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20,840 | precession.precession | eval_S1 |
Spin angular momentum of the heavier black hole.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
Returns
-------
S1: float
Magnitude of the primary spin.
Examples
--------
``S1 = precession.eval_S1(q,chi1)``
| def eval_S1(q, chi1):
"""
Spin angular momentum of the heavier black hole.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
Returns
-------
S1: float
Magnitude of the primary spin.
Examples
--------
``S1 = precession.eval_S1(q,chi1)``
"""
chi1 = np.atleast_1d(chi1).astype(float)
S1 = chi1*(eval_m1(q))**2
return S1
| (q, chi1) | [
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] |
20,841 | precession.precession | eval_S2 |
Spin angular momentum of the lighter black hole.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
S2: float
Magnitude of the secondary spin.
Examples
--------
``S2 = precession.eval_S2(q,chi2)``
| def eval_S2(q, chi2):
"""
Spin angular momentum of the lighter black hole.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
S2: float
Magnitude of the secondary spin.
Examples
--------
``S2 = precession.eval_S2(q,chi2)``
"""
chi2 = np.atleast_1d(chi2).astype(float)
S2 = chi2*(eval_m2(q))**2
return S2
| (q, chi2) | [
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20,842 | precession.precession | eval_alpha |
Evaluate the precession angle spanned by L during an entire cycle.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
alpha: float
Azimuthal angle spanned by L about J during an entire cycle.
Examples
--------
``alpha = precession.eval_alpha(kappa,r,chieff,q,chi1,chi2)``
| def eval_alpha(kappa, r, chieff, q, chi1, chi2, precomputedroots=None):
"""
Evaluate the precession angle spanned by L during an entire cycle.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
alpha: float
Azimuthal angle spanned by L about J during an entire cycle.
Examples
--------
``alpha = precession.eval_alpha(kappa,r,chieff,q,chi1,chi2)``
"""
q = np.atleast_1d(q).astype(float)
r = np.atleast_1d(r).astype(float)
u= eval_u(r=r,q=q)
with warnings.catch_warnings():
# If there are infinitely large separation in the array the following will throw a warning. You can safely ignore it because that value is not used, see below
if 0 in u:
warnings.filterwarnings("ignore", category=Warning)
deltachiminus,deltachiplus,deltachi3 = deltachiroots(kappa, u, chieff, q, chi1, chi2, precomputedroots=precomputedroots)
bigC0, bigCplus, bigCminus,bigRplus,bigRminus = intertial_ingredients(kappa, r, chieff, q, chi1, chi2)
psiperiod = eval_tau(kappa, r, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]),return_psiperiod=True)
m = elliptic_parameter(kappa, u, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]))
alpha = 2 * bigC0 * psiperiod * ( scipy.special.ellipk(m)
- bigCplus / (bigRplus - deltachiminus*(1-q)*r**(-1/2))
* ellippi( (1-q)*r**(-1/2)*(deltachiplus-deltachiminus) / (bigRplus - deltachiminus*(1-q)*r**(-1/2)), np.pi/2, m)
- bigCminus / (bigRminus - deltachiminus*(1-q)*r**(-1/2))
* ellippi( (1-q)*r**(-1/2)*(deltachiplus-deltachiminus) / (bigRminus - deltachiminus*(1-q)*r**(-1/2)), np.pi/2, m) )
# At infinitely large separation use the analytic result
if 0 in u:
mathcalY = 2 * q * (1+q)**3 * kappa * chieff - (1+q)**5 * kappa**2 +(1-q) *(chi1**2 -q**4 * chi2**2)
alphainf1= 2*np.pi*(4+3*q)*q/3/(1-q**2)
alphainf2 = 2*np.pi*(4*q+3)/3/(1-q**2)
alphainf = np.where(mathcalY>=0, alphainf1, alphainf2)
alpha =np.where(u>0,alpha,alphainf)
return alpha
| (kappa, r, chieff, q, chi1, chi2, precomputedroots=None) | [
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20,843 | precession.precession | eval_bracket_omega |
Precession average of the precession frequency deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
bracket_omega: float
Precession-averaged precession frequency.
Examples
--------
``bracket_omega = precession.eval_bracket_omega(kappa,r,chieff,q,chi1,chi2)``
| def eval_bracket_omega(kappa, r, chieff, q, chi1, chi2, precomputedroots=None):
"""
Precession average of the precession frequency deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
bracket_omega: float
Precession-averaged precession frequency.
Examples
--------
``bracket_omega = precession.eval_bracket_omega(kappa,r,chieff,q,chi1,chi2)``
"""
alpha = eval_alpha(kappa, r, chieff, q, chi1, chi2, precomputedroots=precomputedroots)
tau = eval_tau(kappa, r, chieff, q, chi1, chi2, precomputedroots=precomputedroots)
bracket_omega = alpha / tau
return bracket_omega
| (kappa, r, chieff, q, chi1, chi2, precomputedroots=None) | [
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20,844 | precession.precession | eval_bracket_theta |
Precession average of precession amplitude of deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894. Additional keywords arguments are passed to `precession_average`.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
bracket_theta: float
Precession-averaged precession amplitude.
Examples
--------
``bracket_theta = precession.eval_bracket_theta(kappa,r,chieff,q,chi1,chi2)``
| def eval_bracket_theta(kappa, r, chieff, q, chi1, chi2, **kwargs):
"""
Precession average of precession amplitude of deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894. Additional keywords arguments are passed to `precession_average`.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
bracket_theta: float
Precession-averaged precession amplitude.
Examples
--------
``bracket_theta = precession.eval_bracket_theta(kappa,r,chieff,q,chi1,chi2)``
"""
def _integrand(deltachi, kappa, r, chieff, q):
bracket_theta_integrand = eval_thetaL(deltachi, kappa, r, chieff, q)
return bracket_theta_integrand
bracket_theta = precession_average(kappa, r, chieff, q, chi1, chi2, _integrand, kappa, r, chieff, q, **kwargs)
return bracket_theta
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20,845 | precession.precession | eval_chi1 |
Dimensionless spin of the heavier black hole.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
S1: float
Magnitude of the primary spin.
Returns
-------
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
Examples
--------
``chi1 = precession.eval_chi1(q,S1)``
| def eval_chi1(q, S1):
"""
Dimensionless spin of the heavier black hole.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
S1: float
Magnitude of the primary spin.
Returns
-------
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
Examples
--------
``chi1 = precession.eval_chi1(q,S1)``
"""
S1 = np.atleast_1d(S1).astype(float)
chi1 = S1/(eval_m1(q))**2
return chi1
| (q, S1) | [
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20,846 | precession.precession | eval_chi2 |
Dimensionless spin of the lighter black hole.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
S2: float
Magnitude of the secondary spin.
Returns
-------
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Examples
--------
``chi2 = precession.eval_chi2(q,S2)``
| def eval_chi2(q, S2):
"""
Dimensionless spin of the lighter black hole.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
S2: float
Magnitude of the secondary spin.
Returns
-------
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Examples
--------
``chi2 = precession.eval_chi2(q,S2)``
"""
S2 = np.atleast_1d(S2).astype(float)
chi2 = S2/(eval_m2(q))**2
return chi2
| (q, S2) | [
0.02481415867805481,
0.008914518170058727,
0.003233522642403841,
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0.050628744065761566,
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] |
20,847 | precession.precession | eval_chieff |
Eftective spin.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chieff: float
Effective spin.
Examples
--------
``chieff = precession.eval_chieff(theta1,theta2,q,chi1,chi2)``
| def eval_chieff(theta1, theta2, q, chi1, chi2):
"""
Eftective spin.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chieff: float
Effective spin.
Examples
--------
``chieff = precession.eval_chieff(theta1,theta2,q,chi1,chi2)``
"""
theta1 = np.atleast_1d(theta1).astype(float)
theta2 = np.atleast_1d(theta2).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
chieff = (chi1*np.cos(theta1) + q*chi2*np.cos(theta2))/(1+q)
return chieff
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20,848 | precession.precession | eval_chip |
Compute the effective precessing spin. The keyword `which` one of the following definitions:
- `heuristic`, as in Schmidt et al 2015. Required inputs are either
- `generalized`, retail all precession-timescale variations,
- `averaged` (default), averages over precession-timescale variations,
- `rms`, compute the root-mean-square average, which is faster to evaluate.
The required inputs are either (theta1,theta2,deltaphi,r,q,chi1,chi2) or (deltachi,kappa,chieff,r,q,chi1,chi2). In the latter case, deltachi can be omitted and will be resampled from its PN-weighted distribution.
Some inputs will be ignored for some of the chip definitions (for instance the heuristic chip does not depend on either r or deltaphi), but dummy values are still requested for code consistency.
The keywords arguments are only used for the `averaged` formulation and are passed to `precession_average`.
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
r: float, optional (default: None)
Binary separation.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
which: string, optional (default: "averaged")
Select function behavior.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2,which="heuristic")``
``chip = precession.eval_chip(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2,which="generalized")``
``chip = precession.eval_chip(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2,which="averaged")``
``chip = precession.eval_chip(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2,which="rms")``
``chip = precession.eval_chip(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,which="heuristic")``
``chip = precession.eval_chip(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,which="generalized")``
``chip = precession.eval_chip(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,which="averaged")``
``chip = precession.eval_chip(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,which="rms")``
| def eval_chip(theta1=None, theta2=None, deltaphi=None, deltachi=None, kappa=None, r=None, chieff=None, q=None, chi1=None, chi2=None, which="averaged", **kwargs):
"""
Compute the effective precessing spin. The keyword `which` one of the following definitions:
- `heuristic`, as in Schmidt et al 2015. Required inputs are either
- `generalized`, retail all precession-timescale variations,
- `averaged` (default), averages over precession-timescale variations,
- `rms`, compute the root-mean-square average, which is faster to evaluate.
The required inputs are either (theta1,theta2,deltaphi,r,q,chi1,chi2) or (deltachi,kappa,chieff,r,q,chi1,chi2). In the latter case, deltachi can be omitted and will be resampled from its PN-weighted distribution.
Some inputs will be ignored for some of the chip definitions (for instance the heuristic chip does not depend on either r or deltaphi), but dummy values are still requested for code consistency.
The keywords arguments are only used for the `averaged` formulation and are passed to `precession_average`.
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
r: float, optional (default: None)
Binary separation.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
which: string, optional (default: "averaged")
Select function behavior.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2,which="heuristic")``
``chip = precession.eval_chip(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2,which="generalized")``
``chip = precession.eval_chip(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2,which="averaged")``
``chip = precession.eval_chip(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2,which="rms")``
``chip = precession.eval_chip(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,which="heuristic")``
``chip = precession.eval_chip(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,which="generalized")``
``chip = precession.eval_chip(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,which="averaged")``
``chip = precession.eval_chip(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,which="rms")``
"""
if r is None or q is None or chi1 is None or chi2 is None:
raise ValueError("Provide r, q, chi1, and chi2.")
if theta1 is not None and theta2 is not None and deltaphi is not None and deltachi is None and kappa is None and chieff is None:
deltachi, kappa, chieff = angles_to_conserved(theta1, theta2, deltaphi, r, q, chi1, chi2, full_output=False)
elif theta1 is None and theta2 is None and deltaphi is None and kappa is not None and chieff is not None:
if deltachi is None:
if which == 'heuristic' or which == 'generalized':
deltachi = deltachisampling(kappa, r, chieff, q, chi1, chi2)
theta1, theta2, deltaphi = conserved_to_angles(deltachi, kappa, r, chieff, q, chi1, chi2)
else:
raise ValueError("Provide either (theta1,theta2,deltaphi), (deltachi,kappa,chieff), or (kappa,chieff).")
if which == 'heuristic':
chip = eval_chip_heuristic(theta1, theta2, q, chi1, chi2)
elif which == 'generalized':
chip = eval_chip_generalized(theta1, theta2, deltaphi, q, chi1, chi2)
elif which == 'averaged':
chip_finite = eval_chip_averaged(kappa, r, chieff, q, chi1, chi2, **kwargs)
term1, term2 = chip_terms(theta1, theta2, q, chi1, chi2)
chip_infinity = 2* np.abs(term1+term2) * scipy.special.ellipe(4*term1*term2/(term1+term2)**2)/np.pi
chip = np.where(r!=np.inf, chip_finite, chip_infinity)
elif which == 'rms':
chip_finite = eval_chip_rms(kappa, r, chieff, q, chi1, chi2)
term1, term2 = chip_terms(theta1, theta2, q, chi1, chi2)
chip_infinity = (term1**2 + term2**2)**(1/2)
chip = np.where(r!=np.inf, chip_finite, chip_infinity)
else:
raise ValueError("`which` needs to be one of the following: `heuristic`, `generalized`, `averaged`, 'rms`.")
return chip
| (theta1=None, theta2=None, deltaphi=None, deltachi=None, kappa=None, r=None, chieff=None, q=None, chi1=None, chi2=None, which='averaged', **kwargs) | [
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20,849 | precession.precession | eval_chip_averaged |
Averaged definition of the effective precessing spin, see arxiv:2011.11948.
Additional keywords arguments are passed to `precession_average`.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip_averaged(kappa,r,chieff,q,chi1,chi2)``
| def eval_chip_averaged(kappa, r, chieff, q, chi1, chi2, **kwargs):
"""
Averaged definition of the effective precessing spin, see arxiv:2011.11948.
Additional keywords arguments are passed to `precession_average`.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip_averaged(kappa,r,chieff,q,chi1,chi2)``
"""
def _integrand(deltachi, kappa, r, chieff, q, chi1, chi2):
theta1, theta2, deltaphi = conserved_to_angles(deltachi, kappa, r, chieff, q, chi1, chi2)
chip_integrand = eval_chip_generalized(theta1, theta2, deltaphi, q, chi1, chi2)
return chip_integrand
chip = precession_average(kappa, r, chieff, q, chi1, chi2, _integrand, kappa, r, chieff, q, chi1, chi2, **kwargs)
return chip
| (kappa, r, chieff, q, chi1, chi2, **kwargs) | [
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20,850 | precession.precession | eval_chip_generalized |
Generalized definition of the effective precessing spin chip, see arxiv:2011.11948. This definition retains all variations on the precession timescale.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip_generalized(theta1,theta2,deltaphi,q,chi1,chi2)``
| def eval_chip_generalized(theta1, theta2, deltaphi, q, chi1, chi2):
"""
Generalized definition of the effective precessing spin chip, see arxiv:2011.11948. This definition retains all variations on the precession timescale.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip_generalized(theta1,theta2,deltaphi,q,chi1,chi2)``
"""
term1, term2 = chip_terms(theta1, theta2, q, chi1, chi2)
chip = (term1**2 + term2**2 + 2*term1*term2*np.cos(deltaphi))**0.5
return chip
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20,851 | precession.precession | eval_chip_heuristic |
Heuristic definition of the effective precessing spin chip (Schmidt et al 2015), see arxiv:2011.11948. This definition inconsistently averages over some, but not all, variations on the precession timescale.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip_heuristic(theta1,theta2,q,chi1,chi2)``
| def eval_chip_heuristic(theta1, theta2, q, chi1, chi2):
"""
Heuristic definition of the effective precessing spin chip (Schmidt et al 2015), see arxiv:2011.11948. This definition inconsistently averages over some, but not all, variations on the precession timescale.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip_heuristic(theta1,theta2,q,chi1,chi2)``
"""
term1, term2 = chip_terms(theta1, theta2, q, chi1, chi2)
chip = np.maximum(term1, term2)
return chip
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20,852 | precession.precession | eval_chip_rms |
Root-mean-square definition of the effective precessing spin. This is much faster to evaluate than the plain average.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip_rms(kappa,r,chieff,q,chi1,chi2)``
| def eval_chip_rms(kappa, r, chieff, q, chi1, chi2):
"""
Root-mean-square definition of the effective precessing spin. This is much faster to evaluate than the plain average.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chip: float
Effective precessing spin.
Examples
--------
``chip = precession.eval_chip_rms(kappa,r,chieff,q,chi1,chi2)``
"""
kappa = np.atleast_1d(kappa).astype(float)
r = np.atleast_1d(r).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
u=eval_u(r=r,q=q)
# Machine generated with eq_generator.nb
lambdabar = 1/4 * q**(-1) * (1 + q) * ((4 + 3 * q))**(-2) * u**(-1)
# Machine generated with eq_generator.nb
lambda2 = -1 * ((1 + -1 * q))**2 * q * (1 + q) * u
# Machine generated with eq_generator.nb
lambda1 = -2 * (1 + -1 * q) * ((1 + q))**2 * ((4 + 3 * q) * (3 + 4 * \
q) + 7 * q * u * chieff)
# Machine generated with eq_generator.nb
lambda0 = (2 * ((1 + q))**3 * (4 + 3 * q) * (3 + 4 * q) * (2 * kappa \
+ -1 * chieff) + -1 * u * (12 * (1 + -1 * q) * ((4 + 3 * q) * chi1**2 \
+ -1 * q**3 * (3 + 4 * q) * chi2**2) + 49 * q * ((1 + q))**3 * \
chieff**2))
deltachiminus,deltachiplus,deltachi3 = deltachiroots(kappa, u, chieff, q, chi1, chi2)
m = elliptic_parameter(kappa, u, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus, deltachiplus, deltachi3]))
chip = lambdabar**(1/2) * ( (deltachiplus-deltachiminus)**2 * lambda2 * deltachitildeav2(m) +
(deltachiplus-deltachiminus) * (lambda1 + 2*deltachiminus*lambda2) * deltachitildeav(m) +
(deltachiminus*lambda1 + deltachiminus**2*lambda2 + lambda0 ))**(1/2)
# Debug:
# def _integrand(deltachi, kappa, r, chieff, q, chi1, chi2):
# theta1, theta2, deltaphi = conserved_to_angles(deltachi, kappa, r, chieff, q, chi1, chi2)
# chip_integrand = eval_chip_generalized(theta1, theta2, deltaphi, q, chi1, chi2)**2
# return chip_integrand
# chip = precession_average(kappa, r, chieff, q, chi1, chi2, _integrand, kappa, r, chieff, q, chi1, chi2, **kwargs)**0.5
return chip
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] |
20,853 | precession.precession | eval_cosdeltaphi |
Cosine of the angle between the projections of the two spins onto the orbital plane.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
cosdeltaphi: float
Cosine of the angle between the projections of the two spins onto the orbital plane.
Examples
--------
``cosdeltaphi = precession.eval_cosdeltaphi(deltachi,kappa,r,chieff,q,chi1,chi2)``
| def eval_cosdeltaphi(deltachi, kappa, r, chieff, q, chi1, chi2):
"""
Cosine of the angle between the projections of the two spins onto the orbital plane.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
cosdeltaphi: float
Cosine of the angle between the projections of the two spins onto the orbital plane.
Examples
--------
``cosdeltaphi = precession.eval_cosdeltaphi(deltachi,kappa,r,chieff,q,chi1,chi2)``
"""
deltachi = np.atleast_1d(deltachi).astype(float)
kappa = np.atleast_1d(kappa).astype(float)
r = np.atleast_1d(r).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
with warnings.catch_warnings():
# If there are infinitely large separation in the array the following will throw a warning. You can safely ignore it because that value is not used, see below
if np.inf in r:
warnings.filterwarnings("ignore", category=RuntimeWarning)
# Machine generated with eq_generator.nb
cosdeltaphi = q**(-1) * ((4 * q**2 * (chi2)**2 + -1 * ((1 + q))**2 * \
((-1 * deltachi + chieff))**2) * (4 * (chi1)**2 + -1 * ((1 + q))**2 * \
((deltachi + chieff))**2))**(-1/2) * (-2 * ((chi1)**2 + q**4 * \
(chi2)**2) + (2 * q * (1 + q) * (r)**(1/2) * (-1 * (1 + -1 * q) * \
deltachi + (2 * (1 + q) * kappa + -1 * (1 + q) * chieff)) + -1 * q * \
((1 + q))**2 * (-1 * (deltachi)**2 + chieff**2)))
# At infinity, the only thing I can do is putting a random number for deltaphi, unformly distributed
cosdeltaphi = np.where(r!=np.inf, cosdeltaphi, np.cos(np.random.uniform(0,np.pi, len(cosdeltaphi))))
return cosdeltaphi
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20,854 | precession.precession | eval_costheta1 |
Cosine of the angle between the orbital angular momentum and the spin of the primary black hole.
Parameters
----------
deltachi: float
Weighted spin difference.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
Returns
-------
costheta1: float
Cosine of the angle between orbital angular momentum and primary spin.
Examples
--------
``costheta1 = precession.eval_costheta1(deltachi,chieff,q,chi1)``
| def eval_costheta1(deltachi, chieff, q, chi1):
"""
Cosine of the angle between the orbital angular momentum and the spin of the primary black hole.
Parameters
----------
deltachi: float
Weighted spin difference.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
Returns
-------
costheta1: float
Cosine of the angle between orbital angular momentum and primary spin.
Examples
--------
``costheta1 = precession.eval_costheta1(deltachi,chieff,q,chi1)``
"""
deltachi = np.atleast_1d(deltachi).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
costheta1 = (1+q)/(2*chi1)*(chieff+deltachi)
return costheta1
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20,855 | precession.precession | eval_costheta12 |
Cosine of the angle between the two spins. Valid inputs are either (theta1,theta2,deltaphi) or (deltachi,kappa,chieff,q,chi1,chi2).
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
costheta12: float
Cosine of the angle between the two spins.
Examples
--------
``costheta12 = precession.eval_costheta12(theta1=theta1,theta2=theta2,deltaphi=deltaphi)``
``costheta12 = precession.eval_costheta12(deltachi=deltachi,kappa=kappa,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
| def eval_costheta12(theta1=None, theta2=None, deltaphi=None, deltachi=None, kappa=None, chieff=None, q=None, chi1=None, chi2=None):
"""
Cosine of the angle between the two spins. Valid inputs are either (theta1,theta2,deltaphi) or (deltachi,kappa,chieff,q,chi1,chi2).
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
costheta12: float
Cosine of the angle between the two spins.
Examples
--------
``costheta12 = precession.eval_costheta12(theta1=theta1,theta2=theta2,deltaphi=deltaphi)``
``costheta12 = precession.eval_costheta12(deltachi=deltachi,kappa=kappa,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
"""
if theta1 is not None and theta2 is not None and deltaphi is not None and deltachi is None and kappa is None and chieff is None and q is None and chi1 is None and chi2 is None:
theta1=np.atleast_1d(theta1).astype(float)
theta2=np.atleast_1d(theta2).astype(float)
deltaphi=np.atleast_1d(deltaphi).astype(float)
costheta12 = np.sin(theta1)*np.sin(theta2)*np.cos(deltaphi) + np.cos(theta1)*np.cos(theta2)
elif theta1 is None and theta2 is None and deltaphi is None and deltachi is not None and kappa is not None and chieff is not None and q is not None and chi1 is not None and chi2 is not None:
deltachi = np.atleast_1d(deltachi).astype(float)
kappa = np.atleast_1d(kappa).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
# Machine generated with eq_generator.nb
costheta12 = 1/2 * q**(-2) * (chi1)**(-1) * (chi2)**(-1) * (-1 * \
(chi1)**2 + (-1 * q**4 * (chi2)**2 + q * (1 + q) * (r)**(1/2) * (-1 * \
(1 + -1 * q) * deltachi + (2 * (1 + q) * kappa + -1 * (1 + q) * \
chieff))))
else:
raise TypeError("Provide either (theta1,theta2,deltaphi) or (deltachi,kappa,chieff,q,chi1,chi2).")
return costheta12
| (theta1=None, theta2=None, deltaphi=None, deltachi=None, kappa=None, chieff=None, q=None, chi1=None, chi2=None) | [
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20,856 | precession.precession | eval_costheta2 |
Cosine of the angle between the orbital angular momentum and the spin of the secondary black hole.
Parameters
----------
deltachi: float
Weighted spin difference.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
costheta2: float
Cosine of the angle between orbital angular momentum and secondary spin.
Examples
--------
``costheta2 = precession.eval_costheta2(deltachi,chieff,q,chi2)``
| def eval_costheta2(deltachi, chieff, q, chi2):
"""
Cosine of the angle between the orbital angular momentum and the spin of the secondary black hole.
Parameters
----------
deltachi: float
Weighted spin difference.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
costheta2: float
Cosine of the angle between orbital angular momentum and secondary spin.
Examples
--------
``costheta2 = precession.eval_costheta2(deltachi,chieff,q,chi2)``
"""
deltachi = np.atleast_1d(deltachi).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
costheta2 = (1+q)/(2*q*chi2)*(chieff-deltachi)
return costheta2
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20,857 | precession.precession | eval_costhetaL |
Cosine of the angle betwen the orbital angular momentum and the total angular momentum.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
Returns
-------
costhetaL: float
Cosine of the angle betwen orbital angular momentum and total angular momentum.
Examples
--------
``costhetaL = precession.eval_costhetaL(deltachi,kappa,r,chieff,q)``
| def eval_costhetaL(deltachi, kappa, r, chieff, q):
"""
Cosine of the angle betwen the orbital angular momentum and the total angular momentum.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
Returns
-------
costhetaL: float
Cosine of the angle betwen orbital angular momentum and total angular momentum.
