API for the glworia.amp.amplification_factor module

amplification_computation_for_interpolation(T_funcs, helper_funcs, crit_funcs, y, lens_params, **kwargs)

Compute the contour integral for constructing interpolation tables of the time domain amplification factor.

Parameters:

Name	Type	Description	Default
T_funcs	Dict[str, Callable]	A dictionary of functions derived from the Fermat potential needed for computing the amplification factor.	required
helper_funcs	Dict[str, Callable]	A dictionary of helper functions needed for the numerical implementation.	required
crit_funcs	Dict[str, Callable]	A dictionary of functions for computing the caustic curve.	required
y	ndarray	The 2D impact parameter. For now the second component is not used.	required
lens_params	ndarray	The lens model parameter. For now only one parameter is supported.	required

Other Parameters:

Name	Type	Description
im_x_init_low	float	The lower bound for the initial guess of the image position.
im_x_init_high	float	The upper bound for the initial guess of the image position.
im_x_init_num	int	The number of initial guesses of the image position.
im_screen_round_decimal	int	The number of decimal places to round the image position.
T0_max	float	The maximum value of the time delay to compute the time domain amplification up to.
crit_run	bool	Whether the run corresponds to a run on the caustic.
N	int	The number of interpolation node in time in each segment.
return_all	bool	Whether to return all the computed values for debugging.
singular	bool	Whether the center of the lens is singular, i.e. a cusp or a pole in the time delay function.
origin_type	Callable	A function that returns the origin type of the lens model (cusp, pole or regular).
y_crit_override	Callable	A function that overrides the computed values of the caustic curve.
x_im_nan_sub	Callable	A function that substitutes nan values for the image position.
add_to_strong	Callable	A function decides whether to add certain points to the strong lensing regime.
T_vir_low_bound	float	The lower bound in time delay when searching for the maximum point of the time domain amplification.

Returns:

Name	Type	Description
contour_int	contour_integral	The contour integral object.
T0_min_out_segs	list[ndarray]	The corresponding time delays of the interpolation nodes for contour lines around the minimum. Each element of the list corresponds to a segment.
T0_arr_sad_max	ndarray	The corresponding time delays of the interpolation nodes for contour lines around the maximum point.
x_im	ndarray	The image positions.
T_val_max	float	The time delay at the maximum value of the time domain amplification.

amplification_computation_prep(Psi, **kwargs)

Constructs the functions needed for computing the amplification factor.

Parameters:

Name	Type	Description	Default
Psi	Callable	The Fermat potential of the lens model.	required

Other Parameters:

Name	Type	Description
h	float	The step size for numerical differentiation.
newt_tol	float	The tolerance for the Newton's method.
newt_max_iter	int	The maximum number of iterations for the Newton's method.
bisect_tol	float	The tolerance for the bisection method.

Returns:

Name	Type	Description
T_funcs	Dict[str, Callable]	A dictionary of functions needed for computing the amplification factor.
helper_funcs	Dict[str, Callable]	A dictionary of helper functions needed for computing the amplification factor.

chev_first_half(a, b, n)

Returns the first n points out of 2*n Chebyshev points, with the n points covering the interval [a, b].

chev_points(a, b, n)

Returns n Chebyshev points in the interval [a, b].

compute_F(w_interp, y, lens_params, T_funcs, helper_funcs, crit_funcs, N, T0_max, crit_run=False, singular=False, origin='regular', **kwargs)

Compute the amplification factor in the frequency domain.

Parameters:

Name	Type	Description	Default
w_interp	ndarray	The frequencies to compute the amplification factor.	required
y	ndarray	The 2D impact parameter. For now the second component is not used.	required
lens_params	ndarray	The lens model parameter. For now only one parameter is supported.	required
T_funcs	Dict[str, Callable]	A dictionary of functions derived from the Fermat potential needed for computing the amplification factor.	required
helper_funcs	Dict[str, Callable]	A dictionary of helper functions needed for the numerical implementation.	required
crit_funcs	Dict[str, Callable]	A dictionary of functions for computing the caustic curve.	required
N	int	The number of interpolation node in time in each segment.	required
T0_max	float	The maximum value of the time delay to compute the time domain amplification up to.	required
crit_run	bool	Whether the run corresponds to a run on the caustic.	False
singular	bool	Whether the center of the lens is singular, i.e. a cusp or a pole in the time delay function.	False
origin	str	The origin type of the lens model (cusp, pole or regular).	'regular'

Other Parameters:

Name	Type	Description
N_fft	int	The number of points in the Fast Fourier Transform.
t_fft_short_max_fac	float	The factor determining the maximum value of the time delay to compute the amplification factor in the short time regime.
t_fft_long_max_fac	float	The factor determining the maximum value of the time delay to compute the amplification factor in the long time regime.
w_trans_weak_fac	List[float]	The transition frequencies between different FFT regimes and geometrical optics for the weak lensing regime.
w_trans_strong_fac	List[float]	The transition frequencies between different FFT regimes and geometrical optics for the strong lensing regime.
sig_fac	float	The width of the transition region.
**kwargs		Additional keyword arguments passed to amplification_computation_for_interpolation.

Returns:

Name	Type	Description
F_interp	ndarray	The interpolated amplification factor.
F_interp_raw	List[ndarray]	A list of the amplification factor from the different FFT regimes, for debugging.
contour_obj	contour_integral	The contour integral object.
partitions	ndarray	The transition frequencies.