def test_raise(self):
with self.assertRaises(ValueError):
lighModel = LightModel(light_model_list=['WRONG'])
with self.assertRaises(ValueError):
lighModel = LightModel(light_model_list=['UNIFORM'])
lighModel.light_3d(r=1, kwargs_list=[{'amp': 1}])
with self.assertRaises(ValueError):
lighModel = LightModel(light_model_list=['UNIFORM'])
lighModel.profile_type_list = ['WRONG']
lighModel.functions_split(x=0, y=0, kwargs_list=[{}])
with self.assertRaises(ValueError):
lighModel = LightModel(light_model_list=['UNIFORM'])
lighModel.profile_type_list = ['WRONG']
lighModel.num_param_linear(kwargs_list=[{}])
with self.assertRaises(ValueError):
lighModel = LightModel(light_model_list=['UNIFORM'])
lighModel.profile_type_list = ['WRONG']
lighModel.update_linear(param=[1], i=0, kwargs_list=[{}])
with self.assertRaises(ValueError):
lighModel = LightModel(light_model_list=['UNIFORM'])
lighModel.profile_type_list = ['WRONG']
lighModel.total_flux(kwargs_list=[{}])
class LightProfile(object):
"""
class to deal with the light distribution
"""
def __init__(self, profile_list=['HERNQUIST'], kwargs_numerics={}):
"""
:param profile_list:
"""
self.light_model = LightModel(light_model_list=profile_list,
smoothing=0.000001)
self._interp_grid_num = kwargs_numerics.get('interpol_grid_num', 1000)
self._max_interpolate = kwargs_numerics.get('max_integrate', 100)
self._min_interpolate = kwargs_numerics.get('min_integrate', 0.001)
def light_3d(self, r, kwargs_list):
"""
:param kwargs_list:
:return:
"""
light_3d = self.light_model.light_3d(r, kwargs_list)
return light_3d
def light_3d_interp(self, r, kwargs_list, new_compute=False):
"""
:param kwargs_list:
:return:
"""
if not hasattr(self, '_f_light_3d') or new_compute is True:
r_array = np.logspace(np.log10(self._min_interpolate),
np.log10(self._max_interpolate),
self._interp_grid_num)
light_3d_array = self.light_model.light_3d(r_array, kwargs_list)
light_3d_array[light_3d_array < 10**(-100)] = 10**(-100)
f = interp1d(np.log(r_array),
np.log(light_3d_array),
fill_value="extrapolate")
self._f_light_3d = f
return np.exp(self._f_light_3d(np.log(r)))
def light_2d(self, R, kwargs_list):
"""
:param R:
:param kwargs_list:
:return:
"""
kwargs_list_copy = copy.deepcopy(kwargs_list)
kwargs_list_new = []
for kwargs in kwargs_list_copy:
if 'e1' in kwargs:
kwargs['e1'] = 0
if 'e2' in kwargs:
kwargs['e2'] = 0
kwargs_list_new.append({
k: v
for k, v in kwargs.items()
if not k in ['center_x', 'center_y']
})
return self.light_model.surface_brightness(R, 0, kwargs_list_new)
def draw_light_2d_linear(self,
kwargs_list,
n=1,
new_compute=False,
r_eff=1.):
"""
constructs the CDF and draws from it random realizations of projected radii R
:param kwargs_list:
:return:
"""
if not hasattr(self, '_light_cdf') or new_compute is True:
r_array = np.linspace(self._min_interpolate, self._max_interpolate,
self._interp_grid_num)
cum_sum = np.zeros_like(r_array)
sum = 0
for i, r in enumerate(r_array):
if i == 0:
cum_sum[i] = 0
else:
sum += self.light_2d(r, kwargs_list) * r
cum_sum[i] = copy.deepcopy(sum)
cum_sum_norm = cum_sum / cum_sum[-1]
f = interp1d(cum_sum_norm, r_array)
self._light_cdf = f
cdf_draw = np.random.uniform(0., 1, n)
r_draw = self._light_cdf(cdf_draw)
return r_draw
def draw_light_2d(self, kwargs_list, n=1, new_compute=False):
"""
constructs the CDF and draws from it random realizations of projected radii R
:param kwargs_list:
:return:
"""
if not hasattr(self, '_light_cdf_log') or new_compute is True:
r_array = np.logspace(np.log10(self._min_interpolate),
np.log10(self._max_interpolate),
self._interp_grid_num)
