YTEP-0011: Symbol units in yt


Created: March 7, 2013
Authors: Nathan Goldbaum, Casey Stark, Anna Rosen, Matt Turk

This YTEP describes adding symbolic units to yt using the sympy package. The main benefit is to make sure units are carried through calculations in a transparent and intuitive manner. The new components are:

  • a Unit class, which describes the dimensionality (powers of mass, length, time, temperature) and conversion factor of any unit.
  • a UnitRegistry class, which stores valid atomic unit symbols (ex: “g” for gram).
  • a YTArray class, a subclass of NumPy ndarray that attaches a Unit object.
  • a YTQuantity class, a subclass of YTArray which is restricted to a single element (for handling scalars).



Detailed Description


The current system for units is functional but not terribly flexible. All data are treated as scalars and it is up to the user to convert data from CGS, which yt uses internally, to their chosen unit system. A sample workflow might look like this:

from yt.mods import *
from yt.utilities.physical_constants import mass_sun_cgs
pf = load('IsolatedGalaxy/galaxy0030/galaxy0030')
dd = pf.h.all_data()
mass = dd['CellMass']
print "Mass in CGS: ", mass
print "Mass in Solar Masses: ", dd['CellMass']/mass_sun_cgs
print "Mass in code units: ", dd['CellMass']/pf['Mass']

This model works well if a user always uses CGS units. If the user needs a quantity in a different unit system, they run into trouble. This is illustrated above in the example to convert to ‘solar mass’ units, since this isn’t a proper unit, the conversion isn’t stored inside the pf dict, so a user will either need to import the unit definition from yt, or add their own definition to their script. The situation is a little bit better for length conversions:

dx = dd['dx']
print "Cell dx in code units: ", dx
print "Cell dx in centimeters: ", dx*pf['Length']
print "Cell dx in megaparsecs: ", dx*pf['mpc']

This works pretty nicely, since all of the various length units are stored in the pf dictionary. However, this example illustrates another problem; here dx is returned in code units, while most quantities are returned in CGS. If we wanted to enforce that all quantities be returned in CGS, we would need to painstakingly go through the codebase, tweaking the field definitions and places where fields are used so that units are handled properly. Clearly, a better solution is needed.

Cosmological units are also handled in a somewhat ad hoc way. Each of the code frontends need to detect that a simulation was performed using comoving units, and define new scaled, comoving and scaled comoving units (i.e. ‘kpccm’, ‘kpchcm’ and ‘kpch’). This encourages duplication of code in each of the frontends and makes likely that different frontends will ignore some of the cosmological units that are defined in the Enzo frontend. In addition, this is not documented in the frontend docs, making it easier for newly supported codes to miss this. Cosmological units are also not labeled correctly in plots.

To ensure units to display nicely on plots, the unit definition is currently encoded as a raw string in LaTeX format:


This is harmful for readability and has the effect that user-defined or automatically generated fields are not assigned units.

Proposed Solution

We propose to handle units in a more automatic fashion, leveraging the symbolic math library sympy. Instead of returning a NumPy ndarray when users query for fields, the __getitem__ selector on data objects will return a YTArray, a subclass of ndarray. This preserves ndarray’s array operations, including deep and shallow copies, broadcasting, and views.

Additonally, YTArray has a Unit object attached to it that tracks units associated with each value in the array. This is encoded in the __repr__ method of YTArray:

>>> dd['density']
YTArray([  4.92775113e-31,   4.94005233e-31,   4.93824694e-31, ...,
           1.12879234e-25,   1.59561490e-25,   1.09824903e-24]) g/cm**3

YTArray defines several user-visible member functions:

  • convert_to_units

    Converts an array to a valid unit, specified by a string argument. Valid units possess the same dimension expression as the current unit.

  • convert_to_cgs

    Converts the array to CGS units.

  • in_units

    Returns a copy of the array in a valid unit, specified by a string argument. Valid units possess the same dimension expression as the current unit.

  • in_cgs

    Returns a copy of the array in CGS units.

