Models and Fitting (astropy.modeling
)¶
Introduction¶
astropy.modeling
provides a framework for representing models and performing
model evaluation and fitting. It currently supports 1-D and 2-D models and
fitting with parameter constraints.
It is designed to be easily extensible and flexible. Models do not reference fitting algorithms explicitly and new fitting algorithms may be added without changing the existing models (though not all models can be used with all fitting algorithms due to constraints such as model linearity).
The goal is to eventually provide a rich toolset of models and fitters such that most users will not need to define new model classes, nor special purpose fitting routines (while making it reasonably easy to do when necessary).
Note
astropy.modeling
is currently a work-in-progress, and thus it is likely
there will still be API changes in later versions of Astropy. Backwards
compatibility support between versions will still be maintained as much as
possible, but new features and enhancements are coming in future versions.
If you have specific ideas for how it might be improved, feel free to let
us know on the astropy-dev mailing list or at
http://feedback.astropy.org
Getting started¶
The examples here use the predefined models and assume the following modules have been imported:
>>> import numpy as np
>>> from astropy.modeling import models, fitting
Using Models¶
The astropy.modeling
package defines a number of models that are collected
under a single namespace as astropy.modeling.models
. Models behave like
parametrized functions:
>>> from astropy.modeling import models
>>> g = models.Gaussian1D(amplitude=1.2, mean=0.9, stddev=0.5)
>>> print(g)
Model: Gaussian1D
Inputs: ('x',)
Outputs: ('y',)
Model set size: 1
Parameters:
amplitude mean stddev
--------- ---- ------
1.2 0.9 0.5
Model parameters can be accessed as attributes:
>>> g.amplitude
Parameter('amplitude', value=1.2)
>>> g.mean
Parameter('mean', value=0.9)
>>> g.stddev
Parameter('stddev', value=0.5)
and can also be updated via those attributes:
>>> g.amplitude = 0.8
>>> g.amplitude
Parameter('amplitude', value=0.8)
Models can be evaluated by calling them as functions:
>>> g(0.1)
0.22242984036255528
>>> g(np.linspace(0.5, 1.5, 7))
array([ 0.58091923, 0.71746405, 0.7929204 , 0.78415894, 0.69394278,
0.54952605, 0.3894018 ])
As the above example demonstrates, in general most models evaluate array-like inputs according to the standard Numpy broadcasting rules for arrays.
Models can therefore already be useful to evaluate common functions, independently of the fitting features of the package.
Simple 1-D model fitting¶
In this section, we look at a simple example of fitting a Gaussian to a
simulated dataset. We use the Gaussian1D
and Trapezoid1D
models and the
LevMarLSQFitter
fitter to fit the data:
import numpy as np
import matplotlib.pyplot as plt
from astropy.modeling import models, fitting
# Generate fake data
np.random.seed(0)
x = np.linspace(-5., 5., 200)
y = 3 * np.exp(-0.5 * (x - 1.3)**2 / 0.8**2)
y += np.random.normal(0., 0.2, x.shape)
# Fit the data using a box model
t_init = models.Trapezoid1D(amplitude=1., x_0=0., width=1., slope=0.5)
fit_t = fitting.LevMarLSQFitter()
t = fit_t(t_init, x, y)
# Fit the data using a Gaussian
g_init = models.Gaussian1D(amplitude=1., mean=0, stddev=1.)
fit_g = fitting.LevMarLSQFitter()
g = fit_g(g_init, x, y)
# Plot the data with the best-fit model
plt.figure(figsize=(8,5))
plt.plot(x, y, 'ko')
plt.plot(x, t(x), label='Trapezoid')
plt.plot(x, g(x), label='Gaussian')
plt.xlabel('Position')
plt.ylabel('Flux')
plt.legend(loc=2)
(Source code, png, hires.png, pdf)
As shown above, once instantiated, the fitter class can be used as a function
that takes the initial model (t_init
or g_init
) and the data values
(x
and y
), and returns a fitted model (t
or g
).
Simple 2-D model fitting¶
Similarly to the 1-D example, we can create a simulated 2-D data dataset, and fit a polynomial model to it. This could be used for example to fit the background in an image.
import warnings
import numpy as np
import matplotlib.pyplot as plt
from astropy.modeling import models, fitting
# Generate fake data
np.random.seed(0)
y, x = np.mgrid[:128, :128]
z = 2. * x ** 2 - 0.5 * x ** 2 + 1.5 * x * y - 1.
z += np.random.normal(0., 0.1, z.shape) * 50000.