cum_sum = np.zeros_like(r_array)
sum = 0
for i, r in enumerate(r_array):
if i == 0:
cum_sum[i] = 0
else:
sum += self.light_2d(r, kwargs_list) * r * r
cum_sum[i] = copy.deepcopy(sum)
cum_sum_norm = cum_sum / cum_sum[-1]
f = interp1d(cum_sum_norm, np.log(r_array))
self._light_cdf_log = f
cdf_draw = np.random.uniform(0., 1, n)
r_log_draw = self._light_cdf_log(cdf_draw)
return np.exp(r_log_draw)
class LightProfile(object):
"""
class to deal with the light distribution for GalKin
In particular, this class allows for:
- (faster) interpolated calculation for a given profile (for a range that the Jeans equation is computed)
- drawing 3d and 2d distributions from a given (spherical) profile
(within bounds where the Jeans equation is expected to be accurate)
- 2d projected profiles within the 3d integration range (truncated)
"""
def __init__(self, profile_list, interpol_grid_num=2000, max_interpolate=1000, min_interpolate=0.001,
max_draw=None):
"""
:param profile_list: list of light profiles for LightModel module (must support light_3d() functionalities)
:param interpol_grid_num: int; number of interpolation steps (logarithmically between min and max value)
:param max_interpolate: float; maximum interpolation of 3d light profile
:param min_interpolate: float; minimum interpolate (and also drawing of light profile)
:param max_draw: float; (optional) if set, draws up to this radius, else uses max_interpolate value
"""
self.light_model = LightModel(light_model_list=profile_list)
self._interp_grid_num = interpol_grid_num
self._max_interpolate = max_interpolate
self._min_interpolate = min_interpolate
if max_draw is None:
max_draw = max_interpolate
self._max_draw = max_draw
def light_3d(self, r, kwargs_list):
"""
three-dimensional light profile
:param r: 3d radius
:param kwargs_list: list of keyword arguments of light profiles (see LightModule)
:return: flux per 3d volume at radius r
"""
light_3d = self.light_model.light_3d(r, kwargs_list)
return light_3d
def light_3d_interp(self, r, kwargs_list, new_compute=False):
"""
interpolated three-dimensional light profile within bounds [min_interpolate, max_interpolate]
in logarithmic units with interpol_grid_num numbers of interpolation steps
:param r: 3d radius
:param kwargs_list: list of keyword arguments of light profiles (see LightModule)
:param new_compute: boolean, if True, re-computes the interpolation
(becomes valid with updated kwargs_list argument)
:return: flux per 3d volume at radius r
"""
if not hasattr(self, '_f_light_3d') or new_compute is True:
r_array = np.logspace(np.log10(self._min_interpolate), np.log10(self._max_interpolate), self._interp_grid_num)
light_3d_array = self.light_model.light_3d(r_array, kwargs_list)
light_3d_array[light_3d_array < 10 ** (-1000)] = 10 ** (-1000)
f = interp1d(np.log(r_array), np.log(light_3d_array), fill_value=(np.log(light_3d_array[0]), -1000),
bounds_error=False) # "extrapolate"
self._f_light_3d = f
return np.exp(self._f_light_3d(np.log(r)))
def light_2d(self, R, kwargs_list):
"""
projected light profile (integrated to infinity in the projected axis)
:param R: projected 2d radius
:param kwargs_list: list of keyword arguments of light profiles (see LightModule)
:return: projected surface brightness
"""
kwargs_light_circularized = self._circularize_kwargs(kwargs_list)
return self.light_model.surface_brightness(R, 0, kwargs_light_circularized)
def _circularize_kwargs(self, kwargs_list):
"""
:param kwargs_list: list of keyword arguments of light profiles (see LightModule)
:return: circularized arguments
"""