Examples
--------
``costhetaL = precession.eval_costhetaL(deltachi,kappa,r,chieff,q)``
"""
deltachi = np.atleast_1d(deltachi).astype(float)
kappa = np.atleast_1d(kappa).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
# Machine generated with eq_generator.nb
costhetaL = ((1 + 2 * q**(-1) * ((1 + q))**2 * (r)**(-1/2) * \
kappa))**(-1/2) * (1 + 1/2 * q**(-1) * (1 + q) * (r)**(-1/2) * ((1 + \
-1 * q) * deltachi + (1 + q) * chieff))
return costhetaL
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20,858 | precession.precession | eval_cyclesign |
Evaluate if the input parameters are in the first of the second half of a precession cycle. We refer to this as the 'sign' of a precession cycle, defined as +1 if deltachi is increasing and -1 deltachi is decreasing. Valid inputs are one and not more of the following:
- dSdt
- deltaphi
- Lvec, S1vec, S2vec.
Parameters
----------
ddeltachidt: float, optional (default: None)
Time derivative of the total spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
Lvec: array, optional (default: None)
Cartesian vector of the orbital angular momentum.
S1vec: array, optional (default: None)
Cartesian vector of the primary spin.
S2vec: array, optional (default: None)
Cartesian vector of the secondary spin.
Returns
-------
cyclesign: integer
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
Examples
--------
``cyclesign = precession.eval_cyclesign(ddeltachidt=ddeltachidt)``
``cyclesign = precession.eval_cyclesign(deltaphi=deltaphi)``
``cyclesign = precession.eval_cyclesign(Lvec=Lvec,S1vec=S1vec,S2vec=S2vec)``
| def eval_cyclesign(ddeltachidt=None, deltaphi=None, Lvec=None, S1vec=None, S2vec=None):
"""
Evaluate if the input parameters are in the first of the second half of a precession cycle. We refer to this as the 'sign' of a precession cycle, defined as +1 if deltachi is increasing and -1 deltachi is decreasing. Valid inputs are one and not more of the following:
- dSdt
- deltaphi
- Lvec, S1vec, S2vec.
Parameters
----------
ddeltachidt: float, optional (default: None)
Time derivative of the total spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
Lvec: array, optional (default: None)
Cartesian vector of the orbital angular momentum.
S1vec: array, optional (default: None)
Cartesian vector of the primary spin.
S2vec: array, optional (default: None)
Cartesian vector of the secondary spin.
Returns
-------
cyclesign: integer
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
Examples
--------
``cyclesign = precession.eval_cyclesign(ddeltachidt=ddeltachidt)``
``cyclesign = precession.eval_cyclesign(deltaphi=deltaphi)``
``cyclesign = precession.eval_cyclesign(Lvec=Lvec,S1vec=S1vec,S2vec=S2vec)``
"""
if ddeltachidt is not None and deltaphi is None and Lvec is None and S1vec is None and S2vec is None:
ddeltachidt = np.atleast_1d(ddeltachidt).astype(float)
cyclesign = np.sign(ddeltachidt)
elif ddeltachidt is None and deltaphi is not None and Lvec is None and S1vec is None and S2vec is None:
deltaphi = np.atleast_1d(deltaphi).astype(float)
cyclesign = np.sign(deltaphi)
elif ddeltachidt is None and deltaphi is None and Lvec is not None and S1vec is not None and S2vec is not None:
Lvec = np.atleast_2d(Lvec).astype(float)
S1vec = np.atleast_2d(S1vec).astype(float)
S2vec = np.atleast_2d(S2vec).astype(float)
cyclesign = np.sign(dot_nested(S1vec, np.cross(S2vec, Lvec)))
else:
raise TypeError("Please provide one and not more of the following: ddeltachidt, deltaphi, (Lvec, S1vec, S2vec).")
return cyclesign
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] |
20,859 | precession.precession | eval_delta_omega |
Variation of the precession frequency of deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
delta_omega: float
Precession frequency variation due to nutation.
Examples
--------
``delta_omega = precession.eval_delta_omega(kappa,r,chieff,q,chi1,chi2)``
| def eval_delta_omega(kappa, r, chieff, q, chi1, chi2, precomputedroots=None):
"""
Variation of the precession frequency of deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
delta_omega: float
Precession frequency variation due to nutation.
Examples
--------
``delta_omega = precession.eval_delta_omega(kappa,r,chieff,q,chi1,chi2)``
"""
if precomputedroots is None:
deltachimin, deltachiplus = deltachilimits_plusminus(kappa, r, chieff, q, chi1, chi2)
else:
deltachimin, deltachiplus, _ = precomputedroots[:-1]
Omega_minus = eval_OmegaL(deltachiplus, kappa, r, chieff, q, chi1, chi2)
Omega_plus = eval_OmegaL(deltachimin, kappa, r, chieff, q, chi1, chi2)
delta_omega = (Omega_plus - Omega_minus)/2
return delta_omega
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20,860 | precession.precession | eval_delta_theta |
Nutation amplitude of deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
delta_theta: float
Nutation amplitude.
Examples
--------
``delta_theta = precession.eval_delta_theta(kappa,r,chieff,q,chi1,chi2)``
| def eval_delta_theta(kappa, r, chieff, q, chi1, chi2, precomputedroots=None):
"""
Nutation amplitude of deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
delta_theta: float
Nutation amplitude.
Examples
--------
``delta_theta = precession.eval_delta_theta(kappa,r,chieff,q,chi1,chi2)``
"""
if precomputedroots is None:
deltachimin, deltachiplus = deltachilimits_plusminus(kappa, r, chieff, q, chi1, chi2)
else:
deltachimin, deltachiplus, _ = precomputedroots[:-1]
theta_minus = eval_thetaL(deltachiplus, kappa, r, chieff, q)
theta_plus = eval_thetaL(deltachimin, kappa, r, chieff, q)
delta_theta = (theta_plus - theta_minus)/2
return delta_theta
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20,861 | precession.precession | eval_deltachi |
Weighted spin difference.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
deltachi: float
Weighted spin difference.
Examples
--------
``deltachi = precession.eval_deltachi(theta1,theta2,q,chi1,chi2)``
| def eval_deltachi(theta1, theta2, q, chi1, chi2):
"""
Weighted spin difference.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
deltachi: float
Weighted spin difference.
Examples
--------
``deltachi = precession.eval_deltachi(theta1,theta2,q,chi1,chi2)``
"""
theta1 = np.atleast_1d(theta1).astype(float)
theta2 = np.atleast_1d(theta2).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
deltachi = (chi1*np.cos(theta1) -q*chi2*np.cos(theta2))/(1+q)
return deltachi
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] |
20,862 | precession.precession | eval_deltachiinf |
Large-separation limit of the weighted spin difference.
Parameters
----------
kappa: float
Asymptotic angular momentum.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
deltachi: float
Weighted spin difference.
Examples
--------
``deltachi = precession.eval_deltachiinf(kappa,chieff,q,chi1,chi2)``
| def eval_deltachiinf(kappa, chieff, q, chi1, chi2):
"""
Large-separation limit of the weighted spin difference.
Parameters
----------
kappa: float
Asymptotic angular momentum.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
deltachi: float
Weighted spin difference.
Examples
--------
``deltachi = precession.eval_deltachiinf(kappa,chieff,q,chi1,chi2)``
"""
kappa = np.atleast_1d(kappa).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
deltachi = (1+q)/(1-q)*(2*kappa-chieff)
return deltachi
| (kappa, chieff, q, chi1, chi2) | [
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] |
20,863 | precession.precession | eval_deltaphi |
Angle between the projections of the two spins onto the orbital plane.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
cyclesign: integer, optional (default: 1)
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
Returns
-------
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
Examples
--------
``deltaphi = precession.eval_deltaphi(deltachi,kappa,r,chieff,q,chi1,chi2,cyclesign=1)``
| def eval_deltaphi(deltachi, kappa, r, chieff, q, chi1, chi2, cyclesign=1):
"""
Angle between the projections of the two spins onto the orbital plane.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
cyclesign: integer, optional (default: 1)
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
Returns
-------
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
Examples
--------
``deltaphi = precession.eval_deltaphi(deltachi,kappa,r,chieff,q,chi1,chi2,cyclesign=1)``
"""
cyclesign = np.atleast_1d(cyclesign)
cosdeltaphi = eval_cosdeltaphi(deltachi, kappa, r, chieff, q, chi1, chi2)
deltaphi = np.sign(cyclesign)*np.arccos(cosdeltaphi)
return deltaphi
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20,864 | precession.precession | eval_eta |
Symmetric mass ratio eta = m1*m2/(m1+m2)^2 = q/(1+q)^2.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
Returns
-------
eta: float
Symmetric mass ratio 0<=eta<=1/4.
Examples
--------
``eta = precession.eval_eta(q)``
| def eval_eta(q):
"""
Symmetric mass ratio eta = m1*m2/(m1+m2)^2 = q/(1+q)^2.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
Returns
-------
eta: float
Symmetric mass ratio 0<=eta<=1/4.
Examples
--------
``eta = precession.eval_eta(q)``
"""
q = np.atleast_1d(q).astype(float)
eta = q/(1+q)**2
return eta
| (q) | [
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20,865 | precession.precession | eval_kappa |
Asymptotic angular momentum. Provide either (theta1,theta2,deltaphi,r,q,chi1,chhi2) or (J,r,q).
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
J: float, optional (default: None)
Magnitude of the total angular momentum.
r: float, optional (default: None)
Binary separation.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
kappa: float
Asymptotic angular momentum.
Examples
--------
``kappa = precession.eval_kappa(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2)``
``kappa = precession.eval_kappa(J=J,r=r,q=q)``
| def eval_kappa(theta1=None, theta2=None, deltaphi=None, J=None, r=None, q=None, chi1=None, chi2=None):
"""
Asymptotic angular momentum. Provide either (theta1,theta2,deltaphi,r,q,chi1,chhi2) or (J,r,q).
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
J: float, optional (default: None)
Magnitude of the total angular momentum.
r: float, optional (default: None)
Binary separation.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
kappa: float
Asymptotic angular momentum.
Examples
--------
``kappa = precession.eval_kappa(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2)``
``kappa = precession.eval_kappa(J=J,r=r,q=q)``
"""
if theta1 is None and theta2 is None and deltaphi is None and J is not None and r is not None and q is not None and chi1 is None and chi2 is None:
J = np.atleast_1d(J).astype(float)
L = eval_L(r, q)
kappa = (J**2 - L**2) / (2*L)
elif theta1 is not None and theta2 is not None and deltaphi is not None and J is None and r is not None and q is not None and chi1 is not None and chi2 is not None:
theta1 = np.atleast_1d(theta1).astype(float)
theta2 = np.atleast_1d(theta2).astype(float)
deltaphi = np.atleast_1d(deltaphi).astype(float)
r = np.atleast_1d(r).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
kappa = (chi1 * np.cos(theta1) + q**2 * chi2 * np.cos(theta2) )/(1+q)**2 + \
(chi1**2 + q**4 *chi2**2 + 2*chi1*chi2*q**2 * (np.cos(theta1)*np.cos(theta2) + np.cos(deltaphi)*np.sin(theta1)*np.sin(theta2))) / (2*q*(1+q)**2*r**(1/2))
else:
TypeError("Please provide provide either (theta1,theta2,deltaphi,r,q,chi1,chhi2) or (J,r,q).")
return kappa
| (theta1=None, theta2=None, deltaphi=None, J=None, r=None, q=None, chi1=None, chi2=None) | [
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20,866 | precession.precession | eval_m1 |
Mass of the heavier black hole in units of the total mass.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
Returns
-------
m1: float
Mass of the primary (heavier) black hole.
Examples
--------
``m1 = precession.eval_m1(q)``
| def eval_m1(q):
"""
Mass of the heavier black hole in units of the total mass.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
Returns
-------
m1: float
Mass of the primary (heavier) black hole.
Examples
--------
``m1 = precession.eval_m1(q)``
"""
q = np.atleast_1d(q).astype(float)
m1 = 1/(1+q)
return m1
| (q) | [
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20,867 | precession.precession | eval_m2 |
Mass of the lighter black hole in units of the total mass.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
Returns
-------
m2: float
Mass of the secondary (lighter) black hole.
Examples
--------
``m2 = precession.eval_m2(q)``
| def eval_m2(q):
"""
Mass of the lighter black hole in units of the total mass.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
Returns
-------
m2: float
Mass of the secondary (lighter) black hole.
Examples
--------
``m2 = precession.eval_m2(q)``
"""
q = np.atleast_1d(q).astype(float)
m2 = q/(1+q)
return m2
| (q) | [
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20,868 | precession.precession | eval_nutation_freq |
Nutation frequency of deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
littleomega: float
Squared time derivative of the weighted spin difference.
Examples
--------
``littleomega = precession.eval_nutation_freq(kappa,r,chieff,q,chi1,chi2)``
| def eval_nutation_freq(kappa, r, chieff, q, chi1, chi2, precomputedroots=None):
"""
Nutation frequency of deltachi as it oscillates from deltachi- to deltachi+ back to deltachi-.
This of the five phenomenological parameters from arxiv:2103.03894.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
littleomega: float
Squared time derivative of the weighted spin difference.
Examples
--------
``littleomega = precession.eval_nutation_freq(kappa,r,chieff,q,chi1,chi2)``
"""
tau = eval_tau(kappa, r, chieff, q, chi1, chi2, precomputedroots=precomputedroots)
littleomega = (2 * np.pi) / tau
return littleomega
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20,869 | precession.precession | eval_phiL |
Evaluate the azimuthal angle of L in a plane orthogonal to J along the precession cycle.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
cyclesign: integer, optional (default: 1)
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
phiL: float
Azimuthal angle spanned by L about J.
Examples
--------
``phiL = precession.eval_phiL(deltachi,kappa,r,chieff,q,chi1,chi2,cyclesign=1)``
| def eval_phiL(deltachi, kappa, r, chieff, q, chi1, chi2, cyclesign=1, precomputedroots=None):
"""
Evaluate the azimuthal angle of L in a plane orthogonal to J along the precession cycle.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
cyclesign: integer, optional (default: 1)
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
phiL: float
Azimuthal angle spanned by L about J.
Examples
--------
``phiL = precession.eval_phiL(deltachi,kappa,r,chieff,q,chi1,chi2,cyclesign=1)``
"""
q = np.atleast_1d(q).astype(float)
r = np.atleast_1d(r).astype(float)
u= eval_u(r=r,q=q)
deltachiminus,deltachiplus,deltachi3 = deltachiroots(kappa, u, chieff, q, chi1, chi2, precomputedroots=precomputedroots)
bigC0, bigCplus, bigCminus,bigRplus,bigRminus = intertial_ingredients(kappa, r, chieff, q, chi1, chi2)
psiperiod = eval_tau(kappa, r, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]), return_psiperiod=True)
deltachitilde = affine(deltachi,deltachiminus,deltachiplus)
m = elliptic_parameter(kappa, u, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]))
phiL = np.sign(cyclesign) * bigC0 * psiperiod * ( scipy.special.ellipkinc(np.arcsin(deltachitilde**(1/2)), m)
- bigCplus / (bigRplus - deltachiminus*(1-q)*r**(-1/2))
* ellippi( (1-q)*r**(-1/2)*(deltachiplus-deltachiminus) / (bigRplus - deltachiminus*(1-q)*r**(-1/2)), np.arcsin(deltachitilde**(1/2)), m)
- bigCminus / (bigRminus - deltachiminus*(1-q)*r**(-1/2))
* ellippi( (1-q)*r**(-1/2)*(deltachiplus-deltachiminus) / (bigRminus - deltachiminus*(1-q)*r**(-1/2)), np.arcsin(deltachitilde**(1/2)), m) )
return phiL
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20,870 | precession.precession | eval_q |
Mass ratio, 0 < q = m2/m1 < 1.
Parameters
----------
m1: float
Mass of the primary (heavier) black hole.
m2: float
Mass of the secondary (lighter) black hole.
Returns
-------
q: float
Mass ratio: 0<=q<=1.
Examples
--------
``q = precession.eval_q(m1,m2)``
| def eval_q(m1, m2):
"""
Mass ratio, 0 < q = m2/m1 < 1.
Parameters
----------
m1: float
Mass of the primary (heavier) black hole.
m2: float
Mass of the secondary (lighter) black hole.
Returns
-------
q: float
Mass ratio: 0<=q<=1.
Examples
--------
``q = precession.eval_q(m1,m2)``
"""
m1 = np.atleast_1d(m1).astype(float)
m2 = np.atleast_1d(m2).astype(float)
q = m2/m1
assert (q < 1).all(), "The convention used in this code is q=m2/m1<1."
return q
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20,871 | precession.precession | eval_r |
Orbital separation of the binary. Valid inputs are either (L,q) or (u,q).
Parameters
----------
L: float, optional (default: None)
Magnitude of the Newtonian orbital angular momentum.
u: float, optional (default: None)
Compactified separation 1/(2L).
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
Returns
-------
r: float
Binary separation.
Examples
--------
``r = precession.eval_r(L=L,q=q)``
``r = precession.eval_r(u=u,q=q)``
| def eval_r(L=None,u=None,q=None):
"""
Orbital separation of the binary. Valid inputs are either (L,q) or (u,q).
Parameters
----------
L: float, optional (default: None)
Magnitude of the Newtonian orbital angular momentum.
u: float, optional (default: None)
Compactified separation 1/(2L).
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
Returns
-------
r: float
Binary separation.
Examples
--------
``r = precession.eval_r(L=L,q=q)``
``r = precession.eval_r(u=u,q=q)``
"""
q = np.atleast_1d(q).astype(float)
if L is not None and u is None and q is not None:
L = np.atleast_1d(L).astype(float)
r = (L * (1+q)**2 / q )**2
elif L is None and u is not None and q is not None:
u = np.atleast_1d(u).astype(float)
r = (2*u*q/(1+q)**2)**(-2)
else:
raise TypeError("Provide either (L,q) or (u,q).")
return r
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20,872 | precession.precession | eval_tau |
Evaluate the nutation period.
Setting return_psiperiod=True return the phase-period instead of the time period (i.e. returns tau/2K(m) insteaf of tau). This is useful to avoid the evaluation of an elliptic integral when it's not needed.
Setting donotnormalize=True is equivalent to mathcalA=1.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
MISSING: COULD NOT BUILD, optional (default: False)
FILL MANUALLY.
donotnormalize: boolean, optional (default: False)
If True omit the numerical prefactor.
Returns
-------
tau: float
Nutation period.
Examples
--------
``tau = precession.eval_tau(kappa,r,chieff,q,chi1,chi2)``
``tau = precession.eval_tau(kappa,r,chieff,q,chi1,chi2,return_psiperiod=True)``
| def eval_tau(kappa, r, chieff, q, chi1, chi2, precomputedroots=None, return_psiperiod=False, donotnormalize=False):
"""
Evaluate the nutation period.
Setting return_psiperiod=True return the phase-period instead of the time period (i.e. returns tau/2K(m) insteaf of tau). This is useful to avoid the evaluation of an elliptic integral when it's not needed.
Setting donotnormalize=True is equivalent to mathcalA=1.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
MISSING: COULD NOT BUILD, optional (default: False)
FILL MANUALLY.
donotnormalize: boolean, optional (default: False)
If True omit the numerical prefactor.
Returns
-------
tau: float
Nutation period.
Examples
--------
``tau = precession.eval_tau(kappa,r,chieff,q,chi1,chi2)``
``tau = precession.eval_tau(kappa,r,chieff,q,chi1,chi2,return_psiperiod=True)``
"""
q=np.atleast_1d(q).astype(float)
u = eval_u(r,q)
if donotnormalize:
mathcalA = 1
else:
mathcalA = ddchidt_prefactor(r, chieff, q)
deltachiminus,deltachiplus,deltachi3 = deltachiroots(kappa, u, chieff, q, chi1, chi2, precomputedroots=precomputedroots)
m = elliptic_parameter(kappa, u, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]))
psiperiod = 2 / ( mathcalA * (deltachi3 - (1-q)*deltachiminus)**(1/2) )
if return_psiperiod:
tau = psiperiod
else:
tau = 2*scipy.special.ellipk(m) * psiperiod
return tau
| (kappa, r, chieff, q, chi1, chi2, precomputedroots=None, return_psiperiod=False, donotnormalize=False) | [
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20,873 | precession.precession | eval_theta1 |
Angle between the orbital angular momentum and the spin of the primary black hole.
Parameters
----------
deltachi: float
Weighted spin difference.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
Returns
-------
theta1: float
Angle between orbital angular momentum and primary spin.
Examples
--------
``theta1 = precession.eval_theta1(deltachi,chieff,q,chi1)``
| def eval_theta1(deltachi, chieff, q, chi1):
"""
Angle between the orbital angular momentum and the spin of the primary black hole.
Parameters
----------
deltachi: float
Weighted spin difference.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
Returns
-------
theta1: float
Angle between orbital angular momentum and primary spin.
Examples
--------
``theta1 = precession.eval_theta1(deltachi,chieff,q,chi1)``
"""
costheta1 = eval_costheta1(deltachi, chieff, q, chi1)
theta1 = np.arccos(costheta1)
return theta1
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20,874 | precession.precession | eval_theta12 |
Angle between the two spins. Valid inputs are either (theta1,theta2,deltaphi) or (deltachi,kappa,chieff,q,chi1,chi2).
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
theta12: float
Angle between the two spins.
Examples
--------
``theta12 = precession.eval_theta12(theta1=theta1,theta2=theta2,deltaphi=deltaphi)``
``theta12 = precession.eval_theta12(deltachi=deltachi,kappa=kappa,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
| def eval_theta12(theta1=None, theta2=None, deltaphi=None, deltachi=None, kappa=None, chieff=None, q=None, chi1=None, chi2=None):
"""
Angle between the two spins. Valid inputs are either (theta1,theta2,deltaphi) or (deltachi,kappa,chieff,q,chi1,chi2).
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
theta12: float
Angle between the two spins.
Examples
--------
``theta12 = precession.eval_theta12(theta1=theta1,theta2=theta2,deltaphi=deltaphi)``
``theta12 = precession.eval_theta12(deltachi=deltachi,kappa=kappa,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
"""
costheta12 = eval_costheta12(theta1=theta1, theta2=theta2, deltaphi=deltaphi, deltachi=deltachi, kappa=kappa, chieff=chieff, q=q, chi1=chi1, chi2=chi2)
theta12 = np.arccos(costheta12)
return theta12
| (theta1=None, theta2=None, deltaphi=None, deltachi=None, kappa=None, chieff=None, q=None, chi1=None, chi2=None) | [
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20,875 | precession.precession | eval_theta2 |
Angle between the orbital angular momentum and the spin of the secondary black hole.
Parameters
----------
deltachi: float
Weighted spin difference.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
theta2: float
Angle between orbital angular momentum and secondary spin.
Examples
--------
``theta2 = precession.eval_theta2(deltachi,chieff,q,chi2)``
| def eval_theta2(deltachi, chieff, q, chi2):
"""
Angle between the orbital angular momentum and the spin of the secondary black hole.
Parameters
----------
deltachi: float
Weighted spin difference.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
theta2: float
Angle between orbital angular momentum and secondary spin.
Examples
--------
``theta2 = precession.eval_theta2(deltachi,chieff,q,chi2)``
"""
costheta2 = eval_costheta2(deltachi, chieff, q, chi2)
theta2 = np.arccos(costheta2)
return theta2
| (deltachi, chieff, q, chi2) | [
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20,876 | precession.precession | eval_thetaL |
Angle betwen the orbital angular momentum and the total angular momentum.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
Returns
-------
thetaL: float
Angle betwen orbital angular momentum and total angular momentum.
Examples
--------
``thetaL = precession.eval_thetaL(deltachi,kappa,r,chieff,q)``
| def eval_thetaL(deltachi, kappa, r, chieff, q):
"""
Angle betwen the orbital angular momentum and the total angular momentum.
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
Returns
-------
thetaL: float
Angle betwen orbital angular momentum and total angular momentum.
Examples
--------
``thetaL = precession.eval_thetaL(deltachi,kappa,r,chieff,q)``
"""
costhetaL = eval_costhetaL(deltachi, kappa, r,chieff, q)
thetaL = np.arccos(costhetaL)
return thetaL
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] |
20,877 | precession.precession | eval_u |
Compactified orbital separation.
Parameters
----------
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
Returns
-------
u: float
Compactified separation 1/(2L).
Examples
--------
``u = precession.eval_u(r,q)``
| def eval_u(r, q):
"""
Compactified orbital separation.
Parameters
----------
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
Returns
-------
u: float
Compactified separation 1/(2L).
Examples
--------
``u = precession.eval_u(r,q)``
"""
L = eval_L(r, q)
u = 1 / (2*L)
return u
| (r, q) | [
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20,878 | precession.precession | eval_v |
Newtonian orbital velocity of the binary.
Parameters
----------
r: float
Binary separation.
Returns
-------
v: float
Newtonian orbital velocity.
Examples
--------
``v = precession.eval_v(r)``
| def eval_v(r):
"""
Newtonian orbital velocity of the binary.
Parameters
----------
r: float
Binary separation.
Returns
-------
v: float
Newtonian orbital velocity.
Examples
--------
``v = precession.eval_v(r)``
"""
r = np.atleast_1d(r).astype(float)
v = 1/r**0.5
return v
| (r) | [
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20,879 | precession.precession | gwfrequency_to_pnseparation |
Convert GW frequency (in Hz) to PN orbital separation (in natural units, c=G=M=1). We use the 2PN expression reported in Eq. 4.13 of Kidder 1995, arxiv:gr-qc/9506022.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
fGW: float
Gravitational-wave frequency.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
M_msun: float
Total mass of the binary in solar masses.
