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initialize MSA system

Functions:

Name Description
IMRPhenomX_Get_PN_beta

Calculate PN beta coefficient
IMRPhenomX_Get_PN_sigma

Calculate PN sigma coefficient
IMRPhenomX_Get_PN_tau

Internal function to computes PN spin-spin couplings. As in LALSimInspiralFDPrecAngles.c
IMRPhenomX_Initialize_MSA_System

First initialize the system of variables needed for Chatziioannou et al, PRD, 88, 063011, (2013), arXiv:1307.4418:
IMRPhenomX_L_norm_3PN_of_v

Compute L_norm at 3PN order.
IMRPhenomX_Return_Constants_c_MSA

Compute c constants for MSA approximation.
IMRPhenomX_Return_Constants_d_MSA

Compute d constants for MSA approximation.
IMRPhenomX_Return_MSA_Corrections_MSA

Compute MSA corrections for precession angles.
IMRPhenomX_Return_Psi_MSA

Compute psi for MSA approximation.
IMRPhenomX_Return_Psi_dot_MSA

Compute the time derivative of psi for MSA approximation.
IMRPhenomX_Return_Roots_MSA

Compute roots S32, Smi2, Spl2 for MSA approximation.
IMRPhenomX_Return_SNorm_MSA

Compute the spin magnitude SNorm using the MSA approximation.
IMRPhenomX_Return_Spin_Evolution_Coefficients_MSA

Compute spin evolution coefficients B, C, D for MSA approximation.
IMRPhenomX_Return_phi_zeta_costhetaL_MSA

Wrapper to generate phi_z, zeta and cos(theta_L) at a given frequency.
IMRPhenomX_Return_phiz_MSA

Compute the azimuthal precession angle phi_z using the MSA approximation.
IMRPhenomX_Return_zeta_MSA

Compute zeta angle for MSA approximation.
IMRPhenomX_psiofv

Compute psi(v) for the MSA approximation.
IMRPhenomX_vector_L2_norm

Calculate L2 norm of a 3D vector
IMRPhenomX_vector_cross_product

Calculate cross product of two 3D vectors
IMRPhenomX_vector_dot_product

Calculate dot product of two 3D vectors
IMRPhenomX_vector_scalar

Multiply a vector by a scalar
IMRPhenomX_vector_sum

Calculate sum of two 3D vectors
compute_constants_L

Compute coefficients for PN orbital angular momentum at 3PN.
compute_psi0

Compute initial psi0 value for MSA approximation.
compute_spin_norm_squared

Compute the squared norms of the dimensionless spin vectors S1 and S2.

IMRPhenomX_Get_PN_beta(a: FloatLike, b: FloatLike, dotS1L: FloatLike, dotS2L: FloatLike, qq: FloatLike) -> FloatLike ¤

Calculate PN beta coefficient

Parameters:

Name Type Description Default
a FloatLike

First coefficient (FloatLike)

 required
b FloatLike

Second coefficient (FloatLike)

 required
dotS1L FloatLike

Dot product of S1 and L (FloatLike)

 required
dotS2L FloatLike

Dot product of S2 and L (FloatLike)

 required
qq FloatLike

Mass ratio q = m1/m2 (FloatLike)

 required

Returns: FloatLike: PN beta value

IMRPhenomX_Get_PN_sigma(a: FloatLike, b: FloatLike, inveta: FloatLike, dotS1S2: FloatLike, dotS1L: FloatLike, dotS2L: FloatLike) -> FloatLike ¤

Calculate PN sigma coefficient

Parameters:

Name Type Description Default
a FloatLike

First coefficient (FloatLike)

 required
b FloatLike

Second coefficient (FloatLike)

 required
inveta FloatLike

Inverse of symmetric mass ratio (FloatLike)

 required
dotS1S2 FloatLike

Dot product of S1 and S2 (FloatLike)

 required
dotS1L FloatLike

Dot product of S1 and L (FloatLike)

 required
dotS2L FloatLike

Dot product of S2 and L (FloatLike)

 required

Returns: FloatLike: PN sigma value

IMRPhenomX_Get_PN_tau(a: FloatLike, b: FloatLike, qq: FloatLike, S1_norm_2: FloatLike, S2_norm_2: FloatLike, dotS1L: FloatLike, dotS2L: FloatLike, eta: FloatLike) -> FloatLike ¤

