tardis.spectrum.formal_integral.formal_integral_numba module

class tardis.spectrum.formal_integral.formal_integral_numba.NumbaFormalIntegrator(geometry: NumbaRadial1DGeometry, time_explosion: float, plasma, n_impact_parameters: int = 1000)[source]

Bases: object

Helper class for performing the formal integral with Numba.

Parameters:
geometryobject

Geometry object containing shell radii.

time_explosionfloat

Time since explosion (seconds).

plasmaobject

Plasma object containing line list frequencies.

n_impact_parametersint, optional

Number of impact parameters

formal_integral(inner_temperature: float, frequencies: ndarray[tuple[int, ...], dtype[float64]], att_S_ul: ndarray[tuple[int, ...], dtype[float64]], mean_intensity_red_lu: ndarray[tuple[int, ...], dtype[float64]], mean_intensity_blue_lu: ndarray[tuple[int, ...], dtype[float64]], tau_sobolev: ndarray[tuple[int, ...], dtype[float64]], electron_densities: ndarray[tuple[int, ...], dtype[float64]], n_impact_parameters: int) → Tuple[ndarray[tuple[int, ...], dtype[float64]], ndarray[tuple[int, ...], dtype[float64]]][source]

Wrapper for the Numba implementation of the formal integral.

Parameters:
inner_temperaturefloat

Inner boundary temperature.

frequenciesndarray

Array of frequency values.

att_S_ulndarray

Attenuated source function values.

mean_intensity_red_lundarray

mean intensity of each line transition from upper to lower on the red side for each line and shell.

mean_intensity_blue_lundarray

mean intensity of each line transition from upper to lower on the blue side for each line and shell.

tau_sobolevndarray

Sobolev optical depths (2D array: lines x shells).

electron_densitiesndarray

Electron densities per shell.

n_impact_parametersint

Number of impact parameters

Returns:
luminosity_densitiesndarray

Integrated luminosities for each frequency.

intensities_nu_pndarray

Intensities per frequency and impact parameter

tardis.spectrum.formal_integral.formal_integral_numba.calculate_intersection_point(radius: float, impact_parameter: float, inv_t: float) → float[source]

Calculate distance to the impact parameter at radius.

Calculate half of the length of the impact parameter inside a shell of radius in terms of unit length (c * t_exp). If shell and impact parameter do not intersect, return 0.

Parameters:
radiusfloat

Radius of the shell.

impact_parameterfloat

Distance of the impact parameter to the center of the supernova.

inv_tfloat

Inverse of the time_explosion, used to normalize to unit length.

Returns:
float

Half the length of the impact parameter inside the shell, or 0 if no intersection.

tardis.spectrum.formal_integral.formal_integral_numba.get_electron_scattering_optical_depth(escat_optical_depth: float, first_contribution_flag: int, mean_intensity_red_lu_idx: int, intersection_end: float, intersection_start: float, escat_opacity: float, mean_intensity_blue_lu: float, mean_intensity_red_lu: float, intensities_nu_p: float) → Tuple[float, int, int][source]

Compute the electron scattering optical depth for given segment

Parameters:
escat_optical_depthfloat

Current electron scattering contribution.

first_contribution_flagint

Flag indicating if this is the first contribution (1 if first, 0 otherwise).

mean_intensity_red_lu_idxint

Index for mean_intensity_red_lu.

intersection_endfloat

Ending intersection point value for the current segment.

intersection_startfloat

Starting intersection point value for the current segment.

escat_opacityfloat

Electron scattering opacity.

mean_intensity_blue_lufloat

mean intensity of the transition on the blue side for the current segment.

mean_intensity_red_lufloat

mean intensity of the transition on the red side for the current segment.

intensities_nu_pfloat

Intensity at the current frequency and impact parameter.

Returns:
escat_optical_depthfloat

Updated electron scattering contribution.

first_contribution_flagint

Updated flag.

mean_intensity_red_lu_idxint

Updated mean_intensity_red_lu index.

tardis.spectrum.formal_integral.formal_integral_numba.initialize_formal_integral_inputs(frequencies: ndarray[tuple[int, ...], dtype[float64]], inner_temperature: float, n_impact_parameters: int, geometry: NumbaRadial1DGeometry, time_explosion: float, tau_sobolev: ndarray[tuple[int, ...], dtype[float64]]) → Tuple[ndarray[tuple[int, ...], dtype[float64]], ndarray[tuple[int, ...], dtype[float64]], ndarray[tuple[int, ...], dtype[float64]], ndarray[tuple[int, ...], dtype[int64]], ndarray[tuple[int, ...], dtype[int64]], ndarray[tuple[int, ...], dtype[float64]]][source]

Prepare all arrays and values needed for the loops inside the formal integral.

