# Working with unyt¶

## Basic Usage¶

To use unyt in a project:

>>> import unyt


The top-level unyt namespace defines both a number of useful functions as well as a number of units and physical constants populated from the unyt.unit_symbols and unyt.physical_constants namespaces you can use to attach units to NumPy arrays and other common python data container types like list and tuple. For an exhaustive listing of units and physical constants defined in unyt, see Listing of Units.

### An Example from High School Physics¶

To see how you might use unyt to solve a problem where units might be a headache, let’s estimate the orbital periods of Jupiter’s Galilean moons, assuming they have circular orbits and their masses are negligible compared to Jupiter. Under these assumptions, the orbital period is

$T = 2\pi\left( \frac{r^3}{GM}\right)^{1/2}.$

For this exercise let’s calculate the orbital period in days. While it’s possible to do this using plain old floating point numbers (you probably had to do something similar on a calculator in a high school physics class, looking up and plugging in conversion factors by hand), it’s much easier to do this sort of thing symbolically and let unyt handle the unit conversions.

To do this we’ll need to know the mass of Jupiter (fortunately that is built into unyt) and the semimajor axis of the orbits of Jupiter’s moons, which we can look up from Wikipedia and enter by hand:

>>> from unyt import Mjup, G, AU
>>> from math import pi
...
>>> moons = ['Io', 'Europa', 'Ganymede', 'Callisto']
>>> semimajor_axis = [.002819, .0044856, .00715526, .01258513]*AU
...
>>> period = 2*pi*(semimajor_axis**3/(G*Mjup))**0.5
>>> period = period.to('d')
...
>>> for moon, period in zip(moons, period):
...     print('{}: {:04.2f}'.format(moon, period))
Io: 1.77 day
Europa: 3.55 day
Ganymede: 7.15 day
Callisto: 16.69 day


Let’s break up this example into a few components so you can see what’s going on. First, we import the unit symbols we need from the unyt namespace:

>>> from unyt import Mjup, G, km


The unyt namespace has a large number of units and physical constants you can import to apply units to data in your own code. You can see how that works in the example:

>>> semimajor_axis = [.002819, .0044856, .00715526, .01258513]*AU
>>> semimajor_axis
unyt_array([0.002819  , 0.0044856 , 0.00715526, 0.01258513], 'AU')


By multiplying by km, we converted the python list into a unyt.unyt_array instance. This is a class that’s built into unyt, has units attached to it, and knows how to convert itself into different dimensionally equivalent units:

>>> semimajor_axis.value
array([0.002819  , 0.0044856 , 0.00715526, 0.01258513])
>>> semimajor_axis.units
AU
>>> print(semimajor_axis.to('km'))
[ 421716.39764641  671036.20903964 1070411.66066813 1882708.6511216 ] km


Next, we calculated the orbital period by translating the orbital period formula to Python and then converting the answer to the units we want in the end, days:

>>> period = 2*pi*(semimajor_axis**3/(G*Mjup))**0.5
>>> period
unyt_array([ 152864.59689789,  306828.08975058,  618162.17963649,
1441952.18891597], 's')
>>> period.to('d')
unyt_array([ 1.76926617,  3.55125104,  7.15465486, 16.68926145], 'day')


Note that we haven’t added any conversion factors between different units, that’s all handled internally by unyt. Also note how the unyt_array.to method was able to automatically handle the conversion from seconds to days and how the shorthand "d" was automatically interpreted as "day".

### Arithmetic and units¶

The real power of working with unyt is its ability to add, subtract, multiply, and divide quantities and arrays with units in mathematical formulas while automatically handling unit conversions and detecting when you have made a mistake in your units in a mathematical formula. To see what I mean by that, let’s take a look at the following examples:

>>> from unyt import cm, m, ft, yard
>>> print(3.*cm + 4.*m - 5.*ft + 6.*yard)
799.24 cm


Despite the fact that the four unit symbols used in the above example correspond to four different units, unyt is able to automatically convert the value of all three units into a common unit and return the result in those units. Note that for expressions where the return units are ambiguous, unyt always returns data in the units of the leftmost object in an expression:

>>> print(4*m + 3*cm - 5*ft + 6*yard)
7.9924 m


One can also form more complex units out of atomic unit symbols. For example, here is how we’d create an array with units of meters per second and print out the values in the array in miles per hour:

>>> from unyt import m, s
>>> velocities = [20., 22., 25.]*m/s
>>> print(velocities.to('mile/hr'))
[44.73872584 49.21259843 55.9234073 ] mile/hr


Similarly one can multiply two units together to create new compound units:

>>> from unyt import N, m
>>> energy = 3*N * 4*m
>>> print(energy)
12 N*m
>>> print(energy.to('erg'))
120000000.0 erg


In general, one can multiply or divide by an arbitrary rational power of a unit symbol. Most commonly this shows up in mathematical formulas in terms of square roots. For example, let’s calculate the gravitational free-fall time for a person to fall from the surface of the Earth through to a hole dug all the way to the center of the Earth. It turns out that this time is given by:

$t_{\rm ff} = \sqrt{\frac{3\pi}{32 G \rho}}$

where $$\rho$$ is the average density of the Earth.

>>> from unyt import G, Mearth, Rearth
>>> from math import pi
>>> import numpy as np
...
>>> rho = Mearth / (4./3 * pi* Rearth**3)
>>> print(rho.to('g/cm**3'))
5.581225129861083 g/cm**3
>>> tff = np.sqrt(3*pi/(32*G*rho))
>>> print(tff.to('min'))
14.820022043294829 min


If you make a mistake by adding two things that have different dimensions, unyt will raise an error to let you know that you have a bug in your code:

>>> from unyt import kg, m
>>> 3*kg + 5*m  # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE +IGNORE_EXCEPTION_DETAIL
Traceback (most recent call last):
...
unyt.exceptions.UnitOperationError: The <ufunc 'add'> operator for
unyt_arrays with units "kg" (dimensions "(mass)") and
"m" (dimensions "(length)") is not well defined.


while this example is trivial when one writes more complicated formulae it can be easy to accidentally write expressions that are not dimensionally sound.