Internal function to computes PN spin-spin couplings. As in LALSimInspiralFDPrecAngles.c

Parameters:

Name Type Description Default
a FloatLike

First coefficient (FloatLike)

 required
b FloatLike

Second coefficient (FloatLike)

 required
qq FloatLike

Mass ratio q = m1/m2 (FloatLike)

 required
S1_norm_2 FloatLike

Squared norm of spin 1 (FloatLike)

 required
S2_norm_2 FloatLike

Squared norm of spin 2 (FloatLike)

 required
dotS1L FloatLike

Dot product of S1 and L (FloatLike)

 required
dotS2L FloatLike

Dot product of S2 and L (FloatLike)

 required
eta FloatLike

Symmetric mass ratio (FloatLike)

 required

Returns: FloatLike: PN tau value

IMRPhenomX_Initialize_MSA_System(mass_1: FloatLike, mass_2: FloatLike, chi1x: FloatLike, chi1y: FloatLike, chi1z: FloatLike, chi2x: FloatLike, chi2y: FloatLike, chi2z: FloatLike, reference_frequency: float, pflag: int = 223, expansion_order: int = 5) -> Array ¤

First initialize the system of variables needed for Chatziioannou et al, PRD, 88, 063011, (2013), arXiv:1307.4418:

  • Racine et al, PRD, 80, 044010, (2009), arXiv:0812.4413
  • Favata, PRD, 80, 024002, (2009), arXiv:0812.0069
  • Blanchet et al, PRD, 84, 064041, (2011), arXiv:1104.5659
  • Bohe et al, CQG, 30, 135009, (2013), arXiv:1303.7412

IMRPhenomX_L_norm_3PN_of_v(v: FloatLike, L_norm: FloatLike, constants_L_0: FloatLike, constants_L_1: FloatLike, constants_L_2: FloatLike, constants_L_3: FloatLike, constants_L_4: FloatLike) -> FloatLike ¤

Compute L_norm at 3PN order.

Parameters:

Name Type Description Default
v Array

Orbital velocity parameter.

 required
L_norm FloatLike

Normalized orbital angular momentum.

 required
constants_L_0 FloatLike

L polynomial coefficient (index 0).

 required
constants_L_1 FloatLike

L polynomial coefficient (index 1).

 required
constants_L_2 FloatLike

L polynomial coefficient (index 2).

 required
constants_L_3 FloatLike

L polynomial coefficient (index 3).

 required
constants_L_4 FloatLike

L polynomial coefficient (index 4).

 required

Returns:

Name Type Description
FloatLike FloatLike

L_norm at 3PN order.

IMRPhenomX_Return_Constants_c_MSA(v: FloatLike, JNorm: FloatLike, Seff: FloatLike, eta: FloatLike, eta3: FloatLike, inveta: FloatLike, Spl2: FloatLike, Smi2: FloatLike, S1_norm_2: FloatLike, S2_norm_2: FloatLike, delta_qq: FloatLike) ¤

Compute c constants for MSA approximation.

Parameters:

Name Type Description Default
v FloatLike

Orbital velocity parameter.

 required
JNorm FloatLike

Normalized total angular momentum.

 required
Seff FloatLike

Effective spin parameter.

 required
eta FloatLike

Symmetric mass ratio.

 required
eta3 FloatLike

eta cubed.

 required
inveta FloatLike

Inverse of eta (1/eta).

 required
Spl2 FloatLike

S_plus squared.

 required
Smi2 FloatLike

S_minus squared.

 required
S1_norm_2 FloatLike

Spin 1 magnitude squared.

 required
S2_norm_2 FloatLike

Spin 2 magnitude squared.

 required
delta_qq FloatLike

MSA coefficient delta_qq.

 required

Returns:

Type Description

Tuple[float, float, float]: A tuple of (c0, c2, c4) MSA constants.

