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Waveformtools

This is a python module for the handling and analysis of waveforms and data from Numerical Relativity codes, and for carrying out gravitational wave data analysis.

waveformtools is a numerical relativity data handling package that was written to aid the handling and analysis of numerical relativity data.

This package contains implementations of customized algorithms and techniques. Some of these contain the usage of existing python based library functions from pycbc, scipy, etc but effort has been made to keep these to a minimum.

• Handling of numerical relativity data, and retreiving specific information about the physical system. Presently, this supports the EinsteinToolkit data.

  The class container and methods "sim" can load NR data into convenient lists and dictionaries, which can be used to retrieve specific data/ information about the numerical simulation.

  This offers the following functionality, like retreiving:

  • Horizon masses, mass-ratios, and areas.

  • Horizon multipole moments.

  • Merger time/ formation time of common horizon.

  • The strain waveform.

  • The shear data of the dynamical horizons.

  • And computing/ extracting the Frequency, amplitude and phase of waveforms, etc.

• Handling of waveforms.

  A basic class container for handling numerical waveforms.

  This offers functionality like:

  • loading data from hdf5 files.

  • basic information such as time step, time axis, data axis, etc.

  • extrapolating a numerical waveform recorded at a finite radius to null infinity (to be added soon).

  • integrating and differentiating waveforms in the frequency domain (to be added soon).

• Tools for preparation/handling of numerical relativity data, like:

  • checking for discontinuity, removal of duplicated rows, and interpolating for missing rows in the data.

  • integration, differentiation of numerical data.

  • equalizing lengths of waveforms.

  • resampling

  • computing the norm, shifting/ rolling the data, etc.

  • Smoothening, tapering.

  • Extrapolation of waveforms to null infinity.

  • Center of Mass corrections to waveforms.

  • BMS Supertranslations of waveforms.

• Tools for basic data analysis.

  • A match algorithms for matching two waveforms.

  • Binning and interpolation of data.

  • Smooth derivatives: spectral and finite difference derivatives.

• Miscellaneous tools:

  • Progress bar to display progress of loops.

  • A custom print function with message prioritization.

  • Saving data to disk with protocol support (binary, text, etc.)

Citing this code

Please cite the latest version of this code if used in your work. This code was developed for use in the following works:

1. News from Horizons in Binary Black Hole Mergers
2. Tidal deformation of dynamical horizons in binary black hole mergers

We request you to also cite these. Thanks!

Installing this package

Dependencies

This module has the following dependencies:

• Standard packages (come with full anaconda installation)
  • numpy
  • scipy
  • statistics
  • matplotlib
  • h5py
  • termcolor
• Optional dependencies (labelled [EXT])
  • For use with PyCBC data analysis packages.
    • pyCBC
    • lalsuite
    • ligo-common
  • gmpy2

Recommended method

I recommend installing this module through pypi:

pip install waveformtools

Alternate method

Manual install directly from GitHub:

pip install git+https://github.com/vaishakp/waveformtools@main

Or from a clone:

• First, clone this repository:

git clone https://github.com/vaishakp/waveformtools.git

• Second, run python setup from the waveformtools directory:

cd waveformtools
python setup.py install --prefix="<path to your preferred installation dir>"

Manually setup conda environment

• To create an environment with automatic dependency resolution and activate it, run

conda create env -f docs/environment.yml
conda activate wftools

Using this code

>>> from waveformtools.waveforms import modes_array
>>> fdir = "<path to data dir>"
>>> fname = 'ExtrapStrain_RIT-BBH-0001-n100.h5'
>>> wf1 = modes_array(label='RIT001', spin_weight=-2)
>>> wf1.file_name = fname
>>> wf1.data_dir = fdir
>>> wf1.load_modes(ftype='RIT', var_type='Strain', ell_max='auto', resam_type='auto')
>>> wf1.get_metadata()
{'label': 'RIT001',
 'data_dir': '/home/vaishakprasad/Downloads/',
 'file_name': 'ExtrapStrain_RIT-BBH-0001-n100.h5',
 'key_format': None,
 'ell_max': 4,
 'modes_list': [[2, [-2, -1, 0, 1, 2]],
  [3, [-3, -2, -1, 0, 1, 2, 3]],
  [4, [-4, -3, -2, -1, 0, 1, 2, 3, 4]]],
 'r_ext': 500,
 'frequency_axis': None,
 'out_file_name': None,
 'maxtime': None,
 'date': '2023-04-26',
 'time': '17:37:20',
 'key_ex': None,
 'spin_weight': -2}

To access the individual modes, use the :math:\ell, m notation.

>>> ell = 2
>>> emm = 2
>>> wf1.mode(ell, emm)
array([-5.82188926e-17-2.09534621e-18j, -5.96136537e-17-2.06759459e-18j,
       -6.10007697e-17-2.04743540e-18j, ...,
       -7.23538504e-18+4.65415462e-33j, -3.62788145e-18-4.11078069e-33j,
        0.00000000e+00+0.00000000e+00j])

To plot the modes

>>> import matplotlib.pyplot as plt
>>> plt.plot(wf1.time_axis, wf1.mode(ell, emm).real, label='+')
>>> plt.plot(wf1.time_axis, wf1.mode(ell, emm).imag, label='X')
>>> plt.legend()
>>> plt.grid(alpha=0.4)
>>> plt.xlabel(r'$t/M$')
>>> plt.ylabel(f'$rh/M$')
>>> plt.show()

{: .shadow}

LAL mode storage conventions and load_lal_modes_to_modes_array

This section documents how waveformtools stores LAL time-domain and frequency-domain modes, how that representation differs from the raw LAL output, and what limitations apply when using FD modes for matched filtering.

