Arrays, Quantities, and Units

Whenever YT returns physical data, it is typically associated with certain units (e.g., density in grams per cubic centimeter, temperature in Kelvin, and so on). YT exposes the YTArray, YTQuantity, and units facilities from yt so that “unitful” objects may be manipulated and operated on.

Arrays

If we grab the "density" field from a sphere, it will be returned as a YTArray in \(\rm{g}/\rm{cm}^3\):

julia> sp = YT.Sphere(ds, "c", (100.,"kpc"))
YTSphere (sloshing_nomag2_hdf5_plt_cnt_0100): center=[ 0.  0.  0.] code_length,
radius=100.0 kpc

julia> sp["density"]
325184-element YTArray (g/cm**3):
 1.3086558386643183e-26
 1.28922012403754e-26
 1.3036428741306716e-26
 1.2999706649871096e-26
 1.3180126226317337e-26
 1.2829197138546694e-26
 1.297694215792844e-26
 1.2945722063157944e-26
 1.3124175650316954e-26
 1.3088245501274466e-26
 ⋮
 1.6093269371270004e-26
 1.64592576904618e-26
 1.606223724726208e-26
 1.6415200117053996e-26
 1.635422055278283e-26
 1.622938177378765e-26
 1.5840914000284966e-26
 1.6194386856326155e-26
 1.6152527924542866e-26
 1.595660076018442e-26

A YTArray can be manipulated in many of the same ways that normal Julia arrays are, and the units are retained. The following are some simple examples of this.

Finding the maximum density:

julia> maximum(sp["density"])
9.256136409265674e-26 g/cm**3

Multiplying the temperature by a constant unitless number:

julia> sp["temperature"]*5
325184-element YTArray (K):
 4.41628e8
 4.4457548e8
 4.4363016e8
 4.4104716e8
 4.4259016e8
 4.464104e8
 4.4553836e8
 4.429778e8
 4.4458e8
 4.4192136e8
 ⋮
 3.42009e8
 3.3811488e8
 3.3988892e8
 3.3605176e8
 3.341696e8
 3.410656e8
 3.4288464e8
 3.390078e8
 3.369208e8
 3.4209352e8

Adding two YTArrays:

julia> sp["velocity_magnitude"]+sp["sound_speed"]
325184-element YTArray (cm/s):
 1.7494106880789694e8
 1.750480854794736e8
 1.7491905482683247e8
 1.7463744560410416e8
 1.7477896725137833e8
 1.7498621058854717e8
 1.7486426825557864e8
 1.7463176707801563e8
 1.7473392939487094e8
 1.7449670611457497e8
 ⋮
 1.4691744928089392e8
 1.448218647261667e8
 1.4619022766526273e8
 1.4414687202610317e8
 1.4354279490019822e8
 1.4629026827881128e8
 1.4767689116216296e8
 1.45570568978103e8
 1.4486893148240653e8
 1.471462895473701e8

Multiplying element-wise one YTArray by another:

julia> sp["density"].*sp["temperature"]
325184-element YTArray (K*g/cm**3):
 1.1558781214352911e-18
 1.1463113109392978e-18
 1.1566705936668994e-18
 1.1466967397517522e-18
 1.1666788350651973e-18
 1.145417405259497e-18
 1.1563451053716595e-18
 1.1469334957898334e-18
 1.1669492021235823e-18
 1.1567950503874187e-18
 ⋮
 1.1008085928797365e-18
 1.1130239877799136e-18
 1.0918752941511363e-18
 1.1032713780176403e-18
 1.0930166680870434e-18
 1.1070567664611898e-18
 1.0863212188517341e-18
 1.0980046921024092e-18
 1.0884245260718644e-18
 1.0917299442572327e-18

However, attempting to perform an operation that doesn’t make sense will throw an error. For example, suppose that you tried to instead add "density" and "temperature", which aren’t the same type of physical quantity:

julia> sp["density"]+sp["temperature"]
ERROR: The + operator for YTArrays with units
(g/cm**3) and (K) is not well defined.
 in + at /Users/jzuhone/.julia/YT/src/array.jl:141

It is also possible to create a YTArray from a regular Julia Array, like so:

julia> a = YT.YTArray(randn(10), "erg")
10-element YTArray (erg):
 -0.14854525691731818
 -0.44315729646073715
 -1.8669284316708383
 -1.4228733016999084
 -0.0934020019569414
  0.029660552522097813
  0.4280709348298647
 -0.05755731738462625
  1.032874362011772
  0.17854214710697325