Sometimes this can be annoying to deal with, particularly if one is mixing data that has units attached with data from some outside source with no units. To quickly patch over this lack of unit metadata (which could be applied by explicitly attaching units at I/O time), one can use the units attribute of the unyt.unyt_array class to quickly apply units to a scalar, list, or array:

>>> from unyt import cm, s
>>> velocities = [10, 20, 30] * cm/s
>>> velocities + 12  # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE +IGNORE_EXCEPTION_DETAIL
Traceback (most recent call last):
...
unyt.exceptions.UnitOperationError: The <ufunc 'add'> operator for
unyt_arrays with units "cm/s" (dimensions "(length)/(time)") and
"dimensionless" (dimensions "1") is not well defined.
>>> velocities + 12*velocities.units
unyt_array([22, 32, 42], 'cm/s')


### Powers, Logarithms, Exponentials, and Trigonometric Functions¶

The unyt library represents powers using standard python syntax. This means you must use ** and not ^, even when writing a unit as a string:

>>> from unyt import kg, m
>>> print((10.*kg/m**3).to('g/cm**3'))
0.01 g/cm**3


Formally it does not make sense to exponentiate, take the logarithm of, or apply a transcendental function to a quantity with units. However, the unyt library makes the practical affordance to allow this, simply ignoring the units present and returning a result without units. This makes it easy to work with data that has units both in linear space and in log space:

>>> from unyt import g, cm
>>> import numpy as np
>>> print(np.log10(1e-23*g/cm**3))
-23.0


The one exception to this rule is for trigonometric functions applied to data with angular units:

>>> from unyt import degree, radian
>>> import numpy as np
>>> np.sin(np.pi/4*radian)
array(0.70710678)
>>> np.sin(45.*degree)
array(0.70710678)


#### Logarithmic Quantities and Units¶

The logarithmic quantities level-of-power and level-of-field and the units neper and bel are supported. In the next example, we represent the power measurements, p, as a logarithmic quantity at reference level, p_ref, in the units decibel.

>>> import numpy as np
>>> from unyt import dB, mW
>>> dB.dimensions
(logarithmic)
>>> p = [1, 100]*mW
>>> p_ref = 1*mW
>>> level_of_power = 10*np.log10(p/p_ref)*dB
>>> level_of_power
unyt_array([ 0., 20.], 'dB')


You can convert the logarithmic quantity back to physical units through exponentiation, just remember to remove the units using the unyt_array.v property.

>>> 10**(level_of_power.v/10)*p_ref
unyt_array([  1., 100.], 'mW')


### Printing Units¶

The print formatting of unyt_array can be controlled identically to numpy arrays, using numpy.setprintoptions:

>>> import numpy as np
>>> import unyt as u
...
>>> np.set_printoptions(precision=4)
>>> print([1.123456789]*u.km)
[1.1235] km
>>> np.set_printoptions(precision=8)


Print a $$\rm{\LaTeX}$$ representation of a set of units using the unyt.unit_object.Unit.latex_representation() function or unyt.unit_object.Unit.latex_repr attribute:

>>> from unyt import g, cm
>>> (g/cm**3).units.latex_representation()
'\\frac{\\rm{g}}{\\rm{cm}^{3}}'
>>> (g/cm**3).units.latex_repr
'\\frac{\\rm{g}}{\\rm{cm}^{3}}'


### Simplifying Units¶

Unit expressions can often be simplified to cancel pairs of factors with compatible dimensions. For example, we can form a unit with dimensions of length by dividing a unit with dimensions of length squared by another unit with dimensions of length:

>>> from unyt import m, cm
>>> m**2/cm
m**2/cm


The Unit class has a simplify() method that we can call to create a new unit object to that includes the dimensionless ratio m/cm as a constant coefficient:

>>> (m**2/cm).simplify()
100*m


This will also work for units that are the reciprocals of each other, for example:

>>> from unyt import s, Hz
>>> (s*Hz).simplify()
(dimensionless)


Products and quotients of unit objects will not be simplified unless simplify() is called explicitly. However, products and quotients of arrays and quantities will be simplified to make interactive work more intuitive:

>>> from unyt import erg, minute, hour
>>> power = [20, 40, 80] * erg / minute
>>> elapsed_time = 3*hour
>>> print(power*elapsed_time)
[ 3600.  7200. 14400.] erg


### Checking Units¶

If you write a function that accepts data with units as an argument or returns data with units, you can ensure the dimensional correctness of the inputs or outputs using the @accepts and @returns decorators:

>>> from unyt.dimensions import length, time
>>> from unyt import accepts, returns
>>> import unyt as u
>>> @returns(length)
... @accepts(a=time, v=length/time)
... def foo(a, v):
...     return a * v
...
>>> res = foo(a= 2 * u.s, v = 3 * u.m/u.s)
>>> print(res)
6 m


Note

Using these decorators may incur some performance overhead, especially for small arrays.

### Temperature Units¶

The temperature unit degree Celsius has the symbol °C, but since the degree character is an invalid Python identifier, unyt uses the symbol degC. Printing a degree Celsius quantity will show the correct symbol.

>>> from unyt import degC
>>> Ta = 23*degC
>>> print(Ta)
23 °C


The degC symbol has alternative names degree_Celsius, Celsius and °C.

