使用 Symfit 进行全局拟合：数据集的类型结构答案

【问题标题】：Global Fitting with Symfit: typestructure of dataset使用 Symfit 进行全局拟合：数据集的类型结构
【发布时间】：2020-02-08 23:22:05
【问题描述】：

我想使用symfit 对具有共享变量的数据集进行全局拟合。我有一个 numpy 数组 xdata，这对于所有数据集 ydata_i 都很常见，它们也是 numpy 数组。

按照example in the documentation a 可以设置变量、参数和模型，但我无法设置拟合： fit = Fit(model, x_1=xdata_1, x_2=xdata_2, ..., y_1=ydata_1, y_2=ydata_2, ...)

对于少数数据集，我可以手动编写代码或复制/粘贴它，但我有数百个数据集，我希望我可以避免手动输入代码。我尝试使用列表 [xdata, ydata_1, ydata2, ...] 或 [xdata, ydata_1, xdata, ydata2, ...] 或数组，但这似乎不是正确的方法。

有谁知道ordered_data 的结构/类型应该是什么样子的。谢谢

【问题讨论】：

标签： python data-fitting symfit

【解决方案1】：

抱歉，我再次需要您的帮助。我最终得到一个错误wrapped_func() keywords must be strings 或'Variable' object has no attribute 'symbol'。我认为这是一个简单的问题，但我不明白这一点。看看下面的例子好吗？

import numpy as np
import symfit as sf

# creating the data
freq = 10 * np.linspace(0.1,0.3,2)
phase = np.pi * np.linspace(0,0.3,2)
offset = 1.0
amplitude = 0.1

# x - array
x_array = np.arange(0,20,0.02)
# create dataset
dataset = [offset + amplitude * np.cos(freq * x_array + phase) + np.random.normal(size=len(x_array), scale=0.01) for freq,phase in zip(freq,phase)]

# independent variables
xs = sf.variables(', '.join('x_{}'.format(i) for i in range(len(dataset))))
# dependent variables
ys = sf.variables(', '.join('y_{}'.format(i) for i in range(len(dataset))))
# coupled parameters
amp, off = sf.parameters('amp, off', value=[1.0,0.1])
# decoupled parameters
freqc = sf.parameters(', '.join('f_{}'.format(i) for i in range(len(dataset))),value=freq)
phasec = sf.parameters(', '.join('p_{}'.format(i) for i in range(len(dataset))),value=phase)

# setup model
model_dict = {y : off + amp * sf.cos(freq * x + phase) for x, y, freq, phase in zip(xs, ys, freqc, phasec) }
# create dataset_dict
xdata = [x_array for i in range(len(dataset))] # just to have equal length of xdata list and y-data list
#data_dict = {x : data for x, data in zip(xs + ys, xdata + dataset)} # error 'wrapped_func() keywords must be strings'
#data_dict = {str(x) : data for x, data in zip(xs + ys, xdata + dataset)} # error 'Variable' object has no attribute 'symbol'
data_dict = {'x_0': x_array, 'x_1': x_array, 'y_0': dataset[0], 'y_1': dataset[1]} # error 'Variable' object has no attribute 'symbol'
# # do the fit
fit = sf.Fit(model_dict, **data_dict)
fit_result = fit.execute()

我通过 Anconda 在 Windows PC 上使用 Python 3.7.4。 Symfit 版本：0.4.6，Sympy 版本：1.4

Traceback (most recent call last):

  File "C:/Users/dummy/Documents/Scripts/Python/Scripts/SymFit_example.py", line 42, in <module>
    fit_result = fit.execute()

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\fit.py", line 1537, in execute
    minimizer_ans = self.minimizer.execute(**minimize_options)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\minimizers.py", line 359, in execute
    return super(ScipyGradientMinimize, self).execute(jacobian=self.wrapped_jacobian, **minimize_options)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\support.py", line 355, in wrapped_func
    return func(*bound_args.args, **bound_args.kwargs)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\minimizers.py", line 296, in execute
    **minimize_options

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\scipy\optimize\_minimize.py", line 594, in minimize
    return _minimize_bfgs(fun, x0, args, jac, callback, **options)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\scipy\optimize\optimize.py", line 996, in _minimize_bfgs
    gfk = myfprime(x0)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\scipy\optimize\optimize.py", line 326, in function_wrapper
    return function(*(wrapper_args + args))