PNorder: array (default: [0,1,1.5,2])
PN orders considered.
Returns
-------
r: float
Binary separation.
Examples
--------
``r = precession.gwfrequency_to_pnseparation(theta1,theta2,deltaphi,fGW,q,chi1,chi2,M_msun,PNorder=[0,1,1.5,2])``
| def gwfrequency_to_pnseparation(theta1, theta2, deltaphi, fGW, q, chi1, chi2, M_msun, PNorder=[0,1,1.5,2]):
"""
Convert GW frequency (in Hz) to PN orbital separation (in natural units, c=G=M=1). We use the 2PN expression reported in Eq. 4.13 of Kidder 1995, arxiv:gr-qc/9506022.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
fGW: float
Gravitational-wave frequency.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
M_msun: float
Total mass of the binary in solar masses.
PNorder: array (default: [0,1,1.5,2])
PN orders considered.
Returns
-------
r: float
Binary separation.
Examples
--------
``r = precession.gwfrequency_to_pnseparation(theta1,theta2,deltaphi,fGW,q,chi1,chi2,M_msun,PNorder=[0,1,1.5,2])``
"""
theta1 = np.atleast_1d(theta1).astype(float)
theta2 = np.atleast_1d(theta2).astype(float)
deltaphi = np.atleast_1d(deltaphi).astype(float)
fGW = np.atleast_1d(fGW).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
M_msun = np.atleast_1d(M_msun).astype(float)
# Prefactor is pi*Msun*G/c^3/s. It's pi and not 2pi because f is the GW frequency while Kidder's omega is the orbital angular velocity
tildeomega = M_msun * fGW * 1.548e-5
r = tildeomega**(-2/3) * (
(0 in PNorder) * 1
- (1 in PNorder) * tildeomega**(2/3) * ( 1- q/(3*(1+q)**2) )
- (1.5 in PNorder) * tildeomega / (3*(1+q)**2) * ( (2+3*q)*chi1*np.cos(theta1) + q*(3+2*q)*chi2*np.cos(theta2) )
+ (2 in PNorder) * tildeomega**(4/3) * q/(2*(1+q)**2) * (19/2 + (2*q)/(9*(1+q)**2)+ chi1*chi2*(2*np.cos(theta1)*np.cos(theta2) - np.cos(deltaphi)*np.sin(theta1)*np.sin(theta2)) )
)
return r
| (theta1, theta2, deltaphi, fGW, q, chi1, chi2, M_msun, PNorder=[0, 1, 1.5, 2]) | [
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20,880 | precession.precession | inspiral |
Generic wrapper for binary inspirals. The keyword which selects between the different approximation:
- If which=precession use precession-averaged inspiral (i.e. run `inspiral_precav`)
- If which=orbit use orbit-averaged inspiral (i.e. run `inspiral_orbav`)
- If which=hybrid use hybrid inspiral (i.e. run `inspiral_hybrid`)
All other aguments and keyword arguments are passed on to the relevant inspiral function; see their docs for details.
Parameters
----------
**args: unpacked dictionary, optional
Additional arguments.
which: string, optional (default: None)
Select function behavior.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
outputs: dictionary, optional
Set of outputs.
Examples
--------
``outputs = precession.inspiral(*args,which='precession',**kwargs)``
``outputs = precession.inspiral(*args,which='orbit',**kwargs)``
``outputs = precession.inspiral(*args,which='hybrid',**kwargs)``
| def inspiral(*args, which=None, **kwargs):
"""
Generic wrapper for binary inspirals. The keyword which selects between the different approximation:
- If which=precession use precession-averaged inspiral (i.e. run `inspiral_precav`)
- If which=orbit use orbit-averaged inspiral (i.e. run `inspiral_orbav`)
- If which=hybrid use hybrid inspiral (i.e. run `inspiral_hybrid`)
All other aguments and keyword arguments are passed on to the relevant inspiral function; see their docs for details.
Parameters
----------
**args: unpacked dictionary, optional
Additional arguments.
which: string, optional (default: None)
Select function behavior.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
outputs: dictionary, optional
Set of outputs.
Examples
--------
``outputs = precession.inspiral(*args,which='precession',**kwargs)``
``outputs = precession.inspiral(*args,which='orbit',**kwargs)``
``outputs = precession.inspiral(*args,which='hybrid',**kwargs)``
"""
# Precession-averaged integrations
if which in ['precession', 'precav', 'precessionaveraged', 'precessionaverage', 'precession-averaged', 'precession-average', 'precessionav']:
return inspiral_precav(*args, **kwargs)
elif which in ['orbit', 'orbav', 'orbitaveraged', 'orbitaverage', 'orbit-averaged', 'orbit-average', 'orbitav']:
return inspiral_orbav(*args, **kwargs)
elif which in ['hybrid']:
return inspiral_hybrid(*args, **kwargs)
else:
raise ValueError("`which` needs to be `precav`, `orbav` or `hybrid`.")
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20,881 | precession.precession | inspiral_hybrid |
Perform hybrid inspirals, i.e. evolve the binary at large separation with a pression-averaged evolution and at small separation with an orbit-averaged evolution, matching the two. The variables q, chi1, and chi2 must always be provided. The integration range must be specified using either r or u (and not both); provide also uswitch and rswitch consistently.
Either r of u needs to be arrays with lenght >=1, where e.g. r[0] corresponds to the initial condition and r[1:] corresponds to the location where outputs are returned. For past time infinity use either u=0 or r=np.inf.
The function is vectorized: evolving N multiple binaries with M outputs requires kappainitial, chieff, q, chi1, chi2 to be of shape (N,) and u of shape (M,N).
The initial conditions must be specified in terms of one an only one of the following:
- theta1,theta2, and deltaphi (but note that deltaphi is not necessary if integrating from infinite separation).
- kappa, chieff.
The desired outputs can be specified with a list e.g. requested_outputs=['theta1','theta2','deltaphi']. All the available variables are returned by default. These are: ['theta1', 'theta2', 'deltaphi', 'deltachi', 'kappa', 'r', 'u', 'deltachiminus', 'deltachiplus', 'deltachi3', 'chieff', 'q', 'chi1', 'chi2'].
The flag enforce allows checking the consistency of the input variables.
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
r: float, optional (default: None)
Binary separation.
rswitch: float, optional (default: None)
Matching separation between the precession- and orbit-averaged chunks.
u: float, optional (default: None)
Compactified separation 1/(2L).
uswitch: float, optional (default: None)
Matching compactified separation between the precession- and orbit-averaged chunks.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
requested_outputs: list, optional (default: None)
Set of outputs.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
outputs: dictionary
Set of outputs.
Examples
--------
``outputs = precession.inspiral_hybrid(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_hybrid(theta1=theta1,theta2=theta2,deltaphi=deltaphi,u=u,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_hybrid(kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_hybrid(kappa,u=u,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
| def inspiral_hybrid(theta1=None, theta2=None, deltaphi=None, deltachi=None, kappa=None, r=None, rswitch=None, u=None, uswitch=None, chieff=None, q=None, chi1=None, chi2=None, requested_outputs=None,**odeint_kwargs):
"""
Perform hybrid inspirals, i.e. evolve the binary at large separation with a pression-averaged evolution and at small separation with an orbit-averaged evolution, matching the two. The variables q, chi1, and chi2 must always be provided. The integration range must be specified using either r or u (and not both); provide also uswitch and rswitch consistently.
Either r of u needs to be arrays with lenght >=1, where e.g. r[0] corresponds to the initial condition and r[1:] corresponds to the location where outputs are returned. For past time infinity use either u=0 or r=np.inf.
The function is vectorized: evolving N multiple binaries with M outputs requires kappainitial, chieff, q, chi1, chi2 to be of shape (N,) and u of shape (M,N).
The initial conditions must be specified in terms of one an only one of the following:
- theta1,theta2, and deltaphi (but note that deltaphi is not necessary if integrating from infinite separation).
- kappa, chieff.
The desired outputs can be specified with a list e.g. requested_outputs=['theta1','theta2','deltaphi']. All the available variables are returned by default. These are: ['theta1', 'theta2', 'deltaphi', 'deltachi', 'kappa', 'r', 'u', 'deltachiminus', 'deltachiplus', 'deltachi3', 'chieff', 'q', 'chi1', 'chi2'].
The flag enforce allows checking the consistency of the input variables.
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
r: float, optional (default: None)
Binary separation.
rswitch: float, optional (default: None)
Matching separation between the precession- and orbit-averaged chunks.
u: float, optional (default: None)
Compactified separation 1/(2L).
uswitch: float, optional (default: None)
Matching compactified separation between the precession- and orbit-averaged chunks.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
requested_outputs: list, optional (default: None)
Set of outputs.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
outputs: dictionary
Set of outputs.
Examples
--------
``outputs = precession.inspiral_hybrid(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_hybrid(theta1=theta1,theta2=theta2,deltaphi=deltaphi,u=u,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_hybrid(kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_hybrid(kappa,u=u,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
"""
# Outputs available in both orbit-averaged and precession-averaged evolutions
alloutputs = np.array(['theta1', 'theta2', 'deltaphi', 'deltachi', 'kappa', 'r', 'u', 'chieff', 'q', 'chi1', 'chi2'])
if requested_outputs is None:
requested_outputs = alloutputs
# Return only those requested (in1d return boolean array)
wantoutputs = np.intersect1d(alloutputs, requested_outputs)
# Substitute None inputs with arrays of Nones
inputs = [theta1, theta2, deltaphi, deltachi, kappa, r, rswitch, u, uswitch, chieff, q, chi1, chi2]
for k, v in enumerate(inputs):
if v is None:
inputs[k] = np.atleast_1d(np.squeeze(tiler(None, np.atleast_1d(q))))
else:
if k == 5 or k == 7: # Either u or r
inputs[k] = np.atleast_2d(inputs[k])
else: # Any of the others
inputs[k] = np.atleast_1d(inputs[k])
theta1, theta2, deltaphi, deltachi, kappa, r, rswitch, u, uswitch, chieff, q, chi1, chi2 = inputs
def _compute(theta1, theta2, deltaphi, deltachi, kappa, r, rswitch, u, uswitch, chieff, q, chi1, chi2):
if r is None and rswitch is None and u is not None and uswitch is not None:
r = eval_r(u=u, q=tiler(q, u))
rswitch = eval_r(u=uswitch, q=tiler(q, uswitch))
forward = ismonotonic(r, ">=")
backward = ismonotonic(r, "<=")
assert np.logical_or(forward, backward), "r must be monotonic"
assert rswitch > np.min(r) and rswitch < np.max(r), "The switching condition must to be within the range spanned by r or u."
rlarge = r[r >= rswitch]
rsmall = r[r < rswitch]
# Integrating forward: precession-averaged first, then orbit-averaged
if forward:
inspiral_first = inspiral_precav
rfirst = np.append(rlarge, rswitch)
inspiral_second = inspiral_orbav
rsecond = np.append(rswitch, rsmall)
# Integrating backward: orbit-averaged first, then precession-averaged
elif backward:
inspiral_first = inspiral_orbav
rfirst = np.append(rsmall, rswitch)
inspiral_second = inspiral_precav
rsecond = np.append(rswitch, rlarge)
# First chunk of the evolution
evolution_first = inspiral_first(theta1=theta1, theta2=theta2, deltaphi=deltaphi, deltachi=deltachi, kappa=kappa, r=rfirst, chieff=chieff, q=q, chi1=chi1, chi2=chi2, requested_outputs=alloutputs,**odeint_kwargs)
# Second chunk of the evolution
evolution_second = inspiral_second(theta1=np.squeeze(evolution_first['theta1'])[-1], theta2=np.squeeze(evolution_first['theta2'])[-1], deltaphi=np.squeeze(evolution_first['deltaphi'])[-1], r=rsecond, q=q, chi1=chi1, chi2=chi2, requested_outputs=alloutputs,**odeint_kwargs)
# Store outputs
evolution_full = {}
for k in wantoutputs:
# Quantities that vary in both the precession-averaged and the orbit-averaged evolution
if k in ['theta1', 'theta2', 'deltaphi', 'deltachi', 'kappa', 'r', 'u']:
evolution_full[k] = np.atleast_2d(np.append(evolution_first[k][:, :-1], evolution_second[k][:, 1:]))
# Quantities that vary only on the orbit-averaged evolution
if k in ['chieff']:
if forward:
evolution_full[k] = np.atleast_2d(np.append(tiler(evolution_first[k][:], rfirst[:-1]), evolution_second[k][:, 1:]))
elif backward:
evolution_full[k] = np.atleast_2d(np.append(evolution_first[k][:, :-1], tiler(evolution_second[k][:], rsecond[1:])))
# Quanties that do not vary
if k in ['q', 'chi1', 'chi2']:
evolution_full[k] = evolution_second[k]
return evolution_full
allresults = list(map(_compute, theta1, theta2, deltaphi, deltachi, kappa, r, rswitch, u, uswitch, chieff, q, chi1, chi2))
evolution_full = {}
for k in allresults[0].keys():
evolution_full[k] = np.concatenate(list(evolution_full[k] for evolution_full in allresults))
return evolution_full
| (theta1=None, theta2=None, deltaphi=None, deltachi=None, kappa=None, r=None, rswitch=None, u=None, uswitch=None, chieff=None, q=None, chi1=None, chi2=None, requested_outputs=None, **odeint_kwargs) | [
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20,882 | precession.precession | inspiral_orbav |
Perform precession-averaged inspirals. The variables q, chi1, and chi2 must always be provided.
The integration range must be specified using either r or u (and not both). These need to be arrays with lenght >=1, where e.g. r[0] corresponds to the initial condition and r[1:] corresponds to the location where outputs are returned.
The function is vectorized: evolving N multiple binaries with M outputs requires kappainitial, chieff, q, chi1, chi2 to be of shape (N,) and u of shape (M,N).
The initial conditions must be specified in terms of one an only one of the following:
- Lh, S1h, and S2h
- theta1,theta2, and deltaphi.
- deltachi, kappa, chieff, cyclesign.
The desired outputs can be specified with a list e.g. requested_outputs=['theta1','theta2','deltaphi']. All the available variables are returned by default. These are: ['theta1', 'theta2', 'deltaphi', 'deltachi', 'kappa', 'r', 'u', 'deltachiminus', 'deltachiplus', 'deltachi3', 'chieff', 'q', 'chi1', 'chi2'].
The flag enforce allows checking the consistency of the input variables.
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
Lh: array, optional (default: None)
Direction of the orbital angular momentum, unit vector.
S1h: array, optional (default: None)
Direction of the primary spin, unit vector.
S2h: array, optional (default: None)
Direction of the secondary spin, unit vector.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
r: float, optional (default: None)
Binary separation.
u: float, optional (default: None)
Compactified separation 1/(2L).
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
cyclesign: integer, optional (default: +1)
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
PNorderpre: array (default: [0,0.5])
PN orders considered in the spin-precession equations.
PNorderrad: array (default: [0,0.5])
PN orders considered in the radiation-reaction equation.
requested_outputs: list, optional (default: None)
Set of outputs.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
outputs: dictionary
Set of outputs.
Examples
--------
``outputs = precession.inspiral_orbav(Lh=Lh,S1h=S1h,S2h=S2h,r=r,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_orbav(Lh=Lh,S1h=S1h,S2h=S2h,u=u,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_orbav(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_orbav(theta1=theta1,theta2=theta2,deltaphi=deltaphi,u=u,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_orbav(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
| def inspiral_orbav(theta1=None, theta2=None, deltaphi=None, Lh=None, S1h=None, S2h=None, deltachi=None, kappa=None, r=None, u=None, chieff=None, q=None, chi1=None, chi2=None, cyclesign=+1, PNorderpre=[0,0.5], PNorderrad=[0,1,1.5,2,2.5,3,3.5], requested_outputs=None, **odeint_kwargs):
"""
Perform precession-averaged inspirals. The variables q, chi1, and chi2 must always be provided.
The integration range must be specified using either r or u (and not both). These need to be arrays with lenght >=1, where e.g. r[0] corresponds to the initial condition and r[1:] corresponds to the location where outputs are returned.
The function is vectorized: evolving N multiple binaries with M outputs requires kappainitial, chieff, q, chi1, chi2 to be of shape (N,) and u of shape (M,N).
The initial conditions must be specified in terms of one an only one of the following:
- Lh, S1h, and S2h
- theta1,theta2, and deltaphi.
- deltachi, kappa, chieff, cyclesign.
The desired outputs can be specified with a list e.g. requested_outputs=['theta1','theta2','deltaphi']. All the available variables are returned by default. These are: ['theta1', 'theta2', 'deltaphi', 'deltachi', 'kappa', 'r', 'u', 'deltachiminus', 'deltachiplus', 'deltachi3', 'chieff', 'q', 'chi1', 'chi2'].
The flag enforce allows checking the consistency of the input variables.
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
Lh: array, optional (default: None)
Direction of the orbital angular momentum, unit vector.
S1h: array, optional (default: None)
Direction of the primary spin, unit vector.
S2h: array, optional (default: None)
Direction of the secondary spin, unit vector.
deltachi: float, optional (default: None)
Weighted spin difference.
kappa: float, optional (default: None)
Asymptotic angular momentum.
r: float, optional (default: None)
Binary separation.
u: float, optional (default: None)
Compactified separation 1/(2L).
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
cyclesign: integer, optional (default: +1)
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
PNorderpre: array (default: [0,0.5])
PN orders considered in the spin-precession equations.
PNorderrad: array (default: [0,0.5])
PN orders considered in the radiation-reaction equation.
requested_outputs: list, optional (default: None)
Set of outputs.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
outputs: dictionary
Set of outputs.
Examples
--------
``outputs = precession.inspiral_orbav(Lh=Lh,S1h=S1h,S2h=S2h,r=r,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_orbav(Lh=Lh,S1h=S1h,S2h=S2h,u=u,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_orbav(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_orbav(theta1=theta1,theta2=theta2,deltaphi=deltaphi,u=u,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_orbav(deltachi=deltachi,kappa=kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
"""
# Substitute None inputs with arrays of Nones
inputs = [theta1, theta2, deltaphi, Lh, S1h, S2h, deltachi, kappa, r, u, chieff, q, chi1, chi2]
for k, v in enumerate(inputs):
if v is None:
inputs[k] = np.atleast_1d(np.squeeze(tiler(None, np.atleast_1d(q))))
else:
if k == 3 or k == 4 or k == 5 or k == 8 or k == 9: # Lh, S1h, S2h, u, or r
inputs[k] = np.atleast_2d(inputs[k])
else: # Any of the others
inputs[k] = np.atleast_1d(inputs[k])
theta1, theta2, deltaphi, Lh, S1h, S2h, deltachi, kappa, r, u, chieff, q, chi1, chi2 = inputs
def _compute(theta1, theta2, deltaphi, Lh, S1h, S2h, deltachi, kappa, r, u, chieff, q, chi1, chi2,cyclesign):
if q is None or chi1 is None or chi2 is None:
raise TypeError("Please provide q, chi1, and chi2.")
if r is not None and u is None:
assert np.logical_or(ismonotonic(r, '<='), ismonotonic(r, '>=')), 'r must be monotonic'
u = eval_u(r, tiler(q, r))
elif r is None and u is not None:
assert np.logical_or(ismonotonic(u, '<='), ismonotonic(u, '>=')), 'u must be monotonic'
r = eval_r(u=u, q=tiler(q, u))
else:
raise TypeError("Please provide either r or u.")
# User provides Lh, S1h, and S2h
if Lh is not None and S1h is not None and S2h is not None and theta1 is None and theta2 is None and deltaphi is None and deltachi is None and kappa is None and chieff is None:
pass
# User provides theta1, theta2, and deltaphi.
elif Lh is None and S1h is None and S2h is None and theta1 is not None and theta2 is not None and deltaphi is not None and deltachi is None and kappa is None and chieff is None:
Lh, S1h, S2h = angles_to_Jframe(theta1, theta2, deltaphi, r[0], q, chi1, chi2)
# User provides deltachi, kappa, and chieff.
elif Lh is None and S1h is None and S2h is None and theta1 is None and theta2 is None and deltaphi is None and deltachi is not None and kappa is not None and chieff is not None:
# cyclesign=+1 by default
Lh, S1h, S2h = conserved_to_Jframe(deltachi, kappa, r[0], chieff, q, chi1, chi2, cyclesign=cyclesign)
else:
raise TypeError("Please provide one and not more of the following: (Lh,S1h,S2h), (theta1,theta2,deltaphi), (deltachi,kappa,chieff).")
# Make sure vectors are normalized
Lh = Lh/np.linalg.norm(Lh)
S1h = S1h/np.linalg.norm(S1h)
S2h = S2h/np.linalg.norm(S2h)
v = eval_v(r)
# Integration
evaluations = integrator_orbav(Lh, S1h, S2h, v, q, chi1, chi2, PNorderpre=PNorderpre, PNorderrad=PNorderrad,**odeint_kwargs)[0].T
# For solve_ivp implementation
#evaluations = np.squeeze(ODEsolution.item().sol(v))
# Returned output is
# Lx, Ly, Lz, S1x, S1y, S1z, S2x, S2y, S2z, (t)
Lh = evaluations[0:3, :].T
S1h = evaluations[3:6, :].T
S2h = evaluations[6:9, :].T
t = evaluations[9, :]
# Renormalize. The normalization is not enforced by the integrator, it is only maintaied within numerical accuracy.
#Lh = Lh/np.linalg.norm(Lh)
#S1h = S1h/np.linalg.norm(S1h)
#S2h = S2h/np.linalg.norm(S2h)
S1 = eval_S1(q, chi1)
S2 = eval_S2(q, chi2)
L = eval_L(r, tiler(q, r))
Lvec = (L*Lh.T).T
S1vec = S1*S1h
S2vec = S2*S2h
theta1, theta2, deltaphi = vectors_to_angles(Lvec, S1vec, S2vec)
deltachi, kappa, chieff, cyclesign = vectors_to_conserved(Lvec, S1vec, S2vec, tiler(q,r), full_output=True)
return t, theta1, theta2, deltaphi, Lh, S1h, S2h, deltachi, kappa, r, u, chieff, q, chi1, chi2, cyclesign
# This array has to match the outputs of _compute (in the right order!)
alloutputs = np.array(['t', 'theta1', 'theta2', 'deltaphi', 'Lh', 'S1h', 'S2h', 'deltachi', 'kappa', 'r', 'u', 'chieff', 'q', 'chi1', 'chi2', 'cyclesign'])
if cyclesign ==+1 or cyclesign==-1:
cyclesign=np.atleast_1d(tiler(cyclesign,q))
# Here I force dtype=obj | (theta1=None, theta2=None, deltaphi=None, Lh=None, S1h=None, S2h=None, deltachi=None, kappa=None, r=None, u=None, chieff=None, q=None, chi1=None, chi2=None, cyclesign=1, PNorderpre=[0, 0.5], PNorderrad=[0, 1, 1.5, 2, 2.5, 3, 3.5], requested_outputs=None, **odeint_kwargs) | [
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20,883 | precession.precession | inspiral_precav |
Perform precession-averaged inspirals. The variables q, chi1, and chi2 must always be provided.
The integration range must be specified using either r or u (and not both). These need to be arrays with lenght >=1, where e.g. r[0] corresponds to the initial condition and r[1:] corresponds to the location where outputs are returned. For past time infinity use either u=0 or r=np.inf.
The function is vectorized: evolving N multiple binaries with M outputs requires kappainitial, chieff, q, chi1, chi2 to be of shape (N,) and u of shape (M,N).
The initial conditions must be specified in terms of one an only one of the following:
- theta1,theta2, and deltaphi (but note that deltaphi is not necessary if integrating from infinite separation).
- kappa, chieff.
The desired outputs can be specified with a list e.g. requested_outputs=['theta1','theta2','deltaphi']. All the available variables are returned by default. These are: ['theta1', 'theta2', 'deltaphi', 'deltachi', 'kappa', 'r', 'u', 'deltachiminus', 'deltachiplus', 'deltachi3', 'chieff', 'q', 'chi1', 'chi2'].
The flag enforce allows checking the consistency of the input variables.
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
kappa: float, optional (default: None)
Asymptotic angular momentum.
r: float, optional (default: None)
Binary separation.
u: float, optional (default: None)
Compactified separation 1/(2L).
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
requested_outputs: list, optional (default: None)
Set of outputs.
enforce: boolean, optional (default: False)
If True raise errors, if False raise warnings.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
outputs: dictionary
Set of outputs.
Examples
--------
``outputs = precession.inspiral_precav(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_precav(theta1=theta1,theta2=theta2,deltaphi=deltaphi,u=u,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_precav(kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_precav(kappa,u=u,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
| def inspiral_precav(theta1=None, theta2=None, deltaphi=None, kappa=None, r=None, u=None, chieff=None, q=None, chi1=None, chi2=None, requested_outputs=None, enforce=False, **odeint_kwargs):
"""
Perform precession-averaged inspirals. The variables q, chi1, and chi2 must always be provided.
The integration range must be specified using either r or u (and not both). These need to be arrays with lenght >=1, where e.g. r[0] corresponds to the initial condition and r[1:] corresponds to the location where outputs are returned. For past time infinity use either u=0 or r=np.inf.
The function is vectorized: evolving N multiple binaries with M outputs requires kappainitial, chieff, q, chi1, chi2 to be of shape (N,) and u of shape (M,N).
The initial conditions must be specified in terms of one an only one of the following:
- theta1,theta2, and deltaphi (but note that deltaphi is not necessary if integrating from infinite separation).
