def get_braganca_samples(df=None, size=1):
# Get the pdf function
vsini_pdf = get_braganca_pdf()
v = np.arange(0, 500, 0.1)
P = vsini_pdf(v)
# Convert to cdf
cdf = Priors.get_cdf(v, P)
# Remove duplicate cdf values
tmp = pd.DataFrame(data=dict(cdf=cdf, velocity=v))
tmp.drop_duplicates(subset=['cdf'], inplace=True)
# Calculate the inverse cdf
inv_cdf = spline(tmp.cdf.values, tmp.velocity.values, k=1)
# Calculate samples from the inverse cdf
velocity_samples = inv_cdf(np.random.uniform(size=size))
return velocity_samples
def get_zr2011_velocity(mass, size=1e4, reduce_arr=True, df=None):
"""
Get samples from the velocity pdf as tabulated
by Table 4 in Zorec & Royer (2011)
Parameters:
============
- mass: The mass of the star (in solar masses)
- size: The number of samples
- reduce_arr: Boolean flag. Should re only take the unique masses or all of them?
- df: A dataframe with all of the necessary columns. Don't give this
unless you know what you are doing!
Returns:
========
Samples from the PDF for the equatorial velocity (in km/s)
"""
# Read in and update the columns a bit.
if df is None:
df = pd.read_csv('data/velocity_pdfs.csv', header=1)
df['mid_mass'] = (df.mass_high + df.mass_low) / 2.0
df['slow_alpha'] = df.slow_mu / np.sqrt(2)
df['fast_alpha'] = df.fast_mu / np.sqrt(2)
df['slow_frac'] /= 100.0
df['fast_frac'] /= 100.0
# Reduce the size of the mass array, if requested
if reduce_arr:
mass = np.unique(mass)
# Interpolate the parameters as a function of mass
columns = ['slow_frac', 'slow_alpha', 'fast_frac', 'fast_alpha', 'fast_l']
interpolators = {col: spline(df.mid_mass, df[col], k=1) for col in columns}
pars = {col: interpolators[col](mass) for col in interpolators.keys()}
# Make large arrays. This may be memory intensive!
v_arr = np.arange(0, 500, 0.1)
v, slow_frac = np.meshgrid(v_arr, pars['slow_frac'])
v, slow_alpha = np.meshgrid(v_arr, pars['slow_alpha'])
v, fast_frac = np.meshgrid(v_arr, pars['fast_frac'])
v, fast_alpha = np.meshgrid(v_arr, pars['fast_alpha'])
v, fast_l = np.meshgrid(v_arr, pars['fast_l'])
# Get the probability for each mass point
prob = (slow_frac*maxwellian(v=v, alpha=slow_alpha, l=0.0) +
fast_frac*maxwellian(v=v, alpha=fast_alpha, l=fast_l))
# Marginalize over the mass
P_avg = np.mean(prob, axis=0)
# Convert to cdf
cdf = Priors.get_cdf(v_arr, P_avg)
# Remove duplicate cdf values
tmp = pd.DataFrame(data=dict(cdf=cdf, velocity=v_arr))
tmp.drop_duplicates(subset=['cdf'], inplace=True)
# Calculate the inverse cdf
inv_cdf = spline(tmp.cdf.values, tmp.velocity.values, k=1)
# Calculate samples from the inverse cdf
velocity_samples = inv_cdf(np.random.uniform(size=size))
return velocity_samples