# Fit the data using astropy.modeling
p_init = models.Polynomial2D(degree=2)
fit_p = fitting.LevMarLSQFitter()
with warnings.catch_warnings():
# Ignore model linearity warning from the fitter
warnings.simplefilter('ignore')
p = fit_p(p_init, x, y, z)
# Plot the data with the best-fit model
plt.figure(figsize=(8, 2.5))
plt.subplot(1, 3, 1)
plt.imshow(z, origin='lower', interpolation='nearest', vmin=-1e4, vmax=5e4)
plt.title("Data")
plt.subplot(1, 3, 2)
plt.imshow(p(x, y), origin='lower', interpolation='nearest', vmin=-1e4,
vmax=5e4)
plt.title("Model")
plt.subplot(1, 3, 3)
plt.imshow(z - p(x, y), origin='lower', interpolation='nearest', vmin=-1e4,
vmax=5e4)
plt.title("Residual")
(Source code, png, hires.png, pdf)
A list of models is provided in the Reference/API section. The fitting framework includes many useful features that are not demonstrated here, such as weighting of datapoints, fixing or linking parameters, and placing lower or upper limits on parameters. For more information on these, take a look at the Fitting Models to Data documentation.
Model sets¶
In some cases it is necessary to describe many models of the same type but with
different sets of parameter values. This could be done simply by instantiating
as many instances of a Model
as are needed. But that can
be inefficient for a large number of models. To that end, all model classes in
astropy.modeling
can also be used to represent a model set which is a
collection of models of the same type, but with different values for their
parameters.
To instantiate a model set, use argument n_models=N
where N
is the
number of models in the set when constructing the model. The value of each
parameter must be a list or array of length N
, such that each item in
the array corresponds to one model in the set:
>>> g = models.Gaussian1D(amplitude=[1, 2], mean=[0, 0],
... stddev=[0.1, 0.2], n_models=2)
>>> print(g)
Model: Gaussian1D
Inputs: ('x',)
Outputs: ('y',)
Model set size: 2
Parameters:
amplitude mean stddev
--------- ---- ------
1.0 0.0 0.1
2.0 0.0 0.2
This is equivalent to two Gaussians with the parameters amplitude=1, mean=0,
stddev=0.1
and amplitude=2, mean=0, stddev=0.2
respectively. When
printing the model the parameter values are displayed as a table, with each row
corresponding to a single model in the set.
The number of models in a model set can be determined using the len
builtin:
>>> len(g)
2
Single models have a length of 1, and are not considered a model set as such.
When evaluating a model set, by default the input must be the same length as the number of models, with one input per model:
>>> g([0, 0.1])
array([ 1. , 1.76499381])
The result is an array with one result per model in the set. It is also possible to broadcast a single value to all models in the set:
>>> g(0)
array([ 1., 2.])
Model sets are used primarily for fitting, allowing a large number of models of the same type to be fitted simultaneously (and independently from each other) to some large set of inputs. For example, fitting a polynomial to the time response of each pixel in a data cube. This can greatly speed up the fitting process, especially for linear models.
Compound models¶
New in version 1.0: This feature is experimental and expected to see significant further development, but the basic usage is stable and expected to see wide use.
While the Astropy modeling package makes it very easy to define new
models either from existing functions, or by writing a
Model
subclass, an additional way to create new models is
by combining them using arithmetic expressions. This works with models built
into Astropy, and most user-defined models as well. For example, it is
possible to create a superposition of two Gaussians like so:
>>> from astropy.modeling import models
>>> g1 = models.Gaussian1D(1, 0, 0.2)
>>> g2 = models.Gaussian1D(2.5, 0.5, 0.1)
>>> g1_plus_2 = g1 + g2
The resulting object g1_plus_2
is itself a new model. Evaluating, say,
g1_plus_2(0.25)
is the same as evaluating g1(0.25) + g2(0.25)
:
>>> g1_plus_2(0.25)
0.5676756958301329
>>> g1_plus_2(0.25) == g1(0.25) + g2(0.25)
True
This model can be further combined with other models in new expressions. It is also possible to define entire new model classes using arithmetic expressions of other model classes. This allows general compound models to be created without specifying any parameter values up front. This more advanced usage is explained in more detail in the compound model documentation.