- kappa, chieff.
The desired outputs can be specified with a list e.g. requested_outputs=['theta1','theta2','deltaphi']. All the available variables are returned by default. These are: ['theta1', 'theta2', 'deltaphi', 'deltachi', 'kappa', 'r', 'u', 'deltachiminus', 'deltachiplus', 'deltachi3', 'chieff', 'q', 'chi1', 'chi2'].
The flag enforce allows checking the consistency of the input variables.
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
theta1: float, optional (default: None)
Angle between orbital angular momentum and primary spin.
theta2: float, optional (default: None)
Angle between orbital angular momentum and secondary spin.
deltaphi: float, optional (default: None)
Angle between the projections of the two spins onto the orbital plane.
kappa: float, optional (default: None)
Asymptotic angular momentum.
r: float, optional (default: None)
Binary separation.
u: float, optional (default: None)
Compactified separation 1/(2L).
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
requested_outputs: list, optional (default: None)
Set of outputs.
enforce: boolean, optional (default: False)
If True raise errors, if False raise warnings.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
outputs: dictionary
Set of outputs.
Examples
--------
``outputs = precession.inspiral_precav(theta1=theta1,theta2=theta2,deltaphi=deltaphi,r=r,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_precav(theta1=theta1,theta2=theta2,deltaphi=deltaphi,u=u,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_precav(kappa,r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
``outputs = precession.inspiral_precav(kappa,u=u,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
"""
# Substitute None inputs with arrays of Nones
inputs = [theta1, theta2, deltaphi, kappa, r, u, chieff, q, chi1, chi2]
for k, v in enumerate(inputs):
if v is None:
inputs[k] = np.atleast_1d(np.squeeze(tiler(None, np.atleast_1d(q))))
else:
if k == 4 or k == 5: # Either u or r
inputs[k] = np.atleast_2d(inputs[k])
else: # Any of the others
inputs[k] = np.atleast_1d(inputs[k])
theta1, theta2, deltaphi, kappa, r, u, chieff, q, chi1, chi2 = inputs
# This array has to match the outputs of _compute (in the right order!)
alloutputs = np.array(['theta1', 'theta2', 'deltaphi', 'deltachi', 'kappa', 'r', 'u', 'deltachiminus', 'deltachiplus', 'deltachi3', 'chieff', 'q', 'chi1', 'chi2'])
# If in doubt, return everything
if requested_outputs is None:
requested_outputs = alloutputs
def _compute(theta1, theta2, deltaphi, kappa, r, u, chieff, q, chi1, chi2):
# Make sure you have q, chi1, and chi2.
if q is None or chi1 is None or chi2 is None:
raise TypeError("Please provide q, chi1, and chi2.")
# Make sure you have either r or u.
if r is not None and u is None:
assert np.logical_or(ismonotonic(r, '<='), ismonotonic(r, '>=')), 'r must be monotonic'
u = eval_u(r, tiler(q, r))
elif r is None and u is not None:
assert np.logical_or(ismonotonic(u, '<='), ismonotonic(u, '>=')), 'u must be monotonic'
r = eval_r(u=u, q=tiler(q, u))
else:
raise TypeError("Please provide either r or u. Use np.inf for infinity.")
assert np.sum(u == 0) <= 1 and np.sum(u[1:-1] == 0) == 0, "There can only be one r=np.inf location, either at the beginning or at the end."
# User provided theta1,theta2, and deltaphi. Get chieff and kappa.
if theta1 is not None and theta2 is not None and deltaphi is not None and kappa is None and chieff is None:
deltachi, kappa, chieff = angles_to_conserved(theta1, theta2, deltaphi, r[0], q, chi1, chi2)
# User provides kappa, chieff
elif theta1 is None and theta2 is None and deltaphi is None and kappa is not None and chieff is not None:
pass
else:
raise TypeError("Please provide one and not more of the following: (theta1,theta2,deltaphi), (kappa,chieff).")
# Enforce limits. Uncomment if you want to be more restrictive (though some integrations are going to fail for roundoff errors in the resonant finder)
if enforce:
chieffmin, chieffmax = chiefflimits(q, chi1, chi2)
assert chieff >= chieffmin and chieff <= chieffmax, "Unphysical initial conditions [inspiral_precav]."+str(theta1)+" "+str(theta2)+" "+str(deltaphi)+" "+str(kappa)+" "+str(r)+" "+str(u)+" "+str(chieff)+" "+str(q)+" "+str(chi1)+" "+str(chi2)
kappamin,kappamax = kappalimits(r=r[0], chieff=chieff, q=q, chi1=chi1, chi2=chi2)
assert kappa >= kappamin and kappa <= kappamax, "Unphysical initial conditions [inspiral_precav]."+str(theta1)+" "+str(theta2)+" "+str(deltaphi)+" "+str(kappa)+" "+str(r)+" "+str(u)+" "+str(chieff)+" "+str(q)+" "+str(chi1)+" "+str(chi2)
# Actual integration.
kappa = np.squeeze(integrator_precav(kappa, u, chieff, q, chi1, chi2,**odeint_kwargs))
deltachiminus = None
deltachiplus = None
deltachi3 = None
deltachi=None
theta1=None
theta2=None
deltaphi=None
# Roots along the evolution
if any(x in requested_outputs for x in ['theta1', 'theta2', 'deltaphi', 'deltachi', 'deltachiminus', 'deltachiplus', 'deltachi3']):
deltachiminus,deltachiplus,deltachi3 = deltachiroots(kappa, u, tiler(chieff,r), tiler(q,r),tiler(chi1,r),tiler(chi2,r))
# Resample deltachi
if any(x in requested_outputs for x in ['theta1', 'theta2', 'deltaphi', 'deltachi']):
deltachi = deltachisampling(kappa, r, tiler(chieff,r), tiler(q,r),tiler(chi1,r),tiler(chi2,r), precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]))
# Compute the angles. Assign random cyclesign
if any(x in requested_outputs for x in ['theta1', 'theta2', 'deltaphi']):
theta1,theta2,deltaphi = conserved_to_angles(deltachi, kappa, r, tiler(chieff,r), tiler(q,r),tiler(chi1,r),tiler(chi2,r), cyclesign = np.random.choice([-1, 1], r.shape))
return theta1, theta2, deltaphi, deltachi, kappa, r, u, deltachiminus, deltachiplus, deltachi3, chieff, q, chi1, chi2
# Here I force dtype=object because the outputs have different shapes
allresults = np.array(list(map(_compute, theta1, theta2, deltaphi, kappa, r, u, chieff, q, chi1, chi2)), dtype=object).T
# Return only requested outputs (in1d return boolean array)
wa | (theta1=None, theta2=None, deltaphi=None, kappa=None, r=None, u=None, chieff=None, q=None, chi1=None, chi2=None, requested_outputs=None, enforce=False, **odeint_kwargs) | [
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20,884 | precession.precession | integrator_orbav |
Integration of the systems of ODEs describing orbit-averaged inspirals.
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
Lhinitial: array
Initial direction of the orbital angular momentum, unit vector.
S1hinitial: array
Initial direction of the primary spin, unit vector.
S2hinitial: array
Initial direction of the secondary spin, unit vector.
v: float
Newtonian orbital velocity.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
PNorderpre: array (default: [0,0.5])
PN orders considered in the spin-precession equations.
PNorderrad: array (default: [0,0.5])
PN orders considered in the radiation-reaction equation.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
ODEsolution: array
Solution of the ODE.
Examples
--------
``ODEsolution = precession.integrator_orbavintegrator_orbav(Lhinitial,S1hinitial,S2hinitial,v,q,chi1,chi2)``
| def integrator_orbav(Lhinitial, S1hinitial, S2hinitial, v, q, chi1, chi2, PNorderpre=[0,0.5], PNorderrad=[0,1,1.5,2,2.5,3,3.5], **odeint_kwargs):
"""
Integration of the systems of ODEs describing orbit-averaged inspirals.
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
Lhinitial: array
Initial direction of the orbital angular momentum, unit vector.
S1hinitial: array
Initial direction of the primary spin, unit vector.
S2hinitial: array
Initial direction of the secondary spin, unit vector.
v: float
Newtonian orbital velocity.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
PNorderpre: array (default: [0,0.5])
PN orders considered in the spin-precession equations.
PNorderrad: array (default: [0,0.5])
PN orders considered in the radiation-reaction equation.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
ODEsolution: array
Solution of the ODE.
Examples
--------
``ODEsolution = precession.integrator_orbavintegrator_orbav(Lhinitial,S1hinitial,S2hinitial,v,q,chi1,chi2)``
"""
Lhinitial = np.atleast_2d(Lhinitial).astype(float)
S1hinitial = np.atleast_2d(S1hinitial).astype(float)
S2hinitial = np.atleast_2d(S2hinitial).astype(float)
v = np.atleast_2d(v).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
# Defaults for the integrators, can be changed by the user
if 'mxstep' not in odeint_kwargs: odeint_kwargs['mxstep']=5000000
if 'rol' not in odeint_kwargs: odeint_kwargs['rtol']=1e-10
if 'aol' not in odeint_kwargs: odeint_kwargs['atol']=1e-10
odeint_kwargs['full_output']=0 # This needs to be forced for compatibility with the rest of the code
def _compute(Lhinitial, S1hinitial, S2hinitial, v, q, chi1, chi2):
# I need unit vectors
assert np.isclose(np.linalg.norm(Lhinitial), 1)
assert np.isclose(np.linalg.norm(S1hinitial), 1)
assert np.isclose(np.linalg.norm(S2hinitial), 1)
# Pack inputs
ic = np.concatenate([Lhinitial, S1hinitial, S2hinitial, [0]])
# Compute these quantities here instead of inside the RHS for speed
m1 = eval_m1(q).item()
m2 = eval_m2(q).item()
S1 = eval_S1(q, chi1).item()
S2 = eval_S2(q, chi2).item()
eta = eval_eta(q).item()
# solve_ivp implementation. Didn't really work.
#ODEsolution = scipy.integrate.solve_ivp(rhs_orbav, (vinitial, vfinal), ic, method='LSODA', t_eval=(vinitial, vfinal), dense_output=True, args=(q, m1, m2, eta, chi1, chi2, S1, S2, quadrupole_formula),rtol=1e-12,atol=1e-12)
#ODEsolution = scipy.integrate.solve_ivp(rhs_orbav, (vinitial, vfinal), ic, t_eval=(vinitial, vfinal), dense_output=True, args=(q, m1, m2, eta, chi1, chi2, S1, S2, quadrupole_formula))
# Make sure the first step is large enough. This is to avoid LSODA to propose a tiny step which causes the integration to stall
if 'h0' not in odeint_kwargs: odeint_kwargs['h0']= np.sign(v[-1]-v[0]) * v[0]/1e6
ODEsolution = scipy.integrate.odeint(rhs_orbav, ic, v, args=(q, m1, m2, eta, chi1, chi2, S1, S2, PNorderpre, PNorderrad), **odeint_kwargs)#, printmessg=0,rtol=1e-10,atol=1e-10)#,tcrit=sing)
return ODEsolution
ODEsolution = np.array(list(map(_compute, Lhinitial, S1hinitial, S2hinitial, v, q, chi1, chi2)))
return ODEsolution
| (Lhinitial, S1hinitial, S2hinitial, v, q, chi1, chi2, PNorderpre=[0, 0.5], PNorderrad=[0, 1, 1.5, 2, 2.5, 3, 3.5], **odeint_kwargs) | [
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20,885 | precession.precession | integrator_precav |
Integration of ODE dkappa/du describing precession-averaged inspirals. Here u needs to be an array with lenght >=1, where u[0] corresponds to the initial condition and u[1:] corresponds to the location where outputs are returned. For past time infinity use u=0.
The function is vectorized: evolving N multiple binaries with M outputs requires kappainitial, chieff, q, chi1, chi2 to be of shape (N,) and u of shape (M,N).
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
kappainitial: float
Initial value of the regularized momentum kappa.
u: float
Compactified separation 1/(2L).
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
kappa: float
Asymptotic angular momentum.
Examples
--------
``kappa = precession.integrator_precav(kappainitial,u,chieff,q,chi1,chi2)``
| def integrator_precav(kappainitial, u, chieff, q, chi1, chi2, **odeint_kwargs):
"""
Integration of ODE dkappa/du describing precession-averaged inspirals. Here u needs to be an array with lenght >=1, where u[0] corresponds to the initial condition and u[1:] corresponds to the location where outputs are returned. For past time infinity use u=0.
The function is vectorized: evolving N multiple binaries with M outputs requires kappainitial, chieff, q, chi1, chi2 to be of shape (N,) and u of shape (M,N).
Additional keywords arguments are passed to `scipy.integrate.odeint` after some custom-made default settings.
Parameters
----------
kappainitial: float
Initial value of the regularized momentum kappa.
u: float
Compactified separation 1/(2L).
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
**odeint_kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
kappa: float
Asymptotic angular momentum.
Examples
--------
``kappa = precession.integrator_precav(kappainitial,u,chieff,q,chi1,chi2)``
"""
kappainitial = np.atleast_1d(kappainitial).astype(float)
u = np.atleast_2d(u).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
# Defaults for the integrators, can be changed by the user
if 'mxstep' not in odeint_kwargs: odeint_kwargs['mxstep']=5000000
if 'rol' not in odeint_kwargs: odeint_kwargs['rtol']=1e-10
if 'aol' not in odeint_kwargs: odeint_kwargs['atol']=1e-10
# I'm sorry but this needs to be forced for compatibility with the rest of the code
odeint_kwargs['full_output'] = 0
def _compute(kappainitial, u, chieff, q, chi1, chi2, odeint_kwargs):
# h0 controls the first stepsize attempted. If integrating from finite separation, let the solver decide (h0=0). If integrating from infinity, prevent it from being too small.
# h0= 1e-3 if u[0]==0 else 0
# Make sure the first step is large enough. This is to avoid LSODA to propose a tiny step which causes the integration to stall
# if 'h0' not in odeint_kwargs: odeint_kwargs['h0']=min(u[0])/1e6
# Update: This does not seem to be necessary after all.
ODEsolution = scipy.integrate.odeint(rhs_precav, kappainitial, u, args=(chieff, q, chi1, chi2), **odeint_kwargs)#, printmessg=0,rtol=1e-10,atol=1e-10)#,tcrit=sing)
return np.squeeze(ODEsolution)
# solve_ivp implementation. Didn't really work.
#ODEsolution = scipy.integrate.solve_ivp(rhs_precav, (uinitial, ufinal), np.atleast_1d(kappainitial), method='RK45', t_eval=(uinitial, ufinal), dense_output=True, args=(chieff, q, chi1, chi2), atol=1e-8, rtol=1e-8) # ,events=event)
# Return ODE object. The key methods is .sol --callable, sol(t).
#return ODEsolution
ODEsolution = np.array(list(map(_compute, kappainitial, u, chieff, q, chi1, chi2, repeat(odeint_kwargs))))
return ODEsolution
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] |
20,886 | precession.precession | intertial_ingredients |
Numerical prefactors entering the precession frequency.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
bigC0: float
Prefactor in the OmegaL equation.
bigCminus: float
Prefactor in the OmegaL equation.
bigCplus: float
Prefactor in the OmegaL equation.
bigRminus: float
Prefactor in the PhiL equation.
bigRplus: float
Prefactor in the PhiL equation.
Examples
--------
``bigC0,bigCplus,bigCminus,bigRplus,bigRminus = precession.intertial_ingredients(kappa,r,chieff,q,chi1,chi2)``
| def intertial_ingredients(kappa, r, chieff, q, chi1, chi2):
"""
Numerical prefactors entering the precession frequency.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
bigC0: float
Prefactor in the OmegaL equation.
bigCminus: float
Prefactor in the OmegaL equation.
bigCplus: float
Prefactor in the OmegaL equation.
bigRminus: float
Prefactor in the PhiL equation.
bigRplus: float
Prefactor in the PhiL equation.
Examples
--------
``bigC0,bigCplus,bigCminus,bigRplus,bigRminus = precession.intertial_ingredients(kappa,r,chieff,q,chi1,chi2)``
"""
kappa = np.atleast_1d(kappa).astype(float)
r = np.atleast_1d(r).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
# Machine generated with eq_generator.nb
bigC0 = 1/2 * q * ((1 + q))**(-2) * (r)**(-5/2) * ((1 + 2 * q**(-1) * \
((1 + q))**2 * (r)**(-1/2) * kappa))**(1/2)
# Machine generated with eq_generator.nb
bigCplus = 3 * ((1 + 2 * q**(-1) * ((1 + q))**2 * (r)**(-1/2) * \
kappa))**(-1/2) * (1 + -1 * (r)**(-1/2) * chieff) * (q**(-1) * ((1 + \
q))**3 * (r)**(-1/2) * kappa + (-1/2 * (1 + -1 * q) * q**(-2) * \
(r)**(-1) * (chi1**2 + -1 * q**4 * chi2**2) + (1 + q) * (1 + ((1 + 2 \
* q**(-1) * ((1 + q))**2 * (r)**(-1/2) * kappa))**(1/2)) * (1 + \
(r)**(-1/2) * chieff)))
# Machine generated with eq_generator.nb
bigCminus = -3 * ((1 + 2 * q**(-1) * ((1 + q))**2 * (r)**(-1/2) * \
kappa))**(-1/2) * (1 + -1 * (r)**(-1/2) * chieff) * (q**(-1) * ((1 + \
q))**3 * (r)**(-1/2) * kappa + (-1/2 * (1 + -1 * q) * q**(-2) * \
(r)**(-1) * (chi1**2 + -1 * q**4 * chi2**2) + (1 + q) * (1 + -1 * ((1 \
+ 2 * q**(-1) * ((1 + q))**2 * (r)**(-1/2) * kappa))**(1/2)) * (1 + \
(r)**(-1/2) * chieff)))
# Machine generated with eq_generator.nb
bigRplus = (-2 * q * ((1 + q))**(-1) * (1 + ((1 + 2 * q**(-1) * ((1 + \
q))**2 * (r)**(-1/2) * kappa))**(1/2)) + -1 * (1 + q) * (r)**(-1/2) * \
chieff)
# Machine generated with eq_generator.nb
bigRminus = (-2 * q * ((1 + q))**(-1) * (1 + -1 * ((1 + 2 * q**(-1) * \
((1 + q))**2 * (r)**(-1/2) * kappa))**(1/2)) + -1 * (1 + q) * \
(r)**(-1/2) * chieff)
return np.stack([bigC0, bigCplus, bigCminus,bigRplus,bigRminus])
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20,887 | precession.precession | inverseaffine |
Perform an inferse affine trasformation to scale a vector from some upper and lower limits: vec = low + rescaled*(up-low). If rescaled is defined in [0,1], the result will be defined in [low,up].
Parameters
----------
rescaled: float
Rescaled vector.
low: float
Lower limit.
up: float
Upper limit.
Returns
-------
vec: array
Vector in Cartesian coomponents.
Examples
--------
``vec = precession.inverseaffine(rescaled,low,up)``
| def inverseaffine(rescaled, low, up):
"""
Perform an inferse affine trasformation to scale a vector from some upper and lower limits: vec = low + rescaled*(up-low). If rescaled is defined in [0,1], the result will be defined in [low,up].
Parameters
----------
rescaled: float
Rescaled vector.
low: float
Lower limit.
up: float
Upper limit.
Returns
-------
vec: array
Vector in Cartesian coomponents.
Examples
--------
``vec = precession.inverseaffine(rescaled,low,up)``
"""
rescaled = np.atleast_1d(rescaled).astype(float)
up = np.atleast_1d(up).astype(float)
low = np.atleast_1d(low).astype(float)
vec = low + rescaled*(up-low)
return vec
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] |
20,888 | precession.precession | ismonotonic |
Check if an array is monotonic. The parameter `which` can takes the following values:
- `<` check array is strictly increasing.
- `<=` check array is increasing.
- `>` check array is strictly decreasing.
- `>=` check array is decreasing.
Parameters
----------
vec: array
Input array.
which: string
Select function behavior.
Returns
-------
check: boolean
Result
Examples
--------
``check = ismonotonic(vec, which)``
| def ismonotonic(vec, which):
"""
Check if an array is monotonic. The parameter `which` can takes the following values:
- `<` check array is strictly increasing.
- `<=` check array is increasing.
- `>` check array is strictly decreasing.
- `>=` check array is decreasing.
Parameters
----------
vec: array
Input array.
which: string
Select function behavior.
Returns
-------
check: boolean
Result
Examples
--------
``check = ismonotonic(vec, which)``
"""
if which == '<':
return np.all(vec[:-1] < vec[1:])
elif which == '<=':
return np.all(vec[:-1] <= vec[1:])
elif which == '>':
return np.all(vec[:-1] > vec[1:])
elif which == '>=':
return np.all(vec[:-1] >= vec[1:])
else:
raise ValueError("`which` needs to be one of the following: `>`, `>=`, `<`, `<=`.")
| (vec, which) | [
0.004639027640223503,
0.06569792330265045,
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0.0031427876092493534,
0.056734148412942886,
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0.04984734579920769,
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0.00830333586782217,
0.08249589800834656,
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0.023702995851635933,
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] |
20,889 | precession.precession | isotropic_angles |
Sample the angles theta1, theta2, and deltaphi from an isotropic distribution.
Parameters
----------
N: integer, optional (default: 1)
Number of samples.
Returns
-------
vec: array
Vector in Cartesian coomponents.
Examples
--------
``vec = precession.isotropic_angles(N=1)``
| def isotropic_angles(N=1):
"""
Sample the angles theta1, theta2, and deltaphi from an isotropic distribution.
Parameters
----------
N: integer, optional (default: 1)
Number of samples.
Returns
-------
vec: array
Vector in Cartesian coomponents.
Examples
--------
``vec = precession.isotropic_angles(N=1)``
"""
theta1=np.arccos(np.random.uniform(-1,1,N))
theta2=np.arccos(np.random.uniform(-1,1,N))
deltaphi=np.random.uniform(-np.pi,np.pi,N)
return np.stack([theta1,theta2,deltaphi])
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] |
20,890 | precession.precession | kappadiscriminant_coefficients |
Coefficients of the quintic equation in kappa that defines the spin-orbit resonances.
Parameters
----------
u: float
Compactified separation 1/(2L).
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
coeff0: float
Coefficient to the x^0 term in polynomial.
coeff1: float
Coefficient to the x^1 term in polynomial.
coeff2: float
Coefficient to the x^2 term in polynomial.
coeff3: float
Coefficient to the x^3 term in polynomial.
coeff4: float
Coefficient to the x^4 term in polynomial.
coeff5: float
Coefficient to the x^5 term in polynomial.
Examples
--------
``coeff5,coeff4,coeff3,coeff2,coeff1,coeff0 = precession.kappadiscriminant_coefficients(u,chieff,q,chi1,chi2)``
| def kappadiscriminant_coefficients(u, chieff, q, chi1, chi2):
"""
Coefficients of the quintic equation in kappa that defines the spin-orbit resonances.
Parameters
----------
u: float
Compactified separation 1/(2L).
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
coeff0: float
Coefficient to the x^0 term in polynomial.
coeff1: float
Coefficient to the x^1 term in polynomial.
coeff2: float
Coefficient to the x^2 term in polynomial.
coeff3: float
Coefficient to the x^3 term in polynomial.
coeff4: float
Coefficient to the x^4 term in polynomial.
coeff5: float
Coefficient to the x^5 term in polynomial.