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\scipy\optimize\optimize.py", line 756, in approx_fprime
    return _approx_fprime_helper(xk, f, epsilon, args=args)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\scipy\optimize\optimize.py", line 690, in _approx_fprime_helper
    f0 = f(*((xk,) + args))

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\scipy\optimize\optimize.py", line 326, in function_wrapper
    return function(*(wrapper_args + args))

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\minimizers.py", line 273, in wrapped_func
    return np.array(func(**parameters))

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\support.py", line 355, in wrapped_func
    return func(*bound_args.args, **bound_args.kwargs)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\objectives.py", line 151, in __call__
    evaluated_func = self.model(**jac_kwargs)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\fit.py", line 334, in __call__
    return Ans(*self.eval_components(**bound_arguments.arguments))

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\fit.py", line 296, in eval_components
    return [expr(*args, **kwargs) for expr in self.numerical_components]

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\support.py", line 217, in __get__
    setattr(obj, self.cache_attr, self.fget(obj))

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\fit.py", line 457, in numerical_components
    return [sympy_to_py(expr, self.independent_vars, self.params) for expr in self.values()]

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\fit.py", line 457, in <listcomp>
    return [sympy_to_py(expr, self.independent_vars, self.params) for expr in self.values()]

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\symfit\core\support.py", line 91, in sympy_to_py
    return lambdify((vars + params), func, modules='numpy', dummify=False)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\sympy\utilities\lambdify.py", line 767, in lambdify
    funcstr = funcprinter.doprint(funcname, args, expr)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\sympy\utilities\lambdify.py", line 977, in doprint
    argstrs, expr = self._preprocess(args, expr)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\sympy\utilities\lambdify.py", line 1039, in _preprocess
    s = self._argrepr(arg)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\sympy\printing\codeprinter.py", line 100, in doprint
    lines = self._print(expr).splitlines()

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\sympy\printing\printer.py", line 287, in _print
    return getattr(self, printmethod)(expr, **kwargs)

  File "C:\Users\dummy\Anaconda3\envs\spyder-beta\lib\site-packages\sympy\printing\codeprinter.py", line 344, in _print_Variable
    return self._print(expr.symbol)

AttributeError: 'Variable' object has no attribute 'symbol'

【讨论】：

你能发布完整的回溯吗？另外，您安装了哪个版本的 symfit 和 sympy？最后，只是一点堆栈溢出礼仪：这确实应该作为一个新问题发布，因为它是一个新问题。
很抱歉忽略了礼仪。我试着熟悉它。我什至不知道如何处理像这样的追溯这样大的补充。
好的，它适用于 symfit 版本 0.5.1，这似乎无法通过 conda for windows 获得。
这里没有：anaconda.org/conda-forge/symfit ?
如果我用 python 3.6 制作一个新的 conda env，我会得到 symfit 0.5.1。我认为这是因为 sf v 0.5.1 具有非常严格的 scipy 要求（scipy >= 1.0，= 1.0

【解决方案2】：

对于大量数据集，您可以使用字典：

data = {'x_1': xdata_1, 'x_2': xdata_2, ..., 'y_1': ydata_1, 'y_2': ydata_2, ...}
fit = Fit(model, **data)

这样它会以named_data 结束，这是首选。祝你好运！

附言如果您正在使用如此大的模型，您可能还需要考虑使用JacobianModel 或CallableModel 而不是默认模型，因为为此类模型计算雅可比和粗麻布可能既昂贵又不必要。

【讨论】：

感谢您的帮助。顺便说一句，symfit 你构建了一个不错的配件包。也许值得在documentation 中实现这个解释。我对拟合过程背后的所有数学知识并不熟悉。因此，我稍后会使用JacobianModel 或CallableModel 来打扰您。
谢谢，我很高兴听到这个消息。是的，你说得对，这可能应该被添加到文档中，我已经为它打开了一个问题here。当然欢迎任何后续问题，如果这回答了您的问题，那么请考虑将其标记为已接受的答案:)。
抱歉，我再次需要您的帮助。我最终得到一个错误 Wrapped_func() 关键字必须是字符串或“变量”对象没有属性“符号”