>>> from unyt import degree_Celsius, unyt_array
>>> Ta = 23*degree_Celsius
>>> print(Ta)
23 °C
>>> Ta = unyt_array([-40, 23, 70], '°C')
>>> print(Ta)
[-40  23  70] °C


These comments also apply to degree Fahrenheit.

Performing arithmetic with temperature quantities can be ambiguous. To clarify intent, unyt has the convenience units delta_degC and delta_degF.

>>> from unyt import degC, delta_degC, V
>>> t1 = 23*degC
>>> t2 = 1*delta_degC
>>> print(t1 + t2)
24 °C
>>> print(t2 - t1)
-22 °C
>>> tempco = 10.0*V/delta_degC
>>> print(tempco*2*delta_degC)
20.0 V


## Unit Conversions and Unit Systems¶

### Converting Data to Arbitrary Units¶

If you have some data that you want to convert to a different set of units and you know which units you would like to convert it to, you can make use of the unyt_array.to function:

>>> from unyt import mile
>>> (1.0*mile).to('ft')
unyt_quantity(5280., 'ft')


If you try to convert to a unit with different dimensions, unyt will raise an error:

>>> from unyt import mile
>>> (1.0*mile).to('lb')  # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE +IGNORE_EXCEPTION_DETAIL
Traceback (most recent call last):
...
unyt.exceptions.UnitConversionError: Cannot convert between 'mile' (dim
'(length)') and 'lb' (dim '(mass)').


While we recommend using unyt_array.to in most cases to convert arrays or quantities to different units, if you would like to explicitly emphasize that this operation has to do with units, we also provide the more verbose name unyt_array.in_units which behaves identically to unyt_array.to.

### Converting Units In-Place¶

The unyt_array.to method makes a copy of the array data. For most cases this is fine, but when dealing with big arrays, or when performance is a concern, it sometimes is preferable to convert the data in an array in-place, without copying the data to a new array. This can be accomplished with the unyt_array.convert_to_units function:

>>> from unyt import mile
>>> data = [1., 2., 3.]*mile
>>> data
unyt_array([1., 2., 3.], 'mile')
>>> data.convert_to_units('km')
>>> data
unyt_array([1.609344, 3.218688, 4.828032], 'km')


### Converting to MKS and CGS Base Units¶

If you don’t necessarily know the units you want to convert data to ahead of time, it’s often convenient to specify a unit system to convert to. The unyt_array has built-in conversion methods for the two most popular unit systems, MKS (meter kilogram second) and CGS (centimeter gram second). For CGS these are unyt_array.in_cgs and unyt_array.convert_to_cgs. These functions create a new copy of an array in CGS units and convert an array in-place to CGS. respectively. For MKS, there are the unyt_array.in_mks and unyt_array.convert_to_mks methods, which play analogous roles.

See below for details on CGS and MKS electromagnetic units.

### Other Unit Systems¶

The unyt library currently has built-in support for a number of unit systems, as detailed in the table below. Note that all unit systems currently use “radian” as the base angle unit.

If a unit system in the table below has “Other Units” specified, this is a mapping from dimension to a unit name. These units override the unit system’s default unit for that dimension. If no unit is explicitly specified of a dimension then the base unit for that dimension is calculated at runtime by combining the base units for the unit system into the appropriate dimension.

Unit system Base Units Other Units
cgs cm, g, s
• Energy: erg
• Specific Energy: erg/g
• Pressure: dyne/cm**2
• Force: dyne
• Power: erg/s
• Magnetic Field: G
• Charge: esu
• Current: statA
mks m, kg, s
• Energy: J
• Specific Energy: J/kg
• Pressure: Pa
• Force: N
• Power: W
• Magnetic Field: T
• Charge: C
imperial ft, lb, s
• Energy: ft*lbf
• Temperature: R
• Pressure: lbf/ft**2
• Force: lbf
• Power: hp
galactic kpc, Msun, kyr
• Energy: kev
• Magnetic Field: uG
solar AU, Mearth, yr

Note that in MKS units the current unit, Ampere, is a base unit in the unit system. In CGS units the electromagnetic units like Gauss and statA are decomposable in terms of the base mass, length, and time units in the unit system. For this reason quantities defined in E&M units in CGS units are not readily convertible to MKS units and vice verse since the units are not dimensionally equivalent. The unyt library does have limited support for converting electromagnetic units between MKS and CGS, however only simple conversions of data with a single specific unit are supported and no conversions are allowed for complex combinations of units. For example converting between Gauss and Tesla is supported:

>>> from unyt import T
>>> (1.0*T).to('G')
unyt_quantity(10000., 'G')


But converting a more complicated compound unit will raise an error:

>>> from unyt import C, T, V
>>> (1.0*C*T*V).in_cgs()  # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE +IGNORE_EXCEPTION_DETAIL
Traceback (most recent call last):
...
unyt.exceptions.UnitsNotReducible: The unit "C*T*V" (dimensions
"(length)**2*(mass)**2/((current_mks)*(time)**4)") cannot be reduced to
an expression within the cgs system of units.


If you need to work with complex expressions involving electromagnetic units, we suggest sticking to either CGS or SI units for the full calculation. There is no general way to convert an arbitrary quantity between CGS and SI units if the quantity involves electromagnetic units. Instead, it is necessary to do the conversion on the equations under consideration, and then recompute the necessary quantity in the transformed set of equations. This requires understanding the context for a calculation, which unfortunately is beyond the scope of a library like unyt.

