def shift_isochrone(color, magnitude, distance : float, extinction : float):
    mu = 5*np.log10(distance) - 5 + extinction
    aptMag = mu + magnitude
    aptCol = 3.2*extinction + color
    return aptMag, aptCol

def interp_isochrone_age(iso, targetAge):
    logTargetAgeYr= np.log10(targetAge*1e9)
    ageKeys = list(iso.keys())
    distance = [(x-logTargetAgeYr, x) for x in ageKeys]
    below = sorted(filter(lambda x: x[0] <=0, distance), key=lambda x: abs(x[0]))
    above = sorted(filter(lambda x: x[0] > 0, distance), key=lambda x: x[0])
    isoBelow = iso[below[0][1]]
    isoAbove = iso[above[0][1]]
    age1 = isoBelow['log10_isochrone_age_yr'].iloc[0]
    age2 = isoAbove['log10_isochrone_age_yr'].iloc[0]
    
    
    def linearinterpolate(x, other, age1, age2):
        newIso = ((other[x.name] - x)/(age2-age1)) * (logTargetAgeYr - age1) + x
        return newIso
    
    interpolated = isoBelow.apply(lambda x: linearinterpolate(x, isoAbove, age1, age2))
    return interpolated, (isoBelow, isoAbove)

def iso_at_params(iso, age, d, E, f1, f2, f3):
    interpolated, _= interp_isochrone_age(iso, age)
    f1 = interpolated[f"WFC3_UVIS_{f1}_MAG"]
    f2 = interpolated[f"WFC3_UVIS_{f2}_MAG"]
    f3 = interpolated[f"WFC3_UVIS_{f3}_MAG"]
    return shift_isochrone(f1-f2, f3, d, E)