If your YTArray needs to know about code units associated with a specific dataset, you’ll have to create it with a Dataset object passed in:

julia> a = YT.YTArray(ds, [1.0,1.0,1.0], "code_length")
3-element YTArray (code_length):
 1.0
 1.0
 1.0

Quantities

A YTQuantity is just a scalar version of a YTArray. They can be manipulated in the same way:

julia> a = YT.YTQuantity(3.14159, "radian")
3.14159 radian

julia> b = YT.YTQuantity(12, "cm")
12.0 cm

julia> a/b
0.26179916666666664 radian/cm

julia> a\b
3.8197218605865184 cm/radian

julia> c = YT.YTQuantity(13,"m")
13.0 m

julia> b+c
1312.0 cm

julia> d = YT.YTQuantity(ds, 1.0, "code_length")
1.0 code_length

Changing Units

Occasionally you will want to change the units of an array or quantity to something more appropriate. Taking density as the example, we can change it to units of solar masses per kiloparsec:

julia> a = YT.in_units(sp["density"], "Msun/kpc**3")
325184-element YTArray (Msun/kpc**3):
 193361.43661723754
 190489.69785225237
 192620.74223809008
 192078.1521891412
 194743.95533346717
 189558.77596412544
 191741.79371078173
 191280.49883112026
 193917.25335152834
 193386.3647075119
 ⋮
 237787.32295826814
 243195.01114436015
 237328.8054548747
 242544.03512482112
 241643.02694502342
 239798.46209161723
 234058.62702232625
 239281.3920328031
 238662.9022094481
 235767.96552301125

We can switch back to cgs units rather easily:

julia> YT.in_cgs(a)
325184-element YTArray (g/cm**3):
 1.3086558386643183e-26
 1.28922012403754e-26
 1.303642874130672e-26
 1.2999706649871096e-26
 1.318012622631734e-26
 1.2829197138546696e-26
 1.297694215792844e-26
 1.2945722063157944e-26
 1.3124175650316954e-26
 1.308824550127447e-26
 ⋮
 1.6093269371270004e-26
 1.64592576904618e-26
 1.606223724726208e-26
 1.6415200117053996e-26
 1.6354220552782833e-26
 1.622938177378765e-26
 1.5840914000284966e-26
 1.6194386856326155e-26
 1.6152527924542868e-26
 1.595660076018442e-26

or to MKS units:

julia> YT.in_mks(a)
325184-element YTArray (kg/m**3):
 1.3086558386643184e-23
 1.2892201240375402e-23
 1.3036428741306718e-23
 1.2999706649871097e-23
 1.3180126226317338e-23
 1.2829197138546696e-23
 1.297694215792844e-23
 1.2945722063157945e-23
 1.3124175650316956e-23
 1.3088245501274467e-23
 ⋮
 1.6093269371270004e-23
 1.64592576904618e-23
 1.6062237247262084e-23
 1.6415200117053996e-23
 1.6354220552782833e-23
 1.6229381773787652e-23
 1.584091400028497e-23
 1.6194386856326155e-23
 1.6152527924542868e-23
 1.595660076018442e-23

Physical Constants

Some physical constants are represented in YT. They are available via the YT.physical_constants submodule, and are unitful quantities which can be used with other quantities and arrays:

julia> kb = YT.physical_constants.kboltz # Boltzmann constant
1.3806488e-16 erg/K

julia> kT = YT.in_units(kb*sp["temperature"], "keV") # computing kT in kilo-electronvolts
325184-element YTArray (keV):
 7.611310547262892
 7.66210937707406
 7.645817103743251
 7.601299964559187
 7.62789305234897
 7.6937336082128995
 7.6787042911187955
 7.634573897812892
 7.662187277758966
 7.616366508529263
 ⋮
 5.8944104743332275
 5.827296621433712
 5.857871606179393
 5.791739439787011
 5.759301043082916
 5.878151291558838
 5.909501836220619
 5.842685798328886
 5.806717052886709
 5.895867148202309

The physical constants implemented in YT.physical_constants are (in cgs units):

  • G: Newton’s constant of gravitation
  • kboltz: Boltzmann’s constant
  • clight: Speed of light in vacuum
  • me: mass of the electron
  • mp: mass of the proton
  • qp: charge of the proton
  • hcgs: Planck’s constant
  • sigma_thompson: Thompson cross section
  • amu_cgs: Atomic mass unit
  • Na: Avogadro’s number
  • Tcmb: Cosmic microwave background temperature
  • stefan_boltzmann: Stefan-Boltzmann constant