It’s important to remember that convert_to_cgs and convert_to_units do in-place conversion of an existing array and in_units and in_cgs return a copy of the original array in the new unit. This can get complicated if one isn’t careful about the distinction between creating copies and references, as illustrated in the following example:

>>> dens = dd['density']
>>> print dens
[  4.92775113e-31   4.94005233e-31   4.93824694e-31 ...,   1.12879234e-25
   1.59561490e-25   1.09824903e-24] g/cm**3
>>> dens.convert_to_units('Msun/pc**3')
>>> print dens
[  7.27920765e-09   7.29737882e-09   7.29471191e-09 ...,   1.66743685e-03
   2.35702085e-03   1.62231868e-02] Msun/pc**3
>>> dd['density'].in_units('Msun/pc**3')
YTArray([  7.27920765e-09,   7.29737882e-09,   7.29471191e-09, ...,
           1.66743685e-03,   2.35702085e-03,   1.62231868e-02]) Msun/pc**3

In the example above, if a user tries to query dd['density'] again, they will find that it has been converted to solar masses per cubic parsec, since a shallow copy, dens, underwent an in-place unit conversion. In practice this is not a big concern, since the unit metadata is preserved and the array values are still correct in the new unit system, all numerical operations will still be correct.

One of the nicest aspects of this new unit system is that the symbolic algebra for unitful operations is performed automatically by sympy:

>>> print dd['cell_mass']/dd['cell_volume']
[  4.92775113e-31   4.94005233e-31   4.93824694e-31 ...,   1.12879234e-25
   1.59561490e-25   1.09824903e-24] g/cm**3
>>> print dd['density']
[  4.92775113e-31   4.94005233e-31   4.93824694e-31 ...,   1.12879234e-25
   1.59561490e-25   1.09824903e-24] g/cm**3

YTArray is primarily useful for attaching units to NumPy ndarray instances. For scalar data, we have created the new YTQuantity class. In the proposed implementation, YTQuantity is a subclass of YTArray with the requirement that it is limited to one element. YTQuantity is primarily useful for physical constants and ensures that the units are propogated correctly when composing quantities from arrays, physical constants, and unitless scalars:

>>> from yt.utilities.physical_constants import boltzmann_constant
>>> print dd['temperature']*boltzmann_constant
[  1.28901607e-12   1.29145540e-12   1.29077208e-12 ...,   1.63255263e-12
   1.59992074e-12   1.40453862e-12] erg

With this new capability, we will have no need for fields defined only to handle different units (e.g. RadiusCode, Radiuspc, etc.). Instead, there will only be one definition and if a user needs the field in a different unit system, they can quickly convert using convert_to_units or in_units.

When a StaticOutput object is instantiated, it will its self instantiate and set up a UnitRegistry class that contains a full set of units that are defined for the simulation. This is particularly useful for cosmological simulations, since it makes it easy to ensure cosmological units are defined automatically.

The new unit systems lets us to encode the simulation coordinate system and scaling to physical coordinates directly into the unit system. We do this via “code units”.

Every StaticOutput object will have a length_unit, time_unit, mass_unit, and velocity_unit attribute that the user can quickly and easily query to discover the base units of the simulation. For example:

>>> from yt.mods import *
>>> ds = load("Enzo_64/DD0043/data0043")
>>> print ds.length_unit
128 Mpccm/h

Additionally, we will allow conversions to coordinates int the simulation coordinate system defined by the on-disk data. Data in code units will be available by converting to code_length, code_mass, code_time, code_velocity, or any combination of those units. Code units will preserve dimensionality: an array or quantity that has units of cm will be convertible to code_length, but not to code_mass.

On-disk data will also be available to the user, presented in unconverted code units. To obtain on-disk data, a user need only query a data object using an on-disk field name:

>>> from yt.mods import *
>>> ds = load("Enzo_64"/DD0043/data0043")
>>> dd = ds.h.all_data()
>>> print dd['Density']
[  6.74992726e-02   6.12111635e-02   8.92988636e-02 ...,   9.09875931e+01
   5.66932465e+01   4.27780263e+01] code_mass/code_length**3
>>> print dd['density']
[  1.92588950e-31   1.74647714e-31   2.54787551e-31 ...,   2.59605835e-28
   1.61757192e-28   1.22054281e-28] g/cm**3

Here, the first data object query is returned in code units, while the second is returned in CGS. This is because Density is an on-disk field, while density is a ‘standard’ yt field. See YTEP-0003: Standardizing field names.

Unit labels for plots will be programatically generated. This will leverage the sympy LaTeX output module. Even though the field definitions will have their units encoded in plain text, we will be able to automatically generate LaTeX to supply to matplotlib’s mathtext parser.


