Quantities is designed to handle arithmetic and conversions of physical quantities, which have a magnitude, dimensionality specified by various units, and possibly an uncertainty. Quantities is designed to work with numpy’s standard ufuncs, many of which are already supported. The package is actively developed, and while the current features and API are stable, test coverage is incomplete and so the package is not suggested for production use.
It is strongly suggested to import quantities to its own namespace, so units and constants variables are not accidentally overwritten:
>>> import quantities as pq
Here pq stands for “physical quantities” or “python quantities”. There are a number of ways to create a quantity. In practice, it is convenient to think of quantities as a combination of a magnitude and units. These two quantities are equivalent:
>>> import numpy as np
>>> q = np.array([1,2,3]) * pq.J
>>> q = [1,2,3] * pq.J
>>> print q
[ 1. 2. 3.] J
The Quantity constructor can also be used to create quantities, similar to numpy.array. Units can be designated using a string containing standard unit abbreviations or unit names. For example:
>>> q = pq.Quantity([1,2,3], 'J')
>>> q = pq.Quantity([1,2,3], 'joules')
Units are also available as variables, and can be passed to Quantity:
>>> q = pq.Quantity([1,2,3], pq.J)
You can modify a quantity’s units in place:
>>> q = 1 * pq.m
>>> q.units = pq.ft
>>> print q
3.280839895013123 ft
or equivalently:
>>> q = 1 * pq.meter
>>> q.units = 'ft' # or 'foot' or 'feet'
>>> print q
3.280839895013123 ft
Note that, with strings, units can be designated using plural variants. Plural variants of the module variables are not available at this time, in the interest of keeping the units namespace somewhat manageable. q.units = ‘feet’ will work, q.units = pq.feet will not.
The units themselves are special objects that can not be modified in place:
>>> pq.meter.units = 'feet'
AttributeError: can not modify protected units
Instead of modifying a quantity in place, you can create a new quantity, rescaled to the new units:
>>> q = 300 * pq.ft * 600 * pq.ft
>>> q2 = q.rescale('US_survey_acre')
>>> print q2
4.13221487605 US_survey_acre
but rescaling will fail if the requested units fails a dimensional analysis:
>>> q = 10 * pq.joule
>>> q2 = q.rescale(pq.watt)
ValueError: Unable to convert between units of "J" and "W"
Quantities can not be rescaled in place if the unit conversion fails a dimensional analysis:
>>> q = 10 * pq.joule
>>> q.units = pq.watts
ValueError: Unable to convert between units of "J" and "W"
>>> print q
10.0 J
Quantities will attempt to simplify units when the users intent is unambiguous:
>>> q = (10 * pq.meter)**3
>>> q2 = q/(5*pq.meter)**2
>>> print q2
40 m
Quantities will not try to guess in an ambiguous situation:
>>> q = (10 * pq.meter)**3
>>> q2 = q/(5*pq.ft)**2
>>> print q2
40 m**3/ft**2
In that case, it is not clear whether the user wanted ft converted to meters, or meters to feet, or neither. Instead, you can obtain a new copy of the quantity in its irreducible units, which by default are SI units:
>>> q = (10 * pq.meter)**3
>>> q2 = q/(5*pq.ft)**2
>>> print q2
40 m**3/ft**2
>>> qs = q2.simplified
>>> print qs
430.556416668 m
It is also possible to customize the units in which simplified quantities are expressed:
>>> pq.set_default_units('cgs')
>>> print pq.J.simplified
10000000.0 g*cm**2/s**2
>>> pq.set_default_units(length='m', mass='kg')
There are times when you may want to treat a group of units as a single compound unit. For example, surface area per unit volume is a fairly common quantity in materials science. If expressed in the usual way, the quantity will be expressed in units that you may not recognize:
>>> q = 1 * pq.m**2 / pq.m**3
>>> print q
1.0 1/m
Here are some tricks for working with these compound units, which can be preserved:
>>> q = 1 * pq.CompoundUnit("m**2/m**3")
>>> print q
1.0 (m**2/m**3)
and can be simplified:
