Reference/API

Capabilities

astropy.modeling Package

This subpackage provides a framework for representing models and performing model evaluation and fitting. It supports 1D and 2D models and fitting with parameter constraints. It has some predefined models and fitting routines.

Functions

bind_bounding_box(modelinstance, bounding_box)	Set a validated bounding box to a model instance.
bind_compound_bounding_box(modelinstance, ...)	Add a validated compound bounding box to a model instance.
custom_model(*args[, fit_deriv])	Create a model from a user defined function.
fix_inputs(modelinstance, values[, ...])	This function creates a compound model with one or more of the input values of the input model assigned fixed values (scalar or array).
is_separable(transform)	A separability test for the outputs of a transform.
separability_matrix(transform)	Compute the correlation between outputs and inputs.

Classes

CompoundModel(op, left, right[, name])	Base class for compound models.
Fittable1DModel(*args[, meta, name])	Base class for one-dimensional fittable models.
Fittable2DModel(*args[, meta, name])	Base class for two-dimensional fittable models.
FittableModel(*args[, meta, name])	Base class for models that can be fitted using the built-in fitting algorithms.
InputParameterError	Used for incorrect input parameter values and definitions.
Model(*args[, meta, name])	Base class for all models.
ModelDefinitionError	Used for incorrect models definitions.
Parameter([name, description, default, ...])	Wraps individual parameters.
ParameterError	Generic exception class for all exceptions pertaining to Parameters.

Class Inheritance Diagram

astropy.modeling.bounding_box Module

This module is to contain an improved bounding box

Classes

ModelBoundingBox(intervals, model[, ...])	A model's bounding box
CompoundBoundingBox(bounding_boxes, model, ...)	A model's compound bounding box

Class Inheritance Diagram

astropy.modeling.mappings Module

Special models useful for complex compound models where control is needed over which outputs from a source model are mapped to which inputs of a target model.

Classes

Mapping(mapping[, n_inputs, name, meta])	Allows inputs to be reordered, duplicated or dropped.
Identity(n_inputs[, name, meta])	Returns inputs unchanged.
UnitsMapping(mapping[, ...])	Mapper that operates on the units of the input, first converting to canonical units, then assigning new units without further conversion.

Class Inheritance Diagram

astropy.modeling.fitting Module

This module implements classes (called Fitters) which combine optimization algorithms (typically from scipy.optimize) with statistic functions to perform fitting. Fitters are implemented as callable classes. In addition to the data to fit, the __call__ method takes an instance of FittableModel as input, and returns a copy of the model with its parameters determined by the optimizer.

Optimization algorithms, called “optimizers” are implemented in optimizers and statistic functions are in statistic. The goal is to provide an easy to extend framework and allow users to easily create new fitters by combining statistics with optimizers.

There are two exceptions to the above scheme. LinearLSQFitter uses Numpy’s lstsq function. LevMarLSQFitter uses leastsq which combines optimization and statistic in one implementation.

Classes

LinearLSQFitter([calc_uncertainties])	A class performing a linear least square fitting.
LevMarLSQFitter([calc_uncertainties])	Levenberg-Marquardt algorithm and least squares statistic.
TRFLSQFitter([calc_uncertainties, ...])	Trust Region Reflective algorithm and least squares statistic.
DogBoxLSQFitter([calc_uncertainties, ...])	DogBox algorithm and least squares statistic.
LMLSQFitter([calc_uncertainties])	scipy.optimize.least_squares Levenberg-Marquardt algorithm and least squares statistic.
FittingWithOutlierRemoval(fitter, outlier_func)	This class combines an outlier removal technique with a fitting procedure.
SLSQPLSQFitter()	Sequential Least Squares Programming (SLSQP) optimization algorithm and least squares statistic.
SimplexLSQFitter()	Simplex algorithm and least squares statistic.
JointFitter(models, jointparameters, initvals)	Fit models which share a parameter.
Fitter(optimizer, statistic)	Base class for all fitters.
ModelLinearityError	Raised when a non-linear model is passed to a linear fitter.
ModelsError	Base class for model exceptions

Class Inheritance Diagram

astropy.modeling.optimizers Module

Optimization algorithms used in fitting.

Classes

Optimization(opt_method)	Base class for optimizers.
SLSQP()	Sequential Least Squares Programming optimization algorithm.
Simplex()	Neald-Mead (downhill simplex) algorithm.