Our unit system has 6 base dimensions, mass, length, time, temperature, metallicity, and angle. The unitless dimensionless dimension, which we use to represent scalars is also technically a base dimension, although a trivial one.

For each dimension, we choose a base unit. Our system’s base units are grams, centimeters, seconds, Kelvin, metal mass fraction, and radian. All units can be described as combinations of these base dimensions along with a conversion factor to equivalent base units.

The choice of CGS as the base unit system is somewhat arbitrary. Most unit systems choose SI as the reference unit system. We use CGS to stay consistent with the rest of the yt codebase and to reflect the standard practice in astrophysics. In any case, using a physical coordinate system makes it possible to compare quantities and arrays produced by different datasets, possibly with different conversion factors to CGS and to code units. We go into more detail on this point below.

We provide sympy Symbol objects for the base dimensions. The dimensionality of all other units should be sympy Expr objects made up of the base dimension objects and the sympy operation objects Mul and Pow.

Let’s use some common units as examples: gram (g), erg (erg), and solar mass per cubic megaparsec (Msun / Mpc**3). g is an atomic, CGS base unit, erg is an atomic unit in CGS, but is not a base unit, and Msun/Mpc**3 is a combination of atomic units, which are not in CGS, and one of them even has a prefix. The dimensions of g are mass and the cgs factor is 1. The dimensions of erg are mass * length**2 * time**-2 and the cgs factor is 1. The dimensions of Msun/Mpc**3 are mass / length**3 and the cgs factor is about 6.8e-41.

We use the UnitRegistry class to define all valid atomic units. All unit registries contain a unit symbol lookup table (dict) containing the valid units’ dimensionality and cgs conversion factor. Here is what it would look like with the above units:

{ "g":    (mass, 1.0),
  "erg":  (mass * length**2 * time**-2, 1.0),
  "Msun": (mass, 1.98892e+33),
  "pc":   (length, 3.08568e18), }

Note that we only define atomic units here. There should be no operations in the registry symbol strings. When we parse non-atomic units like Msun/Mpc**3, we use the registry to look up the symbols. The unit system in yt knows how to handle units like Mpc by looking up unit symbols with and without prefixes and modify the conversion factor appropriately.

We construct a Unit object by providing a string containing atomic unit symbols, combined with operations in Python syntax, and the registry those atomic unit symbols are defined in. We use sympy’s string parsing features to create the unit expression from the user-provided string. Here’s how this works on Msun/Mpc**3:

>>> from sympy.parsing.sympy_parser import parse_expr
>>> unit_expr = parse_expr("Msun/Mpc**3")
>>> from sympy.printing import print_tree
>>> print_tree(unit_expr)
    Mul: Msun/Mpc**3
    +-Symbol: Msun
    | comparable: False
    +-Pow: Mpc**(-3)
      +-Symbol: Mpc
      | comparable: False
      +-Integer: -3
        real: True

When presented with a new unit specification string, a new Unit is created by first decomposing the unit specification into atomic unit symbols. This may require considering SI prefixes, which we allow for a whitelisted subset of atomic unit symbols, listed in the table of unit symbols below. The Unit instance is then created by combining a sympy expression for the unit and the appropriate CGS factors, found by combining the CGS factors of the base unit and optional SI prefixes.

Unit objects are associated with four instance members, a unit Expression object, a dimensionality Expression object, a UnitRegistry instance, and a scalar conversion factor to CGS units. These data are available for a Unit object by accessing the expr, dimensions, registry, and cgs_value attributes, respectively.

Unit provides the methods same_dimensions_as, which returns True if passed a Unit object that has equivalent dimensions, get_cgs_equivalent, which returns the equivalent cgs base units of the Unit, and the is_code_unit property, which is True if the unit is composed purely of code units and False otherwise. Unit also defines the mul, div, pow, and eq operations with other unit objects, making it easy to compose compound units algebraically.

The UnitRegistry class provides the add, remove, and modify methods which allows users to add, remove, and modify atomic unit definitions present in UnitRegistry objects. A dictionary lookup table is also attached to the UnitRegistry object, providing an interface to look up unit symbols. In general, unit registries should only be adjusted inside of a code frontend, since otherwise quantities and arrays might be created with inconsistent unit metadata. Once a unit object is created, it will not recieve updates if the original unit registry is modified.