You can convert data to a unit system unyt knows about using the unyt_array.in_base and unyt_array.convert_to_base methods:

>>> from unyt import g, cm, horsepower
>>> (1e-9*g/cm**2).in_base('galactic')
unyt_quantity(4.78843804, 'Msun/kpc**2')
>>> data = [100., 500., 700.]*horsepower
>>> data
unyt_array([100., 500., 700.], 'hp')
>>> data.convert_to_base('mks')
>>> data
unyt_array([ 74569.98715823, 372849.93579114, 521989.91010759], 'W')


#### Defining and Using New Unit Systems¶

To define a new custom unit system, one need only create a new instance of the unyt.UnitSystem class. The class initializer accepts a set of base units to define the unit system. If you would like to additionally customize any derived units in the unit system, you can do this using item setting.

As an example, let’s define an atomic unit system based on typical scales for atoms and molecules:

>>> from unyt import UnitSystem
>>> atomic_unit_system = UnitSystem('atomic', 'nm', 'mp', 'fs', 'nK', 'rad')
>>> atomic_unit_system['energy'] = 'eV'
>>> atomic_unit_system
atomic Unit System
Base Units:
length: nm
mass: mp
time: fs
temperature: nK
angle: rad
current_mks: A
luminous_intensity: cd
logarithmic: Np
Other Units:
energy: eV
>>> print(atomic_unit_system)
atomic
>>> atomic_unit_system['number_density']
nm**(-3)
>>> atomic_unit_system['angular_momentum']
mp*nm**2/fs


It is also legal to define a unit system using unyt.Unit instances:

>>> from unyt.unit_symbols import Msun, second, megaparsec
>>> UnitSystem('cosmological', megaparsec, Msun, second)
cosmological Unit System
Base Units:
length: Mpc
mass: Msun
time: s
temperature: K
angle: rad
current_mks: A
luminous_intensity: cd
logarithmic: Np
Other Units:


Or with a quantity:

>>> UnitSystem('quasmological', 3*megaparsec, .8*Msun, 42*second)
quasmological Unit System
Base Units:
length: 3*Mpc
mass: 0.8*Msun
time: 42*s
temperature: K
angle: rad
current_mks: A
luminous_intensity: cd
logarithmic: Np
Other Units:


Once you have defined a new unit system that will register the new system with a global registry of unit systems known to the unyt library. That means you will immediately be able to use it just like the built-in unit systems:

>>> from unyt import W
>>> (1.0*W).in_base('atomic')
unyt_quantity(0.59746607, 'mp*nm**2/fs**3')


If you would like your unit system to include an MKS current unit (e.g. something that is directly convertible to the MKS Ampere unit), then specify a current_mks_unit in the UnitSystem initializer.

## Equivalencies¶

An equivalency is a way to define a mapping to convert from one unit to another even if the two units are not dimensionally equivalent. This usually involves some sort of shorthand or heuristic understanding of the problem under consideration. Only use one of these equivalencies if it makes sense to use it for the problem you are working on.

The unyt library implements the following equivalencies:

• "thermal": conversions between temperature and energy ($$E = k_BT$$)
• "spectral": conversions between wavelength, spatial frequency, frequency, and energy for photons ($$E = h\nu = hc/\lambda$$, $$c = \lambda\nu$$)
• "mass_energy": conversions between mass and energy ($$E = mc^2$$)
• "lorentz": conversions between velocity and Lorentz factor ($$\gamma = 1/\sqrt{1-(v/c)^2}$$)
• "schwarzschild": conversions between mass and Schwarzschild radius ($$R_S = 2GM/c^2$$)
• "compton": conversions between mass and Compton wavelength ($$\lambda = h/mc$$)

You can convert data to a specific set of units via an equivalency appropriate for the units of the data. To see the equivalencies that are available for an array, use the unit_array.list_equivalencies method:

>>> from unyt import gram, km
>>> gram.list_equivalencies()
mass_energy: mass <-> energy
schwarzschild: mass <-> length
compton: mass <-> length
>>> km.list_equivalencies()
spectral: length <-> spatial_frequency <-> frequency <-> energy
schwarzschild: mass <-> length
compton: mass <-> length


All of the unit conversion methods described above have an equivalence keyword argument that allows one to optionally specify an equivalence to use for the unit conversion operation. For example, let’s use the schwarzschild equivalence to calculate the mass of a black hole with a radius of one AU:

>>> from unyt import AU
>>> (1.0*AU).to('Msun', equivalence='schwarzschild')
unyt_quantity(50656851.7815179, 'Msun')


Both the methods that convert data in-place and the ones that return a copy support optionally specifying equivalence. In addition to the methods described above, unyt also supplies two more conversion methods that require an equivalence to be specified: unyt_array.to_equivalent and unyt_array.convert_to_equivalent. These are identical to their counterparts described above, except they equivalence is a required positional argument to the function rather than an optional keyword argument. Use these functions when you want to emphasize that an equivalence is being used.

If the equivalence has optional keyword arguments, these can be passed to the unit conversion function. For example, here’s an example where we specify a custom mean molecular weight (mu) for the number_density equivalence:

>>> from unyt import g, cm
>>> rho = 1e-23 * g/cm**3
>>> rho.to('cm**-3', equivalence='number_density', mu=1.4)
unyt_quantity(4.26761476, 'cm**(-3)')


For full API documentation and an autogenerated listing of the built-in equivalencies in unyt as well as a short usage example for each, see the unyt.equivalencies API listing.

## Dealing with code that doesn’t use unyt¶

Optimally, a function will work the same irrespective of whether the data passed in has units attached or not:

>>> from unyt import cm
>>> def square(x):
...     return x**2
>>> print(square(3.))
9.0
>>> print(square(3.*cm))
9.0 cm**2


However in the real world that is not always the case. In this section we describe strategies for dealing with that situation.