Parameters:
frequenciesndarray

Array of frequency values.

inner_temperaturefloat

Inner boundary temperature.

n_impact_parametersint

Number of impact parameters.

geometryobject

Geometry object containing shell radii.

time_explosionfloat

Time since explosion (seconds).

tau_sobolevndarray

Sobolev optical depths for each line and shell.

Returns:
intensities_nu_pndarray

Intensities at each frequency and impact parameter.

impact_parametersndarray

Array of impact parameters.

intersection_pointsndarray

Array of intersection points for each impact parameter and shell.

shell_idsndarray

Array of shell IDs for each impact parameter and shell intersection.

n_intersectionsndarray

Number of intersections for each impact parameter.

exp_tau_sobolevndarray

Exponential of negative Sobolev optical depths (flattened).

Find the index to insert a value into an array of line frequencies.

Parameters:
nundarray

Array of line frequencies.

nu_insertfloat

Value of the frequency to insert.

number_of_linesint

Number of lines in the line list.

Returns:
int

Index of the next line to the red. If the key value is redder than the reddest line, returns number_of_lines.

tardis.spectrum.formal_integral.formal_integral_numba.numba_formal_integral(geometry: NumbaRadial1DGeometry, time_explosion: float, plasma, inner_temperature: float, frequencies: ndarray[tuple[int, ...], dtype[float64]], att_S_ul: ndarray[tuple[int, ...], dtype[float64]], mean_intensity_red_lu: ndarray[tuple[int, ...], dtype[float64]], mean_intensity_blue_lu: ndarray[tuple[int, ...], dtype[float64]], tau_sobolev: ndarray[tuple[int, ...], dtype[float64]], electron_densities: ndarray[tuple[int, ...], dtype[float64]], n_impact_parameters: int) → Tuple[ndarray[tuple[int, ...], dtype[float64]], ndarray[tuple[int, ...], dtype[float64]]][source]

Compute the formal integral.

Parameters:
geometryobject

Geometry object containing shell radii.

time_explosionfloat

Time since explosion (seconds).

plasmaobject

Plasma object containing line list frequencies.

inner_temperaturefloat

Inner boundary temperature.

frequenciesndarray

Array of frequencies.

att_S_ulndarray

Attenuated source function for each line and shell.

mean_intensity_red_lundarray

mean intensity of each line transition from upper to lower on the red side for each line and shell.

mean_intensity_blue_lundarray

mean intensity of each line transition from upper to lower on the blue side for each line and shell.

tau_sobolevndarray

Sobolev optical depths for each line and shell.

electron_densitiesndarray

Electron densities per shell.

n_impact_parametersint

Number of impact parameters.

Returns:
luminosity_densitiesndarray

Integrated luminosities for each frequency.

intensities_nu_pndarray

Intensities per frequency and impact parameter

tardis.spectrum.formal_integral.formal_integral_numba.populate_intersection_points(geometry: NumbaRadial1DGeometry, time_explosion: float, impact_parameter: float, intersection_points: ndarray[tuple[int, ...], dtype[float64]], shell_ids: ndarray[tuple[int, ...], dtype[int64]]) → int[source]

Calculate the intersection points of the impact parameter with each shell.

Parameters:
geometryobject

Geometry object containing shell radii.

time_explosionfloat

Time since explosion (seconds).

impact_parameterfloat

Distance of the integration line to the center.

intersection_pointsndarray

Output array to be filled with intersection_point values.

shell_idsndarray

Output array to be filled with the corresponding shell IDs.

Returns:
int

Number of intersection points found.

Find the insertion index for a value in an inversely sorted float array.

Parameters:
xndarray

Inversely (largest to lowest) sorted float array.

x_insertfloat

Value to insert.

iminint

Lower bound index.

imaxint

Upper bound index.

Returns:
int

Index of the next boundary to the left.