"""
Module containing the spacing functions for the binarycpython package. Very under-populated at the moment, but more are likely to come soon
Tasks:
TODO: add more spacing functions to this module.
"""
from typing import Union
import functools
import math
import numpy as np
import py_rinterpolate
import sys
from binarycpython.utils.grid import Population
@functools.lru_cache(maxsize=16)
def const(
min_bound: Union[int, float], max_bound: Union[int, float], steps: int
) -> list:
"""
Samples a range linearly. Uses numpy linspace.
Args:
min_bound: lower bound of range
max_bound: upper bound of range
steps: number of segments between min_bound and max_bound
Returns:
np.linspace(min_bound, max_bound, steps+1)
"""
return np.linspace(min_bound, max_bound, steps + 1)
############################################################
@functools.lru_cache(maxsize=16)
def const_ranges(ranges) -> list:
"""
Samples a series of ranges linearly.
Args:
ranges: a tuple of tuples passed to the const() spacing function.
Returns:
numpy array of masses
Example:
The following allocates 10 stars between 0.1 and 0.65, 20 stars between 0.65
and 0.85, and 10 stars between 0.85 and 10.0 Msun.
spacingfunc="const_ranges((({},{},{}),({},{},{}),({},{},{})))".format(
0.1,0.65,10,
0.65,0.85,20,
0.85,10.0,10
),
"""
masses = np.empty(0)
for range in ranges:
masses = np.append(masses,const(*range))
return np.unique(masses)
############################################################
def peak_normalized_gaussian_func(
x: Union[int, float], mean: Union[int, float], sigma: Union[int, float]
) -> Union[int, float]:
"""
Function to evaluate a Gaussian at a given point, note
that the normalization is such that the peak is always 1.0,
not that the integral is 1.0
Args:
x: location at which to evaluate the distribution
mean: mean of the Gaussian
sigma: standard deviation of the Gaussian
Returns:
value of the Gaussian at x
"""
gaussian_prefactor = 1.0 # / math.sqrt(2.0 * math.pi)
r = 1.0 / sigma
y = (x - mean) * r
return math.exp(-0.5 * y ** 2)
############################################################
@functools.lru_cache(maxsize=16)
def gaussian_zoom(
min_bound: Union[int, float],
max_bound: Union[int, float],
zoom_mean: Union[int, float],
zoom_dispersion: Union[int, float],
zoom_magnitude: Union[int, float],
steps: int,
) -> list:
"""
Samples such that a region is zoomed in according to a 1-Gaussian function
Args:
min_bound: lower bound of range
max_bound: upper bound of range
zoom_mean: mean of the Gaussian zoom location
zoom_dispersion: dispersion of the Gaussian
zoom_magnitude: depth of the Gaussian (should be 0<= zoom_magntiude <1)
steps: number of segments between min_bound and max_bound assuming a linear step
this is what you'd normally call "resolution"
Returns:
Numpy array of sample values
"""
# linear spacing: this is what we'd have
# in the absence of a Gaussian zoom
linear_spacing = (max_bound - min_bound) / (steps - 1)
# make the list of values
x = min_bound
array = np.array([])
while x <= max_bound:
array = np.append(array, x)
g = peak_normalized_gaussian_func(x, zoom_mean, zoom_dispersion)
f = 1.0 - zoom_magnitude * g
dx = linear_spacing * f
x = x + dx
# force the last array member to be max_bound if it's not
if array[-1] != max_bound:
array[-1] = max_bound
return np.unique(array)
@functools.lru_cache(maxsize=16)
def const_dt(self,
dt=1000.0,
dlogt=0.1,
mmin=0.07,
mmax=100.0,
nres=1000,
logspacing=False,
tmin=3.0, # start at 3Myr
tmax=None, # use max_evolution_time by default
mindm=None, # tuple of tuples
maxdm=((0.07,1.0,0.1),(1.0,300.0,1.0)), # tuple of tuples
fsample=1.0,
factor=1.0,
logmasses=False,
log10masses=False,
showlist=False,
showtable=False):
"""
const_dt returns a list of masses spaced at a constant age difference
Args:
dt: the time difference between the masses (1000.0 Myr, used when logspacing==False)
dlogt : the delta log10(time) difference between masses (0.1 dex, used when logspacing==True)