We also provide a singleton default_unit_registry instance that frontend developers can copy and modify to build a simulation-specific unit symbol registry.

The YTArray class works by tacking a Unit object onto an ndarray instance. Besides the conversion methods already listed, most of the implementation of YTArray depends on defining all possible ndarray operations on YTArray instances. We want to preserve normal ndarray operations, while getting the correct units on the resulting YTArray (be it in-place or a copy). The proper way to handle operations on ndarray subclasses is explained in the NumPy docs page, subclassing ndarray. We follow this approach and describe the desired behavior in the next section below.

The code for these new classes will live in a new top-level yt.units package. This package will contain five submodules:

  • unit_lookup_table

    Contains all static unit metadata used to generate the sympy unit system

  • unit_object

    Contains the Unit class

  • unit_registry

    Contains the UnitRegistry class

  • yt_array

    Contains the YTArray and YTQuantity classes.

  • unit_symbols

    Contains a host of predefined unit quantities, useful for applying units to raw scalar data.

Creating YTArray and YTQuantity instances

In the current implementation, there are two ways to create new array and quantity objects, via a constructor, and by multiplying scalar data by a unit quantity.

Class Constructor

The primary internal interface for creating new arrays and quantities is through the class constructor for YTArray. The constructor takes three arguments. The first argument is the input scalar data, which can be an integer, float, list, or array. The second argument, input_units, is a unit specification which must be a string or Unit instance. Last, users may optionally supply a UnitRegistry instance, which will be attached to the array. If no UnitRegistry is supplied, the default_unit_registry is used instead.

Unit specification strings must be algebraic combinations of unit symbol names, using standard Python mathematical syntax (i.e. ** for the power function, not ^).

Here is a simple example of YTArray creation:

>>> from yt.units import yt_array, YTQuantity
>>> YTArray([1, 2, 3], 'cm')
YTArray([1, 2, 3]) cm
>>> YTQuantity(3, 'J')
3 J

In addition to the class constructor, we have also defined two convenience functions, quan, and arr, for quantity and array creation that are attached to the StaticOutput base class. These were added to syntactically simplify the creation of arrays with the UnitRegistry instance associated with a dataset. These functions work exactly like the YTArray and YTQuantity constructors, but pass the UnitRegistry instance attached to the dataset to the underlying constructor call. For example:

>>> from yt.mods import *
>>> ds = load("Enzo_64/DD0043/data0043")
>>> ds.arr([1, 2, 3], 'code_length').in_cgs()
YTArray([  5.55517285e+26,   1.11103457e+27,   1.66655186e+27]) cm

This example illustrates that the array is being created using ds.unit_registry, rather than the default_unit_registry, for which code_length is equivalent to cm.


New YTArray and YTQuantity instances can also be created by multiplying YTArray or YTQuantity instances by float or ndarray instances. To make it easier to create arrays using this mechanism, we have populated the yt.units namespace with predefined YTQuantity instances that correspond to common unit symbol names. For example:

>>> from yt.units import meter, gram, kilogram, second, joule
>>> kilogram*meter**2/second**2 == joule
>>> from yt.units import m, kg, s, W
>>> kg*m**2/s**3 == W
>>> from yt.units import kilometer
>>> three_kilometers = 3*kilometer
>>> print three_kilometers
3.0 km
>>> from yt.units import gram, kilogram
>>> print gram+kilogram
1001.0 g
>>> print kilogram+gram
1.001 kg
>>> print kilogram/gram
1000.0 dimensionless

Handling code units

If users want to work in code units, they can now ask for data in code units, just like any other unit system. For example:

>>> dd["density"].in_units("code_mass/code_length**3")

will return the density field in code units.

Code units are tightly coupled to on-disk parameters. To handle this fact of life, the yt unit system can modify, add, and remove unit symbols via the UnitRegistry.

Associating arrays with a coordinate system

To create quantities and arrays in units defined by a simulation coordinate system, we associate a UnitRegistry instance with StaticOutput instances. This unit registry contains the metadata necessary to convert the array to CGS from some other known unit system and is available via the unit_registry attribute that is attached to all StaticOutput instances.

To avoid repetitive references to the unit_registry, we also define two new member functions in the StaticOutput base class, quan and arr. These functions simply pass the appropriate unit_registry object to the YTQuantity and YTArray constructors, returning the resulting quantity or array.

