testbed/astropy__astropy/astropy/modeling/tests/example_models.py

# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Here are all the test parameters and values for the each
`~astropy.modeling.FittableModel` defined. There is a dictionary for 1D and a
dictionary for 2D models.

Explanation of keywords of the dictionaries:

"parameters" : list or dict
    Model parameters, the model is tested with. Make sure you keep the right
    order.  For polynomials you can also use a dict to specify the
    coefficients. See examples below.

"x_values" : list
    x values where the model is evaluated.

"y_values" : list
    Reference y values for the in x_values given positions.

"z_values" : list
    Reference z values for the in x_values and y_values given positions.
    (2D model option)

"x_lim" : list
    x test range for the model fitter. Depending on the model this can differ
    e.g. the PowerLaw model should be tested over a few magnitudes.

"y_lim" : list
    y test range for the model fitter. Depending on the model this can differ
    e.g. the PowerLaw model should be tested over a few magnitudes.  (2D model
    option)

"log_fit" : bool
    PowerLaw models should be tested over a few magnitudes. So log_fit should
    be true.

"requires_scipy" : bool
    If a model requires scipy (Bessel functions etc.) set this flag.

"integral" : float
    Approximate value of the integral in the range x_lim (and y_lim).

"deriv_parameters" : list
    If given the test of the derivative will use these parameters to create a
    model (optional)

"deriv_initial" : list
    If given the test of the derivative will use these parameters as initial
    values for the fit (optional)
"""


from astropy.modeling.functional_models import (
    Gaussian1D, Sine1D, Box1D, Linear1D, Lorentz1D,
    MexicanHat1D, Trapezoid1D, Const1D, Moffat1D,
    Gaussian2D, Const2D, Box2D, MexicanHat2D,
    TrapezoidDisk2D, AiryDisk2D, Moffat2D, Disk2D,
    Ring2D, Sersic1D, Sersic2D, Voigt1D, Planar2D)
from astropy.modeling.polynomial import Polynomial1D, Polynomial2D
from astropy.modeling.powerlaws import (
    PowerLaw1D, BrokenPowerLaw1D, SmoothlyBrokenPowerLaw1D, ExponentialCutoffPowerLaw1D,
    LogParabola1D)
import numpy as np

# 1D Models
models_1D = {
    Gaussian1D: {
        'parameters': [1, 0, 1],
        'x_values': [0, np.sqrt(2), -np.sqrt(2)],
        'y_values': [1.0, 0.367879, 0.367879],
        'x_lim': [-10, 10],
        'integral': np.sqrt(2 * np.pi)
    },

    Sine1D: {
        'parameters': [1, 0.1, 0],
        'x_values': [0, 2.5],
        'y_values': [0, 1],
        'x_lim': [-10, 10],
        'integral': 0
    },

    Box1D: {
        'parameters': [1, 0, 10],
        'x_values': [-5, 5, 0, -10, 10],
        'y_values': [1, 1, 1, 0, 0],
        'x_lim': [-10, 10],
        'integral': 10
    },

    Linear1D: {
        'parameters': [1, 0],
        'x_values': [0, np.pi, 42, -1],
        'y_values': [0, np.pi, 42, -1],
        'x_lim': [-10, 10],
        'integral': 0
    },

    Lorentz1D: {
        'parameters': [1, 0, 1],
        'x_values': [0, -1, 1, 0.5, -0.5],
        'y_values': [1., 0.2, 0.2, 0.5, 0.5],
        'x_lim': [-10, 10],
        'integral': 1
    },

    MexicanHat1D: {
        'parameters': [1, 0, 1],
        'x_values': [0, 1, -1, 3, -3],
        'y_values': [1.0, 0.0, 0.0, -0.088872, -0.088872],
        'x_lim': [-20, 20],
        'integral': 0
    },

    Trapezoid1D: {
        'parameters': [1, 0, 2, 1],
        'x_values': [0, 1, -1, 1.5, -1.5, 2, 2],
        'y_values': [1, 1, 1, 0.5, 0.5, 0, 0],
        'x_lim': [-10, 10],
        'integral': 3
    },

