P_astro_project.p_astro_utils
A place for storing the functions required for the P_astro analysis
Module Contents
Classes
A class for holding the spin calculation functions. |
Functions
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Ensure formatting of the input pdf for use in the cdf functions. |
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Compute the normalised CDF of the probability distribution x. |
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Create and normalise the cdf and return a sample from it. |
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Calculate the FAR using the parameterisations from the Lynch at al paper https://arxiv.org/abs/1803.02880. |
- P_astro_project.p_astro_utils.convert(pdf)
Ensure formatting of the input pdf for use in the cdf functions.
- Parameters
- pdf: pandas dataframe
The probability distribution of interest.
- Returns
- pdf: ndarray
The pdf converted to numpy.
- P_astro_project.p_astro_utils.cdf(pdf)
Compute the normalised CDF of the probability distribution x.
- Parameters
- pdf: ndarray
The probability distribution of interest.
- Returns
- cdf: ndarray
The normalised cumulative distribution of the input probability distribution.
- P_astro_project.p_astro_utils.cdf_samp(pdf, param)
Create and normalise the cdf and return a sample from it.
- Parameters
- pdf: ndarray
The probability distribution of interest.
- param: ndarray
The range of values the parameter being sampled can take.
- Returns
- sample: float or complex (corresponding to fp) or ndarray
Random sample from the cdf.
- class P_astro_project.p_astro_utils.spin(a1, a2, tilt_1, tilt_2, q)
A class for holding the spin calculation functions.
- chi_eff()
Compute the effective spin parameter, which is that aligned with the orbital angular momentum.
\[\chi_{eff} = \frac{a_{1}\cos{\theta_{1}} + q a_{2} \cos{\theta_{2}}}{1+q}\]- Parameters
- a1, a2: float
Spin magnitudes.
- tilt_1, tilt_2: float
The tilt angles for bodies 1 and 2.
- q: float
Mass ratio (\(\frac{m_2}{m_1}\)).
- Returns
- chi_eff: float
Effective spin parameter.
- chi_p()
Compute the effective spin precession parameter, which is that projected into the plane of the orbit.
\[\chi_{p} = max(a_{1}\sin{\theta_{1}}, \frac{4q + 3}{4+3q}qa_{2}\sin{\theta_2})\]- Parameters
- a1, a2: float
Spin magnitudes.
- tilt_1, tilt_2: float
The tilt angles for bodies 1 and 2.
- q: float
Mass ratio (\(\frac{m_2}{m_1}\)).
- Returns
- chi_p: float
Effective spin precession parameter.
- P_astro_project.p_astro_utils.SNR_to_FAR(snr, FAR8=5500, alpha=0.18)
Calculate the FAR using the parameterisations from the Lynch at al paper https://arxiv.org/abs/1803.02880.
\[\mathrm{FAR} = \mathrm{FAR}_8 \times \exp{\left[-\frac{\rho - 8}{\alpha}\right]}\]- Parameters
- snr: float
Signal to noise ratio.
- FAR8: float
The approximate false alarm rate for an SNR=8.
- alpha: float
The steepness of the exponential function (\(\alpha\))
- Returns
- FAR: float
The approximate false alarm rate for the input SNR.