gravelamps.models.navarro_frenk_white¶

Navarro, Frenk, and White Lensing Implementation

These functions are wrappers around the C++ functions implemeted in gravelamps/models/navrro-frenk-white.h. These are able to compute the amplification factor in both the wave and geometric optics regimes.

gravelamps.models.navarro_frenk_white.amplification()¶

Computes the amplification factor.

Will compute in the wave optics regime with the specified precision below the specified dimensionless frequency and in the geometric optics regime with standard double precision above it. Adheres to numpy broadcasting rules.

Parameters:

dimensionless_frequency: float or ArrayLike: Dimensionless frequencies.
source_position: float or ArrayLike: Dimensionless displacements of the source.
scaling_constant: float: Scale factor for the NFW profile.
integration_limit: int, optional, default=100: Upper limit of the indefinite integral to compute in wave optics.
precision: int, optional, default=128: Number of bits of precision for arbitrary precision calculations in wave optics.
image_positions: ArrayLike, optional: Image positions corresponding to source positions. Shape must be M x 3 where M corresponds to the total number of elements of source position. This will be handled in the order given by np.flatten(source_position). On rows corresponding to source positions that yield a single image, the other spaces should be filled with np.NaN. Will be ignored if minimum_phase is not also given.
minimum_phase: ArrayLike, optional: Phases required for minimum time delay corresponding to source position. Will be ignored if image_positions is not also given.

Returns:

amp: complex or ArrayLike: Amplification factor values.

Raises:

RuntimeError: If arguments cannot be parsed.
ValueError: If image_positions has incorrect dimensions.
RuntimeWarning: If one of the two linked keyword arguments is missing when the other is given or is not the required shape.

gravelamps.models.navarro_frenk_white.generate_data()¶

Constructs interpolator data file for the Navarro, Frenk, and White mass density profile.

From the input files, the amplification factor files will be populated with a grid of amplification factor values correpsonding to the dimensionless frequency and source position values in their respective files. This function will checkpoint the files and return 85 upon receiving a SIGALRM or SIGINT.

Parameters:

dimensionless_frequency_file: str: Path to file containing dimensionless freuqency values.
source_position_file: str: Path to file containing source position values.
amplification_factor_real_file: str: Path to file containing real component of amplification factor values.
amplification_factor_imag_file: str: Path to file containing imaginary component of amplification factor values.
scaling_constant: float: Scale factor the NFW profile.
integration_limit: int, optional, default=100: Upper limit of the indefinite integral to compute in wave optics.
geo_switch: int, optional, default=1000: Dimensionless frequnecy above which to use geometric optics.
precision: int, optional, default=128: Number of bits of precision for arbitrary precision calculations in wave optics.

Returns:

int: 0 if completed sucessfully, 85 if received checkpoint instruction.

Raises:

RuntimeError: If arguments cannot be understood.
RuntimeWarning: If precision > 50000 warns about run time.

gravelamps.models.navarro_frenk_white.geometric_amplification()¶

Computes the amplification factor in the geometric optics regime. Adheres to numpy broadcasting rules.

Parameters:

dimensionless_frequency: float or ArrayLike: Dimensionless frequencies.
source_position: float or ArrayLike: Dimensionless displacements of the source.
scaling_constant: float: Scale factor for the NFW profile.
image_positions: ArrayLike, optional: Image positions corresponding to source positions. Shape must be M x 3 where M corresponds to the total number of elements of source position. This will be handled in the order given by np.flatten(source_position). On rows corresponding to source positions that yield a single image, the other spaces should be filled with np.NaN. Will be ignored if minimum_phase is not also given.
minimum_phase: ArrayLike, optional: Phases required for minimum time delay corresponding to source position. Will be ignored if image_positions is not also given.

Returns:

amp: complex or ArrayLike: Amplification factor values.

Raises:

RuntimeError: If arguments cannot be parsed
ValueError: If image_positions has incorrect dimensions.
RuntimeWarning: If one of the kwargs is missing when the other is given or if one of the given kwarg arrays is not the required shape.

gravelamps.models.navarro_frenk_white.geometric_contribution()¶

Computes the contribution to the amplification factor in the geometric optics regime for the image at the specified position. Adheres to numpy broadcasting rules.