We have modified the definition for set_code_units in the StaticOutput base class. In this new implemenation, the predefined code_mass, code_length, code_time, and code_velocity symbols are adjusted to the appropriate values and length_unit, time_unit, mass_unit, velocity_unit attributes are attached to the StaticOutput instance. If there are frontend specific code units, like MHD units, they should also be defined in subclasses by extending this function.

Mixing modified unit registries

It becomes necessary to consider mixing unit registries whenever data needs to be compared between disparate datasets. The most straightforward example where this comes up is a cosmological simulation time series, where the code units evolve with time. The problem is quite general – we want to be able to compare any two datasets, even if they are unrelated.

We have designed the unit system to refer to a physical coordinate system based on CGS conversion factors. This means that operations on quantities with different unit registries will always agree since the final calculation is always performed in CGS.

The examples below illustrate the consistency of this choice:

>>> from yt.mods import *
>>> pf1 = load('Enzo_64/DD0002/data0002')
>>> pf2 = load('Enzo_64/DD0043/data0043')
>>> print pf1.length_unit, pf2.length_unit
128 Mpccm/h, 128 Mpccm/h
>>> print pf1.length_unit.in_cgs(), pf2.length_unit.in_cgs()
6.26145538088e+25 cm 5.55517285026e+26 cm
>>> print pf1.length_unit*pf2.length_unit
145359.100149 Mpccm**2/h**2
>>> print pf2.length_unit*pf1.length_unit
1846.7055432 Mpccm**2/h**2

Note that in both cases, the answer is not the seemingly trivial 128^2\/=\/16384\,\rm{Mpccm}^2/h^2. This is because the new quantity returned by the multiplication operation inherits the unit registry from the left object in binary operations. This convention is enforced for all binary operations on two YTarray objects. In any case, results are always consistent in CGS:

>>> print (pf1.length_unit*pf2.length_unit).in_cgs()
3.4783466935e+52 cm**2
>>> print pf1.length_unit.in_cgs()*pf2.length_unit.in_cgs()
3.4783466935e+52 cm**2

Handling cosmological units

We also want to handle comoving length units and the hubble little “h” unit. In StaticOutput.set_units, we implement this by checking if the simulation is cosmological, and if so adding comoving units to the dataset’s unit registry. Comoving length unit symbols are still named following the pattern “(length symbol)cm”, i.e. “pccm”.

The little “h” symbol is treated as a base unit, h, which defaults to unity. StaticOutput.set_units should update the h symbol to the correct value when loading a cosmological simulation.

LaTeX printing

We will make use of sympy’s LaTeX pretty-printing functionality to generate axis and colorbar labels automatically for unit symbols. The LaTeX strings used for atomic units are encoded in the latex_symbol_lut. This is necessary because, for the purposes of LaTeX representation, sympy interprets symbol names as if they were algebraic variables, and so get displayed using an italic font. Since our symbols represent units, we want to display them in a roman font and need to wrap them in \rm{}. New units do not need to be explicitly added to the look-up-table, by default the LaTeX symbol will simply be the string name of the unit, wrapped using \rm{}.

Using these LaTeX representations of atomic unit symbols, we then use sympy to generate labels, composing the LaTeX expressions for compound units according to the algebraic relationships between the atomic unit symbols.

YTArray operations

When working interactively, it is important to make sure quick workflows are possible. To this end, we want to make it possible to use our new dimensionful operations while still leveraging the syntactic simplicity NumPy offers. We want to avoid mandating that all user-defined data be a YTArray or YTQuantity.

To this end, we define operations between native Python objects like float, NumPy float, NumPy ndarray, and YTArray. In the table below, we have enumerated all combinations of YTArray, scalar (native Python float or np.float64), and ndarray for binary operations. In most cases, unitful operations are well defined, however in cases where the unitful operations are not well defined, we raise a new exception, YTInvalidUnitOperation.

Since NumPy defines in-place, left, and right versions of all mathematical operations (i.e. add, iadd, ladd, radd), we only list the ‘basic’ version of each operation, with the expectation the implemenation accounts for all four variants, which all have the same behavior with respect to passing units.