Class Inheritance Diagram

astropy.modeling.statistic Module

Statistic functions used in fitting.

Functions

leastsquare(measured_vals, updated_model, ...)	Least square statistic, with optional weights, in N-dimensions.
leastsquare_1d(measured_vals, updated_model, ...)	Least square statistic with optional weights.
leastsquare_2d(measured_vals, updated_model, ...)	Least square statistic with optional weights.
leastsquare_3d(measured_vals, updated_model, ...)	Least square statistic with optional weights.

astropy.modeling.separable Module

Functions to determine if a model is separable, i.e. if the model outputs are independent.

It analyzes n_inputs, n_outputs and the operators in a compound model by stepping through the transforms and creating a coord_matrix of shape (n_outputs, n_inputs).

Each modeling operator is represented by a function which takes two simple models (or two coord_matrix arrays) and returns an array of shape (n_outputs, n_inputs).

Functions

is_separable(transform)	A separability test for the outputs of a transform.
separability_matrix(transform)	Compute the correlation between outputs and inputs.

Pre-Defined Models

astropy.modeling.functional_models Module

Mathematical models.

Classes

AiryDisk2D([amplitude, x_0, y_0, radius])	Two dimensional Airy disk model.
Moffat1D([amplitude, x_0, gamma, alpha])	One dimensional Moffat model.
Moffat2D([amplitude, x_0, y_0, gamma, alpha])	Two dimensional Moffat model.
Box1D([amplitude, x_0, width])	One dimensional Box model.
Box2D([amplitude, x_0, y_0, x_width, y_width])	Two dimensional Box model.
Const1D([amplitude])	One dimensional Constant model.
Const2D([amplitude])	Two dimensional Constant model.
Ellipse2D([amplitude, x_0, y_0, a, b, theta])	A 2D Ellipse model.
Disk2D([amplitude, x_0, y_0, R_0])	Two dimensional radial symmetric Disk model.
Gaussian1D([amplitude, mean, stddev])	One dimensional Gaussian model.
Gaussian2D([amplitude, x_mean, y_mean, ...])	Two dimensional Gaussian model.
Linear1D([slope, intercept])	One dimensional Line model.
Lorentz1D([amplitude, x_0, fwhm])	One dimensional Lorentzian model.
RickerWavelet1D([amplitude, x_0, sigma])	One dimensional Ricker Wavelet model (sometimes known as a "Mexican Hat" model).
RickerWavelet2D([amplitude, x_0, y_0, sigma])	Two dimensional Ricker Wavelet model (sometimes known as a "Mexican Hat" model).
RedshiftScaleFactor([z])	One dimensional redshift scale factor model.
Multiply([factor])	Multiply a model by a quantity or number.
Planar2D([slope_x, slope_y, intercept])	Two dimensional Plane model.
Scale([factor])	Multiply a model by a dimensionless factor.
Sersic1D([amplitude, r_eff, n])	One dimensional Sersic surface brightness profile.
Sersic2D([amplitude, r_eff, n, x_0, y_0, ...])	Two dimensional Sersic surface brightness profile.
Shift([offset])	Shift a coordinate.
Sine1D(*args[, meta, name])	One dimensional Sine model.
Cosine1D(*args[, meta, name])	One dimensional Cosine model.
Tangent1D(*args[, meta, name])	One dimensional Tangent model.
ArcSine1D(*args[, meta, name])	One dimensional ArcSine model returning values between -pi/2 and pi/2 only.
ArcCosine1D(*args[, meta, name])	One dimensional ArcCosine returning values between 0 and pi only.
ArcTangent1D(*args[, meta, name])	One dimensional ArcTangent model returning values between -pi/2 and pi/2 only.
Trapezoid1D([amplitude, x_0, width, slope])	One dimensional Trapezoid model.
TrapezoidDisk2D([amplitude, x_0, y_0, R_0, ...])	Two dimensional circular Trapezoid model.
Ring2D([amplitude, x_0, y_0, r_in, width, r_out])	Two dimensional radial symmetric Ring model.
Voigt1D([x_0, amplitude_L, fwhm_L, fwhm_G, ...])	One dimensional model for the Voigt profile.
KingProjectedAnalytic1D([amplitude, r_core, ...])	Projected (surface density) analytic King Model.
Exponential1D([amplitude, tau])	One dimensional exponential model.
Logarithmic1D([amplitude, tau])	One dimensional logarithmic model.

