用约束拟合¶
fitting 但是，不同的装配工支持不同类型的约束。这个 supported_constraints 属性显示特定装配工支持的约束类型：
>>> from astropy.modeling import fitting
>>> fitting.LinearLSQFitter.supported_constraints
['fixed']
>>> fitting.LevMarLSQFitter.supported_constraints
['fixed', 'tied', 'bounds']
>>> fitting.SLSQPLSQFitter.supported_constraints
['bounds', 'eqcons', 'ineqcons', 'fixed', 'tied']
固定参数约束¶
所有装配工通过 fixed 模型参数或设置 fixed 属性直接作用于参数。
对于线性拟合，冻结一个多项式系数意味着在将没有该项的多项式拟合到结果之前，将从数据中减去相应的项。例如，固定 c0 在多项式模型中，将拟合一个多项式，数据减去该常数后，第零阶项缺失。将固定系数和相应的项恢复到拟合多项式，这是拟合器返回的多项式：
>>> import numpy as np
>>> np.random.seed(seed=12345)
>>> from astropy.modeling import models, fitting
>>> x = np.arange(1, 10, .1)
>>> p1 = models.Polynomial1D(2, c0=[1, 1], c1=[2, 2], c2=[3, 3],
... n_models=2)
>>> p1 # doctest: +FLOAT_CMP
<Polynomial1D(2, c0=[1., 1.], c1=[2., 2.], c2=[3., 3.], n_models=2)>
>>> y = p1(x, model_set_axis=False)
>>> n = (np.random.randn(y.size)).reshape(y.shape)
>>> p1.c0.fixed = True
>>> pfit = fitting.LinearLSQFitter()
>>> new_model = pfit(p1, x, y + n) # doctest: +IGNORE_WARNINGS
>>> print(new_model) # doctest: +SKIP
Model: Polynomial1D
Inputs: ('x',)
Outputs: ('y',)
Model set size: 2
Degree: 2
Parameters:
c0 c1 c2
--- ------------------ ------------------
1.0 2.072116176718454 2.99115839177437
1.0 1.9818866652726403 3.0024208951927585
The syntax to fix the same parameter ``c0`` using an argument to the model
instead of ``p1.c0.fixed = True`` would be::
>>> p1 = models.Polynomial1D(2, c0=[1, 1], c1=[2, 2], c2=[3, 3],
... n_models=2, fixed={'c0': True})
有界约束¶
边界拟合通过 bounds 模型参数或通过设置 min 和 max 参数的属性。边界 LevMarLSQFitter 总是完全满足——如果参数的值在拟合间隔之外，它将重置为边界处的值。这个 SLSQPLSQFitter 优化算法在内部处理边界。
约束条件¶
这个 tied 约束通常用于 Compound models . 在本例中，我们将从一个名为 spec.txt 在连接OIII_1和OIII_2线的通量时，同时将高斯数拟合到这些线上。
import numpy as np
from astropy.io import ascii
from astropy.utils.data import get_pkg_data_filename
from astropy.modeling import models, fitting
fname = get_pkg_data_filename('data/spec.txt', package='astropy.modeling.tests')
spec = ascii.read(fname)
wave = spec['lambda']
flux = spec['flux']
# Use the rest wavelengths of known lines as initial values for the fit.
Hbeta = 4862.721
OIII_1 = 4958.911
OIII_2 = 5008.239
# Create Gaussian1D models for each of the Hbeta and OIII lines.
h_beta = models.Gaussian1D(amplitude=34, mean=Hbeta, stddev=5)
o3_2 = models.Gaussian1D(amplitude=170, mean=OIII_2, stddev=5)
o3_1 = models.Gaussian1D(amplitude=57, mean=OIII_1, stddev=5)
# Tie the ratio of the intensity of the two OIII lines.
def tie_ampl(model):
return model.amplitude_2 / 3.1
o3_1.amplitude.tied = tie_ampl
# Also tie the wavelength of the Hbeta line to the OIII wavelength.
def tie_wave(model):
return model.mean_0 * OIII_1 / Hbeta
o3_1.mean.tied = tie_wave
# Create a Polynomial model to fit the continuum.
mean_flux = flux.mean()
cont = np.where(flux > mean_flux, mean_flux, flux)
linfitter = fitting.LinearLSQFitter()
poly_cont = linfitter(models.Polynomial1D(1), wave, cont)
# Create a compound model for the three lines and the continuum.
hbeta_combo = h_beta + o3_1 + o3_2 + poly_cont
# Fit all lines simultaneously.
fitter = fitting.LevMarLSQFitter()
fitted_model = fitter(hbeta_combo, wave, flux)
fitted_lines = fitted_model(wave)
from matplotlib import pyplot as plt
fig = plt.figure(figsize=(9, 6))
p = plt.plot(wave, flux, label="data")
p = plt.plot(wave, fitted_lines, 'r', label="fit")
p = plt.legend()
p = plt.xlabel("Wavelength")
p = plt.ylabel("Flux")
t = plt.text(4800, 70, 'Hbeta', rotation=90)
t = plt.text(4900, 100, 'OIII_1', rotation=90)
t = plt.text(4950, 180, 'OIII_2', rotation=90)
plt.show()