### Stripping units off of data¶

The unyt library provides a number of ways to convert unyt_quantity instances into floats and unyt_array instances into numpy arrays. These methods either return a copy of the data as a numpy array or return a view onto the underlying array data owned by a unyt_array instance.

To obtain a new array containing a copy of the original data, use either the unyt_array.to_value function or the unyt_array.value or unyt_array.v properties. All of these are equivalent to passing a unyt_array to the numpy.array() function:

>>> from unyt import g
>>> import numpy as np
>>> data = [1., 2., 3.]*g
>>> data
unyt_array([1., 2., 3.], 'g')
>>> np.array(data)
array([1., 2., 3.])
>>> data.to_value('kg')
array([0.001, 0.002, 0.003])
>>> data.value
array([1., 2., 3.])
>>> data.v
array([1., 2., 3.])


Similarly, to obtain a ndarray containing a view of the data in the original array, use either the unyt_array.ndview or the unyt_array.d properties:

>>> data.view(np.ndarray)
array([1., 2., 3.])
>>> data.ndview
array([1., 2., 3.])
>>> data.d
array([1., 2., 3.])


### Applying units to data¶

Note

A numpy array that shares memory with another numpy array points to the array that owns the data with the base attribute. If arr1.base is arr2 is True then arr1 is a view onto arr2 and arr2.base will be None.

When you create a unyt_array instance from a numpy array, unyt will create a copy of the original array:

>>> from unyt import g
>>> data = np.random.random((100, 100))
>>> data_with_units = data*g
>>> data_with_units.base is data
False


If you would like to create a view rather than a copy, you can apply units like this:

>>> from unyt import unyt_array
>>> data_with_units = unyt_array(data, g)
>>> data_with_units.base is data
True


Any set of units can be used for either of these operations. For example, if you already have an existing array, you could do this to create a new array with the same units:

>>> more_data = [4, 5, 6]*data_with_units.units
>>> more_data
unyt_array([4, 5, 6], 'g')


### Working with code that uses astropy.units¶

The unyt library can convert data contained inside of an Astropy Quantity instance. It can also produce a Quantity from an existing unyt_array instance. To convert data from astropy.units to unyt use the unyt_array.from_astropy function:

>>> from astropy.units import km
>>> from unyt import unyt_quantity
>>> unyt_quantity.from_astropy(km)
unyt_quantity(1., 'km')
>>> a = [1, 2, 3]*km
>>> a
<Quantity [1., 2., 3.] km>
>>> unyt_array.from_astropy(a)
unyt_array([1., 2., 3.], 'km')


To convert data to astropy.units use the unyt_array.to_astropy method:

>>> from unyt import g, cm
>>> data = [3, 4, 5]*g/cm**3
>>> data.to_astropy()
<Quantity [3., 4., 5.] g / cm3>
>>> (4*cm).to_astropy()
<Quantity 4. cm>


### Working with code that uses Pint¶

The unyt library can also convert data contained in Pint Quantity instances. To convert data from Pint to unyt, use the unyt_array.from_pint function:

>>> from pint import UnitRegistry
>>> import numpy as np
>>> ureg = UnitRegistry()
>>> a = np.arange(4)
>>> b = ureg.Quantity(a, "erg/cm**3")
>>> b
<Quantity([0 1 2 3], 'erg / centimeter ** 3')>
>>> c = unyt_array.from_pint(b)
>>> c
unyt_array([0, 1, 2, 3], 'erg/cm**3')


And to convert data contained in a unyt_array instance, use the unyt_array.to_pint method:

>>> from unyt import cm, s
>>> a = 4*cm**2/s
>>> print(a)
4 cm**2/s
>>> a.to_pint()
<Quantity(4, 'centimeter ** 2 / second')>
>>> b = [1, 2, 3]*cm
>>> b.to_pint()
<Quantity([1 2 3], 'centimeter')>


## User-Defined Units¶

Often it is convenient to define new custom units. This can happen when you need to make use of a unit that the unyt library does not have a definition for already. It can also happen when dealing with data that uses a custom unit system or when writing software that needs to deal with such data in a flexible way, particularly when the units might change from dataset to dataset. This comes up often when modeling a physical system since it is often convenient to rescale data from a physical unit system to an internal “code” unit system in which the values of the variables under consideration are close to unity. This approach can help minimize floating point round-off error but is often done for convenience or to non-dimensionalize the problem under consideration.

The unyt library provides two approaches for dealing with this problem. For more toy one-off use-cases, we suggest using unyt.define_unit which allows defining a new unit name in the global, default unit system that unyt ships with by default.

This function makes it possible to easily define a new unit that is unknown to the unyt library:

>>> import unyt as u
>>> two_weeks = 14.0*u.day
>>> one_day = 1.0*u.day
>>> u.define_unit("fortnight", two_weeks)
>>> print((3*u.fortnight)/one_day)
42.0 dimensionless


This is primarily useful for one-off definitions of units that the unyt library does not already have predefined. For more complex uses cases that need more flexibility, it is possible to use a custom unit system by ensuring that the data you are working with makes use of a UnitRegistry customized for your use case, as described below.

## Dealing with data types¶

The unyt library supports creating unyt.unyt_array and unyt.unyt_quantity instances with arbitrary integer or floating point data types:

>>> import numpy as np
>>> from unyt import km
...
>>> int_data = [1, 2, 3]*km
>>> int_data
unyt_array([1, 2, 3], 'km')
>>> float32_data = np.array([1, 2, 3], dtype='float32')*km
>>> float32_data
unyt_array([1., 2., 3.], dtype=float32, units='km')


The dtype of a unyt_array instance created by multiplying an iterable by a unit will be the same as passing the iterable to np.array(). You can also manually specify the dtype by calling np.array() yourself or by using the unyt_array initializer directly:

>>> np.array([1, 2, 3], dtype='float64')*km
unyt_array([1., 2., 3.], 'km')


Operations that convert an integer array to a new unit will convert the array to the floating point type with an equivalent size. For example, Calling in_units on a 32 bit integer array with units of kilometers will return a 32 bit floating point array.