Examples
--------
``coeff5,coeff4,coeff3,coeff2,coeff1,coeff0 = precession.kappadiscriminant_coefficients(u,chieff,q,chi1,chi2)``
"""
u = np.atleast_1d(u).astype(float)
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
coeff5 = -u
# Machine generated with eq_generator.nb
coeff4 = 1/16 * q**(-1) * ((1 + q))**(-4) * (1 + (q**6 + (q * (2 + \
(80 * u**2 * chi1**2 + 40 * u * chieff)) + (q**5 * (2 + (80 * u**2 * \
chi2**2 + 40 * u * chieff)) + (4 * q**3 * (-1 + (60 * u * chieff + 8 \
* u**2 * chieff**2)) + (q**2 * (-1 + (160 * u * chieff + 16 * u**2 * \
(-3 * chi1**2 + chieff**2))) + q**4 * (-1 + (160 * u * chieff + 16 * \
u**2 * (-3 * chi2**2 + chieff**2)))))))))
# Machine generated with eq_generator.nb
coeff3 = -1/8 * q**(-1) * ((1 + q))**(-8) * (((-1 + q))**2 * ((1 + \
q))**8 * chieff + (8 * q * u**3 * ((10 + (-12 * q + 3 * q**2)) * \
chi1**4 + (-2 * q * chi1**2 * (6 * q**2 * chi2**2 + (6 * q**4 * \
chi2**2 + (-2 * chieff**2 + (-3 * q * chieff**2 + q**3 * (-11 * \
chi2**2 + chieff**2))))) + q**4 * chi2**2 * (10 * q**4 * chi2**2 + \
(-2 * chieff**2 + (4 * q**3 * (-3 * chi2**2 + chieff**2) + 3 * q**2 * \
(chi2**2 + 2 * chieff**2)))))) + (4 * q * ((1 + q))**3 * u**2 * \
chieff * (-1 * (-20 + (3 * q + q**2)) * chi1**2 + q * (20 * q**4 * \
chi2**2 + (4 * chieff**2 + (12 * q * chieff**2 + (-1 * q**2 * \
(chi2**2 + -12 * chieff**2) + q**3 * (-3 * chi2**2 + 4 * \
chieff**2)))))) + 2 * ((1 + q))**4 * u * (-1 * ((-1 + q))**2 * (-1 + \
5 * q) * chi1**2 + q * (q**5 * chi2**2 + (8 * chieff**2 + (40 * q * \
chieff**2 + (q**4 * (-7 * chi2**2 + 8 * chieff**2) + (q**3 * (11 * \
chi2**2 + 40 * chieff**2) + q**2 * (-5 * chi2**2 + 64 * \
chieff**2))))))))))
# Machine generated with eq_generator.nb
coeff2 = 1/16 * q**(-1) * ((1 + q))**(-12) * (-16 * q * (-10 + (18 * \
q + (-9 * q**2 + q**3))) * u**4 * chi1**6 + (chieff**2 + (4 * q * \
chieff**2 * (3 + 2 * u * chieff) + (q**(14) * (6 * u**2 * chi2**4 + \
(chieff**2 + chi2**2 * (-1 + 6 * u * chieff))) + (q**2 * (-1 * \
chi2**2 + chieff**2 * (59 + (144 * u * chieff + 16 * u**2 * \
chieff**2))) + (4 * q**(13) * (40 * u**4 * chi2**6 + (chieff**2 * (3 \
+ 2 * u * chieff) + (12 * u**2 * chi2**4 * (-1 + 5 * u * chieff) + \
chi2**2 * (-1 + (-4 * u * chieff + 24 * u**2 * chieff**2))))) + (-4 * \
q**3 * (chi2**2 * (1 + 2 * u * chieff) + -2 * chieff**2 * (19 + (126 \
* u * chieff + 24 * u**2 * chieff**2))) + (q**4 * (-2 * chi2**2 * (1 \
+ (43 * u * chieff + 4 * u**2 * chieff**2)) + chieff**2 * (201 + \
(3920 * u * chieff + 976 * u**2 * chieff**2))) + (4 * q**5 * \
(chieff**2 * (13 + (2430 * u * chieff + 704 * u**2 * chieff**2)) + \
chi2**2 * (3 + (-72 * u * chieff + (10 * u**2 * chieff**2 + 8 * u**3 \
* chieff**3)))) + (-4 * q**7 * (u**2 * chi2**4 * (19 + 8 * u * \
chieff) + (-4 * chieff**2 * (-27 + (1218 * u * chieff + 392 * u**2 * \
chieff**2)) + -2 * chi2**2 * (-1 + (20 * u * chieff + (169 * u**2 * \
chieff**2 + 32 * u**3 * chieff**3))))) + (q**(12) * (-288 * u**4 * \
chi2**6 + (chieff**2 * (59 + (144 * u * chieff + 16 * u**2 * \
chieff**2)) + (2 * u**2 * chi2**4 * (-67 + (204 * u * chieff + 48 * \
u**2 * chieff**2)) + 2 * chi2**2 * (-1 + (-95 * u * chieff + (296 * \
u**2 * chieff**2 + 48 * u**3 * chieff**3)))))) + (4 * q**9 * (2 * \
u**2 * chi2**4 * (13 + (6 * u * chieff + -8 * u**2 * chieff**2)) + \
(chieff**2 * (13 + (2430 * u * chieff + 704 * u**2 * chieff**2)) + 2 \
* chi2**2 * (-1 + (70 * u * chieff + (379 * u**2 * chieff**2 + 100 * \
u**3 * chieff**3))))) + (4 * q**(11) * (36 * u**4 * chi2**6 + (u**2 * \
chi2**4 * (5 + (-16 * u * chieff + 24 * u**2 * chieff**2)) + (2 * \
chieff**2 * (19 + (126 * u * chieff + 24 * u**2 * chieff**2)) + \
chi2**2 * (3 + (-102 * u * chieff + (406 * u**2 * chieff**2 + 112 * \
u**3 * chieff**3)))))) + (q**8 * (2 * u**2 * chi2**4 * (-53 + (28 * u \
* chieff + 8 * u**2 * chieff**2)) + (chieff**2 * (-261 + (16416 * u * \
chieff + 5152 * u**2 * chieff**2)) + 4 * chi2**2 * (-7 + (189 * u * \
chieff + (614 * u**2 * chieff**2 + 120 * u**3 * chieff**3))))) + \
(q**6 * (-8 * u**2 * chi2**4 + (chieff**2 * (-261 + (16416 * u * \
chieff + 5152 * u**2 * chieff**2)) + chi2**2 * (17 + (-338 * u * \
chieff + (424 * u**2 * chieff**2 + 128 * u**3 * chieff**3))))) + \
(q**10 * (-16 * u**4 * chi2**6 + (-2 * u**2 * chi2**4 * (-121 + (136 \
* u * chieff + 40 * u**2 * chieff**2)) + (chieff**2 * (201 + (3920 * \
u * chieff + 976 * u**2 * chieff**2)) + chi2**2 * (17 + (-148 * u * \
chieff + (2680 * u**2 * chieff**2 + 832 * u**3 * chieff**3)))))) + (2 \
* u**2 * chi1**4 * (3 + (-4 * q**8 + (2 * q**7 * (-19 + (36 * u**2 * \
chi2**2 + -8 * u * chieff)) + (24 * q * (-1 + 5 * u * chieff) + (2 * \
q**3 * (5 + (-16 * u * chieff + 24 * u**2 * chieff**2)) + (q**2 * \
(-67 + (204 * u * chieff + 48 * u**2 * chieff**2)) + (4 * q**5 * (13 \
+ (6 * u * chieff + 8 * u**2 * (9 * chi2**2 + -1 * chieff**2))) + \
(q**6 * (-53 + (28 * u * chieff + 8 * u**2 * (-27 * chi2**2 + \
chieff**2))) + -1 * q**4 * (-121 + (136 * u * chieff + 8 * u**2 * (18 \
* chi2**2 + 5 * chieff**2))))))))))) + -1 * chi1**2 * (1 + (q**(12) + \
(-6 * u * chieff + (q**(11) * (4 + (60 * u**2 * chi2**2 + 8 * u * \
chieff)) + (q * (4 + (16 * u * chieff + -96 * u**2 * chieff**2)) + \
(q**2 * (2 + (190 * u * chieff + (-592 * u**2 * chieff**2 + -96 * \
u**3 * chieff**3))) + (q**10 * (2 + (288 * u**4 * chi2**4 + (86 * u * \
chieff + (24 * u**3 * chi2**2 * chieff + 4 * u**2 * (chi2**2 + 2 * \
chieff**2))))) + (-4 * q**3 * (3 + (-102 * u * chieff + (112 * u**3 * \
chieff**3 + u**2 * (-15 * chi2**2 + 406 * chieff**2)))) + (-4 * q**9 \
* (3 + (-72 * u * chieff + (8 * u**3 * chieff * (-3 * chi2**2 + \
chieff**2) + (2 * u**2 * (29 * chi2**2 + 5 * chieff**2) + 24 * u**4 * \
(6 * chi2**4 + -1 * chi2**2 * chieff**2))))) + (q**4 * (-17 + (148 * \
u * chieff + (4 * u**2 * (chi2**2 + -670 * chieff**2) + 8 * u**3 * (3 \
* chi2**2 * chieff + -104 * chieff**3)))) + (8 * q**5 * (1 + (-70 * u \
* chieff + (12 * u**4 * chi2**2 * chieff**2 + (-1 * u**2 * (29 * \
chi2**2 + 379 * chieff**2) + 4 * u**3 * (3 * chi2**2 * chieff + -25 * \
chieff**3))))) + (4 * q**6 * (7 + (-189 * u * chieff + (8 * u**4 * \
chi2**2 * chieff**2 + (-1 * u**2 * (chi2**2 + 614 * chieff**2) + 6 * \
u**3 * (7 * chi2**2 * chieff + -20 * chieff**3))))) + (q**8 * (-17 + \
(338 * u * chieff + (-4 * u**2 * (chi2**2 + 106 * chieff**2) + (16 * \
u**4 * (27 * chi2**4 + 2 * chi2**2 * chieff**2) + 8 * u**3 * (21 * \
chi2**2 * chieff + -16 * chieff**3))))) + -8 * q**7 * (-1 + (20 * u * \
chieff + (u**2 * (-43 * chi2**2 + 169 * chieff**2) + (2 * u**4 * (9 * \
chi2**4 + 8 * chi2**2 * chieff**2) + -8 * u**3 * (3 * chi2**2 * \
chieff + -4 * chieff**3)))))))))))))))))))))))))))))))))))
# Machine generated with eq_generator.nb
coeff1 = -1/8 * q* | (u, chieff, q, chi1, chi2) | [
-0.03548770025372505,
0.007766586262732744,
0.010225599631667137,
-0.021210813894867897,
-0.015640297904610634,
0.002192417159676552,
-0.04062971472740173,
-0.04226581007242203,
-0.03235184773802757,
0.010293769650161266,
0.03953898325562477,
0.05500398576259613,
-0.008832969702780247,
0.07148180902004242,
-0.03572142496705055,
0.04417458921670914,
0.04982301592826843,
-0.04955033212900162,
0.01103390846401453,
0.01524101197719574,
-0.06380774080753326,
-0.010469065979123116,
0.009451375342905521,
0.11125452071428299,
-0.04152567312121391,
0.012816084548830986,
0.001525318599306047,
-0.03509815037250519,
-0.02980031818151474,
-0.01120920479297638,
-0.06287282705307007,
-0.0005980149726383388,
0.011754569597542286,
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20,891 | precession.precession | kappalimits |
Limits on the asymptotic angular momentum. The contraints considered depend on the inputs provided.
- If r, q, chi1, chi2 are provided, returns the geometrical limits.
- If r, chieff, q, chi1, and chi2 are provided, returns the spin-orbit resonances.
The boolean flag enforce raises an error in case the inputs are not compatible. Additional kwargs are passed to kapparesonances.
Parameters
----------
r: float, optional (default: None)
Binary separation.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
enforce: boolean, optional (default: False)
Perform additional checks.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
kappamax: float
Maximum value of the asymptotic angular momentum kappa.
kappamin: float
Minimum value of the asymptotic angular momentum kappa.
Examples
--------
``kappamin,kappamax = precession.kappalimits(r=r,q=q,chi1=chi1,chi2=chi2)``
``kappamin,kappamax = precession.kappalimits(r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
``kappamin,kappamax = precession.kappalimits(r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,enforce=True)``
| def kappalimits(r=None, chieff=None, q=None, chi1=None, chi2=None, enforce=False, **kwargs):
"""
Limits on the asymptotic angular momentum. The contraints considered depend on the inputs provided.
- If r, q, chi1, chi2 are provided, returns the geometrical limits.
- If r, chieff, q, chi1, and chi2 are provided, returns the spin-orbit resonances.
The boolean flag enforce raises an error in case the inputs are not compatible. Additional kwargs are passed to kapparesonances.
Parameters
----------
r: float, optional (default: None)
Binary separation.
chieff: float, optional (default: None)
Effective spin.
q: float, optional (default: None)
Mass ratio: 0<=q<=1.
chi1: float, optional (default: None)
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float, optional (default: None)
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
enforce: boolean, optional (default: False)
Perform additional checks.
**kwargs: unpacked dictionary, optional
Additional keyword arguments.
Returns
-------
kappamax: float
Maximum value of the asymptotic angular momentum kappa.
kappamin: float
Minimum value of the asymptotic angular momentum kappa.
Examples
--------
``kappamin,kappamax = precession.kappalimits(r=r,q=q,chi1=chi1,chi2=chi2)``
``kappamin,kappamax = precession.kappalimits(r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2)``
``kappamin,kappamax = precession.kappalimits(r=r,chieff=chieff,q=q,chi1=chi1,chi2=chi2,enforce=True)``
"""
if r is not None and chieff is None and q is not None and chi1 is not None and chi2 is not None:
kappamin, kappamax = kappalimits_geometrical(r, q, chi1, chi2)
elif r is not None and chieff is not None and q is not None and chi1 is not None and chi2 is not None:
kappamin, kappamax = kapparesonances(r, chieff, q, chi1, chi2, **kwargs)
# Check precondition
kappamin_cond, kappamax_cond = kappalimits_geometrical(r , q, chi1, chi2)
if (kappamin >= kappamin_cond).all() and (kappamax <= kappamax_cond).all():
pass
else:
if enforce:
raise ValueError("Input values are not compatible [kappalimits].")
else:
warnings.warn("Input values are not compatible [kappalimits].", Warning)
else:
raise TypeError("Provide either (r,q,chi1,chi2) or (r,chieff,q,chi1,chi2).")
return np.stack([kappamin, kappamax])
| (r=None, chieff=None, q=None, chi1=None, chi2=None, enforce=False, **kwargs) | [
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20,892 | precession.precession | kappalimits_geometrical |
Limits in kappa conditioned on r, q, chi1, chi2.
Parameters
----------
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
kappamax: float
Maximum value of the asymptotic angular momentum kappa.
kappamin: float
Minimum value of the asymptotic angular momentum kappa.
Examples
--------
``kappamin,kappamax = precession.kappalimits_geometrical(r,q,chi1,chi2)``
| def kappalimits_geometrical(r , q, chi1, chi2):
"""
Limits in kappa conditioned on r, q, chi1, chi2.
Parameters
----------
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
kappamax: float
Maximum value of the asymptotic angular momentum kappa.
kappamin: float
Minimum value of the asymptotic angular momentum kappa.
Examples
--------
``kappamin,kappamax = precession.kappalimits_geometrical(r,q,chi1,chi2)``
"""
r = np.atleast_1d(r).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
k1 = -q*r**(1/2)/(2*(1+q)**2)
k2 = np.where(q*r**(1/2)>=chi1+chi2*q**2,
(chi1+chi2*q**2)/(1+q)**2 *(-1+ (chi1+chi2*q**2)/(2*q*r**(1/2))),
1/(1+q)**2 * (-q*r**(1/2) + (chi1+chi2*q**2) - (chi1+chi2*q**2)**2 /(2*q*r**(1/2)))
)
k3 = np.where(np.abs(chi1-chi2*q**2)>= q*r**(1/2),
np.abs(chi1-chi2*q**2)/(1+q)**2 *(-1+ np.abs(chi1-chi2*q**2)/(2*q*r**(1/2))),
1/(1+q)**2 * (-q*r**(1/2) + np.abs(chi1-chi2*q**2) - (chi1-chi2*q**2)**2 /(2*q*r**(1/2)))
)
kappamin = np.maximum.reduce([k1,k2,k3])
# An alternative implementation that breaks down for r=inf
# def squarewithsign(x):
# return x*np.abs(x)
# kappamin_old= q*r**(1/2)/(2*(1+q)**2)*(
# np.maximum.reduce([np.zeros(q.shape),
# squarewithsign( 1- (chi1+chi2*q**2) / (q*r**(1/2))),
# squarewithsign( np.abs(chi1-chi2*q**2) / (q*r**(1/2)) - 1 )] )
# -1)
kappamax = (chi1+chi2*q**2) / (1+q)**2 * ( (chi1+chi2*q**2) / (2*q*r**(1/2)) +1 )
return np.stack([kappamin,kappamax])
| (r, q, chi1, chi2) | [
0.005900758784264326,
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0.041183896362781525,
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] |
20,893 | precession.precession | kapparescaling |
Compute kappa from the rescaled parameter 0<=kappatilde<=1.
Parameters
----------
kappatilde: float
Rescaled version of the asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
kappa: float
Asymptotic angular momentum.
Examples
--------
``kappa = precession.kapparescaling(kappatilde,r,chieff,q,chi1,chi2)``
| def kapparescaling(kappatilde, r, chieff, q, chi1, chi2):
"""
Compute kappa from the rescaled parameter 0<=kappatilde<=1.
Parameters
----------
kappatilde: float
Rescaled version of the asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
kappa: float
Asymptotic angular momentum.
Examples
--------
``kappa = precession.kapparescaling(kappatilde,r,chieff,q,chi1,chi2)``
"""
kappatilde = np.atleast_1d(kappatilde)
kappaminus, kappaplus = kapparesonances(r, chieff, q, chi1, chi2)
kappa = inverseaffine(kappatilde,kappaminus,kappaplus)
return kappa
| (kappatilde, r, chieff, q, chi1, chi2) | [
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0.030553823336958885,
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20,894 | precession.precession | kapparesonances |
asymptotic angular momentum of the two spin-orbit resonances. The resonances minimizes and maximizes kappa for given values of r, chieff, q, chi1, chi2. The minimum corresponds to deltaphi=pi and the maximum corresponds to deltaphi=0.
Parameters
----------
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
tol: float, optional (default: 1e-4)
Numerical tolerance, see source code for details.
Returns
-------
kappamax: float
Maximum value of the asymptotic angular momentum kappa.
kappamin: float
Minimum value of the asymptotic angular momentum kappa.
Examples
--------
``kappamin,kappamax = precession.kapparesonances(u,chieff,q,chi1,chi2,tol=1e-4)``
| def kapparesonances(r, chieff, q, chi1, chi2,tol=1e-4):
"""
asymptotic angular momentum of the two spin-orbit resonances. The resonances minimizes and maximizes kappa for given values of r, chieff, q, chi1, chi2. The minimum corresponds to deltaphi=pi and the maximum corresponds to deltaphi=0.
Parameters
----------
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
tol: float, optional (default: 1e-4)
Numerical tolerance, see source code for details.
Returns
-------
kappamax: float
Maximum value of the asymptotic angular momentum kappa.
kappamin: float
Minimum value of the asymptotic angular momentum kappa.
Examples
--------
``kappamin,kappamax = precession.kapparesonances(u,chieff,q,chi1,chi2,tol=1e-4)``
"""
chieff = np.atleast_1d(chieff).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
u = eval_u(r,q)
#kapparoots = wraproots(kappadiscriminant_coefficients, u, chieff, q, chi1, chi2)
coeffs = kappadiscriminant_coefficients(u, chieff, q, chi1, chi2)
kapparootscomplex = np.sort_complex(roots_vec(coeffs.T))
#sols = np.real(np.where(np.isreal(sols), sols, np.nan))
# There are in principle five solutions, but only two are physical.
def _compute(kapparootscomplex, u, chieff, q, chi1, chi2):
kappares=None
# At infinitely large separations the resonances are analytic...
if u==0:
kappaminus = np.maximum((q*(1+q)*chieff - (1-q)*chi1)/(1+q)**2 , ((1+q)*chieff - q*(1-q)*chi2)/(1+q)**2)
kappaplus = np.minimum((q*(1+q)*chieff + (1-q)*chi1)/(1+q)**2, ((1+q)*chieff + q*(1-q)*chi2)/(1+q)**2)
kappares = np.array([kappaminus,kappaplus])
return kappares
kapparoots = np.real(kapparootscomplex[np.isreal(kapparootscomplex)])
upup,updown,downup,downdown=eval_chieff([0,0,np.pi,np.pi], [0,np.pi,0,np.pi], np.repeat(q,4), np.repeat(chi1,4), np.repeat(chi2,4))
# If too close to perfect alignment, return the analytical result.
if np.isclose(np.repeat(chieff,2),np.squeeze([upup,downdown])).any():
warnings.warn("Close to either up-up or down-down configuration. Using analytical results.", Warning)
S1 = eval_S1(q, chi1)
S2 = eval_S2(q, chi2)
L=1/(2*u)
kappar = ((L+np.sign(chieff)*(S1+S2))**2 - L**2) / (2*L)
kappares=np.squeeze([kappar,kappar])
# In this case, the spurious solution is always the smaller one. Just leave it out.
elif len(kapparoots)==3:
kappares = kapparoots[1:]
# Here we have two candidate pairs of resonances...
elif len(kapparoots)==5:
# Edge case with two coincident roots that are exactly zeros. This happens for q=chi1=chi2=1
if np.count_nonzero(kapparoots)==3:
kappares = kapparoots[kapparoots != 0][1:]
elif np.count_nonzero(kapparoots)==1:
kappares = np.sort(np.concatenate([[0],kapparoots[kapparoots != 0]]))
else:
# Compute the corresponding values of deltachi at the resonances
deltachires = deltachiresonance(kappa=kapparoots, u=tiler(u,kapparoots), chieff=tiler(chieff,kapparoots), q=tiler(q,kapparoots), chi1=tiler(chi1,kapparoots), chi2=tiler(chi2,kapparoots))
# Check which of those values is within the allowed region
deltachimin,deltachimax = deltachilimits_rectangle(chieff, q, chi1, chi2)
check = np.squeeze(np.logical_and(deltachires>deltachimin,deltachires<deltachimax))
# The first root cannot possibly be right
if check[0] and not np.isclose(kapparoots[1],kapparoots[0]):
raise ValueError("Input values are not compatible [kapparesonances].")
elif check[1] and check[2] and not check[3] and not check[4]:
kappares = kapparoots[1:3]
elif not check[1] and not check[2] and check[3] and check[4]:
kappares = kapparoots[3:5]
elif check[1] and check[2] and check[3] and check[4]:
warnings.warn("Unphysical resonances detected and removed", Warning)
# Root 1 is a spurious copy of root 0
if np.isclose(kapparoots[1],kapparoots[0]):
kappares = np.array([np.mean(kapparoots[2:4]),kapparoots[4]])
#err = np.abs( (kapparoots[2]-kapparoots[3])/np.mean(kapparoots[2:4]))
#warnings.warn("Unphysical resonances detected and removed. Relative accuracy Delta_kappa/kappa="+str(err)+", [kapparesonances].", Warning)
else:
kappares=np.array([kapparoots[1],kapparoots[4]])
# # Root 1 is a spurious copy of root 0:
# if kapparoots[1]-kapparoots[0]<kapparoots[3]-kapparoots[2]:
# kappares = kapparoots[3:5]
# # Root 2 and 3 are actually complex but appear real because of numerical errors
# else:
# kappares=np.array([kapparoots[1],kapparoots[4]])
# This is an edge (and hopefully rare) case where the resonances are missed because of numerical errors
elif len(kapparoots)==1:
# 5 complex solutions correspond to 3 real parts (i.e. thare are two conjugate pairs)
kapparoots = np.unique(np.real(kapparootscomplex))
deltachires = deltachiresonance(kappa=kapparoots, u=tiler(u,kapparoots), chieff=tiler(chieff,kapparoots), q=tiler(q,kapparoots), chi1=tiler(chi1,kapparoots), chi2=tiler(chi2,kapparoots))
deltachimin,deltachimax = deltachilimits_rectangle(chieff, q, chi1, chi2)
check = np.squeeze(np.logical_and(deltachires>deltachimin,deltachires<deltachimax))
# Two of these are compatible
if np.sum(check)==2:
kappares=kapparoots[check]
warnings.warn("Resonances not detected, best guess returned (soft sanitizing)", Warning)
# In case that also fails, returns the closest two
else:
diffmin = np.abs(deltachires-deltachimin)
diffmax = np.abs(deltachires-deltachimax)
try:
kappares = np.sort(np.squeeze([kapparoots[diffmin==min(diffmin)], kapparoots[diffmax==min(diffmax)]]))
except:
# If that also fails and you're close to q=1, return the analytic result
if np.isclose(q,1):
r=float(eval_r(u=u,q=q))
kappamin = np.maximum((chi1-chi2)**2 / 8 , chieff**2 /2) /r**0.5 + chieff/2
kappamax = (chi1+chi2)**2 / 8 /r**0.5 + chieff/2
kappares=np.array([kappamin,kappamax])
warnings.warn("Resonances not detected, best guess returned (using analytic result for q=1)", Warning)
else:
warnings.warn("Resonances not detected, best guess returned (aggressive sanitizing)", Warning)
# Up-down and down-up are challenging.
# Evaluate the resonances outside of those points and interpolate linearly.
# Note usage of recursive functions.
elif np.isclose(np.repeat(chieff,2),np.squeeze([updown,downup])).any():
warnings.warn("Close to either up-down or down-up configuration. Using recursive approach (tol="+str(tol)+") and analytical results.", Warning)
chieff1 = max(min(chieff+tol/2,upup),downdown)
coeffs = kappadiscriminant_coefficients(u, chieff1, q, chi1, chi2)
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] |
20,895 | precession.precession | morphology |
Evaluate the spin morphology. Returns:
- L0 for librating about deltaphi=0,
- Lpi for librating about deltaphi=pi
- C- for circulating from deltaphi=pi to deltaphi=0,
- C+ for circulating from deltaphi=0 to deltaphi=pi.
If simpler=True, do not distinguish between the two circulating morphologies and return C for both.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
simpler: boolean, optional (default: False)
If True simplifies output.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
morph: string
Spin morphology.
Examples
--------
``morph = precession.morphology(kappa,r,chieff,q,chi1,chi2,simpler=False)``
| def morphology(kappa, r, chieff, q, chi1, chi2, simpler=False, precomputedroots=None):
"""
Evaluate the spin morphology. Returns:
- L0 for librating about deltaphi=0,
- Lpi for librating about deltaphi=pi
- C- for circulating from deltaphi=pi to deltaphi=0,
- C+ for circulating from deltaphi=0 to deltaphi=pi.
If simpler=True, do not distinguish between the two circulating morphologies and return C for both.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
simpler: boolean, optional (default: False)
If True simplifies output.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
morph: string
Spin morphology.
