astropy.modeling中的捆绑参数

Question

我试图在Model.tied (或Parameter.tied)属性中使用astropy.modelling，但似乎无法理解它是如何工作的。例如，假设我想创建一个包含两个参数的复合模型：flux_0和flux_1。然而，我只希望flux_0用于拟合：flux_1应该始终带有1 - flux_0值。(最终，我需要扩展这个功能，以便flux_0 + flux_1 + ... + flux_n = 1。)

我为tied属性定义了一个模型类和一个“可调用”，如下所示：

>>> from astropy.modeling import Fittable1DModel, Parameter
>>>
>>> class MyModel(Fittable1DModel):
...     flux = Parameter()
...     @staticmethod
...     def evaluate(x, flux):
...         return flux
...
>>> def tie_fluxes(model):
...     flux_1 = 1 - model.flux_0
...     return flux_1
...
>>> TwoModel = MyModel + MyModel
>>>
>>> TwoModel
<class '__main__.CompoundModel0'>
Name: CompoundModel0
Inputs: ('x',)
Outputs: ('y',)
Fittable parameters: ('flux_0', 'flux_1')
Expression: [0] + [1]
Components:
    [0]: <class '__main__.MyModel'>
    Name: MyModel
    Inputs: ('x',)
    Outputs: ('y',)
    Fittable parameters: ('flux',)

    [1]: <class '__main__.MyModel'>
    Name: MyModel
    Inputs: ('x',)
    Outputs: ('y',)
    Fittable parameters: ('flux',)

然后检查tied属性。我的理解是，这应该是一本字典(见脚注)，但事实并非如此：

>>> TwoModel.tied
<property object at 0x109523958>
>>>
>>> TwoModel.tied['flux_1'] = tie_fluxes
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: 'property' object does not support item assignment

如果我尝试将它设置为字典，它将不会更新适当的Parameter。

>>> TwoModel.tied = {'flux_1': tie_fluxes}
>>>
>>> TwoModel.flux_1.tied
False

但是，当我尝试立即创建一个对象而不是一个复合模型类(这不是我最终想要做的)时，对象的tied属性是一个字典。不幸的是，设置本词典仍然没有产生预期的效果：

>>> TwoSetModel = MyModel(0.2) + MyModel(0.3)
>>>
>>> TwoSetModel
<CompoundModel1(flux_0=0.2, flux_1=0.3)>
>>>
>>> TwoSetModel.tied
{'flux_1': False, 'flux_0': False}
>>>
>>> TwoSetModel.tied['flux_1'] = tie_fluxes
>>>
>>> TwoSetModel
<CompoundModel1(flux_0=0.2, flux_1=0.3)>
>>>
>>> TwoSetModel.flux_1.tied
<function tie_fluxes at 0x102987730>

因此，在本例中，tied属性确实包含正确的函数，但是参数的value没有相应地更新。

我在这里做错什么了？我是否完全误解了tied属性？

(在上述示例中，我使用的是Python3.5.2和Astropy 1.3.3 )

脚注：

运行help(TwoModel)，我得到以下信息：

⁝
 |  tied : dict, optional
 |      Dictionary ``{parameter_name: callable}`` of parameters which are
 |      linked to some other parameter. The dictionary values are callables
 |      providing the linking relationship.
 |
 |      Alternatively the `~astropy.modeling.Parameter.tied` property of a
 |      parameter may be used to set the ``tied`` constraint on individual
 |      parameters.
⁝
 |  Examples
 |  --------
 |  >>> from astropy.modeling import models
 |  >>> def tie_center(model):
 |  ...         mean = 50 * model.stddev
 |  ...         return mean
 |  >>> tied_parameters = {'mean': tie_center}
 |
 |  Specify that ``'mean'`` is a tied parameter in one of two ways:
 |
 |  >>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3,
 |  ...                        tied=tied_parameters)
 |
 |  or
 |
 |  >>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3)
 |  >>> g1.mean.tied
 |  False
 |  >>> g1.mean.tied = tie_center
 |  >>> g1.mean.tied
 |  <function tie_center at 0x...>
⁝

Answer 1

下面的示例类似于“无意义文档”中给出的示例。

两个一维高斯函数的复合Model=Sum

约束: mean_1=2*mean_

import numpy as np
import matplotlib.pyplot as plt
from astropy.modeling import models, fitting


def tie_center(model):
    mean = 2* model.mean_0
    return mean

tied_parameters = {'mean_1': tie_center}
np.random.seed(42)
g1 = models.Gaussian1D(2, 0.4, 0.3)
g2 = models.Gaussian1D(2.5, 0.2, 0.2)
TwoGaussians = (models.Gaussian1D + 
models.Gaussian1D).rename('TwoGaussians')
x = np.linspace(-1, 1, 200)
y = g1(x) + g2(x) + np.random.normal(0., 0.2, x.shape)

gg_init = TwoGaussians(amplitude_0=1.4, mean_0=1.2, stddev_0=0.1,\
amplitude_1=1.0,stddev_1=0.2, tied=tied_parameters)
fitter = fitting.SLSQPLSQFitter()
gg_fit = fitter(gg_init, x, y)


plt.figure(figsize=(8,5))
plt.plot(x, y, 'ko')
plt.plot(x, gg_fit(x))
plt.xlabel('Position')
plt.ylabel('Flux')
plt.show()
print(gg_fit.mean_0,gg_fit.mean_1)

当三个一维高斯函数的Compund_model=和约束时，三种均值的和应总是等于1。

def tie_center(model):
    mean = 1-(model.mean_0+ model.mean_1)
    return mean
tied_parameters = {'mean_2': tie_center}

np.random.seed(42)
g1 = models.Gaussian1D(2, 0.4, 0.3)
g2 = models.Gaussian1D(2.5, 0.2, 0.2)
g3 = models.Gaussian1D(1.5, 0.4, 0.1)
ThreeGaussians = (models.Gaussian1D + models.Gaussian1D + 
models.Gaussian1D).rename('ThreeGaussians')
x = np.linspace(-1, 1, 200)
y = g1(x) + g2(x) + g3(x) + np.random.normal(0., 0.2, x.shape)

gg_init = ThreeGaussians(amplitude_0=1.4, mean_0=0.3, stddev_0=0.1, 
amplitude_1=1.0, mean_1=0.3,stddev_1=0.2, \
amplitude_2=1.5,stddev_2=0.1,tied=tied_parameters)
fitter = fitting.SLSQPLSQFitter()
gg_fit = fitter(gg_init, x, y)
plt.figure(figsize=(8,5))
plt.plot(x, y, 'ko')
plt.plot(x, gg_fit(x))
plt.xlabel('Position')
plt.ylabel('Flux')
plt.show()
print(gg_fit.mean_0,gg_fit.mean_1, gg_fit.mean_2)