IMRPhenomX_Return_Constants_d_MSA(LNorm: FloatLike, JNorm: FloatLike, Spl: FloatLike, Spl2: FloatLike, Smi2: FloatLike) ¤

Compute d constants for MSA approximation.

Parameters:

Name Type Description Default
LNorm FloatLike

Normalized orbital angular momentum.

 required
JNorm FloatLike

Normalized total angular momentum.

 required
Spl FloatLike

S_plus.

 required
Spl2 FloatLike

S_plus squared.

 required
Smi2 FloatLike

S_minus squared.

 required

Returns:

Type Description

Tuple[float, float, float]: A tuple of (d0, d2, d4) MSA constants.

IMRPhenomX_Return_MSA_Corrections_MSA(v: FloatLike, LNorm: FloatLike, JNorm: FloatLike, Seff: FloatLike, eta: FloatLike, eta3: FloatLike, inveta: FloatLike, Spl: FloatLike, Spl2: FloatLike, Smi2: FloatLike, Spl2mSmi2: FloatLike, S1_norm_2: FloatLike, S2_norm_2: FloatLike, S32: FloatLike, delta_qq: FloatLike, g0: FloatLike, psi0: FloatLike, psi1: FloatLike, psi2: FloatLike) ¤

Compute MSA corrections for precession angles.

Parameters:

Name Type Description Default
v FloatLike

Orbital velocity parameter.

 required
LNorm FloatLike

Normalized orbital angular momentum.

 required
JNorm FloatLike

Normalized total angular momentum.

 required
Seff FloatLike

Effective spin parameter.

 required
eta FloatLike

Symmetric mass ratio.

 required
eta3 FloatLike

eta cubed.

 required
inveta FloatLike

Inverse of eta (1/eta).

 required
Spl FloatLike

S_plus.

 required
Spl2 FloatLike

S_plus squared.

 required
Smi2 FloatLike

S_minus squared.

 required
Spl2mSmi2 FloatLike

Spl2 - Smi2.

 required
S1_norm_2 FloatLike

Spin 1 magnitude squared.

 required
S2_norm_2 FloatLike

Spin 2 magnitude squared.

 required
S32 FloatLike

S_3 squared.

 required
delta_qq FloatLike

MSA coefficient delta_qq.

 required
g0 FloatLike

MSA coefficient g0.

 required
psi0 FloatLike

Initial psi value.

 required
psi1 FloatLike

MSA coefficient psi1.

 required
psi2 FloatLike

MSA coefficient psi2.

 required

Returns:

Type Description

Tuple[float, float]: A tuple of (vMSA_x, vMSA_y) MSA corrections.

IMRPhenomX_Return_Psi_MSA(v: FloatLike, v2: FloatLike, g0: FloatLike, delta_qq: FloatLike, psi1: FloatLike, psi2: FloatLike) -> FloatLike ¤

Compute psi for MSA approximation.

Parameters:

Name Type Description Default
v FloatLike

Orbital velocity parameter.

 required
v2 FloatLike

v squared.

 required
g0 FloatLike

MSA coefficient g0.

 required
delta_qq FloatLike

MSA coefficient delta_qq.

 required
psi1 FloatLike

MSA coefficient psi1.

 required
psi2 FloatLike

MSA coefficient psi2.

 required

Returns:

Name Type Description
FloatLike FloatLike

Psi value.

IMRPhenomX_Return_Psi_dot_MSA(v: FloatLike, Seff: FloatLike, inveta: FloatLike, Spl2: FloatLike, S32: FloatLike) -> FloatLike ¤

Compute the time derivative of psi for MSA approximation.

Parameters:

Name Type Description Default
v FloatLike

Orbital velocity parameter.

 required
Seff FloatLike

Effective spin parameter.

 required
inveta FloatLike

Inverse of symmetric mass ratio (1/eta).

 required
Spl2 FloatLike

S_plus squared.

 required
S32 FloatLike

S_3 squared.

 required

Returns:

Name Type Description
FloatLike FloatLike

Time derivative of psi.