# TODO make sure averaging is done azimuthally
if not hasattr(self, '_kwargs_light_circularized'):
kwargs_list_copy = copy.deepcopy(kwargs_list)
kwargs_list_new = []
for kwargs in kwargs_list_copy:
if 'e1' in kwargs:
kwargs['e1'] = 0
if 'e2' in kwargs:
kwargs['e2'] = 0
kwargs_list_new.append({k: v for k, v in kwargs.items() if not k in ['center_x', 'center_y']})
self._kwargs_light_circularized = kwargs_list_new
return self._kwargs_light_circularized
def _light_2d_finite_single(self, R, kwargs_list):
"""
projected light profile (integrated to FINITE 3d boundaries from the max_interpolate)
for a single float number of R
:param R: projected 2d radius (between min_interpolate and max_interpolate)
:param kwargs_list: list of keyword arguments of light profiles (see LightModule)
:return: projected surface brightness
"""
# here we perform a logarithmic integral
stop = np.log10(np.maximum(np.sqrt(self._max_interpolate**2 - R**2), self._min_interpolate + 0.00001))
x = np.logspace(start=np.log10(self._min_interpolate), stop=stop, num=self._interp_grid_num)
r_array = np.sqrt(x**2 + R**2)
flux_r = self.light_3d(r_array, kwargs_list)
dlog_r = (np.log10(x[2]) - np.log10(x[1])) * np.log(10)
flux_r *= dlog_r * x
# linear integral
#x = np.linspace(start=self._min_interpolate, stop=np.sqrt(self._max_interpolate ** 2 - R ** 2),
# num=self._interp_grid_num)
#r_array = np.sqrt(x ** 2 + R ** 2)
#dr = x[1] - x[0]
#flux_r = self.light_3d(r_array + dr / 2, kwargs_circ)
#dr = x[1] - x[0]
#flux_r *= dr
flux_R = np.sum(flux_r)
# perform finite integral
#out = integrate.quad(lambda x: self.light_3d(np.sqrt(R ** 2 + x ** 2), kwargs_circ), self._min_interpolate,
# np.sqrt(self._max_interpolate**2 - R**2))
#print(out_1, out, 'test')
#flux_R = out[0]
return flux_R * 2 # integral in both directions
def light_2d_finite(self, R, kwargs_list):
"""
projected light profile (integrated to FINITE 3d boundaries from the max_interpolate)
:param R: projected 2d radius (between min_interpolate and max_interpolate
:param kwargs_list: list of keyword arguments of light profiles (see LightModule)
:return: projected surface brightness
"""
kwargs_circ = self._circularize_kwargs(kwargs_list)
n = len(np.atleast_1d(R))
if n <= 1:
return self._light_2d_finite_single(R, kwargs_circ)
else:
light_2d = np.zeros(n)
for i, R_i in enumerate(R):
light_2d[i] = self._light_2d_finite_single(R_i, kwargs_circ)
return light_2d
def draw_light_2d_linear(self, kwargs_list, n=1, new_compute=False):
"""
constructs the CDF and draws from it random realizations of projected radii R
The interpolation of the CDF is done in linear projected radius space
:param kwargs_list: list of keyword arguments of light profiles (see LightModule)
:param n: int; number of draws
:param new_compute: boolean, if True, re-computes the interpolation
(becomes valid with updated kwargs_list argument)
:return: draw of projected radius for the given light profile distribution
"""
if not hasattr(self, '_light_cdf') or new_compute is True:
r_array = np.linspace(self._min_interpolate, self._max_draw, self._interp_grid_num)
cum_sum = np.zeros_like(r_array)
sum = 0
for i, r in enumerate(r_array):
if i == 0:
cum_sum[i] = 0
else:
sum += self.light_2d(r, kwargs_list) * r
cum_sum[i] = copy.deepcopy(sum)
cum_sum_norm = cum_sum/cum_sum[-1]
f = interp1d(cum_sum_norm, r_array)
self._light_cdf = f
cdf_draw = np.random.uniform(0., 1, n)
r_draw = self._light_cdf(cdf_draw)
return r_draw
def draw_light_2d(self, kwargs_list, n=1, new_compute=False):
"""
constructs the CDF and draws from it random realizations of projected radii R
CDF is constructed in logarithmic projected radius spacing