Operation Combination Result (pseudocode)
mul, div, truediv, floordiv scalar, YTArray ndarray, YTArray
YTArray, units = input_units (op) 1
YTArray, YTArray
YTArray, units = left_units (op) right_units
add, sub scalar, YTArray ndarray, YTArray
if YTArray is dimensionless:
return YTArray
YTArray, YTArray
if left_units same dimensions as right_units:
return YTArray, in left_units
raise YTInvalidUnitOperation

scalar, YTArray

ndarray, YTArray

if YTArray is dimensionless:
return scalar**YTArray
raise YTInvalidUnitOperation
YTArray, scalar
return YTArray**scalar (note units change)
YTArray, ndarray
if YTArray is dimensionless:
return YTArray**ndarray
raise YTInvalidUnitOperation [1]
YTArray, YTArray
if YTArray and YTArray are dimensionless:
return YTArray**YTArray
raise YTInvalidUnitOperation [1]
le, lt, ge, gt, eq scalar, YTArray ndarray, YTArray
if YTArray is dimensionless:
return YTArray
raise YTInvalidUnitOperation
YTArray, YTArray
if left_units same dimensions as right units:
return left (op) (right in left units)
raise YTInvalidUnitOperation
[1](1, 2) This one is a little tricky, since it is defined for ndarrays. Technically, it’s a well-defined unitful operation if the ndarray is the exponent. Unfortunately, this will make all the elements of the ndarray have different units, so we don’t allow it in practice.

Now we list the behavior of unary operations on YTArray objects.

Operation Result (pseudocode)
abs, sqrt neg YTArray
if YTArray is dimensionless:
return exp(YTArray)
raise YTInvalidUnitOperation

Unit symbol names

In the table below we provide a listing of all units that are in the current implementation. We also list the dimensions of the unit, if the unit is in the whitelist to be prefixable with SI abbreviations, the dimensions of the unit, and the adopted CGS conversion factor.

Unit Symbol name Dimensions SI Prefixable? CGS Conversion factor
Base units
Gram g mass yes 1.0
Meter m length yes 100.0
Second s time yes 1.0
Kelvin K temperature yes 1.0
Radian radian angle no 1.0
Gauss gauss magnetic_field yes 1.0
Code units
Code mass units code_mass mass no ?
Code length units code_length length no ?
Code time units code_time time no ?
Code velocity units code_velocity velocity no ?
Code magnetic field units code_magnetic magnetic_field no ?
Code temperature units code_temperatre temperature no ?
Code metallicity units code_metallicity metallicity no ?
Normalized domain units unitary length no Domain width
Misc CGS
Dyne dyne force yes 1.0
Erg erg energy yes 1.0
Electrostatic unit esu (energy*length)**0.5 yes 1.0
Gauss gauss magnetic_field yes 1.0
Misc SI
Joule J energy yes 1.0e7
Watt W power yes 1.0e7
Hertz Hz rate yes 1.0
Imperial units
Foot ft length no 30.48
Mile mile length no 160934
Cosmological “units”
Little h h dimensionless no ?
Time units
Minute min time no 60
Hour hr time no 3600
Day day time no 86400
Year yr time yes 31557600
Solar units
Solar mass Msun mass no 1.98841586e33
Solar radius Rsun length no 6.9550e10
Solar luminosity Lsun power no 3.8270e33
Solar temperature Tsun temperature no 5870.0
Solar metallicity Zsun metallicity no 0.02041
Astronomical distances
Astronomical unit AU length no 1.49597871e13
Light year ly length no 9.4605284e17
Parsec pc length yes 3.0856776e18
Degree degree angle no \pi/180
Arcminute arcmin angle no \pi/10800
Arcsecond arcsec angle no \pi/648000
Milliarcsecond mas angle no \pi/648000000
Physical units
Electron volt eV energy no 1.602176562e-12
Atomic mass unit amu mass no 1.660538921e-24
Electron mass me mass no 9.10938291e-28


We have written a set of unit tests that check to make sure all valid and invalid unit operations succeed or fail as appropriate. We will also need to verify that the extant unit and answer tests pass before this can be accepted.

Backwards Compatibility

This is a serious break in backwards compatibility. Once this is accepted, units will no longer be stored in the StaticOutput dict. This means that all scripts which use the pf[unit] construction will no longer be valid. We will also need to eliminate instances of this construction within the yt codebase.

We will need to check to make sure the analysis modules and external tools that operate on yt data can either work appropriately with YTArray or figure out a way to degrade to ndarray gracefully.