>>> qs = q.simplified
>>> qs
1.0 1/m
and then rescaled back into compound units:
>>> q2 = qs.rescale(CompoundUnit("m**2/m**3"))
>>> print q2
1.0 (m**2/m**3)
Compound units can be combined with regular units as well:
>>> q = 1 * pq.CompoundUnit('parsec/cm**3') * pq.cm**2
>>> print q
1.0 cm**2*(parsec/cm**3)
It is easy to define a unit that is not already provided by quantities. For example:
>>> uK = pq.UnitQuantity('microkelvin', pq.degK/1e6, symbol='uK')
>>> print uK
1 uK (microkelvin)
>>> q = 1000*uK
>>> print q.simplified
0.001 K
There is also support for quantities with uncertainty:
>>> q = UncertainQuantity(4,J,.2)
>>> q
4.0*J
+/-0.2*J (1 sigma)
By assuming that the uncertainties are uncorrelated, the uncertainty can be propagated during arithmetic operations:
>>> length = UncertainQuantity(2.0, m, .001)
>>> width = UncertainQuantity(3.0, m, .001)
>>> area = length*width
>>> area
6.0*m**2
+/-0.00360555127546*m**2 (1 sigma)
In that case, the measurements of the length and width were independent, and the two uncertainties presumed to be uncorrelated. Here is a warning though:
>>> q*q
16.0*J**2
+/-1.1313708499*J**2 (1 sigma)
This result is probably incorrect, since it assumes the uncertainties of the two multiplicands are uncorrelated. It would be more accurate in this case to use:
>>> q**2
16.0*J**2
+/-1.6*J**2 (1 sigma)
There is an entire subpackage dedicated to physical constants. The values of all the constants are taken from values published by the National Institute of Standards and Technology at http://physics.nist.gov/constants . Most physical constants have some form of uncertainty, which has also been published by NIST. All uncertainties are one standard deviation. There are lots of constants and quantities includes them all (with one exception: F*, the Faraday constant for conventional electrical current, which is defined in units of C_90, for which I have not found a hard reference value). Physical constants are sort of similar to compound units, for example:
>>> print pq.constants.proton_mass
1 m_p (proton_mass)
>>> print pq.constants.proton_mass.simplified
1.672621637e-27 kg
+/-8.3e-35 kg (1 sigma)
A Latex representation of the dimensionality may be obtained in the following fashion:
>>> g = pq.Quantity(9.80665,'m/s**2')
>>> mass = 50 * pq.kg
>>> weight = mass*g
>>> print weight.dimensionality.latex
$\mathrm{\frac{kg{\cdot}m}{s^{2}}}$
>>> weight.units = pq.N
>>> print weight.dimensionality.latex
$\mathrm{N}$
The Latex output is compliant with the MathText subset used by Matplotlib. To add formatted units to the axis label of a Matplotlib figure, one could use:
>>> ax.set_ylabel('Weight ' + weight.dimensionality.latex)
Greater customization is available via the markup.format_units_latex function. It allows the user to modify the font, the multiplication symbol, or to encapsulate the latex string in parentheses. Due to the complexity of CompoundUnits, the latex rendering of CompoundUnits will utilize the latex frac{num}{den} construct.
Although it is not illustrated in this guide, unicode symbols can be used to provide a more compact representation of the units. This feature is disabled by default. It can be enabled by setting the following in your ~/.pythonrc.py:
quantities_unicode = True
or you can change this setting on the fly by doing:
from quantities import markup
markup.config.use_unicode = True # or False
Even when unicode is enabled, when you pass strings to designate units, they should still conform to valid python expressions.
Attention
Quantities is not a package for describing coordinate systems that require a point of reference, like positions on a map. In particular, Quantities does not support absolute temperature scales. Instead, temperatures are assumed to be temperature differences. For example:
>>> T = 20 * pq.degC
>>> print T.rescale('K')
20.0 K
Proper support of coordinate systems would be a fairly large undertaking and is outside the scope of this project.