Class Inheritance Diagram

astropy.modeling.physical_models Module

Models that have physical origins.

Classes

BlackBody(*args, **kwargs)	Blackbody model using the Planck function.
Drude1D([amplitude, x_0, fwhm])	Drude model based one the behavior of electons in materials (esp.
Plummer1D([mass, r_plum])	One dimensional Plummer density profile model.
NFW([mass, concentration, redshift, ...])	Navarro–Frenk–White (NFW) profile - model for radial distribution of dark matter.

Class Inheritance Diagram

astropy.modeling.powerlaws Module

Power law model variants

Classes

PowerLaw1D([amplitude, x_0, alpha])	One dimensional power law model.
BrokenPowerLaw1D([amplitude, x_break, ...])	One dimensional power law model with a break.
SmoothlyBrokenPowerLaw1D([amplitude, ...])	One dimensional smoothly broken power law model.
ExponentialCutoffPowerLaw1D([amplitude, ...])	One dimensional power law model with an exponential cutoff.
LogParabola1D([amplitude, x_0, alpha, beta])	One dimensional log parabola model (sometimes called curved power law).
Schechter1D([phi_star, m_star, alpha])	Schechter luminosity function (Schechter 1976), parameterized in terms of magnitudes.

Class Inheritance Diagram

astropy.modeling.polynomial Module

This module contains models representing polynomials and polynomial series.

Classes

Chebyshev1D(degree[, domain, window, ...])	Univariate Chebyshev series.
Chebyshev2D(x_degree, y_degree[, x_domain, ...])	Bivariate Chebyshev series..
Hermite1D(degree[, domain, window, ...])	Univariate Hermite series.
Hermite2D(x_degree, y_degree[, x_domain, ...])	Bivariate Hermite series.
InverseSIP(ap_order, bp_order[, ap_coeff, ...])	Inverse Simple Imaging Polynomial
Legendre1D(degree[, domain, window, ...])	Univariate Legendre series.
Legendre2D(x_degree, y_degree[, x_domain, ...])	Bivariate Legendre series.
Polynomial1D(degree[, domain, window, ...])	1D Polynomial model.
Polynomial2D(degree[, x_domain, y_domain, ...])	2D Polynomial model.
SIP(crpix, a_order, b_order[, a_coeff, ...])	Simple Imaging Polynomial (SIP) model.
OrthoPolynomialBase(x_degree, y_degree[, ...])	This is a base class for the 2D Chebyshev and Legendre models.
PolynomialModel(degree[, n_models, ...])	Base class for polynomial models.

Class Inheritance Diagram

astropy.modeling.projections Module

Implements projections–particularly sky projections defined in WCS Paper II [1].

All angles are set and and displayed in degrees but internally computations are performed in radians. All functions expect inputs and outputs degrees.

References

[1]

Calabretta, M.R., Greisen, E.W., 2002, A&A, 395, 1077 (Paper II)

