sage.data.waveform.approximants.IMRPhenomD

Filename : IMRPhenomD.py Description : Short description of the file

Created on 2026-01-22 10:38:25

__author__ = Narenraju Nagarajan __copyright__ = Copyright 2026, ProjectName __license__ = MIT Licence __version__ = 0.0.1 __maintainer__ = Narenraju Nagarajan __affiliation__ = N/A __email__ = N/A __status__ = [‘inProgress’, ‘Archived’, ‘inUsage’, ‘Debugging’]

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Classes

IMRPhenomD

GPU-native batched IMRPhenomD frequency-domain waveform model.

Module Contents

class IMRPhenomD(f, f_ref, **kwargs)

Bases: sage.data.waveform.approximants.phenom.PhenomConstants

GPU-native batched IMRPhenomD frequency-domain waveform model.

Implements the IMRPhenomD aligned-spin binary black hole waveform approximant entirely in PyTorch, allowing batch generation of (hp, hc) polarisations on GPU without any Python-level loops. Inherits all pre-allocated constants and QNM interpolation tables from PhenomConstants.

The waveform is computed on the frequency grid f supplied at construction time. Low-frequency bins below f[0] are zero-padded so that the output arrays span [0, f_max] inclusive.

Parameters:

• f (torch.Tensor, shape (B, F)) – Frequency grid in Hz for the batch.

• f_ref (torch.Tensor, shape (B, 1)) – Reference frequency for the phase calculation.

• **kwargs – Forwarded to PhenomConstants.

f

df

sample_length_in_s

f_numel

f_ref

B

n_pad

hp_buffer

hc_buffer

get_hphc(theta, reproduce_lal=False)

Compute the FD plus and cross polarisations for a parameter batch.

Parameters:

• theta (torch.Tensor, shape (B, P)) – Batch of waveform parameters: [m1, m2, chi1, chi2, distance, tc, inclination, ...].

• reproduce_lal (bool) – If True, skip FD tapering and tc application to reproduce raw LALSuite output (default False).

Returns:

hp, hc – Plus and cross polarisations in the frequency domain.

Return type:

torch.Tensor, shape (B, F) complex

apply_tc(hp, hc, tc)

Apply a frequency-domain phase shift equivalent to a time-domain shift by tc.

pad_missing_frequencies(hp, hc)

Zero-pad hp and hc below f_min (DC to the starting frequency).

compute_derived_parameters(theta)

Compute mass-related derived quantities from the parameter batch.

Returns [m1_s, m2_s, M_s, eta_s] where each column uses SI-scaled masses (m * G / c³).

get_coeffs(chi1, chi2, eta)

Compute the IMRPhenomD phenomenological coefficient matrix.

Builds monomials in (chiPN - 1) and eta up to third order, then multiplies by the pre-loaded coefficient table to produce a (B, N_coeffs) tensor of phenomenological fitting coefficients.

get_components(theta, coeffs, derived)

Compute the amplitude A, phase Psi, and frequency cutoff fcut_true.

Evaluates the full IMRPhenomD frequency-domain waveform components from the parameter batch, phenomenological coefficients, and derived mass quantities. Returns tensors ready for combining into h+ and hx.

static DPhiMRD(f, coeffs, eta, fx_Ms, Rholm=1.0, Taulm=1.0)

First frequency derivative of PhiMRDAnsatzInt

Parameters:

• f – Tensor of frequencies, shape (B,1) or (B,)

• p – object with attributes alpha1, alpha2,

• alpha3

• alpha4

• alpha5

• fDM

• fRD

• etaInv

• Rholm (float) – ratio of fRD22/fRDlm, default 1.0

• Taulm (float) – ratio of damping times, default 1.0

Returns:

Tensor of same shape as f

get_transition_frequencies(theta, derived, gamma2, gamma3)

Return the six IMRPhenomD transition frequencies [f1, f2, f3, f4, f_RD, f_damp] in Hz for a parameter batch.