Two-sided frequency axis

LAL's SimInspiralChooseFDModes returns a SphHarmFrequencySeries whose underlying fdata axis is two-sided and sorted: it runs from -f_max up through 0 to +f_max. With default parameters this produces an array of N = 2*ceil(f_upper/delta_f) + 1 bins.

For IMRPhenomXPHM (and other FD approximants):

• Positive-m modes (e.g., (l=2, m=2)) carry physical content at negative frequencies in this sorted representation.
• Negative-m modes (e.g., (l=2, m=−2)) carry physical content at positive frequencies.

Both start from f_lower (e.g., 20 Hz), not from 2×f_ISCO. The placement is a consequence of the GW convention for the two-sided spectrum, not a model-domain cutoff.

Empirical check for M=75 M☉, f_lower=20 Hz (Schwarzschild 2×f_ISCO ≈ 59 Hz):

(2,  2) first nonzero frequency: −20 Hz    ← positive-m, negative-freq side
(2, −2) first nonzero frequency: +20 Hz    ← negative-m, positive-freq side
(3,  3) first nonzero frequency: −20 Hz
(4,  4) first nonzero frequency: −20 Hz

load_lal_modes_to_modes_array storage

waveformtools.waveformtools.load_lal_modes_to_modes_array(lal_modes, ...) iterates the raw linked-list of modes (both positive and negative m for each ℓ).

For time-domain LAL modes it stores

stored_td[l, m](t) = np.conjugate(mode.data.data)

For frequency-domain LAL modes it stores

stored_fd[l, m](f) = (1/N) * np.conjugate(mode.data.data)

where mode.data.data is the full N-element two-sided FD array. Key points:

• All modes are stored, including negative m. Calling code must sum over both signs of m to reconstruct the strain.
• A conjugate is taken for both TD and FD LAL modes. This flips the sign of the imaginary part relative to the raw LAL output.
• A factor 1/N normalisation is applied only to FD modes. This cancels the implicit N from an IFFT if you want time-domain modes, but must be accounted for if you use the stored modes in a purely frequency-domain context.

For FD approximants such as IMRPhenomXPHM, get_td_waveform_modes() routes through get_fd_waveform_modes_as_td(). That path recovers the raw LAL FD samples as conj(stored_fd) * N, applies a direct inverse FFT, and conjugates the TD result so the final object follows waveformtools' TD mode convention.

ModesArray.evaluate_angular(theta, phi)

Reconstructs the strain at orientation (θ, φ) via

h(f; θ, φ) = Σ_{l,m} stored[l,m](f) · ₋₂Y_{lm}(θ, φ)

summed over all stored (l, m) pairs (positive and negative m). The two-sided frequency axis is preserved; the caller is responsible for extracting the desired frequency range.

Comparison with SphHarmFrequencySeriesGetMode

LAL's SphHarmFrequencySeriesGetMode(hlms, l, m) is a helper that extracts a single mode and returns a COMPLEX16FrequencySeries on the standard f≥0 LAL grid (bin k → k·Δf). For positive-m modes (e.g., (2,2)), whose physical content sits at negative frequencies in the two-sided sorted representation, this standard-grid extraction can return only the positive-frequency tail. In practice this can look like the mode starts near the merger/ringdown region (often around 2×f_ISCO, depending on the system and model) even though the underlying two-sided linked-list data contain the inspiral from f_lower.

Code that uses SphHarmFrequencySeriesGetMode directly (e.g., paralleltempatebank.waveform.generate_waveform_modes) can therefore obtain positive-m FD modes that miss the inspiral even though the underlying waveform covers the full range from f_lower. Using load_lal_modes_to_modes_array + the raw linked list (as waveformtools does) captures the full two-sided frequency range.

Summary table

Documentation

The documentation for this module is available at Link to the Documentation. This was built automatically using Read the Docs.

In some cases where the CI service is unavailable or quota-limited, the documentation may not be automatically built. In such cases, we request the user to access the documentation through the index.html file in docs directory.

Bug tracker

If you run into any issues while using this package, please report the issue on the issue tracker.

Acknowledgements

This project was originally hosted on GitLab and is now developed on GitHub. Several CI and deployment tools are used for testing, version control, and releases.

The work of this was developed in aiding my PhD work at Inter-University Centre for Astronomy and Astrophysics (IUCAA, Pune, India)](https://www.iucaa.in/). The PhD is in part supported by the Shyama Prasad Nukherjee Fellowship awarded to me by the Council of Scientific and Industrial Research (CSIR, India). Resources of the Inter-University Centre for Astronomy and Astrophysics (IUCAA, Pune, India) were are used in part.