These new compound models can also be fitted to data, like most other models:
import numpy as np
import matplotlib.pyplot as plt
from astropy.modeling import models, fitting
# Generate fake data
np.random.seed(42)
g1 = models.Gaussian1D(1, 0, 0.2)
g2 = models.Gaussian1D(2.5, 0.5, 0.1)
x = np.linspace(-1, 1, 200)
y = g1(x) + g2(x) + np.random.normal(0., 0.2, x.shape)
# Now to fit the data create a new superposition with initial
# guesses for the parameters:
gg_init = models.Gaussian1D(1, 0, 0.1) + models.Gaussian1D(2, 0.5, 0.1)
fitter = fitting.SLSQPLSQFitter()
gg_fit = fitter(gg_init, x, y)
# Plot the data with the best-fit model
plt.figure(figsize=(8,5))
plt.plot(x, y, 'ko')
plt.plot(x, gg_fit(x))
plt.xlabel('Position')
plt.ylabel('Flux')
(Source code, png, hires.png, pdf)
This works for 1-D models, 2-D models, and combinations thereof, though there are some complexities involved in correctly matching up the inputs and outputs of all models used to build a compound model. You can learn more details in the Compound Models documentation.
Using astropy.modeling
¶
Reference/API¶
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¶
custom_model (*args, **kwargs) |
Create a model from a user defined function. |
Classes¶
Fittable1DModel |
Base class for one-dimensional fittable models. |
Fittable2DModel |
Base class for two-dimensional fittable models. |
FittableModel |
Base class for models that can be fitted using the built-in fitting algorithms. |
InputParameterError |
Used for incorrect input parameter values and definitions. |
LabeledInput (*args, **kwargs) |
Deprecated since version 1.0. |
Model |
Base class for all models. |
ModelDefinitionError |
Used for incorrect models definitions |
Parameter ([name, description, default, ...]) |
Wraps individual parameters. |
SerialCompositeModel |
Deprecated since version 1.0. |
SummedCompositeModel |
Deprecated since version 1.0. |
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 |
Allows inputs to be reordered, duplicated or dropped. |
Identity |
Returns inputs unchanged. |
Class Inheritance Diagram¶
astropy.modeling.functional_models Module¶
Mathematical models.
Functions¶
custom_model_1d (*args, **kwargs) |
Deprecated since version 1.0. |
Classes¶
AiryDisk2D |
Two dimensional Airy disk model. |
Box1D |
One dimensional Box model. |
Box2D |
Two dimensional Box model. |
Const1D |
One dimensional Constant model. |
Const2D |
Two dimensional Constant model. |
Disk2D |
Two dimensional radial symmetric Disk model. |
Ellipse2D |
A 2D Ellipse model. |
Gaussian1D |
One dimensional Gaussian model. |
Gaussian2D |
Two dimensional Gaussian model. |
GaussianAbsorption1D |
One dimensional Gaussian absorption line model. |
Linear1D |
One dimensional Line model. |
Lorentz1D |
One dimensional Lorentzian model. |
MexicanHat1D |
One dimensional Mexican Hat model. |
MexicanHat2D |
Two dimensional symmetric Mexican Hat model. |
Moffat1D |
One dimensional Moffat model. |
Moffat2D |
Two dimensional Moffat model. |
Redshift |
One dimensional redshift model. |
Ring2D |
Two dimensional radial symmetric Ring model. |
Scale |
Multiply a model by a factor. |
Sersic1D |
One dimensional Sersic surface brightness profile. |
Sersic2D |
Two dimensional Sersic surface brightness profile. |
Shift |
Shift a coordinate. |
Sine1D |
One dimensional Sine model. |
Trapezoid1D |
One dimensional Trapezoid model. |
TrapezoidDisk2D |
Two dimensional circular Trapezoid model. |
Voigt1D |
One dimensional model for the Voigt profile. |
Class Inheritance Diagram¶
astropy.modeling.powerlaws Module¶
Power law model variants
Classes¶
BrokenPowerLaw1D |
One dimensional power law model with a break. |
ExponentialCutoffPowerLaw1D |
One dimensional power law model with an exponential cutoff. |
LogParabola1D |
One dimensional log parabola model (sometimes called curved power law). |
PowerLaw1D |
One dimensional power law model. |
Class Inheritance Diagram¶
astropy.modeling.polynomial Module¶
This module contains predefined polynomial models.
