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Dimensionality and Compatibility

The dimensional analysis of a quantity or a unit, no matter the form, can be performed invoking the method pyunitwizard.get_dimensionality():

import pyunitwizard as puw
puw.configure.load_library(['pint', 'openmm.unit'])

q = puw.quantity(1.4, 'kJ/mol', form='openmm.unit')
puw.get_dimensionality(q)

{'[L]': 2.0,
 '[M]': 1.0,
 '[T]': -2.0,
 '[K]': 0,
 '[mol]': -1.0,
 '[A]': 0,
 '[Cd]': 0}

Let’s see a second example:

q = puw.quantity('3.5N/(2.0nm**2)')
puw.get_dimensionality(q)

{'[L]': -1, '[M]': 1, '[T]': -2, '[K]': 0, '[mol]': 0, '[A]': 0, '[Cd]': 0}

Where dimensions correspond to the following fundamental quantities:

Fundamental Quantity	Dimension
Length	[L]
Mass	[M]
Time	[T]
Temperature	[K]
Substance	[mol]
Electric Current	[A]
Luminous Intensity	[Cd]

In addition, PyUnitWizard can check the dimensional compatibility between quantities with pyunitwizard.compatibility(), again, regardless their pythonic form:

q1 = puw.quantity(1.0, 'kJ/mol', form='openmm.unit')
q2 = puw.quantity(1.0, 'kcal/mol', form='pint')

puw.compatibility(q1, q2)

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[5], line 4
      1 q1 = puw.quantity(1.0, 'kJ/mol', form='openmm.unit')
      2 q2 = puw.quantity(1.0, 'kcal/mol', form='pint')
----> 4 puw.compatibility(q1, q2)

AttributeError: module 'pyunitwizard' has no attribute 'compatibility'

q1 = puw.quantity(1.0, 'nm**3', form='pint')
q2 = puw.quantity(1.0, 'litre', form='pint')

puw.compatibility(q1, q2)

True

q1 = puw.quantity(1.0, 'degrees', form='pint')
q2 = puw.quantity(1.0, 'radians', form='pint')

puw.compatibility(q1, q2)

True

q1 = puw.quantity(1.0, 'degrees', form='openmm.unit')
q2 = puw.quantity(1.0, 'hertzs', form='pint')

puw.compatibility(q1, q2)

False

q1 = puw.quantity(1.0, 'meters/seconds', form='openmm.unit')
q2 = puw.quantity(1.0, 'newtons/meter**2', form='pint')

puw.compatibility(q1, q2)

False

With the help of the method pyunitwizard.check we can also compare the dimensionality of a quantity or unit with a set of dimensions given by the user:

puw.check('meter', dimensionality={'[L]':1})

True

puw.check('1 meter', dimensionality={'[L]':1, '[T]':-1})

False

puw.check('1 meter/seconds', dimensionality={'[L]':1, '[T]':-1})

True