IMRPhenomX_Return_Roots_MSA(LNorm: FloatLike, JNorm: FloatLike, S1_norm_2: FloatLike, S2_norm_2: FloatLike, qq: FloatLike, eta: FloatLike, delta_qq: FloatLike, Seff: FloatLike, dotS1Ln: FloatLike, dotS2Ln: FloatLike, S_0_norm: FloatLike) -> Float[Array, 3] ¤

Compute roots S32, Smi2, Spl2 for MSA approximation.

Parameters:

Name Type Description Default
LNorm FloatLike

Normalized orbital angular momentum.

 required
JNorm FloatLike

Normalized total angular momentum.

 required
S1_norm_2 FloatLike

Spin 1 magnitude squared.

 required
S2_norm_2 FloatLike

Spin 2 magnitude squared.

 required
qq FloatLike

Mass ratio q = m2/m1.

 required
eta FloatLike

Symmetric mass ratio.

 required
delta_qq FloatLike

Mass difference parameter (m1-m2)/(m1+m2).

 required
Seff FloatLike

Effective spin parameter.

 required
dotS1Ln FloatLike

Dot product of S1 with L_hat.

 required
dotS2Ln FloatLike

Dot product of S2 with L_hat.

 required
S_0_norm FloatLike

Initial total spin magnitude.

 required

Returns:

Type Description
Float[Array, 3]

Float[Array, "3"]: Array of [S32, Smi2, Spl2] roots.

IMRPhenomX_Return_SNorm_MSA(v: FloatLike, Smi2: FloatLike, Spl2: FloatLike, S32: FloatLike, psi0: FloatLike, psi1: FloatLike, psi2: FloatLike, g0: FloatLike, delta_qq: FloatLike) -> FloatLike ¤

Compute the spin magnitude SNorm using the MSA approximation.

Based on Equations 23 and 25 of Chatziioannou et al, PRD 95, 104004, (2017), arXiv:1703.03967.

Parameters:

Name Type Description Default
v FloatLike

Orbital velocity parameter.

 required
Smi2 FloatLike

S_minus squared.

 required
Spl2 FloatLike

S_plus squared.

 required
S32 FloatLike

S_3 squared.

 required
psi0, psi1, psi2 FloatLike

Psi expansion coefficients.

 required
g0 FloatLike

Precession coefficient g0.

 required
delta_qq FloatLike

Mass difference parameter delta_qq.

 required

Returns:

Name Type Description
SNorm FloatLike

The spin magnitude.

IMRPhenomX_Return_Spin_Evolution_Coefficients_MSA(LNorm: FloatLike, JNorm: FloatLike, S1_norm_2: FloatLike, S2_norm_2: FloatLike, qq: FloatLike, eta: FloatLike, delta_qq: FloatLike, Seff: FloatLike) ¤

Compute spin evolution coefficients B, C, D for MSA approximation.

Parameters:

Name Type Description Default
LNorm FloatLike

Normalized orbital angular momentum.

 required
JNorm FloatLike

Normalized total angular momentum.

 required
S1_norm_2 FloatLike

Spin 1 magnitude squared.

 required
S2_norm_2 FloatLike

Spin 2 magnitude squared.

 required
qq FloatLike

Mass ratio q = m2/m1.

 required
eta FloatLike

Symmetric mass ratio.

 required
delta_qq FloatLike

Mass difference parameter (m1-m2)/(m1+m2).

 required
Seff FloatLike

Effective spin parameter.

 required

Returns:

Type Description

Tuple[float, float, float]: A tuple of (B_coeff, C_coeff, D_coeff) spin evolution coefficients for the MSA approximation.

