Я пытаюсь подогнать кривую к некоторым данным (модель будет иметь 3 гауссиана плюс фон). Данные находятся внизу этого поста (не знаю, как их прикрепить), а столбцы (x, y, err_y), где err_y - квадратный корень из y. Вот мой код:
import numpy as np
from matplotlib import pyplot as plt
from lmfit.models import GaussianModel, LinearModel
data = np.loadtxt("data.txt")
x = data[:,0]
y = data[:,1]
err = data[:,2]
background = LinearModel(prefix='line1_')
pars = background.guess(y,x=x)
peak1 = GaussianModel(prefix='g1_')
pars.update(peak1.make_params())
pars['g1_center'].set(9200, min=9000, max=10000)
pars['g1_sigma'].set(300, min=100, max=700)
peak2 = GaussianModel(prefix='g2_')
pars.update(peak2.make_params())
pars['g2_center'].set(10500, min=10000, max=11000)
pars['g2_sigma'].set(300, min=100, max=700)
peak3 = GaussianModel(prefix='g3_')
pars.update(peak3.make_params())
pars['g3_center'].set(13000, min=12000, max=14000)
pars['g3_sigma'].set(300, min=100, max=700)
model = peak1 + peak2 + peak3 + background
weight = 1/err**2/np.sum(1/err**2)
out = model.fit(y, pars, x=x)#, weights = weight)
print(out.fit_report(min_correl=0.1))
plt.errorbar(x,y,err, fmt="b.")
plt.plot(x, out.best_fit, 'r-')
plt.show()
Если для подгонки я использую это: out = model.fit(y, pars, x=x), поэтому, не используя ошибок для y, я получаю эти значения для параметров (я выкладываю только mu и sigma здесь):
mu_1 = 9359.791209085675 +/- 5.509374978209427
sigma_1 = 348.86904194695535 +/- 6.18259118657156
mu_2 = 10522.11131671362 +/- 3.288369260611981
sigma_2 = 243.53890651538205 +/- 3.43678656935972
mu_3 = 13098.71965433265 +/- 4.737992827401577
sigma_3 = 324.0256260123612 +/- 5.054936854719746
и это сама подгонка:
Если я хочу учесть ошибки: out = model.fit(y, pars, x=x, weights = weight) (вес - обратное значение квадратов ошибок, поскольку формула для подгонки по методу наименьших квадратов равна сумме {1 / sigma ^ 2 * (y_data-y_pred) ^ 2}, верно?) Я получаю эти числа:
mu_1 = 9979.839872555114 +/- 12.208145818989209
sigma_1 = 296.96756984463025 +/- 30.943773101487675
mu_2 = 10000.004017862604 +/- 14.082237906871443
sigma_2 = 424.30653650290424 +/- 22.751836748822086
mu_3 = 13103.00302126283 +/- 10.795125319448884
sigma_3 = 328.0535307828716 +/- 8.157121458823843
и это подгонка:
Не только подгонка выглядит плохо, но напечатанные параметры даже не такие, какна рисунке показано (центр первого пика точно меньше 9980). Может кто-нибудь сказать мне, что происходит? Использую ли я весовой параметр так, как его предполагается использовать? Почему посадка выглядит так плохо сейчас? Почему напечатанные параметры неверны? И как я могу это исправить? Спасибо!
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