:param kwargs_list: light model keyword argument list
:param n: int, number of draws per functino call
:param new_compute: re-computes the interpolated CDF
:return: realization of projected radius following the distribution of the light model
"""
if not hasattr(self, '_light_cdf_log') or new_compute is True:
r_array = np.logspace(np.log10(self._min_interpolate), np.log10(self._max_draw), self._interp_grid_num)
cum_sum = np.zeros_like(r_array)
sum = 0
for i, r in enumerate(r_array):
if i == 0:
cum_sum[i] = 0
else:
sum += self.light_2d(r, kwargs_list) * r * r
cum_sum[i] = copy.deepcopy(sum)
cum_sum_norm = cum_sum/cum_sum[-1]
f = interp1d(cum_sum_norm, np.log(r_array))
self._light_cdf_log = f
cdf_draw = np.random.uniform(0., 1, n)
r_log_draw = self._light_cdf_log(cdf_draw)
return np.exp(r_log_draw)
def draw_light_3d(self, kwargs_list, n=1, new_compute=False):
"""
constructs the CDF and draws from it random realizations of 3D radii r
:param kwargs_list: light model keyword argument list
:param n: int, number of draws per function call
:param new_compute: re-computes the interpolated CDF
:return: realization of projected radius following the distribution of the light model
"""
if not hasattr(self, '_light_3d_cdf_log') or new_compute is True:
r_array = np.logspace(np.log10(self._min_interpolate), np.log10(self._max_draw), self._interp_grid_num)
dlog_r = np.log10(r_array[1]) - np.log10(r_array[0])
r_array_int = np.logspace(np.log10(self._min_interpolate) + dlog_r / 2, np.log10(self._max_draw) + dlog_r / 2, self._interp_grid_num)
cum_sum = np.zeros_like(r_array)
sum = 0
for i, r in enumerate(r_array_int[:-1]):
#if i == 0:
# cum_sum[i] = 0
#else:
sum += self.light_3d(r, kwargs_list) * r**2 * (r_array[i+1] - r_array[i])# * r
cum_sum[i+1] = copy.deepcopy(sum)
cum_sum_norm = cum_sum/cum_sum[-1]
f = interp1d(cum_sum_norm, np.log(r_array))
self._light_3d_cdf_log = f
cdf_draw = np.random.uniform(0., 1, n)
r_log_draw = self._light_3d_cdf_log(cdf_draw)
return np.exp(r_log_draw)
def delete_cache(self):
"""
deletes cached interpolation function of the CDF for a specific light profile
:return: None
"""
if hasattr(self, '_light_cdf_log'):
del self._light_cdf_log
if hasattr(self, '_light_cdf'):
del self._light_cdf
if hasattr(self, '_f_light_3d'):
del self._f_light_3d
if hasattr(self, '_kwargs_light_circularized'):
del self._kwargs_light_circularized
class LightProfile(object):
"""
class to deal with the light distribution
"""
def __init__(self,
profile_list,
interpol_grid_num=2000,
max_interpolate=1000,
min_interpolate=0.001):
"""
:param profile_list:
"""
self.light_model = LightModel(light_model_list=profile_list)
self._interp_grid_num = interpol_grid_num
self._max_interpolate = max_interpolate
self._min_interpolate = min_interpolate
def light_3d(self, r, kwargs_list):
"""
:param kwargs_list:
:return:
"""
light_3d = self.light_model.light_3d(r, kwargs_list)
return light_3d
def light_3d_interp(self, r, kwargs_list, new_compute=False):
"""
:param kwargs_list:
:return:
"""
if not hasattr(self, '_f_light_3d') or new_compute is True:
r_array = np.logspace(np.log10(self._min_interpolate),
np.log10(self._max_interpolate),
self._interp_grid_num)
light_3d_array = self.light_model.light_3d(r_array, kwargs_list)
light_3d_array[light_3d_array < 10**(-100)] = 10**(-100)
f = interp1d(np.log(r_array),
np.log(light_3d_array),
fill_value=(np.log(light_3d_array[0]), -1000),
bounds_error=False) # "extrapolate"
self._f_light_3d = f
return np.exp(self._f_light_3d(np.log(r)))
def light_2d(self, R, kwargs_list):
"""
:param R:
:param kwargs_list:
:return:
"""
# TODO make sure averaging is done azimuthally
if not hasattr(self, '_kwargs_light_circularized'):
kwargs_list_copy = copy.deepcopy(kwargs_list)
kwargs_list_new = []
for kwargs in kwargs_list_copy:
if 'e1' in kwargs:
kwargs['e1'] = 0
if 'e2' in kwargs:
kwargs['e2'] = 0
kwargs_list_new.append({
k: v
for k, v in kwargs.items()
if not k in ['center_x', 'center_y']
})
self._kwargs_light_circularized = kwargs_list_new
return self.light_model.surface_brightness(
R, 0, self._kwargs_light_circularized)
def draw_light_2d_linear(self,
kwargs_list,
n=1,
new_compute=False,
r_eff=1.):
"""
constructs the CDF and draws from it random realizations of projected radii R
:param kwargs_list:
:return:
"""
if not hasattr(self, '_light_cdf') or new_compute is True:
r_array = np.linspace(self._min_interpolate, self._max_interpolate,
self._interp_grid_num)
cum_sum = np.zeros_like(r_array)
sum = 0
for i, r in enumerate(r_array):
if i == 0:
cum_sum[i] = 0
else:
sum += self.light_2d(r, kwargs_list) * r
cum_sum[i] = copy.deepcopy(sum)
cum_sum_norm = cum_sum / cum_sum[-1]
f = interp1d(cum_sum_norm, r_array)
self._light_cdf = f
cdf_draw = np.random.uniform(0., 1, n)
r_draw = self._light_cdf(cdf_draw)
return r_draw
def draw_light_2d(self, kwargs_list, n=1, new_compute=False):
"""
constructs the CDF and draws from it random realizations of projected radii R
:param kwargs_list: light model keyword argument list
:param n: int, number of draws per functino call
:param new_compute: re-computes the interpolated CDF
:return: realization of projected radius following the distribution of the light model
"""
if not hasattr(self, '_light_cdf_log') or new_compute is True:
r_array = np.logspace(np.log10(self._min_interpolate),
np.log10(self._max_interpolate),
self._interp_grid_num)
cum_sum = np.zeros_like(r_array)
sum = 0
for i, r in enumerate(r_array):
if i == 0:
cum_sum[i] = 0
else:
sum += self.light_2d(r, kwargs_list) * r * r
cum_sum[i] = copy.deepcopy(sum)
cum_sum_norm = cum_sum / cum_sum[-1]
f = interp1d(cum_sum_norm, np.log(r_array))
self._light_cdf_log = f
cdf_draw = np.random.uniform(0., 1, n)
r_log_draw = self._light_cdf_log(cdf_draw)
return np.exp(r_log_draw)
def draw_light_3d(self, kwargs_list, n=1, new_compute=False):
"""
constructs the CDF and draws from it random realizations of 3D radii r
:param kwargs_list: light model keyword argument list
:param n: int, number of draws per functino call
:param new_compute: re-computes the interpolated CDF
:return: realization of projected radius following the distribution of the light model
"""
if not hasattr(self, '_light_3d_cdf_log') or new_compute is True:
r_array = np.logspace(np.log10(self._min_interpolate),
np.log10(self._max_interpolate),
self._interp_grid_num)
cum_sum = np.zeros_like(r_array)
sum = 0
for i, r in enumerate(r_array):
if i == 0:
cum_sum[i] = 0
else:
sum += self.light_3d(
r, kwargs_list
) * r * r**2 # 1x r for the log spacing and r**2 for the shell area
cum_sum[i] = copy.deepcopy(sum)
cum_sum_norm = cum_sum / cum_sum[-1]
f = interp1d(cum_sum_norm, np.log(r_array))
self._light_3d_cdf_log = f
cdf_draw = np.random.uniform(0., 1, n)
r_log_draw = self._light_3d_cdf_log(cdf_draw)
return np.exp(r_log_draw)
def delete_cache(self):
"""
deletes cached interpolation function of the CDF for a specific light profile
:return: None
"""
if hasattr(self, '_light_cdf_log'):
del self._light_cdf_log
if hasattr(self, '_light_cdf'):
del self._light_cdf
if hasattr(self, '_f_light_3d'):
del self._f_light_3d
if hasattr(self, '_kwargs_light_circularized'):
del self._kwargs_light_circularized