IMRPhenomX_Return_phi_zeta_costhetaL_MSA(v: FloatLike, eta: FloatLike, eta2: FloatLike, eta3: FloatLike, eta4: FloatLike, inveta: FloatLike, c1: FloatLike, c1_over_eta: FloatLike, SAv: FloatLike, SAv2: FloatLike, invSAv: FloatLike, invSAv2: FloatLike, constants_L_0: FloatLike, constants_L_1: FloatLike, constants_L_2: FloatLike, constants_L_3: FloatLike, constants_L_4: FloatLike, S1_norm_2: FloatLike, S2_norm_2: FloatLike, qq: FloatLike, delta_qq: FloatLike, Seff: FloatLike, dotS1Ln: FloatLike, dotS2Ln: FloatLike, S_0_norm: FloatLike, psi0: FloatLike, psi1: FloatLike, psi2: FloatLike, g0: FloatLike, Omegaz0_coeff: FloatLike, Omegaz1_coeff: FloatLike, Omegaz2_coeff: FloatLike, Omegaz3_coeff: FloatLike, Omegaz4_coeff: FloatLike, Omegaz5_coeff: FloatLike, phiz_0: FloatLike, Omegazeta0_coeff: FloatLike, Omegazeta1_coeff: FloatLike, Omegazeta2_coeff: FloatLike, Omegazeta3_coeff: FloatLike, Omegazeta4_coeff: FloatLike, Omegazeta5_coeff: FloatLike, zeta_0: FloatLike) ¤

Wrapper to generate phi_z, zeta and cos(theta_L) at a given frequency.

Parameters:

Name Type Description Default
v FloatLike

Velocity parameter (FloatLike)

 required
eta FloatLike

Symmetric mass ratio (FloatLike)

 required
eta2 FloatLike

eta squared (FloatLike)

 required
eta3 FloatLike

eta cubed (FloatLike)

 required
eta4 FloatLike

eta to the fourth (FloatLike)

 required
inveta FloatLike

Inverse of eta (FloatLike)

 required
c1 FloatLike

c1 coefficient (FloatLike)

 required
c1_over_eta FloatLike

c1 divided by eta (FloatLike)

 required
SAv FloatLike

Spin average (FloatLike)

 required
SAv2 FloatLike

Spin average squared (FloatLike)

 required
invSAv FloatLike

Inverse of SAv (FloatLike)

 required
invSAv2 FloatLike

Inverse of SAv squared (FloatLike)

 required
constants_L

Array of L constants [L0, L1, L2, L3, L4] (array)

 required
S1_norm_2 FloatLike

Squared norm of spin 1 (FloatLike)

 required
S2_norm_2 FloatLike

Squared norm of spin 2 (FloatLike)

 required
qq FloatLike

Mass ratio q = m1/m2 (FloatLike)

 required
delta_qq FloatLike

Delta mass ratio term (FloatLike)

 required
Seff FloatLike

Effective spin (FloatLike)

 required
dotS1Ln FloatLike

Dot product of S1 and Lhat (FloatLike)

 required
dotS2Ln FloatLike

Dot product of S2 and Lhat (FloatLike)

 required
S_0_norm FloatLike

Initial total spin norm (FloatLike)

 required
psi0 FloatLike

Psi coefficient 0 (FloatLike)

 required
psi1 FloatLike

Psi coefficient 1 (FloatLike)

 required
psi2 FloatLike

Psi coefficient 2 (FloatLike)

 required
g0 FloatLike

g0 coefficient (FloatLike)

 required
Omegaz0_coeff through Omegaz5_coeff

Omega_z coefficients (floats)

 required
phiz_0 FloatLike

Initial phi_z value (FloatLike)

 required
Omegazeta0_coeff through Omegazeta5_coeff

Omega_zeta coefficients (floats)

 required
zeta_0 FloatLike

Initial zeta value (FloatLike)

 required

Returns:

Type Description

Tuple[float, float, float]: A tuple of (phi_z + phi_z_MSA, zeta + zeta_MSA, cos(theta_L))

IMRPhenomX_Return_phiz_MSA(v: FloatLike, JNorm: FloatLike, eta: FloatLike, inveta: FloatLike, eta2: FloatLike, eta4: FloatLike, c1: FloatLike, SAv: FloatLike, SAv2: FloatLike, invSAv: FloatLike, invSAv2: FloatLike, Omegaz0_coeff: FloatLike, Omegaz1_coeff: FloatLike, Omegaz2_coeff: FloatLike, Omegaz3_coeff: FloatLike, Omegaz4_coeff: FloatLike, Omegaz5_coeff: FloatLike, phiz_0: FloatLike) -> FloatLike ¤

Compute the azimuthal precession angle phi_z using the MSA approximation.