    Const1D: {
        'parameters': [1],
        'x_values': [-1, 1, np.pi, -42., 0],
        'y_values': [1, 1, 1, 1, 1],
        'x_lim': [-10, 10],
        'integral': 20
    },

    Moffat1D: {
        'parameters': [1, 0, 1, 2],
        'x_values': [0, 1, -1, 3, -3],
        'y_values': [1.0, 0.25, 0.25, 0.01, 0.01],
        'x_lim': [-10, 10],
        'integral': 1,
        'deriv_parameters': [23.4, 1.2, 2.1, 2.3],
        'deriv_initial': [10, 1, 1, 1]
    },

    PowerLaw1D: {
        'parameters': [1, 1, 2],
        'constraints': {'fixed': {'x_0': True}},
        'x_values': [1, 10, 100],
        'y_values': [1.0, 0.01, 0.0001],
        'x_lim': [1, 10],
        'log_fit': True,
        'integral': 0.99
    },

    BrokenPowerLaw1D: {
        'parameters': [1, 1, 2, 3],
        'constraints': {'fixed': {'x_break': True}},
        'x_values': [0.1, 1, 10, 100],
        'y_values': [1e2, 1.0, 1e-3, 1e-6],
        'x_lim': [0.1, 100],
        'log_fit': True
    },

    SmoothlyBrokenPowerLaw1D: {
        'parameters': [1, 1, -2, 2, 0.5],
        'constraints': {'fixed': {'x_break': True, 'delta': True}},
        'x_values': [0.01, 1, 100],
        'y_values': [3.99920012e-04, 1.0, 3.99920012e-04],
        'x_lim': [0.01, 100],
        'log_fit': True
    },

    ExponentialCutoffPowerLaw1D: {
        'parameters': [1, 1, 2, 3],
        'constraints': {'fixed': {'x_0': True}},
        'x_values': [0.1, 1, 10, 100],
        'y_values': [9.67216100e+01, 7.16531311e-01, 3.56739933e-04,
                     3.33823780e-19],
        'x_lim': [0.01, 100],
        'log_fit': True
    },

    LogParabola1D: {
        'parameters': [1, 2, 3, 0.1],
        'constraints': {'fixed': {'x_0': True}},
        'x_values': [0.1, 1, 10, 100],
        'y_values': [3.26089063e+03, 7.62472488e+00, 6.17440488e-03,
                     1.73160572e-06],
        'x_lim': [0.1, 100],
        'log_fit': True
    },

    Polynomial1D: {
        'parameters': {'degree': 2, 'c0': 1., 'c1': 1., 'c2': 1.},
        'x_values': [1, 10, 100],
        'y_values': [3, 111, 10101],
        'x_lim': [-3, 3]
     },

    Sersic1D: {
        'parameters': [1, 20, 4],
        'x_values': [0.1, 1, 10, 100],
        'y_values': [2.78629391e+02, 5.69791430e+01, 3.38788244e+00,
                     2.23941982e-02],
        'requires_scipy': True,
        'x_lim': [0, 10],
        'log_fit': True
    },

    Voigt1D: {
        'parameters': [0, 1, 0.5, 0.9],
        'x_values': [0, 2, 4, 8, 10],
        'y_values': [0.520935, 0.017205, 0.003998, 0.000983, 0.000628],
        'x_lim': [-3, 3]
     }
}


# 2D Models
models_2D = {
    Gaussian2D: {
        'parameters': [1, 0, 0, 1, 1],
        'constraints': {'fixed': {'theta': True}},
        'x_values': [0, np.sqrt(2), -np.sqrt(2)],
        'y_values': [0, np.sqrt(2), -np.sqrt(2)],
        'z_values': [1, 1. / np.exp(1) ** 2, 1. / np.exp(1) ** 2],
        'x_lim': [-10, 10],
        'y_lim': [-10, 10],
        'integral': 2 * np.pi,
        'deriv_parameters': [137., 5.1, 5.4, 1.5, 2., np.pi/4],
        'deriv_initial': [10, 5, 5, 4, 4, .5]
    },

    Const2D: {
        'parameters': [1],
        'x_values': [-1, 1, np.pi, -42., 0],
        'y_values': [0, 1, 42, np.pi, -1],
        'z_values': [1, 1, 1, 1, 1],
        'x_lim': [-10, 10],
        'y_lim': [-10, 10],
        'integral': 400
    },