>>> data = np.array([1, 2, 3], dtype='int32')*km
>>> data.in_units('mile')
unyt_array([0.62137121, 1.24274242, 1.86411357], dtype=float32, units='mile')


In-place operations will also mutate the dtype from float to integer in these cases, again in away that will preserve the byte size of the data.

>>> data.convert_to_units('mile')
>>> data
unyt_array([0.62137121, 1.24274242, 1.86411357], dtype=float32, units='mile')


It is possible that arrays containing large integers (16777217 for 32 bit and 9007199254740993 for 64 bit) will lose precision when converting data to a different unit. In these cases a warning message will be printed.

## Integrating unyt Into a Python Library¶

The unyt library began life as the unit system for the yt data analysis and visualization package, in the form of yt.units. In this role, unyt was deeply integrated into a larger python library. Due to these origins, it is straightforward to build applications that ensure unit consistency by making use of unyt. Below we discuss a few topics that most often come up when integrating unyt into a new or existing Python library.

### Unit registries¶

It is also possible to define a custom database of units completely independent of the global default unit database exposed by the unyt namespace or to create namespaces in your own package that expose listings of units. In these cases it becomes important to understand how unyt stores unit metadata in an internal database, how to add custom entries to the database, how to modify them, and how to persist custom units.

In practice, the unit metadata for a unit object is contained in an instance of the UnitRegistry class. Every Unit instance contains a reference to a UnitRegistry instance:

>>> from unyt import g
>>> g.registry  # doctest: +ELLIPSIS
<unyt.unit_registry.UnitRegistry ...>


All the unit objects in the unyt namespace make use of the default unit registry, importable as unyt.unit_registry.default_unit_registry. This registry object contains all of the real-world physical units that the unyt library ships with out of the box.

The unit registry itself contains a look-up table that maps from unit names to the metadata necessary to construct a unit. Note that the unit registry only contains metadata for “base” units, and not, for example, SI-prefixed units like centimeter of kilogram, it will instead only contain entries for meter and gram.

Sometimes it is convenient to create a unit registry containing new units that are not available in the default unit registry. A common example would be adding a code_length unit that corresponds to the scaling to from physical lengths to an internal unit system. In practice, this value is arbitrary, but will be fixed for a given problem. Let’s create a unit registry and a custom "code_length" unit to it, and then create a "code_length" unit and a quantity with units of "code_length". For the sake of example, let’s set the value of "code_length" equal to 10 meters.

>>> from unyt import UnitRegistry, Unit
>>> from unyt.dimensions import length
>>> reg = UnitRegistry()
>>> reg.add("code_length", base_value=10.0, dimensions=length,
...         tex_repr=r"\rm{Code Length}")
>>> 'code_length' in reg
True
>>> u = Unit('code_length', registry=reg)
>>> data = 3*u
>>> print(data)
3 code_length


As you can see, you can test whether a unit name is in a registry using the Python in operator.

In an application that depends on unyt, it is often convenient to define methods or functions to automatically attach the correct unit registry to unit objects associated with an object. For example, consider a Simulation class. Let’s give this class two methods named array and quantity to create new unyt_array and unyt_quantity instances, respectively:

>>> class Simulation(object):
...     def __init__(self, registry):
...         self.registry = registry
...
...     def array(self, value, units):
...         return unyt_array(value, units, registry=self.registry)
...
...     def quantity(self, value, units):
...         return unyt_quantity(value, units, registry=self.registry)
...
>>> registry = UnitRegistry()
>>> registry.add("code_length", base_value=3.2, dimensions=length)
>>> s = Simulation(registry)
>>> s.array([1, 2, 3], 'code_length')
unyt_array([1, 2, 3], 'code_length')


We can create an array with "code_length" here because s.registry, the UnitRegistry instance associated with our Simulation instance has a "code_length" unit defined.

As for arrays with different units, for operations between arrays created with different unit registries, the result of the operation will use the same unit registry as the leftmost unit. This can sometimes lead to surprising behaviors where data will seem to “forget” about custom units. In this situation it is important to make sure ahead of time that all data are created with units using the same unit registry. If for some reason that is not possible (for example, when comparing data from two different simulations with different internal units), then care must be taken when working with custom units. To avoid these sorts of ambiguities it is best to do work in physical units as much as possible.

When writing tests, it is convenient to use unyt.testing. In particular, assert_allclose_units can be used to check for floating-point equality.

>>> from unyt import assert_allclose_units, m
>>> import numpy as np
>>> actual = [1e-5, 1e-3, 1e-1] * m
>>> desired = actual.to("cm")
>>> assert_allclose_units(actual, desired)


### Custom Unit Systems¶

By default unyt uses the SI MKS unit system. However, libraries can create a unit registry using another unit system to expose that unit system to their users by creating a unit registry with a custom unit system. For example, to make CGS units the default unit for all operations, one might modify the Simulation class defined above like so:

>>> class Simulation(object):
...     def __init__(self, registry):
...         self.registry = registry
...
...     def array(self, value, units):
...         return unyt_array(value, units, registry=self.registry)
...
...     def quantity(self, value, units):
...         return unyt_quantity(value, units, registry=self.registry)
...
>>> registry = UnitRegistry(unit_system='cgs')
>>> registry.add("code_length", base_value=3.2, dimensions=length)
>>> s_cgs = Simulation(registry)
>>> data = s_cgs.array([1, 2, 3], 'code_length')
>>> data
unyt_array([1, 2, 3], 'code_length')
>>> data.in_base()
unyt_array([320., 640., 960.], 'cm')


Note that the base_value parameter of UnitRegistry.add must be specified in MKS units. All unit data are stored internally in unyt in MKS units.