Based on Eq. 66 and D22-D27 of Chatziioannou et al, PRD 95, 104004, (2017), arXiv:1703.03967.

Parameters:

Name Type Description Default
v FloatLike

Orbital velocity parameter.

 required
JNorm FloatLike

Magnitude of the total angular momentum.

 required
eta FloatLike

Symmetric mass ratio.

 required
inveta FloatLike

Inverse of symmetric mass ratio (1/eta).

 required
eta2 FloatLike

eta squared.

 required
eta4 FloatLike

eta to the fourth power.

 required
c1 FloatLike

Precession constant c1.

 required
SAv FloatLike

Spin parameter SAv.

 required
SAv2 FloatLike

SAv squared.

 required
invSAv FloatLike

Inverse of SAv (1/SAv).

 required
invSAv2 FloatLike

Inverse of SAv squared (1/SAv^2).

 required
Omegaz0_coeff, ..., Omegaz5_coeff FloatLike

Omega_z expansion coefficients from Eqs. D15-D20.

 required
phiz_0 FloatLike

Initial phi_z value.

 required

Returns:

Name Type Description
phiz_out FloatLike

The azimuthal precession angle phi_z.

IMRPhenomX_Return_zeta_MSA(v: FloatLike, eta: FloatLike, Omegazeta0_coeff: FloatLike, Omegazeta1_coeff: FloatLike, Omegazeta2_coeff: FloatLike, Omegazeta3_coeff: FloatLike, Omegazeta4_coeff: FloatLike, Omegazeta5_coeff: FloatLike, zeta_0: FloatLike) -> FloatLike ¤

Compute zeta angle for MSA approximation.

Parameters:

Name Type Description Default
v FloatLike

Orbital velocity parameter.

 required
eta FloatLike

Symmetric mass ratio.

 required
Omegazeta0_coeff FloatLike

Zeta precession coefficient (order 0).

 required
Omegazeta1_coeff FloatLike

Zeta precession coefficient (order 1).

 required
Omegazeta2_coeff FloatLike

Zeta precession coefficient (order 2).

 required
Omegazeta3_coeff FloatLike

Zeta precession coefficient (order 3).

 required
Omegazeta4_coeff FloatLike

Zeta precession coefficient (order 4).

 required
Omegazeta5_coeff FloatLike

Zeta precession coefficient (order 5).

 required
zeta_0 FloatLike

Initial zeta value.

 required

Returns:

Name Type Description
FloatLike FloatLike

Zeta angle.

IMRPhenomX_psiofv(v, v2, psi0, psi1, psi2, g0, delta_qq) ¤

Compute psi(v) for the MSA approximation.

Based on Equation 51 in arXiv:1703.03967.

Parameters:

Name Type Description Default
v FloatLike

Orbital velocity parameter.

 required
v2 FloatLike

v squared.

 required
psi0, psi1, psi2 FloatLike

Psi expansion coefficients.

 required
g0 FloatLike

Precession coefficient g0.

 required
delta_qq FloatLike

Mass difference parameter delta_qq.

 required

Returns:

Name Type Description
psi FloatLike

The psi angle at velocity v.

IMRPhenomX_vector_L2_norm(v1: Float[Array, 3]) -> FloatLike ¤

Calculate L2 norm of a 3D vector

Parameters:

Name Type Description Default
v1 Float[Array, 3]

3D vector as JAX array [x, y, z] (Float[Array, "3"])

 required

Returns: FloatLike: L2 norm of the vector

IMRPhenomX_vector_cross_product(v1: Float[Array, 3], v2: Float[Array, 3]) -> Float[Array, 3] ¤

Calculate cross product of two 3D vectors

Parameters:

Name Type Description Default
v1 Float[Array, 3]

First 3D vector as JAX array [x, y, z] (Float[Array, "3"])

 required
v2 Float[Array, 3]

Second 3D vector as JAX array [x, y, z] (Float[Array, "3"])

 required

Returns:

Type Description
Float[Array, 3]

Float[Array, "3"]: Cross product vector

IMRPhenomX_vector_dot_product(v1: Float[Array, 3], v2: Float[Array, 3]) -> FloatLike ¤

