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.. _predef_models2D:
*********
2D Models
*********
These models take as input x and y arrays.
Operations
==========
These models perform simple mathematical operations.
- :class:`~astropy.modeling.functional_models.Const2D` model returns the
constant replicated by the number of input x and y values.
Shapes
======
These models provide shapes, often used to model general x, y, z data.
- :class:`~astropy.modeling.functional_models.Planar2D` model computes
a tilted plan with specified x,y slopes and z intercept
Profiles
========
These models provide profiles, often used sources in images.
All models have parameters giving the x,y location of the center and
an amplitude.
- :class:`~astropy.modeling.functional_models.AiryDisk2D` model computes
the Airy function for a radius
- :class:`~astropy.modeling.functional_models.Box2D` model computes a box
with x,y dimensions
- :class:`~astropy.modeling.functional_models.Disk2D` model computes a
disk a radius
- :class:`~astropy.modeling.functional_models.Ellipse2D` model computes
an ellipse with major and minor axis and rotation angle
- :class:`~astropy.modeling.functional_models.Gaussian2D` model computes
a Gaussian with x,y standard deviations and rotation angle
- :class:`~astropy.modeling.functional_models.Moffat2D` model computes
a Moffat with x,y dimensions and alpha (power index) and gamma (core width)
- :class:`~astropy.modeling.functional_models.Lorentz2D` model computes
a Lorentz profile with x,y dimensions and full width at half maximum
- :class:`~astropy.modeling.functional_models.RickerWavelet2D` model computes
a symmetric RickerWavelet function with the specified sigma
- :class:`~astropy.modeling.functional_models.Sersic2D` model computes
a Sersic profile with an effective half-light radius, rotation, and
Sersic index
- :class:`~astropy.modeling.functional_models.GeneralSersic2D` model
computes a generalized Sersic profile with an effective half-light
radius, rotation, Sersic index, and a parameter to control the shape of
the isophotes (e.g., boxy or disky)
- :class:`~astropy.modeling.functional_models.TrapezoidDisk2D` model
computes a disk with a radius and slope
- :class:`~astropy.modeling.functional_models.Ring2D` model computes
a ring with inner and outer radii
.. plot::
import numpy as np
import math
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
from astropy.modeling.models import (AiryDisk2D, Box2D, Disk2D, Ellipse2D,
Gaussian2D, Moffat2D, Lorentz2D,
RickerWavelet2D, Sersic2D,
GeneralSersic2D,
TrapezoidDisk2D, Ring2D)
x = np.linspace(-4.0, 6.0, num=100)
r = np.logspace(-1.0, 2.0, num=100)
fig, sax = plt.subplots(nrows=5, ncols=3, figsize=(9, 12))
ax = sax.flatten()
# setup the x,y coordinates
x_npts = 100
y_npts = x_npts
x0, x1 = -4, 6
y0, y1 = -3, 7
x = np.linspace(x0, x1, num=x_npts)
y = np.linspace(y0, y1, num=y_npts)
X, Y = np.meshgrid(x, y)
# plot the different 2D profiles
mods = [AiryDisk2D(amplitude=10.0, x_0=1.0, y_0=2.0, radius=1.0),
Box2D(amplitude=10.0, x_0=1.0, y_0=2.0, x_width=1.0, y_width=2.0),
Disk2D(amplitude=10.0, x_0=1.0, y_0=2.0, R_0=1.0),
Ellipse2D(amplitude=10.0, x_0=1.0, y_0=2.0, a=1.0, b=2.0, theta=math.pi/4.),
Gaussian2D(amplitude=10.0, x_mean=1.0, y_mean=2.0, x_stddev=1.0, y_stddev=2.0, theta=math.pi/4.),
Moffat2D(amplitude=10.0, x_0=1.0, y_0=2.0, alpha=3, gamma=4),
Lorentz2D(amplitude=10.0, x_0=1.0, y_0=2.0, fwhm=3),
RickerWavelet2D(amplitude=10.0, x_0=1.0, y_0=2.0, sigma=1.0),
Sersic2D(amplitude=10.0, x_0=1.0, y_0=2.0, r_eff=1.0, ellip=0.5, theta=math.pi/4.),
GeneralSersic2D(amplitude=10.0, x_0=1.0, y_0=2.0, r_eff=1.0, ellip=0.5, theta=math.pi/4., c=-1),
GeneralSersic2D(amplitude=10.0, x_0=1.0, y_0=2.0, r_eff=1.0, ellip=0.5, theta=math.pi/4., c=1),
TrapezoidDisk2D(amplitude=10.0, x_0=1.0, y_0=2.0, R_0=1.0, slope=5.0),
Ring2D(amplitude=10.0, x_0=1.0, y_0=2.0, r_in=1.0, r_out=2.0)]
for k, mod in enumerate(mods):
cname = mod.__class__.__name__
if cname == "AiryDisk2D":
normfunc = LogNorm(vmin=0.001, vmax=10.)
elif cname in ["Gaussian2D", "Sersic2D", "GeneralSersic2D"]:
normfunc = LogNorm(vmin=0.1, vmax=10.)
else:
normfunc = None
if cname == "GeneralSersic2D":
cname = f'{cname}, c={mod.c.value:.1f}'
ax[k].set_title(cname)
ax[k].imshow(mod(X, Y), extent=[x0, x1, y0, y1], origin="lower", cmap=plt.cm.gray_r,
norm=normfunc)
for k in range(len(mods)):
ax[k].set_xlabel("x")
ax[k].set_ylabel("y")
# remove axis for any plots not used
for k in range(len(mods), len(ax)):
ax[k].axis("off")
plt.tight_layout()
plt.show()
|
