import numpy as np
from .. import units as u
from numba import njit
from .. import utils
from .template import Model
[docs]class PowerLaw(Model):
"""This is a model for a simple power law synchrotron model."""
def __init__(
self,
map_I,
freq_ref_I,
map_pl_index,
nside,
max_nside=None,
has_polarization=True,
map_Q=None,
map_U=None,
freq_ref_P=None,
unit_I=None,
unit_Q=None,
unit_U=None,
map_dist=None,
):
"""This function initialzes the power law model of synchrotron
emission.
The initialization of this model consists of reading in emission
templates from file, reading in spectral parameter maps from
file.
Parameters
----------
map_I, map_Q, map_U: `pathlib.Path` object
Paths to the maps to be used as I, Q, U templates.
If has_polarization is True and map_Q is None, assumes map_I is IQU
unit_* : string or Unit
Unit string or Unit object for all input FITS maps, if None, the input file
should have a unit defined in the FITS header.
freq_ref_I, freq_ref_P: Quantity or string
Reference frequencies at which the intensity and polarization
templates are defined. They should be a astropy Quantity object
or a string (e.g. "1500 MHz") compatible with GHz.
map_pl_index: `pathlib.Path` object
Path to the map to be used as the power law index.
nside: int
Resolution parameter at which this model is to be calculated.
"""
super().__init__(nside, max_nside=max_nside, map_dist=map_dist)
# do model setup
self.is_IQU = has_polarization and map_Q is None
self.I_ref = self.read_map(
map_I, field=[0, 1, 2] if self.is_IQU else 0, unit=unit_I
)
# This does unit conversion in place so we do not copy the data
# we do not keep the original unit because otherwise we would need
# to make a copy of the array when we run the model
self.I_ref <<= u.uK_RJ
self.freq_ref_I = u.Quantity(freq_ref_I).to(u.GHz)
self.freq_ref_P = (
None if freq_ref_P is None else u.Quantity(freq_ref_P).to(u.GHz)
)
self.has_polarization = has_polarization
if self.has_polarization and map_Q is not None:
self.Q_ref = self.read_map(map_Q, unit=unit_Q)
self.Q_ref <<= u.uK_RJ
self.U_ref = self.read_map(map_U, unit=unit_U)
self.U_ref <<= u.uK_RJ
elif self.has_polarization: # unpack IQU map to 3 arrays
self.Q_ref = self.I_ref[1]
self.U_ref = self.I_ref[2]
self.I_ref = self.I_ref[0]
try: # input is a number
self.pl_index = u.Quantity(map_pl_index, unit="")
except TypeError: # input is a path
self.pl_index = self.read_map(map_pl_index, unit="")
return
[docs] @u.quantity_input
def get_emission(self, freqs: u.GHz, weights=None):
freqs = utils.check_freq_input(freqs)
weights = utils.normalize_weights(freqs, weights)
if not self.has_polarization:
outputs = (
get_emission_numba_IQU(
freqs,
weights,
self.I_ref.value,
None,
None,
self.freq_ref_I.value,
None,
self.pl_index.value,
)
<< u.uK_RJ
)
else:
outputs = (
get_emission_numba_IQU(
freqs,
weights,
self.I_ref.value,
self.Q_ref.value,
self.U_ref.value,
self.freq_ref_I.value,
self.freq_ref_P.value,
self.pl_index.value,
)
<< u.uK_RJ
)
return outputs
@njit(parallel=True)
def get_emission_numba_IQU(
freqs, weights, I_ref, Q_ref, U_ref, freq_ref_I, freq_ref_P, pl_index
):
has_pol = Q_ref is not None
output = np.zeros((3, len(I_ref)), dtype=I_ref.dtype)
I, Q, U = 0, 1, 2
for i, (freq, weight) in enumerate(zip(freqs, weights)):
utils.trapz_step_inplace(
freqs, weights, i, I_ref * (freq / freq_ref_I) ** pl_index, output[I]
)
if has_pol:
pol_scaling = (freq / freq_ref_P) ** pl_index
utils.trapz_step_inplace(freqs, weights, i, Q_ref * pol_scaling, output[Q])
utils.trapz_step_inplace(freqs, weights, i, U_ref * pol_scaling, output[U])
return output
[docs]class CurvedPowerLaw(PowerLaw):
def __init__(
self,
map_I,
freq_ref_I,
map_pl_index,
nside,
spectral_curvature,
freq_curve,
max_nside=None,
has_polarization=True,
map_Q=None,
map_U=None,
freq_ref_P=None,
unit_I=None,
unit_Q=None,
unit_U=None,
map_dist=None,
):
super().__init__(
map_I=map_I,
freq_ref_I=freq_ref_I,
map_pl_index=map_pl_index,
nside=nside,
max_nside=max_nside,
has_polarization=has_polarization,
map_Q=map_Q,
map_U=map_U,
freq_ref_P=freq_ref_P,
unit_I=unit_I,
unit_Q=unit_Q,
unit_U=unit_U,
map_dist=map_dist,
)
try: # input is a number
self.spectral_curvature = u.Quantity(spectral_curvature, unit="")
except TypeError: # input is a path
self.spectral_curvature = self.read_map(spectral_curvature, unit="")
self.freq_curve = u.Quantity(freq_curve).to(u.GHz)
[docs] @u.quantity_input
def get_emission(self, freqs: u.GHz, weights=None):
freqs = utils.check_freq_input(freqs)
weights = utils.normalize_weights(freqs, weights)
if not self.has_polarization:
outputs = (
get_emission_numba_IQU_curved(
freqs,
weights,
self.I_ref.value,
None,
None,
self.freq_ref_I.value,
None,
self.pl_index.value,
self.freq_curve.value,
self.spectral_curvature.value,
)
<< u.uK_RJ
)
else:
outputs = (
get_emission_numba_IQU_curved(
freqs,
weights,
self.I_ref.value,
self.Q_ref.value,
self.U_ref.value,
self.freq_ref_I.value,
self.freq_ref_P.value,
self.pl_index.value,
self.freq_curve.value,
self.spectral_curvature.value,
)
<< u.uK_RJ
)
return outputs
@njit(parallel=True)
def get_emission_numba_IQU_curved(
freqs,
weights,
I_ref,
Q_ref,
U_ref,
freq_ref_I,
freq_ref_P,
pl_index,
freq_curve,
curvature,
):
has_pol = Q_ref is not None
output = np.zeros((3, len(I_ref)), dtype=I_ref.dtype)
I, Q, U = 0, 1, 2
for i, (freq, weight) in enumerate(zip(freqs, weights)):
curvature_term = np.log((freq / freq_curve) ** curvature)
utils.trapz_step_inplace(
freqs,
weights,
i,
I_ref * (freq / freq_ref_I) ** (pl_index + curvature_term),
output[I],
)
if has_pol:
pol_scaling = (freq / freq_ref_P) ** (pl_index + curvature_term)
utils.trapz_step_inplace(freqs, weights, i, Q_ref * pol_scaling, output[Q])
utils.trapz_step_inplace(freqs, weights, i, U_ref * pol_scaling, output[U])
return output