Calculate dot product of two 3D vectors

Parameters:

Name Type Description Default
v1 Float[Array, 3]

First 3D vector as JAX array (Float[Array, "3"])

 required
v2 Float[Array, 3]

Second 3D vector as JAX array (Float[Array, "3"])

 required

Returns: FloatLike: Dot product

IMRPhenomX_vector_scalar(v1: Float[Array, 3], a: FloatLike) -> Float[Array, 3] ¤

Multiply a vector by a scalar

Parameters:

Name Type Description Default
v1 Float[Array, 3]

3D vector as JAX array [x, y, z] (Float[Array, "3"])

 required
a FloatLike

Scalar multiplier (FloatLike)

 required

Returns:

Type Description
Float[Array, 3]

Float[Array, "3"]: Scaled vector

IMRPhenomX_vector_sum(v1: Float[Array, 3], v2: Float[Array, 3]) -> Float[Array, 3] ¤

Calculate sum of two 3D vectors

Parameters:

Name Type Description Default
v1 Float[Array, 3]

First 3D vector as JAX array (Float[Array, "3"])

 required
v2 Float[Array, 3]

Second 3D vector as JAX array (Float[Array, "3"])

 required

Returns:

Type Description
Float[Array, 3]

Float[Array, "3"]: Sum of the vectors

compute_constants_L(eta, dotS1L, dotS2L, q) ¤

Compute coefficients for PN orbital angular momentum at 3PN.

As per LALSimInspiralFDPrecAngles_internals.c

Parameters:

Name Type Description Default
eta

Symmetric mass ratio

 required
dotS1L

Dot product of S1 and L

 required
dotS2L

Dot product of S2 and L

 required
q

Mass ratio m2/m1 (q < 1)

 required

Returns:

Type Description

tuple[FloatLike, FloatLike, FloatLike, FloatLike, FloatLike]: 5 constants [constants_L_0, ..., constants_L_4]

compute_psi0(Smi2: FloatLike, Spl2: FloatLike, S32: FloatLike, S_0_norm: FloatLike, v_0: FloatLike, v_0_2: FloatLike, psi1: FloatLike, psi2: FloatLike, g0: FloatLike, delta_qq: FloatLike, L_0: Float[Array, 3], S1v: Float[Array, 3], S2v: Float[Array, 3]) -> FloatLike ¤

Compute initial psi0 value for MSA approximation.

Parameters:

Name Type Description Default
Smi2 FloatLike

S_minus squared root (FloatLike)

 required
Spl2 FloatLike

S_plus squared root (FloatLike)

 required
S32 FloatLike

S_3 squared root (FloatLike)

 required
S_0_norm FloatLike

Initial total spin norm (FloatLike)

 required
v_0 FloatLike

Initial velocity parameter (FloatLike)

 required
v_0_2 FloatLike

v_0 squared (FloatLike)

 required
psi1 FloatLike

Psi coefficient 1 (FloatLike)

 required
psi2 FloatLike

Psi coefficient 2 (FloatLike)

 required
g0 FloatLike

g0 coefficient (FloatLike)

 required
delta_qq FloatLike

Delta mass ratio term (FloatLike)

 required
L_0 Float[Array, 3]

Initial orbital angular momentum vector (array)

 required
S1v Float[Array, 3]

Spin 1 vector (array)

 required
S2v Float[Array, 3]

Spin 2 vector (array)

 required

Returns: FloatLike: Initial psi0 value

compute_spin_norm_squared(chi1x, chi1y, chi1z, chi2x, chi2y, chi2z, mass_1, mass_2) ¤

Compute the squared norms of the dimensionless spin vectors S1 and S2.

Parameters:

Name Type Description Default
chi1x, chi1y, chi1z

Components of dimensionless spin vector for mass 1

 required
chi2x, chi2y, chi2z

Components of dimensionless spin vector for mass 2

 required
mass_1

Mass of the primary (m1 > m2)

 required
mass_2

Mass of the secondary

 required

Returns:

Name Type Description
tuple

(S1_norm_2, S2_norm_2) - squared norms of the spin vectors