. What is the concentration of the protein, in micromolar (uM)?
print((8 / (3 * um**3)) / uM)   # Answer --> 0.0044

# 5 kcal / mol is how many joules?
print((5 * kcal / mol) / J)   # Answer --> 3.47e-20

# How many molecules are in 2.3 femtomoles?
print(2.3 * fmol)   # Answer --> 1.39e9The package cannot convert temperatures between Fahrenheit, Celsius, and
kelvin. The reason is that these scales have different zeros, so the units
cannot be treated as multiplicative factors. It is, however, possible to
convert temperatureintervals, via the unitsdegCinterval(which is a
synonym of kelvin,K) anddegFinterval.