get_fRD_fdamp(chi1, chi2, m1_s, m2_s, M_s, eta_s)

Return the ringdown frequency and damping frequency by interpolating the pre-loaded QNM table with the final-spin estimate.

static final_spin_0815_s(eta, S)

Phenomological final-spin fit (Eq. 3.6, arXiv:1508.07250).

static erad_rational_0815(eta, chi1, chi2)

Rational-function fit for the dimensionless radiated mass (arXiv:1508.07250).

static get_phi_IIa(f_Ms, eta, coeffs, beta1corr)

IMRPhenomD intermediate-region IIa phase including the beta1 continuity correction.

static get_IIa_raw_phase(f_Ms, eta, coeffs)

Raw intermediate region IIa phase ansatz (without continuity correction).

static get_IIb_raw_phase(f_Ms, eta, coeffs, fx_Ms)

Raw merger-ringdown region IIb phase ansatz.

phase(theta, coeffs, derived, f_Ms, fx_Ms)

Compute the full IMRPhenomD gravitational-wave phase across all frequency regions.

Stitches together inspiral, intermediate (IIa), and merger-ringdown (IIb) phase contributions with C¹-continuity corrections.

DPhiInsAnsatzInt(fxi_Ms, coeffs, TF2_coeffs, TF2_log_coeffs, eta)

First frequency derivative of PhiInsAnsatzInt

Parameters:

• Mf – Tensor, shape (B,1) or (B,)

• coeffs – Tensor, shape (B, Nc)

• pn_v – Tensor, shape (B, 8)

• pn_vlogv – Tensor, shape (B, 8)

Returns:

Tensor of same shape as Mf

static DPhiIntAnsatz(fxi_Ms, coeffs, eta)

First frequency derivative of PhiIntAnsatz

Parameters:

• Mf – tensor of shape (B, 1) or (B,)

• coeffs – tensor of shape (B, N) containing beta coefficients

• eta – tensor of shape (B, 1) or (B,)

Returns:

Tensor of same shape as Mf

static DPhiIntTemp(fxi_Ms, coeffs, eta, beta1corr)

Temporary first frequency derivative of PhiIntAnsatz used to enforce C(1) continuity between regions.

Parameters:

• ff – Tensor of shape (B, 1) or (B,)

• coeffs – Tensor of shape (B, N) with PhenomD coefficients

• eta – Tensor of shape (B, 1) or (B,)

Returns:

Tensor of same shape as ff

spin_spin_3pn_correction(theta, eta_s)

Compute the 3PN spin-spin TaylorF2 correction term subtracted from the PhenomD inspiral phase (LALSimInspiralPNCoefficients.c, v[6]).

get_inspiral_phase(fxi_Ms, derived, chi, coeffs, phi6corr)

Calculate the inspiral phase for IMRPhenomD exactly equivalent to LAL.

get_fcut_true(M_s)

Return the physical frequency cutoff in Hz from the dimensionless fM_CUT.

amp(f, theta, coeffs, trans_fs, derived, f_Ms, fx_Ms, fcut_true=None)

Computes the amplitude of the PhenomD frequency domain waveform Refer 1508.07253 for more details Note that this waveform also assumes that object one is the more massive.

get_inspiral_Amp(f_Ms, chi1, chi2, eta_s, coeffs)

Compute the TaylorF2-like inspiral amplitude ansatz (Region I).

Implements the PN series A0…A6 plus three fitted coefficients A7–A9 from LALSimIMRPhenomD_internals.c (lines 302–351).

Parameters:

• f_Ms (torch.Tensor, shape (B, n_freq)) – Dimensionless frequency grid f × M_s.

• chi1 (torch.Tensor, shape (B, 1)) – Dimensionless aligned spin of the larger BH.

• chi2 (torch.Tensor, shape (B, 1)) – Dimensionless aligned spin of the smaller BH.

• eta_s (torch.Tensor, shape (B, 1)) – Symmetric mass ratio.

