我希望将对数正态曲线拟合到大致遵循对数正态分布的数据。
我得到的数据来自激光衍射仪，该仪测量喷雾的粒度分布。该代码的最终目标是为我的数据重新创建this method，该代码使用专为XRD数据曲线拟合设计的OriginPro软件。一个类似的问题。我想将该方法集成到我自己的研究分析中，这是用Python完成的。
我将this post中的代码改编为（理想情况下）处理对数正态分布。我简化了代码，仅处理数据中的第一个对数正态峰，因此现在它仅尝试适应一个对数正态分布。我提供的数据也简化为只有一个峰适合。示例数据和代码在这篇文章的底部给出。
尽管我使用用户定义的状态空间模型进行时间建模和LMFIT minimize()函数，但我在使用LMFIT进行模型拟合方面已有一些经验。我不确定从哪里开始调试此代码的曲线拟合组件。
有人可以帮我弄清楚为什么我无法拟合这些数据吗？请注意，我得到的结果是微不足道的（y = 0处的直线）。
在Windows 7（笔记本电脑）和10（台式机）上工作
在CMD窗口中运行python -V会给出：
Python 3.5.3 :: Anaconda 4.1.1 (64-bit)
以下是样本分发的数据：
sizes = np.array([ 1.26500000e-01, 1.47000000e-01, 1.71500000e-01,
2.00000000e-01, 2.33000000e-01, 2.72000000e-01,
3.17000000e-01, 3.69500000e-01, 4.31000000e-01,
5.02500000e-01, 5.86000000e-01, 6.83500000e-01,
7.97000000e-01, 9.29000000e-01, 1.08300000e+00,
1.26250000e+00, 1.47200000e+00, 1.71650000e+00,
2.00100000e+00, 2.33300000e+00, 2.72050000e+00,
3.17200000e+00, 3.69800000e+00, 4.31150000e+00,
5.02700000e+00, 5.86100000e+00, 6.83300000e+00,
7.96650000e+00, 9.28850000e+00, 1.08295000e+01,
1.26265000e+01, 1.47215000e+01, 1.71640000e+01,
2.00115000e+01, 2.33315000e+01, 2.72030000e+01,
3.17165000e+01, 3.69785000e+01, 4.31135000e+01,
5.02665000e+01, 5.86065000e+01, 6.83300000e+01,
7.96670000e+01, 9.28850000e+01, 1.08296000e+02,
1.26264000e+02, 1.47213000e+02, 1.71637500e+02,
2.00114500e+02, 2.33316500e+02])
y_exp = np.array([ 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.01,
0.02, 0.03, 0.04, 0.06, 0.07, 0.08, 0.09, 0.1 , 0.11,
0.13, 0.19, 0.3 , 0.48, 0.74, 1.1 , 1.56, 2.11, 2.72,
3.37, 3.99, 4.55, 4.99, 5.3 , 5.48, 5.53, 5.48, 5.36,
5.19, 4.97, 4.67, 4.28, 3.79, 3.18, 2.48, 1.73, 1. ,
0.35, 0. , 0. , 0. , 0. ])
以下是功能：
def generate_model(spec):
composite_model = None
params = None
x = spec['x']
y = spec['y']
x_min = np.min(x)
x_max = np.max(x)
x_range = x_max - x_min
y_max = np.max(y)
for i, basis_func in enumerate(spec['model']):
# prefix = f'm{i}_'
prefix = 'm{0}_'.format(i)
model = getattr(models, basis_func['type'])(prefix=prefix)
if basis_func['type'] in ['LognormalModel','GaussianModel', 'LorentzianModel', 'VoigtModel']: # for now VoigtModel has gamma constrained to sigma
model.set_param_hint('sigma', min=1e-6, max=x_range)
model.set_param_hint('center', min=x_min, max=x_max)
model.set_param_hint('height', min=1e-6, max=1.1*y_max)
model.set_param_hint('amplitude', min=1e-6)
# default guess is horrible!! do not use guess()
default_params = {
prefix+'center': x_min + x_range * random.random(),
prefix+'height': y_max * random.random(),
prefix+'sigma': x_range * random.random()
}
else:
# raise NotImplemented(f'model {basis_func["type"]} not implemented yet')
raise NotImplemented('model {0} not implemented yet'.format(basis_func["type"]))
if 'help' in basis_func: # allow override of settings in parameter
for param, options in basis_func['help'].items():
model.set_param_hint(param, **options)
model_params = model.make_params(**default_params, **basis_func.get('params', {}))
if params is None:
params = model_params
else:
params.update(model_params)
if composite_model is None:
composite_model = model
else:
composite_model = composite_model + model
return composite_model, params
def update_spec_from_peaks(spec, model_indicies, peak_widths=np.arange(1,10), **kwargs):
