# Working with multipolar decompositions¶

Gravitational waves are typically studied in terms of their multipolar decompositions $$(l, m)$$. In Einstein Toolkit, Multipoles is responsable for computing these quantities, which can be read and analyzed by cactus_multipoles (Reference on kuibit.cactus_multipoles). Since the main application is gravitational waves, we will use the word “detector” to mean “radius of the sphere where the multipoles are computed”.

## Accessing multipole data¶

cactus_multipoles has three main classes to work with multipoles. The most basic one is MultipoleOneDet. All the three different classes can be printed to see what is the content.

Note

The classes MultipoleOneDet and MultipoleAllDets are not designed to be initialized directly. They should be obtained using SimDir.

### MultipoleOneDet¶

MultipoleOneDet represent the entire available multipolar decomposition for one variable on one radius.

You can see the available values of l and m with the available_lm attribute. MultipoleOneDet is like a dictionary, so you can access the variables with the bracket operator, alternatively you can call with parentheses:

# Assuming mdet is a MultipoleOneDet
l2m2 = mdet(2,2)
l2m2 = mdet[(2,2)]


These are TimeSeries for the requested multipole. Conviently, you can loop over the available multipoles:

for l, m, mult_ts in mdet:
# do stuff


MultipoleOneDet has a useful to method to operate on each single multipole component and accumulate all the results. This is a convenient way to “loop over all the monopoles” performing some operation. This is how, for example, get_strain() is computed. This method, total_function_on_available_lm() takes as input a function. This function will be called with function(mp_timeseries, mult_l, mult_m, mult_r), plus all the additional arguments and keyword arguments that are passed to total_function_on_available_lm(). Hence, the function has to have a compatible signature. In case some of the quantities passed are not used, you can always add a *args* to the argument of your function to capture them.

### MultipoleAllDets¶

MultipoleAllDets collects all the MultipoleOneDet for a given variable and multiple radii. available_lm can be used to see what multipoles are available and radii to see which radii. In case you want to check, you can use the method has_detector(l, m, re)().

MultipoleAllDets is similar to class:~.MultipoleOneDet with the :py:exception that the index is the radius and the return value is a :py:MultipoleOneDet.

# Assuming mall is a MultipoleAllDets
mul_r100 = mall(100)
mul_r100 = mall[100]


mull_r100 is a MultipoleOneDet, so to access a specific timeseries you have to use another bracket or parentheses operator:

l2_m2_r100 = mall[100][(2,2)]


Once again, MultipoleAllDets can be looped over, with the difference that the loop is on the radii.

You can quickly obtain the outer most detector with the outermost attribute. This returns a MultipoleOneDet.

### MultipolesDir¶

MultipolesDir organizes all the variables for which there’s multipole information available. The structure is similar to ScalarsDir: MultipolesDir is a dictionary like object and the keys are the names of the variables and the values are MultipoleAllDets. So we can see the three levels of multipoles: MultipoleOneDet is one variable, one radius; MultipoleAllDets is one variable, multiple radii; MultipolesDir is multiple variable, multiple radii.

MultipolesDir is initialized by providing a SimDir. The class finds both ASCII file and h5 files with multipole information. These files are read when needed, with h5 files having precedence. As in ScalarsDir, there are three ways to access data:

# Assuming mdir is MultipolesDir
psi4 = mdir['Psi4']
psi4 = mdir.get('Psi4')
psi4 = mdir.fields.psi4


The return value is a MultipoleAllDets, so to obtain a timeseries for the $$l = 2, m = 2, r=100$$ monopole:

psi4_l2_m2_r100 = mdir['Psi4'][100][(2,2)]


Or, alternatively you can combine the other possiblities described.