Source code for gwinferno.preprocess.conversions
"""
a module that stores helpful conversion functions between parameters
"""
import numpy as np
[docs]
def chieff_from_q_component_spins(q, a1, a2, ct1, ct2):
r"""Calculate the effective spin from, mass ratio, component spin magnitudes
and tilts.
.. math::
\chi_\mathrm{eff} = \frac{a_1 \cos t_1 + q a_2 \cos \theta_2}{1 + q}
Parameters
----------
q : array_like
Mass ratio (defined from 0 to 1).
a1 : array_like
Spin magnitude of the primary component.
a2 : array_like
Spin magnitude of the secondary component.
ct1 : array_like
Cosine of the spin tilt of the primary component.
ct2 : array_like
Cosine of the spin tilt of the secondary component.
Returns
-------
array_like
Effective spin.
"""
return (a1 * ct1 + q * a2 * ct2) / (1.0 + q)
[docs]
def chip_from_q_component_spins(q, a1, a2, ct1, ct2, math=np):
"""Calculate the effective precessing spin, :math:`\chi_\mathrm{p}`, from
the mass ratio, component spin magnitudes and tilts.
Parameters
----------
q : array_like
Mass ratio (defined from 0 to 1).
a1 : array_like
Spin magnitude of the primary component.
a2 : array_like
Spin magnitude of the secondary component.
ct1 : array_like
Cosine of the spin tilt of the primary component.
ct2 : array_like
Cosine of the spin tilt of the secondary component.
math : module, default=`numpy`
Math module to use.
Returns
-------
array_like
Effective precessing spin.
"""
sint1 = math.sqrt(1.0 - ct1**2)
sint2 = math.sqrt(1.0 - ct2**2)
return math.maximum(a1 * sint1, ((3.0 + 4.0 * q) / (4.0 + 3.0 * q)) * q * a2 * sint2)
[docs]
def mu_var_from_alpha_beta(alpha, beta, xmax=1):
"""Convert α, β shape parameters of the Beta distribution to the mean and variance.
Parameters
----------
alpha : array_like
α shape parameter.
beta : array_like
β shape parameter.
xmax : array_like, default=1
Maximum value with support.
Returns
-------
array_like, array_like
Tuple of arrays with shape matching inputs that represent the
means and variances corresponding to the shape parameters.
"""
mu = alpha / (alpha + beta) * xmax
var = alpha * beta / ((alpha + beta) ** 2 * (alpha + beta + 1)) * xmax**2
return mu, var
[docs]
def alpha_beta_from_mu_var(mu, var, xmax=1):
"""Convert desired mean and variance to α, β shape parameters of the Beta distribution.
Parameters
----------
mean : array_like
Desired mean.
var : array_like
Desired variance.
xmax : array_like, default=1
Maximum value with support.
Returns
-------
array_like, array_like
Tuple of arrays with shape matching inputs that represent the
α, β shape parameters corresponding to the desired means and variances.
"""
mu /= xmax
var /= xmax**2
alpha = (mu**2 * (1 - mu) - mu * var) / var
beta = (mu * (1 - mu) ** 2 - (1 - mu) * var) / var
return alpha, beta