Classes¶
Chebyshev1D |
1D Chebyshev polynomial of the 1st kind. |
Chebyshev2D |
2D Chebyshev polynomial of the 1st kind. |
InverseSIP |
Inverse Simple Imaging Polynomial |
Legendre1D |
1D Legendre polynomial. |
Legendre2D |
Legendre 2D polynomial. |
Polynomial1D |
1D Polynomial model. |
Polynomial2D |
2D Polynomial model. |
SIP |
Simple Imaging Polynomial (SIP) model. |
OrthoPolynomialBase |
This is a base class for the 2D Chebyshev and Legendre models. |
PolynomialModel |
Base class for polynomial models. |
Class Inheritance Diagram¶
astropy.modeling.projections Module¶
Implements projections–particularly sky projections defined in WCS Paper II [R45].
All angles are set and and displayed in degrees but internally computations are performed in radians.
Classes¶
Projection |
Base class for all sky projections. |
Pix2SkyProjection |
Base class for all Pix2Sky projections. |
Sky2PixProjection |
Base class for all Sky2Pix projections. |
Zenithal |
Base class for all Zenithal projections. |
Cylindrical |
Base class for Cylindrical projections. |
PseudoCylindrical |
Base class for pseudocylindrical projections. |
Conic |
Base class for conic projections. |
PseudoConic |
Base class for pseudoconic projections. |
QuadCube |
Base class for quad cube projections. |
HEALPix |
Base class for HEALPix projections. |
AffineTransformation2D |
Perform an affine transformation in 2 dimensions. |
Pix2Sky_ZenithalPerspective |
Zenithal perspective projection - pixel to sky. |
Sky2Pix_ZenithalPerspective |
Zenithal perspective projection - sky to pixel. |
Pix2Sky_SlantZenithalPerspective |
Slant zenithal perspective projection - pixel to sky. |
Sky2Pix_SlantZenithalPerspective |
Zenithal perspective projection - sky to pixel. |
Pix2Sky_Gnomonic |
Gnomonic projection - pixel to sky. |
Sky2Pix_Gnomonic |
Gnomonic Projection - sky to pixel. |
Pix2Sky_Stereographic |
Stereographic Projection - pixel to sky. |
Sky2Pix_Stereographic |
Stereographic Projection - sky to pixel. |
Pix2Sky_SlantOrthographic |
Slant orthographic projection - pixel to sky. |
Sky2Pix_SlantOrthographic |
Slant orthographic projection - sky to pixel. |
Pix2Sky_ZenithalEquidistant |
Zenithal equidistant projection - pixel to sky. |
Sky2Pix_ZenithalEquidistant |
Zenithal equidistant projection - sky to pixel. |
Pix2Sky_ZenithalEqualArea |
Zenithal equidistant projection - pixel to sky. |
Sky2Pix_ZenithalEqualArea |
Zenithal equidistant projection - sky to pixel. |
Pix2Sky_Airy |
Airy projection - pixel to sky. |
Sky2Pix_Airy |
Airy - sky to pixel. |
Pix2Sky_CylindricalPerspective |
Cylindrical perspective - pixel to sky. |
Sky2Pix_CylindricalPerspective |
Cylindrical Perspective - sky to pixel. |
Pix2Sky_CylindricalEqualArea |
Cylindrical equal area projection - pixel to sky. |
Sky2Pix_CylindricalEqualArea |
Cylindrical equal area projection - sky to pixel. |
Pix2Sky_PlateCarree |
Plate carrée projection - pixel to sky. |
Sky2Pix_PlateCarree |
Plate carrée projection - sky to pixel. |
Pix2Sky_Mercator |
Mercator - pixel to sky. |
Sky2Pix_Mercator |
Mercator - sky to pixel. |