Examples
--------
``morph = precession.morphology(kappa,r,chieff,q,chi1,chi2,simpler=False)``
"""
deltachiminus,deltachiplus = deltachilimits_plusminus(kappa, r, chieff, q, chi1, chi2)
# Pairs of booleans based on the values of deltaphi at S- and S+
status = np.transpose([eval_cosdeltaphi(deltachiminus, kappa, r, chieff, q, chi1, chi2) > 0, eval_cosdeltaphi(deltachiplus, kappa, r, chieff, q, chi1, chi2) > 0])
# Map to labels
dictlabel = {(False, False): "Lpi", (True, True): "L0", (False, True): "C-", (True, False): "C+"}
# Subsitute pairs with labels
morphs = np.zeros(deltachiminus.shape)
for k, v in dictlabel.items():
morphs = np.where((status == k).all(axis=1), v, morphs)
# Simplifies output, only one circulating morphology
if simpler:
morphs = np.where(np.logical_or(morphs == 'C+', morphs == 'C-'), 'C', morphs)
return morphs
| (kappa, r, chieff, q, chi1, chi2, simpler=False, precomputedroots=None) | [
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20,896 | precession.precession | norm_nested |
Norm of 2D array of shape (N,3) along last axis.
Parameters
----------
x : array
Input array.
Returns
-------
n : array
Norm of the input arrays.
Examples
--------
``n = norm_nested(x)``
| def norm_nested(x):
"""
Norm of 2D array of shape (N,3) along last axis.
Parameters
----------
x : array
Input array.
Returns
-------
n : array
Norm of the input arrays.
Examples
--------
``n = norm_nested(x)``
"""
return np.linalg.norm(x, axis=1)
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20,897 | precession.precession | normalize_nested |
Normalize 2D array of shape (N,3) along last axis.
Parameters
----------
x : array
Input array.
Returns
-------
y : array
Normalized array.
Examples
--------
``y = normalize_nested(x)``
| def normalize_nested(x):
"""
Normalize 2D array of shape (N,3) along last axis.
Parameters
----------
x : array
Input array.
Returns
-------
y : array
Normalized array.
Examples
--------
``y = normalize_nested(x)``
"""
return x/norm_nested(x)[:, None]
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] |
20,899 | precession.precession | omegasq_aligned |
Squared oscillation frequency of a given perturbed aligned-spin binary.
The flag which needs to be set to `uu` for up-up, `ud` for up-down, `du` for down-up or `dd` for down-down where the term before (after) the hyphen refers to the spin of the heavier (lighter) black hole.
Parameters
----------
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
which: string
Select function behavior.
Returns
-------
omegasq: float
Squared frequency.
Examples
--------
``omegasq = precession.omegasq_aligned(r,q,chi1,chi2,which)``
| def omegasq_aligned(r, q, chi1, chi2, which):
"""
Squared oscillation frequency of a given perturbed aligned-spin binary.
The flag which needs to be set to `uu` for up-up, `ud` for up-down, `du` for down-up or `dd` for down-down where the term before (after) the hyphen refers to the spin of the heavier (lighter) black hole.
Parameters
----------
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
which: string
Select function behavior.
Returns
-------
omegasq: float
Squared frequency.
Examples
--------
``omegasq = precession.omegasq_aligned(r,q,chi1,chi2,which)``
"""
r = np.atleast_1d(r).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
# These are all the valid input flags
uulabels = np.array(['uu', 'up-up', 'upup', '++'])
udlabels = np.array(['ud', 'up-down', 'updown', '+-'])
dulabels = np.array(['du', 'down-up', 'downup', '-+'])
ddlabels = np.array(['dd', 'down-down', 'downdown', '--'])
assert np.isin(which, np.concatenate([uulabels, udlabels, dulabels, ddlabels])).all(), "Set `which` flag to either uu, ud, du, or dd."
# +1 if primary is co-aligned, -1 if primary is counter-aligned
alpha1 = np.where(np.isin(which, np.concatenate([uulabels, udlabels])), 1, -1)
# +1 if secondary is co-aligned, -1 if secondary is counter-aligned
alpha2 = np.where(np.isin(which, np.concatenate([uulabels, dulabels])), 1, -1)
theta1 = np.arccos(alpha1)
theta2 = np.arccos(alpha2)
deltachi = eval_deltachi(theta1, theta2, q, chi1, chi2)
chieff = eval_chieff(theta1, theta2, q, chi1, chi2)
omegasq = (9/4) * (1/r)**7 * (r**0.5-chieff)**2 * (
((1-q)/(1+q))**2*r - 2*((1-q)/(1+q))*deltachi*r**0.5 + chieff**2
)
return omegasq
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] |
20,900 | precession.precession | pnseparation_to_gwfrequency |
Convert PN orbital separation in natural units (c=G=M=1) to GW frequency in Hz. We use the 2PN expression reported in Eq. 4.5 of Kidder 1995, arxiv:gr-qc/9506022.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
M_msun: float
Total mass of the binary in solar masses.
PNorder: array (default: [0,1,1.5,2])
PN orders considered.
Returns
-------
fGW: float
Gravitational-wave frequency.
Examples
--------
``fGW = precession.pnseparation_to_gwfrequency(theta1,theta2,deltaphi,r,q,chi1,chi2,M_msun,PNorder=[0,1,1.5,2])``
| def pnseparation_to_gwfrequency(theta1, theta2, deltaphi, r, q, chi1, chi2, M_msun, PNorder=[0,1,1.5,2]):
"""
Convert PN orbital separation in natural units (c=G=M=1) to GW frequency in Hz. We use the 2PN expression reported in Eq. 4.5 of Kidder 1995, arxiv:gr-qc/9506022.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
M_msun: float
Total mass of the binary in solar masses.
PNorder: array (default: [0,1,1.5,2])
PN orders considered.
Returns
-------
fGW: float
Gravitational-wave frequency.
Examples
--------
``fGW = precession.pnseparation_to_gwfrequency(theta1,theta2,deltaphi,r,q,chi1,chi2,M_msun,PNorder=[0,1,1.5,2])``
"""
theta1 = np.atleast_1d(theta1).astype(float)
theta2 = np.atleast_1d(theta2).astype(float)
deltaphi = np.atleast_1d(deltaphi).astype(float)
r = np.atleast_1d(r).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
M_msun = np.atleast_1d(M_msun).astype(float)
tildeomega = r**(-3/2) * (
(0 in PNorder) * 1
- (1 in PNorder) * r**(-1) *(3- q/(1+q)**2)
- (1.5 in PNorder) * r**(-3/2) * 1/(1+q)**2 *( (2+3*q)*chi1*np.cos(theta1) + q*(3+2*q)*chi2*np.cos(theta2) )
+ (2 in PNorder) * r**(-2) * (6 + 41*q/(4*(1+q)**2) + q**2/(1+q)**4 +3*q/(2*(1+q)**2) *chi1*chi2*(2*np.cos(theta1)*np.cos(theta2) - np.cos(deltaphi)*np.sin(theta1)*np.sin(theta2)))
)**(1/2)
# Prefactor is pi*Msun*G/c^3/s. It's pi and not 2pi because f is the GW frequency while Kidder's omega is the orbital angular velocity
fGW = tildeomega / (1.548e-5 * M_msun)
return fGW
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20,902 | precession.precession | precession_average |
Average a generic function over a precession cycle. The function needs to have call: func(deltachi, *args). Keywords arguments are not supported.
There are integration methods implemented:
- method='quadrature' uses scipy.integrate.quad. This is set by default and should be preferred.
- method='montecarlo' samples t(deltachi) and approximate the integral with a Monte Carlo sum. The number of samples can be specifed by Nsamples.
Additional keyword arguments are passed to scipy.integrate.quad.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
func: function
Function to precession-average.
*args: tuple
Extra arguments to pass to func.
method: string (default: 'quadrature')
Either 'quadrature' or 'montecarlo'
Nsamples: integer, optional (default: 1e4)
Number of Monte Carlo samples.
Returns
-------
func_av: float
Precession average of func.
Examples
--------
``func_av = precession.precession_average(kappa,r,chieff,q,chi1,chi2,func,*args,method='quadrature',Nsamples=1e4)``
| def precession_average(kappa, r, chieff, q, chi1, chi2, func, *args, method='quadrature', Nsamples=1e4):
"""
Average a generic function over a precession cycle. The function needs to have call: func(deltachi, *args). Keywords arguments are not supported.
There are integration methods implemented:
- method='quadrature' uses scipy.integrate.quad. This is set by default and should be preferred.
- method='montecarlo' samples t(deltachi) and approximate the integral with a Monte Carlo sum. The number of samples can be specifed by Nsamples.
Additional keyword arguments are passed to scipy.integrate.quad.
Parameters
----------
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
func: function
Function to precession-average.
*args: tuple
Extra arguments to pass to func.
method: string (default: 'quadrature')
Either 'quadrature' or 'montecarlo'
Nsamples: integer, optional (default: 1e4)
Number of Monte Carlo samples.
Returns
-------
func_av: float
Precession average of func.
Examples
--------
``func_av = precession.precession_average(kappa,r,chieff,q,chi1,chi2,func,*args,method='quadrature',Nsamples=1e4)``
"""
kappa=np.atleast_1d(kappa).astype(float)
r=np.atleast_1d(r).astype(float)
chieff=np.atleast_1d(chieff).astype(float)
q=np.atleast_1d(q).astype(float)
chi1=np.atleast_1d(chi1).astype(float)
chi2=np.atleast_1d(chi2).astype(float)
u = eval_u(r=r,q=q)
deltachiminus,deltachiplus,deltachi3 = deltachiroots(kappa, u, chieff, q, chi1, chi2)
if method == 'quadrature':
tau = eval_tau(kappa, r, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]), donotnormalize=True)
# Each args needs to be iterable
args = [np.atleast_1d(a) for a in args]
# Compute the numerator explicitely
def _integrand(deltachi, deltachiminus,deltachiplus,deltachi3, kappa, r, chieff, q, chi1, chi2, *args):
dchidt2 = dchidt2_RHS(deltachi, kappa, r, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]),donotnormalize=True)
return func(deltachi, *args) / dchidt2**(1/2)
def _compute(deltachiminus,deltachiplus,deltachi3, kappa, r, chieff, q, chi1, chi2, *args):
return scipy.integrate.quad(_integrand, deltachiminus, deltachiplus, args=(deltachiminus,deltachiplus,deltachi3, kappa, r, chieff, q, chi1, chi2, *args))[0]
func_av = np.array(list(map(_compute, deltachiminus,deltachiplus,deltachi3, kappa, r, chieff, q, chi1, chi2, *args))) / tau * 2
elif method == 'montecarlo':
deltachi = deltachisampling(kappa, r, chieff, q, chi1, chi2, N=int(Nsamples), precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]))
evals = func(deltachi, *args)
func_av = np.sum(evals, axis=-1)/Nsamples
func_av = np.atleast_1d(func_av)
else:
raise ValueError("Available methods are 'quadrature' and 'montecarlo'.")
return func_av
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] |
20,903 | precession.precession | reminantspindirection |
Angle between the spin of the remnant and the binary angular momentum, assuming that the spins stays in the direction of the total angular momentum 'at plunge'.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
thetaL: float
Angle betwen orbital angular momentum and total angular momentum.
Examples
--------
``thetaL = precession.reminantspindirection(theta1,theta2,deltaphi,r,q,chi1,chi2)``
| def reminantspindirection(theta1, theta2, deltaphi, r, q, chi1, chi2):
"""
Angle between the spin of the remnant and the binary angular momentum, assuming that the spins stays in the direction of the total angular momentum 'at plunge'.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
thetaL: float
Angle betwen orbital angular momentum and total angular momentum.
Examples
--------
``thetaL = precession.reminantspindirection(theta1,theta2,deltaphi,r,q,chi1,chi2)``
"""
Lvec,S1vec,S2vec = angles_to_Lframe(theta1, theta2, deltaphi, r, q, chi1, chi2)
Jvec = Lvec + S1vec + S2vec
hatL = normalize_nested(Lvec)
hatJ = normalize_nested(Jvec)
thetaL = np.arccos(dot_nested(hatL,hatJ))
return thetaL
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] |
20,904 | precession.precession | remnantkick |
Estimate the kick of the merger remnant. We collect various numerical-relativity
results, as described in Gerosa and Kesden 2016. Flags let you switch the
various contributions on and off (all on by default): superkicks (Gonzalez et al. 2007a;
Campanelli et al. 2007), hang-up kicks (Lousto & Zlochower 2011),
cross-kicks (Lousto & Zlochower 2013). The orbital-plane kick components are
implemented as described in Kesden et al. 2010a. The final kick depends on
the orbital phase at merger. By default, this is assumed to be uniformly
distributed in [0,2pi]. The maximum kick is realized for Theta=0 and can be
computed with the optional argument maxphase. The final kick is returned in
geometrical units (i.e. vkick/c) by default, and converted to km/s if
kms=True. This formula has to be applied *close to merger*, where
numerical relativity simulations are available. You should do a PN evolution
to transfer binaries at r~10M.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
kms: boolean, optional (default: False)
Return velocities in km/s.
maxphase: boolean, optional (default: False)
Maximize over orbital phase at merger.
superkick: boolean, optional (default: True)
Switch kick terms on and off.
hangupkick: boolean, optional (default: True)
Switch kick terms on and off.
crosskick: boolean, optional (default: True)
Switch kick terms on and off.
full_output: boolean, optional (default: False)
Return additional outputs.
Returns
-------
vk: float
Kick of the black-hole remnant (magnitude).
vk_array: array, optional
Kick of the black-hole remnant (in a frame aligned with L).
Examples
--------
``vk = precession.remnantkick(theta1,theta2,deltaphi,q,chi1,chi2,full_output=False)``
``vk,vk_array = precession.remnantkick(theta1,theta2,deltaphi,q,chi1,chi2,full_output=True)``
| def remnantkick(theta1, theta2, deltaphi, q, chi1, chi2, kms=False, maxphase=False, superkick=True, hangupkick=True, crosskick=True, full_output=False):
"""
Estimate the kick of the merger remnant. We collect various numerical-relativity
results, as described in Gerosa and Kesden 2016. Flags let you switch the
various contributions on and off (all on by default): superkicks (Gonzalez et al. 2007a;
Campanelli et al. 2007), hang-up kicks (Lousto & Zlochower 2011),
cross-kicks (Lousto & Zlochower 2013). The orbital-plane kick components are
implemented as described in Kesden et al. 2010a. The final kick depends on
the orbital phase at merger. By default, this is assumed to be uniformly
distributed in [0,2pi]. The maximum kick is realized for Theta=0 and can be
computed with the optional argument maxphase. The final kick is returned in
geometrical units (i.e. vkick/c) by default, and converted to km/s if
kms=True. This formula has to be applied *close to merger*, where
numerical relativity simulations are available. You should do a PN evolution
to transfer binaries at r~10M.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
kms: boolean, optional (default: False)
Return velocities in km/s.
maxphase: boolean, optional (default: False)
Maximize over orbital phase at merger.
superkick: boolean, optional (default: True)
Switch kick terms on and off.
hangupkick: boolean, optional (default: True)
Switch kick terms on and off.
crosskick: boolean, optional (default: True)
Switch kick terms on and off.
full_output: boolean, optional (default: False)
Return additional outputs.
Returns
-------
vk: float
Kick of the black-hole remnant (magnitude).
vk_array: array, optional
Kick of the black-hole remnant (in a frame aligned with L).
Examples
--------
``vk = precession.remnantkick(theta1,theta2,deltaphi,q,chi1,chi2,full_output=False)``
``vk,vk_array = precession.remnantkick(theta1,theta2,deltaphi,q,chi1,chi2,full_output=True)``
"""
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
eta = eval_eta(q)
Lvec,S1vec,S2vec = angles_to_Lframe(theta1, theta2, deltaphi, 1, q, chi1, chi2)
hatL = normalize_nested(Lvec)
hatS1 = normalize_nested(S1vec)
hatS2 = normalize_nested(S2vec)
#More spin parameters.
Delta = - scalar_nested(1/(1+q), (scalar_nested(q*chi2,hatS2)-scalar_nested(chi1,hatS1)) )
Delta_par = dot_nested(Delta,hatL)
Delta_perp = norm_nested(np.cross(Delta,hatL))
chit = scalar_nested(1/(1+q)**2, (scalar_nested(chi2*q**2,hatS2)+scalar_nested(chi1,hatS1)) )
chit_par = dot_nested(chit,hatL)
chit_perp = norm_nested(np.cross(chit,hatL))
#Coefficients are quoted in km/s
#vm and vperp from Kesden at 2010a. vpar from Lousto Zlochower 2013
zeta=np.radians(145)
A=1.2e4
B=-0.93
H=6.9e3
#Multiply by 0/1 boolean flags to select terms
V11 = 3677.76 * superkick
VA = 2481.21 * hangupkick
VB = 1792.45 * hangupkick
VC = 1506.52 * hangupkick
C2 = 1140 * crosskick
C3 = 2481 * crosskick
#maxkick
bigTheta=np.random.uniform(0, 2*np.pi,q.shape) * (not maxphase)
vm = A * eta**2 * (1+B*eta) * (1-q)/(1+q)
vperp = H * eta**2 * Delta_par
vpar = 16*eta**2 * (Delta_perp * (V11 + 2*VA*chit_par + 4*VB*chit_par**2 + 8*VC*chit_par**3) + chit_perp * Delta_par * (2*C2 + 4*C3*chit_par)) * np.cos(bigTheta)
kick = np.array([vm+vperp*np.cos(zeta),vperp*np.sin(zeta),vpar]).T
if not kms:
kick = kick/299792.458 # speed of light in km/s
vk = norm_nested(kick)
if full_output:
return np.concatenate([vk[:, None], kick], axis=-1)
else:
return vk
| (theta1, theta2, deltaphi, q, chi1, chi2, kms=False, maxphase=False, superkick=True, hangupkick=True, crosskick=True, full_output=False) | [
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] |
20,905 | precession.precession | remnantmass |
Estimate the final mass of the post-merger renmant. We implement the fitting
formula to numerical relativity simulations by Barausse Morozova Rezzolla
2012. This formula has to be applied *close to merger*, where numerical
relativity simulations are available. You should do a PN evolution to
transfer binaries to r~10M.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
mfin: float
Mass of the black-hole remnant.
Examples
--------
``mfin = precession.remnantmass(theta1,theta2,q,chi1,chi2)``
| def remnantmass(theta1, theta2, q, chi1, chi2):
"""
Estimate the final mass of the post-merger renmant. We implement the fitting
formula to numerical relativity simulations by Barausse Morozova Rezzolla
2012. This formula has to be applied *close to merger*, where numerical
relativity simulations are available. You should do a PN evolution to
transfer binaries to r~10M.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
mfin: float
Mass of the black-hole remnant.
Examples
--------
``mfin = precession.remnantmass(theta1,theta2,q,chi1,chi2)``
"""
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
eta = eval_eta(q).astype(float)
chit_par = ( chi2*q**2 * np.cos(theta2) + chi1*np.cos(theta1) ) / (1+q)**2
#Final mass. Barausse Morozova Rezzolla 2012
p0 = 0.04827
p1 = 0.01707
Z1 = 1 + (1-chit_par**2)**(1/3)* ((1+chit_par)**(1/3)+(1-chit_par)**(1/3))
Z2 = (3* chit_par**2 + Z1**2)**(1/2)
risco = 3 + Z2 - np.sign(chit_par) * ((3-Z1)*(3+Z1+2*Z2))**(1/2)
Eisco = (1-2/(3*risco))**(1/2)
#Radiated energy, in units of the initial total mass of the binary
Erad = eta*(1-Eisco) + 4* eta**2 * (4*p0+16*p1*chit_par*(chit_par+1)+Eisco-1)
Mfin = 1- Erad # Final mass
return Mfin
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20,906 | precession.precession | remnantspin |
Estimate the final spin of the post-merger renmant. We implement the fitting
formula to numerical relativity simulations by Barausse and Rezzolla 2009
and Hofmann, Barausse and Rezzolla 2016. This can be selected by the keywork `
`which`, see those references for details. By default this returns the
Hofmann+ expression with nM=3, nJ=4 and corrections for the effective
angles (HBR16_34corr). This formula has to be applied *close to merger*,
where numerical relativity simulations are available. You should do a PN
evolution to transfer binaries at r~10M.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
which: string, optional (default: 'HBR16_34corr')
Select function behavior.
Returns
-------
chifin: float
Spin of the black-hole remnant.
Examples
--------
``chifin = precession.remnantspin(theta1,theta2,deltaphi,q,chi1,chi2)``
| def remnantspin(theta1, theta2, deltaphi, q, chi1, chi2, which='HBR16_34corr'):
"""
Estimate the final spin of the post-merger renmant. We implement the fitting
formula to numerical relativity simulations by Barausse and Rezzolla 2009
and Hofmann, Barausse and Rezzolla 2016. This can be selected by the keywork `
`which`, see those references for details. By default this returns the
Hofmann+ expression with nM=3, nJ=4 and corrections for the effective
angles (HBR16_34corr). This formula has to be applied *close to merger*,
where numerical relativity simulations are available. You should do a PN
evolution to transfer binaries at r~10M.
Parameters
----------
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
which: string, optional (default: 'HBR16_34corr')
Select function behavior.
Returns
-------
chifin: float
Spin of the black-hole remnant.
Examples
--------
``chifin = precession.remnantspin(theta1,theta2,deltaphi,q,chi1,chi2)``
"""
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
eta = eval_eta(q).astype(float)
if which in ['HBR16_12', 'HBR16_12corr', 'HBR16_33', 'HBR16_33corr', 'HBR16_34', 'HBR16_34corr']:
kfit = {}
if 'HBR16_12' in which:
kfit = np.array( [[np.nan, -1.2019, -1.20764] ,
[3.79245, 1.18385, 4.90494] ] )
xifit = 0.41616
if 'HBR16_33' in which:
kfit = np.array( [[np.nan, 2.87025, -1.53315, -3.78893] ,
[32.9127, -62.9901, 10.0068, 56.1926],
[-136.832, 329.32, -13.2034, -252.27],
[210.075, -545.35, -3.97509, 368.405]] )
xifit = 0.463926
if 'HBR16_34' in which:
kfit = np.array( [[np.nan, 3.39221, 4.48865, -5.77101, -13.0459] ,
[35.1278, -72.9336, -86.0036, 93.7371, 200.975],
[-146.822, 387.184, 447.009, -467.383, -884.339],
[223.911, -648.502, -697.177, 753.738, 1166.89]])
xifit = 0.474046
# Calculate K00 from Eq 11
kfit[0,0] = 4**2 * ( 0.68646 - np.sum( kfit[1:,0] /(4**(3+np.arange(kfit.shape[0]-1)))) - (3**0.5)/2)
theta12 = eval_theta12(theta1=theta1, theta2=theta2, deltaphi=deltaphi)
# Eq. 18
if 'corr' in which:
eps1 = 0.024
eps2 = 0.024
eps12 = 0
theta1 = theta1 + eps1 * np.sin(theta1)
theta2 = theta2 + eps2 * np.sin(theta2)
theta12 = theta12 + eps12 * np.sin(theta12)
# Eq. 14 - 15
atot = ( chi1*np.cos(theta1) + chi2*np.cos(theta2)*q**2 ) / (1+q)**2
aeff = atot + xifit*eta* ( chi1*np.cos(theta1) + chi2*np.cos(theta2) )
# Eq. 2 - 6 evaluated at aeff, as specified in Eq. 11
Z1= 1 + (1-(aeff**2))**(1/3) * ( (1+aeff)**(1/3) + (1-aeff)**(1/3) )
Z2= ( (3*aeff**2) + (Z1**2) )**(1/2)
risco= 3 + Z2 - np.sign(aeff) * ( (3-Z1)*(3+Z1+2*Z2) )**(1/2)
Eisco=(1-2/(3*risco))**(1/2)
Lisco = (2/(3*(3**(1/2)))) * ( 1 + 2*(3*risco - 2 )**(1/2) )
# Eq. 13
etatoi = eta[:,np.newaxis]**(1+np.arange(kfit.shape[0]))
innersum = np.sum(kfit.T * etatoi[:,np.newaxis],axis=2)
aefftoj = aeff[:,np.newaxis]**(np.arange(kfit.shape[1]))
sumell = (np.sum(innersum * aefftoj,axis=1))
ell = np.abs( Lisco - 2*atot*(Eisco-1) + sumell )
# Eq. 16
chifin = (1/(1+q)**2) * ( chi1**2 + (chi2**2)*(q**4) + 2*chi1*chi2*(q**2)*np.cos(theta12)
+ 2*(chi1*np.cos(theta1) + chi2*(q**2)*np.cos(theta2))*ell*q + ((ell*q)**2) )**(1/2)
else:
raise ValueError("`which` needs to be one of the following: `HBR16_12`, `HBR16_12corr`, `HBR16_33`, `HBR16_33corr`, `HBR16_34`, `HBR16_34corr`.")
return np.minimum(chifin,1)
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20,908 | precession.precession | rhs_orbav |
Right-hand side of the systems of ODEs describing orbit-averaged inspiral. The equations are reported in Sec 4A of Gerosa and Kesden, arXiv:1605.01067. The format is d[allvars]/dv=RHS where allvars=[Lhx,Lhy,Lhz,S1hx,S1hy,S1hz,S2hx,S2hy,S2hz,t], h indicates unit vectors, v is the orbital velocity, and t is time.
This is an internal function used by the ODE integrator and is not array-compatible.
Parameters
----------
allvars: array
Packed ODE input variables.
v: float
Newtonian orbital velocity.
q: float
Mass ratio: 0<=q<=1.
m1: float
Mass of the primary (heavier) black hole.
m2: float
Mass of the secondary (lighter) black hole.
eta: float
Symmetric mass ratio 0<=eta<=1/4.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
S1: float
Magnitude of the primary spin.