    Box2D: {
        'parameters': [1, 0, 0, 10, 10],
        'x_values': [-5, 5, -5, 5, 0, -10, 10],
        'y_values': [-5, 5, 0, 0, 0, -10, 10],
        'z_values': [1, 1, 1, 1, 1, 0, 0],
        'x_lim': [-10, 10],
        'y_lim': [-10, 10],
        'integral': 100
    },

    MexicanHat2D: {
        'parameters': [1, 0, 0, 1],
        'x_values': [0, 0, 0, 0, 0, 1, -1, 3, -3],
        'y_values': [0, 1, -1, 3, -3, 0, 0, 0, 0],
        'z_values': [1.0, 0.303265, 0.303265, -0.038881, -0.038881,
                     0.303265, 0.303265, -0.038881, -0.038881],
        'x_lim': [-10, 11],
        'y_lim': [-10, 11],
        'integral': 0
    },

    TrapezoidDisk2D: {
        'parameters': [1, 0, 0, 1, 1],
        'x_values': [0, 0.5, 0, 1.5],
        'y_values': [0, 0.5, 1.5, 0],
        'z_values': [1, 1, 0.5, 0.5],
        'x_lim': [-3, 3],
        'y_lim': [-3, 3]
    },

    AiryDisk2D: {
        'parameters': [7, 0, 0, 10],
        'x_values': [0, 1, -1, -0.5, -0.5],
        'y_values': [0, -1, 0.5, 0.5, -0.5],
        'z_values': [7., 6.50158267, 6.68490643, 6.87251093, 6.87251093],
        'x_lim': [-10, 10],
        'y_lim': [-10, 10],
        'requires_scipy': True
    },

    Moffat2D: {
        'parameters': [1, 0, 0, 1, 2],
        'x_values': [0, 1, -1, 3, -3],
        'y_values': [0, -1, 3, 1, -3],
        'z_values': [1.0, 0.111111, 0.008264, 0.008264, 0.00277],
        'x_lim': [-3, 3],
        'y_lim': [-3, 3]
    },

    Polynomial2D: {
        'parameters': {'degree': 1, 'c0_0': 1., 'c1_0': 1., 'c0_1': 1.},
        'x_values': [1, 2, 3],
        'y_values': [1, 3, 2],
        'z_values': [3, 6, 6],
        'x_lim': [1, 100],
        'y_lim': [1, 100]
    },

    Disk2D: {
        'parameters': [1, 0, 0, 5],
        'x_values': [-5, 5, -5, 5, 0, -10, 10],
        'y_values': [-5, 5, 0, 0, 0, -10, 10],
        'z_values': [0, 0, 1, 1, 1, 0, 0],
        'x_lim': [-10, 10],
        'y_lim': [-10, 10],
        'integral': np.pi * 5 ** 2
    },

    Ring2D: {
        'parameters': [1, 0, 0, 5, 5],
        'x_values': [-5, 5, -5, 5, 0, -10, 10],
        'y_values': [-5, 5, 0, 0, 0, -10, 10],
        'z_values': [1, 1, 1, 1, 0, 0, 0],
        'x_lim': [-10, 10],
        'y_lim': [-10, 10],
        'integral': np.pi * (10 ** 2 - 5 ** 2)
    },

    Sersic2D: {
        'parameters': [1, 25, 4, 50, 50, 0.5, -1],
        'x_values': [0.0, 1, 10, 100],
        'y_values': [1, 100, 0.0, 10],
        'z_values': [1.686398e-02, 9.095221e-02, 2.341879e-02, 9.419231e-02],
        'requires_scipy': True,
        'x_lim': [1, 1e10],
        'y_lim': [1, 1e10]
    },

    Planar2D: {
        'parameters': [1, 1, 0],
        'x_values': [0, np.pi, 42, -1],
        'y_values': [np.pi, 0, -1, 42],
        'z_values': [np.pi, np.pi, 41, 41],
        'x_lim': [-10, 10],
        'y_lim': [-10, 10],
        'integral': 0
    }
}