Classes

Projection(*args, **kwargs)	Base class for all sky projections.
Pix2SkyProjection(*args, **kwargs)	Base class for all Pix2Sky projections.
Sky2PixProjection(*args, **kwargs)	Base class for all Sky2Pix projections.
Zenithal(*args, **kwargs)	Base class for all Zenithal projections.
Cylindrical(*args, **kwargs)	Base class for Cylindrical projections.
PseudoCylindrical(*args, **kwargs)	Base class for pseudocylindrical projections.
Conic(*args, **kwargs)	Base class for conic projections.
PseudoConic(*args, **kwargs)	Base class for pseudoconic projections.
QuadCube(*args, **kwargs)	Base class for quad cube projections.
HEALPix(*args, **kwargs)	Base class for HEALPix projections.
AffineTransformation2D([matrix, translation])	Perform an affine transformation in 2 dimensions.
Pix2Sky_ZenithalPerspective(*args, **kwargs)	Zenithal perspective projection - pixel to sky.
Pix2Sky_AZP	alias of Pix2Sky_ZenithalPerspective
Pix2Sky_SlantZenithalPerspective(*args, **kwargs)	Slant zenithal perspective projection - pixel to sky.
Pix2Sky_SZP	alias of Pix2Sky_SlantZenithalPerspective
Pix2Sky_Gnomonic(*args, **kwargs)	Gnomonic projection - pixel to sky.
Pix2Sky_TAN	alias of Pix2Sky_Gnomonic
Pix2Sky_Stereographic(*args, **kwargs)	Stereographic Projection - pixel to sky.
Pix2Sky_STG	alias of Pix2Sky_Stereographic
Pix2Sky_SlantOrthographic(*args, **kwargs)	Slant orthographic projection - pixel to sky.
Pix2Sky_SIN	alias of Pix2Sky_SlantOrthographic
Pix2Sky_ZenithalEquidistant(*args, **kwargs)	Zenithal equidistant projection - pixel to sky.
Pix2Sky_ARC	alias of Pix2Sky_ZenithalEquidistant
Pix2Sky_ZenithalEqualArea(*args, **kwargs)	Zenithal equidistant projection - pixel to sky.
Pix2Sky_ZEA	alias of Pix2Sky_ZenithalEqualArea
Pix2Sky_Airy(*args, **kwargs)	Airy projection - pixel to sky.
Pix2Sky_AIR	alias of Pix2Sky_Airy
Pix2Sky_CylindricalPerspective(*args, **kwargs)	Cylindrical perspective - pixel to sky.
Pix2Sky_CYP	alias of Pix2Sky_CylindricalPerspective
Pix2Sky_CylindricalEqualArea(*args, **kwargs)	Cylindrical equal area projection - pixel to sky.
Pix2Sky_CEA	alias of Pix2Sky_CylindricalEqualArea
Pix2Sky_PlateCarree(*args, **kwargs)	Plate carrée projection - pixel to sky.
Pix2Sky_CAR	alias of Pix2Sky_PlateCarree
Pix2Sky_Mercator(*args, **kwargs)	Mercator - pixel to sky.
Pix2Sky_MER	alias of Pix2Sky_Mercator
Pix2Sky_SansonFlamsteed(*args, **kwargs)	Sanson-Flamsteed projection - pixel to sky.
Pix2Sky_SFL	alias of Pix2Sky_SansonFlamsteed
Pix2Sky_Parabolic(*args, **kwargs)	Parabolic projection - pixel to sky.
Pix2Sky_PAR	alias of Pix2Sky_Parabolic
Pix2Sky_Molleweide(*args, **kwargs)	Molleweide's projection - pixel to sky.
Pix2Sky_MOL	alias of Pix2Sky_Molleweide
Pix2Sky_HammerAitoff(*args, **kwargs)	Hammer-Aitoff projection - pixel to sky.
Pix2Sky_AIT	alias of Pix2Sky_HammerAitoff
Pix2Sky_ConicPerspective(*args, **kwargs)	Colles' conic perspective projection - pixel to sky.
Pix2Sky_COP	alias of Pix2Sky_ConicPerspective
Pix2Sky_ConicEqualArea(*args, **kwargs)	Alber's conic equal area projection - pixel to sky.
Pix2Sky_COE	alias of Pix2Sky_ConicEqualArea
Pix2Sky_ConicEquidistant(*args, **kwargs)	Conic equidistant projection - pixel to sky.
Pix2Sky_COD	alias of Pix2Sky_ConicEquidistant
Pix2Sky_ConicOrthomorphic(*args, **kwargs)	Conic orthomorphic projection - pixel to sky.
Pix2Sky_COO	alias of Pix2Sky_ConicOrthomorphic
Pix2Sky_BonneEqualArea(*args, **kwargs)	Bonne's equal area pseudoconic projection - pixel to sky.
Pix2Sky_BON	alias of Pix2Sky_BonneEqualArea
Pix2Sky_Polyconic(*args, **kwargs)	Polyconic projection - pixel to sky.
Pix2Sky_PCO	alias of Pix2Sky_Polyconic
Pix2Sky_TangentialSphericalCube(*args, **kwargs)	Tangential spherical cube projection - pixel to sky.
Pix2Sky_TSC	alias of Pix2Sky_TangentialSphericalCube
Pix2Sky_COBEQuadSphericalCube(*args, **kwargs)	COBE quadrilateralized spherical cube projection - pixel to sky.
Pix2Sky_CSC	alias of Pix2Sky_COBEQuadSphericalCube
