Three slightly different ways to do get stellar mass using the Torres calibration

fast.py

def massTorres(teff, erteff, logg, erlogg, feh, erfeh, 
                ntrials=10000, corrected=True):
    randomteff = teff + erteff * np.random.randn(ntrials)
    randomlogg = logg + erlogg * np.random.randn(ntrials)
    randomfeh = feh + erfeh * np.random.randn(ntrials)

    # Parameters for the Torres calibration
    a1 = 1.5689
    a2 = 1.3787
    a3 = 0.4243
    a4 = 1.139
    a5 = -0.1425
    a6 = 0.01969
    a7 = 0.1010

    X = np.log10(randomteff) - 4.1
    
    logMass = a1 + a2*X + a3*X**2 + a4*X**3 + a5*randomlogg**2 \
              + a6*randomlogg**3 + a7*randomfeh

    meanlogMass = np.mean(logMass)
    siglogMass = np.sum((logMass - meanlogMass)**2) / (ntrials - 1)
    siglogMassTot = np.sqrt(0.027*0.027 + siglogMass)

    meanMass = 10**meanlogMass
    sigMass = 10**(meanlogMass + siglogMassTot) - meanMass

    if corrected:
        # correction comes from Santos+(2013), the SWEET-Cat paper
        corrected_meanMass = 0.791 * meanMass**2 - 0.575 * meanMass + 0.701
        return corrected_meanMass, sigMass
    else:
        return meanMass, sigMass

faster.py

import numba
@numba.jit
def massTorres3(teff, erteff, logg, erlogg, feh, erfeh, 
                ntrials=10000, corrected=True):
    randomteff = teff + erteff * np.random.randn(ntrials)
    randomlogg = logg + erlogg * np.random.randn(ntrials)
    randomfeh = feh + erfeh * np.random.randn(ntrials)

    # Parameters for the Torres calibration
    a1 = 1.5689
    a2 = 1.3787
    a3 = 0.4243
    a4 = 1.139
    a5 = -0.1425
    a6 = 0.01969
    a7 = 0.1010

    X = np.log10(randomteff) - 4.1
    
    logMass = a1 + a2*X + a3*X**2 + a4*X**3 + a5*randomlogg**2 \
              + a6*randomlogg**3 + a7*randomfeh

    meanlogMass = np.mean(logMass)
    siglogMass = np.sum((logMass - meanlogMass)**2) / (ntrials - 1)
    siglogMassTot = np.sqrt(0.027*0.027 + siglogMass)

    meanMass = 10**meanlogMass
    sigMass = 10**(meanlogMass + siglogMassTot) - meanMass

    if corrected:
        # correction comes from Santos+(2013), the SWEET-Cat paper
        corrected_meanMass = 0.791 * meanMass**2 - 0.575 * meanMass + 0.701
        return corrected_meanMass, sigMass
    else:
        return meanMass, sigMass

slow.py

def massTorres(teff, erteff, logg, erlogg, feh, erfeh):
    ntrials = 10000
    randomteff = teff + erteff * np.random.randn(ntrials)
    randomlogg = logg + erlogg * np.random.randn(ntrials)
    randomfeh = feh + erfeh * np.random.randn(ntrials)

    # Parameters for the Torres calibration:
    a1 = 1.5689
    a2 = 1.3787
    a3 = 0.4243
    a4 = 1.139
    a5 = -0.1425
    a6 = 0.01969
    a7 = 0.1010

    M = np.zeros(ntrials)
    logM = np.zeros(ntrials)

    for i in range(len(randomteff)):
        X = np.log10(randomteff[i]) - 4.1
        logMass = a1 + a2 * X + a3 * X * X + a4 * X * X * X + a5 *\
            randomlogg[i] * randomlogg[i] + a6 * randomlogg[i] *\
            randomlogg[i] * randomlogg[i] + a7 * randomfeh[i]
        logM[i] = logMass
        M[i] = 10 ** logMass

    meanMasslog = np.mean(logM)
    sigMasslog = np.sqrt(np.sum([(logMi - meanMasslog)**2 for logMi in logM]) /
                         (ntrials - 1))
    sigMasslogTot = np.sqrt(0.027*0.027 + sigMasslog*sigMasslog)

    meanMass = 10**meanMasslog
    sigMass = 10**(meanMasslog + sigMasslogTot) - meanMass

    corrected_meanMass = 0.791 * meanMass**2 - 0.575 * meanMass + 0.701

    return corrected_meanMass, sigMass