Parameters:

dimensionless_frequency: float or ArrayLike: Dimensionless frequencies.
source_position: float: Dimensionless displacement of the source.
image_position: float or ArrayLike: Dimensionless displacement of the image.
scaling_constant: float: Scale factor for the NFW profile.
minimum_phase: float: Phase required for the minimum time delay to be zero.

Returns:

contrib: complex or ArrayLike: Contribution to amplification factor from specified image.

Raises:

RuntimeError: If arguments cannot be parsed.
ValueError: If dimensionless frequency or image position are given as ArrayLike with greater than one dimension.

gravelamps.models.navarro_frenk_white.image_position()¶

Computes the dimensionless displacements of the images in the geometric optics regime.

Parameters:

source_position: float or ArrayLike: Dimensionless displacement of the source.
scaling_constant: float: Scale factor for the NFW profile.

Returns:

ArrayLike: Positions of the images. Where images do not exist, i.e. in 1 image only regime, other images will be set to NaN such that three values exist for each source position.

Raises:

RuntimeError: If arguments cannot be parsed.

gravelamps.models.navarro_frenk_white.lensing_potential()¶

Computes the lensing potenital for the Navarro, Frenk, and White lensing profile.

Parameters:

image_position: float or ArrayLike: Dimensionless displacements of the images.
scaling_constant: float: Scale factor for NFW profile.

Returns:

complex or ArrayLike: Lensing Potential Values.

Raises:

RuntimeError: If arguments cannot be parsed.

gravelamps.models.navarro_frenk_white.magnification()¶

Computes the magnification in the geometic optics regime.

Parameters:

image_position: float or ArrayLike: Dimensionless displacements of the images.
scaling_constant: float: Scale factor for the NFW profile.

Returns:

complex or ArrayLike: Magnification of the images.

Raises:

RuntimeError: If arguments cannot be parsed.

gravelamps.models.navarro_frenk_white.minimum_phase()¶

Computes the minimum phase required for the time delay to be zero.

Parameters:

source_position: float or ArrayLike: Dimensionless displacement of the source.
scaling_constant: float: Scale factor for the NFW profile.

Returns:

complex or ArrayLike: Minimum phases

Raises:

RuntimeError: If arguments cannot be parsed.

gravelamps.models.navarro_frenk_white.morse_factor()¶

Computes the Morse factor for the given images in the geometric optics regime.

Parameters:

image_position: float or ArrayLike: Dimensionless displacements of the images.
scaling_constant: float: Scale factor for the NFW profile.

Returns:

float or ArrayLike: Morse factor of each of the images.

Raises:

RuntimeError: If arguments cannot be parsed.

gravelamps.models.navarro_frenk_white.time_delay()¶

Computes the dimensionless time delay for the Navarro, Frenk, and White lensing profile.

Parameters:

image_position: float or ArrayLike: Dimensionless displacements of the images.
source_position: float: Dimensionless displacement of the source.
scaling_constant: float: Scale factor for the NFW profile.
minimum_phase: float: Phase required for minimum time delay to be zero.

Returns:

complex or ArrayLike: Dimensionless time delays.

Raises:

RuntimeError: If arguments cannot be parsed.

gravelamps.models.navarro_frenk_white.wave_amplification()¶

Computes the amplification factor in the wave optics reigme.

Computation is done with the specified precision and approximating the indefinite integral up to the specified limit. Adheres to numpy broadcasting rules.

Parameters:

dimensionless_frequency: float or ArrayLike: Dimensionless frequencies.
source_position: float or ArrayLike: Dimensionless displacement from the optical axis.
scaling_constant: float: Scale factor for the NFW profile.
integration_limit: float, optional, default=100: Upper limit of the indefinite integral to compute.
precision: int, optional, default=128: Number of bits of precision for arbitrary precision calculations.

Returns:

amp: complex or ArrayLike: Amplification factor values.

Raises:

RuntimeError: If arguments cannot be parsed.
RuntimeWarning: If precision > 50000 warns about runtime. If integration_limit > 2 * precision warns about accuracy.