mmin: the minimum mass to be considered in the stellar lifetime interpolation table (0.07 Msun)
mmax: the maximum mass to be considered in the stellar lifetime interpolation table (100.0 Msun)
nres: the resolution of the stellar lifetime interpolation table (100)
logspacing: whether to use log-spaced time, in which case dt is actually d(log10(t))
tmin: the minimum time to consider (Myr, default 3.0 Myr)
tmax: the maximum time to consider (Myr, default None which means we use the grid option 'max_evolution_time')
mindm: a tuple of tuples containing a mass range and minimum mass spacing in that range. The default is ((0.07,1.0,0.1),(1.0,300.0,1.0)) allocated a minimum dm of 0.1Msun in the mass range 0.07 to 1.0 Msun and 1.0Msun in the range 1.0 to 300.0 Msun. Anything you set overrides this. Note, if you use only one tuple, you must set it with a trailing comma, thus, e.g. ((0.07,1.0,0.1),). (default None)
maxdm: a list of tuples similar to mindm but specifying a maximum mass spacing. In the case of maxdm, if the third option in each tuple is negative it is treated as a log step (its absolute value is used as the step). (default None)
fsample: a global sampling (Shannon-like) factor (<1) to improve resolution (default 1.0, set to smaller to improve resolution)
factor: all masses generated are multiplied by this after generation
showtable: if True, the mass list and times are shown to stdout after generation
showlist: if True, show the mass list once generated
logmasses: if True, the masses are logged with math.log()
log10masses: if True, the masses are logged with math.log10()
Returns:
Array of masses.
Example:
# these are lines set as options to Population.add_grid_value(...)
# linear time bins of 1Gyr
spacingfunc="const_dt(self,dt=1000,nres=100,mmin=0.07,mmax=2.0,showtable=True)"
# logarithmic spacing in time, generally suitable for Galactic
# chemical evolution yield grids.
spacingfunc="const_dt(self,dlogt=0.1,nres=100,mmin=0.07,mmax=80.0,maxdm=((0.07,1.0,0.1),(1.0,10.0,1.0),(10.0,80.0,2.0)),showtable=True,logspacing=True,fsample=1.0/4.0)"
"""
# first, make a stellar lifetime table
#
# we should use the bse_options from self
# so our lifetime_population uses the same physics
lifetime_population = Population()
lifetime_population.bse_options = dict(self.bse_options)
# we only want to evolve the star during nuclear burning,
# we don't want a dry run of the grid
# we want to use the right number of CPU cores
lifetime_population.set(
do_dry_run = False,
num_cores = self.grid_options['num_cores'],
max_stellar_type_1=10
)
# make a grid in M1
lifetime_population.add_grid_variable(
name="lnM_1",
parameter_name="M_1",
longname="log Primary mass", # == single-star mass
valuerange=[math.log(mmin),math.log(mmax)],
resolution=0,
spacingfunc="const(math.log({mmin}),math.log({mmax}),{nres})".format(mmin=mmin,mmax=mmax,nres=nres),
probdist="1", # dprob/dm1 : we don't care, so just set it to 1
dphasevol="dlnM_1",
precode="M_1=math.exp(lnM_1)",
condition="", # Impose a condition on this grid variable. Mostly for a check for yourself
gridtype="edge"
)
# set up the parse function
def _parse_function(self,output):
if output:
for line in output.splitlines():
data = line.split()
if data[0] == 'SINGLE_STAR_LIFETIME':
# append (log10(mass), log10(lifetime)) tuples
logm = math.log10(float(data[1]))
logt = math.log10(float(data[2]))
#print(line)
#print("logM=",logm,"M=",10.0**logm," -> logt=",logt)
self.grid_results['interpolation table m->t'][logm] = logt
self.grid_results['interpolation table t->m'][logt] = logm
lifetime_population.set(
parse_function=_parse_function,
)
# run to build the interpolation table
print("Running population to make lifetime interpolation table, please wait")
lifetime_population.evolve()
#print("Data table",lifetime_population.grid_results['interpolation table t->m'])