Pix2Sky_QuadSphericalCube(*args, **kwargs)	Quadrilateralized spherical cube projection - pixel to sky.
Pix2Sky_QSC	alias of Pix2Sky_QuadSphericalCube
Pix2Sky_HEALPix(*args, **kwargs)	HEALPix - pixel to sky.
Pix2Sky_HPX	alias of Pix2Sky_HEALPix
Pix2Sky_HEALPixPolar(*args, **kwargs)	HEALPix polar, aka "butterfly" projection - pixel to sky.
Pix2Sky_XPH	alias of Pix2Sky_HEALPixPolar
Sky2Pix_ZenithalPerspective(*args, **kwargs)	Zenithal perspective projection - sky to pixel.
Sky2Pix_AZP	alias of Sky2Pix_ZenithalPerspective
Sky2Pix_SlantZenithalPerspective(*args, **kwargs)	Zenithal perspective projection - sky to pixel.
Sky2Pix_SZP	alias of Sky2Pix_SlantZenithalPerspective
Sky2Pix_Gnomonic(*args, **kwargs)	Gnomonic Projection - sky to pixel.
Sky2Pix_TAN	alias of Sky2Pix_Gnomonic
Sky2Pix_Stereographic(*args, **kwargs)	Stereographic Projection - sky to pixel.
Sky2Pix_STG	alias of Sky2Pix_Stereographic
Sky2Pix_SlantOrthographic(*args, **kwargs)	Slant orthographic projection - sky to pixel.
Sky2Pix_SIN	alias of Sky2Pix_SlantOrthographic
Sky2Pix_ZenithalEquidistant(*args, **kwargs)	Zenithal equidistant projection - sky to pixel.
Sky2Pix_ARC	alias of Sky2Pix_ZenithalEquidistant
Sky2Pix_ZenithalEqualArea(*args, **kwargs)	Zenithal equidistant projection - sky to pixel.
Sky2Pix_ZEA	alias of Sky2Pix_ZenithalEqualArea
Sky2Pix_Airy(*args, **kwargs)	Airy - sky to pixel.
Sky2Pix_AIR	alias of Sky2Pix_Airy
Sky2Pix_CylindricalPerspective(*args, **kwargs)	Cylindrical Perspective - sky to pixel.
Sky2Pix_CYP	alias of Sky2Pix_CylindricalPerspective
Sky2Pix_CylindricalEqualArea(*args, **kwargs)	Cylindrical equal area projection - sky to pixel.
Sky2Pix_CEA	alias of Sky2Pix_CylindricalEqualArea
Sky2Pix_PlateCarree(*args, **kwargs)	Plate carrée projection - sky to pixel.
Sky2Pix_CAR	alias of Sky2Pix_PlateCarree
Sky2Pix_Mercator(*args, **kwargs)	Mercator - sky to pixel.
Sky2Pix_MER	alias of Sky2Pix_Mercator
Sky2Pix_SansonFlamsteed(*args, **kwargs)	Sanson-Flamsteed projection - sky to pixel.
Sky2Pix_SFL	alias of Sky2Pix_SansonFlamsteed
Sky2Pix_Parabolic(*args, **kwargs)	Parabolic projection - sky to pixel.
Sky2Pix_PAR	alias of Sky2Pix_Parabolic
Sky2Pix_Molleweide(*args, **kwargs)	Molleweide's projection - sky to pixel.
Sky2Pix_MOL	alias of Sky2Pix_Molleweide
Sky2Pix_HammerAitoff(*args, **kwargs)	Hammer-Aitoff projection - sky to pixel.
Sky2Pix_AIT	alias of Sky2Pix_HammerAitoff
Sky2Pix_ConicPerspective(*args, **kwargs)	Colles' conic perspective projection - sky to pixel.
Sky2Pix_COP	alias of Sky2Pix_ConicPerspective
Sky2Pix_ConicEqualArea(*args, **kwargs)	Alber's conic equal area projection - sky to pixel.
Sky2Pix_COE	alias of Sky2Pix_ConicEqualArea
Sky2Pix_ConicEquidistant(*args, **kwargs)	Conic equidistant projection - sky to pixel.
Sky2Pix_COD	alias of Sky2Pix_ConicEquidistant
Sky2Pix_ConicOrthomorphic(*args, **kwargs)	Conic orthomorphic projection - sky to pixel.
Sky2Pix_COO	alias of Sky2Pix_ConicOrthomorphic
Sky2Pix_BonneEqualArea(*args, **kwargs)	Bonne's equal area pseudoconic projection - sky to pixel.
Sky2Pix_BON	alias of Sky2Pix_BonneEqualArea
Sky2Pix_Polyconic(*args, **kwargs)	Polyconic projection - sky to pixel.
Sky2Pix_PCO	alias of Sky2Pix_Polyconic
Sky2Pix_TangentialSphericalCube(*args, **kwargs)	Tangential spherical cube projection - sky to pixel.
Sky2Pix_TSC	alias of Sky2Pix_TangentialSphericalCube
Sky2Pix_COBEQuadSphericalCube(*args, **kwargs)	COBE quadrilateralized spherical cube projection - sky to pixel.
Sky2Pix_CSC	alias of Sky2Pix_COBEQuadSphericalCube
Sky2Pix_QuadSphericalCube(*args, **kwargs)	Quadrilateralized spherical cube projection - sky to pixel.
Sky2Pix_QSC	alias of Sky2Pix_QuadSphericalCube
Sky2Pix_HEALPix(*args, **kwargs)	HEALPix projection - sky to pixel.
Sky2Pix_HPX	alias of Sky2Pix_HEALPix
Sky2Pix_HEALPixPolar(*args, **kwargs)	HEALPix polar, aka "butterfly" projection - pixel to sky.
Sky2Pix_XPH	alias of Sky2Pix_HEALPixPolar