You can also use two helper functions provided by unyt, unyt.unit_systems.add_constants() and unyt.unit_systems.add_symbols(), to populate a namespace with a set of predefined unit symbols or physical consants. This namespace could correspond to the names importable from a module or the names of attributes of an object, or any other generic dictionary.

One example of doing this would be to make a UnitContainer class that contains units that are compatible with the Simulation instance we named s_cgs in the example above:

>>> from unyt.unit_systems import add_symbols
>>> class UnitContainer(object):
...    def __init__(self, registry):
...        add_symbols(vars(self), registry)
>>> units = UnitContainer(s_cgs.registry)
>>> units.kilometer
km
>>> units.code_length
code_length
>>> (10.0 * units.kilometer).in_base()
unyt_quantity(1000000., 'cm')
>>> (10.0 * units.kilometer).in_units('code_length')
unyt_quantity(3125., 'code_length')


Note how the result of the call to in_base() comes out in centimeters because of the the CGS unit system used by the UnitRegistry instance associated with the Simulation.

### Writing Data with Units to Disk¶

The unyt library has support for serializing data stored in a unyt.unyt_array instance to HDF5 files, text files, and via the Python pickle protocol. We give brief examples below, but first describe how to handle saving units manually as string metadata.

#### Dealing with units as strings¶

If all you want to do is save data to disk in a physical unit or you are working in a physical unit system, then you only need to save the unit name as a string and treat the array data you are trying to save as a regular numpy array, as in this example:

>>> import numpy as np
>>> import os
>>> from unyt import cm
...
>>> data = [1, 2, 3]*cm
>>> np.save('my_data_cm.npy', data)
>>> new_data = np.load('my_data_cm.npy')
>>> new_data
array([1, 2, 3])
>>> new_data_with_units = new_data * cm
>>> os.remove('my_data_cm.npy')


Of course in this example using numpy.save we need to hard-code the units because the .npy format doesn’t have a way to store metadata along with the array data. We could have stored metadata in a sidecar file, but this is much more natural with hdf5 via h5py:

>>> import h5py
>>> import os
>>> from unyt import cm, Unit
...
>>> data = [1, 2, 3]*cm
...
>>> with h5py.File('my_data.h5', 'a') as f:
...     d = f.create_dataset('my_data', data=data)
...     f['my_data'].attrs['units'] = str(data.units)
...
>>> with h5py.File('my_data.h5', 'r') as f:
...     new_data = f['my_data'][:]
...     unit_str = f['my_data'].attrs['units']
...
>>> unit = Unit(unit_str)
>>> new_data = new_data*unit
>>> new_data
unyt_array([1, 2, 3], 'cm')
>>> os.remove('my_data.h5')


#### HDF5 Files¶

The unyt library provides a hook for writing data both to a new HDF5 file and an existing file and then subsequently reading that data back in to restore the array. This works via the unyt_array.write_hdf5 and unyt_array.from_hdf5 methods. The simplest way to use these functions is to write data to a file that does not exist yet:

>>> from unyt import cm
>>> import os
>>> data = [1, 2, 3]*cm
>>> data.write_hdf5('my_data.h5')
...
>>> unyt_array.from_hdf5('my_data.h5')
unyt_array([1, 2, 3], 'cm')
>>> os.remove('my_data.h5')


By default the data will be written to the root group of the HDF5 file in a dataset named 'array_data'. You can also specify that you would like the data to be saved in a particular group or dataset in the file:

>>> data.write_hdf5('my_data.h5', dataset_name='my_special_data',
...                 group_name='my_special_group')
>>> unyt_array.from_hdf5('my_data.h5', dataset_name='my_special_data',
...                      group_name='my_special_group')
unyt_array([1, 2, 3], 'cm')
>>> os.remove('my_data.h5')


You can even write to files and groups that already exist:

>>> with h5py.File('my_data.h5') as f:
...     g = f.create_group('my_custom_group')
...
>>> data.write_hdf5('my_data.h5', group_name='my_custom_group')
...
>>> with h5py.File('my_data.h5') as f:
...     print(f['my_custom_group/array_data'][:])
[1 2 3]
>>> os.remove('my_data.h5')


If the dataset that you would like to write to already exists, unyt will clobber that dataset.

Note that with this method of saving data to hdf5 files, the unyt.UnitRegistry instance associated with the units of the data will be saved in the HDF5 file. This means that if you create custom units and save a unit to disk, you will be able to convert data to those custom units even if you are dealing with those units later after restoring the data from disk. Here is a short example illustrating this:

>>> import os
>>> from unyt import UnitRegistry
>>> reg = UnitRegistry()
>>> reg.add("code_length", base_value=10.0, dimensions=length,
...         tex_repr=r"\rm{Code Length}")
>>> u = Unit('cm', registry=reg)
>>> data = [1., 2., 3.]*u
>>> data.write_hdf5('my_code_data.h5')
>>> read_data = data.from_hdf5('my_code_data.h5')
>>> read_data
unyt_array([1., 2., 3.], 'cm')
>>> read_data.to('code_length')
unyt_array([0.001, 0.002, 0.003], 'code_length')
>>> os.remove('my_code_data.h5')


#### Text Files¶

The unyt library also has wrappers around numpy.savetxt and numpy.loadtxt for saving data as an ASCII table. For example:

