[pymc]pymc安装后测试教程之将非线性函数拟合到数据/观察值

import time

import pymc
import numpy as np
import matplotlib.pyplot as plt

plt.ion()

x = np.arange(5, 400, 10) * 1e3

# Parameters for gaussian
amp_true = 0.2
size_true = 1.8
ps_true = 0.1

# Gaussian function
gauss = lambda x, amp, size, ps: amp * np.exp(
    -1 * (np.pi ** 2 / (3600. * 180.) * size * x) ** 2 / (4. * np.log(2.))) + ps
f_true = gauss(x=x, amp=amp_true, size=size_true, ps=ps_true)

# add noise to the data points
noise = np.random.normal(size=len(x)) * .02
f = f_true + noise
f_error = np.ones_like(f_true) * 0.05 * f.max()


# define the model/function to be fitted.
def model(x, f):
    amp = pymc.Uniform('amp', 0.05, 0.4, value=0.15)
    size = pymc.Uniform('size', 0.5, 2.5, value=1.0)
    ps = pymc.Normal('ps', 0.13, 40, value=0.15)

    @pymc.deterministic(plot=False)
    def gauss(x=x, amp=amp, size=size, ps=ps):
        e = -1 * (np.pi ** 2 * size * x / (3600. * 180.)) ** 2 / (4. * np.log(2.))
        return amp * np.exp(e) + ps

    y = pymc.Normal('y', mu=gauss, tau=1.0 / f_error ** 2, value=f, observed=True)
    return locals()


MDL = pymc.MCMC(model(x, f))
MDL.sample(1e4)

# extract and plot results
y_min = MDL.stats()['gauss']['quantiles'][2.5]
y_max = MDL.stats()['gauss']['quantiles'][97.5]
y_fit = MDL.stats()['gauss']['mean']
plt.plot(x, f_true, 'b', marker='None', ls='-', lw=1, label='True')
plt.errorbar(x, f, yerr=f_error, color='r', marker='.', ls='None', label='Observed')
plt.plot(x, y_fit, 'k', marker='+', ls='None', ms=5, mew=2, label='Fit')
plt.fill_between(x, y_min, y_max, color='0.5', alpha=0.5)
plt.legend()
plt.ioff()
plt.show()

结果：

测试通过环境：

anaconda3+python3.8

pymc==2.3.8

window10 x64系统