S2: float
Magnitude of the secondary spin.
PNorderpre: array (default: [0,0.5])
PN orders considered in the spin-precession equations.
PNorderrad: array (default: [0,0.5])
PN orders considered in the radiation-reaction equation.
Returns
-------
RHS: float
Right-hand side.
Examples
--------
``RHS = precession.rhs_orbav(allvars,v,q,m1,m2,eta,chi1,chi2,S1,S2,PNorderpre=[0,0.5],PNorderrad=[0,1,1.5,2,2.5,3,3.5])``
| def rhs_orbav(allvars, v, q, m1, m2, eta, chi1, chi2, S1, S2, PNorderpre=[0,0.5], PNorderrad=[0,1,1.5,2,2.5,3,3.5]):
"""
Right-hand side of the systems of ODEs describing orbit-averaged inspiral. The equations are reported in Sec 4A of Gerosa and Kesden, arXiv:1605.01067. The format is d[allvars]/dv=RHS where allvars=[Lhx,Lhy,Lhz,S1hx,S1hy,S1hz,S2hx,S2hy,S2hz,t], h indicates unit vectors, v is the orbital velocity, and t is time.
This is an internal function used by the ODE integrator and is not array-compatible.
Parameters
----------
allvars: array
Packed ODE input variables.
v: float
Newtonian orbital velocity.
q: float
Mass ratio: 0<=q<=1.
m1: float
Mass of the primary (heavier) black hole.
m2: float
Mass of the secondary (lighter) black hole.
eta: float
Symmetric mass ratio 0<=eta<=1/4.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
S1: float
Magnitude of the primary spin.
S2: float
Magnitude of the secondary spin.
PNorderpre: array (default: [0,0.5])
PN orders considered in the spin-precession equations.
PNorderrad: array (default: [0,0.5])
PN orders considered in the radiation-reaction equation.
Returns
-------
RHS: float
Right-hand side.
Examples
--------
``RHS = precession.rhs_orbav(allvars,v,q,m1,m2,eta,chi1,chi2,S1,S2,PNorderpre=[0,0.5],PNorderrad=[0,1,1.5,2,2.5,3,3.5])``
"""
# Unpack inputs
Lh = allvars[0:3]
S1h = allvars[3:6]
S2h = allvars[6:9]
t = allvars[9]
# Angles
ct1 = np.dot(S1h, Lh)
ct2 = np.dot(S2h, Lh)
ct12 = np.dot(S1h, S2h)
# Spin precession for S1
Omega1 = (0 in PNorderpre) * eta*v**5*(2+3*q/2)*Lh + (0.5 in PNorderpre) * v**6*(S2*S2h-3*S2*ct2*Lh-3*q*S1*ct1*Lh)/2
dS1hdt = np.cross(Omega1, S1h)
# Spin precession for S2
Omega2 = (0 in PNorderpre) * eta*v**5*(2+3/(2*q))*Lh + (0.5 in PNorderpre) * v**6*(S1*S1h-3*S1*ct1*Lh-3*S2*ct2*Lh/q)/2
dS2hdt = np.cross(Omega2, S2h)
# Conservation of angular momentum
dLhdt = -v*(S1*dS1hdt+S2*dS2hdt)/eta
dvdt = (32*eta*v**9/5) * (
+ (0 in PNorderrad) * 1
- (1 in PNorderrad)*v**2
* (743+924*eta)/336
+ (1.5 in PNorderrad) * v**3
* (4*np.pi
- chi1*ct1*(113*m1**2/12 + 25*eta/4)
- chi2*ct2*(113*m2**2/12 + 25*eta/4))
+ (2 in PNorderrad) * v**4
* (34103/18144 + 13661*eta/2016 + 59*eta**2/18
+ eta*chi1*chi2 * (721*ct1*ct2 - 247*ct12)/48
+ ((m1*chi1)**2 * (719*ct1**2-233))/96
+ ((m2*chi2)**2 * (719*ct2**2-233))/96)
- (2.5 in PNorderrad) * v**5
* np.pi*(4159+15876*eta)/672
+ (3 in PNorderrad)*v**6
* (16447322263/139708800 + 16*np.pi**2/3
- 1712*(0.5772156649+np.log(4*v))/105
+ (451*np.pi**2/48 - 56198689/217728)*eta
+ 541*eta**2/896 - 5605*eta**3/2592)
+ (3.5 in PNorderrad) * v**7
* np.pi*(-4415/4032 + 358675*eta/6048
+ 91495*eta**2/1512))
# Integrate in v, not in time
dtdv = 1./dvdt
dLhdv = dLhdt*dtdv
dS1hdv = dS1hdt*dtdv
dS2hdv = dS2hdt*dtdv
# Pack outputs
return np.concatenate([dLhdv, dS1hdv, dS2hdv, [dtdv]])
| (allvars, v, q, m1, m2, eta, chi1, chi2, S1, S2, PNorderpre=[0, 0.5], PNorderrad=[0, 1, 1.5, 2, 2.5, 3, 3.5]) | [
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20,909 | precession.precession | rhs_precav |
Right-hand side of the dkappa/du ODE describing precession-averaged inspiral.
This is an internal function used by the ODE integrator and is not array-compatible.
Parameters
----------
kappa: float
Asymptotic angular momentum.
u: float
Compactified separation 1/(2L).
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
RHS: float
Right-hand side.
Examples
--------
``RHS = precession.rhs_precav(kappa,u,chieff,q,chi1,chi2)``
| def rhs_precav(kappa, u, chieff, q, chi1, chi2):
"""
Right-hand side of the dkappa/du ODE describing precession-averaged inspiral.
This is an internal function used by the ODE integrator and is not array-compatible.
Parameters
----------
kappa: float
Asymptotic angular momentum.
u: float
Compactified separation 1/(2L).
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
RHS: float
Right-hand side.
Examples
--------
``RHS = precession.rhs_precav(kappa,u,chieff,q,chi1,chi2)``
"""
if u <= 0:
# In this case use analytic result
if q==1: # TODO: think about this again
Ssav = (chi1**2+q**4 * chi2**2)/(1 + q)**4 #- ( 2*q*(kappa*(1+q) -chieff)*(kappa*(1+q) -q*chieff)/((-1 + q)**2 *(1 + q)**2))
else:
Ssav = (chi1**2+q**4 * chi2**2)/(1 + q)**4 - ( 2*q*(kappa*(1+q) -chieff)*(kappa*(1+q) -q*chieff)/((1-q)**2 *(1 + q)**2))
else:
# I don't use deltachiroots here because I want to keep complex numbers. This is needed to sanitize the output in some tricky cases
coeffs = deltachicubic_coefficients(kappa, u, chieff, q, chi1, chi2)
coeffsr = deltachicubic_rescaled_coefficients(kappa, u, chieff, q, chi1, chi2, precomputedcoefficients=coeffs)
deltachiminus, deltachiplus, _ = np.squeeze(np.sort_complex(roots_vec(coeffs.T)))
_, _, deltachi3 = np.squeeze(np.sort_complex(roots_vec(coeffsr.T)))
# deltachiminus, deltachiplus are complex. This can happen if the binary is very close to a spin-orbit resonance
if np.iscomplex(deltachiminus) and np.iscomplex(deltachiplus):
warnings.warn("Sanitizing RHS output; too close to resonance. [rhs_precav].", Warning)
deltachiav = np.mean(np.real([deltachiminus, deltachiplus]))
# Normal case
else:
deltachiminus, deltachiplus, deltachi3 = np.real([deltachiminus, deltachiplus, deltachi3])
m = elliptic_parameter(kappa, u, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus, deltachiplus, deltachi3]))
deltachiav = inverseaffine( deltachitildeav(m), deltachiminus, deltachiplus)
Ssav = (2*kappa - chieff - (1-q)/(1+q)*deltachiav)/(2*u)
return float(Ssav)
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0.003360397182404995,
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0.009496774524450302
] |
20,910 | precession.precession | roots_vec |
Locate roots of polynomial using a vectorized version of numpy.roots.
Credit to stackoverflow user 'pv' (https://stackoverflow.com/a/35853977) for some of this code, which we generalize to accomodate equations of different degrees.
Parameters
----------
p: float
Polynomial coefficients.
Returns
-------
roots: float
Polynomial roots.
Examples
--------
``roots = precession.roots_vec(p)``
| def roots_vec(p): #, enforce=False):
"""
Locate roots of polynomial using a vectorized version of numpy.roots.
Credit to stackoverflow user 'pv' (https://stackoverflow.com/a/35853977) for some of this code, which we generalize to accomodate equations of different degrees.
Parameters
----------
p: float
Polynomial coefficients.
Returns
-------
roots: float
Polynomial roots.
Examples
--------
``roots = precession.roots_vec(p)``
"""
p = np.atleast_1d(p).astype(float)
non_zeros = np.count_nonzero(p, axis=1)
# Mask arrays with all zeros with a dummy equation
p[non_zeros==0,0]=1
#if not non_zeros.all()!=0:
# if enforce:
# raise ValueError("There is at least one coefficients line with all zeros [roots_vec_zeros].")
# else:
# warnings.warn("There is at least one coefficients line with all zeros [roots_vec_zeros].", Warning)
#https://stackoverflow.com/a/20361561
B = np.append(p, np.ones(p.shape[0])[:,None], axis=1)
nz = np.argmax(B!=0,axis=1)
rows, columns = np.ogrid[:p.shape[0], :p.shape[1]]
shift = np.copy(nz)
shift[shift > 0] -= p.shape[1]
columns = columns + shift[:, np.newaxis]
p = p[rows, columns]
n = p.shape[-1]
A = np.zeros(p.shape[:1] + (n-1, n-1), float)
A[..., 1:, :-1] = np.eye(n-2)
A[..., 0, :] = -p[..., 1:]/p[..., None, 0]
results = np.linalg.eigvals(A)
nansol = np.reshape(np.repeat(nz, results.shape[1], axis=0), results.shape)
resind = np.mgrid[0:results.shape[0], 0:results.shape[1]][1]
resind = np.where(resind<nansol, np.nan, results)
# Replace nans for arrays where it's all zeros
resind = np.where(non_zeros==0, np.ones(resind.shape).T*np.nan, resind.T).T
return resind
| (p) | [
0.009406143799424171,
-0.02708047442138195,
0.042867813259363174,
0.05074227973818779,
0.006073900498449802,
0.012032565660774708,
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0.03927629068493843,
0.02030075341463089,
0.03184356540441513,
-0.03322639688849449,
0.016709228977560997,
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-0.0739431381225586,
0.02500622533261776,
0.04060150682926178,
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0.051817815750837326,
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0.03241974487900734,
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0.014462125487625599,
-0.06549249589443207,
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0.04736202210187912,
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0.0037379697896540165,
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0.022086910903453827,
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0.0729060173034668,
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0.03722124919295311,
-0.01525917463004589,
-0.037605367600917816,
0.050319746136665344,
-0.03991008922457695,
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0.0688343420624733,
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0.01792881079018116,
0.058463092893362045,
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0.004964753519743681,
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] |
20,911 | precession.precession | rotate_nested |
Rotate a given vector vec to a frame such that the vector align_zaxis lies along z and the vector align_xzplane lies in the xz plane.
Parameters
----------
vec : array
Input array.
align_zaxis : array
Reference array.
align_xzplane : array
Reference array.
Returns
-------
vecrot : array
Rotated array.
Examples
--------
``vecrot = rotate_nested(vec, align_zaxis, align_xzplane)``
| def rotate_nested(vec, align_zaxis, align_xzplane):
"""
Rotate a given vector vec to a frame such that the vector align_zaxis lies along z and the vector align_xzplane lies in the xz plane.
Parameters
----------
vec : array
Input array.
align_zaxis : array
Reference array.
align_xzplane : array
Reference array.
Returns
-------
vecrot : array
Rotated array.
Examples
--------
``vecrot = rotate_nested(vec, align_zaxis, align_xzplane)``
"""
vec = np.atleast_2d(vec)
align_zaxis = np.atleast_2d(align_zaxis)
align_xzplane = np.atleast_2d(align_xzplane)
align_zaxis = normalize_nested(align_zaxis)
angle1 = np.arccos(align_zaxis[:,2])
vec1 = np.cross(align_zaxis,[0,0,1])
vec1 = normalize_nested(vec1)
r1 = scipy.spatial.transform.Rotation.from_rotvec(angle1[:,None] * vec1)
align_xzplane = r1.apply(align_xzplane)
align_xzplane[:,2]=0
align_xzplane = normalize_nested(align_xzplane)
angle2= -np.sign(align_xzplane[:,1])*np.arccos(align_xzplane[:,0])
vec2 = np.array([0,0,1])
r2 = scipy.spatial.transform.Rotation.from_rotvec(angle2[:,None] * vec2)
vecrot = r2.apply(r1.apply(vec))
return vecrot
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] |
20,912 | precession.precession | rupdown |
The critical separations r_ud+/- marking the region of the up-down precessional instability.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
rudm: float
Inner orbital separation in the up-down instability.
rudp: float
Outer orbital separation in the up-down instability.
Examples
--------
``rudp,rudm = precession.rupdown(q,chi1,chi2)``
| def rupdown(q, chi1, chi2):
"""
The critical separations r_ud+/- marking the region of the up-down precessional instability.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
rudm: float
Inner orbital separation in the up-down instability.
rudp: float
Outer orbital separation in the up-down instability.
Examples
--------
``rudp,rudm = precession.rupdown(q,chi1,chi2)``
"""
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
#Ignore q=1 "divide by zero" warning here
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=RuntimeWarning)
rudp = (chi1**0.5+(q*chi2)**0.5)**4/(1-q)**2
rudm = (chi1**0.5-(q*chi2)**0.5)**4/(1-q)**2
return np.stack([rudp, rudm])
| (q, chi1, chi2) | [
-0.058760855346918106,
0.025800535455346107,
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20,913 | precession.precession | sample_unitsphere |
Sample points uniformly on a sphere of unit radius. Returns array of shape (N,3).
Parameters
----------
N: integer, optional (default: 1)
Number of samples.
Returns
-------
vec: array
Vector in Cartesian coomponents.
Examples
--------
``vec = sample_unitsphere(N=1)``
| def sample_unitsphere(N=1):
"""
Sample points uniformly on a sphere of unit radius. Returns array of shape (N,3).
Parameters
----------
N: integer, optional (default: 1)
Number of samples.
Returns
-------
vec: array
Vector in Cartesian coomponents.
Examples
--------
``vec = sample_unitsphere(N=1)``
"""
vec = np.random.randn(3, N)
vec /= np.linalg.norm(vec, axis=0)
return vec.T
| (N=1) | [
-0.016927074640989304,
-0.01000920683145523,
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20,914 | precession.precession | scalar_nested |
Nested scalar product between a 1D and a 2D array.
Parameters
----------
k : float
Input scalar.
x : array
Input array.
Returns
-------
y : array
Scalar product array.
Examples
--------
``y = scalar_nested(k, x)``
| def scalar_nested(k, x):
"""
Nested scalar product between a 1D and a 2D array.
Parameters
----------
k : float
Input scalar.
x : array
Input array.
Returns
-------
y : array
Scalar product array.
Examples
--------
``y = scalar_nested(k, x)``
"""
return k[:,np.newaxis]*x
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] |
20,916 | precession.precession | tiler |
Repeat the quantity thing a numer of times give by the shape of shaper.
Parameters
----------
thing: float
Quantity to be repeated
shaper: array
Quantity providing the shape.
Returns
-------
thing: float
Quantity to be repeated
Examples
--------
``thing = precession.tiler(thing,shaper)``
| def tiler(thing,shaper):
"""
Repeat the quantity thing a numer of times give by the shape of shaper.
Parameters
----------
thing: float
Quantity to be repeated
shaper: array
Quantity providing the shape.
Returns
-------
thing: float
Quantity to be repeated
Examples
--------
``thing = precession.tiler(thing,shaper)``
"""
thing =np.atleast_1d(thing)
shaper =np.atleast_1d(shaper)
assert thing.ndim == 1 and shaper.ndim==1
return np.squeeze(np.tile(thing, np.shape(shaper)).reshape(len(shaper),len(thing)))
| (thing, shaper) | [
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20,917 | precession.precession | tofdeltachi |
Time as a function of deltachi on the precessional timescale (without radiation reaction).
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
cyclesign: integer, optional (default: 1)
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
t: float
Time.
Examples
--------
``t = precession.tofdeltachi(deltachi,kappa,r,chieff,q,chi1,chi2,cyclesign=1)``
| def tofdeltachi(deltachi, kappa , r, chieff, q, chi1, chi2, cyclesign=1, precomputedroots=None):
"""
Time as a function of deltachi on the precessional timescale (without radiation reaction).
Parameters
----------
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
r: float
Binary separation.
chieff: float
Effective spin.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
cyclesign: integer, optional (default: 1)
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
precomputedroots: array, optional (default: None)
Pre-computed output of deltachiroots for computational efficiency.
Returns
-------
t: float
Time.
Examples
--------
``t = precession.tofdeltachi(deltachi,kappa,r,chieff,q,chi1,chi2,cyclesign=1)``
"""
u= eval_u(r=r,q=q)
deltachiminus,deltachiplus,deltachi3 = deltachiroots(kappa, u, chieff, q, chi1, chi2, precomputedroots=precomputedroots)
psiperiod = eval_tau(kappa, r, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]), return_psiperiod=True)
deltachitilde = affine(deltachi,deltachiminus,deltachiplus)
m = elliptic_parameter(kappa, u, chieff, q, chi1, chi2, precomputedroots=np.stack([deltachiminus,deltachiplus,deltachi3]))
t = np.sign(cyclesign) * psiperiod * scipy.special.ellipkinc(np.arcsin(deltachitilde**(1/2)), m)
return t
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] |
20,918 | precession.precession | updown_endpoint |
Endpoint of the up-down precessional instability.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
Examples
--------
``theta1,theta2,deltaphi = precession.updown_endpoint(q,chi1,chi2)``
| def updown_endpoint(q, chi1, chi2):
"""
Endpoint of the up-down precessional instability.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
Examples
--------
``theta1,theta2,deltaphi = precession.updown_endpoint(q,chi1,chi2)``
"""
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
costhetaupdown = (chi1 - q * chi2) / (chi1 + q * chi2)
theta1 = np.arccos(costhetaupdown)
theta2 = np.arccos(costhetaupdown)
deltaphi = np.zeros(len(theta1))
return np.stack([theta1, theta2, deltaphi])
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] |
20,919 | precession.precession | vectors_to_Jframe |
Rotate vectors of the three momenta onto a frame where J is along z and L lies in the x-z plane.
Parameters
----------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Returns
-------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Examples
--------
``Lvec,S1vec,S2vec = precession.vectors_to_Jframe(Lvec,S1vec,S2vec)``
| def vectors_to_Jframe(Lvec, S1vec, S2vec):
"""
Rotate vectors of the three momenta onto a frame where J is along z and L lies in the x-z plane.
Parameters
----------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Returns
-------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Examples
--------
``Lvec,S1vec,S2vec = precession.vectors_to_Jframe(Lvec,S1vec,S2vec)``
"""
Jvec = Lvec + S1vec + S2vec
rotation = lambda vec: rotate_nested(vec, Jvec, Lvec)
Lvecrot = rotation(Lvec)
S1vecrot = rotation(S1vec)
S2vecrot = rotation(S2vec)
return np.stack([Lvecrot, S1vecrot, S2vecrot])
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] |
20,920 | precession.precession | vectors_to_Lframe |
Rotate vectors of the three momenta onto a frame where L is along z and S1 lies in the x-z plane.
Parameters
----------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Returns
-------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Examples
--------
``Lvec,S1vec,S2vec = precession.vectors_to_Lframe(Lvec,S1vec,S2vec)``
| def vectors_to_Lframe(Lvec, S1vec, S2vec):
"""
Rotate vectors of the three momenta onto a frame where L is along z and S1 lies in the x-z plane.
Parameters
----------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Returns
-------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Examples
--------
``Lvec,S1vec,S2vec = precession.vectors_to_Lframe(Lvec,S1vec,S2vec)``
"""
Jvec = Lvec + S1vec + S2vec
rotation = lambda vec: rotate_nested(vec, Lvec, S1vec)
Lvecrot = rotation(Lvec)
S1vecrot = rotation(S1vec)
S2vecrot = rotation(S2vec)
return np.stack([Lvecrot, S1vecrot, S2vecrot])
| (Lvec, S1vec, S2vec) | [
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] |
20,921 | precession.precession | vectors_to_angles |
Convert cartesian vectors (L,S1,S2) into angles (theta1,theta2,deltaphi).
Parameters
----------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Returns
-------
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
Examples
--------
``theta1,theta2,deltaphi = precession.vectors_to_angles(Lvec,S1vec,S2vec)``
| def vectors_to_angles(Lvec, S1vec, S2vec):
"""
Convert cartesian vectors (L,S1,S2) into angles (theta1,theta2,deltaphi).
Parameters
----------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
Returns
-------
deltaphi: float
Angle between the projections of the two spins onto the orbital plane.
theta1: float
Angle between orbital angular momentum and primary spin.
theta2: float
Angle between orbital angular momentum and secondary spin.
Examples
--------
``theta1,theta2,deltaphi = precession.vectors_to_angles(Lvec,S1vec,S2vec)``
"""
Lvec = np.atleast_2d(Lvec).astype(float)
S1vec = np.atleast_2d(S1vec).astype(float)
S2vec = np.atleast_2d(S2vec).astype(float)
S1vec = normalize_nested(S1vec)
S2vec = normalize_nested(S2vec)
Lvec = normalize_nested(Lvec)
theta1 = np.arccos(dot_nested(S1vec, Lvec))
theta2 = np.arccos(dot_nested(S2vec, Lvec))
S1crL = np.cross(S1vec, Lvec)
S2crL = np.cross(S2vec, Lvec)
absdeltaphi = np.arccos(dot_nested(normalize_nested(S1crL), normalize_nested(S2crL)))
cyclesign = eval_cyclesign(Lvec=Lvec, S1vec=S1vec, S2vec=S2vec)
deltaphi = absdeltaphi*cyclesign
return np.stack([theta1, theta2, deltaphi])
| (Lvec, S1vec, S2vec) | [
-0.032074496150016785,
-0.02971387282013893,
0.010838257148861885,
0.008529155515134335,
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] |
20,922 | precession.precession | vectors_to_conserved |
Convert vectors (L,S1,S2) to conserved quanties (deltachi,kappa,chieff).
Parameters
----------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
q: float
Mass ratio: 0<=q<=1.
full_output: boolean, optional (default: False)
Return additional outputs.
Returns
-------
chieff: float
Effective spin.
cyclesign: integer, optional
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
Examples
--------
``deltachi,kappa,chieff = precession.vectors_to_conserved(Lvec,S1vec,S2vec,q)``
``deltachi,kappa,chieff,cyclesign = precession.vectors_to_conserved(Lvec,S1vec,S2vec,q,full_output=True)``
| def vectors_to_conserved(Lvec, S1vec, S2vec, q,full_output=False):
"""
Convert vectors (L,S1,S2) to conserved quanties (deltachi,kappa,chieff).
Parameters
----------
Lvec: array
Cartesian vector of the orbital angular momentum.
S1vec: array
Cartesian vector of the primary spin.
S2vec: array
Cartesian vector of the secondary spin.
q: float
Mass ratio: 0<=q<=1.
full_output: boolean, optional (default: False)
Return additional outputs.
Returns
-------
chieff: float
Effective spin.
cyclesign: integer, optional
Sign (either +1 or -1) to cover the two halves of a precesion cycle.
deltachi: float
Weighted spin difference.
kappa: float
Asymptotic angular momentum.
Examples
--------
``deltachi,kappa,chieff = precession.vectors_to_conserved(Lvec,S1vec,S2vec,q)``
``deltachi,kappa,chieff,cyclesign = precession.vectors_to_conserved(Lvec,S1vec,S2vec,q,full_output=True)``
"""
L = norm_nested(Lvec)
S1 = norm_nested(S1vec)
S2 = norm_nested(S2vec)
r = eval_r(L=L,q=q)
chi1 = eval_chi1(q,S1)
chi2 = eval_chi2(q,S2)
theta1,theta2,deltaphi = vectors_to_angles(Lvec, S1vec, S2vec)
deltachi, kappa, chieff, cyclesign= angles_to_conserved(theta1, theta2, deltaphi, r, q, chi1, chi2, full_output=True)
if full_output:
return np.stack([deltachi, kappa, chieff, cyclesign])
else:
return np.stack([deltachi, kappa, chieff])
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] |
20,924 | precession.precession | widenutation_condition |
Conditions for wide nutation to take place. The returned flag which is
- `wide1` if wide nutation is allowed for the primary BH.
- `wide2` if wide nutation is allowed for the secondary BH.
- `nowide` if wide nutation is not allowed.
Parameters
----------
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chieff: float
Effective spin.
kappa: float
Asymptotic angular momentum.
which: string
Select function behavior.
Examples
--------
``which,kappa,chieff = precession.widenutation_condition(r,q,chi1,chi2)``
| def widenutation_condition(r, q, chi1, chi2):
"""
Conditions for wide nutation to take place. The returned flag which is
- `wide1` if wide nutation is allowed for the primary BH.
- `wide2` if wide nutation is allowed for the secondary BH.
- `nowide` if wide nutation is not allowed.
Parameters
----------
r: float
Binary separation.