Class Inheritance Diagram

astropy.modeling.rotations Module

Implements rotations, including spherical rotations as defined in WCS Paper II [1]

RotateNative2Celestial and RotateCelestial2Native follow the convention in WCS Paper II to rotate to/from a native sphere and the celestial sphere.

The implementation uses EulerAngleRotation. The model parameters are three angles: the longitude (lon) and latitude (lat) of the fiducial point in the celestial system (CRVAL keywords in FITS), and the longitude of the celestial pole in the native system (lon_pole). The Euler angles are lon+90, 90-lat and -(lon_pole-90).

References

[1]

Calabretta, M.R., Greisen, E.W., 2002, A&A, 395, 1077 (Paper II)

Classes

RotateCelestial2Native(lon, lat, lon_pole, ...)	Transform from Celestial to Native Spherical Coordinates.
RotateNative2Celestial(lon, lat, lon_pole, ...)	Transform from Native to Celestial Spherical Coordinates.
Rotation2D([angle])	Perform a 2D rotation given an angle.
EulerAngleRotation(phi, theta, psi, ...)	Implements Euler angle intrinsic rotations.
RotationSequence3D(angles, axes_order[, name])	Perform a series of rotations about different axis in 3D space.
SphericalRotationSequence(angles, axes_order)	Perform a sequence of rotations about arbitrary number of axes in spherical coordinates.

Class Inheritance Diagram

astropy.modeling.spline Module

Spline models and fitters.

Classes

Spline1D([knots, coeffs, degree, bounds, ...])	One dimensional Spline Model
SplineInterpolateFitter()	Fit an interpolating spline
SplineSmoothingFitter()	Fit a smoothing spline
SplineExactKnotsFitter()	Fit a spline using least-squares regression.
SplineSplrepFitter()	Fit a spline using the scipy.interpolate.splrep function interface.

Class Inheritance Diagram

astropy.modeling.tabular Module

Tabular models.

Tabular models of any dimension can be created using tabular_model. For convenience Tabular1D and Tabular2D are provided.

Examples

>>> table = np.array([[ 3.,  0.,  0.],
...                  [ 0.,  2.,  0.],
...                  [ 0.,  0.,  0.]])
>>> points = ([1, 2, 3], [1, 2, 3])
>>> t2 = Tabular2D(points, lookup_table=table, bounds_error=False,
...                fill_value=None, method='nearest')

Functions

tabular_model(dim[, name])

Make a Tabular model where n_inputs is based on the dimension of the lookup_table.

Classes

Tabular1D([points, lookup_table, method, ...])	Tabular model in 1D.
Tabular2D([points, lookup_table, method, ...])	Tabular model in 2D.

Class Inheritance Diagram