Pix2Sky_SansonFlamsteed |
Sanson-Flamsteed projection - pixel to sky. |
Sky2Pix_SansonFlamsteed |
Sanson-Flamsteed projection - sky to pixel. |
Pix2Sky_Parabolic |
Parabolic projection - pixel to sky. |
Sky2Pix_Parabolic |
Parabolic projection - sky to pixel. |
Pix2Sky_Molleweide |
Molleweide’s projection - pixel to sky. |
Sky2Pix_Molleweide |
Molleweide’s projection - sky to pixel. |
Pix2Sky_HammerAitoff |
Hammer-Aitoff projection - pixel to sky. |
Sky2Pix_HammerAitoff |
Hammer-Aitoff projection - sky to pixel. |
Pix2Sky_ConicPerspective |
Colles’ conic perspective projection - pixel to sky. |
Sky2Pix_ConicPerspective |
Colles’ conic perspective projection - sky to pixel. |
Pix2Sky_ConicEqualArea |
Alber’s conic equal area projection - pixel to sky. |
Sky2Pix_ConicEqualArea |
Alber’s conic equal area projection - sky to pixel. |
Pix2Sky_ConicEquidistant |
Conic equidistant projection - pixel to sky. |
Sky2Pix_ConicEquidistant |
Conic equidistant projection - sky to pixel. |
Pix2Sky_ConicOrthomorphic |
Conic orthomorphic projection - pixel to sky. |
Sky2Pix_ConicOrthomorphic |
Conic orthomorphic projection - sky to pixel. |
Pix2Sky_BonneEqualArea |
Bonne’s equal area pseudoconic projection - pixel to sky. |
Sky2Pix_BonneEqualArea |
Bonne’s equal area pseudoconic projection - sky to pixel. |
Pix2Sky_Polyconic |
Polyconic projection - pixel to sky. |
Sky2Pix_Polyconic |
Polyconic projection - sky to pixel. |
Pix2Sky_TangentialSphericalCube |
Tangential spherical cube projection - pixel to sky. |
Sky2Pix_TangentialSphericalCube |
Tangential spherical cube projection - sky to pixel. |
Pix2Sky_COBEQuadSphericalCube |
COBE quadrilateralized spherical cube projection - pixel to sky. |
Sky2Pix_COBEQuadSphericalCube |
COBE quadrilateralized spherical cube projection - sky to pixel. |
Pix2Sky_QuadSphericalCube |
Quadrilateralized spherical cube projection - pixel to sky. |
Sky2Pix_QuadSphericalCube |
Quadrilateralized spherical cube projection - sky to pixel. |
Pix2Sky_HEALPix |
HEALPix - pixel to sky. |
Sky2Pix_HEALPix |
HEALPix projection - sky to pixel. |
Pix2Sky_HEALPixPolar |
HEALPix polar, aka “butterfly” projection - pixel to sky. |
Sky2Pix_HEALPixPolar |
HEALPix polar, aka “butterfly” projection - pixel to sky. |
Pix2Sky_AZP |
alias of Pix2Sky_ZenithalPerspective |
Sky2Pix_AZP |
alias of Sky2Pix_ZenithalPerspective |
Pix2Sky_SZP |
alias of Pix2Sky_SlantZenithalPerspective |
Sky2Pix_SZP |
alias of Sky2Pix_SlantZenithalPerspective |
Pix2Sky_TAN |
alias of Pix2Sky_Gnomonic |
Sky2Pix_TAN |
alias of Sky2Pix_Gnomonic |
Pix2Sky_STG |
alias of Pix2Sky_Stereographic |
Sky2Pix_STG |
alias of Sky2Pix_Stereographic |
Pix2Sky_SIN |
alias of Pix2Sky_SlantOrthographic |
Sky2Pix_SIN |
alias of Sky2Pix_SlantOrthographic |
Pix2Sky_ARC |
alias of Pix2Sky_ZenithalEquidistant |
Sky2Pix_ARC |
alias of Sky2Pix_ZenithalEquidistant |
Pix2Sky_ZEA |
alias of Pix2Sky_ZenithalEqualArea |
Sky2Pix_ZEA |
alias of Sky2Pix_ZenithalEqualArea |
Pix2Sky_AIR |
alias of Pix2Sky_Airy |
Sky2Pix_AIR |
alias of Sky2Pix_Airy |
Pix2Sky_CYP |
alias of Pix2Sky_CylindricalPerspective |