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
chieff: float
Effective spin.
kappa: float
Asymptotic angular momentum.
which: string
Select function behavior.
Examples
--------
``which,kappa,chieff = precession.widenutation_condition(r,q,chi1,chi2)``
"""
r = np.atleast_1d(r).astype(float)
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
rwide = widenutation_separation(q, chi1, chi2)
kappawide1 = (chi1**2 - 2*q*chi1**2 + q**4*chi2**2 - 2*q**2*(1-q)*r)/(2*q*(1+q)**2 * r**0.5)
chieffwide1 = -(1-q)*r**0.5/(1+q)
kappawide2 = (chi1**2 - 2*q**3*chi1**2 + q**4*chi2**2 + 2*q*(1-q)*r)/(2*q*(1+q)**2 * r**0.5)
chieffwide2 = (1-q)*r**0.5/(1+q)
which = np.where(r<=rwide, np.where(chi1<=chi2,"wide1","wide2"), "nowide")
kappa = np.where(r<=rwide, np.where(chi1<=chi2,kappawide1,kappawide2), np.nan)
chieff = np.where(r<=rwide, np.where(chi1<=chi2,chieffwide1,chieffwide2), np.nan)
return np.stack[(which, kappa, chieff)]
| (r, q, chi1, chi2) | [
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] |
20,925 | precession.precession | widenutation_separation |
The critical separation r_wide below which the binary component with
smaller dimensionless spin may undergo wide nutations.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
r_wide: float
Orbital separation where wide nutations becomes possible.
Examples
--------
``r_wide = precession.widenutation_separation(q,chi1,chi2)``
| def widenutation_separation(q, chi1, chi2):
"""
The critical separation r_wide below which the binary component with
smaller dimensionless spin may undergo wide nutations.
Parameters
----------
q: float
Mass ratio: 0<=q<=1.
chi1: float
Dimensionless spin of the primary (heavier) black hole: 0<=chi1<=1.
chi2: float
Dimensionless spin of the secondary (lighter) black hole: 0<=chi2<=1.
Returns
-------
r_wide: float
Orbital separation where wide nutations becomes possible.
Examples
--------
``r_wide = precession.widenutation_separation(q,chi1,chi2)``
"""
q = np.atleast_1d(q).astype(float)
chi1 = np.atleast_1d(chi1).astype(float)
chi2 = np.atleast_1d(chi2).astype(float)
rwide = ((chi1 - q*chi2) / (1-q))**2
return rwide
| (q, chi1, chi2) | [
-0.05320606380701065,
0.045944154262542725,
0.015197880566120148,
0.00504648732021451,
0.022846251726150513,
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20,926 | precession.precession | wraproots |
Find roots of a polynomial given coefficients, ordered according to their real part. Complex roots are masked with nans. This is essentially a wrapper of numpy.roots.
Parameters
----------
coefficientfunction: callable
Function returning the polynomial coefficients ordered from highest to lowest degree.
*args, **kwargs:
Parameters of `coefficientfunction`.
Returns
-------
sols: array
Roots of the polynomial.
Examples
--------
``sols = precession.wraproots(coefficientfunction, *args, **kwargs)``
| def wraproots(coefficientfunction, *args, **kwargs):
"""
Find roots of a polynomial given coefficients, ordered according to their real part. Complex roots are masked with nans. This is essentially a wrapper of numpy.roots.
Parameters
----------
coefficientfunction: callable
Function returning the polynomial coefficients ordered from highest to lowest degree.
*args, **kwargs:
Parameters of `coefficientfunction`.
Returns
-------
sols: array
Roots of the polynomial.
Examples
--------
``sols = precession.wraproots(coefficientfunction, *args, **kwargs)``
"""
coeffs = coefficientfunction(*args, **kwargs)
sols = np.sort_complex(roots_vec(coeffs.T))
sols = np.real(np.where(np.isreal(sols), sols, np.nan))
return sols
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20,928 | pproxy.server | proxies_by_uri | null | def proxies_by_uri(uri_jumps):
jump = DIRECT
for uri in reversed(uri_jumps.split('__')):
jump = proxy_by_uri(uri, jump)
return jump
| (uri_jumps) | [
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20,929 | pproxy.server | compile_rule | null | def compile_rule(filename):
if filename.startswith("{") and filename.endswith("}"):
return re.compile(filename[1:-1]).match
with open(filename) as f:
return re.compile('(:?'+''.join('|'.join(i.strip() for i in f if i.strip() and not i.startswith('#')))+')$').match
| (filename) | [
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] |
20,934 | qt_api | example_function | null | def example_function():
return 1 + 1
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] |
20,935 | argufy.formatter | ArgufyHelpFormatter | Provide formatting for Argufy. | class ArgufyHelpFormatter(HelpFormatter):
"""Provide formatting for Argufy."""
# argparse.HelpFormatter(prog, max_help_position=80, width=130)
def add_usage(
self,
usage: Optional[str],
actions: Iterable[Action],
# groups: Iterable['ArgumentGroup'],
groups: Iterable['MutuallyExclusiveGroup'],
prefix: Optional[str] = 'usage: ',
) -> None:
"""Format usage message."""
if prefix is not None:
prefix = self.font(prefix)
super().add_usage(usage, actions, groups, prefix)
@staticmethod
def font(text: str, width: str = 'BRIGHT') -> str:
"""Set the string thickness."""
return getattr(Style, width) + text + Style.RESET_ALL
@staticmethod
def shade(text: str, color: str = 'CYAN') -> str:
"""Set the string color."""
return getattr(Fore, color.upper()) + text + Style.RESET_ALL
# def _format_action_invocation(self, action: Action) -> str:
# """Format arguments summary."""
# # TODO: find alternative that does not modify action
# if isinstance(action, argparse._SubParsersAction):
# if action.choices is not None:
# for choice in list(action.choices):
# parser = action.choices.pop(choice)
# choice = self.shade(choice)
# action.choices[choice] = parser
# return super(
# ArgufyHelpFormatter, self
# )._format_action_invocation(action)
def _expand_help(self, action: Action) -> str:
"""Format help message."""
if action.help:
return self.shade(
super()._expand_help(action).rstrip('.').lower(),
'YELLOW',
)
return ''
def _format_action(self, action: Action) -> str:
"""Format arguments."""
if isinstance(action, argparse._SubParsersAction._ChoicesPseudoAction):
subcommand = self.shade(
self.font(self._format_action_invocation(action))
)
help_text = self._expand_help(action)
# TODO: calculate correct spacing
return f" {subcommand.ljust(37)}{help_text}\n"
# action.option_strings = [
# self.font(self.shade(option))
# for option in action.option_strings
# ]
return super()._format_action(action)
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20,936 | argparse | __init__ | null | def __init__(self,
prog,
indent_increment=2,
max_help_position=24,
width=None):
# default setting for width
if width is None:
import shutil
width = shutil.get_terminal_size().columns
width -= 2
self._prog = prog
self._indent_increment = indent_increment
self._max_help_position = min(max_help_position,
max(width - 20, indent_increment * 2))
self._width = width
self._current_indent = 0
self._level = 0
self._action_max_length = 0
self._root_section = self._Section(self, None)
self._current_section = self._root_section
self._whitespace_matcher = _re.compile(r'\s+', _re.ASCII)
self._long_break_matcher = _re.compile(r'\n\n\n+')
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20,939 | argufy.formatter | _expand_help | Format help message. | def _expand_help(self, action: Action) -> str:
"""Format help message."""
if action.help:
return self.shade(
super()._expand_help(action).rstrip('.').lower(),
'YELLOW',
)
return ''
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20,940 | argparse | _fill_text | null | def _fill_text(self, text, width, indent):
text = self._whitespace_matcher.sub(' ', text).strip()
import textwrap
return textwrap.fill(text, width,
initial_indent=indent,
subsequent_indent=indent)
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] |
20,941 | argufy.formatter | _format_action | Format arguments. | def _format_action(self, action: Action) -> str:
"""Format arguments."""
if isinstance(action, argparse._SubParsersAction._ChoicesPseudoAction):
subcommand = self.shade(
self.font(self._format_action_invocation(action))
)
help_text = self._expand_help(action)
# TODO: calculate correct spacing
return f" {subcommand.ljust(37)}{help_text}\n"
# action.option_strings = [
# self.font(self.shade(option))
# for option in action.option_strings
# ]
return super()._format_action(action)
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20,958 | argufy.formatter | add_usage | Format usage message. | def add_usage(
self,
usage: Optional[str],
actions: Iterable[Action],
# groups: Iterable['ArgumentGroup'],
groups: Iterable['MutuallyExclusiveGroup'],
prefix: Optional[str] = 'usage: ',
) -> None:
"""Format usage message."""
if prefix is not None:
prefix = self.font(prefix)
super().add_usage(usage, actions, groups, prefix)
| (self, usage: Optional[str], actions: Iterable[argparse.Action], groups: Iterable[ForwardRef('MutuallyExclusiveGroup')], prefix: Optional[str] = 'usage: ') -> None | [
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20,960 | argufy.formatter | font | Set the string thickness. | @staticmethod
def font(text: str, width: str = 'BRIGHT') -> str:
"""Set the string thickness."""
return getattr(Style, width) + text + Style.RESET_ALL
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20,962 | argufy.formatter | shade | Set the string color. | @staticmethod
def shade(text: str, color: str = 'CYAN') -> str:
"""Set the string color."""
return getattr(Fore, color.upper()) + text + Style.RESET_ALL
| (text: str, color: str = 'CYAN') -> str | [
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20,964 | argufy.argument | Argument | Represent argparse arguments. | class Argument: # pylint: disable=too-many-instance-attributes
"""Represent argparse arguments."""
__short_flags: List[str] = ['-h']
def __init__(
self,
docstring: Optional[DocstringParam] = None,
parameters: Optional[Parameter] = None,
) -> None:
"""Initialize argparse argument."""
# self.attributes: Dict[Any, Any] = {}
# set parameter default
if parameters:
self.default = parameters.default
self.name = parameters # type: ignore
else:
self.default = None
# set parameter type
if parameters and parameters.annotation != empty:
self.__parse_parameters(parameters)
elif docstring and docstring.type_name:
self.__parse_docstring(docstring)
elif self.default is not None:
self.type = type(self.default)
# if hasattr(self, 'type'):
# self.metavar = (self.type.__name__)
# set parameter help message
if docstring and docstring.description:
self.help = docstring.description
def __parse_parameters(self, parameters: Parameter) -> None:
"""Get parameter types from type inspection."""
# if typing.get_origin(parameters.annotation) is Union:
# XXX need to handle types from typing
# print(
# '---', parameters.annotation,
# typing.get_origin(parameters.annotation),
# )
if hasattr(parameters.annotation, '__origin__'):
annotation = typing.get_args(parameters.annotation)
# print('annotation', annotation, parameters.annotation)
# check if annotation is optional
if type(None) in annotation:
self.nargs = '?'
else:
# self.type = annotation
self.type = typing.get_origin(parameters.annotation)
else:
self.type = parameters.annotation
def __parse_docstring(self, docstring: DocstringParam) -> None:
"""Get parameter types from docstring."""
# Parse docstring for parameter types and defaults
if docstring.type_name and ',' in docstring.type_name:
for arg in docstring.type_name.split(',', 1):
if not hasattr(self, 'type'):
# NOTE: Limit input that eval will parse
if arg.__class__.__module__ == 'builtins':
self.type = literal_eval(arg) if arg != 'str' else str
if arg.lower() == 'optional' and not hasattr(self, 'default'):
# XXX: should optional not exist instead of 'None'
self.default = None
# TODO: tighten regex
if re.search(r'^\s*\{.*\}\s*$', arg):
self.choices = literal_eval(arg.strip())
if not hasattr(self, 'type'):
# NOTE: Limit input that eval will parse
if docstring.type_name in (
('float', 'int', 'str', 'list', 'dict', 'tuple')
):
self.type = locate(docstring.type_name)
@property
def name(self) -> List[str]:
"""Get argparse command/argument name."""
return self.__name
@name.setter
def name(self, parameters: Parameter) -> None:
"""Set argparse command/argument name."""
name = parameters.name.replace('_', '-')
# parse positional argument
if not hasattr(self, 'default') and not str(parameters).startswith(
'**'
):
self.__name = [name]
if str(parameters).startswith('*'):
self.nargs = '*'
# parse optional argument
else:
if str(parameters).startswith('**'):
self.nargs = '*'
flags = [f"--{name}"]
# NOTE: check for conflicting flags
if '-' not in name:
# TODO: check if common short flag (ex: version)
n = name[:1]
if n not in Argument.__short_flags:
Argument.__short_flags.append(n)
flags.insert(0, f"-{n}")
elif n.upper() not in Argument.__short_flags:
Argument.__short_flags.append(n.upper())
flags.insert(0, f"-{n.upper()}")
self.__name = flags
@property
def type(self) -> Any:
"""Get argparse argument type."""
return self.__type # type: ignore
@type.setter
def type(self, annotation: Any) -> None:
"""Set argparse argument type."""
# log.debug('prematched annotation:', annotation)
# print(annotation)
if annotation == bool:
# NOTE: these store bool type internally
if self.default or not hasattr(self, 'default'):
self.action = 'store_false'
else:
self.action = 'store_true'
elif annotation == int:
self.__type = annotation
self.action = 'append'
elif annotation == list:
self.__type = lambda v: int(v) if v.isdigit() else v
self.action = 'append'
elif annotation == tuple:
self.__type = annotation
self.nargs = '+'
elif annotation == set:
self.__type = annotation
self.nargs = '+'
else:
# log.debug('unmatched annotation:', annotation)
self.__type = annotation
# self.nargs = 1
@property
def metavar(self) -> str:
"""Get argparse argument metavar."""
return self.__metavar
@metavar.setter
def metavar(self, metavar: str) -> None:
"""Set argparse argument metavar."""
# NOTE: Only positional arguments use metavars
if not hasattr(self, 'default'):
self.__metavar = metavar
# @property
# def const(self) -> str:
# """Get argparse argument const."""
# return self.__const
# @const.setter
# def const(self, const: str) -> None:
# """Set argparse argument const."""
# self.__const = const
# @property
# def dest(self) -> str:
# """Get argparse command/argument dest."""
# return self.__dest
# @dest.setter
# def dest(self, dest: str) -> None:
# """Set argparse command/argument dest."""
# self.__dest = dest
# @property
# def required(self) -> bool:
# """Get argparse required argument."""
# return self.__required
# @required.setter
# def required(self, required: bool) -> None:
# """Set argparse required argument."""
# self.__required = required
@property
def action(self) -> str:
"""Get argparse argument action."""
return self.__action
@action.setter
def action(self, action: str) -> None:
"""Set argparse argument action."""
self.__action = action
@property
def choices(self) -> List[str]:
"""Get argparse argument choices."""
return self.__choices
@choices.setter
def choices(self, choices: set) -> None:
"""Set argparse argument choices."""
self.__choices = list(choices)
@property
def nargs(self) -> Union[int, str]:
"""Get argparse argument nargs."""
return self.__nargs
@nargs.setter
def nargs(self, nargs: Union[int, str]) -> None:
"""Set argparse argument nargs."""
# TODO: map nargs to argparse with typing
# 1: set number of values
# ?: a single optional value
# *: a flexible list of values
# +: like * requiring at least one value
# REMAINDER: unused args
self.__nargs = nargs
@property
def default(self) -> Any:
"""Get argparse argument default."""
return self.__default
@default.setter
def default(self, default: Any) -> None:
"""Set argparse argument default."""
if default != empty:
self.__default = default
# XXX: this keeps conflicting with positional arguments
# else:
# self.__default = None
@property
def help(s | (docstring: Optional[docstring_parser.common.DocstringParam] = None, parameters: Optional[inspect.Parameter] = None) -> None | [
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20,965 | argufy.argument | __parse_docstring | Get parameter types from docstring. | def __parse_docstring(self, docstring: DocstringParam) -> None:
"""Get parameter types from docstring."""
# Parse docstring for parameter types and defaults
if docstring.type_name and ',' in docstring.type_name:
for arg in docstring.type_name.split(',', 1):
if not hasattr(self, 'type'):
# NOTE: Limit input that eval will parse
if arg.__class__.__module__ == 'builtins':
self.type = literal_eval(arg) if arg != 'str' else str
if arg.lower() == 'optional' and not hasattr(self, 'default'):
# XXX: should optional not exist instead of 'None'
self.default = None
# TODO: tighten regex
if re.search(r'^\s*\{.*\}\s*$', arg):
self.choices = literal_eval(arg.strip())
if not hasattr(self, 'type'):
# NOTE: Limit input that eval will parse
if docstring.type_name in (
('float', 'int', 'str', 'list', 'dict', 'tuple')
):
self.type = locate(docstring.type_name)
| (self, docstring: docstring_parser.common.DocstringParam) -> NoneType | [
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20,966 | argufy.argument | __parse_parameters | Get parameter types from type inspection. | def __parse_parameters(self, parameters: Parameter) -> None:
"""Get parameter types from type inspection."""
# if typing.get_origin(parameters.annotation) is Union:
# XXX need to handle types from typing
# print(
# '---', parameters.annotation,
# typing.get_origin(parameters.annotation),
# )
if hasattr(parameters.annotation, '__origin__'):
annotation = typing.get_args(parameters.annotation)
# print('annotation', annotation, parameters.annotation)
# check if annotation is optional
if type(None) in annotation:
self.nargs = '?'
else:
# self.type = annotation
self.type = typing.get_origin(parameters.annotation)
else:
self.type = parameters.annotation
| (self, parameters: inspect.Parameter) -> NoneType | [
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20,967 | argufy.argument | __init__ | Initialize argparse argument. | def __init__(
self,
docstring: Optional[DocstringParam] = None,
parameters: Optional[Parameter] = None,
) -> None:
"""Initialize argparse argument."""
# self.attributes: Dict[Any, Any] = {}
# set parameter default
if parameters:
self.default = parameters.default
self.name = parameters # type: ignore
else:
self.default = None
# set parameter type
if parameters and parameters.annotation != empty:
self.__parse_parameters(parameters)
elif docstring and docstring.type_name:
self.__parse_docstring(docstring)
elif self.default is not None:
self.type = type(self.default)
# if hasattr(self, 'type'):
# self.metavar = (self.type.__name__)
# set parameter help message
if docstring and docstring.description:
self.help = docstring.description
| (self, docstring: Optional[docstring_parser.common.DocstringParam] = None, parameters: Optional[inspect.Parameter] = None) -> NoneType | [
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20,968 | argufy.parser | Parser | Provide CLI parser for function. | class Parser(ArgumentParser):
"""Provide CLI parser for function."""
exclude_prefixes = ('@', '_')
def __init__(self, **kwargs: Any) -> None:
"""Initialize parser.
Parameters
----------
prog: str
The name of the program
usage: str
The string describing the program usage
description: str
Text to display before the argument help
epilog: str
Text to display after the argument help
parents: list
A list of ArgumentParser objects whose arguments should also
be included
formatter_class: Object
A class for customizing the help output
prefix_chars: char
The set of characters that prefix optional arguments
fromfile_prefix_chars: None
The set of characters that prefix files from which additional
arguments should be read
argument_default: None
The global default value for arguments
conflict_handler: Object
The strategy for resolving conflicting optionals
add_help: str
Add a -h/--help option to the parser
allow_abbrev: bool
Allows long options to be abbreviated if the abbreviation is
unambiguous
"""
# TODO: handle environment variables
module = self.__get_parent_module()
if module and module.__doc__:
docstring = docparse(module.__doc__)
if not kwargs.get('description'):
kwargs['description'] = docstring.short_description
if 'prog' not in kwargs:
kwargs['prog'] = module.__name__.split('.')[0]
if 'version' in kwargs:
self.prog_version = kwargs.pop('version')
# if 'prefix' in kwargs:
# self.prefix = kwargs.pop('prefix')
# else:
# self.prefix = kwargs['prog'].upper()
# log.debug(str(self.prefix))
if 'log_level' in kwargs:
log.setLevel(getattr(logging, kwargs.pop('log_level').upper()))
if 'log_handler' in kwargs:
log_handler = kwargs.pop('log_handler')
log.addHandler(logging.StreamHandler(log_handler))
self.use_module_args = kwargs.pop('use_module_args', False)
self.main_args_builder = kwargs.pop('main_args_builder', None)
self.command_type = kwargs.pop('command_type', None)
self.command_scheme = kwargs.pop('command_scheme', None)
if 'formatter_class' not in kwargs:
self.formatter_class = ArgufyHelpFormatter
super().__init__(**kwargs)
# NOTE: cannot move to formatter
self._positionals.title = ArgufyHelpFormatter.font(
self._positionals.title or 'arguments'
)
self._optionals.title = ArgufyHelpFormatter.font(
self._optionals.title or 'flags'
)
# XXX version lookup infinite loop when absent
if hasattr(self, 'prog_version'):
self.add_argument(
'--version',
action='version',
version=f"%(prog)s {self.prog_version}",
help='display application version',
)
@staticmethod
def __get_parent_module() -> Optional[ModuleType]:
"""Get name of module importing this module."""
stack = inspect.stack()
# TODO: need way to better identify parent module
stack_frame = stack[2]
result = inspect.getmodule(stack_frame[0]) or None
return result
@staticmethod
def __clean_args(argument: Argument) -> Dict[Any, Any]:
"""Retrieve cleaned parameters from an Argument."""
size = len('_Argument__')
return {
k[size:]: v
for k, v in vars(argument).items()
if k.startswith('_Argument__')
}
@staticmethod
def _get_excludes(exclude_prefixes: Tuple[str, ...] = tuple()) -> tuple:
"""Combine class excludes with instance."""
if exclude_prefixes != ():
return tuple(exclude_prefixes) + Parser.exclude_prefixes
return Parser.exclude_prefixes
@staticmethod
def __get_description(
name: str, docstring: 'Docstring'
) -> Optional['DocstringParam']:
"""Get argument description from docstring."""
return next((d for d in docstring.params if d.arg_name == name), None)
@staticmethod
def __get_keyword_args(
signature: 'Signature', docstring: 'Docstring'
) -> List[str]:
"""Get keyward arguments from docstring."""
return [
x.arg_name
for x in docstring.params
if x.arg_name not in list(signature.parameters)
]
@staticmethod
def __generate_parameter(name: str, module: ModuleType) -> Parameter:
"""Generate inpect parameter."""
parameter = Parameter(
name,
ParameterKind.POSITIONAL_OR_KEYWORD,
default=getattr(module, name),
annotation=empty,
)
return parameter
def add_commands( # pylint: disable=too-many-locals,too-many-branches
self,
module: ModuleType,
parser: Optional[ArgumentParser] = None,
exclude_prefixes: tuple = tuple(),
command_type: Optional[str] = None,
) -> 'Parser':
"""Add commands.
Parameters
----------
module: ModuleType,
Module used to import functions for CLI commands.
parser: ArgumentParser, optional
Parser used to append subparsers to create subcommands.
exclude_prefixes: tuple,
Methods from a module that should be excluded.
command_type: str, optional
Choose format type of commands to be created.
Returns
-------
self:
Return object itself to allow chaining functions.
"""
# use self or an existing parser
if not parser:
parser = self
parser.formatter_class = ArgufyHelpFormatter
module_name = module.__name__.split('.')[-1]
docstring = docparse(module.__doc__) if module.__doc__ else None
excludes = Parser._get_excludes(exclude_prefixes)
# use exsiting subparser or create a new one
if not any(isinstance(x, SubParsersAction) for x in parser._actions):
# TODO: use metavar for hidden commands
parser.add_subparsers(dest=module_name, parser_class=Parser)
# check if command exists
command = next(
(x for x in parser._actions if isinstance(x, SubParsersAction)),
None,
)
# set command name scheme
if command_type is None:
command_type = self.command_type
# create subcommand for command
if command_type == 'subcommand':
if command:
msg = docstring.short_description if docstring else None
subcommand = command.add_parser(
module_name.replace('_', '-'),
description=msg,
formatter_class=self.formatter_class,
help=msg,
)
subcommand.set_defaults(mod=module)
# append subcommand to exsiting command or create a new one
return self.add_commands(
module=module,
parser=subcommand,
exclude_prefixes=Parser._get_excludes(exclude_prefixes),
command_type='command',
)
# TODO: separate into method
# pylint: disable-next=too-many-nested-blocks
for name, value in inspect.getmembers(module):
# TODO: Possible singledispatch candidate
if not name.startswith(excludes):
# skip classes for now
if inspect.isclass(value):
# TODO: check if dataclass instance
# TODO: check if class instance
continue # pragma: no cover
# create commands from functions
if inspect.isfunction(value):
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20,969 | argufy.parser | __clean_args | Retrieve cleaned parameters from an Argument. | @staticmethod
def __clean_args(argument: Argument) -> Dict[Any, Any]:
"""Retrieve cleaned parameters from an Argument."""
size = len('_Argument__')
return {
k[size:]: v
for k, v in vars(argument).items()
if k.startswith('_Argument__')
}
| (argument: argufy.argument.Argument) -> Dict[Any, Any] | [
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] |
20,970 | argufy.parser | __generate_parameter | Generate inpect parameter. | @staticmethod
def __generate_parameter(name: str, module: ModuleType) -> Parameter:
"""Generate inpect parameter."""
parameter = Parameter(
name,
ParameterKind.POSITIONAL_OR_KEYWORD,
default=getattr(module, name),
annotation=empty,
)
return parameter
| (name: str, module: module) -> inspect.Parameter | [
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] |
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