# convert to nested lists for the interpolator
#
# make time -> mass table
data_table_time_mass = []
times = sorted(lifetime_population.grid_results['interpolation table t->m'].keys())
for time in times:
mass = lifetime_population.grid_results['interpolation table t->m'][time]
# we have to make sure the time is monotonic (not guaranteed at high mass)
if len(data_table_time_mass)==0:
data_table_time_mass.append( [ time, mass ] )
elif mass < data_table_time_mass[-1][1]:
data_table_time_mass.append( [ time, mass ] )
# make mass -> time table
data_table_mass_time = []
masses = sorted(lifetime_population.grid_results['interpolation table m->t'].keys())
for mass in masses:
time = lifetime_population.grid_results['interpolation table m->t'][mass]
data_table_mass_time.append( [ mass, time ] )
# set up interpolators
interpolator_time_mass = py_rinterpolate.Rinterpolate(
table = data_table_time_mass,
nparams = 1, # mass
ndata = 1, # lifetime
verbosity = 0)
interpolator_mass_time = py_rinterpolate.Rinterpolate(
table = data_table_mass_time,
nparams = 1, # lifetime
ndata = 1, # mass
verbosity = 0)
# function to get a mass given a time (Myr)
def _mass_from_time(linear_time):
return 10.0**interpolator_time_mass.interpolate([math.log10(linear_time)])[0]
# function to get a time given a mass (Msun)
def _time_from_mass(mass):
return 10.0**interpolator_mass_time.interpolate([math.log10(mass)])[0]
# return a unique list
def _uniq(_list):
return sorted(list(set(_list)))
# format a whole list like %g
def _format(_list):
return [ float("{x:g}".format(x=x)) for x in _list]
# construct mass list, always include the min and max
mass_list = [mmin,mmax]
# first, make sure the stars are separated by only
# maxdm
if maxdm:
for x in maxdm:
range_min = x[0]
range_max = x[1]
dm = x[2]
if dm < 0.0:
# use log scale
dlogm = -dm
logm = math.log(mmin)
logmmax = math.log(mmax)
logrange_min = math.log(range_min)
logrange_max = math.log(range_max)
while logm <= logmmax:
if logm>=logrange_min and logm<=logrange_max:
mass_list.append(math.exp(logm))
logm += dlogm
else:
# use linear scale
m = mmin
while m <= mmax:
if m>=range_min and m<=range_max:
mass_list.append(m)
m += dm
# start time loop at tmax or max_evolution_time
t = tmax if tmax else self.bse_options['max_evolution_time']
# set default mass list
if logspacing:
logt = math.log10(t)
logtmin = math.log10(tmin)
while logt > logtmin:
m = _mass_from_time(10.0**logt)
mass_list.append(m)
logt = max(logtmin, logt - dlogt * fsample)
else:
while t > tmin:
m = _mass_from_time(t)
mass_list.append(m)
t = max(tmin,t - dt * fsample)
# make mass list unique
mass_list = _uniq(mass_list)
if mindm:
for x in mindm:
range_min = x[0]
range_max = x[1]
mindm = x[2]
# impose a minimum dm: if two masses in the list
# are separated by < this, remove the second
for index,mass in enumerate(mass_list):
if index > 0 and mass>=range_min and mass<=range_max:
dm = mass_list[index] - mass_list[index-1]
if dm < mindm:
mass_list[index-1] = 0.0
mass_list = _uniq(mass_list)
if mass_list[0] == 0.0:
mass_list.remove(0.0)
# apply multiplication factor if given
if factor and factor!=1.0:
mass_list = [m * factor for m in mass_list]
# reformat numbers
mass_list = _format(mass_list)
# show the mass<>time table?
if showtable:
twas = 0.0
logtwas = 0.0
for i,m in enumerate(mass_list):
t = _time_from_mass(m)
logt = math.log10(t)
if twas > 0.0:
print("{i:4d} m={m:13g} t={t:13g} log10(t)={logt:13g} dt={dt:13g} dlog10(t)={dlogt:13g}".format(i=i,m=m,t=t,logt=logt,dt=twas-t,dlogt=logtwas-logt))
else:
print("{i:4d} m={m:13g} t={t:13g} log10(t)={logt:13g}".format(i=i,m=m,t=t,logt=logt))
twas = t
logtwas = logt
exit()
# return the mass list as a numpy array
mass_list = np.unique(np.array(mass_list))
# perhaps log the masses
if logmasses:
mass_list = np.log(mass_list)
if log10masses:
mass_list = np.log10(mass_list)
if showlist:
print("const_dt mass list ({} masses)\n".format(len(mass_list)),mass_list)
return mass_list