• coeffs (torch.Tensor, shape (B, 7+)) – PhenomD fit coefficients; columns 0–2 are A7, A8, A9.

Returns:

Amp_Ins – Inspiral amplitude (unnormalised, dimensionless).

Return type:

torch.Tensor, shape (B, n_freq)

get_IIa_Amp(f_Ms, fx_Ms, theta, derived, coeffs)

Compute the intermediate (IIa) amplitude via the quintic polynomial ansatz.

Solves for the five delta coefficients by matching the values and first derivatives of the inspiral and merger-ringdown amplitudes at the transition frequencies f1 and f3, then evaluates the quintic.

Parameters:

• f_Ms (torch.Tensor, shape (B, n_freq)) – Dimensionless frequency grid for the IIa region.

• fx_Ms (torch.Tensor, shape (B, 8)) – Special frequency scale products (fref, f1, f2, f3, f4, fRD, fdamp, fmid).

• theta (torch.Tensor, shape (B, 5+)) – Waveform parameters; columns 2–3 are chi1, chi2.

• derived (torch.Tensor, shape (B, 4+)) – Derived parameters; column 3 is eta.

• coeffs (torch.Tensor, shape (B, 7+)) – PhenomD fit coefficients.

Returns:

Amp_IIa – Intermediate amplitude on f_Ms.

Return type:

torch.Tensor, shape (B, n_freq)

DAmpInsAnsatz(f, chi1, chi2, eta, coeffs)

Analytical derivative of the Inspiral Amplitude. Matches LALSimIMRPhenomD_internals.c: DAmpInsAnsatz.

static DAmpMRDAnsatz(f, coeffs, fx_Ms)

EXACT analytical derivative of the MRD Amplitude. Matches LALSimIMRPhenomD_internals.c: DAmpMRDAnsatz exactly.

static get_IIb_Amp(f_Ms, fx_Ms, coeffs)

Compute the merger-ringdown (IIb) amplitude via the Lorentzian ansatz.

Parameters:

• f_Ms (torch.Tensor, shape (B, n_freq)) – Dimensionless frequency grid for the IIb region.

• fx_Ms (torch.Tensor, shape (B, 8)) – Special frequency scale products; columns 5–6 are fRD·M_s and fdamp·M_s.

• coeffs (torch.Tensor, shape (B, 7+)) – PhenomD coefficients; columns 4–6 are gamma1, gamma2, gamma3.

Returns:

Amp_IIb – Merger-ringdown amplitude on f_Ms.

Return type:

torch.Tensor, shape (B, n_freq)

static get_delta0(f1, f2, f3, v1, v2, v3, d1, d3)

Compute the δ₀ coefficient of the IIa quintic amplitude polynomial.

static get_delta1(f1, f2, f3, v1, v2, v3, d1, d3)

Compute the δ₁ coefficient of the IIa quintic amplitude polynomial.

static get_delta2(f1, f2, f3, v1, v2, v3, d1, d3)

Compute the δ₂ coefficient of the IIa quintic amplitude polynomial.

static get_delta3(f1, f2, f3, v1, v2, v3, d1, d3)

Compute the δ₃ coefficient of the IIa quintic amplitude polynomial.

static get_delta4(f1, f2, f3, v1, v2, v3, d1, d3)

Compute the δ₄ coefficient of the IIa quintic amplitude polynomial.

get_Amp0(f_Ms, eta)

Compute the overall GW amplitude prefactor A₀(f, η).

This is the leading-order Newtonian factor that scales the full PhenomD amplitude: A₀ = (2η/3)^(1/2) × (fM_s)^(-7/6) × π^(-1/6).

Parameters:

• f_Ms (torch.Tensor, shape (B, n_freq)) – Dimensionless frequency f × M_s.

• eta (torch.Tensor, shape (B, 1)) – Symmetric mass ratio.

Returns:

Amp0 – Newtonian amplitude prefactor.

Return type:

torch.Tensor, shape (B, n_freq)