>>> import unyt as u
>>> import os
>>> data = [[1, 2, 3]*u.cm, [4, 5, 6]*u.kg]
>>> u.savetxt('my_data.txt', data)
>>> with open('my_data.txt') as f:
...     print("".join(f.readlines()))    # doctest: +NORMALIZE_WHITESPACE
# Units
# cm  kg
1.000000000000000000e+00      4.000000000000000000e+00
2.000000000000000000e+00      5.000000000000000000e+00
3.000000000000000000e+00      6.000000000000000000e+00
<BLANKLINE>
>>> os.remove('my_data.txt')


#### Pickles¶

Note

Pickle files are great for serializing data to disk or over a network for internal usage by a package. They are ill-suited for long-term data storage or for communicating data between different Python installations. If you want to use pickle files for data storage, consider using a format designed for long-term data storage, like HDF5.

Both unyt.unyt_array and unyt.Unit instances can be saved using the pickle protocol:

>>> from unyt import kg
>>> import pickle
>>> import numpy as np
...
>>> assert kg == pickle.loads(pickle.dumps(kg))
>>> data = [1, 2, 3]*kg
>>> reloaded_data = pickle.loads(pickle.dumps(data))
>>> assert np.array_equal(data.value, reloaded_data.value)
>>> assert data.units == reloaded_data.units


As for HDF5 data, the unit registry associated with the unit object is saved to the pickle. If you have custom units defined, the reloaded data will know about your custom unit and be able to convert data to and from the custom unit.

### Performance Considerations¶

Tracking units in an application will inevitably add overhead. Judging where overhead is important or not depends on what real-world workflows look like. Ultimately, profiling code is the best way to find out whether handling units is a performance bottleneck. Optimally handling units will be amortized over the cost of an operation. While this is true for large arrays (bigger than about one million elements), this is not true for small arrays that contain only a few elements.

In addition, it is sometimes easy to write code that needlessly checks unit consistency when we know ahead of time that data are already in the correct units. Often we can get away with only checking unit consistency once and then stripping units after that.

A good rule of thumb is that units should be checked on input, stripped off of data during a calculation, and then re-applied when returning data from a function. In other words, apply or check units at interfaces, but during an internal calculation it is often worth stripping units, especially if the calculation involves many operations on arrays with only a few elements.

## unyt_array.name attribute¶

The unyt_array has a name attribute for use in structured-data applications or similar applications that require labeled data. For example, Numpy has record arrays and when constructed as shown below, it is possible to retain the units while taking advantage of the labeled record fields.

>>> import numpy as np
>>> from unyt import unyt_array
>>> x = unyt_array([0, 1, 2], "s", name="time")
>>> y = unyt_array([3, 4, 5], "m", name="distance")
>>> data = (x, y)
>>> dt = [(a.name, "O") for a in data]
>>> data_points = np.array(list(zip(*data)), dtype=dt).view(np.recarray)
>>> data_points.time
unyt_quantity(0, 's')
>>> data_points.distance
unyt_quantity(3, 'm')


Note

The name attribute does not propagate through mathematical operations. Other operations such as indexing, copying, and unit conversion, will preserve the name attribute where the semantic meaning of the quantity remains the same.

## Plotting with Matplotlib¶

Note

• This is an experimental feature. Please report issues.
• This feature works in Matplotlib versions 2.2.4 and above
• Matplotlib is not a dependency of Unyt

Matplotlib is Unyt aware. After enabling support in unyt using the unyt.matplotlib_support context manager, Matplotlib will label the x and y axes with the units.

>>> import matplotlib.pyplot as plt
>>> from unyt import matplotlib_support, s, K
>>> x = [0.0, 60.0, 120.0]*s
>>> y = [298.15, 308.15, 318.15]*K
>>> with matplotlib_support:
...   plt.plot(x, y)
...   plt.show()
[<matplotlib.lines.Line2D object at ...>] You can change the plotted units without affecting the original data.

>>> with matplotlib_support:
...   plt.plot(x, y, xunits="min", yunits=("J", "thermal"))
...   plt.show()
[<matplotlib.lines.Line2D object at ...>] It is also possible to set the label style; the choices "()", "[]" and "/" are supported.

>>> matplotlib_support.label_style = "[]"
>>> with matplotlib_support:
...   plt.plot(x, y)
...   plt.show()
[<matplotlib.lines.Line2D object at ...>] The axis label will include the unyt_array.name attribute if set.

>>> x.name = "Time"
>>> y.name = "Temperature"
>>> with matplotlib_support:
...   plt.plot(x, y)
...   plt.show()
[<matplotlib.lines.Line2D object at ...>] With label_style set to “/”, the axis label conforms to the SI standard where the axis label is a mathematical expression rather than a caption. In this case, set the unyt_array.name attribute to the latex expression for the physical quantity symbol.

>>> x.name = "$t$"
>>> y.name = ""
>>> matplotlib_support.label_style = "/"
>>> with matplotlib_support:
...   plt.plot(x, y)
...   plt.show()
[<matplotlib.lines.Line2D object at ...>] There are three ways to use the context manager:

1. As a conventional context manager in a with statement as shown above
2. As a feature toggle in an interactive session:
>>> import matplotlib.pyplot as plt
>>> from unyt import s, K, matplotlib_support
>>> matplotlib_support.enable()
>>> plt.plot([0, 1, 2]*s, [3, 4, 5]*K)
[<matplotlib.lines.Line2D object at ...>]
>>> plt.show()
>>> matplotlib_support.disable()

1. As an enable for a complete session:
>>> import unyt
>>> unyt.matplotlib_support()
>>> import matplotlib.pyplot as plt