Sky2Pix_CYP |
alias of Sky2Pix_CylindricalPerspective |
Pix2Sky_CEA |
alias of Pix2Sky_CylindricalEqualArea |
Sky2Pix_CEA |
alias of Sky2Pix_CylindricalEqualArea |
Pix2Sky_CAR |
alias of Pix2Sky_PlateCarree |
Sky2Pix_CAR |
alias of Sky2Pix_PlateCarree |
Pix2Sky_MER |
alias of Pix2Sky_Mercator |
Sky2Pix_MER |
alias of Sky2Pix_Mercator |
Pix2Sky_SFL |
alias of Pix2Sky_SansonFlamsteed |
Sky2Pix_SFL |
alias of Sky2Pix_SansonFlamsteed |
Pix2Sky_PAR |
alias of Pix2Sky_Parabolic |
Sky2Pix_PAR |
alias of Sky2Pix_Parabolic |
Pix2Sky_MOL |
alias of Pix2Sky_Molleweide |
Sky2Pix_MOL |
alias of Sky2Pix_Molleweide |
Pix2Sky_AIT |
alias of Pix2Sky_HammerAitoff |
Sky2Pix_AIT |
alias of Sky2Pix_HammerAitoff |
Pix2Sky_COP |
alias of Pix2Sky_ConicPerspective |
Sky2Pix_COP |
alias of Sky2Pix_ConicPerspective |
Pix2Sky_COE |
alias of Pix2Sky_ConicEqualArea |
Sky2Pix_COE |
alias of Sky2Pix_ConicEqualArea |
Pix2Sky_COD |
alias of Pix2Sky_ConicEquidistant |
Sky2Pix_COD |
alias of Sky2Pix_ConicEquidistant |
Pix2Sky_COO |
alias of Pix2Sky_ConicOrthomorphic |
Sky2Pix_COO |
alias of Sky2Pix_ConicOrthomorphic |
Pix2Sky_BON |
alias of Pix2Sky_BonneEqualArea |
Sky2Pix_BON |
alias of Sky2Pix_BonneEqualArea |
Pix2Sky_PCO |
alias of Pix2Sky_Polyconic |
Sky2Pix_PCO |
alias of Sky2Pix_Polyconic |
Pix2Sky_TSC |
alias of Pix2Sky_TangentialSphericalCube |
Sky2Pix_TSC |
alias of Sky2Pix_TangentialSphericalCube |
Pix2Sky_CSC |
alias of Pix2Sky_COBEQuadSphericalCube |
Sky2Pix_CSC |
alias of Sky2Pix_COBEQuadSphericalCube |
Pix2Sky_QSC |
alias of Pix2Sky_QuadSphericalCube |
Sky2Pix_QSC |
alias of Sky2Pix_QuadSphericalCube |
Pix2Sky_HPX |
alias of Pix2Sky_HEALPix |
Sky2Pix_HPX |
alias of Sky2Pix_HEALPix |
Pix2Sky_XPH |
alias of Pix2Sky_HEALPixPolar |
Sky2Pix_XPH |
alias of Sky2Pix_HEALPixPolar |
Class Inheritance Diagram¶
astropy.modeling.rotations Module¶
Implements rotations, including spherical rotations as defined in WCS Paper II [R46]
RotateNative2Celestial
and RotateCelestial2Native
follow the convention in
WCS Paper II to rotate to/from a native sphere and the celestial sphere.
The user interface sets and displays angles in degrees but the values are stored internally in radians. This is managed through the parameter setters/getters.
Classes¶
RotateCelestial2Native |
Transform from Celestial to Native to Spherical Coordinates. |
RotateNative2Celestial |
Transform from Native to Celestial Spherical Coordinates. |
Rotation2D |
Perform a 2D rotation given an angle in degrees. |
EulerAngleRotation |
Implements Euler angle intrinsic rotations. |
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 () |
A class performing a linear least square fitting. |
LevMarLSQFitter () |
Levenberg-Marquardt algorithm and least squares statistic. |
SLSQPLSQFitter () |
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. |
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 [1]. |
Class Inheritance Diagram¶
astropy.modeling.statistic Module¶
Statistic functions used in fitting
.
Functions¶
leastsquare (measured_vals, updated_model, ...) |
Least square statistic with optional weights. |