x = spec['x']
y = spec['y']
x_range = np.max(x) - np.min(x)
peak_indicies = signal.find_peaks_cwt(y, peak_widths)
np.random.shuffle(peak_indicies)
# for peak_indicie, model_indicie in zip(peak_indicies.tolist(), model_indicies):
for peak_indicie, model_indicie in zip(peak_indicies, model_indicies):
model = spec['model'][model_indicie]
if model['type'] in ['LognormalModel','GaussianModel', 'LorentzianModel', 'VoigtModel']:
params = {
'height': y[peak_indicie],
'sigma': x_range / len(x) * np.min(peak_widths),
'center': x[peak_indicie]
}
if 'params' in model:
model.update(params)
else:
model['params'] = params
else:
# raise NotImplemented(f'model {basis_func["type"]} not implemented yet')
raise NotImplemented('model {0} not implemented yet'.format(model["type"]))
return peak_indicies
这是主线：
spec = {
'x': sizes,
'y': y_exp,
'model': [
{
'type': 'LognormalModel',
'params': {'center': 20, 'height': 3, 'sigma': 1},
# 'help': {'center': {'min': 10, 'max': 30}}
}]}
num_comp = list(range(0,len(spec['model'])))
peaks_found = update_spec_from_peaks(spec, num_comp, peak_widths=np.arange(1,10))
#For checking peak fitting
print(peaks_found)
fig, ax = plt.subplots()
ax.scatter(spec['x'], spec['y'], s=4)
for i in peaks_found:
ax.axvline(x=spec['x'][i], c='black', linestyle='dotted')
model, params = generate_model(spec)
output = model.fit(spec['y'], params, x=spec['x'])
fig, gridspec = output.plot()
感谢您的帮助，祝您度过愉快的一天。
以撒
答案 0 :(得分：0)
有关Stackoverflow以及通常用于解决问题的标准建议是将问题减少到一个显示问题的最小脚本。参见，例如，https://stackoverflow.com/help/mcve。这种方法鼓励简化问题，并且通常有助于指出问题在代码中的位置。这是解决问题的经典方法。
事实证明，您的脚本还有很多额外的东西。 精简要领将给出：
import numpy as np
from lmfit import models
import matplotlib.pyplot as plt
x = np.array([ 1.26500000e-01, 1.47000000e-01, 1.71500000e-01,
2.00000000e-01, 2.33000000e-01, 2.72000000e-01,
3.17000000e-01, 3.69500000e-01, 4.31000000e-01,
5.02500000e-01, 5.86000000e-01, 6.83500000e-01,
7.97000000e-01, 9.29000000e-01, 1.08300000e+00,
1.26250000e+00, 1.47200000e+00, 1.71650000e+00,
2.00100000e+00, 2.33300000e+00, 2.72050000e+00,
3.17200000e+00, 3.69800000e+00, 4.31150000e+00,
5.02700000e+00, 5.86100000e+00, 6.83300000e+00,
7.96650000e+00, 9.28850000e+00, 1.08295000e+01,
1.26265000e+01, 1.47215000e+01, 1.71640000e+01,
2.00115000e+01, 2.33315000e+01, 2.72030000e+01,
3.17165000e+01, 3.69785000e+01, 4.31135000e+01,
5.02665000e+01, 5.86065000e+01, 6.83300000e+01,
7.96670000e+01, 9.28850000e+01, 1.08296000e+02,
1.26264000e+02, 1.47213000e+02, 1.71637500e+02,
2.00114500e+02, 2.33316500e+02])
y = np.array([ 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.01, 0.02,
0.03, 0.04, 0.06, 0.07, 0.08, 0.09, 0.1 , 0.11, 0.13, 0.19,
0.3 , 0.48, 0.74, 1.1 , 1.56, 2.11, 2.72, 3.37, 3.99, 4.55,
4.99, 5.3 , 5.48, 5.53, 5.48, 5.36, 5.19, 4.97, 4.67, 4.28,
3.79, 3.18, 2.48, 1.73, 1. , 0.35, 0. , 0. , 0. , 0. ])
model = models.LognormalModel()
params = model.make_params(center=20, sigma=3, amplitude=5)
result = model.fit(y, params, x=x)
print(result.fit_report())
plt.plot(x, y, label='data')
plt.plot(x, result.best_fit, label='fit')
plt.legend()
plt.show()
这样运行，即使不是很完美，也可以得到不错的配合。
通常，我不鼓励您根据数据范围设置“参数提示”。仅在模型固有的地方使用这种限制来设置这种限制（例如，sigma<0毫无意义）。
我不知道您的代码使用什么随机数来设置初始值，但是在我看来，它似乎很可能会设置非常差的初始值。