Calling sxs from Mathematica#
Newer versions of Mathematica (version 11.3 and greater) include a convenient
way to call Python code from a Mathematica session: you just tell Mathematica
where to find the python executable, and then evaluate Mathematica commands
containing the Python code you want to run.
Getting Mathematica working with Python#
As of this writing, Mathematica claims that it works with all reasonably
modern versions of Python — specificaly "Python 2.6+ and Python
3.4+".
Assuming this is true, the only extra thing to worry about is that Mathematica
requires the pyzmq package to interface with Python.
If you have already installed sxs, you should be able to install pyzmq in
the same way. Alternatively, you may want to create a separate environment with
both. Using conda, you can run
Note that this command just creates the environment; if you want to use it
directly, you need to run conda activate sxs_mathematica, which basically
changes the PATH in your current terminal so that it uses this version of
python by default; that change will disappear the next time you open a terminal
or if you call conda deactivate.
Finally, you'll need to tell Mathematica the full path to your python executable. You can print that out with
You may never need to activate the environment again except to update; just don't delete it if you intend to continue using it from Mathematica.
Usage#
In Mathematica, you can call something like the following:
session = StartExternalSession[<|
"System" -> "Python",
"Executable" -> "/full/path/to/bin/python"
|>];
py = ExternalEvaluate[session];
Remember to set the full path to your python executable in the first command.
Running this code will start up a python session, which will remain running
until you quit this Mathematica kernel or call DeleteObject[session]. And
you pass all your python code to the py function as strings. To get started,
import the sxs module like this:
To load the catalog, you can run
The python session will hang onto this catalog object, and you can use it
again later. For example, you can extract the table of metadata for all
simulations like this:
The result is a Mathematica Dataset, which you can search and slice in ways
comparable to the pandas interface in python. For example, to select systems
with mass ratios greater than 8 and both spin magnitudes less than 0.1, then
list only selected columns (initial mass ratio, and so on), use code like this:
sims[
Select[#["reference_mass_ratio"] > 8
&& #["reference_dimensionless_spin1_mag"] < 0.1
&& #["reference_dimensionless_spin2_mag"] < 0.1 &],
{"initial_mass_ratio", "initial_separation", "reference_chi1_mag",
"reference_chi2_mag", "reference_eccentricity_bound"}]
Of course, more complex python code can be used. For example, we could write
the selections above directly in python using the usual pandas interface to
achieve the same result. But this approach is presumably less natural for
Mathematica users.
We can also extract horizon data:
py["horizons = sxs.load('SXS:BBH:1107/Lev/Horizons.h5')"]
time = Normal[py["horizons.A.time"]];
arealmass = Normal[py["horizons.A.areal_mass"]];
coordcenterinertial = Normal[py["horizons.A.coord_center_inertial"]];
Here, we have wrapped the py calls in Normal, which converts the numeric
arrays into standard Mathematica Lists, so that we can use them more naturally.
(If you can use the NumericArray object directly, just omit this call.) For
example, to plot the coordinate trajectory of horizon A as a function of time,
we can run
to plot the components of the coordinate trajectory as functions of time.
We can similarly extract the data from waveforms:
py["waveform = sxs.load('SXS:BBH:1107/Lev/rhOverM', extrapolation_order=2)"]
time = Normal[py["waveform.time"]];
mode22 = Normal[py["waveform.data[:, waveform.index(2, 2)]"]];
ListLinePlot[{Transpose[{time, Re[mode22]}], Transpose[{time, Im[mode22]}]}]
This plots the real and imaginary parts of the (2,2) mode of the waveform. And, of course, you can still access all the features of the python object containing the waveform, like evaluation in some particular direction: